Manufacturing Frontiers

National Science Foundation Directorate for Engineering

Adnan Akay

Manufacturing Contribution to US GDP

Source: National Association of Manufacturers, U.S. Department of Commerce

Manufacturing Contribution to US GDP and Employment

Data Source: US Dept of Labor, NAM GDP calculations using 1982 constant-weighted price index

Issues & Drivers

!  Competition – emerging economies !  Enabling technologies !  Environment, sustainability, resource issues !  Socio-economics !  Regulations

EU Manufuture!

Response

!  New products and service with high added values

!  New business models !  Emerging manufacturing sciences and

engineering

EU Manufuture!

Manufacturing Research: Example Directions

!  Improving decision making (tolerancing, fixturing, tool path optimization)

!  New processes (nanomanufacturing, lithography, solid freeform fabrication)

!  Metrology and process monitoring (nanometrology)

!  Predictive modeling (incorporation of uncertainty)

(J. Lee-Ohio State U)! (S. Girshik-U. Minnesota)!

(P.Gouma-SUNY SB)!

Challenge: Manufacturing Across Scales

Manufacturing Miniaturization Trends

Macro!Meso!Micro!!Nano-Manufacturing!

ME325/580 Handout: Engineering Materials

Spring 2010 I. Kao Descriptions and comparisons of the three basic categories of engineering materials (metals, ceramics, and polymers) and their mechanical, physical, and other properties

Metals Ceramics Polymers

Description

Ferrous and non-ferrous metals

Compound containing metallic (or semi-metallic) and nonmetallic elements

Compound formed of repeating structural units called “mers” whose atoms share electrons to form very large structure

Structure Crystalline (solid state) Crystalline or non-crystalline (amorphous; e.g., glass, SiO2)

Glassy or Glassy + Crystalline

Mechanical Properties

Strong, hard, ductile (esp. FCC)

High hardness High stiffness High brittleness

Strength & stiffness vary

Physical Properties

High electrical conductivity High thermal conductivity

Electrical insulation Thermally resistant (refractoriness)

Low density High electric resistivity Low thermal conduction

Other Properties

Opaqueness Reflectivity

Chemical inertness Carbon +(H2,N2,O2,Cl2)

In addition to the basic three categories described above, the composite materials are typically combinations of two of the three engineering materials, as illustrated in the diagram (also called the Venn diagram).

100

1000

10000

20000

0 1 2 3 4 5 6 7

2000

5000

200

500

Shear rate (1/s)

ratio=1.25

ratio=1.0ratio=0.5

ratio=0.75

Typical viscosity for slurry used in industrial processesThe slurry used here consists of glycol carrier with silicon carbide gritsat F400 grain size (average grain size is 17 microns). The mixing ratiois in kilogram of silicon carbide grits vs. liter of carrier fluid. Theviscosity as a function of temperature also resembles the shape of curveshown here.

MEC325/580 Handout: Viscosity for Industrial Slurry

I. Kao Spring 2010

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MEC 325/580 Handout: Geometric Dimensioning and Tolerancing

Spring 2010 I. Kao Geometric Dimensioning and Tolerancing (GD&T) is a language for communicating engineering design specifications. GD&T includes all the symbols, definitions, mathematical formulae, and application rules necessary to embody a variable engineering language. It conveys both the nominal dimensions (ideal geometry), and the tolerance for a part. It is now the predominant language used worldwide as well as the standard language approved by the American Society of Mechanical Engineers (ASME), the American National Standards Institute (ANSI), and the United States Department of Defense (DoD). GD&T is the language that designers should use to translate design requirements into measurable specifications. The following American National Standards define GD&T’s vocabulary and provide its grammatical rules.

• ASME Y14.5M-1994, Dimensioning and Tolerancing • ASME Y14.5.1M-1994, Mathematical Definition of Dimensioning and Tolerancing

Principles • ASME Y14.41-2003, Digital Product Definition Data Practices

These are often referred to as the “Y14.5” and “the Math Standards,” respectively.

Usage of GD&T and why do we use GD&T The following drawing is an example for the identification of hole location.

Figure 1: Drawing showing distance to ideal hole location

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A drawing which does not use GD&T (Figure 2) can be potentially misunderstood and fabricated incorrectly (see Figure 3 for the illustration).

Figure 2: Drawing that does not use GD&T

Figure 3: Manufactured part that conforms to the drawing without GD&T in Figure 2

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GD&T provides unique, unambiguous meaning for each control, precluding each person’s having his own competing interpretation. GD&T is simply a means of controlling surfaces more precisely and unambiguously. See Figure 4 for an illustration.

Figure 4: Drawing that uses GD&T with unique and unambiguous interpretation

More information and a list of symbols of GD&T can be found in the reference [1].

ASME Y14.41-2003 Standard for CAD ASME Y14.41-2003 standard is an extension of the Y14.5 standard for 2-dimensional drawings to 3D computer-aided design (CAD) environments. The standard also provides a guide for CAD software developers working on improved modeling and annotation practices for the engineering community. ASME Y14.41 sets forth the requirements for tolerances, dimensional data, and other annotations, and advances the capabilities of Y14.5. Y14.41 defines the exceptions as well as additional requirements to existing ASME standards for using product definition data or drawings in 3-D digital format. [2] The standard is separated into 3 industrial practices: (i) Models Only: These portions cover the practices, requirements, and interpretation of the CAD data when there is no engineering drawing. While ASME Y14.41-2003 is commonly called the “solid model standard,” this is misleading. The standard was intentionally written for different user levels; (ii) Models and Drawing: These portions cover what is commonly called “reduced content drawings” or

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“minimally dimensioned drawings,” where an engineering drawing is available, but does not contain all the necessary information for producing the part or assembly; (iii) Drawings only: These portions of the standard allow the historical practices of using engineering drawings to define a product. However, this standard adds to the practices defined in ASME Y14.5 for Geometric Dimensioning and Tolerancing with some additional symbols, the use of axinometric views as dimensionable views, and the concept of supplemental geometry–all of which can help to clarify the drawing and its interpretation. [3]

Part of the materials in this handout have been taken from the following reference. Reference:

[1] Walter M. Stites and Paul Drake, Jr., “Dimensioning and Tolerancing Handbook,” Editor Paul J. Drake, Jr., Ch. 5, McGraw-Hill, 1999

[2] ASME Y14.41-2003 Standard on Digital Product Definition Data Practices, ISBN: 0791828107, 2003

[3] Wikipedia, http://en.wikipedia.org/wiki/ASME_Y14.41-2003

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ME325/580 Handout: CNC Machining

Spring 2010 I. Kao Introduction Computer numerical control (CNC) is the process of manufacturing machined parts in a production environment, as controlled and allocated by a computerized controller that used motors to drive each axis. The CNC technology has been one of manufacturing’s major development in the 20th century. The controller is designed to control the direction, speed, and length of time each motor rotates. The operator downloads programmed path to the computer connected to the machine and then executes the code. The idea of Numerical Control (NC) was conceived by John Parsons, taken up by USAF, in 1948. This term is used interchangeably with CNC. The CNC technology not only has facilitated the development of new techniques and achievement of higher production levels but also has helped to increase product quality. The CNC technology was developed to:

1. increase production 2. improve the quality and accuracy of manufactured parts 3. stabilize manufacturing costs 4. manufacture complex or otherwise impossible jobs

Numerical control was also designed to help produce parts with the following characteristics: • similar in terms of raw material • various sizes and geometry • small- to medium-sized batches • a sequence of similar steps was used to complete each workpiece

CNC is now a well-established process, especially with the information and computer technology, compared to the NC technology first demonstrated in 1952. The CNC technology has the following advantages over the NC technology:

1. Programs can be entered at the machine and stored into memory. 2. Programs are easier to edit, so part programming process design time is reduced. 3. There is greater flexibility in the complexity of parts that can be produced. 4. Three-dimensional geometric models of parts, stored in the computer, can be used to

generate CNC part programs with tool path almost automatically, thus saving manual programming labor. This is referred to as CAD/CAM integration.

5. Computers can be connected to other computers worldwide through network, thereby allowing part programs to be transmitted directly to remote CNC machines.

Training is required for the operator of a CNC machine. The CNC machine also requires maintenance for smooth operations and extended life.

Two very similar standards are generally followed worldwide: the ISO 6983 and the EIA RS274. ISO (International Standardization Organization) and EIA (Electronic Industries Association) developed the main standard for CNC, which used simple programming instructions to enable a machine tool to carry out a particular operation. The flow charts of CNC processing, with and without computer aided process, are shown below.

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CNC Programming A CNC program is a sequential list of machining instructions for the CNC machine to execute. CNC code consists of blocks (also called lines), each of which contains an individual command for a movement or specific action. There are two major types of CNC codes, or letter addresses, in any program. The major CNC codes are G-codes and M-codes.

• G-code are preparatory functions, which involve actual tool moves (for example, control of the machine). These include rapid moves, feed moves, radial feed moves, dwells, and roughing and profiling cycles.

• M-codes are miscellaneous functions, which include actions necessary for machining, but not those that are an actual tool movement (for example, auxiliary functions). These

develop part drawing

Flow of CNC Processing

decide machine for the part

choose the required tooling

design machining sequence

calculate the coordinates

calculate spindle speed and feedrate

write the CNC program

preapre setup sheets and tool lists

verify/edit: simulator/machine tool

verify/edit on actual machine

Run the program to produce part

3D geometric CAD model

Flow of Computer-Aided CNC Processing

decide machining ops for the part

choose the required tooling

use CAM to generate CNC program

download the part program

verify/edit via simulator

verify/edit on actual machine

Run the program to produce part

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include spindle on and off, tool changes, coolant on and off, program stops, and other similar related functions.

Other letter addresses or variable are used in the G- and M-codes to make words. Most G-codes contain a variable, defined by the programmer, for each specific function. Each designation used in CNC programming is called a letter address. The letters used for programming are as follows:

N Block number – specifies the start of a block G Preparatory function, as previously explained X X-axis coordinate Y Y-axis coordinate Z Z-axis coordinate I X-axis location of arc center J Y-axis location of arc center K Z-axis location of arc center S Set the spindle speed F Assign a feed rate T Specify tool to be used M Miscellaneous function, as previously explained

The Three Major Phases of a CNC Program The three phases of a CNC program can be illustrated with the following sample code.

Phase CNC program Descriptions % Program start flag (syntax & format are machine-dependent) :1001 Four digit program number; up to four digits, 0-9999 N5 G90 G20 Use absolute units, and inch programming N10 M06 T2 Stop for tool change, use Tool #2 Pr

ogra

m

setu

p

N15 M03 S1200 Turn the spindle on CW to 1200 rpm N20 G00 X1 Y1 Rapid to (X1, Y1) from the origin N25 Z0.125 Rapid down to Z0.125 N30 G01 Z-0.125 F5 Feed down to Z-0.125 at 5 in./min N35 G01 X2 Y2 Feed diagonally to (X2, Y2) N40 G00 Z1 Rapid up to Z1 M

ater

ial

rem

oval

N45 X0 Y0 Rapid to (X0, Y0) N50 M05 Turn the spindle off N55 M30 End of program Sy

s sh

ut

(1) Program setup: This phase is virtually identical in every program. It always begins with the program start flag (% sign). Note: The actual setup for each CNC machine may differ. For example, the CNC in our machine shop uses “0100” to start the CNC code. Line two always has a program number from 0 to 9999. Line three is the first actually numbered. G90 tells the controller that all distances (X and Z) are absolute, that is, measured from the origin. G20 instructs the controller that all coordinates are measured in inch units.

(2) Material removal: This phase deals exclusively with the actual cutting feed moves. It contains all the commands that designate linear or circular feed moves, rapid moves,

4

canned cycles such as grooving or profiling, or any other function required for that particular part.

(3) System shutdown: It contains all those G-codes and M-codes that turn off all options that were turned on in the setup phase. Functions such as coolant and spindle rotation must be shut off prior to removal of the part from the machine. The shutdown phase also is virtually identical in every program.

Using A Programming Sheet Each row in the following program sheet contains all the data required to write one CNC block.

Part Name: Programmed by: Machine: Date: Page:

CNC Programming Sheet

Setup information: N

Seq G/M Code

X Pos

Y Pos

Z Pos

IJK Loc

F Feed

R Rad/ret

S Speed

T Tool

Others

5 G90,G20 10 M6 2 15 M3 1200 20 G00 0 0 25 0.1 30 G01 -0.1 2 35 G01 1.5 Block Format Each block of CNC code needs to be entered correctly. The block comprises of different components which can produce tool moves on the machine. Here is a sample:

N105 G01 X1.0 Y1.0 Z0.125 F5 N105 Block number Shows the current CNC block number G01 G-code Tells the machine what to do. In this case, a linear feed

move X1.0 Y1.0 Z0.125 Coordinate Gives the machine an end point for its move. X

designates an X-axis coordinates, Y/Z for Y/Z-axis. F5 Special function Contains any special function or related parameter. In

this case, a feed rate of 5 in/min is specified. There are some simple restrictions on CNC blocks, as follows:

• Each may contain only one tool move. • Each may contain any number of non-tool move G-codes (e.g., G90 G20 for absolute

system and inch system), provided that they do not conflict between each other (for example, G42 and G43).

• Each may contain only one feedrate per block. • Each may contain only one specified tool or spindle speed. • The block numbers should be sequential. • Both the program start flag and the program number must be independent of all other

commands. • The data within a block follow the sequence shown in the above sample block.

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Preparing to Program Before you start writing a CNC program, you must first prepare to write it. The steps include

(a) Develop an order of operations (b) Calculate coordinates and complete a coordinate sheet (c) Choose tooling with clamping devices, and calculate speeds and feeds

Program Zero Program zero allows the programmer to specify a position from which all other coordinates will be referenced. Program zero is also called “part zero” or “machine home.” “Program zero” is particularly important in absolute programming. In incremental programming (where coordinates are related incrementally), one has a floating program zero that changes all the time. Tool Motion There are three types of tool motions used in a CNC machine. They are:

(1) G00: rapid tool move (2) G01: straight line feed move (3) G02/03: circular interpolation or arc feed moves

All cycles such as G71 rough turning are either one of these types or a combination of these types of motion. These motion command are modal. That is, if you program one of these commands, you do not need to program the same code again until you want to change the type of tool motion. The command will be in effect until it is changed or turned off. Using Canned Cycles Canned cycles combine many standard programming operations and are designed to shorten the program length, minimize math calculations, and optimize cutting conditions to improve the production of the machine. Examples of canned cycles on a mill are drilling, boring, spot facing, tapping, … etc; on a lathe, threading and pattern repeating cycles. On the lathe, canned cycles are also referred to as multiple repetitive cycles. Canned cycles also facilitate programming. You should check out the canned cycles that your CNC control offers. Subroutines are also available on many CNC controllers. You can utilize these routines to make your own canned cycles. Tooling Separate tools are used for roughing and finishing, and tasks such as drilling, slotting, and thread cutting require specific tools. Feedrates, spindle speeds and Cutting Fluids A good surface finish and economical production rates require proper use of spindle speeds and feed rates, as well as cutting fluids.

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CNC Milling The following tables list G-codes and M-codes. The G-codes, which include preparatory functions, involve actual tool moves. The following table lists G-codes in CNC milling.

G-Code name Function Op* G00 Positioning in rapid Modal G01 Linear interpolation Modal G02 Circular interpolation (CW) Modal G03 Circular interpolation (CCW) Modal G04 Dwell G17 XY plane Modal G18 XZ plane Modal G19 YZ plane Modal G20/G70 Inch unit system Modal G21/G71 Metric unit system Modal G28 Automatic return to reference point G29 Automatic return from reference point G40 Cutter compensation cancel Modal G41 Cutter compensation left Modal G42 Cutter compensation right Modal G43 Tool length compensation (Plus) Modal G44 Tool length compensation (Minus) Modal G49 Tool length compensation cancel Modal G80 Cancel canned cycles Modal G81 Drilling cycle Modal G82 Counter boring cycle Modal G83 Deep hole (peck) drilling cycle Modal G90 Absolute positioning Modal G91 Incremental positioning Modal G92 Reposition origin point G98 Set initial plane default G99 Return to retract (rapid) plane

Op: When noted as “modal”, it means that the function remain active until cancelled by another G-code. * Check your CNC machine manuals for G-codes which are not listed here.

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The M-codes, miscellaneous functions, include actions necessary for machining, but not those that are actual tool movements. That is, they are auxiliary functions, such as spindle on and off, tool changes, coolant on and off, program stops, other similar related functions. The following table lists M-codes in CNC milling.

M-Code Function M00 Program stop M01 Optional program stop M02 Program end M03 Spindle on clockwise (CW) M04 Spindle on counterclockwise (CCW) M05 Spindle stop M06 Tool change M08 Coolant on M09 Coolant off M10 Clamps on M11 Clamps off M30 Program end, reset to start

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Letter Address Listing Letter addresses are variables used in the different G-codes and M-codes. Most G-codes contain a variable, defined by the programmer, for each specific function. Each letter used in conjunction with G-codes or M-codes is called words. The letter used for programming are as follows:

Letter address Function D Diameter offset register number H Height offset register number F Assigns a feed rate G Preparatory function I X-axis location of arc center J Y-axis location of arc center K Z-axis location of arc center M Miscellaneous function N Block number (specifies the start of a block) P Dwell time R Retract distance used with G81, 82, 83

Radius when used with G02 or G03 S Sets the spindle speed T Specifies the tool to be used X X-axis coordinates Y Y-axis coordinates Z Z-axis coordinates

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Appendix: CNC Programming Sheet

Part Name: Programmed by: Machine: Date: Page:

CNC Programming Sheet

Setup information: N

Seq G/M Code

X Pos

Y Pos

Z Pos

IJK Loc

F Feed

R Rad/ret

S Speed

T Tool

Others

5 10 15 20 25 30 35

MEC325/580 HANDOUT: CNC TURNING OPERATION AND LATHE

MEC325/580, Spring 2010 I. Kao

In this handout, CNC programming for turning operations will be presented. The coordinate references arediscussed with an example of code based on thediameter programming reference.

CNC lathe programming: Before writing CNC code for turning operation, it is important to first identifyand calculate the coordinates of points of transition in turning. The machining may include multiple passes.We will use a CNC lathe program with the finishing cut of the following lathe part, shown in Figure 1, as anexample to illustrate the concept of CNC programming in turning operations.

−2 −1 10

1

2

3

4

−3−4−5−6−7−8−91 +Z axis

+X axis

−ZProgram zero

345

67

89

2

Figure 1: An example of CNC part for the illustration of CNC turning operation. All units are in inches.

First the coordinate frame with a right-hand coordinate system is shown in Figure 1. The conventionalcoordinates of parts in turning operation are in the second quadrant with+X and−Z coordinates. Since aturning operation is always axisymmetric with respect to the Z axis, the profile shown includes point 1 topoint 9, as shown in Figure 1. Note that the entire profile for programming consideration fits in the secondquadrant. The other half in the third quadrant is a mirror image of the profile shown in Figure 1. AllXvalues are positive, while allZ values are negative.

However, there are two types of programming references to theXZ dimension. The “diameter program-ming” relates theX-axis to the diameter of the workpiece. The “radius programming” relates theX-axis tothe radius of the workpiece. Although many controller can work in either mode,diameter programmingis the most common and is the default for most CNC lathe. To change the default, one can enable the radiusprogramming mode.

Based on Figure 1, the coordinates of the diameter programming for points 1 to 9 are identified and listedin Table 1, using thediameter programming reference. The workpiece is a cylindrical stock of diameterof8”; tool #1 is the regular right-hand turning tool, and the tool start position isX4, Z3. The CNC code withcomments is in the following for this turning operation of the finishing cut shown in Figure 1.

N5 ____ Code for program start (machine-dependent)N10 G90 G20 Absolute, inches systemN15 M06 T1 Tool change to Tool #1N20 M03 S500 spindle CW with speed 500 RPMN25 G00 X0 Z0.1 M08 Rapid to X0,Z0.1, coolant on (ready to start)

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Table 1: Coordinates of the points identified in Figure 1, under the diameter programming reference.Point # X Z

1 0 02 6 −3

3 6 −4

4 5 −4.5

5 5 −5.5

6 4 −5.5

7 4 −6

8 8 −7

9 8 −9

N30 G01 Z0 F0.02 Feed to point 1 at 0.02 in/revN35 G03 X6 Z-3 I0 K-3 CCW circular feed to point 2N40 G01 Z-4 Linear Feed to point 3N45 X5 Z-4.5 Feed to point 4N50 Z-5.5 Feed to point 5N55 X4 Feed to point 6N60 Z-6 Feed to point 7N65 X8 Z-7 Feed to point 8N70 Z-9 Feed to point 9N75 G00 Z2 M09 Rapid to Z2, coolant offN80 M05 Spindle offN85 M02 End program

Note that block 35 usesG03 to do a circular feed in CCW direction to arrive at the destination point (X6,Z−3), with center of the90 arc at (I0, K−3), using the notation of I,J,K to express theX,Y,Z coordinatesof the center. In block 40, the G-codeG01 is used to do linear interpolation. Since this is a “modal” code,it stays in effect from block 40 to 70 until it is turned off byG00, another modal code, in block 75. At theend, the M-code is used to turn off coolant, spindle, and to end the program.

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CNC Turning Machining Example: A part is to be finished using turning operation, as shown in thefollowing figure. The information about the workpiece and tool is in the following.

Workpiece size: 4" diameter by 5" lengthTool: Tool #1, right-hand turning toolTool start position: X4,Z3

1

234

567

8

9

0.60 1.002.00 2.40 4.00

0.201.10

1.50

2.30

5.00

0.30 radius

1. The coordinates of the finished part, as indicated in the v figure, are calculated using the diameterprogramming and listed in the following table.

Point # X Z

1 0 02 0.6 03 1 −0.2

4 1 −1.1

5 2 −1.1

6 2.4 −1.5

7 2.4 −2

8 3 −2.3

9 4 −2.3

2. The following CNC program is written for the finishing passof the lathe part.

N05____ Start of the programN10 G90 G20 Absolute, inches systemN15 M06 T1 Tool change to Tool #1N20 M03 Spindle on CWN25 G00 X0 Z0.1 M08 Rapid to X0,Z0.1, coolant on (ready to start)N30 G01 Z0 F0.012 Feed to point 1 at 0.012 in/revN35 X0.6 Feed to point 2N40 X1 Z-0.2 Feed to point 3N45 Z-1.1 Feed to point 4N50 X2 Feed to point 5N55 X2.4 Z-1.5 Feed to point 6N60 Z-2 Feed to point 7N65 G02 X3 Z-2.3 I0.3 K0 Cicular feed to point 8N70 G01 X4 Feed to point 9N75 G00 Z3 M09 Rapid to Z3, coolant offN80 M05 Spindle offN85 M02 End program

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1

CNC Programming Example (Lecture, Spring 2010)

CNC Programming Sheet

Part Name: Programmed by: Machine: Date: Page:

CNC Programming Sheet

Setup information: N

Seq G/M Code

X Pos

Y Pos

Z Pos

IJK Loc

F Feed

R Rad/ret

S Speed

T Tool

Others

5 (start) 10 G20 15 G00 20 G17 25 G40 30 G49 35 G80 40 G90 45 M06 T30 50 G00 55 G00 X3.0 Y-0.5 Z0.5 60 M03 S2000 65 M08 70 G01 Z-0.25 F5.0 75 G03 X3.0 Y-3.5 I0 J-1.5 F4.0 80 G01 X7.0 F5.0 85 G00 Z0.2 90 G00 X3.0 Y-0.5 95 G01 Z-0.25 F5.0

100 G01 X7.0 105 G02 X7.0 Y-3.5 I0 J-1.5 F4.5 110 G00 Z0.5 115 X4.0 Y-2.0 120 G81 Z-0.5 F8.0 R0.1 125 X6.0 130 G00 Z0.5

2

N Seq

G/M Code

X Pos

Y Pos

Z Pos

IJK Loc

F Feed

R Rad/ret

S Speed

T Tool

Others

135 M05 140 G28 Z0 145 M09 150 M30

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MEC325/580 Handout: Introduction of Rapid Prototyping Spring 2010 I. Kao 1. What is Rapid Prototyping? The idea behind Rapid Prototyping (RP) is to have a machine or machines that can create a desired solid model directly from a computer-aided design (CAD) file without any human intervention. A 3-D model is decomposed into multiple 2-dimensional layers with the use of computer software, and a machine will then manufacture the model one layer at a time. When the layers are sequentially stacked up and connected, a 3D model will emerge at the end of the fabrication process.

Since its development in the mid 1980’s numerous Rapid Prototyping1 methods have been devised. One of the first machine that was devised to fabricate rapid prototypes was the stereo lithography which used laser to solidify 2D features of a solid model layer by layer in a polymer liquid bath. Many other methods have since come out. Some of the more common methods include:

• Stereo Lithography (SLA) • Selective Laser Sintering (SLS) • Laminated Object Modeling (LOM) • Fused Deposition Modeling (FDM)

The RP technique was initially designed to make prototypes quickly for the designers to

evaluate the design and to revise as needed. Owing to the typically high cost of making prototypes and discarding them after initial evaluation to render the final design, the RP methods feature the advantages of short time to fabricate and low cost for prototyping. Since then, some machines, especially those use the laser sintering approach, have been revised and designed to include metal powder metallurgy with bonder (e.g., resin) and baking process to cure metal solids with near shape and strength. Nevertheless, this type of efforts still cannot replace the conventional process of machining. From its inception, the RP technique was not meant to replace the conventional manufacturing, and it appears that it will not in the foreseeable future.

In many cases where actual parts are required for design consideration, RP is better than the “virtual” prototyping in which computer is used to view and manipulate solids from different angles to simulate the design. For example, in the design of ink refilling of an ink-jet printer cartridge in which the cartridge was decapitated and replaced by a new polymer cap, after replacing the sponges and inks inside the ink compartments, through ultrasonic welding process. The physical prototype of the cap design is crucial and needed to actually mesh with the ink cartridge for the inspection of the statistical range of the parameters of cartridges. A virtual prototype, no matter how sophisticated it may be, just will not do.

In the following, we briefly explain each of the methods for rapid prototyping.

1 In a broader context, sometimes the “free-form machining” (FFM) is used to refer to these types of forming processes, distinct from the conventional machining or forming processes.

2

1.1 Stereo Lithography (SLA) The stereo lithography (SLA or STL) process is based on the principle of curing or hardening a liquid photo polymer into a specific shape. A laser is used to focus on spot-curing the polymer, providing the necessary energy to polymerization. Based on the Beer-Lambert law, the exposure decreases exponentially with depth according to the rule

€

E(z) = E0−z /Dp (1)

where E is the exposure in energy per area, E0 is the exposure at the resin surface (z=0), and Dp is the “penetration depth” at the laser wavelength and is a property of the resin. At the surface depth, the polymer is sufficiently exposed for it to gel, or

€

Ec = E0−Cd /Dp (2)

where Ec is the critical threshold exposure and Cd is the cure depth. Thus, the cure depth is given by the following equation

€

Cd = DpE0

Ec

⎛

⎝ ⎜

⎞

⎠ ⎟ (3)

The cure depth represents the thickness in which the resin has polymerized into a gel, but it does not have high strength at this state. Thus, the controlling software will slightly overlaps the cured volumes, but curing under fluorescent lamps is often necessary as a finishing operation.

Stereo lithography has a vat container with a platform on which the part to be fabricated can be raised or lowered vertically. This vat is filled with a photo-curable liquid acrylate polymer, a mixture of acrylic monomers, oligomers (polymer intermediates), and a phtoinitiator. A laser, generating an ultraviolet beam, is then focused along a selected surface area of photopolymer at surface to lay out the required feature. As these 2D features are laid, the platform is lowered to expose a fresh layer of liquid ready for the next layer of 2D features. Successive operations will render the final 3D solid.

Depending on the capacity of the machine, the cost ranges from $100,000 to $500,000, with cost of liquid polymer at $300 per gallon. The fume released by the liquid polymer during the fabrication process needs to be vented out for health consideration. One major area of application for stereo lithography is in the making of molds and dies for casting and injection molding.

1.2 Selective Laser Sintering (SLS) Selective laser sintering is a process based on the sintering of polymer and metallic powders selectively into an individual object. Two cylinders are used in the process chamber: (i) part-build cylinder which is lowered incrementally to where the sintered part is formed, and (ii) powder-feed cylinder which is raised incrementally to supply powder to the part-build cylinder through a roller mechanism. A thin layer is first deposited in the part-build cylinder. A laser beam, guided by the process-control computer is then focused on that layer, tracing and melting (or for metal, sintering) a particular cross-section, which then quickly solidifies into a solid mass. This is repeated for layers after layers of 2D slices of features of the solid. At the end, the loose particles are shaken off and the part recovered.

Typical cost of a SLS machine is about $500,000.

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1.3 Laminated Object Modeling (LOM) Lamination implies a laying down of layers that are adhesively bonded to one another. Laminated Object Modeling (LOM) uses layers of paper or plastic sheets with glue on one side to produce parts sheet by sheet. The adhesion process can be done by laser beam through heating, or simply by gluing. The excess materials are removed manually. LOM usually uses materials of thickness about 0.5 mm (0.02 in.) although materials as thin as 0.05mm (0.002 in.) have been used.

One example of such system is the SilverScreen+ JP 5 system which uses back-glue papers and a cutter on a printer setup to cut (or print onto) the papers into series of 2D features, to be glued together to make 3D solids. This type of systems can be very inexpensive.

1.4 Fused Deposition Modeling (FDM) In a Fused Deposition Modeling (FDM) process, a platform is used to move in the vertical (Z) direction to raise or lower the part to be made, and a nozzle assembly with both model and support materials controlled by a XY table is used to trace and lay out molten polymer filament through nozzles to make solid parts layer by layer. The support material is constructed as part of the slicing algorithm to ensure that overhanging features of the solid part is supported throughout the fabrication process. More details will follow in the next section.

2. Rapid Prototyping Using the FDM 3000 2.1 What is FDM? The FDM rapid prototyping machines use the Fused Deposition Modeling (FDM) method to create prototypes. Fused Deposition Modeling is a process whereby the layers of the model are created by forcing a special material filament through a heating system, causing the material to melt into a smooth hot molten paste, which is then forced through a delivery nozzle, and emerges as a thin ribbon of hot paste. The nozzle is guided along the XY plane, depositing the ribbon at desired positions to form a layer. After completing one layer, the entire model is lowered. The machine will then deposit another layer on top of the previous one.

Fused Deposition Modeling uses two different materials to manufacture a model; the first material is called the model material, and is what the final model will consist of, the second material is called the support material, this material is laid underneath any overhanging parts of the model so that the model will not collapse during fabrication. The temperature of the P-400 set includes P-400 ABS model material (Tm=270ºF) and P-400 water-soluble support material (Tm=235ºF) under an envelop temperature of 70ºF.

Each material is delivered through its own nozzle, which are both mounted on the underside of the of the FDM head. Apart from two nozzles, the head contains two heating elements, two thermocouples, two motors and one solenoid actuator. The two motors force the two materials into the two heating elements, and then through the delivery nozzles. The solenoid actuator lowers the support nozzle below the level of the model nozzle every time support material is needed.

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2.1.1 Motion, the Head and the Z-table The head can only move in the XY-plain. To accomplish this, the head is mounted on sliders for motion in the X-direction, while the sliders are mounted on rollers for motion in the Y-direction. Both X and Y motions are cable-driven.

Vertical or Z-directional motion is accomplished with the use of the z-table. The model is build directly onto the sponge insert in the z-table, thus when the z-table is lowered so will the model. The z-table is moved with the use of 4 lead screws.

2.1.2 Materials A range of plastics and waxes can be used to create models. Different materials display different physical properties, with each material having its own melting and envelope temperatures. The envelope temperature is the temperature of the air inside the FDM, and is set to the optimal solidification temperature of the materials. As a result of the required envelope temperature for a specific material, all model and support materials come as a couple and should not be mixed.

One particularly interesting model-support combination is that of the P400 ABS model and P400 water-soluble support. The P400 support material can be removed by means of submerging the finished part in an ultrasonic bath consisting of a heated-water-chemical solution. The ultrasound breaks down the support and dissolves it away until only the model remains. This enable very complicated models to be created, models that could not be created by conventional machinery.

2.1.3 Nozzles (Tips) The nozzles come in three different combinations pairs. They are classified according to the diameter of the outlet opening and are as follows, 0.010", 0.012" and 0.016". All the nozzles are coded with the use of rings around their lower surface. The codes can be found in the user manuals.

2.2 Steps Required to Create a Prototype on FDM 3000 The block diagram below shows the basic steps required to create a prototype.

Solid Modeling (I-DEAS or others)

• Create a Solid Model

InsightV34 • Position & Scale STL • Slice STL File • Add Support and Base • Edit Curves • Create Roads

FDM 3000 • Fabricate Model

SSL File

SML File

Model

STL File

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2.2.1 Computer Aided Design and the STL file First of all, a solid model of the prototype must be designed using any solid modeling package such as I-DEAS or AutoCAD or ProEngineer. Once this model is complete, it must undergo a process known as tessellation in order to become an STL file (STereoLithography File). Tessellation is an approximation of the solid model surface; it is accomplished by breaking the surface of the solid model into hundreds of small, interconnected triangles, each with a normal vector pointing outward from the solid. Most solid modeling software will automatically create an STL file if prompted by the user.

Note: Step by step instructions on how to create an STL file using I-DEAS can be found in the User Manual. 2.2.2 Procedures to fabricate the rapid prototype with your STL file Note: You are expected to do this part with the assistance of a staff or TA. You should NOT attempt the following procedures alone!

(a) Start the FDM3000 machine. Check if the temperatures of the Model and Support are set correct. Incase they are not, then wait till they reach the required temperature.

(b) In the selection display on the machine, select Model and try to load the model. Confirm that the Model is flowing smooth. Similarly confirm that the support is also flowing smooth.

(c) On the PC: Go to ‘Start’, then go to ‘Programs’ and then run the ‘InsightV34’ and select Insight.

(d) Go to ‘File’ menu option. Select ‘Open’ and select ‘STL’ option and open your STL file. You would see your model on the screen.

(e) Now go to ‘Orient STL’ option in the software menu. Then rotate the model so that you obtain the orientation in which you want to make the model. Select the orientation such that the support needed is minimum.

(f) Click (Slice icon). (g) Click (Support icon). (h) Click (Toolpath icon). (i) Click (Build icon). (j) Click Build icon one more time.

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(k) Next, on the FDM machine press the pause button so that the pause light will start blinking and the door will open. Now you can set the nozzle position at appropriate place so that your part is made on desired location on the supporting plate. You can set the X and Y positions it by pressing the appropriate buttons on the panel of the FDM machine. You can also set Z by first selected Z axis button. Set Z such that the model nozzle just touches the surface of the fixture plate.

(l) After setting the nozzle at appropriate position close the door of the machine and press the pause button. The door will get locked and the machine will start making the model.

(m) Wait near the machine till it finished making the part. (n) After the solid model is made, the door would get unlocked. Then open the door and

remove the model from the machine very carefully. Using the ultrasonic water bath and appropriate tools to remove the support material from the prototype. Apply proper post-fabrication processes, if necessary, such as polishing the model by sand paper or painting.

(o) Don’t forget to turn off the machine after you have finished your work. (p) Ask the TA to inspect and sign you off.

2.2.3 FDM 3000 The SML file can now be inputted into the FDM 3000. The FDM 3000 will follow the Roads created during the generation of the SML file.

Although a large part of the fabrication is autonomous, the FDM sill requires an operator, especially during the first layers of a model. Furthermore, the FDM 3000 requires constant maintenance and cleaning. Due to the nature of Fused Deposition Modeling, the nozzles, head and envelope of the FDM require thorough cleaning after every model. Calibration and general lubrication are also commonly required.

t0

tc

chip

Tool

shear plane

: shear plane angle: rake angle: clearance angleor relief angle

t0: depth of cuttc: chip thicknessr= t0/tc: chip thickness ratio

chip

t0

tc

workpiece

cutting edge of toolshear deformationto form chips

VsVc

V

Tool

shear plane

MEC325/580 Orthogonal Cutting Model

B

C

A

B

C

A

D

thickness of plate

shear deformation approximatedby a series of parallel platessliding against one anotherto form the chips

(Idealized assumption)chips = parallel shear plates

AD+DCBD

ACBD

shear strain

I. Kao

chip

Tool

N

FR

Fn

Fs

R’

R = total force acting on chipR’= force imposed by the work on the chip

(R = R’)R”= force measured by the dynamometer

Fs: shear forceFn: normal force to shearF : friction forceN : normal force to frictionFc: cutting forceFt: thrust force

chip

Tool

Ft

R”

Fc

MEC325/580 Forces in the Orthogonal Cutting Model I. Kao

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ME325/580 Handout: Copper-Nickel Phase Diagram

Spring 2010 I. Kao Phase diagram is an equilibrium diagram showing the way an alloy forms. The equilibrium diagram for the binary copper-nickel alloy is illustrated on the next page. For example, “Monel,” which resists saltwater corrosion, has 67% nickel and 33% copper shown in the diagram and is used in packaging beverages and foods. It has a range of working temperatures from –100° to 400°F (–75° to 205°C).

The Copper-Nickel phase diagram shown on the next page is the simplest phase diagram. The illustration of its usage will be presented in the following with an example. The temperature under consideration is at T=1260°C. Several states are considered and discussed in the following.

(I) At T=1260°C and under equilibrium condition, there are three possible states, as follows.

(1) When the percentage of Ni is smaller than 36% Liquid state (2) When the percentage of Ni is larger than 62% Solid state (3) When the percentage of Ni is between 36% and 62% co-existence of Liquid and

Solid (II) When liquid and solid co-exist, the following “inverse lever rule” should be applied to

determine the percentage of solid (and percentage of liquid) in the co-existing state. The Inverse Lever Rule is defined to determine the contents of solid and liquid when they co-exist within specific temperature range. Here, we use an example of 50% Ni and 50% Cu alloy at the temperature of 1260°C, as shown in the following diagram, for the illustration of this rule.

The % of solid at the state C is:

€

LCLS

=LC

(LC + CS)=(50 − 36)%(62 − 36)%

=1426

= 53.8% (1)

The % of liquid at the state C is:

€

CSLS

=CS

(LC + CS)=(62 − 50)%(62 − 36)%

=1226

= 46.2% (2)

Note the ratios formulated in equation (1) and (2). Based on the results in the equations, the percentage of solid at 1260°C with 50%Ni-50%Cu alloy is 53.8%, and with 46.2% liquid. For this alloy with 50%Ni-50%Cu, both liquid and solid co-exist from 1210°C to 1316°C, as shown in the figure. The percentage of solid and liquid can be determined by equations (1) and (2) at any given temperature within this range for the 50%Ni-50%Cu alloy. The verification of results is on the next page. In the preceding analysis, we consider different compositions of Cu and Ni at a constant given temperature (1260°C). Similarly, we can also consider a given alloying composition and vary the temperatures to acquire and analyze different states at different temperatures. For example, with the alloy composition of 67% nickel and 33% copper, as the temperature cools down from liquid state, it transitions to co-existence of liquid and solid at 2510°F and becomes complete solid as the temperature cools further to 2320°F. Thereafter, the alloy becomes entirely solid.

2

Verification of the results: Because the solid and liquid states at 1260°C have their own respective percentage of Ni and Cu, we can use the information to verify the answers obtained in equations (1) and (2). It can be obtained from the figure that at 1260°C

the solid state of this alloy has 62% of Ni and 38% of Cu (point S) the liquid state of this alloy has 36% of Ni and 64% of Cu (point L)

Thus, the total percentage of the Ni is the sum of the that in the solid and liquid states. That is,

total % of Ni = (53.8%) x 62% + (46.2%) x 36% = 50% This is as expected since the total weight percentage of the Ni element in the alloy remains 50% and cannot be changed. Similarly, the total percentage of Cu is

total % of Cu = (53.8%) x 38% + (46.2%) x 64% = 50% as expected.

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ME325/580 Handout: Tin-Lead Phase Diagram

Spring 2010 I. Kao The equilibrium diagrams for binary alloys can assume different shapes. For example, the copper-nickel alloy is very simple with only three regions, as discussed earlier. The following is the phase diagram for tin-lead (Sn-Pb) alloy, which has α and β phases as well as combinations of them with liquid and solid phases. A few important observations are in order.

(1) The freezing point of pure tin (point C) is 232ºC. As the alloying element (or impurity) of lead is added, the freezing point is decreased (just like the way that salt lowers the freezing point of water). This trend of lowering freezing point is shown in CB curve. The same is true for pure lead (point A; 327ºC) and the curve AB with decreasing freezing point. The point of intersection between the curves AB and BC (i.e., point B) indicates the eutectic mixture at 61.9% tin (Sn) and 38.1% lead (Pb). The eutectic composition gives rise to the lowest possible temperature of solidification for the Sn-Pb binary alloy. The eutectic temperature of this binary alloy is 183ºC.

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(2) In the two freezing zones ABD and CBF, the alloy is “pasty.” In other words, they contain both liquid and solid phases. Taking region ABD as an example, crystals of composition α will be forming whilst the rest of the alloy is still liquid. These crystals will grow into dendritic structure (similar to the formation of ice crystals in water with pointy tips) until such time as the alloy solidifies completely. Then the granular structure will consist of α dendrite cores in a β crystal mix. Because the β crystals form virtually instantaneously as the alloy temperature drops below 183ºC, they tend to be small. The resulting alloy is characterized by a coarse grained structure (large α, small β) and tends to be mechanically weaker and a poorer conductor. It does have its usage, however. A good example is plumber’s solder (34%Sn+66%Pb). In this case, electrical conductivity is not an issue, and the extended pasty stage is advantageous for making “wiped” joints.

(3) The tin-lead binary alloy diagram contains a eutectic point, unlike the Cu-Ni alloy which does not have one. Electronic solder made of 62%Sn and 38%Pb, or called the eutectic solder, not only has the lowest melting point and reverts from liquid to solid (and vice versa) virtually instantaneously (point B on the phase diagram). In addition, it has lowest melting point at 183ºC, which makes it ideal for electronic grade solder. The electronic grade solder alloys, or eutectic solder, fall in a narrow band ranging from 60%Sn+40%Pb to 65%Sn+35%Pb.

(4) The crystal structure of eutectic solder alloys consists of fine equally sized grains of α and β (because they have limited time to grow) with no evidence of potentially strength-reducing dendritic core. This fine grain structure also maintains a high degree of electrical conductivity—a characteristic that lends itself to becoming an ideal electronic solder.

(5) The inverse lever rule discussed previously also can be applied in the regions indicated above based on the same rules used in the Cu-Ni phase diagram.

ME325/580 HANDOUT: IRON-CARBON PHASE DIAGRAM

MEC325/580, Spring 2010 I. Kao

Iron-Carbon or Fe-Fe3C phase diagram: Iron-Carbon phase diagram (also called the iron and iron carbidephase diagram), as shown in the following figure, is an equilibrium diagram of iron and carbon that is veryuseful in dealing with steel and heat treatment.

400

600

800

1000

Tem

pera

ture

, o C

727oC (1341oF)

1200

1400

1600

0 1 2 3 4 5 6 6.67

1800

1154oC (2109oF)

1252oC

912oC (1674oF)

1394oC (2541oF)

1539oC (2802oF)

4.30%

2.11%

0.77%

0.022%

γγ+liquid

Liquid

Liquid+graphite

γ+graphite

α+graphite

(solid)

(solid)

α+γα

δ

% Carbon (C)

steel cast iron

eutectic

eutectoid

Fe3C

Figure 1: The equilibrium phase diagram of iron and iron-carbon

As shown in Figure 1, at carbon composition of 2.11% the diagram is partitioned into regions of steel(%C < 2.11%) and cast iron (%C > 2.11%). Within the region of steel, it can be further broken into tworegions, divided by the eutectoid line with carbon composition of 0.77% (some use 0.80% or 0.83%): (i)hypo-eutectoid (%C < 0.77%), and (ii) hyper-eutectoid (%C > 0.77%).

The Fe-C phase diagram has oneeutectic state at1154C with 4.30% of carbon (some use1130C and4.0%) at which the alloy transforms from liquid toγ-austenite and Fe3C-graphite. In addition, it also hasoneeutectoid state at727C with 0.77% of carbon (some use723C and 0.80% or 0.83%) at which thealloy transitions from one solid (γ-austenite) to two solids (α-ferrite and Fe3C-graphite).

Remarks:

(i) Phasesα andδ are both ferrite (BCC). Theα-ferrite (or simply ferrite) is stable at room temperature;whereas theδ-ferrite is only stable at high temperature. Phaseγ is austenite (FCC).

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(ii) α → γ: The transition for pure iron from BCC to FCC takes place at912C.

(iii) γ → δ: The transition for pure iron from FCC to BCC takes place at1394C.

(iv) Pure iron melts at1539C.

(v) Fe3C-graphite is cementite, also called carbide, and is hard and brittle.

Figure 2 illustrates the equilibrium cooling of a hypoeutectoid (which means “less than eutectoid” inGreek) steel alloy and the changes of phases as it cools to different regions of the phase diagram. The mi-crostructures of the hypoeutectoid alloy are illustrated at different temperatures, as shown in the figure. Thephase changes fromγ-austenite to (α-ferrite+γ-austenite) to (α-ferrite+Fe3C-graphite) as the temperature isdecreased. While at the state with co-existence ofα-ferrite andγ-austenite, the percentage of each can becalculated using the inverse lever rule. In the following, an example is used for illustration.

M

O

1000

900

800

700

600

500

400

Tem

pera

ture

(o C)

Composition (wt% C)0 1.0 2.0

γ

γγ

γ

γ

γ + Fe3C

γ

γ γ

γ

α

γ

γ γ

γ

α + Fe3C

Fe3C

Pearlite

Proeutectoid αEutectoid α

α

α+γ

Figure 2: Hypoeutectoid alloy in the equilibrium phase diagram and the phase change subject to equilibriumcooling.

Example: Given the Fe-Fe3C phase diagram in Figure 1, calculate the phases present fora 1020 steel at thefollowing temperatures:

(a) T = 1600C

(b) T = 1200C

(c) T = 728C

2

(d) T = 710C

(e) T = 400C

Solution: The 1020 steel has a carbon content of%C = 0.20% at the hypo-eutectoid region to the left ofthe eutectoid state. Figure 1 will be employed to perform thefollowing calculation.

(a) At T = 1600C, it is in liquid state.

(b) At T = 1200C, γ-austenite exists as a single-phase state.

(c) At T = 728C, just above the temperature at the eutectoid point (T = 727C, shown in the figure),two phases exist:α-ferrite andγ-austenite. The percentage can be determined by the inverseleverrule.

α-ferrite =0.77 − 0.20

0.77 − 0.022= 76.2% (1)

γ-austenite =0.20 − 0.022

0.77 − 0.022= 23.8% (2)

A zoom-in view of the eutectoid region is shown in Figure 2, and can be used for the application ofthe inverse lever rule as demonstrated in equations (1) and (2).

(d) At T = 710C, just below the temperature at the eutectoid point, a small amount of Fe3C-graphite(cementite) will precipitate following the solubility line from 0.022% carbon at727C to 0.022%carbon at room temperature. The percentage ofα-ferrite and Fe3C-graphite are:

α-ferrite =6.67 − 0.20

6.67 − 0.022= 97.3% (3)

Fe3C-graphite =0.20 − 0.022

6.67 − 0.022= 2.7% (4)

(e) At T = 400C: Similar to Part (d), the percentages are:

α-ferrite =6.67 − 0.20

6.67 − 0.0= 97.0% (5)

Fe3C-graphite =0.20 − 0.0

6.67 − 0.0= 3.0% (6)

The results are not very different from those in Part (d), showing a slight increase in the Fe3C precip-itation.

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MEC325/580 Handout: Stainless Steel Spring 2010 I. Kao Supplementary Lecture about Stainless Steel The corrosion resistance is imparted by the formation of a strong adherent chromium oxide on the surface of metal. On the other hand, existence of carbon will form chromium carbide which takes away ability for chromium to form the shielding chromium oxide. When the amount of atomic chromium in solution exceeds 12%, improved corrosion resistance and outstanding appearance are achieved. This category forms what has been commonly called the true stainless steels. Several classification schemes have been devised to categorize the stainless steel alloys. The American Iron and Steel Institute (AISI) groups the metals by chemistry and assigns a three-digit number that identifies the basic family and the particular alloy within that family. The following table presents the AISI designation scheme for stainless steels and correlates it with the microstructural families.

Series Alloys Structure Magnetic? 200 chromium, nickel, manganese, or nitrogen austenitic No 300 chromium, nickel austenitic No 400 chromium only ferritic or martensitic Yes 500 low chromium (<12%) martensitic Yes

The material can also be grouped by microstructural families. In general, there are five main types as will be described in the following, although new stainless steel alloys have been developed to meet special needs. (1) Austenitic (200 and 300 series): These steels are generally composed of chromium, nickel,

and manganese in iron. Nickel is an austenite stabilizer, and with sufficient amounts of both chromium and nickel, it is possible to produce a stainless steel in which austenite is the stable structure at room temperature. Known as austenitic stainless steels, these alloys may cost twice as much as the ferritic variety, with the added expense being attributed to the cost of the alloying nickel and chromium. Manganese and nitrogen are also austenite stabilizers and may be substituted for some of the nickel to produce a lower-cost, somewhat lower-quality austenitic stainless steel. Austenitic stainless steels are nonmagnetic and are highly resistant to corrosion in almost all media except hydrochloric acid and other halide acids and salts. However, they are susceptible to stress-corrosion cracking. In addition, they may be polished to a mirror finish and thus combine attractive appearance and corrosion resistance. Formability is outstanding (characteristic of the FCC crystal structure), and these steel strengthen considerably when cold worked. The popular 304 alloy, suited for all types of dairy equipment, brewing industry, citrus and fruit juice industry, dye tanks, pipelines buckets, dippers, and food processing industry, is also known as the 18-8 because of the composition of 18% chromium and 8% nickel (18-8 also refers to 302, 303, 305, and 384). Austenitic stainless steels are hardened by cold-working. They are most ductile of all stainless steels, so they can be easily formed, although, with increasing cold work, their

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formability is reduced. These steels are in a wide variety of applications, such as kitchenware, fittings, welded construction, lightweight transportation equipment, furnace and heat-exchanger parts, and components for severe chemical environment.

(2) Ferrite (400 series): These steels have a high chromium content—up to 27%. Chromium is a ferrite stabilizer, the addition of chromium tending to increase the temperature range over which ferrite is the stable structure. If sufficient chromium is added to the iron, and carbon is kept low, an alloy can be produced that is ferrite at all temperatures below solidification. These alloys are known as ferritic stainless steels. Such ferrite alloys are also the cheapest type among stainless steels. They are magnetic and have good corrosion resistance. Ferrite stainless steels possess rather poor ductility or formability because of the BCC crystal structure (they have lower ductility than austenitic stainless steels), but they are readily weldable. They are hardened by cold-working and are not heat-treatable. They are generally used for nonstructural applications such as kitchen equipment and automotive trim.

(3) Martensitic (400 and 500 series): Most martensitic stainless steels do not contain nickel and are hardenable by heat treatment. Their chromium content may be as much as 18%. If increased strength is needed, the martensitic stainless steels should be considered. However, caution should be taken to assure more than 12% chromium in solution. Slow cools may allow the carbon and chromium to react and form chromium carbides. When this occurs, the chromium is not available to react with oxygen and form the protective oxide. Thus the martensitic stainless steels may only be “stainless” when in the martensitic condition (when the chromium is trapped in atomic solution), and may be susceptible to red rust when annealed or normalized for machining or fabrication. The martensitic stainless steel cost about 1.5 times as much as the ferritic alloys, part of being due to the additional heat treatment, which generally consists of an austenitization, quench, stress relief, and temper. These stainless steels are magnetic. Martensitic stainless steels have high strength, hardness, and fatigue resistance, good ductility, and moderate corrosion resistance. They are typically used for cutlery, surgical tools, instruments, valves, and springs.

(4) Precipitation-hardening (PH): A fourth and special class of stainless steels is the precipitation-hardening variety. These steels contain chromium and nickel, along with copper, aluminum, titanium, or molybdenum. These alloys are basically martensitic or austenitic types, modified by the addition of alloying elements such as aluminum that permit age hardening at relatively low temperatures. By adding age hardening to the existing strengthening mechanisms, these materials are capable of attaining properties such as a 260-ksi (1790-MPa) yield strength and 265-ksi (1825-MPa) tensile strength with a 2% elongation.

They have good corrosion resistance and ductility, and they have high strength at elevated temperatures. Their main application is in aircraft and aerospace structural components.

(5) Duplex structure: Duplex stainless steels contain between 21 to 25% chromium and 5 to 7% nickel and are water quenched from a hot-working temperature that is between 1830 and 1920°F to produce a microstructure that is approximately half ferrite and half austenite. The structure offers a higher yield strength and greater resistance to stress corrosion cracking than either then austenitic or ferritic grades. These steels have a mixture of austenite and ferrite.

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They have good strength, and they have higher resistance to both corrosion and stress-corrosion cracking than do the 300 series of austenite steels. Typical applications are in water-treatment plants and in heat-exchanger components.

(6) Other stainless steels: Still other stainless alloys have been developed to meet special needs.

Ordinary stainless steels are difficult to machine because of their work-hardening properties and their tendency to seize during cutting. Special free-machining alloys have been produced within each family, with addition of sulfur or selenium raising the machinability to approximately that of a medium-carbon steel.

The following tables shows typical alloy compositions, structure, and usage for the first three families of stainless steels.

TABLE: Typical Composition (in wt. %) of the ferritic, martensitic, and austenitic Stainless Steels

Element Ferritic Martensitic Austenitic Carbon 0.08-0.20 0.15-1.2 0.03-0.25 Chromium 11-27 11.5-18 16-26 Manganese 1-1.5 1 2 (5.5-10) Molybdenum some cases Nickel 3.5-22 Phosphorus and sulfur Normal (0) Silicon 1 1 1-2 (0) Titanium Some cases

TABLE: Popular alloys structures and AISI designation for three primary types of stainless steel

AISI Type Martensitic (Hardenable by heat treatment )

410, 420, 440C

Ferritic (More corrosion resistant than martensitic, but not hardenable by heat treatment)

405, 430, 446

Austenitic (best corrosion resistance, but hardenable only by cold working)

201, 202, 301, 302, 302B, 304L, 310, 316, 321

TABLE: Key purpose and usage for different stainless steel alloys

Purpose and Usage AISI Types General purpose 410, 430, 202, 302 Automobile parts 301, 409, 430, 434 Hardenable by heat treatment 410, 420, 440C Hardenable by cold working 201, 301 For elevated-temperature service 446, 302B, 310

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Modified for welding 405, 304L, 321 Superior corrosion resistance 316 Catalytic converters 409

Remarks: (1) Sensitization: Problems with stainless steels are often due to the loss of corrosion resistance

(sensitization) when the amount of chromium in solution drops below 12%. Since chromium depletion is usually caused by the formation of chromium carbides along grain boundaries, and these carbides form at elevated temperatures, various means have been developed to prevent their formation. One approach is to keep the carbon content of stainless steels as low as possible, usually less than 0.10%. Another method is to tie up the carbon with small amounts of “stabilizing” elements, such as titanium or niobium, that have a stronger affinity for carbon than does chromium. Rapidly cooling of these metals through the carbide-forming range of 900 to 1500°F (480 to 820°C) also works to prevent carbide formation.

(2) Embrittlement: Another problem with high-chromium stainless steels is an embrittlement that occurs after long times at elevated temperatures. This is attributed to the formation of sigma phase, a brittle compound that forms at elevated temperatures and coats grain boundaries, thereby producing a brittle crack path through the metal. Stainless steels used in high-temperature service should be checked periodically to detect sigma-phase formation.

(3) Passivation & surface treatment: According to ASTM A380, passivation is “the removal of exogenous iron or iron compounds from the surface of stainless steel by means of a chemical dissolution, most typically by a treatment with an acid solution that will remove the surface contamination, it will not significantly affect the stainless itself.” In addition, it also describes passivation as “the chemical treatment of stainless steel with a mild oxidant, such as a nitric acid solution, for the purpose of enhancing the spontaneous formation of the protective passive film.” Passivation is recommended where the surface must be free of iron. Passivation can also aid in the rapid development of the passive surface layer on the steel, but usually does not result in a marked change in appearance of the steel surface. Passivation is performed with acid solutions (or pastes) to remove contaminants and promote the formation of the passive film on a freshly created surface (for example, via grinding, machining or mechanical damage). Common passivation treatments include nitric acid (HNO3) solutions or pastes which will clean the steel surface of free iron contaminants. Since dangerous acids are involved, only trained personnel can perform such process. In addition, stainless steel pickling acids are highly corrosive to carbon steel, and should be thoroughly removed by rinsing the component after completing the process, and/or neutralize with alkali before the rising. Residual hydrofluoric acid will initiate pitting corrosion.

1

MEC325/580 Handout: Milling Process and Machines Spring 2010 I. Kao Milling—A machining operation in which a workpiece is fed past a rotating cylindrical tool with multiple cutting edges. Two (2) basic types of milling operations:

1. peripheral milling: the axis of tool is parallel to the surface being machined; the machining is performed by cutting edges on the outside peripheral of the cutter.

2. face milling: the axis of cutter is perpendicular to the surface being machined; common type of end mill found in machine shop.

An illustration of these two basic types of milling operations is shown in the following figure.

Classification of milling machines: Various classifications are used, as follows

1. Horizontal spindle (for peripheral milling) or Vertical spindle (for face milling, end mill, …) 2. Types including (i) knee and column (most common type), (ii) bed type, (iii) planer type, (iv) tracer

mills, and (v) CNC milling machines

Two forms of milling processes: up milling and down milling Milling is an interrupted cutting process wherein entering and leaving the cut subjects the tool to impact loading, cyclic heating, and cycle cutting forces. Two common types of milling configurations are: up milling (or conventional milling) and down milling (or climb milling). The former has the tool and workpiece moving in

2

opposite directions; whereas in the latter, the tool moves in the same direction as the work feed. In up milling, the chip is very thin at the beginning, where the tooth contacts the work, and increases in thickness, becoming a maximum where the tooth leaves the work.

Advantages include: (1) The cutter tends to push the work along and lift it upward from the table. This action tends to

eliminate any effect of looseness in the feed screw and nut of the milling machine table and results in a smooth cut.

(2) Tooth engagement is not a function of workpiece surface characteristics, and contamination or scale on the surface does not affect tool life.

(3) There is a tendency for the tool to chatter.

Disadvantages include: (1) The action also tends to loosen the work from the clamping device; therefore, greater clamping

forces must be employed. (2) The smoothness of the generated surface depends greatly on the sharpness of the cutting edges. (3) The chips can be carried into the newly machined surface, causing the surface finish to be poorer

(rougher) than in down milling. In down milling, maximum chip thickness occurs close to the point at which the tooth contacts the work. Because the relative motion tends to pull the workpiece into the cutter, any possibility of looseness in the table feed screw must be eliminated if down milling is to be used. It should never be attempted on machines that are not designed for this type of milling. Virtually all modern milling machines are capable of doing down milling. Metals that readily work harden should be climb milled.

Advantages include: (1) Because the material yields in approximately a tangential direction at the end of the tooth

engagement, there is less tendency (than when up milling is used) for the machined surface to show toothmarks.

(2) The cutting process is smoother with less chatter. (3) The cutting force tends to hold the work against the machine table, permitting lower clamping

forces, particularly for slender parts. (4) Recommended for maximum cutter life when CNC machine tools are used. (5) Suitable for finishing cuts, e.g., on aluminum.

Disadvantages include: (1) The fact that the cutter teeth strike against the surface of the work at the beginning of each chip can

be a disadvantage if the workpiece has a hard surface, as casting sometimes does. (2) The teeth may dull more rapidly. (3) Because of the resulting high impact forces when the teeth engage the workpiece, this operation

must have a rigid setup, and backlash must be eliminated in the table feed mechanism. (4) It is not suitable for workpiece having surface scale, such as hot-worked metals, forgings, and

castings – because the scale is hard and abrasive and causes excessive wear and damage to cutter teeth, thus tool life can be short.

3

Probable Cause of Milling Problems and Cures (cf. DeGarmo, et al. “Materials and Process in Manufacturing”)

Problem Probable Cause Cures Chatter (vibration)

1. Lack of rigidity in machine,

fixture, arbor, or workpiece 2. Cutting load too great 3. Dull cutter 4. Poor lubrication 5. Straight-tooth cutter 6. Radial relief too great 7. Rubbing, insufficient clearance

Use large arbors Decrease feed per tooth or number of teeth in contact Sharpen or replace inserts Flood coolant Use helical cutter Check tool angles

Loss of accuracy (cannot hold size)

1. High cutting load causing deflection

2. Chip packing, between teeth 3. Chips not cleaned away before

mounting new piece of work

Decrease number of teeth in contact with work or feed per tooth Adjust cutting fluid to wash chips out of teeth

Cutter rapidly dulls 1. Cutting load too great 2. Insufficient coolant

Decrease feed per tooth or number of teeth in contact Add blending oil or coolant

Poor surface finish 1. Feed too high 2. Tool dull 3. Speed too low 4. Not enough cutter teeth

Check to see if all teeth are set at same height

Cutter dig in (hogs into work)

1. Radial relief too great 2. Rake angle too large 3. Improper speed

Check to see that workpiece is not deflecting and is clamped securely

Work burns 1. Cut is too light 2. Tool edge worn 3. Insufficient radial relief 4. Land too wide

Enlarge feed per tooth Sharpen cutter

Cutter burns 1. Not enough lubricant 2. Speed too high

Add sulfur-based oil Reduce cutting speed Flood coolant

Teeth breaking 1. Feed too high

Decrease feed per tooth Use cutter with more teeth Reduce table feed rate

MEC325/580 HANDOUT: TAYLOR ’ S TOOL WEAR EQUATION

Spring 2010 I. Kao

1 Introduction

The Taylor’s equation for tool wear is expressed in a power-law equation form, as follows

v T n = C (1)

Equation (1) is a standard nonlinear power equation. In the case of equation presented in equation (1), wecan take logarithmic relationship of the variables and makea linear equation in the log-log coordinates, asexpressed in the following equation

log v + n log T = log C (2)

Equation (2) represents a line in the(log T, log v) space.In the next sections, an example is given for finding the exponentn, and the coefficient,C, for a tool byapplying the Taylor equation for tool wear.

2 Finding Parameters of the Taylor’s Tool Wear Equation

Equation (2) is a result of taking logarithmic form of equation (1). At least two sets of experimental data oftool speed and life are required to find the exponentn and the coefficientC. If the two experimental datasets are given as(T1, v1) and(T2, v2), we can write equation (2) for the two data sets as

log v1 + n log T1 = log C (3)

log v2 + n log T2 = log C (4)

Equation (3) minus (4) renders the following

n =log v2 − log v1

log T1 − log T2

=log(v2/v1)

log(T1/T2)(5)

Once the exponentn is obtained from equation (5), the result can be substitutedinto equation (1) to find thecoefficientC = v1 T n

1.

3 Example: Experimental Results

Experiments were conducted to characterize the parametersof tool wear based on the Taylor’s equation.The experimental results of the relationship between the tool speed and tool life are tabulated in thefollowing. The points are corresponding to the following figure (the first two circled points).

exp data tool life, T velocity,vset 1 100min 400m/min

set 2 240min 300m/min

Applying the data of experiments in the table to equation (5), we obtain

n =log(300/400)

log(100/240)=

−0.1249

−0.3802= 0.3286 (6)

1

101

102

103

102

103

Tool life (min)

spee

d of

tool

(m

/min

)

Plot of Taylor’s tool life equation

Figure 1: The raw data of experiments are indicated by ’o’. The results of equation of tool wear is plottedas a line in the logarithmic space oflog T versuslog v.

Substituting into equation (1), we findC = 1817. Thus, the Taylor’s equation of tool wear is

v (T )0.3296 = 1817 (7)

where the tool speedv has a unit ofm/min and the tool lifeT is in minutes.The result of the tool life relationship in equation (7) is plotted in Figure 1, in logarithmic scale. The twocircles indicate the two sets of experimental measurementsgiven in the table.

2

MEC580: HANDOUT ON THE LEAST-SQUARES BEST FIT ALGORITHM

MEC580 Spring 2010 I. Kao

1 Introduction

In engineering applications, experiments are often conducted with multiple sets of data points for best curvefitting. If the case when the governing equation between the two parameters is linear, the “linear regression”algorithm can be applied. However, such linear regression method can not be applied directly if the equationis in a power equation form, such as that in the Taylor’s equation for tool wear:

v T n = C (1)

Equation (1) is a standard nonlinear power equation. In the case of equation presented in equation (1), wecan take logarithmic relationship of the variables and makea linear equation in the log-log coordinates, asexpressed in the following equation

log v + n log T = log C (2)

Equation (2) represents a line in the(log T, log v) space.In the next section, a standard technique for determining the least-squares best fit solution is presented

as a matrix solution.

2 Algorithm of the Weighted Least-Squares Fit for Power Equations

Equation (2) is a result of taking logarithmic form of equation (1). It can be re-arranged in the followingform

log v = log C + ζ log T (3)

whereζ = −n.With a total ofi data sets of(v, T ) from experiments, we can re-arrange equation (3) in the following

matrix form for least-squares fity = Ax (4)

where

y =

log v1

log v2

...log vi

A =

1 log T1

1 log T2

......

1 log Ti

x =

[

log C

ζ

]

(5)

The least-squares solution ofx in equation (4) can be obtained using the Penrose-Moore generalized inversethat minimizes the norm of errors iny [3]. That is,

x = A∗ y (6)

where the superscript ‘*’ denotes the generalized inverse.The left inverse is used in equation (6);i.e.,A∗ = (ATA)−1AT .

Equation (6) minimizes the norm of the squared errors iny = log v instead ofv. In order to compensatefor such discrepancy, we utilize a weighted least-squares fit of the following form

x = (WA)∗ Wy (7)

where the weighting matrix isW = diag[ey1 . . . eyi ] = diag[v1 . . . vi] that corrects the logarithmic scaleof the norm of squared errors to be minimized.

The equation and derivation presented in this section can also be found in references [1, 2].

1

3 Example: Experimental Results and Curve Fitting

An example is used in this section to illustrate the application of the LS fit equations in (6) and (7). We willuse relationship between the tool speed and tool life, as characterized in the Taylor’s equation in (1). Theexperimental results are tabulated in the following:

exp data velocity,v tool life, T

set 1 400m/min 100min

set 2 300m/min 240min

set 3 200m/min 820min

When the three data sets are used to find the LS solution of the exponent,n, and constant,C, we canobtain the following terms based on the experimental data and equations (6) and (7). We have

A =

1 2.00001 2.38021 2.9138

y =

2.60212.47712.3010

W =

400.0 0 00 300.0 00 0 200.0

(8)

The generalized inverse ofA andWA are

A∗ =

[

2.8217 0.6283 −2.4500−1.0235 −0.1213 1.1448

]

(WA)∗ =

[

8.8962 −2.1113 −9.6255−3.3497 1.4018 4.5967

]

× 10−3 (9)

Substituting into equations (6) and (7), respectively, we obtain

without weighting: n = 0.3295;C = 1824.3 (10)

with weighting: n = 0.3293;C = 1822.7 (11)

It is noted that equations (10) and (11) differ only slightly. Thus, either solution is acceptable. We will adopt

v (T )0.3293 = 1823 (12)

wherev has a unit ofm/min andT is in minutes.If a fourth data set was added via experiments with

exp data velocity,v tool life, T

set 1 400m/min 100min

set 2 300m/min 240min

set 3 200m/min 820min

set 4 50m/min 54, 000min

Employing the same procedures above, by including the additional data, we obtain:

without weighting: n = 0.3306;C = 1836.1 (13)

with weighting: n = 0.3298;C = 1827.0 (14)

It is noted that the solution in equation (14) with the weighting matrix renders a result that is more consistentwith those in equations (10) and (11). This is because the addition of the weighting matrix will restore thescales ofv andT in the LS fitting, instead of using the logarithmic scales oflog v andlog T .

The results of equation (14) are plotted in Figure 1, to compare with the raw data points in a log-logplot.

2

100

101

102

103

104

105

101

102

103

104

Figure 1: Comparison between the raw data (indicated by ’o’)and the results of the weighted least-squaresbest fit using the power equation (1) and LS fit equation (7).

References

[1] N. Xydas and I. Kao, “Modeling of contact mechanics and friction limit surface for soft fingers withexperimental results,”International Journal of Robotic Research, vol. 18, no. 9, pp. 941–950, September1999.

[2] I. Kao and F. Yang,Stiffness and Contact Mechanics for Soft Fingers in Grasping and Manipulation toappear on the IEEE Transactions of Robotics and Automation, 2004

[3] G. Strang,Linear Algebra and Its Applications, Academic Press, 2nd edition, 1980.

3

Taguchi Methods!

Taguchi Methods Lecture (I)

•  “Taguchi Methods” refer to a collection of – Non-dynamic methods in product

design – Dynamic method – Newest: Mohalanobis-Taguchi

method

Taguchi Methods!

Taguchi Methods Lecture (II)

•  Non-Dynamic Taguchi Method (Handouts on bboard)!– ASME magazine: vol. 14, no. 8, December 1994!

– His visit to ASME after the one-day workshop at Stony Brook!

–  Introduction & parameter design!– Orthogonal arrays!– Case study 1: canon example!– Case study 2: RL circuit design!

– With Excel spreadsheet for calculation!– Handout for further details!

Taguchi Methods Myth? Or Good Engineering?

Professor Imin Kao!Department of Mechanical Engineering!

SUNY at Stony Brook!Phone: 631-632-8308 kao@mal.eng.sunysb.edu!

Taguchi Methods!

Quality Engineering

“Quality Is The Loss A Product Causes To!Society After Being Shipped,!

Other Than Any Losses Caused By!Its Intrinsic Functions.”!

! ! ! !-- by Dr. Genichi Taguchi!

Taguchi Methods!

Loss Function

Products That Meet Tolerance Also Inflict A Loss!

where x is the value of the quality characteristic!! m is the target value!! k=A/!2 with A= cost to handle a defective; !=tolerance!

Taguchi Methods!

How to Reduce Loss: 2 steps

Starting ! ! Reduce ! ! Place on!

Conditions ! Variation ! Target!

Taguchi Methods!

R & D Activities

Robust!Technology!

Taguchi Methods!

Parameter Design

•  Control Factors!–  Factors you can and want to control during

manufacturing and during use!–  e.g., gun powder, angle of incline!

•  Noise Factors!–  Factors you cannot or do not want to

control during manufacturing or during use!–  e.g. temperature, wind, uncertainties!

Taguchi Methods!

Sources of Noises

! Inner Noise!–  Material or dimensional deterioration!–  A function of time or usage!

! Outer Noise!–  Conditions such as temperature, humility, voltage!

! Unit-to-Unit Variation!–  Variation in manufacturing under same conditions!–  Such as parts in different locations of an oven!

Taguchi Methods!

Comparison Between Traditional and Taguchi Methods

Traditional Methods:!Remove cause of defect!

Taguchi Methods:!Reduce effects of cause!

Traditional approaches may be expensive or impossible or may be more difficult to implement!

Taguchi Methods!

Case Studies

Parameter Design!1.  Canon Example!

–  A system with well-known mechanics model : to design for target distance!

2.  Circuit Design Example!–  A simple RL circuit: to maintain constant

level of current output!

Taguchi Methods!

Orthogonal Arrays in Experimental Design

" L4, L8, L9, L12, L16, L18, L27, and L36!" Recommended: L9 and L18!

–  Number of experiments: 9 and 18!–  Number of readings: product array!

" Product Array:!–  inner array: control factors!–  outer array: noise factors!

Taguchi Methods!

Parameter Design: Definition of S/N Ratios

Professor Imin Kao, Manufacturing Automation Laboratory, SUNY at Stony Brook; kao@mal.eng.sunysb.edu!

Taguchi Methods!

Smaller-the-Better Criterion Definition of S/N Ratios

Professor Imin Kao, Manufacturing Automation Laboratory, SUNY at Stony Brook; kao@mal.eng.sunysb.edu!

Taguchi Methods!

Larger-the-Better Criterion Definition of S/N Ratios

Professor Imin Kao, Manufacturing Automation Laboratory, SUNY at Stony Brook; kao@mal.eng.sunysb.edu!

Taguchi Methods!

Nominal-the-Best Criterion Definition of S/N Ratios

Professor Imin Kao, Manufacturing Automation Laboratory, SUNY at Stony Brook; kao@mal.eng.sunysb.edu!

Taguchi Methods!

Case Study of Taguchi Methods: Canon Example

Professor Imin Kao!Department of Mechanical Engineering!

SUNY at Stony Brook!631-632-8308; email: kao@mal.eng.sunysb.edu!

Taguchi Methods!

Cannon Example

Distance ! !y= (F!t/m)2 /g sin2" = k F2 sin2" !Ball weight & !!t !m = 0.2 kg, !t=0.1sec!Constant (k) ! !k = 0.02549 m/N2!Range of " ! !0 < " " 45º!Range of F ! !0 < F " 170 N!

Taguchi Methods!

Traditional Approach

Starts with F=130N and apply the !projectile equation!

y = y(F, ") = k F2 sin2"!150 = (0.02549)1302 sin(2 ")!

Solve for " = 10.19º!

Taguchi Methods!

Parameter Design

!  Control factors!

!  Noise factors!

!  Compound factor!

F1 = 30 N "1 = 5°!F2 = 90 N "2 = 23°!F3 = 150 N "3 = 42°!

Fi+ = nominal + 10% Fi

= nominal!Fi- = nominal -10% "i

+ = nominal + 3°! "i = nominal "i

- = nominal - 3°!

N1 = y(Fi+ , "i

+)!N2 = y(Fi

- , "i- ) for i=1,2,3!

Calculations of Flying Distance N1=y(F1’!1’)

F1 = 30 N !1=5º !2=23º !3=42º

F1 = 33 != 8º != 26º != 45º

F2 = 90 N !1=5º !2=23º !3=42ºF2 = 150 N !1=5º !2=23º !3=42º

F2 = 99 != 8º != 26º != 45º

F3 = 165 != 8º != 26º != 45º

y

7.6521.8827.76

68.87196.88249.85

191.30546.89694.02

N2=y(F3’!3’)

F1 = 27 != 2º != 20º != 39º

F2 = 81 != 2º != 20º != 39º

F3 = 135 != 2º != 20º != 39º

y

1.3011.9518.18

11.67107.51163.60

32.41298.63454.44

nominal

Taguchi Methods!

Calculation of S/N Ratio and Mean

Taguchi Methods!

Response Tables

Response table (#)! Response table (mean)!

Optimum Condition: " = 42º! (within chosen range) F = 76.9 N!

F avg@30N 6.06 (!=5º)-0.0386

1st

!

2nd 3rdavg@90N 6.06(!=23º) 7.63

avg@150N 6.06(!=42º) 10.60

Taguchi Methods!

Plot of Response

Taguchi Methods!

Comparison of Variability

Traditional Solution!(F=130 N, "=10.19º) !=45!

Parameter Design!(F=76.9 N, " = 42º) !=26!

Taguchi Methods!

Conclusions of First Iteration

" Conclusions From Response Table (#)!–  The parameter " is more sensitive to parameter

variation so we pick one with largest S/N!–  F has constant S/N ratio so it is insensitive to

parameter variations!" Conclusions From Response Table (mean)!

–  The mean values increase with F!–  The mean values increase with " for the range of

values in the first iteration!

Taguchi Methods!

Graphical Interpretations

Increase S/N ratio !Output variations are much!smaller at "=42o than those!at 5o, for input variation!of ±3o!

Move mean to target!The slope at F=30N!is about 88o so the output is nearly linear when F>30N!

Taguchi Methods!

Summary

•  Quality and Loss Function!•  Two Steps to Increase Robustness and

to Enhance Quality!•  Use Signal-to-Noise Ratio (S/N) in

Parameter Design for Robust Technology!

•  More Robust Results are obtained by Using Parameter Design!

Using Taguchi Methods in Circuit Design1

Manufacturing Automation Laboratory (MAL)Department of Mechanical Engineering

SUNY at Stony Brook

1 Purpose

To design a simple circuit with a resistance,R, and self-inductance,L, so that the output current is at 10amperes. The loss function, in terms of dollars, is estimated at $200 if the current deviates more than 4amperes which will cause the circuit to cease functioning.

2 Theoretical Equations to Calculate Currenty and Sensitivity

The output current subject to theRL circuit is given by the following equation.

y =V

√

R2 + (2πfL)2(1)

whereV is the input voltage,R is the resistance,f is the frequency, andL is the inductance. The followingterms are also defined:

m =1

n(y1 + y2 + · · · + yn)

Sm =1

n(y1 + y2 + · · · + yn)2

Ve =1

n − 1(y2

1 + y2

2 + · · · + y2

n − Sm)

The sensitivity is defined in this case (nominal-the-better) to be

S =1

n(Sm − Ve) (2)

with the signal-to-noise ratio

η = 10 log1

n

Sm − Ve

Ve(3)

The loss function is defined as

L =A0

∆20

σ2 (4)

whereA0 is the loss due to malfunction of this circuit,∆0 is the function limit, andσ2 is the variance.

1The example was adapted from theTaguchi Methods – Research and Development.

1

Control factors Values selected for parameter designResistance (R) R1 = 0.5Ω R1 = 5.0Ω R1 = 9.5ΩInductance (L) L1 = 0.010H L1 = 0.020H L1 = 0.030H

Noise factors Values estimated for parameter designVoltage (V ) 90V 100V 110V

Frequency (f ) 50Hz 55Hz 60Hz

R′−10% 0 10%

L′−10% 0 10%

Table 1: Values and estimated ranges of control and noise factors

Results S/N ratio SensitivityNo. R L N1 N2 η S

1 1 1 21.5 38.4 7.6 29.22 1 2 10.8 19.4 7.5 23.23 1 3 7.2 13.0 7.4 19.74 2 1 13.1 20.7 9.7 24.35 2 2 9.0 15.2 8.5 21.46 2 3 6.6 11.5 8.0 18.87 3 1 8.0 12.2 10.4 20.08 3 2 6.8 10.7 9.8 18.69 3 3 5.5 9.1 8.9 17.0

Table 2: Calculation of S/N ratios and sensitivities

3 Specification of Design Parameters

In the parameter design, we first need to identify the controland noise factors. Control factors are the factorsthat we can control or select freely. The noise factors are the ones that we can not or do not want to control,such as the actual voltage and frequency of input power and the variations in the actual values of resistanceand inductance (assume that the actual values vary within certain ranges).

The control factors are the resistance,R, and inductance,L. Each control parameter is chosen to havethree levels in our analysis. The noise factors include the voltage of power input,V , and frequency,f ,and the uncertainties of the resistor and inductor components which are assume to vary±10% from theirnominal values. Table 1 summarizes the factors.

4 Parameter Design

Using the parameter design, we can calculate the signal-to-noise ratios and sensitivities using equations (2)and (3). The results are tabulated in Table 2.

2

η S

R1 7.5 24.0R2 8.7 21.5R3 9.7 18.5

η S

L1 9.2 24.5L2 8.6 21.1L3 8.1 18.5

Table 3: Factorial effects

Table 3 of average values are computed in order to compare thecontrol factors of each level using theS/N ratios,η, and sensitivities,S. From Table 3, we conclude that the optimal design isR3L1 which hasthe highest S/N ratios inR andL, respectively. In order to determine the difference between average outputand the target value, a confirmation experiment is performed. The currents are found to bey1 = 8.0A andy2 = 12.2A with an average of 10.1. There is nearly no difference between the average and the target valuein this case and thus no further adjustment is needed. If, however, there is a large difference, the output willneed to be adjusted using a factor that has larger sensitivity but affects S/N less. Such a factor is called theadjustment factor.

5 Loss Calculation

Using the loss function defined in equation (4) as a basis, we employ the following equation to calculateLwith a similar definition in order to obtain figures of loss function for the purpose of comparison. The lossusing parameter design is

L =A0

∆20

1

10η/10=

200

42

1

101.04= $1.14

This value is much smaller than $200.

If traditional design is chosen,i.e. R2L2, we obtain

L =200

42

1

100.85= $1.76

The improvement by using the parameter design is $0.62 per each product – about 35% improvement.

6 Conclusion

The parameter design of the Taguchi Methods, when applied tothis electronic design problem, yields satis-factory results. The S/N ratio enhances the robustness of the product and reduces the loss. The quality ofdesign of this circuit is improved over the traditional solution.

References

[1] G. TaguchiSystem of Experimental Design, vols. 1 and 2Quality Resources, Dearborn Michigan, vol.1 and 2, 1991

3

[2] G. Taguchi and S. KonishiTaguchi Methods – Research and DevelopmentASI press, vol. 1 in QualityEngineering Series, 1992

4

Taguchi Methods!

Case Study of Taguchi Methods: RL circuit example

Professor Imin Kao!Department of Mechanical Engineering!

SUNY at Stony Brook!631-632-8308; email: kao@mal.eng.sunysb.edu!

Taguchi Methods!

RL Circuit Design

! Design RL circuit such that the current, y, is at 10 A.!

! The loss function is estimated at $200 if current deviates more than 4A!

Taguchi Methods!

Control and Noise Factors

Taguchi Methods!

Calculating S/N Ratios

•  Apply Nominal-the-Best Criterion!•  S/N ratio equation for 2 data points!

Taguchi Methods!

Parameter Design Using Orthogonal Array

Taguchi Methods!

S/N Ratio: Factorial Effects

! The S/N ratios from the orthogonal array!

! The optimal design is R3L1 which has highest S/N ratios in R and L!

! Confirmation Run: y1=8.0A, y2=12.2A with average at 10.1A!

Taguchi Methods

Parameter Design:Definition of S/N Ratios

Professor Imin Kao, Manufacturing Automation Laboratory, SUNY at Stony Brook; kao@mal.eng.sunysb.edu

Orthogonal Arrays forTaguchi Methods

Manufacturing Automation LaboratoryDepartment of Mechanical Engineering

SUNY at Stony BrookStony Brook, NY 11794-2300

Abstract

This article contains the orthogonal arrays that are listed in Appendix 3 of the “Taguchi Methods:Research and Development”. The book is Volume One of the Quality Engineering Series, published bythe ASI Press.

According to Dr. Taguchi, however, only

,

, and

are preferred for parameter design.

1 The

orthogonal array

The orthogonal array is for 3 control factors, each with two-level variations. This is denoted as .

No. 1 1 1 12 1 2 23 2 1 24 2 2 1

Table 1: orthogonal array

1

2 The

orthogonal array

The orthogonal array is for 7 control factors, each with two-level variations. This is denoted as .

No. 1 1 1 1 1 1 1 12 1 1 1 2 2 2 23 1 2 2 1 1 2 24 1 2 2 2 2 1 15 2 1 2 1 2 1 26 2 1 2 2 1 2 17 2 2 1 1 2 2 18 2 2 1 2 1 1 2

Table 2: orthogonal array

3 The

orthogonal array

The orthogonal array is for 4 control factors, with 4 three-level variations. This is denoted as .

No. 1 1 1 1 12 1 2 2 23 1 3 3 34 2 1 2 35 2 2 3 16 2 3 1 27 3 1 3 28 3 2 1 39 3 3 2 1

Table 3: orthogonal array

2

4 The

orthogonal array

The orthogonal array is for 11 control factors, with 11 two-level variations. This is denoted as .

No. 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 2 2 2 2 2 23 1 1 2 2 2 1 1 1 2 2 24 1 2 1 2 2 1 2 2 1 1 25 1 2 2 1 2 2 1 2 1 2 16 1 2 2 2 1 2 2 1 2 1 17 2 1 2 2 1 1 2 2 1 2 18 2 1 2 1 2 2 2 1 1 1 29 2 1 1 2 2 2 1 2 2 1 1

10 2 2 2 1 1 1 1 2 2 1 211 2 2 1 2 1 2 1 1 1 2 212 2 2 1 1 2 1 2 1 2 2 1

Table 4: orthogonal array

3

5 The

orthogonal array

The orthogonal array is for 15 control factors, with 15 two-level variations. This is denoted as .

No. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 2 2 2 2 2 2 2 23 1 1 1 2 2 2 2 1 1 1 1 2 2 2 24 1 1 1 2 2 2 2 2 2 2 2 1 1 1 15 1 2 2 1 1 2 2 1 1 2 2 1 1 2 26 1 2 2 1 1 2 2 2 2 1 1 2 2 1 17 1 2 2 2 2 1 1 1 1 2 2 2 2 1 18 1 2 2 2 2 1 1 2 2 1 1 1 1 2 29 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

10 2 1 2 1 2 1 2 1 2 1 2 1 2 1 211 2 1 2 2 1 2 1 1 2 1 2 2 1 2 112 2 1 2 2 1 2 1 2 1 2 1 1 2 1 213 2 2 1 1 2 2 1 1 2 2 1 1 2 2 114 2 2 1 1 2 2 1 2 1 1 2 2 1 1 215 2 2 1 2 1 1 2 1 2 2 1 2 1 1 216 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1

Table 5: orthogonal array

4

6 The

orthogonal array

The orthogonal array is for 8 control factors, with 1 two-level and 7 three-level variations. This is denotedas .

No.

1 1 1 1 1 1 1 1 12 1 1 2 2 2 2 2 23 1 1 3 3 3 3 3 34 1 2 1 1 2 2 3 35 1 2 2 2 3 3 1 16 1 2 3 3 1 1 2 27 1 3 1 2 1 3 2 38 1 3 2 3 2 1 3 19 1 3 3 1 3 2 1 2

10 2 1 1 3 3 2 2 111 2 1 2 1 1 3 3 212 2 1 3 2 2 1 1 313 2 2 1 2 3 1 3 214 2 2 2 3 1 2 1 315 2 2 3 1 2 3 2 116 2 3 1 3 2 3 1 217 2 3 2 1 3 1 2 318 2 3 3 2 1 2 3 1

Table 6: orthogonal array

5

7 The

orthogonal array

The orthogognal array is for 13 contrl factors, with 13 three level variations. This is denoted as .

No. 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 2 2 2 2 2 2 2 2 23 1 1 1 1 3 3 3 3 3 3 3 3 34 1 2 2 2 1 1 1 2 2 2 3 3 35 1 2 2 2 2 2 2 3 3 3 1 1 16 1 2 2 2 3 3 3 1 1 1 2 2 27 1 3 3 3 1 1 1 3 3 3 2 2 28 1 3 3 3 2 2 2 1 1 1 3 3 39 1 3 3 3 3 3 3 2 2 2 1 1 1

10 2 1 2 3 1 2 3 1 2 3 1 2 311 2 1 2 3 2 3 1 2 3 1 2 3 112 2 1 2 3 3 1 2 3 1 2 3 1 213 2 2 3 1 1 2 3 2 3 1 3 1 214 2 2 3 1 2 3 1 3 1 2 1 2 315 2 2 3 1 3 1 2 1 2 3 2 3 116 2 3 1 2 1 2 3 3 1 2 2 3 117 2 3 1 2 2 3 1 1 2 3 3 1 218 2 3 1 2 3 1 2 2 3 1 1 2 319 3 1 3 2 1 3 2 1 3 2 1 3 220 3 1 3 2 2 1 3 2 1 3 2 1 321 3 1 3 2 3 2 1 3 2 1 3 2 122 3 2 1 3 1 3 2 2 1 3 3 2 123 3 2 1 3 2 1 3 3 2 1 1 3 224 3 2 1 3 3 2 1 1 3 2 2 1 325 3 3 2 1 1 3 2 3 2 1 2 1 326 3 3 2 1 2 1 3 1 3 2 3 2 127 3 3 2 1 3 2 1 2 1 3 1 3 2

Table 7: orthogonal array

6

8 The

orthogonal array

The orthogognal array is for 23 contrl factors, with 11 two level variations and 12 three level variations.This is denoted as .

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1’ 2’ 3’ 4’

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 14 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 3 3 3 3 1 2 2 15 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1 1 2 2 16 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 1 2 2 17 1 1 2 2 2 1 1 1 2 2 2 1 1 2 3 1 2 3 3 1 2 2 3 2 1 2 18 1 1 2 2 2 1 1 1 2 2 2 2 2 3 1 2 3 1 1 2 3 3 1 2 1 2 19 1 1 2 2 2 1 1 1 2 2 2 3 3 1 2 3 1 2 2 3 1 1 2 2 1 2 1

10 1 2 1 2 2 1 2 2 1 1 2 1 1 3 2 1 3 2 3 2 1 3 2 2 2 1 111 1 2 1 2 2 1 2 2 1 1 2 2 2 1 3 2 1 3 1 3 2 1 3 2 2 1 112 1 2 1 2 2 1 2 2 1 1 2 3 3 2 1 3 2 1 2 1 3 2 1 2 2 1 113 1 2 2 1 2 2 1 2 1 2 1 1 2 3 1 3 2 1 3 3 2 1 2 1 1 1 214 1 2 2 1 2 2 1 2 1 2 1 2 3 1 2 1 3 2 1 1 3 2 3 1 1 1 215 1 2 2 1 2 2 1 2 1 2 1 3 1 2 3 2 1 3 2 2 1 3 1 1 1 1 216 1 2 2 2 1 2 2 1 2 1 1 1 2 3 2 1 1 3 2 3 3 2 1 1 2 2 217 1 2 2 2 1 2 2 1 2 1 1 2 3 1 3 2 2 1 3 1 1 3 2 1 2 2 218 1 2 2 2 1 2 2 1 2 1 1 3 1 2 1 3 3 2 1 2 2 1 3 1 2 2 219 2 1 2 2 1 1 2 2 1 2 1 1 2 1 3 3 3 1 2 2 1 2 3 2 1 2 220 2 1 2 2 1 1 2 2 1 2 1 2 3 2 1 1 1 2 3 3 2 3 1 2 1 2 221 2 1 2 2 1 1 2 2 1 2 1 3 1 3 2 2 2 3 1 1 3 1 2 2 1 2 222 2 1 2 1 2 2 2 1 1 1 2 1 2 2 3 3 1 2 1 1 3 3 2 2 2 1 223 2 1 2 1 2 2 2 1 1 1 2 2 3 3 1 1 2 3 2 2 1 1 3 2 2 1 224 2 1 2 1 2 2 2 1 1 1 2 3 1 1 2 2 3 1 3 3 2 2 1 2 2 1 225 2 1 1 2 2 2 1 2 2 1 1 1 3 2 1 2 3 3 1 3 1 2 2 1 1 1 326 2 1 1 2 2 2 1 2 2 1 1 2 1 3 2 3 1 1 2 1 2 3 3 1 1 1 327 2 1 1 2 2 2 1 2 2 1 1 3 2 1 3 1 2 2 3 2 3 1 1 1 1 1 328 2 2 2 1 1 1 1 2 2 1 2 1 3 2 2 2 1 1 3 2 3 1 3 1 2 2 329 2 2 2 1 1 1 1 2 2 1 2 2 1 3 3 3 2 2 1 3 1 2 1 1 2 2 330 2 2 2 1 1 1 1 2 2 1 2 3 2 1 1 1 3 3 2 1 2 3 2 1 2 2 331 2 2 1 2 1 2 1 1 1 2 2 1 3 3 3 2 3 2 2 1 2 1 1 2 1 2 332 2 2 1 2 1 2 1 1 1 2 2 2 1 1 1 3 1 3 3 2 3 2 2 2 1 2 333 2 2 1 2 1 2 1 1 1 2 2 3 2 2 2 1 2 1 1 3 1 3 3 2 1 2 334 2 2 1 1 2 1 2 1 2 2 1 1 3 1 2 3 2 3 1 2 2 3 1 2 2 1 335 2 2 1 1 2 1 2 1 2 2 1 2 1 2 3 1 3 1 2 3 3 1 2 2 2 1 336 2 2 1 1 2 1 2 1 2 2 1 3 2 3 1 2 1 2 3 1 1 2 3 2 2 1 3

Table 8: orthogonal array

References

[1] G. Taguchi System of Experimental Design, vols. 1 and 2 Quality Resources, Dearborn Michigan, vol. 1and 2, 1991

[2] G. Taguchi and S. Konishi Taguchi Methods – Research and Development ASI press, vol. 1 in QualityEngineering Series, 1992

7

MEC325/580 HANDOUT: AN EXAMPLE OF THE TAGUCHI METHOD

MEC325/580, Spring 2010 I. Kao

This handout explains the application of the non-dynamic Taguchi method using an example of experimentaldesign withL4 orthogonal array on a practical manufacturing process withexperimental measurements.

Problem Statement: Experiments were conducted for a tile making process using the Taguchi method.Three control factors are identified as crucial to the strength of the tiles, as described in the following.

A: ingredient #1,B: ingredient #2, andC: temperature of the curing process

with each control factor having two levels. The experimentswere conducted with the results tabulated inTable 1. Note that in Table 1, the orthogonal array employed is theL4 array. (cf. the handout on variousorthogonal arrays) The data measured (or thereadings) in Table 1 are the strength of the tiles, inMPa.

ResultsNo. A B C N1 N2

1 1 1 1 100 2502 1 2 2 160 1853 2 1 2 495 2954 2 2 1 360 313

Table 1: AL4 array and experimental results

1. Since the strength of the tile is considered here as the measure to evaluate the tile making process,which criterion should you use:larger-the-better, smaller-the-better, or nominal-the-best?

2. Determine the optimal condition of each control factor, based on the parameter design with the S/Nratios to maximize the strength.

Solution: The experimental design has 4 experiments, each with 2 readings. The terms “experiment” and“reading” are explained in theRemarks at the end of this handout.

1. Because the strength of the tile is to be maximized, we willuselarger-the-better criterion.

2. Once thelarger-the-better criterion is chosen, the following equations for calculating the S/N ratiosare employed.

σ2 =1

2

(

1

y2

1

+1

y2

2

)

(1)

η = −10 log σ2 (2)

wherey1 andy2 are the data under the 2 columnsN1 andN2. Substituting the readings in Table 1 intoequations (1) and (2), we obtain theL4 orthogonal array with the calculated data ofσ2 andη listed inTable 2.

Once the S/N ratios,η, are calculated, as listed in the last column in Table 2, we can calculate theaverage S/N ratios associated with each level of the three control factors. For example, the average

1

Results S/N RatiosNo. A B C N1 N2 σ2 η

1 1 1 1 100 250 0.00005800 42.372 1 2 2 160 185 0.00003414 44.673 2 1 2 495 295 0.00000779 51.094 2 2 1 360 313 0.00000896 50.48

Table 2: Calculating the S/N ratios based on the measurements and readings

A B C

level 1 43.52 46.73 46.42level 2 50.78 47.57 47.88

Table 3: The response table

S/N ratio forA1 (first level of control parameterA) is the average of experiment No. 1 and 2 (row 1and 2) by virtue of the designation of levels under the columnfor the control factorA. Similarly, theaverage S/N ratio forB2 is the average of experiment No. 2 and 4. The entries of the response tablesare calculated and listed in Table 3.

The response table can be used to plot the following responsechart for the signal-to-noise ratios, asshown in Figure 1.

38

40

42

44

46

48

50

52

A1 A2 B1 B2 C1 C2

Figure 1: The plot of response chart based on the values obtained in the response table.

Optimal Levels of Control Factors:

From the response chart (or the response table), the optimaldesign corresponding to the choice ofthe combination of one of the two levels of the three control factors is found to beA2 B2 C2 (i.e.,level 2 of parameterA, level 2 of parameterB, and level 2 of parameterC) which corresponds to thecombination of highest S/N ratios from each parameter.

For example, if the first and second levels of the curing temperatures (C1 andC2) are150F and200F , respectively, we will choose level 2 with a curing temperature at200F as our design basedon the results of Taguchi method.

Remarks:

2

(i) Each row of the orthogonal array is call an “experiment” which represents a set of experimental setupusing the designated levels of the control factors. For example, in theL4 array in Table 1, each of the4 rows represents one experiment.

(ii) In each experiment, there are “readings”—typically two readings if two compound noise levels areused, as in the case of the example here withN1 andN2.

(iii) Note that the largest S/N ratio is always chosen for optimal design levels regardless of the criterionused. This applies to both positive and negative S/N ratios.

(iv) For other orthogonal arrays, the number of experimentswill change and the combination of the levelsof the control factors will also change. For example, aL9 array has 9 experiments and each controlfactor has 3 levels. Yet, the methodology of finding the S/N ratios and the response table/chart remainsthe same.

3

FORGING AND THE LOAD-STROKE CURVE

MEC325/580, Spring 2010 I. Kao

Forging Problem: In an impression-die forging operation on a moderately complex part with flash madefrom a cylindrical workpiece in a cold upset forging, the height changes fromh0 = 6mm to h

f= 1.5mm

(with diameter changing fromD0 = 12mm to Df

= 24mm). Use a value ofKf

= 7.0 as the forgingshape factor. The material is low carbon steel, annealed with flow curve parameters:K = 530MPa andn = 0.26.

1. Determine the force required to start the plastic deformation; that is, stress beyond the linear elasticregion (assumeǫ = 0.2%).

2. Determine the instantaneous force required for the following heights:

h = 5.75, 5.5, 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.5 mm

3. Based on the results in Part (2), plot the load-stroke curve. What is your conclusion about such curve?

Solution : The force required for the forging process is

F = KfY

fA = K

f(K ǫn)A (1)

whereǫ = ln(

h0

h

)

, Kf

is the shape factor (Kf

= 7.0, given),A is the area. The workpiece has a volume of

V =π

4(12)2 × 6 = 678.58mm3

1. At the starting of yielding (assumeǫ = 0.002 = 0.2%), the flow stress is

Yf

= K ǫn = 530(0.002)0.26 = 105.3MPa (2)

We have from equation (1) the force require for the forging operation

F = KfY

fA = (7.0)(105.3 × 106) ·

π

4(12 × 10−3)2 = 83, 573N (3)

The force required is83.57 kN .

2. At h = 5.75mm the stroke is(h0 − h) = 6 − 5.75 = 0.25mm. The force is

F = (7.0)

[

530

(

ln6

5.75

)

0.26]

(

678.58

5.75

)

= 192, 686N (4)

Repeat the calculation forh = 5.5, 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.5 mm, we can tabulate the resultsin the following.

1

height,h Diameter,D area,A true strain,ǫ Flow stress,Yf

Force,F stroke,h0 − h

(mm) (mm) (mm2) (MPa) (N ) (mm)

6 12.00 113.10 0 0 0 05.988 12.01 113.32 0.00200 105.355 83575 0.0125.75 12.26 118.01 0.04256 233.247 192686 0.255.5 12.53 123.38 0.08701 280.909 242608 0.5

5 13.15 135.72 0.18232 340.482 323464 14.5 13.86 150.80 0.28768 383.348 404653 1.5

4 14.70 169.65 0.40547 419.125 497720 23.5 15.71 193.88 0.53900 451.324 612522 2.5

3 16.97 226.19 0.69315 481.826 762906 32.5 18.59 271.43 0.87547 511.986 972792 3.5

2 20.78 339.29 1.09861 543.120 1289933 41.5 24.00 452.39 1.38629 576.977 1827127 4.5

The results of the force-stroke curve are plotted in Figure 1.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 1 2 3 4 5stroke (h0-h), in mm

load

, in

kN

Figure 1: The load-stroke curve of a impression-die forgingprocess.

2

EXTRUSION AND ANALYSIS OF PRESSUREDURING PROCESS

MEC325/580, Spring 2010 I. Kao

Extrusion Problem: In an direct extrusion process, pressure needs to be appliedto extrude a billet of lengthL0 = 75mm and diameterD0 = 25mm with an extrusion ratio ofrx = 4.0. The die angle isα = 90.The billet material has the following parameters for the plastic flow stress equation:K = 415MPa andn = 0.18. Use the Johnson’s formula witha = 0.8 andb = 1.5.

1. Determine the ram pressures needed for the extrusion process at the following lengths:

L = 75, 50, 25, 0mm

2. Based on the results in Part (1), plot the pressure-strokecurve. What is your conclusion about suchcurve?

Solution : Use the Johnson’s formula with

p = Yf

ǫx (1)

whereǫx = a + b ln rx, with a = 0.8 andb = 1.5. Thus,

ǫ = ln rx = ln 4.0 = 1.3893

ǫx = 0.8 + 1.5(ln rx) = 2.8795

Yf

=415(1.3863)0.18

(1 + 0.18)= 373MPa

1. Use the die angle ofα = 90, the billet material is to be forced through the die opening almostimmediately. The ram pressures are calculated in the following at the respective lengths.

At L = 75mm the ram pressure is

p = 373

[

2.8795 +2(75)

25

]

= 3312MPa (2)

where the additional pressure due to friction was added in the term2(75)/25.

Repeat the calculation forL = 50, 25, 0mm, we find

p = 373

[

2.8795 +2(50)

25

]

= 2566MPa

p = 373

[

2.8795 +2(25)

25

]

= 1820MPa

p = 373

[

2.8795 +2(0)

25

]

= 1074MPa

2. The ram stroke is(L0 − L). The pressure-stroke curve is plotted in Figure 1.

It is noted that the pressure required for the indirect extrusion is constant, as shown in Figure 1, and itis equal to the pressure of the direct extrusion at the end when L = 0mm.

1

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

3000

Ram stroke (mm)

Ram

pre

ssur

e (M

Pa)

Direct extrusion in solid line; Indirect in dashed line

Figure 1: The pressure-stroke curves of direct and indirectextrusion processes are in solid and dashed lines,respectively.

2

WIRE DRAWING PROCESS ANDANALYSIS

MEC325/580, Spring 2010 I. Kao

Extrusion Problem: In a wire drawing process to reduce the diameter of a plain carbon steel wire fromD0 = 220µm to D

f= 175µm in a cold working process, the angle of the die isα = 15 and the

coefficient of friction isµ = 0.1. The plastic strength of the material isK = 500MPa with a strainhardening exponent ofn = 0.25. The tensile strength of the steel wire isSut = 390MPa.

1. Determine if the process is feasible?

2. If the drawing process is feasible, what is the force required for the wire drawing process?

3. Determine the safety margin of the drawing force versus the rupture force of the wire. Is this wiredrawing process safe?

Solution : First, we need to determine if the drawing process is feasible, based on the parameters given.

1. The maximum reduction per pass is

A0

Af

= e = 2.71828 =⇒ rmax = 63.2% (1)

Here, the reduction isr =A0−Af

A0=

D2

0−D

2

f

D2

0

= 36.7%. Thus, the drawing process is feasible.

2. The drawing force is

F = Af

Yf

(

1 +µ

tan α

)

φ lnA0

Af

=π

4

(

175 × 10−6)2

× 3.29 × 108(

1 +0.1

tan 5

)

(0.9719)(0.4577)

= 7.54N

whereǫ = ln A0

Af

= 0.4577, Yf

= 500×106(0.4577)0.25

(1+0.25) = 329MPa, D =D0+Df

2 = 197.5µm,

Lc =(D0−Df )

2 sinα= 258µm, andφ = 0.88 + 0.12 D

Lc= 0.9719.

3. The force to rupture, depending on the tensile strength, is

Fr = Af· Sut =

π

4D2

f· Sut =

π

4(175 × 10−6)(390 × 106) = 9.38N (2)

Thus, the safety margin is

ns =Fr − F

Fr

=9.38 − 7.54

9.38= 20% (3)

MEC325/580: Food/Soda Cans Manufacturing

Facts and Manufacturing Processes

Imin Kao, Professor Dept. of Mechanical Engineering

College of Engineering and App. Sci. SUNY at Stony Brook

Prof. Imin Kao

Do You Know?

•  Formaldehyde is added to many food cans •  The formaldehyde flavor legacy in can-

making •  You should NEVER cook food with the can •  A single can-tooling machine spits out 400

cans per minute •  250 millions cans per day are consumed

(one can per person per day)

Prof. Imin Kao

Why Using Formaldehyde in Can?

•  To kill bacteria! –  Steel cans in 1940s use an emulsion (95% water

and 5% oil) for lubrication in mfg process –  Certain bacteria eats oil in the emulsion, so the

biocide is added –  Amount is not enough to cause health hazard, but

enough to taste –  This results in the famous preservative flavor (e.g.,

in Budweiser)

Prof. Imin Kao

Formaldehyde Flavor Legacy

•  Why not use biocides without flavor? –  Yes, mfg’ers do that in recent years (e.g., Miller

Genuine Draft and other similar brews)

•  Almost every new emulsion formula had to be made to taste like formaldehyde or else people aren’t going to accept it.

•  Are there any other things/additives in your food or beer/soda cans?

Prof. Imin Kao

Polymer in Your Food Can

•  Polymer (in solvent) is spray-coated inside to serve two functions: –  Plasters any microscopic debris (resulting from mfg proc) to

the can wall and away from the food –  Keeps the food from interacting with can material (e.g.,

tomato acid to corrode the can)

•  Don’t cook the food in the can when you go camping! –  Or else you will be eating polymer (since they degrade when

heated) –  Typical consequence of such a culinary blunder: headaches

and constipation

Prof. Imin Kao

Soda Can Manufacturing

•  Soda can manufacturers are competing with low-priced plastic and glass bottles

•  A single can-tooling machine can spit 400 cans a minute (i.e. 7 cans per second!!)

•  For one can per a person per day –  Need 250 million cans per day

•  Employ the “Deep Drawing” process

Prof. Imin Kao

Manufacture of Aluminum Can Starting Material:

Canstock from a roll

Cupper

Bodymaker (inkl.domer and trimmer)

Washer Printer Printerdrier oven

Insidecoating

Inside coatingdrier oven

Shipment ofcan to filler

Flanger

Necker

Prof. Imin Kao

Manufacturing Process (I)

Source: J. E. Wang, Texas A&M University

Prof. Imin Kao

Manufacturing Process (II)

Source: J. E. Wang, Texas A&M University

Prof. Imin Kao

Finished Product of Can

Source: J. E. Wang, Texas A&M University

Prof. Imin Kao

Can Top: material and design

Source: J. E. Wang, Texas A&M University

Prof. Imin Kao

Video Clip (source: Discovery Channel)

Prof. Imin Kao

Process & Materials

•  Cost of mfg: $40 per 1,000 cans (4 cent @) •  Major cost is on the lid of the can

–  Body made of AA3004 aluminum (Al 97.8%; Mg 1.0%) with a yield strength 170 MPa and tensile strength 215 Mpa.

–  Lid made of a stronger aluminum alloy of AA5182 (Al 95.2%; Mg 4.5%) with a yield strength 395 MPa and tensile strength 420 Mpa.

•  The necking at the lid: to reduce cost of material

Prof. Imin Kao

What Are You Paying?

•  A typical breakdown of what you are paying in a can of soda: –  4 cents for making the can (major cost:

magnesium aluminum alloy with higher ductility) –  10 cents (or more) goes for advertising –  Less than 1 cent for the 12 ounces of beverage!

•  That’s why the no-name brand soda sells for much less in stores!

Prof. Imin Kao

Summary

•  Formaldehyde smell in food and beer cans •  Do not cook food with the can when go

camping •  Addition of polymer inside the can to

protect the can/food, and to enclose mfg remains

•  How much are you paying in a can of soda

Chapter 20

Sheet Metalworking

Part V: Metal Forming and Sheet Metal Working

Groover “Manufacturing Processes”

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

SHEET METALWORKING

!  Three Basic Processes 1.  Cutting Operations 2.  Bending Operations 3.  Drawing

!  Other Sheet Metal Forming Operations 1.  Dies and Presses for Sheet Metal Processes 2.  Sheet Metal Operations Not Performed on Presses 3.  Bending of Tube Stock

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Sheet Metalworking Defined

Cutting and forming operations performed on relatively thin sheets of metal

!  Thickness of sheet metal = 0.4 mm (1/64 in) to 6 mm (1/4 in)

!  Thickness of plate stock > 6 mm !  Operations usually performed as cold working

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Sheet and Plate Metal Products

!  Sheet and plate metal parts for consumer and industrial products such as !  Automobiles and trucks !  Airplanes !  Railway cars and locomotives !  Farm and construction equipment !  Small and large appliances !  Office furniture !  Computers and office equipment

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Sheet Metalworking Terminology

!  Punch and die – tooling to perform cutting, bending, and drawing

!  Stamping press – machine tool that performs most sheet metal operations

!  Stampings – sheet metal products

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Three Basic Types of Sheet Metal Processes

1.  Cutting !  Shearing to separate large sheets !  Blanking to cut part perimeters out of sheet metal !  Punching to make holes in sheet metal

2.  Bending !  Straining sheet around a straight axis

3.  Drawing !  Forming of sheet into convex or concave shapes

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

(1) Just before punch contacts work; (2) punch pushes into work, causing plastic deformation; (3) punch penetrates into work causing a smooth cut surface; and (4) fracture is initiated at opposing cutting edges to separate the sheet

Sheet Metal Cutting

Characteristics of Sheared Edge

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Blanking and Punching

!  Blanking (a) - sheet metal cutting to separate piece (called a blank) from surrounding stock

!  Punching (b) - similar to blanking except cut piece is scrap, called a slug

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Clearance in Sheet Metal Cutting

Distance between punch cutting edge and die cutting edge

!  Typical values range between 4% and 8% of stock thickness !  If too small, fracture lines pass each other,

causing double burnishing and larger force !  If too large, metal is pinched between cutting

edges and excessive burr results

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Clearance in Sheet Metal Cutting

!  Recommended clearance is calculated by: c = at where c = clearance; a = allowance; and t = stock thickness

!  Allowance a is determined according to type of metal

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Sheet Metal Groups Allowances

Metal group a 1100S and 5052S aluminum alloys, all tempers

0.045

2024ST and 6061ST aluminum alloys; brass, soft cold rolled steel, soft stainless steel

0.060

Cold rolled steel, half hard; stainless steel, half hard and full hard

0.075

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Punch and Die Sizes

!  For a round blank of diameter Db: !  Blanking punch diameter = Db 2c !  Blanking die diameter = Db where c = clearance

!  For a round hole of diameter Dh: !  Hole punch diameter = Dh !  Hole die diameter = Dh + 2c where c = clearance

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

!  Die size determines blank size Db

!  Punch size determines hole size Dh

!  c = clearance

Punch and Die Sizes

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

!  Purpose: allows slug or blank to drop through die !  Typical values: 0.25° to 1.5° on each side

Angular Clearance

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Cutting Forces

!  Important for determining press size (tonnage) F = S t L = (0.7) Sut t L

where S = shear strength of metal; Sut = ultimate tensile strength of metal; t = stock thickness, and L = length of cut edge

Example of Cutting

Problem: A sheet metal under cutting process has the following parameters: hole=1”-dia; thickness=!”; Sut=140,000 psi. Estimate the force required for cutting.

!  Solution: Fmax= (0.7)(140,000)(!) (" "1) = 38,500 lb = 19.25 tons = 170,000 Newtons

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

(a) Straining of sheet metal around a straight axis to take a permanent bend

(b) Metal on inside of neutral plane is compressed, while metal on outside of neutral plane is stretched

Sheet Metal Bending

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Types of Sheet Metal Bending

!  V bending - performed with a V shaped die !  Edge bending - performed with a wiping die

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

(1) Before bending (2) After bending !  Application notes:

!  Low production !  Performed on a

press brake !  V-dies are simple

and inexpensive

V-Bending

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

(1) Before bending (2) After bending !  Application notes:

!  High production !  Pressure pad

required !  Dies are more

complicated and costly

Edge Bending

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Stretching during Bending

!  If bend radius is small relative to stock thickness, metal tends to stretch during bending

!  Important to estimate amount of stretching, so final part length = specified dimension

!  Problem: to determine the length of neutral axis of the part before bending

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Bend Allowance Formula

where Ab = bend allowance; ! = bend angle; R= bend radius; t = stock thickness; and Kba is factor to estimate stretching

!  If R < 2t, Kba = 0.33 !  If R ! 2t, Kba = 0.50

Handout & Example

!  (See Handout) !  Equations and example to calculate

!  the Bend Allowance !  the Bending Force !  the Springback

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Drawing

Sheet metal forming to make cup shaped, box shaped, or other complex curved, hollow shaped parts

!  Sheet metal blank is positioned over die cavity and then punch pushes metal into opening

!  Products: beverage cans, ammunition shells, automobile body panels

!  Also known as deep drawing (to distinguish it from wire and bar drawing)

Deep Drawing of a Soda Can

!  (See the Soda Can Manufacture PPT)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Shapes other than Cylindrical Cups

!  Each of the following shapes presents its own unique technical problems in drawing !  Square or rectangular boxes (as in sinks) !  Stepped cups !  Cones !  Cups with spherical rather than flat bases !  Irregular curved forms (as in automobile body

panels)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Other Sheet Metal Forming on Presses

!  Other sheet metal forming operations performed on conventional presses can be classified as !  Operations performed with metal tooling !  Operations performed with flexible rubber tooling

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Ironing

!  Achieves thinning and elongation of wall in a drawn cup: (1) start of process; (2) during process

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

!  Creates indentations in sheet, such as raised (or indented) lettering or strengthening ribs

!  (a) Punch and die configuration during pressing; (b) finished part with embossed ribs

Embossing

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

(1) before and (2) after

Guerin Process

Tools for the Sheet Metalworking Processes

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

!  Components of a punch and die for a blanking operation

Punch and Die Components

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

!  Components of a typical mechanical drive stamping press

Stamping Press

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Gap Frame Press

!  Gap frame press for sheet metalworking (photo courtesy of E. W. Bliss Co.)

!  Capacity = 1350 kN (150 tons)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Press Brake

!  Press brake (photo courtesy of Niagara Machine & Tool Works)

!  Bed width = 9.15 m (30 ft)

!  Capacity = 11,200 kN (1250 tons)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

CNC Turret Press

!  Computer numerical control turret press (photo courtesy of Strippet, Inc.)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

CNC Turret Press Parts

!  Sheet metal parts produced on a turret press, showing variety of hole shapes possible (photo courtesy of Strippet Inc.)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Straight-Sided Frame Press

!  Straight sided frame press (photo courtesy of Greenerd Press & Machine Company, Inc.)

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Power and Drive Systems

!  Hydraulic presses - use a large piston and cylinder to drive the ram !  Longer ram stroke than mechanical types !  Suited to deep drawing !  Slower than mechanical drives

!  Mechanical presses – convert rotation of motor to linear motion of ram !  High forces at bottom of stroke !  Suited to blanking and punching

©2010 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 4/e

Operations Not Performed on Presses

!  Stretch forming !  Roll bending and forming !  Spinning !  High energy rate forming processes

ME325/580 HANDOUT: SHEET-METAL BENDING

MEC325/580, Spring 2010 I. Kao

Sheet-Metal Bending: This handout concerns the sheet metal bending process and analysis. [The materialis from “Fundamentals of Modern Manufacturing: materials, processes, and systems” by M. P. Groover,Wiley, 2002; and other sources]

Bend Allowance: If the bend radius is small relative to stock thickness, the metal tends to stretch duringbending. It is important to be able to estimate the amount of stretching that occurs, if any, so that the finalpart length will match the specified dimension. The problem is to determine the length of the neutral axisbefore bending to account for stretching of the final bent section. This length is called the bend allowance,and it can be estimated as follows: (1)

where

= bend allowance (in or mm),! #" $ is the bend angle (in degrees), is the bend

radius (in or mm), is the stock thickness (in or mm), as shown in Figure 1(a), and % is a factor to estimatestretching. Note the term

'&($) *,+ is the bend angle in radians. The following design values are recommendedfor - . - 0/2131

if 54768- 0/29 if 5:768 (2)

This only applies when the bend radius is small relative to sheet thickness. An illustration is shown inFigure 1.

F

punch

AiRi

die

Rf

Af

(a) During punch (b) After punch: springback

t

Figure 1: Illustration of sheet-metal bending V-die. The included angle of the part is , which is the same

as that of the V-die, and becomes;

after the springback.

Bending Force: The force required to perform bending depends on the geometry of the punch and die andthe strength, thickness, and width of the sheet metal. The maximum bending force can be estimated by thefollowing equation, based on bending of a simple beam

<= ;?>A@3B DCE (3)

where<

is the bending force (in lb or N),>@

is the tensile strength of the sheet metal (in psi or MPs),B

isthe width of part in the direction of the bend axis (in or mm), is the stock thickness (in or mm), and

Eis

1

the die opening dimension as defined in Figure 2. The constant ! ; accounts for differences encountered inan actual bending process. Its value depends on type of bending, as defined in the following. - ; /2131

for "

- ; 0/29 for

(4)

die

punch

D

V-diewiping die

D

Figure 2: Illustration of die opening dimensions for V-bending and edge bending.

Example: A sheet-metal blank is to be bent as shown in Figure 3. The metal has a modulus of elasticity5 1 , yield strength ,33

, and tensile strength>@ ! 9,33

.

1.500

t=0.125 R=0.187120 o

1.000

w=1.750

Figure 3: Example of sheet-metal bending

1. Determine the starting blank size, and

2. Calculate the bending force if a V-die will be used with a die opening dimensionE / "$#

.

Solution: Refer to the dimensions in Figure 3.

1. The starting blank has a width ofB /&% 9'(#

. Its length is equal to /29 / 3

. For anincluded angle

6 , as shown, the bend angle is)

. The value of - in equation (2) is0.33 since 54768 . The bend allowance is obtained from equation (1) 0/ *% 0/2131+ 0/ 6 9 0/ 6 1,-(#Thus, the required length of the blank is

. 6 /29 3 0/ 6 1, 6 /&% 1,-(# /2. The required bending force is obtained from equation (3) using ! ; /2131

in equation (4) for V-die.Thus, < /2131 /&% 9 9,33 0/ 6 9 C / 6 1 -0/21 (5)

2

Springback: When the bending pressure is removed at the end of the deformation operation, elastic energyremains in the bent part, causing it to recover partially towards its original shape. This elastic recovery iscalled springback, as shown in Figure 1, defined as the increase in the included angle of the bent part relativeto the included angle of the forming tool after the tool is removed. That is,

> = #; " (6)

where>

is the springback, is the included angle of the bending die tool, and

;is the included angle

of the sheet-metal part after it is removed from the bending die, as shown in Figure 1.

Analysis of Spring Back in Bending of Sheet-Metal: The following empirical equation defines the amountof springback in a bending operation on a sheet metal with the geometry shown in Figure 4.

; " 1 (7)

where and ;are the bend radii before and after the spring back, is the yield strength,

is the Young’s

modulus, and is the thickness of the sheet metal.

t

Ri

Rf

θi

Ai

Figure 4: Springesback during the bending process of a sheet metal of thickness The springback defined in equation (6) is based on the included angle before and after the springback. It isuseful, however, to use the radii of curvature ( and ;

in Figure 4) to represent the amount of springback.To this end, we assume that the arc length of the curved bend is the same before and after springback, asshown in Figure 4; that is,

; ; 8; 8; ; (8)

Since " and

#; " ;, we can write

#; " ; " ; ; (9)

Since ; and 4 , the springback is

> #; " " ; " (10)

3

Equation (10) depends on the ratio of , which can be substituted by equation (7), and the included angleof the bending die tool

.In a design problem with synthesis, the radius of curvature of the bending die angle, , often needs to bedesigned in order to render the final radius at the desired value after springback. In this case, equation (7)needs to be solved using an equation solver (root finder) or by iteration.

Example: In a bending operation of a 1010 cold-drawn steel sheet metal of thickness () , with a yieldstrength of

9,33and the Young’s modulus of

1 , the radius of curvature of the bending die

tool is 6 .

1. When the bending operation on the die tool is finished, what will be the final radius of the bend basedon equation (7), as the sheet metal is removed from the die tool?

2. What is the springback as a function of the included angle of the bending die tool ? Plot the

springback as a function of the angle .

Solution: Several equations in this section are employed to solve this problem.

1. Applying equation (7), we find

6 ; 6 9,33 1 " 1 6 9,33 1 0/ , 6 0Solve for ; 6 / 939 .

2. Employing equation (10), we have

> " 0/ , 6 0 " If

& C , the springback is> 0/ % 6 % / 6 . If

& , the springback is> 0/ 6

6 / . The springback as a function of the bending die angle (included angle, ) is plotted in Figure 5.

4

40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25

include angle in degrees, Ai

spin

gbac

k

Figure 5: Plot of springback as a function of the included angle

5

MEC325/580 HANDOUT: VOLUMETRIC CHANGES AND

DEFECTS INMETAL CASTING

Spring 2010 I. Kao

The following lecturing materials are adapted from the textbook [1].

Shrinkage in metal casting: Metals shrink or contract during solidification and coolingprocesses. Shrink-age, which causes dimensional changes in casting, is the result of the following three factors:

1. Contraction of the molten metal as it cools prior to solidification;

2. Contraction of the metal during phase change from liquid to solid (latent heat of fusion); and

3. Contraction of the solidified metal (the casting) as its temperature drops to ambient temperature.

The largest amount of shrinkage occurs during the cooling ofthe casting in factor 2 above. In thefollowing table, the percentages of contraction for several metals during solidification are listed. Note,however, some metals expand during cooling, including graycast iron.

Table 1: Volumetric contraction or expansion percentage for various metals in casting during solidification

metal volumetric contractionAluminum 7.1%Zinc 6.5%Al, 4.5% Cu 6.3%Gold 5.5%White iron 4–5.5%Copper 4.9%Brass (70-30%) 4.5%Magnesium 4.2%90% Cu, 10% Al 4%Carbon steels 2.5–4%Al, 12% Si 3.8%Lead 3.2%

metal volumetricexpansionBismuth 3.3%Silicon 2.9%Gray cast iron 2.5%

Defects in Casting: Defects are important in casting. Different names have beenused to associate the sameor similar defects. As a result, theInternational Committee of Foundry Technical Associations has developedstandardized nomenclature, consisting of seven basic categories of casting defects, as follows.

1. Metallic projections: This category consists of fins, flash, or massive projectionssuch as swells andrough surfaces.

1

2. Cavities: This category consists of rounded or rough internal or exposed cavities, including blow-holes, pinholes, and shrinkage cavities.

3. Discontinuities: Examples are such as cracks, cold or hot tearing, and cold shuts. If the solidifyingmetal is constrained from shrinking freely, cracking and tearing can occur. Although many factorsare involved in tearing, coarse grain size and the presence of low-melting segregates along the grainboundaries (intergranular) increase the tendency for hot tearing. Incomplete castings result from themolten metal being at too low a temperature or from the metal being poured too slowly. Cold shut isan interface in a casting that lacks complete fusion becauseof the meeting of two streams of partiallysolidified metal.

4. Defective surface: This includes defects such as surface folds, laps, scars, adhering sand layers (insand casting), and oxide scale.

5. Incomplete casting: This category includes defects such as misruns (due to premature solidification),insufficient volume of metal poured, and runout (due to loss of metal from the mold after pouring).

6. Incorrect dimension or shape: Such defects are owing to factors such as improper shrinkageal-lowance, pattern-mounting error, irregular contraction,deformed pattern, or warped casting.

7. Inclusions: Inclusions usually form during melting, solidification, and molding. Generally nonmetal-lic, they are regarded as harmful because they act like stress raisers and reduce the strength of thecasting. Hard inclusions (spots) also tend to chip or break tools in machining. They can be filteredout during processing of the molten metal with the environment (usually with oxygen) or the cruciblematerial. Chemical reactions among components in the molten metal may produce inclusions; slugsand other foreign materials entrapped in the molten metal also become inclusions. Reactions betweenthe metal and the mold material may produce inclusions as well. In addition, spalling of the moldand core surfaces produces inclusions, suggesting the importance of maintaining melt quality andmonitoring the conditions of the molds.

References

[1] S. Kalpakjian and S. R. SchmidManufacturing Processes for Engineering Materials Prentice Hall,fourth ed., 2003

2

MEC325/580 HANDOUT: METAL CASTING AND RISER DESIGN

Spring 2010 I. Kao

An important aspect of design for metal casting using sand mold is the consideration of solidification time,and the inclusion of riser design to elongate the time to solidification in order to reduce defects or otherfailures in the casting process.

The solidification time in metal casting is governed by the following empirical equation called theChvorinov’s rule

TST = Cm

(

V

A

)

n

(1)

whereTST is the total solidification time,Cm is the mold constant,VA

is the volume-to-surface-area ratio,andn is the exponent, usually taken as 2. The mold constant,Cm depends on the particular conditions ofthe cast operation, including mold material, thermal properties of case metal, and pouring temperature. Themold constant can be obtained based on experimental data with the same mold, metal, pouring temperature,... etc, even though the part may be very different. The Chvorinov’s rule suggests that a casting with highervolume-to-surface-area ratio will cool and solidify more slowly than one with a lower ratio.

The riser design can be used to prevent part of the metal cast from prematurely solidified which causescasting defects. Risers by its relative position can beside riser or top riser, or by its configuration can beopen riser or blind riser. The following figure shows a closed mold with a complex mold geometry whichrequires a riser design. Note the different terminology of the parts of the cast and mold, as illustrated inFigure 1.

Figure 1: A closed mold in which the mold geometry is more complex and requires a passageway systemleading into the cavity, with a riser design.

Example: Riser design using the Chvorinov’s rule.A cylindrical riser must be designed for the sand casting mold shown in Figure 1. The passageway leadingto the cavity casting is a steel rectangular plate with dimension of3′′ × 5′′ × 1′′. Previous observations haveindicated that the total solidification time (TST ) for this casting is1.6 min. The cylindrical riser will havea diameter-to-height ratio of 1.0. Determine the dimensions of the riser so that theTST is 2.0 minutes toallow more time for the flow of metal to cavity for a successfulcasting.

Solution: First, we need to determineCm for the casting:

1

The volume isV = 3 × 5 × 1 = 15 in3; the surface area isA = 2(3 × 5 + 3 × 1 + 5 × 1) = 46 in2.GivenTST = 1.6 min, we taken = 2 and apply the Chvorinov’s rule,

1.6 = Cm

(

15

46

)

2

=⇒ Cm = 15.05 min/in2 (2)

Therefore, the mold constant for the riser is alsoCm = 15.05 min/in2.

For the cylindrical riser, the volume isV =πD

2

4h =

πD3

4since D

h= 1 (given); the surface area is

A = πDh + 2

(

πD2

4

)

= 1.5πD2. Thus, the ratio is

V

A=

(1

4)

1.5D =

D

6(3)

Substituting into the Chvorinov’s equation, we have

2.0 = 15.05

(

D

6

)2

=⇒ D = h = 2.187′′ (4)

Therefore, the cylindrical riser with a diamter-to-heightratio of 1.0 should have a diamter ofD = 2.187′′.

Remarks: For the riser and cast, the following comparison can be made.

volume surface area

riser Vr = 8.216 in3 Ar = 22.54 in2

cast Vc = 15 in3 Ac = 46 in2

Based on the table, we haveVr

Vc= 55%. That is, the volume of the cast is increased by 55% due to the

riser if only the rectangular part is concerned. However, the gain in time is 25% that allows the cavity to befilled more completely.

References

[1] M. P. GrooverFundamentals of Modern Manufacturing: materials, processes, and systems Wiley, thirded., 2006

2

1

Metal CastingIntroduction

Manufacturing Processes –– Podcast Series

Imin Kao, ProfessorDept. of Mechanical EngineeringCollege of Engineering and App. Sci.SUNY at Stony Brook

An Introduction of Casting• Process in which molten metal/materials

flows by gravity or other force into a moldwhere it solidifies in the shape of the moldcavity

• Solidification processes can be classifiedaccording to engineering material processed:– Metals– Ceramics, specifically glasses– Polymers and polymer matrix composites (PMCs)

2

Metal Casting

Open mold Closed mold

Two Categories of Casting Processes

1. Expendable mold processes – uses anexpendable mold which must be destroyedto remove casting

– Mold materials: sand, plaster, and similarmaterials, plus binders

2. Permanent mold processes – uses apermanent mold which can be used overand over to produce many castings

– Made of metal (or, less commonly, a ceramicrefractory material

3

Solidification Time• Heat content ∝ volume & heat transfer ∝ surface area• Solidification time depends on size and shape of

casting by relationship known as Chvorinov's Rule

where TST = total solidification time; V = volume ofthe casting; A = surface area of casting; n = exponentwith typical value = 2; and Cm is mold constant.

!

TST = Cm

V

A

"

# $

%

& '

n

Mold Constant in Chvorinov's Rule• Mold constant Cm depends on:

– Mold material– Thermal properties of casting metal– Pouring temperature relative to melting point

• Value of Cm for a given casting operationcan be based on experimental data fromprevious operations carried out using samemold material, metal, and pouringtemperature, even though the shape of thepart may be quite different

4

Chvorinov’s Rule & Cast Design

• A casting with a higher V/A ratio cools andsolidifies more slowly than one with lower ratio– To feed molten metal to main cavity, TST for riser

must greater than TST for main casting

• Since mold constants of riser and casting will beequal, design the riser to have a larger V/A ratioso that the main casting solidifies first– Riser acts as heat & cast reservoir– This minimizes the effects of shrinkage

Furnaces for Casting Processes

Furnaces most commonly used in foundries:• Cupolas• Direct fuel‑fired furnaces• Crucible furnaces• Electric‑arc furnaces• Induction furnaces

5

Metals for Casting• Most commercial castings are made of

alloys rather than pure metals– Alloys are generally easier to cast, and

properties of product are better• Casting alloys can be classified as:

– Ferrous: (1) gray cast iron, (2) nodular iron, (3)white cast iron, (4) malleable iron, and (5) alloycast irons (∼ 1400°C or 2500°F) & (6) steel (1650°C or 3000°F)

– Nonferrous: (1) Aluminum (660°C or 1220°F), (2)Copper Alloys (1083°C or 1981°F), (3) Zinc Alloys(419°C or 786°F), (4) others

Post-Solidification Processes• Trimming• Removing the core• Surface cleaning• Inspection• Repair, if required• Heat treatment

6

Casting Quality• There are numerous opportunities for things to

go wrong in a casting operation, resulting inquality defects in the product

• The defects can be classified as follows:– Common defects to all casting processes: (a)

misrun, (b) cold shut, (c) cold shots, (d) shrinkagecavity, (e) microporosity, (f) hot tearing

– Defects related to sand casting process: (a) sandblow, (b) pinholes, (c) sand wash, (d) scabs, (e)penetration, (f) mold shift, (g) core shift, (h) moldcrack

Misrun: A casting that hassolidified before completelyfilling mold cavity

Cold shot: Two portions ofmetal flow together but thereis a lack of fusion due topremature freezing

Common Casting Defects (a) & (b)

7

Common Casting Defects (c) & (d)Cold shots: Metal splattersduring pouring and solidglobules form and becomeentrapped in casting

Shrinkage cavity: Depression in surfaceor internal void caused by solidificationshrinkage that restricts amount ofmolten metal available in last region tofreeze

Common Casting Defects (e) & (f)Microporosity: network ofsmall voids due to localshrinkage in the dendriticstructure

Hot tearing: hot crackingcaused by unyielding mold incontraction during cooling,with separation of metal cast

1

Expendable-MoldCasting

Manufacturing Processes –– Podcast Series

Imin Kao, ProfessorDept. of Mechanical EngineeringCollege of Engineering and App. Sci.SUNY at Stony Brook

Metal Casting

Open mold Closed mold

2

Riser Design for Casting• Riser is waste metal that is separated from

the casting and can be re-melted to makemore castings

• To minimize waste in the unit operation, itis desirable for the volume of metal in theriser to be a minimum

• Since the geometry of the riser is normallyselected to maximize the V/A ratio (why?),this allows riser volume to be reduced to theminimum possible value

Figure 11.1 (textbook) A large sand casting weighing over680 kg (1500 lb) for an air compressor frame (photocourtesy of Elkhart Foundry).

3

Types of Patterns for Sand CastingFigure 11.3 (textbook) Types of patterns used in

sand casting:(a) solid pattern (b) split pattern(c) match‑plate pattern (d) cope and drag pattern

Sand Casting• Core:

– inserted into the mold cavity prior to pouring– May require supports to hold it in position in the mold cavity

during pouring, called chaplets

• Desirable Mold Properties:– Strength; Permeability; Thermal stability; Collapsibility;

Reusability

• Foundry Sands: Silica (SiO2) or silica mixed withother minerals– Good refractory properties; Small grain size yields better

surface finish on the cast part; Large grain size is morepermeable; Irregular grain shapes strengthen molds due tointerlocking

4

Sand Casting Defects (a) & (b)Sand blow: Balloon‑shapedgas cavity caused by releaseof mold gases during pouring

Pinholes: Formation of manysmall gas cavities at or slightlybelow surface of casting

Sand Casting Defects (c) & (d)Sand wash: irregularity in thesurface resulting from erosionof sand mold during pouring

Scabs: rough area on the surfacedue to encrustations of sand andmetal, due to mold surfaceflaking off during solidification

5

Sand Casting Defects (e) & (f)Penetration: When fluidity of liquidmetal is high, it may penetrate intosand mold or core, causing castingsurface to consist of a mixture ofsand grains and metal

Mold shift: A step in castproduct at parting linecaused by sidewiserelative displacement ofcope and drag

Sand Casting Defects (g) & (h)Core shift: the core beingdisplaced from its intendedposition, usually vertical, causedby buoyancy of the molten metal

Mold crack: a crack developsdue to insufficient mold strengthwith molten seeping into themold to form a ‘fin’

6

Other Expendable Mold Processes

• Shell Molding

• Vacuum Molding• Expanded Polystyrene Process• Investment Casting• Plaster Mold and Ceramic Mold Casting

Investment Casting (Lost Wax Process)A pattern made of wax is coated with a refractory

material to make mold, after which wax is meltedaway prior to pouring molten metal

• “Investment” comes from a less familiardefinition of “invest” – “to cover completely,”which refers to coating of refractory materialaround wax pattern

• It is a precision casting process - capable ofproducing castings of high accuracy and intricatedetail

7

Investment Casting

Figure 11.8 (textbook) Steps in investment casting: (1)wax patterns are produced, (2) several patterns areattached to a sprue to form a pattern tree

Investment Casting (cont.)

Figure 11.8 (textbook) Steps in investment casting: (3) the patterntree is coated with a thin layer of refractory material, (4) the fullmold is formed by covering the coated tree with sufficientrefractory material to make it rigid

8

Investment Casting (cont.)

Figure 11.8 (textbook) Steps in investment casting: (5) the mold is heldin an inverted position and heated to melt the wax and permit it to dripout of the cavity, (6) the mold is preheated to a high temperature, themolten metal is poured, and it solidifies

Investment Casting (cont.)

Figure 11.8 (textbook) Steps in investment casting: (7) the mold isbroken away from the finished casting and the parts are separated fromthe sprue

9

Investment Casting

Figure 11.9 (textbook) A one‑piece compressor stator with108 separate airfoils made by investment casting (photocourtesy of Howmet Corp.).

Metals for Casting• Most commercial castings are made of

alloys rather than pure metals– Alloys are generally easier to cast, and

properties of product are better• Casting alloys can be classified as:

– Ferrous: (1) gray cast iron, (2) nodular iron, (3)white cast iron, (4) malleable iron, and (5) alloycast irons (∼ 1400°C or 2500°F) & (6) steel (1650°C or 3000°F)

– Nonferrous: (1) Aluminum (660°C or 1220°F), (2)Copper Alloys (1083°C or 1981°F), (3) Zinc Alloys(419°C or 786°F), (4) others

10

SME Video Clip

• Next, let’s watch the SMEvideo clip about Castingwhich came with the textbookfor classroom use ONLY…

1

Permanent-MoldCasting

Manufacturing Processes –– Podcast Series

Imin Kao, ProfessorDept. of Mechanical EngineeringCollege of Engineering and App. Sci.SUNY at Stony Brook

Metal Casting

2

Permanent Mold Casting Processes• Economic disadvantage of expendable mold

casting: a new mold is required for everycasting

• In permanent mold casting, the mold is reusedmany times

• The processes include:– Basic permanent mold casting– Die casting– Centrifugal casting

Permanent Mold Casting

3

Permanent Mold Casting

Figure 11.10 (textbook) Steps in permanent mold casting: (2) cores (ifused) are inserted and mold is closed, (3) molten metal is poured intothe mold, where it solidifies.

Advantages and Limitations• Advantages of permanent mold casting:

– Good dimensional control and surface finish– More rapid solidification caused by the cold metal

mold results in a finer grain structure, so castings arestronger

• Limitations:– Generally limited to metals of lower melting point– Simpler part geometries compared to sand casting

because of need to open the mold– High cost of mold

4

Die CastingA permanent mold casting process in which

molten metal is injected into mold cavity underhigh pressure

• Pressure is maintained during solidification,then mold is opened and part is removed

• Molds in this casting operation are called dies;hence the name die casting

• Use of high pressure to force metal into diecavity is what distinguishes this from otherpermanent mold processes

Die Casting Machines• Designed to hold and accurately close two

mold halves and keep them closed whileliquid metal is forced into cavity

• Two main types:1. Hot‑chamber machine: Metal is melted in a

container, and a piston injects liquid metal underhigh pressure into the die

2. Cold‑chamber machine: Molten metal is pouredinto unheated chamber from external meltingcontainer, and a piston injects metal under highpressure into die cavity

5

Hot-Chamber Die Casting

Cold‑Chamber Die Casting

(2)

6

Molds for Die Casting

• Usually made of tool steel, mold steel, ormaraging steel

• Tungsten and molybdenum (good refractoryqualities) used to die cast steel and cast iron

• Ejector pins required to remove part fromdie when it opens

• Lubricants must be sprayed into cavities toprevent sticking

Advantages and Limitations• Advantages of die casting:

– Economical for large production quantities– Good accuracy and surface finish– Thin sections are possible– Rapid cooling provides small grain size and good

strength to casting

• Disadvantages:– Generally limited to metals with low melting points– Part geometry must allow removal from die

7

Metals for Casting• Most commercial castings are made of

alloys rather than pure metals– Alloys are generally easier to cast, and

properties of product are better• Casting alloys can be classified as:

– Ferrous: (1) gray cast iron, (2) nodular iron, (3)white cast iron, (4) malleable iron, and (5) alloycast irons (∼ 1400°C or 2500°F) & (6) steel (1650°C or 3000°F)

– Nonferrous: (1) Aluminum (660°C or 1220°F), (2)Copper Alloys (1083°C or 1981°F), (3) Zinc Alloys(419°C or 786°F), (4) others

SME Video Clip

• Next, let’s watch the SMEvideo clip about Die Castingwhich came with the textbookfor classroom use ONLY…

Manufacturing Automation

Imin Kao Professor Department of Mechanical Engineering SUNY at Stony Brook

Manufacturing Automation •  Manufacturing Automation

– Fixed automation – Flexible automation – Agile automation – …

•  Societal Impacts –  (name impacts …; See the next page)

•  Positioning System & Accuracy –  (See Handout)

Impacts of Automation •  Increased production rate •  Reduction of labor (economic impact on

society) •  Societal impact on labor force •  Technological innovation •  Precision & repeatability in production •  Hostile/hazardous environment •  24-hour operation •  …

Concurrent Engineering •  Concurrent Engineering

– History & perspectives – What is it? – Famous case studies

•  Design for X – Design for assembly – Design for manufacturing/manufacturability – Design for XXX

CE vs. Traditional Prod. Dev. (a) Traditional product development

(b) Product development using Concurrent Engineering

Programmable Automation Systems •  Numerical control (NC) and CNC

– Presented earlier …

•  Industrial robots – History – Kinematics – Robotic programming language (RPL) – Workspace or work envelope

•  Programmable login control (PLC) – Automation on manufacturing floors

Introduction to Robotics •  “Robot” – history and origin

–  1920 by Czech author K. !apek in his play R.U.R. (Rossum’s Universal robots); from Czech word “robota” meaning “worker”

– Webster Dictionary: “An automated apparatus or device that performs functions ordinarily ascribed to humans or operates with what appears to be almost human intelligence”

Robots: Fiction or Reality? •  Ahead of Its Time?

– Star Wars: C3-PO like humanoid? – The six-million dollar man?

•  Today – AIBO pet robot (a dog which can learn) – HONDA’s ASIMO humanoid robot

•  Speed: 2 km/h; hand load: 2~5kg/hand; weight: 130~210 kg; height: 160~182 cm

– Others

Robotics Research Today Robotics Research Today:

1.  Where are we now? 2.  Where is the robotics research heading

to? 3.  Different fields of robotics research

Classification of Robots •  By Coordinate System

1.  Cylindrical coordinate robots 2.  Spherical coordinate robots 3.  Jointed arm (articulated) robots 4.  Cartesian coordinate robots

•  By Mechanism Types 1.  Revolute 2.  Prismatic

Kinematics of a 2-link robot arm •  A 2-link SCARA (Selectively Compliant

Arm for Robotic Assembly) – Kinematics: forward and inverse kinematics –  Joint space and tool (Cartesian) space – Workspace consideration

(see handout: 2-link-robot.pdf )

Workspace of a SCARA Robot

Workspace Synthesis

Robot Programming Language •  Robot Programming Language (RPL)

– High-level macro language to control motions of a robot

•  Examples: – Adept: V++ –  IBM: AML (A manufacturing language) – RobotWorld: RAIL – …

RPL Example PL1:NEW 0; -- PAYLOAD SET TO DEFAULT PL2:NEW 15; -- PAYLOAD SET TO 50% LIN1:NEW 0; -- LINEAR OFF LIN2:NEW 20; -- LINEAR(20)

PT1:NEW PT(-132.95,490.45,0,-27); -- COORDINATE PT2:NEW PT(-161.55,521.20,0,-27); -- POSITIONS PT3:NEW PT(-187.05,553.90,0,-27); -- FOR PT4:NEW PT(-214.95,583.80,0,-27); -- POINTS PT5:NEW PT(-457.50,201.15,0,-27); -- 1 THROUGH 8 PT6:NEW PT(-483.85,236.10,0,-27); PT7:NEW PT(-512.70,264.50,0,-27); PT8:NEW PT(-541.35,297.75,0,-27); HOME:NEW PT(650,0,0,0); -- HOME POSITION

HGT1:NEW 0; HGT2:NEW -90; HGT3:NEW -184.0;

MAIN:SUBR; -- MANUFACTURING SUBROUTINE

FASTSPEED:SUBR; -- DEFAULT SPEEDS & LINEAR OFF

LINEAR(LIN1); PAYLOAD(PL1); END; -- END FASTSPEED SUBROUTINE

SLOWSPEED:SUBR; -- Z DOWN & SLOW SPEED ZMOVE(HGT2); PAYLOAD(PL2); ZMOVE(HGT3); END; -- END SLOWSPEED SUBROUTINE

PICKUP:SUBR; -- GRASP, Z UP & LINEAR ON GRASP; DELAY(1.0); ZMOVE(HGT2); PAYLOAD(PL1); ZMOVE(HGT1); LINEAR(LIN2); END; -- END PICKUP SUBROUTINE

DROPOFF:SUBR; -- RELEASE & Z UP RELEASE; DELAY(1.0); ZMOVE(HGT2); PAYLOAD(PL1); ZMOVE(HGT1); END; -- END DROPOFF SUBROUTINE

RPL Example (cont.) FASTSPEED; -- MOVES FROM POSITION 1 TO 5 PMOVE(PT1); SLOWSPEED; PICKUP; PMOVE(PT5); SLOWSPEED; DROPOFF;

FASTSPEED; -- MOVES FROM POSITION 2 TO 6 PMOVE(PT2); SLOWSPEED; PICKUP; PMOVE(PT6); SLOWSPEED; DROPOFF; …

KINEMATICS AND WORKSPACE OF SERIAL ROBOT ARM

MEC325/580, Spring 2010 I. Kao

This handout explains the kinematics and workspace of a two-link planar serial manipulator, or robot arm.Analysis of a two-link arm, shown in Figure 1, is the most basic kinematic analysis for serial robots. TheIBM 7545 SCARA robot in the lab has a similar kinematics. Here, we will discuss the forward kinematicsand workspace of such robot arm.

P(x, y)

L2

X

Y

θ1

L1

θ2

O

Figure 1: A 2-link planar manip-ulator.

Kinematics: As shown in Figure 1, the Cartesian coordinates of the end-effector point

can be obtained as follows !"

(1) $#&%' ()$#&% !"(2)

Note that the angle*

is measured from the + axis and

is measuredfrom the extension line of the base link

, . With equations (1) and (2),

we can define the Jacobian matrix which relates the infinitesimal dis-placement in the Cartesian space ( -. ) to that in the joint space ( - ) asfollows

/01-.- 32454 076 454 0984:4 0 6 4$:4 0 8; =<?>' $#&%' > 7#&%@ !A > B$#&% !"' !A B !"C (3)

where -. ED - - GFIH is the vector of the Cartesian coordinates, and - JED "K!7FIH is the vectorcontaining the joint coordinates. The Jacobian matrix relates the infinitesimal displacement - (in radians)to the resulting infinitesimal displacement -. in the Cartesian space by the following equation

-. L/B0 - M@N < - - OC P/0Q< - - !RC (4)

An important note is in order here. Note that any time when the angles are involved in direct algebra, suchas that in equation (4) with

/0 - , you have to use angles in “radians” instead of “degrees.”

Example of forward kinematics and Jacobian: Two configurations of the 2-link arm are given atS $ TUWVYXZ![\]Z

andXZ!$XZ^

, with _XO`bac

and LXO`bVc

.

From equations (1) and (2), the coordinates of the end-effector and the Jacobian matrices are:

At A$!ATUWVYX Z [\ Z ed < C < XO`b\]fgYVXO`b\]h]f]h C /0 <?> XO`b\]h]f]h > XO`bi]h]f]hXO`b\]fgYV XO`jXg]gYa CAt A$ATUX Z $X Z ed < C < XO`bfYXX C /0 < X XXO`bfYX XO`bVYX C

Note that the Jacobian matrix for the second configuration is singular. This is because the two-link arm atthat configuration cannot move along

,direction instantaneously. When this happens, we call the robot

being at a singular configuration. In fact, you should be able to prove that the Jacobian matrix is always

1

singular (i.e., the robot is at a singular configuration) whenever the distal link is aligned with the base link,with

! _X.

With infinitesimal angular displacement of - D XO`jX XO`jX FH - (note the angles are in “radi-ans”), the displacement of the end-effector in the Cartesian coordinates for the two configurations can beobtained from equation (4), and are

-. < - - C <9> XO`jX]XhgYf]aXO`jX]Xag[f C c and -. < - - C < XXO`jX iYXC c (5)

respectively. Again, we find that the two-link manipulator can not move in the

-direction instantaneouslyat configuration 2 because - is identically zero.

Workspace: Workspace of a robot (or called the work envelope) represents the space within which the robotcan reach without singularity. The boundary of the workspace represents the singular configuration of therobot. The workspace depends on the angular range of the two angles of the arms,

and!

. The typicalworkspace for a two-link arm is illustrated in Figure 2 by the shaded region.

X

Y

L2L1

θ2

θ1

O

L1

L2

Figure 2: The workspace of a two-link manipulator with link lengths

and

and the range ofX G

[h]ZandX ! hYXZ

.

2

Manufacturing Automation: Programmable Logic Controller

(PLC)

Imin Kao Professor Department of Mechanical Engineering SUNY at Stony Brook

Programmable Logic Controller •  History of PLC

– First introduced in 1970 – Used for automated factory which provide

system reliability, product quality, information flow, reduced costs, efficiency, and flexibility

– Today's PLC are designed using the latest in microprocessor design and electronic circuitry which provides reliable operation in industry applications

Advantages Over Other Devices •  PLC offers many advantages over other

control devices such as relay, electrical timers/counters. Advantages include –  Improved reliability –  Smaller space required –  Easier to maintain –  Reusable –  Reprogrammable if requirements change –  More flexible-performs more functions

Schematic of PLC

I/O CPU &Memory

Basic PLC Block DiagramUser SuppliedField Devices

Programmer

Nomenclature & Example

(See handout)

Ladder Logic Diagram

•  Example of programming PLC using a ladder login diagram

PLC Logic Table: an example Logic States

X1 1 1 0 0

X2 1 0 1 0

C1 1 1 0 1

S1 1 1 0 1

T1 1 1 0 1

S2 1 1 0 1

MEC326/580 HANDOUT: POSITIONING SYSTEMS AND ACCURACY

MEC325/580, Spring 2010 I. Kao

This handout discusses the positioning systems and accuracy [1]. Positioning systems, depending on theircontrol scheme, can be broken into two categories: (i) open-loop positioning systems, and (ii) closed-looppositioning systems. Furthermore, they can also be either linear positioning or rotational positioning. Mostelectromechanical motors are rotary, with some capable of delivering linear motion directly. For closed-looppositioning system, encoders (both rotary and linear) are typically used to provide the positions for feedbackcontrol. In the following, positioning and accuracy of motorized systems are discussed.

Open-Loop Positioning: Stepper motors are typically used for open-loop linear or rotary systems. Forexample, a XY table utilizing two leadscrews in orthogonal directions to index(x, y) position on a planecan be made an open-loop positioning system. The step angle is determined by the stepper motor—usuallycomes in1.8 or 0.9. For example, a0.9 stepper motor has a total of 400 steps per revolution. Thefollowing equation relates the step angle and number of steps of a stepper motor.

α =360

ns

(1)

whereα is the step angle in degrees andns is the total number of steps in one full revolution of the motor.In the previous example, we havens = 400 andα = 0.9.

Note that a open-loop positioning system counts on the motorto rotate without slip. If the motor slipsand misses counts (which can take place when the load is larger than the rated load and the torque generatedcannot consistently move from one step to another), the positioning error will accumulated.

The resolution (or the smallest linear displacement or control resolution) of the leadscrew driven by astepper motor can be determined by the following equation.

r = l p( α

360

)

=l p

ns

(2)

wherel is 1 for single-thread screw, 2 for double-thread screw,· · · etc, andp is the pitch of the leadscrewmeasuring the axial distance between two adjacent threads in the unit ofinch/rev or mm/rev. Equation(2) corresponds to one step of the stepper motor, and thus is the resolution of the linear positioning. Thetotal number of pulses,Np, (one pulse per step) needed for the required linear displacement,x, is

Np =x

r=

xns

l p(3)

The corresponding angle of rotation for the stepper motor is

θ = Np α = 360

x

l p(4)

where the unit ofθ is degree. The total number of revolution is

Rev =x

l p(5)

When continuous motion is required, typically at a constantspeed, the following equation relates therequired linear speed with respect to the rotational speed of the stepper motor.

v =N

60(l p) (6)

1

wherev is the linear speed ininch/sec or mm/sec, andN is the rotational speed of the stepper motor inRPM. Conversely, the constant rotational speed of motor required to keep a constant linear motion is

N = 60v

l p(7)

Closed-Loop Positioning: All closed-loop positioning systems require sensory information for feedbackcontrol. Typical sensory information of angular or linear displacement is provided by optical encoders orpotentiometers. DC servo motors are often used with opticalencoders for the control of angular or linearposition and speed. Sometimes, tachometers are also used toprovide information of angular speed, basedon the fact thatback emf is proportional to the speed of rotation. Equations that describe the motion andanalysis are similar to those in equations (1) to (7).

Example: A 1.8-stepper motor is connected to a leadscrew via a coupler connection for motion control ofa platform mounted and carried by the leadscrew. The single-thread leadscrew has a pitch of5mm. Theplatform is to move a distance of70mm at a top speed of7mm/sec. Answer the following questions.

1. What is the smallest linear displacement that this motionsystem can realize?

2. Determine the total angle of revolution of the stepper motor, as well as the number of pulses, requiredto move the platform over the specified distance.

3. What is the required angular speed of the stepper motor in order to achieve the top speed of the linearmotion?

Solution: Note the leadscrew is single-thread; thus,l = 1 in equations (2) to (7). Since the step angle is1.8, equation (1) gives the total number of steps per a full revolution as

ns =360

1.8= 200 (8)

1. The smallest linear displacement that this motion systemcan realize is the resolution given by equation(2). That is,

r = p

(

1.8

360

)

= 5/200 = 0.025mm = 25µm or r =p

ns

=5

200= 0.025mm (9)

2. To move the entire distance of70mm, the total angle of revolution and number of pulses requiredare

Np =x

r=

70

0.025= 2, 800

θ = Np α = (2800)(1.8) = 5040

= 14 rev.

respectively.

3. The angular speed of the stepper motors is given by equation (7):

N = 60 ×

v

p= 60 ×

7

5= 84RPM (10)

2

Precision in Positioning: Three important measures of precision in positioning are (i) control resolution,(ii) accuracy, and (iii) repeatability.

Control resolution is defined as the distance separating two adjacent control points in the axis of move-ment. The control resolution is determined by the pitch of leadscrew, gear ratio, step angles (in the case ofstepper motor), and the angles between slots in an encoder disk. For a stepper motor system without gearreduction, the control resolution is the same asr given in equation (2). If digital encoders are used in acontrol system, the number of bits also affects the resolution–known as the quantization effect. IfB is thenumber of bits in the storage register (for example, the number of bits in the representation of encoder data,say a 12-bit encoder), then the number of control points intowhich the axis range can be divided is2B .For example, a 12-bit encoder has212 = 4096 control points and 4095 equal divisions. Assuming that thecontrol points are separated equally within the range, we have

s =L

2B− 1

(11)

wheres is the control resolution of the computer control system ininch or mm, andL is the range of axisin inch or mm. Similarly, if the range of consideration is angular displacement with a range of angle ofΘ

(Θ ≤ 360), then the angular control resolution is

sΘ =Θ

2B− 1

(12)

The resulting control resolution of the positioning systemis the maximum of the two values; that is,

CR = Maxr, s (13)

wherer ands are calculated from equations (2) and (11), respectively. In general, it is desirable thats ≤ r.In modern sensor and computer technology, this is typicallythe case.

In an actual environment, many practical factors influence the performance of the control of systems.These factors include the backlash in the leadscrews or ballscrews, backlash in the gearing and transmission,and deflection and elasticity due to loading. If assuming a normal distribution with mean value beingzero, we can define the random nature of accuracy of positioning systems by the 3-σ principle with±3σencompassing 99.7% of the population.

Accuracy is thus defined in a worst-case scenario in which the desired target point lies exactly betweentwo adjacent control points. An illustration in Figure 1 helps to visualize the situation. If the target wascloser to one of the control points, then the control system can be moved to the closer control point and theerror would be smaller. The accuracy of any given axis of a positioning system is the maximum possibleerror that can occur between the desired target point and theactual position taken by the system, using the3σ range,

Accuracy = 0.5CR + 3σ (14)

whereCR is the control resolution given by equation (13), andσ is the standard deviation of the distributionof errors.

Repeatability is defined as the capability of a positioning system to returnto a given control point thathas been previously designated. Therefore, the repeatability is given by

Repeatability = ±3σ (15)

3

axisaccuracy=0.5(CR)+3σ repeatability= 3σ

control resolution= CR

controlpoint

controlpoint

Desired targetpoint

distribution of errors

Figure 1: Terminology for positioning and accuracy

Example: A closed-loop control system is assumed to have random errors which are normally distributed(Gaussian) with a standard deviation ofσ = 0.004mm. The range of the workspace is700mm with 16-bitstorage register. The single-thread ball screw has a pitch of 5mm, with a1.8-stepper motor. Determine (a)control resolution, (b) accuracy, and (c) repeatability ofthe positioning system.

Solution: Apply the equations formulated above. For single-thread ball screw,l = 1.

(a) The deterministic resolution defined in equation (2) andquantization in equation (11) are

r =p

ns

=5

200= 0.025mm

s =L

2B− 1

=700

216− 1

=700

65536 − 1= 0.0107mm

respectively. Sinces < r, the control resolution is

CR = Max0.025, 0.0107 = 0.025mm (16)

(b) The accuracy is given by equation (14),

Accuracy = 0.5(0.025) + 3(0.004) = 0.0245mm (17)

(c) The repeatability is given by equation (15),

Repeatability = ±3(0.004) = ±0.012mm (18)

References

[1] M. P. Groover Fundamentals of Modern Manufacturing: materials, processes, and systems Wiley,second ed., 2002

4

Shop Scheduling with Many Parts

Imin Kao Professor Department of Mechanical Engineering SUNY at Stony Brook

Terminology •  Sequencing:

– The process of defining the order in which jobs are to be run on a machine

•  Scheduling: – The process of adding start and finish time

information to the job order dictated by the sequence

Sequence determines the schedule

Assumptions of Shop Scheduling •  Each job is started on a machine as

soon as the job has finished all predecessor operations and the machine has completed all earlier job in its sequence

•  All jobs are in the shop and ready for processing at time zero (t =0)

•  Flow time = completion time

Definitions •  Scheduling process variables:

– N : the number of jobs to be scheduled – M : the number of machines; each job is

assumed to visit each machine once – Pij : set up and processing time of job i on

machine j (elements in the time matrix)

Objectives ① Minimize average flow time ② Minimize the time required to complete

all jobs (Cmax = makespan)!③ Minimize average tardiness ④ Minimize maximum tardiness ⑤ Minimize the number of tardy jobs

Choice of “objective” depends on tasks and requirements

Permutation Schedule •  Assumptions:

– All machines process jobs in the same order – Nearly the optimal solution for flow shops

•  Given the sequence, scheduling is: ①  At time 0, the first job is started on machine 1 ②  As soon as this operation is completed, the

first job begins on machine 2 & the second job begins on machine 1

③  Repeat 1 & 2 until the last job finishes on machine M

Remarks •  Permutation Scheduling: Need to

consider (N!) total of job sequences, where N is the number of jobs

•  As N grows, (N!) grows even more!! •  The Permutation Scheduling is not

suitable for too many jobs (N < 7~10)

N! = N×(N-1)! … !2!1

Example: Shop Scheduling •  Consider the set of jobs (N=3) and

processing times in the following time matrix. The unit of time is in minutes.

M N

Lathe (m/c 1)

Milling (m/c 2)

Milling (m/c 3)

Job 1 2.0 3.5 1.5 Job 2 4.5 3.0 2.5 Job 3 1.5 1.5 5.0

Example (cont.) •  Process variables:

– N = 3 (number of jobs) – M = 3 (number of machines: lathe, milling,

milling machines) •  Gantt Chart is used to illustrate the

permutation scheduling of each job sequence

•  First example: use the job sequence of 1, 2, 3

Example: Job Seq=1,2,3 M N Lathe (m/c 1) Milling (m/c 2) Milling (m/c 3)

Job 1 2.0 3.5 1.5

Job 2 4.5 3.0 2.5

Job 3 1.5 1.5 5.0

Job Sequence = 1, 2, 3

m/c 1

m/c 2

m/c 3 0 2 4 6 8 10 12 14 16 18 time (minutes)

Job 1 Job 1

Job 1

Job 2 Job 2

Job 3

Job 2

Job 3

Job 3

Makespan = 17 17

Now, you do it … M N Lathe (m/c 1) Milling (m/c 2) Milling (m/c 3)

Job 1 2.0 3.5 1.5

Job 2 4.5 3.0 2.5

Job 3 1.5 1.5 5.0

Job Sequence = 3, 2, 1

m/c 1

m/c 2

m/c 3 0 2 4 6 8 10 12 14 16 18 time (minutes)

Job 3

Job 3

Job 3

Job 2

Job 2 Job 2

Job 1 Job 1

Job 1

Makespan = 14

About the Makespan •  The “makespan” must accommodate: ①  The delay before the machine j can begin

processing ②  The total processing time on the machine j ③  The remaining processing time for the last job

after it leaves the machine j •  Calculate the “theoretical” lower bound

(LB)j based on machine j!

Theoretical Lower Bound (LB) •  A lower bound (LBj) based on machine j is

•  where pij is the (setup+processing) time of job i on machine j, N is the number of jobs, and M is the number of machines. The largest lower bound amongst all (LBj) is the lower bound for reference. That is,

!

LB j =mini

pirr=1

j"1

#$ % &

' ( )

+ piji=1

N

# +mini

pirr= j+1

M

#$ % *

& *

' ( *

) *

!

LBref =max LB1, LB2, ! , LBM

Calculating Theoretical LB

Machine 1 to 3 (j= 1, 2, 3) (LB)1= 0+(2+4.5+1.5)+min(3.5+1.5),(3+2.5),(1.5+5)= 13 (LB)2= min2,4.5,1.5+(3.5+3+1.5)+min1.5,2.5,5= 11 (LB)3= min(2+3.5),(4.5+3),(1.5+1.5)+(1.5+2.5+5)+0= 12

LB = max13,11,12 = 13 minutes

M N Lathe (m/c 1) Milling (m/c 2) Milling (m/c 3)

Job 1 2.0 3.5 1.5

Job 2 4.5 3.0 2.5

Job 3 1.5 1.5 5.0

Remarks •  The theoretical lower bound is 13

minutes. Thus, job sequence 1,2,3, having makespan of 17 minutes, most likely is not optimal/minimum

•  There are a total of 6 (3!=3!2!1=6) permutations of job sequence.

•  The job sequence of 3,1,2 has a makespan of 13.5 minutes ! minimum makespan

Procedures of Permutation Scheduling ① Establish the time matrix based on data/

time of machining, including set-up time ② Determine (LB)1, (LB)2, … , (LB)M for the

M machines ③ Determine the theoretical lower bound

④ Draw the Gantt chart based on permutation scheduling (a total of N! Gantt charts)

Note: there may be zero in the time matrix

!

LBref =max LB1, LB2, ! , LBM

1

ME325/580 Handout: Shop Scheduling with Many Products

Spring 2010 I. Kao Consider the set of jobs and processing times shown in the following table for three jobs on three machines. Generate the schedule assuming jobs are processed in the order of 1, 2, 3. The unit of the time in the following time matrix table is in minutes.

Milling (machine 1) Lathe (machine 2) Milling (machine 3) Job 1 2.0 3.5 1.5 Job 2 4.5 3.0 2.5 Job 3 1.5 1.5 5.0

Solution: The solution of the processing order 1, 2, 3 is summarized in the Gantt chart below. We start by assigning job 1 to machine 1 at time 0. Since p11 =2.0, the operation lasts until 2.0 minutes. Since all jobs must go to machine 1 first, the other machines are idle and the other jobs are queued. At 2.0 minutes, job 1 is loaded onto machine 2 and machine 1 starts on job 2, the second job in the sequence. Machine 2 finishes job 1, p12 =3.5 minutes later (time is now 5.5 min.). Machine 1 is still busy with job 2; thus, while job 1 is begun on machine 3, machine 2 is idle, waiting for job 2. The remainder of the schedule is shown in the figure. Note that the schedule reflects the rule that machine j starts job i when job i is finished on machine (j−1) and all jobs with earlier locations in the schedule have finished with machine j.

Mach 1 Job 1 Job 2 job 3 Mach 2 Job 1 Job 2 job 3 Mach 3 job 1 Job 2 Job 3 0 2 4 6 8 10 12 14 16

A few observations are in order: • Machine utilization probably can be made higher with less idle time via change of job

sequence. • Makespan is 17 minutes for 1, 2, 3 job sequence: machine 1 takes 8 minutes; machine 2

takes 9 minutes; machine 3 takes 11.5 minutes. • Lower bounds of time span can be established for reference of process scheduling efficiency.

2

Improve the efficiency and reduce makespan The makespan must accommodate:

(1) the delay before the machine can begin processing (2) the total processing time on the machine (3) the remaining processing time for the last job after it leaves the machine

Thus, a lower bound (LBj) based on machine j is

LBj = mini

pirr=1

j−1

∑⎧ ⎨ ⎩

⎫ ⎬ ⎭

+ piji=1

N

∑ + mini

pirr= j+1

M

∑⎧ ⎨ ⎩

⎫ ⎬ ⎭

where pij is the (setup+processing) time of job i on machine j, N is the number of jobs, and M is the number of machines. The largest lower bound amongst all (LBj) is the lower bound for reference. That is,

€

LBref =max LB1, LB2, , LBM where the (LBj) terms are obtained from the equation above. This LBref is the lower bound that is used as a reference in your design. In this example, the lower bounds can be calculated as follows. Machines 1 to 3 (j=1, 2, 3):

LB1= 0 + (2.0+4.5+1.5) + min(3.5+1.5), (3.0+2.5), (1.5+5.0) = 0+8+5 = 13 LB2= min2.0, 4.5, 1.5 + (3.5+3.0+1.5) + min1.5, 2.5, 5.0 = 11 LB3= min(2.0+3.5), (4.5+3.0), (1.5+1.5) + 9 + 0 = 12

Therefore, the reference lower bound is LB=13 minutes. Since the makespan for the job order 1, 2, 3 is 17 minutes, we suspect that it can be improved though we may not necessarily be able to reduce the makespan to 13 minute – the lower bound. There are 6 (3!= 3x2x1) permutations of the job order. Employ the same method to the other 5 permutations, we find that the most efficient scheduling is 3, 1, 2 with a makespan of 13.5 minutes. Exercise: Try to follow the above procedure to confirm that the 3, 1, 2 is indeed the most efficient scheduling with a makespan of 13.5 minutes.

HANDOUT ON STATISTICAL PROCESSCONTROL (SPC)

MEC325/580, Spring 2010 I. Kao

1 Statistical Process Control and Methodology

The “statistical process control” (SPC) uses various statistical methods to assess and analyze variations in aprocess. SPC keeps record of production data, histogram, process capability, and control charts. Two controlcharts are most widely used in SPC, which will be discussed inSection 2.

There are two types of variations considered in SPC: (1) random variations and (2) assignable variations.The former is present if the process is in statistical control; the latter indicates departure from statisticalcontrol. The control charts are used to identify when the process has gone out of statistical control, thussignaling that some corrective actions should be taken. A process is out of control if there are significantchanges in eitherprocess mean or process variability.

2 Control Charts of SPC

The use of control charts is a technique in which statistics computed from measured values of a certain processcharacteristics are plotted over time to determine if the process remains in statistical control. The chart consistsof three horizontal lines: a center, a lower control limit (LCL), and a upper control limit (UCL), as shown inFigure 1. The process is said to be out of statistical controlif sample is out of these limits.

Two types of control charts are commonly used in SPC. They arethe x-chart and theR-chart. Thex-chart plots the average measured value of a series of samples, with LCL and UCL bounds corresponding to3σ standard variation; whereas, theR-chart plots the range of each sample, with its corresponding LCL andUCL.

In SPC, samples are taken at every designated time period (e.g., every 15 minutes) and certain number ofmeasurements (or parts) are taken per each sample.The variablem denotes the number of samples, andnis the number of measurements (d1, d2, · · · , dn) per sample, or thesample size that is designated in Table 1.Therefore, for each sample, we can compute

x =

∑

n

i=1di

n(1)

R = maxd1, · · · dn − mind1, · · · dn (2)

The mean values ofx and the range are thus

¯x =

∑

m

j=1xj

m(3)

R =

∑

m

j=1Rj

m(4)

1

Table 1: Constants for thex andR charts. Note that the “Sample size” (n) is the number of measurement pereach sample.

Sample size x-chart R-chartn A2 D3 D4

3 1.023 0 2.5744 0.729 0 2.2825 0.577 0 2.1146 0.483 0 2.0047 0.419 0.076 1.9248 0.373 0.136 1.8649 0.337 0.184 1.816

10 0.308 0.223 1.77711 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.6914 0.24 0.33 1.6715 0.22 0.35 1.6516 0.21 0.36 1.6417 0.20 0.38 1.6218 0.19 0.39 1.6119 0.19 0.40 1.6020 0.18 0.41 1.59

The equations for computing the upper and lower bounds are:

x − chart:

LCL = x − 3σ = ¯x − A2RUCL = x + 3σ = ¯x + A2R

(5)

R − chart:

LCL = D3RUCL = D4R

(6)

where the constants:A2,D3, andD4 are listed in Table 1.Note that Table 1 is listed according to the samplesizen, or preferably called thenumber of measurement, not the number of samplesm.

The procedure for constructing the charts is in the following.

1. Compute the mean (x) out of n measurements, and the range (R) for each of them samples usingequations (1) and (2).

2. Compute the grand meanx, which is the mean of thex values for them samples using equation (3).This will be the center for thex-chart.

3. ComputeR, which is the mean of theR values for them samples using equation (4). This will be thecenter for theR-chart.

4. DetermineUCL andLCL, based on equations (5) and (6) and the constants listed in Table 1.

2

Sample number d1 d2 d3 d4

1 2.46 2.40 2.44 2.462 2.45 2.43 2.47 2.393 2.38 2.48 2.42 2.424 2.42 2.44 2.53 2.495 2.42 2.45 2.43 2.446 2.44 2.45 2.44 2.397 2.39 2.41 2.42 2.468 2.45 2.41 2.43 2.41

Table 2: SPC for 8 samples, each with 4 measurements

2.1 LCL and UCL with known mean and standard deviation

For some processes, the mean and standard deviation of the process may be known. Under such circumstances,the parameters of thex-chart can be obtained as follows:

x = µ (7)

LCL = µ −

3σ√

n(8)

UCL = µ +3σ√

n(9)

whereµ is the process mean,σ is the standard deviation of the process,n is the number of measurement (orsample size), andσ

√

nis the standard deviation of the sample mean.

Equations ofLCL andUCL this section and the previous section have control limits set at 99.73% of thesamples at 3-sigma range.

3 An Example

Samples are collected from an extrusion process that is in statistical process control, and the diameter of theextrudate is measured incm. Eight samples are taken with a time interval of 15 minutes between each samplefor a duration of 2 hours. Four measurements (d1 to d4) are performed in each sample. The quantityx is theaverage of four measurements in each sample, andR is the range of measurements. The measurements aretabulated in Table 2. Answer the following questions.

1. Find the grand average,¯x, and the control limits (LCL andUCL) of thex-chart.

2. Calculate the average ofR, and the control limits (LCL andUCL) of theR-chart.

3. Construct thex-chart andR-chart.

4. Another sample was taken with four measurements as follows: 2.41, 2.50, 2.49, 2.55. Determine ifthe process is out of (statistical) control, based on the previously established control charts.

Solution: We first identify that the number of measurement per each sample (or sample size) isn = 4 with atotal number of 8 sample batches,m = 8. The averagex and the rangeR are calculated and shown in Table 3.

3

x = (∑

di)/4 R

1 2.440 0.062 2.435 0.083 2.425 0.104 2.470 0.115 2.435 0.036 2.430 0.067 2.420 0.078 2.425 0.04

Table 3: The tabulated data forx andR

From Table 3, we find¯x = 2.435 R = 0.06875 (10)

1. From the above results, equations (5) and (6), and Table 1 with 4 measurements per sample (or thesample size), we haven = 4. Thus, we compute:

¯x = 2.435 (11)

LCL = 2.435 − (0.729) × 0.06875 = 2.3849 (12)

UCL = 2.435 + (0.729) × 0.06875 = 2.4851 (13)

Thex-chart is plotted in Figure 1.

2. Similarly, we can compute forR-chart:

R = 0.06875 (14)

LCL = D3R = 0 (15)

UCL = D4R = (2.282) × 0.06875 = 0.1569 (16)

TheR-chart is plotted in Figure 1.

3. See Figure 1.

4. For the next sample with four measurements: 2.41, 2.50, 2.49, 2.55, we find

x =

∑

4

i=1di

4= 2.4875 R = 2.55 − 2.41 = 0.14 (17)

Hence, it is out of control (due to thex-chart).

4 Control Charts for Attributes

In addition to thex-chart andR-chart, two other charts are used for attributes. They are used to monitor thenumber of defects present in sample, or the fraction of defect rate, for example, the number of defects perautomobile, existence or absence of flash in a plastic molding. Two types of charts are used: thep-chart andthec-chart.

4

R-chart

0.000

0.020

0.040

0.060

0.080

0.100

0.120

1 2 3 4 5 6 7 8

0.06875

0.140

0.160

LCL= 0.0

UCL= 0.1569

x-chart

2.390

2.400

2.410

2.420

2.430

2.440

2.450

2.460

2.470

2.480

1 2 3 4 5 6 7 8

2.435

2.380

2.490

UCL= 2.4851

LCL= 2.3849

Figure 1: Thex-chart andR-chart

4.1 The p-chart

Thep-chart plots the fraction defect rate in successive samples. The “p” stands forproportion which is definedas

pi =di

n(18)

for m samples of equal sizen, wheredi is the number of defective items, andn is the number of parts in

sample. The parameters are calculated based on binomial distribution with standard deviationσ =

√

p(1−p)

n.

Form samples of equal sizen, the center and control limits are

p =

∑

m

i=1pi

m(19)

LCL = p − 3

√

p(1 − p)

n(20)

UCL = p + 3

√

p(1 − p)

n(21)

If LCL < 0 then useLCL = 0 in equation (20).

5

4.2 The c-chart

The c-chart plots the number of defects or flaws per sample. Thec stands forcount. The parameters of thec-chart are based on the Poisson distribution. They are

c =

∑

m

i=1ci

m(22)

LCL = c − 3√

c (23)

UCL = c + 3√

c (24)

whereci is the number of imperfections or number of events occurringwithin a defined sample space (e.g.,defects per car). IfLCL < 0 then useLCL = 0 in equation (23).

References

[1] M. P. GrooverFundamentals of Modern Manufacturing: materials, processes, and systems Wiley, seconded., 2002

[2] S. Kalpakjian and S. R. SchmidManufacturing Processes for Engineering Materials Prentice Hall, fourthed., 2003

6

Statistical Process Control (SPC)

Imin Kao Professor Department of Mechanical Engineering SUNY at Stony Brook

What is SPC? •  SPC

–  is based on the 3-! principle –  uses various statistical methods to assess and

analyze variations in a process –  keeps record of production data, histogram,

process capability, and control charts

•  Two Types of Variations Considered 1.  Random variations 2.  Assignable variations

SPC and Control Charts •  Control charts are used to identify when

the process has gone out of statistical control ! require corrective action

•  A process is “out of control”, if there are significant changes in – Process mean, or – Process variability

Control Charts •  Three horizontal lines

– Center – LCL: Lower control limit – UCL: Upper control limit

Control Chart: Types •  Two Types:

– The – The R-chart

!

x " chart

Variables for Control Charts •  SPC takes samples at designated time

interval (e.g., every 15 minutes) •  Variables:

– m: the number of samples –  n: the number of measurement per sample (or

the sample size) – Example: takes samples every 15 minutes for 8

hours, each time with 8 parts in the sample ! m = 32; n = 8

Computing the Parameters The n measurements are denoted as: d1, d2, … dn

Computing LCL and ULC •  The LCL and UCL for the two charts

Constants for the Charts

Note: The tables is based on the “Sample size” (n, or the number of measurement in each sample), not “m”

Procedures ① Compute the mean out of n

measurements, and the range R for each of the m samples

② Compute the grand mean for the m samples ! center of the x-chart

③ Compute the mean of range for the m samples ! center of the R-chart

④ Determine UCL and LCL to complete the charts

Example SPC for 8 samples, each with 4 measurements

Example (cont.)

Control Charts

UCL & LCL with known Std Dev

Control Charts for Attributes •  The p-Chart

The proportion is defined as:

with

Control Charts for Attributes •  The c-Chart