EPT 221

PARAMETRIC DESIGN

Objectives of Lecture

• Describe the parametric design phase.• Describe and apply the steps involve in the

parametric design phase.• Describe and apply methods to evaluate

alternative designs.

Configuration Design

ConfigurationDesign

ConfigurationDesign

Special Purpose Parts: Features Arrangements Relative dimensions Attribute list (variables)Standard Parts: Type Attribute list (variables)

Abstract embodiment Physical principles Material Geometry

Architecture

Information Flow

Systematic Parametric Design

Determine best alternative

Predict Performance Check Feasibility: Functional? Manufacturable ?

Generate Alternatives

Formulate Problem

Analyze Alternatives

Evaluate Alternatives

Re-Design

Re-Specify

Select Design Variables Determine constraints

Select values for Design Variables

all alternatives

feasible alternatives

best alternative

Refine Optimize

refined best alternative

Systematic Steps in Parametric Design

• 5 major steps:Step 1: Formulate the parametric design problem.

— Performance Parameters/ Solution Evaluation Parameter

— Design Variables (DVs)— Problem Definition Parameters (PDPs)— Preliminary Plan for Solving the Problem

Step 2: Generate alternative designs.

Step 3: Analyze/ predict the performance of the alternatives.— Analytical Methods— Experimental Methods

Step 4: Evaluate the performance of each alternative.

Step 5: Refine/ optimize

Example:The design problem:A ½ -hp electric motor, running at 1,800 rpm, will be used to drive a grinding wheel operating at 6,000 rpm. A flat belt-and-pulley drive system configuration has been selected, as shown. The design team has also determined that:

— the drive motor will have a 2 inch-diameter pulley mounted to its ½-inch output shaft,

— candidate designs should be able to utilize the full horsepower available, — the customer desires a compact system design,— the drive pulley will slip first, before the driven pulley,— the purchasing department has located a vendor that can provide a flat belt that

can withstand a maximum 35-pound tensile load,— the coefficient of friction between the belt and pulley is 0.3, — other design engineers in our group will design the mountings, bearings, and

protective equipment, therefore— parametric design efforts should focus on distance between centres and driven-

pulley diameter.

Principal Function:To transform the power of the motor from a high speedto a low speed.

The belt-and-pulley system wouldfail to perform its principal functionif the belt slipped or if the belt brokedue excessive tension

Formulating the parameters:• Determine the type of parameter:

Solution Evaluation Parameters (SEPs) Design Variables (DVs) Problem Definition Parameters (PDPs)

• Identify specifics of each parameter: Name (parameter/ variable) Symbols Units Limits

Solution Evaluation Parameters (SEPs)

Parameter Symbol Units Lower Limit Upper Limit 1 belt torque Tb lb-in Tm - 2 belt tension F1 lbs - 35 3 center distance c in. small -

Related to function

Why belt torque and tension? The tension forces in the belt are limited by the amount of friction between the belton the driver pulley, up to the point of impending slip.So, need to calculate the maximum belt tension F1 to make sure it does not exceed 35 (lbs) limit.Tb is the torque that the motor can supply. Why centre of distance?Because the customer would be more satisfied with a compact design.

Design Variables (DVs)

Design Variable Symbol Units Lower Limit Upper Limit 1 center distance c in. small - 2 driven pulley diameter d1 in. - -

Related to form

Centre distance effects the size of the design.Driven pulley diameter effects the torque and tension.

Problem Definition Parameters (PDPs)

Parameter Symbol Units Lower Limit Upper Limit 1 friction coefficient f none 0.3 0.3 2 belt strength Fmax lbs - 30 3 motor power W hp ½ ½ 4 motor pulley diameter d1 in. 2 2

Values that are known,given

Parameter ValuesSomething extra

Plan for solving the Design Problem• Analyze engineering characteristics:

1. Grinding wheel pulley speed, n2,2. Angle of wrap as a function of the centre distance, c,3. Belt torque, Tb,4. Maximum belt tension, F1,5. Slack-side belt tension, F2, and6. Initial tension (before torque is applied), Fi.

• Check for constraints violation: Belt delivers full motor torque to the grinding-wheel

pulley. Belt tension does not exceed the belt strength limit.

For the belt-and-

pulley example

Generating and Analyzing

• Develop analytical means to predict the behaviour of the systemModel the behaviour of the system using

relations from physics and mathematicsDevelop a system of equations to analyze the

performance of each candidate design (by substituting different values for the design variables)

System of equations for the belt-and-pulley analysis

Objective 1: to compare between Tm, i.e. the maximum torque delivered by the motor with Tb, i.e. the belt torque. If Tb < Tm, the belt will slip.

Objective 2: to find the driven-pulley diameter and the distance between the pulley centres (i.e. to satisfy the compact design customer requirement)

Free-body diagram of motor pulley

• Can use spreadsheet to reduce effort in computing the expected performance of the system.

Spreadsheet for Analysing Belt-Pulley Performance

Why? Because during calculation you will have a variety of design variable values. So, you need to make sure that the values obtained satisfy the requirements of the design (i.e. the principle function and customer requirements).

• Redesigning: finding feasible values• Generating and analyzing are carried out to find feasible

values, i.e. those design variables that satisfy the constraints given.

• But are feasible values the best values?• Trade-offs: one attribute improves as the other

degrades.• Caused by the interdependency of variables (i.e

coupling)

e.g.: as the centre distance increases, the belt tension is reduced and as a result the Factor of safety becomes higher (this is good!)

BUTBy increasing the centre distance, the size of the system increases (this is not good!)

So, which is more important???EVALUATE!!!

Evaluating: Weighted Rating Method

Step 1: Establish a set of evaluation criteria.

Evaluation criteria are often developed from the list of solution evaluation parameters, of from engineering characteristics.

e.g. belt-pulley example2 most important engineering characteristics: belt tension and centre distance Solution evaluation parameters.The team decided to consider belt tension as ‘very important’ weight = 0.6

and centre distance as ‘ important’ weight = 0.4.

Step 2: Rate the feasible designs for each criterion.

• Rating should be done according to customer satisfaction.

• Customer satisfaction curve a means to assess

customer satisfaction.

Customer satisfaction w.r.t belt tension Customer satisfaction

w.r.t centre distance

Step 3: Weight the ratings according to importance.

Multiply the satisfaction rating by the importance weight.

Step 4: Sum the weighted ratings to calculate an overall weighted rating.

Weighted Satisfaction Based on Different Centre Distances c

Satisfaction curve for belt-pulley system

Value of c between 9 and 14. so which is the best?

Systematic Parametric Design

Design for Robustness

• Term used to describe a number of methods aimed at reducing the sensitivity of product performance and variations.

• Variations includes: manufacturing, wear, operating environment

• Alternative design can be generated and analyzed for their sensitivity to variations.

• Two methods used:1. Probabilistic optimal design2. Taguchi method – design of experiments

Computer-Aided Engineering• CAE refers to computer software and hardware systems used in the analysis of engineering

designs to validate functional performance.• 4 main categories:

Dynamic analysis– The kinematics and kinetics of bodies i.e. the motion and the forces and moment that cause motion.– Analyses:

• Positions, velocities, accelerations• Contacts and collisions • Joint forces, shaking forces• Relative motions.

Finite element analysis

– A method that essentially divides a part into smaller discrete elements to analyze the functional performance of a part.

– Analyses: • Stresses and strains throughout a part• Factors of safety• Buckling of parts in compression• Temperature gradients and resulting heat transfer• Fluid pressures and flows• Natural frequencies of vibration• Displacement of nodes

General purpose– Refers to computer applications covering word processing, spreadsheets, mathematics, oral presentations,

and project management.

Other– QFD, DFMA, MATLAB (systems simulation), etc