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Polytechnic University Puerto RicoHato Rey, PR
Department of Mechanical Engineering
Final Project:Design of a Jackscrew
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Abstract
In this group project we were presented with a great job in our hands developing a
screw jack. The first part of the developing we gathered information to know the best
way to start the design with the right tools according to the requirement made by the
professor. Our Jack needed to lift 2tons and have a maximum lift of .8m. The material
use for the jack is steel 1030. We did various test to assure our jack works correctly
and with efficiency, body stresses, even the buckling consideration. An automotive jack
is a device used to raise all or part of a vehicle into the air in order to facilitate repairs.
Any time a jack is used, it's critical that the vehicle be in a stable position on a flat
surface. Be sure that the jack is pushing up against a solid frame member that will
support the weight of the vehicle, or else you will need to repair more than your tire.
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Table of Contents
Abstract ...................................................................................................................... 2
Introduction ................................................................................................................ 4
Theory ........................................................................................................................ 5
Materials and strength ................................................................................. 6
Mechanical Analysis .................................................................................... 7
Tensile Strength ........................................................................................... 8
Types of Screw .......................................................................................... 10
Power Screws ............................................................................................ 10
Bending Stress........................................................................................... 12
Shear Stress .............................................................................................. 12
Tensile /Compressive stresses .................................................................. 12
Combined stresses .................................................................................... 13
B kli t 13
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IntroductionA mechanical jack is a device which lifts heavy equipment. The most common form
is a car jack, floor jack or garage jack which lifts vehicles so that maintenance can be
performed. Car jacks usually use mechanical advantage to allow a human to lift a
vehicle by manual force alone. More powerful jacks use hydraulic power to provide
more lift over greater distances. Mechanical jacks are usually rated for a maximum
lifting capacity.
For this design it is required for the jack to be able to have a lifting capacity of
2Tons and a lifting clearance of .8m.
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Theory
A screw is one of the six simple machines. A simple screw is a helical inclined plane.
A screw can convert a rotational force (torque) to a linear force and vice versa. The ratio
of threading determines the mechanical advantage of the machine. More threading
increases the mechanical advantage. A rough comparison of mechanical advantage
can be done by taking the circumference of the shaft of the screw and divide by the
distance between the thread
A screw is a shaft with a helical groove or thread formed on its surface and provision
at one end to turn the screw. Its main uses are as a threaded fastener used to hold
objects together, and as a simple machine used to translate torque into linear force. It
can also be defined as an inclined plane wrapped around a shaft.
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The same type of screw or bolt can be made in many different grades of
material. For critical high-tensile-strength applications, low-grade bolts may fail,resulting in damage or injury. On SAE-standard bolts, a distinctive pattern of marking is
impressed on the heads to allow inspection and validation of the strength of the bolt.
However, low-cost counterfeit fasteners may be found with actual strength far less than
indicated by the markings. Such inferior fasteners are a danger to life and property
when used in aircraft, automobiles, heavy trucks, and similar critical applications.Gradings are indicated as markings, while grade 0 is the lowest, grade 10 is the
highest. Here is the sequence of bolt strength and markings, from least to most. Grade
0, 1 and 2 bolts have no markings, grade 3 has 2 radial lines, grade 5 has 3, grade 6
has 4, grade 7 has 5, grade 8 has 6, grade 9 has 7, grade 10 has 8.
In some applications joints are designed so that the screw or bolt willintentionally fail before more expensive components. In this case replacing an existing
fastener with a higher strength fastener can result in equipment damage. Thus it is
generally good practice to replace fasteners with the same grade originally installed.
Mechanical Analysis
A screw or bolt is a specialized application of the inclined plane. The inclined
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is very similar to that performed to predict wedge behavior. Wedges are discussed in
the article on simple machines.Critical applications of screws and bolts will specify a torque that must be applied
when driving it. The main concept is to tension the bolt, and compress parts being held
together, creating a spring-like assembly. The stress thus introduced to the bolt is
called a preload. When external forces try to separate the parts, the bolt experiences no
strain unless the preload force is exceeded.As long as the preload is never exceeded, the bolt or nut will never come loose
(assuming the full strength of the bolt is used). If the full strength of the bolt is not
used (for example, a steel bolt threaded into aluminium, then a thread-locking adhesive
or insert may be used.
If the preload is exceeded during normal use, the joint will eventually fail. Thepreload is calculated as a percentage of the bolt's yield tensile strength, or the strength
of the threads it goes into, or the compressive strength of the clamped layers (plates,
washers, gaskets), whichever is least.
Tensile Strength
Screws and bolts are usually in tension when properly fitted. In most applications
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tensile yield strength to tensile ultimate strength. For example, a property class 5.8 bolt
has a nominal (minimum) tensile ultimate strength of 500 MPa, and a tensile yield
strength of 0.8 times tensile ultimate strength or 0.8(500) = 400 MPa.
Tensile ultimate strength is the stress at which the bolt fails (breaks in half).
Tensile yield strength is the stress at which the bolt will receive a permanent set (an
elongation from which it will not recover when the force is removed) of 0.2 % offset
strain. When elongating a fastener prior to reaching the yield point, the fastener is saidto be operating in the elastic region; whereas elongation beyond the yield point is
referred to as operating in the plastic region, since the fastener has suffered permanent
plastic deformation.
Mild steel bolts have property class 4.6. High-strength steel bolts have property
class 8.8 or above. An M10, property class 8.8 bolt can very safely hold a static tensileload of about 15 kN.
There is no simple method to measure the tension of a bolt already in place
other than to tighten it and identify at which point the bolt starts moving. This is known
as 're-torqueing'. An electronic torque wrench is used on the bolt under test, and the
torque applied is constantly measured. When the bolt starts moving (tightening) thetorque briefly drops sharply - this drop-off point is considered the measure of tension.
Recent developments enable bolt tensions to be estimated by using ultrasonic
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torques. Steel nuts are used for only occasional adjustment and limited duty so as to
avoid galling of like materials.
Standard pitches for metric diameters
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Bending Stress
The maximum bending stress occurs at the root of the thread. It is calculated byassuming the thread is a simple cantilever beam built in at the root. The load is
assumed to act at mid point on the thread. The maximumum stress is provided by the
bending moment relationship M/I = /(y) =e/R. that is = M.y/I
The section under bending has a length = .dm.n
The width of the section at the thread root = b. The Moment of Inertia at the root I = .dm.n.b
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The distance from the centroid the the most remote fibre ..y = b/2.
The Bending Moment M = W.h/2
The maximum bending stress is therefore.
Shear Stress
Both the nut and screw threads are subject to traverse shear stress resulting from
the bending forces. For a rectangular section the maximums shear stress occurs at the
neutral axis and equals
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Combined stresses
Based on maximum shear stress theory...
The shear stress caused by torque on the screw =
The value of the combined stress is therefore
This equation always applies when the screw is in tension. When a screw is in
compression and the length is greater than 8 time the root diameter then the buckling
stress has to be considered.
Buckling stress
When the screw is longer than 8 times the root diameter it must be considered a
column. Long columns with are dealt with using the Euler equation. Columns with
slenderness ratios of less than 100 are considered as short columns. The slenderness
ti i th l th (b t t ) / L t di f ti f th ti
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Analysis of ResultsData and Assumption:
Coefficient of Friction:
Safety Factor:
Single thread:
Screw, Crown and Base Material:
Carbon Steel 1030 (C, 0.27% - 0.34%; Fe, 98.67% - 99.13%; Mn, 0.6% - 0.9%; P,
0.04% ; F, 0.05% )
Given Force:
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Using the Bearing System table for Dimensional Series 02, the approximated valueof C is:
Dimensions of the Bearing ( ):
Calculus to find : Part 2: Buckling Analysis
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Part 3: Maximum Diameter (), Minimum Diameter (), Mean Diameter ()y Pitch (
)
According with the Square Thread Table for Metric
(http://en.wikipedia.org/wiki/Square_thread_form)
For a Maximum Diameter of 44mm, the correct pitch is 7mm.
Part 4: Calculus to find the Lead:
Part 5: Thread Dimensions
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Part 7: Calculus to find the Load-Lowering Torque
Part 8: Calculus to confirm the Self-Locking between the power screw and
the crown
According with our design, the power screw has Self-Locking.
Part 8: Efficiency:
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Part 11: The bearing stress B is, with one thread ( ) carrying 0.38F Part 12: The thread-root bending stress b with one thread ( ) carrying0.38F
Part 13: Tri-Axial Analysis and Distortion Energy Theory (von Mises stress)
( ) ( ) ( )
[ ]
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Part 14: Maximum Shear
The Maximum Shear is lower than the Allow Shear, therefore our design accomplish
with the basic fundamentals of mechanical to avoid mechanical failure due to the
chosen material and apply forces
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Mohr Circle Diagram for three-dimensional stress
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Conclusion
By studying the conditions under which the jack will be subjected to we were able to
identify the principle dimensions of the power screw. For a major diameter of 44 mm we
find that the screw will withstand the loads associated with that of a power screw.
Moreover, with a applied load of 2 tons and the allow force equation we find the minor
diameter for the our power screw, the value of this diameter is 35.12 mm. Using the
Square Thread Table for Metric, the maximum diameter is 44 mm and the pitch is 7
mm.
After calculating the dimensions of the power screw and the axial bearing we
calculate the Load-Raising Torque and Load-Lowering Torque, our results is 278.93
Nm and 233.48 Nm, respectively. Assuming a friction coefficient of 0.2 and lead of
7mm our power screw has self-locking. The efficiency of this power screw is 7.83%.
According with assigned load of 2 tons and our minor diameter of 37mm the power
screw jack wont buckle assuming a safety factor of 3. After calculating the Shear and
Axial stress we find the 3 axial stresses and 3 shear stresses for the three-dimensional
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References
Screw Jacks . (n.d.). Engineering ToolBox. Retrieved October 17, 2010, from
http://www.engineeringtoolbox.com/screw-jack-d_1308.html
Budynas, R., & Nisbett, J. K. (2006). Shigley's Mechanical Engineering Design (Mcgraw-Hill
Series in Mechanical Engineering) (8 ed.). New York: McGraw-Hill
Science/Engineering/Math.
Jackscrew - Wikipedia, the free encyclopedia. (n.d.). Wikipedia, the free encyclopedia. Retrieved
October 17, 2010, from http://en.wikipedia.org/wiki/Jackscrew
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Appendix
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All units are in milimeter and de gree
CC
Group #3 - Jac k screw:Assembly Detail
SECTION C-C
SCALE 1 : 3
SCALE 1 : 30
D
DETAIL DSCALE 1 : 1
70
30
45
6215
44
20R
138
28
201
12
20
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Fina l Projec t: Jac k Sc rew
Axia l BearingSHEET 1 OF 1SCALE: 1:2 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
CHEC KED
DRAWN
Group # 3
All units are in m ilimeter a nd de gree
ITEM NO. PART NUMBER QTY.1 inner housing 1
2 ba ll b earing 243 outer housing 1
3
1
19
118
110
2
62
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Group # 3
Fina l Projec t: Jac k Sc rew
All units are in milimet er and de gree
CHEC KED
ba ll bea ringSHEET 1 OF 1SCALE: 4:1 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
DRAWN
12
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Group # 3
Fina l Projec t: Jac k Sc rew
All units are in milimeter and de gree
ENG A PPR.
SCALE: 1:16
CHEC KED
SHEET 1 OF 1baseWEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
DRAWN
819.793
C
C
SECTION C-CSCALE 1 : 4
110
670
30 50.706
120.00
38.119
120.00
120.00
105.750
R
853.822
25
15
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5
396
800
1716.822
2
Group # 3
Fina l Projec t: Jac k Sc rew
1
3
4
All units are in milimeter and de gree
120.00
439.822
R69
ITEM NO. PART NUMBER QTY.1 power sc rew 1
2 lever 13 Axia l Bearing 1
4 base 15 tube 1
ENG A PPR.
CHEC KED
SCALE: 1:25Emsablaje2SHEET 1 OF 1WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
DRAWN
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CC
DETAIL DSCALE 1 : 1
R
15
28
20
30
70
138
45
20
62
441
12
20
SECTION C-C
SCALE 1 : 3
SCALE 1 : 30
D
Group #3 - Jac k screw:Assembly Detail
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Group # 3
Fina l Projec t: Jac k Sc rew
All units are in m ilimeter a nd de gree
ENG A PPR.
CHEC KED
inner housingSHEET 1 OF 1SCALE: 2:3 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
DRAWN
12
110 R1
70
4
4
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Group # 3
Fina l Projec t: Jac k Sc rew
All units are in milimeter and de gree
ITEM NO. PART NUMBER QTY.
1 power sc rew 1
2 lever 13 Axia l Bearing 1
4 base 15 tube 1
CHEC KED
Jack ScrewSHEET 1 OF 1SCALE: 1.20
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
DRAWN
5
3
2
1
4
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SECTION A-A
B
38
30
138
DETAIL BSCALE 3 : 2
3.500
3.500
7
Fina l Projec t: Jac k Sc rew
Group # 3
All units are in milimete r and d egree
CHEC KED
lever SHEET 1 OF 1SCALE: 1:2 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
DRAWN
15
A
A
20R
126R
62
62
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SECTION A-ASCALE 1 : 10
B
44
DETAIL BSCALE 3 : 2
3.50
3.50
7100
100 R20
Fina l Projec t: Jac k Sc rew
Group # 3
All units are in milimeter and de gree
CHEC KED
power sc rewSHEET 1 OF 1SCALE: 1:10 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
DRAWN
850
15
A
A
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R2
R2
Fina l Projec t: Jac k Sc rew
Group # 3
All units are in milimete r and d egree
CHEC KED
tube SHEET 1 OF 1SCALE: 1 : 4 WEIGHT:
REVDWG. NO.
A
SIZE
TITLE:
NAME DATE
CO MM ENTS:
Q.A.
MFG A PPR.
ENG A PPR.
DRAWN
15 20
400
30