principles of form synthesis i
DESCRIPTION
Principles of Form Synthesis I. Images: www.freeimage.co.uk. Evaluate. Preliminary Design. Concepts. Intermediate Design. Functional. Problem. create. Requirements. Need or. Conceptual. Selected. Synthesis. Source. Identification. design. Desire. Stage. Concepts. Stage. - PowerPoint PPT PresentationTRANSCRIPT
Department of Mechanical Engineering, The Ohio State UniversitySl. #1
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Principles of
Form Synthesis I
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Design Process
Source Need or Desire
Problem Identification
Stage
Functional Requirements
Constraintsequations cost life noise
Conceptual Stage
Selected Concepts
Synthesis Stage
create design configuration
Intermediate DesignPreliminary Design
1) Determine what is exactly wanted
2) Identify all elements of design
List ways of accomplishing design requirements
Analysis Stage
Detail Design
Tentative
Design
Evaluation Stage
System Performance
Production Stage
Fin
al D
esignSell your design
Design development: Make judgment on design
User
1) Be prepared for criticism 2) Be prepared to explain design 3) Cite good and bad points 4) Illustrate design and build models
Optimization
Evaluate Concepts
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Structural Design
Structural design involves two issues Form Synthesis Stress analysis
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What we need to know for design» Forces (location, direction, magnitude)
» Design life for part
» Maximum allowable cost
» Weight limit
» Space limit
» Environmental conditions
» Number required
» Aesthetic factors
» Material selection
» Kinematics
» Function
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Simple Example
1) Forces Types of forces are given2) Design life for part Too early for a stress analysis3) Maximum allowable cost Assume moderate cost4) Weight limit Medium weight but must be strong and light5) Space limitSmall size (say 20 cm long)6) Environmental conditions Assume ambient environment (for material
selection)7) Number required (<100)8) Aesthetic factors Looks not important9) Material selection Assume common cold-rolled steel10) Kinematics Assume high speed11) Function Connecting link in high speed mechanism
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Possible Solution
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Anatomy of a Part
Body Joints Body
Body
Joints
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Principles Governing Form Synthesis
• Form the size and shape of the part so that the stress is uniform over as large an area as possible.
• Minimize the weight and/or volume of the part consistent with cost, manufacturing processes, and other constraints.
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Stress Patterns
Variation of stress across a given cross section Functions of
Position of load Orientation of load Shape of part
Uniform stress patterns are “Strong” Non-uniform stress patterns are “Weak”
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State of Stress at Point
Applies to all possible planes through point
Nomenclature: refers
to the stress on the i face
and in the j direction.
Z
X
Y
xxxyyz
yy
zx
yx
zz
zyxz
ij
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Common Stress Patterns
Uniform Tension
Uniform Compression
Bending
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Common Stress Patterns (cont’d)
Transverse Shear
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Common Stress Patterns (cont’d)
Torsion
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Common Stress Patterns (cont’d)
Bending of I-beam
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Common Stress Patterns (cont’d)
Contact stresses
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Things Affecting Stress Patterns
Shape of part Force orientation Material (if stress-strain curve nonlinear)
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Comparison of Stresses
Force = 1000 lbs Identify stresses for various orientations
of load and shape of part.
10"
1" diameter
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Tension/Compression
PA
Pd 2 / 4
1000 / 4
1270 psi
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Bending
McI
PL(d / 2)d4 / 64
1000(10)(32)(1)3 102,000 psi
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Transverse Shear
VQIb
43
PA
43 ave 4
3P
(d2 / 4)4
3(1000)(1)2 / 4
1,700 psi
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Torsion
TrJ
PL(d / 2)d4 / 32
1000(10)(16)(1)3 51,000 psi
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Tensile vs. Shear Stresses
For ductile materials, shear stresses alone are numerically twice as bad as tensile stresses
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Maximum Shear Stress Theory
1
2
1, 2
max 12
( x y)2 4 2 1 2
2
max yp
2
• General state of stress
• Simple tension test
yp
2
• For pure torsion ( ) 1 2
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Comparing Stresses
When comparing severity, use
Or
and 2
and 2
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Torsion of Hollow Section
Use tube with outside radius of 2” but with same area as 1” diameter rod
J 32
do4 di
4 di do t
J 32
do4 do 2t 4
J 32
do4 do
4 8do3t do
3t4
dot do2
4A do
2
4
= Tr J
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Torsion of a Hollow Tube (cont’d)
TrJ
T do / 2
Ado2
4
T do / 2
Ado2
4
2TAdo
2(1000)(10)4[(1)2 / 4]
6,370 psi
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Two 1” Diameter Rods in Contact
c 1.5Pcd
c PKDCE3
d PKDCE3
KD D1D2
D1 D2
CE 1 12
E11 2
2
E2
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Getting and
Depends on D1 / D2
For the bars, D 1 = D2 = 1 and1 = 2 = 0.3E1 = E2 = 30,000,000 psi = = 0.908.
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Stress Calculation
KD 12
,
CE 1 (0.3)2
30x106 1 (0.3)2
30x106 6.0666x10 8
cd 0.908 1000 12
6.0666x1083 0.0283
c 1.5(1000) (0.0283)(0.0283)
596,000 psi
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Comparison of Transverse Stress and Bending
When are transverse shear and bending equally severe?
b McI
32FLd3
VQIb
4F3A
4F3d2 / 4
16F3d2
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Comparison of Transverse Stress and Bending (cont’d)
Therefore
b Syp
Syp
2
b 2
Syp b 32FLd3 2 32F
3d2
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Comparison of Transverse Stress and Bending (cont’d)
Ld
13 L d / 3
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Comparison of Torsion and Transverse Shear
Determine the relative value of e and d for which transverse shear and torsional shear are equally serious.
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Comparison of Torsion and Transverse Shear (cont’d)
Maximum torsional stress
T TrJ
Fed / 2d4 / 32
16Fed3
Maximum transverse shear stress
s 4F3A
16F3d2
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Comparison of Torsion and Transverse Shear (cont’d)
Because both are shear stresses, set
s T 16F3d2 16Fe
d3
ored
13
F
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Comparison of Tension and Bending
When is tensile stress comparable to bending stress on round section
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Comparison of Tension and Bending (cont’d)
Tension stress
T FA
Fd2 / 4
4Fd2
Bending stress
b McI
Fed / 2d4 / 64
32Fed3
When the stresses are equal
b T 4Fd2 32Fe
d3
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Comparison of Tension and Bending (cont’d)
Finallye d
8
• If e is only 10% of this (e = d/80), the stress is increased by 10% over simple tension case alone (eccentricity of 1.25%)
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I-Beam in Bending
Consider following I-beam 10 in long Area same as 1-in diameter bar 90% of area in flanges (10% in web) 4 in high
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I-Beam in Bending (cont’d)
Flange area = 0.9 A = 0.707 in2
Approximate moment of inertia
I Ar2 0.707(4 / 2)2 2.827
• Area calculation for round barA d2 / 4 12 / 4 / 4 0.7853 in2
in4
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Bending Stress
Bending stress
McI
1000(10)(2)2.827
7073 psi
Note: Area moved to where it carries load
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Optimum Shapes for Bending and Torsion
Optimum for bending
Optimum for torsion
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Examples of Optimum Shapes
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Summary of Stresses
Stress Type Compression Tension Bending(bar) Bending(I-beam) Torsion (solid) Torsion (hollow) Transverse shear Spot contact*
Value 1,200 1,200 102,000 7,070 51,000 6,370 1,700 596,000
Stress Index 1,200 1,200 102,000 7,070 102,000 12,740 3,400 596,000
Comments Efficient, i.e., strong stress pattern Efficient, i.e., strong stress pattern Inefficient, i.e., weak stress pattern Efficient, i.e., strong stress pattern Inefficient, i.e., weak stress pattern Efficient, i.e., strong stress pattern Efficient, i.e., strong stress pattern Inefficient, i.e., weak stress pattern
* The material will yield so that this is not a true stress value.
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Summary of Form Synthesis
Form synthesis and analysis is very important in design.
The engineer must use certain assumptions and information to determine the optimal design shapes with considerations for size, shape and material.
The design greatly affects the overall performance and capabilities of the design.
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Credits
This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC-9109794). Contributing members include:
Gary Kinzel …………………………………….. Primary author Walter Starkey……………..Primary source of original material Phuong Pham and Matt Detrick ……….…….. Module revisions
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Disclaimer
This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.