principles of form synthesis i

Department of Mechanical Engineering, The Ohio State UniversitySl. #1

GATEWAYGATEWAY

Principles of

Form Synthesis I

Images: www.freeimage.co.uk


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Structural Design

Structural design involves two issues Form Synthesis Stress analysis

Images: www.freeimage.co.uk


GATEWAYGATEWAY

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


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Possible Solution


GATEWAYGATEWAY

Anatomy of a Part

Body Joints Body

Body

Joints


GATEWAYGATEWAY

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.


GATEWAYGATEWAY

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”


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Common Stress Patterns

Uniform Tension

Uniform Compression

Bending


GATEWAYGATEWAY

Common Stress Patterns (cont’d)

Transverse Shear


GATEWAYGATEWAY


Torsion


GATEWAYGATEWAY


Bending of I-beam


GATEWAYGATEWAY


Contact stresses


GATEWAYGATEWAY

Things Affecting Stress Patterns

Shape of part Force orientation Material (if stress-strain curve nonlinear)


GATEWAYGATEWAY

Comparison of Stresses

Force = 1000 lbs Identify stresses for various orientations

of load and shape of part.

10"

1" diameter


GATEWAYGATEWAY

Tension/Compression

PA

Pd 2 / 4

1000 / 4

1270 psi


GATEWAYGATEWAY

Bending

McI

PL(d / 2)d4 / 64

1000(10)(32)(1)3 102,000 psi


GATEWAYGATEWAY

Transverse Shear

VQIb

43

PA

43 ave 4

3P

(d2 / 4)4

3(1000)(1)2 / 4

1,700 psi


GATEWAYGATEWAY

Torsion

TrJ

PL(d / 2)d4 / 32

1000(10)(16)(1)3 51,000 psi


GATEWAYGATEWAY

Tensile vs. Shear Stresses

For ductile materials, shear stresses alone are numerically twice as bad as tensile stresses


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Comparing Stresses

When comparing severity, use

Or

and 2

and 2


GATEWAYGATEWAY

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


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Two 1” Diameter Rods in Contact

c 1.5Pcd

c PKDCE3

d PKDCE3

KD D1D2

D1 D2

CE 1 12

E11 2

2

E2


GATEWAYGATEWAY

Getting and

Depends on D1 / D2

For the bars, D 1 = D2 = 1 and1 = 2 = 0.3E1 = E2 = 30,000,000 psi = = 0.908.


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Comparison of Transverse Stress and Bending

When are transverse shear and bending equally severe?

b McI

32FLd3

VQIb

4F3A

4F3d2 / 4

16F3d2


GATEWAYGATEWAY

Comparison of Transverse Stress and Bending (cont’d)

Therefore

b Syp

Syp

2

b 2

Syp b 32FLd3 2 32F

3d2


GATEWAYGATEWAY

Comparison of Transverse Stress and Bending (cont’d)

Ld

13 L d / 3


GATEWAYGATEWAY

Comparison of Torsion and Transverse Shear

Determine the relative value of e and d for which transverse shear and torsional shear are equally serious.


GATEWAYGATEWAY

Comparison of Torsion and Transverse Shear (cont’d)

Maximum torsional stress

T TrJ

Fed / 2d4 / 32

16Fed3

Maximum transverse shear stress

s 4F3A

16F3d2


GATEWAYGATEWAY

Comparison of Torsion and Transverse Shear (cont’d)

Because both are shear stresses, set

s T 16F3d2 16Fe

d3

ored

13

F


GATEWAYGATEWAY

Comparison of Tension and Bending

When is tensile stress comparable to bending stress on round section


GATEWAYGATEWAY

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


GATEWAYGATEWAY

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%)


GATEWAYGATEWAY

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


GATEWAYGATEWAY

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


GATEWAYGATEWAY

Bending Stress

Bending stress

McI

1000(10)(2)2.827

7073 psi

Note: Area moved to where it carries load


GATEWAYGATEWAY

Optimum Shapes for Bending and Torsion

Optimum for bending

Optimum for torsion


GATEWAYGATEWAY

Examples of Optimum Shapes


GATEWAYGATEWAY

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.


GATEWAYGATEWAY

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.


GATEWAYGATEWAY

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


GATEWAYGATEWAY

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.

principles of form synthesis i

Documents