MODULE 3 DESIGN OF SIMPLE MACHINE ELEMENTS

ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University

ME311MECHANICAL DESIGN

MODULE 3DESIGN OF SIMPLE MACHINE ELEMENTS

Dulyachot CholaseukMechanical Engineering Department

Thammasat University


ME311 Module 3 : Design of simple machine elements 2

Contents

1. Stresses in simple machine elements2. Moment of inertia and sectional modulus3. Beam design4. Shaft design5. Optimum design



Stresses in simple machine elements1



Stresses in shaft



Stresses in thin walled elements



Stresses and deformation of beams



Stresses and deformation of beams (2)



Stresses and deformation of beams (3)



Area moment of inertia and sectional modulus2



Area moment of inertia and sectional modulus (2)



Importance of I, J and z

I deflection

J angular deflection

z bending stress

J/r shear stress in shaft

Larger values = stronger



Sections under bending

Same area distribute material away from neutral axis = higher I and z



Sections under bending



Sections under torsion

Same area distribute material away from centroid = higher J and J/r



Beam design3Stress and Deflection Constraints



Example : Gantry Crane







Notes:1. Typically, the maximum deflection is limited to the beam's spanlength divided by 250. However, L/600 is widely used in steelgantry crane design.2. Safety factor of 1.5 is recommended for overhead crane withvariable load.3. Pre-camber can be used to offset the beam deflection.




I-BEAM



SHAPE FACTOR



SHAPE FACTOR



MATERIAL FACTOR and SHAPE FACTOR



Shaft design4Shafts transmit power in the form of torsion and rotation

P Tω= 602 ( )

PTrpmπ

=



Exercise



General guidelines:

Make it as short as possible.

• Avoid sharp step.

• A round shaft is ideal.

• A hollow shaft saves weight.



Basic equation for static load

( )1

32 24 8 48s

y

Nd M Fd TSπ

= + +

Design with stress constraints using DET



Hollow shafts -- weight control



Hollow shafts – strength control



Optimum Design

5



SHEAR"

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Fully stressed beam

F

F



SHEAR"

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Fully stressed beam

F

236

12

2)(bhFx

bh

hFx

IMcx =

⋅==σ

x

M=Fx



Fully stressed beam

Let σ(x) = Sy everywhere

ySbhFx

=26

xkbFxh ==

6

kxhFxb == 2

6



Exercise

Design fully stressed beams under the following conditions and find the

volume and the deflection of each f.s. beams in comparison to its prismatic

counterpart:

(a) a cantilever beam with rectangular cross-section (b x h) under

end point load. Vary h.

(b) a cantilever beam with rectangular cross-section (b x h) under

end point load. Vary b.

(c) a simply supported beam with rectangular cross-section (b x h)

under mid point load. Vary h.

(d) a simply supported beam with rectangular cross-section (b x h)

under mid point load. Vary b.



Fully stressed beam in 3D



Trajectorial Design

Principal stress

Max. shear stress



Trajectorial Design in Nature



Trajectorial Design in Composite Materials

σI σII

w/o fibre

w/ fibre



Homework

Select a proper beam



Homework

3.4 Size a shaft for a pump to provide 600 US gpm @ 200 ft. TDH and operate at 2900 rpm.



Project 1: Optimum Design



Fixed Support Beam Under Distributed Load

BMD



Possible Solution


ME311MECHANICAL DESIGN

SPECIAL LECTURE ON OPTIMUM MATERIAL DISTRIBUTION



Various forms of stress-based shape optimization

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Initial shape

Boundary shape optimization (Fully-stressed design)

Topology optimization(solid-empty approach)



Comparison

Boundary shape optimization

Simple implementation. High manufacturability.

Limited geometric complexity. Local optimum.

Topology optimization

Mathematical based. Unlimited complexity. Global optimum.

Material properties are altered. May yield production problem.



Stress-based material distribution

Intuitive approach. Higher geometric complexity than the Boundary Opt. Method. 2D problem -> 3D result Near-global optimum.

Currently limited to 2D-load problem. Plane stress assumption.

Higher stress = More material



Iteration 1

Iteration 0

How the method works

Adjust thickness of each element according to its von Mises stress

Thin element are removed



Design of a short cantilever beam

l / h = 2

F

l

h

x

yunchanged



Optimum design of a short cantilever beam



History of convergence

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250iteration

Max stress

Min stress

Volume



The optimum design

75% volume reduction I-beam shaped cross section



SUMMARY

The proposed design method is based on a simple fact: ‘add

more material to the area that have high stress’.

Thickness of each element is varied according to its von

Mises stress.

The design method can be used to provide better initial

design various mechanical elements.

Improvement will be made to expand the idea to 3D



Application example: Design of a bicycle frame

A contour shown represents thickness.

Design domain.

Date post:	17-Oct-2021
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MODULE 3 DESIGN OF SIMPLE MACHINE ELEMENTS

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