MODULE 3 DESIGN OF SIMPLE MACHINE ELEMENTS

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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

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

32 24 8 48s

Nd M Fd TSπ

Design with stress constraints using DET

Hollow shafts -- weight control

Hollow shafts – strength control

Optimum Design

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Fully stressed beam

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Fully stressed beam

2)(bhFx

IMcx =

⋅==σ

Fully stressed beam

Let σ(x) = Sy everywhere

ySbhFx

xkbFxh ==

kxhFxb == 2

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

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

yunchanged

Optimum design of a short cantilever beam

History of convergence

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.

MODULE 3 DESIGN OF SIMPLE MACHINE ELEMENTS

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