module 3 design of simple machine elements
TRANSCRIPT
ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311MECHANICAL DESIGN
MODULE 3DESIGN OF SIMPLE MACHINE ELEMENTS
Dulyachot CholaseukMechanical Engineering Department
Thammasat University
ME TUMechanical Engineering DepartmentFaculty of Engineering, 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
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ME311 Module 3 : Design of simple machine elements 3
Stresses in simple machine elements1
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Stresses in shaft
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Stresses in thin walled elements
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Stresses and deformation of beams
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Stresses and deformation of beams (2)
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Stresses and deformation of beams (3)
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Area moment of inertia and sectional modulus2
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Area moment of inertia and sectional modulus (2)
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Importance of I, J and z
I deflection
J angular deflection
z bending stress
J/r shear stress in shaft
Larger values = stronger
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Sections under bending
Same area distribute material away from neutral axis = higher I and z
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Sections under bending
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Sections under torsion
Same area distribute material away from centroid = higher J and J/r
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Beam design3Stress and Deflection Constraints
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Example : Gantry Crane
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Example : Gantry Crane
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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.
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Example : Gantry Crane
I-BEAM
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SHAPE FACTOR
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SHAPE FACTOR
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MATERIAL FACTOR and SHAPE FACTOR
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Shaft design4Shafts transmit power in the form of torsion and rotation
P Tω= 602 ( )
PTrpmπ
=
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Exercise
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General guidelines:
Make it as short as possible.
• Avoid sharp step.
• A round shaft is ideal.
• A hollow shaft saves weight.
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Basic equation for static load
( )1
32 24 8 48s
y
Nd M Fd TSπ
= + +
Design with stress constraints using DET
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Hollow shafts -- weight control
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Hollow shafts – strength control
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Optimum Design
5
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SHEAR"
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Fully stressed beam
F
F
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Fully stressed beam
F
236
12
2)(bhFx
bh
hFx
IMcx =
⋅==σ
x
M=Fx
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ME311 Module 3 : Design of simple machine elements 32
Fully stressed beam
Let σ(x) = Sy everywhere
ySbhFx
=26
xkbFxh ==
6
kxhFxb == 2
6
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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.
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Fully stressed beam in 3D
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Trajectorial Design
Principal stress
Max. shear stress
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Trajectorial Design in Nature
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Trajectorial Design in Composite Materials
σI σII
w/o fibre
w/ fibre
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Homework
Select a proper beam
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Homework
3.4 Size a shaft for a pump to provide 600 US gpm @ 200 ft. TDH and operate at 2900 rpm.
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Project 1: Optimum Design
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Fixed Support Beam Under Distributed Load
BMD
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Possible Solution
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ME311MECHANICAL DESIGN
SPECIAL LECTURE ON OPTIMUM MATERIAL DISTRIBUTION
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Various forms of stress-based shape optimization
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Initial shape
Boundary shape optimization (Fully-stressed design)
Topology optimization(solid-empty approach)
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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.
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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
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Iteration 1
Iteration 0
How the method works
Adjust thickness of each element according to its von Mises stress
Thin element are removed
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Design of a short cantilever beam
l / h = 2
F
l
h
x
yunchanged
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Optimum design of a short cantilever beam
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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
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The optimum design
75% volume reduction I-beam shaped cross section
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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
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Application example: Design of a bicycle frame
A contour shown represents thickness.
Design domain.