module 3 design of simple machine elements
TRANSCRIPT
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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
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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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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 3
Stresses in simple machine elements1
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 4
Stresses in shaft
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 5
Stresses in thin walled elements
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 6
Stresses and deformation of beams
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 7
Stresses and deformation of beams (2)
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 8
Stresses and deformation of beams (3)
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 9
Area moment of inertia and sectional modulus2
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 10
Area moment of inertia and sectional modulus (2)
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ME311 Module 3 : Design of simple machine elements 11
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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ME311 Module 3 : Design of simple machine elements 12
Sections under bending
Same area distribute material away from neutral axis = higher I and z
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ME311 Module 3 : Design of simple machine elements 13
Sections under bending
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ME311 Module 3 : Design of simple machine elements 14
Sections under torsion
Same area distribute material away from centroid = higher J and J/r
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ME311 Module 3 : Design of simple machine elements 15
Beam design3Stress and Deflection Constraints
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 16
Example : Gantry Crane
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 17
Example : Gantry Crane
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 18
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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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 19
Example : Gantry Crane
I-BEAM
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ME311 Module 3 : Design of simple machine elements 20
SHAPE FACTOR
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ME311 Module 3 : Design of simple machine elements 21
SHAPE FACTOR
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ME311 Module 3 : Design of simple machine elements 22
MATERIAL FACTOR and SHAPE FACTOR
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ME311 Module 3 : Design of simple machine elements 23
Shaft design4Shafts transmit power in the form of torsion and rotation
P Tω= 602 ( )
PTrpmπ
=
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311 Module 3 : Design of simple machine elements 24
Exercise
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ME311 Module 3 : Design of simple machine elements 25
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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ME311 Module 3 : Design of simple machine elements 26
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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ME311 Module 3 : Design of simple machine elements 27
Hollow shafts -- weight control
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ME311 Module 3 : Design of simple machine elements 28
Hollow shafts – strength control
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ME311 Module 3 : Design of simple machine elements 29
Optimum Design
5
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ME311 Module 3 : Design of simple machine elements 30
SHEAR"
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Fully stressed beam
F
F
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ME311 Module 3 : Design of simple machine elements 31
SHEAR"
6587866133745679625225504771384317263863153409032954912500792046671592561138446843223020.1
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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ME311 Module 3 : Design of simple machine elements 33
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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ME311 Module 3 : Design of simple machine elements 34
Fully stressed beam in 3D
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ME311 Module 3 : Design of simple machine elements 35
Trajectorial Design
Principal stress
Max. shear stress
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ME311 Module 3 : Design of simple machine elements 36
Trajectorial Design in Nature
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ME311 Module 3 : Design of simple machine elements 37
Trajectorial Design in Composite Materials
σI σII
w/o fibre
w/ fibre
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ME311 Module 3 : Design of simple machine elements 38
Homework
Select a proper beam
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ME311 Module 3 : Design of simple machine elements 39
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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ME311 Module 3 : Design of simple machine elements 40
Project 1: Optimum Design
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ME311 Module 3 : Design of simple machine elements 41
Fixed Support Beam Under Distributed Load
BMD
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ME311 Module 3 : Design of simple machine elements 42
Possible Solution
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ME TUMechanical Engineering DepartmentFaculty of Engineering, Thammasat University
ME311MECHANICAL DESIGN
SPECIAL LECTURE ON OPTIMUM MATERIAL DISTRIBUTION
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ME311 Module 3 : Design of simple machine elements 44
Various forms of stress-based shape optimization
SHEAR"
6587866133745679625225504771384317263863153409032954912500792046671592561138446843223020.1
Initial shape
Boundary shape optimization (Fully-stressed design)
Topology optimization(solid-empty approach)
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ME311 Module 3 : Design of simple machine elements 45
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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ME311 Module 3 : Design of simple machine elements 46
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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ME311 Module 3 : Design of simple machine elements 47
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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ME311 Module 3 : Design of simple machine elements 48
Design of a short cantilever beam
l / h = 2
F
l
h
x
yunchanged
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ME311 Module 3 : Design of simple machine elements 49
Optimum design of a short cantilever beam
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ME311 Module 3 : Design of simple machine elements 50
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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ME311 Module 3 : Design of simple machine elements 51
The optimum design
75% volume reduction I-beam shaped cross section
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ME311 Module 3 : Design of simple machine elements 52
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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ME311 Module 3 : Design of simple machine elements 53
Application example: Design of a bicycle frame
A contour shown represents thickness.
Design domain.