MEC613 Machine Design I
2021 Winter Semester
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Instructor: Dr. Shudong Yu
Office: EPH321
Phones: x557687 (O); 416 888 0962 (cell)
Email: syu@ryerson.ca
TAs: TBD
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Course
Briefing
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Course Outline (available in the course D2L; minor revision)
Textbook
Shigley’s Mechanical Engineering Design , 11th ed. © 2019, McGraw Hill
Richard Budynas and J. Keith Nisbett.
regular print can be purchased through Ryerson bookstore.
Also available: 180 days unrestricted electronic access at $61.50.
Lectures: 4 hrs/wk (Mon 1-3, 4-6; Wed 3-5, 6-8)
Tutorials weeks 2-13: 1 hr/wk by GAs
Counselling hours: Wed 10-12, Thursdays 2-4, Additional upon request.
6 sets of homework (0%) – for better understanding of course materials and good
preparation for the test and exam.
Fatigue Hardware Lab and Report (5%0%, demonstration only)
Surprise in-class assessment (5 in total, 5% in weight)
Design Project (30%, challenges with use of gears!)
2 hr Term Test (20%, week 7, after reading week; outside the regular class)
3 hr Final Exam (45%)
This semester, we will focus more on problem solving.
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Scope
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A mechanical system (or electrical, electromechanical,
structural, etc.) consists of many components joined together
rigidly or kinematically at various locations to deliver its
intended functions.
Deformations and stresses (static, quasi-static, and dynamic) are
experienced by all components as a result of direct application
of loads (forces/moments) and/or transfer via joints. Loads can
include gravity and other effects: inertial, thermal, flow, etc.
This course is concerned with design for rigidities (the
allowable deformations of components, e.g., a shaft) and design
for strengths (allowable stresses, static, quasi-static, and
dynamic)
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Methods
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Analytical methods and hand calculations for determination of nominal values
of stresses by incorporating various modifying factors to account for
complicating effects (e.g., local stress concentration due to key/keyway, hole,
fillet) without conducting comprehensive tests – experimental or
computational (FEM, CFD, FSI). This is important in initial design stage
during which frequent modifications are necessary to address various
functionalities and constraints.
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Use of codes and standards like ASTM (general material properties), SAE
(fatigue and material props for automotive industry), ASME (piping, machine
tools), ABMA (bearings) and AGMA (gears) for design of specific machine
components against common failures.
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Skills/knowledge – math, statics, stress, dynamics, fluid mechanics, heat
transfer, FEM, etc.
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Designer often needs rounds of iterations/modifications to resolve conflict and
make compromises (less optimal) before a design is finalized. Use of
analytical skills in connection with the industry-specific codes and standards
help speed up the completion of each iteration.
Examples of Failures and Consequences
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Florida International University
pedestrian bridge collapse
(2018)
The Nipigon River Bridge (built
and commissioned in Nov. 2015,
broke in Jan. 2016, due to
“mechanical” failure)
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Fatigue failure of a
food processor blade
Many other …
Design for Static Strength
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 Failure criteria
 Ductile materials (Yield criteria):
Distortion Energy, Maximum Shear Stress,
Coulomb-Mohr
f (, S )  0


S

 Brittle Materials: Maximum Normal Stress,critical effective stress strength
Coulomb-Mohr, modified Mohr
 Design Formula
 n>1  factor of safety, industrydependent, ASME, SAE codes and
standards
 Find some time to review chapters 1-5
of the textbook.

S
n
Example 1: A poor cleat design
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 Design of cleats to supporting spare
tires for a truck.
 Problem: Cleat fractured; causing the
bogie along with the tires to fly out of
control. It had caused damages to
other vehicles and human lives.
 The contributed to a series of “flying tire
accidents on Ontario highways during
1997-98 as a result of poor mechanical
design.
 One lawsuit case went to a Provincial
Court in Kingston.
Side View
Back Cleat
Front Cleat
Circular Cross Bar
Transferring loads to the Chasse/Frame
Spare tire assembly
(bogie)
Weight
Initial design
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 Analysis done by
Manufacturing Co.
a
Design
Engineer
at
XX
Truck
 Assumed that the total load (W/2) was uniformly distributed
across the interface line of cleat-beam contact.
 The Jr.-Eng. determined that the maximum principal stress in
the cleat is 50% of the yield strength.
 His conclusion: safe for steel cleat and shock load (a safety
factor of 2).
 What’s wrong?
Front View and Mechanical Model
Side View
Back Cleat
Front Cleat
Back Cleat
W/2 – total load
Circular Cross Bar
Transferring loads to the Chasse/Frame
Spare tire assembly
(bogie)
Weight
Beam
Line of contact
before deformation
Re-examination
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FE Analysis by ANSYS
 Cleat – shell elements
 Cross bar – beam element
 Lateral contact elements along the line of contact
 Findings: the maximum stress in the cleat is 30 ksi!
 Yield strength for typical steel is about 30 ksi.
 My conclusion: unsafe for shocking load.
Back Cleat
deformation is small.
Beam
W/2 – total load Line of contact after deformation
(unknown load distribution)
Where majority of load is
concentrated.
Example 2: Solving Conflicts – CANDU Fuel Element
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A CANDU 6 fuel bundle (FB)
 4 rings of 37 fuel elements
welded to two endplates
 Fuel elements are separated
by spacer pads at various
axial cross sections for
adequate coolant flow in all
sub-channels
 During operations, FB rests
on the inside of a pressure
tube (PT) through bearing
pads
Design of fuel element or fuel rod
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A C6 fuel element
 a thin and hollow Zircaloy
sheath
 a number of solid UO2 pellets
Pellet R 1
Pellet R Np/2
sheath
Midplane
endcap
 two end-caps
Design A
•
Perfect for heat transfer
•
Terrible for containing harmful
fission products
•
Lack of integrity for fuel
handling
Coolant
UO2
Coolant
UO2
Thin Zircaloy
Design A: no cladding
Design B: with cladding
Coolant
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Cont…
UO2
Coolant
UO2
Thin Zircaloy
Design A: no cladding
Design B: with cladding
Design B
 Reduced heat transfer rate (gap, Zircaloy thermal
conductivity, degradation of irradiated Zircaloy)
 Secured fission product containment (<0.1% failure rate
for CANDU fuel bundles)
 Increased fuel integrity
 Increased fuel element stiffness or rigidity
 Key is to determine the right thickness to balance the
conflict between heat transfer engineers and stress
engineers while considering manufacturability and cost.
 Use common engineering sense and set achievable and
affordable tolerance
 Mention the impact on tightening thickness tolerances on
collapse pressure and cost.
Example 3:Design for rigidity and minimization of contact
force – Fuel Bundle
CANFLEX Bundle
 43 fuel elements; 2 end plates
 Bearing pads are introduced to the
outer elements at three axial
locations to reduce contact areas
between fuel bundle and the
pressure tube for efficient heat
transfer.
 Why three locations? Not two?
 Benefits and issues with 3 arrays of
BPs
 Benefits and issues with 2 arrays of
BPs
 Decision
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Example 4
Design for Optimal Support to Minimize Max Bending
Stress or Max Lateral Deflection
 Want to locate the supports so that the maximum deflection is
minimized.
• Uniform load is q.
• Beam flexural rigidity is EI in plane bending)
• Ignore shear deformation
• Euler-Bernoulli beam theory
 Quick analysis of Single Span Beam
• Symmetry
Load q
• Two ends?
• Midspan?
Beam or shaft
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Design for rigidities - Fuel bundle bending as
a background application
 Case A (ends, ref case)
max, A
5qL4
qL4

 0.01302
384EI
EI
Case A: supports are at the two ends.
 Case B (Mid,)
 max, B
q(0.5L) 4
qL4

 0.0078125
8EI
EI
60% of max ref deflection
 Case C (0.32L from either end,
optimal locations)
 max, B
Case B: supports are at the midspan.
ends.
qL4
 0.003694
EI
28% of max ref deflection
Case C: supports are at optimal locations
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Design for Natural Frequencies
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 Operating speed 3540 rpm (59 Hz)
 Design the supporting beam-motor
system so that its fundamental
frequency is outside the range (<50 Hz
or >68Hz) to avoid resonance.
AC Motor Supported by a Simply supported Beam
 Strengths
 Other constraints (clearance, cost,
etc.)
 Theory (EB?, Timoshenko, Reddy, Etc.)
 Selection of material, cross section,
support, etc.)
Different Cross Sections
y
x
Neutral axis
Beam
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Wind induced
vibration example
Design of Insertion Shape for Minimizing
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Membrane
Stresses in Pressure Vessel
 It is common practice to weld a variety of attachments support pads, lifting lugs, instrument ports and
reinforcements to the pressure boundary of the vessel.
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Impact of attachments and
optimization
 Attachments locally stiffen the vessel shell and
alter the membrane stress (hoop and axial) field
due to internal pressure in the vicinity of the
attachment.
 Depending on the type of weld and geometry of
the weld footprint, the local stress field in the
vessel shell at the attachment boundary can
increase significantly.
 Question: Does an optimal shape of attachment
(insertion) exist so that the impact on local stress
along the boundary is minimized? If so, what is
the optimal shape?
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Optimal shape of rigid attachment in a biaxial stress
field (Gordon Bjorkman)
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ANSYS Simulations: max principal stress 11.9 kpsi
Design of Optimal Hole Shape for Minimizing
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Membrane
Stresses
 Similar to attachments,
membrane stresses increase
significantly near the hole
boundary.
 Question: Does an optimal
shape of hole exist so that
the impact on local stresses
on the boundary is
minimized? If so, what is the
optimal shape?
Optimal shape of hole in a biaxial stress field
(Gordon Bjorkman)
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A circular hole: non-optimal
Nominal max principal
stress w/o hole: 10 ksi
An “non-optimal” circular
hole : max principal stress
25.5 ksi
Increase by 155%
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An optimal elliptical hole (a/b=2): max
principal stress: 15.3 kpsi,  53% increase
Optimal shape of airplane window
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 Treat the fuselage as an cylindrical pressure vessel
 Hoop stress vs axial stress
 Shape: elliptical or near
 What is the optimal ratio of height to width, or
ratio major to minor axes?
Design of a Machine Component
Based on Static Load
Forces
Moments
Loads
Geometry: 1,2,3D
Materials:
Constraints:
Machine
Component
DE, MSS, Mohr, MNS
u,,,Pcr
Methods of Solution: Buckling, Rigidity,
Temperature, etc.
Analytical, FEM
Design
Criteria
Static
Response
Modifications
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Met?
Yes
Stop
No
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Home Work
 Read Chapter 1-5 for Some
Fundamentals of Mechanical
Engineering Design
 Units (SI, Imperial)
 Stress and Strength
 Tolerances and Costs
 Uncertainty
 Reliability (redundancy)
 Calculations and Significant Figures