What is machine design

Alexandra Schönning, Ph.D.Alexandra Schönning, Ph.D.
Machine Design:Machine Design:
An OverviewAn Overview

Presentation OutlinePresentation Outline
Introduction: What is Machine Design?Introduction: What is Machine Design?
Machine Design: Research AreasMachine Design: Research Areas
Research Applications:Research Applications:
– Gear Tooth FEM/FEA and Optimization
– Machine Design Optimization
– Customized Knee Implant: Design, Stress
Analysis and Manufacturing

Introduction:Introduction:
What is Machine Design?What is Machine Design?
Core of mechanicalCore of mechanical
engineeringengineering
– Stress and strain
– Designing for safety
– Static failure theories
– Fatigue failure
theories
– Machine elements
– Mechanical material
properties
– Stress
Concentrations
– Fracture Mechanics
– Optimization
– Composite Materials
– Manufacturing
Processes
– Computer Aided
Machine Design and
Analysis
– Measuring Stress
and Strain

Stress and strainStress and strain
– Normal stresses and strains
– Shear stresses and strains
– Principal stresses and strains
– Mohr’s circle and analytical relationships
Introduction: Stress and StrainIntroduction: Stress and Strain
τ
σ
σ1σ2σ3
22
2,1 )
2
(
2
xy
yxyx
τ
σσσσ
σ +
−
±
+
=
22
max )
2
( xy
yx
τ
σσ
τ +
−
±=
yx
xy
σσ
τ
θ
−
=
2
)2tan(
θ σx
σy
τxy

Introduction: Static FailureIntroduction: Static Failure
Ductile BehaviorDuctile Behavior
– Maximum Shear-Stress Theory
(Tresca/Coulomb/Guest Theory)
– Distortion Energy Theory (von Mises)
Brittle Behavior (even and uneven materials)Brittle Behavior (even and uneven materials)
– Coulomb-Mohr Theory
FS
S
σσ
y
31 ≤−
FS
S
)σ(σ)σ(σ)σ(σ
2
2
σ
y2
13
2
32
2
21eff ≤−+−+−=
σ
τ
Compression
test Tension
test
σ1
σ3
Sut,Sut
Sut,-Sut
Sut,-Sut
-Sut,Sut-Suc,Sut
uneven

Introduction: Fatigue FailureIntroduction: Fatigue Failure
Alternating and mean stressAlternating and mean stress
Stress-Life ApproachStress-Life Approach
– High Cycle Fatigue Criteria
– Load amplitude is consistent
– Common for rotating machinery
Strain-Life ApproachStrain-Life Approach
– Low cycle fatigue (<103
)
– Variations in loads and high
temperatures
– Common for service machinery
Fracture MechanicsFracture Mechanics
ApproachApproach
– Low cycle fatigue
– Generally used to determine
remaining life of a cracked part
– Paris equation n
KA
dN
da
)(∆⋅= n,A: empirical values
K: stress intensity factor
σ
t
103
104 106
107
105
1.0
0.6
0.8
0.4
Corrected endurance limit:
Se
=Cload
Csize
Csurf
Ctemp
Creliab
Se‘
Corrected fatigue strength
Sf
=Cload
Csize
Csurf
Ctemp
Creliab
Sf'

Introduction:Introduction:
Machine ElementsMachine Elements
SpringsSprings
FastenersFasteners
BearingsBearings
ShaftsShafts
GearsGears
Machined Universal
Joint Coiled

Machine Design:Machine Design:
Research AreasResearch Areas
Finite Element AnalysisFinite Element Analysis
Design OptimizationDesign Optimization
BiomechanicsBiomechanics
NanotechnologyNanotechnology
Fracture MechanicsFracture Mechanics
Mechanical Material PropertiesMechanical Material Properties
Composite MaterialsComposite Materials
Designing for ManufacturingDesigning for Manufacturing
WeldingWelding

Research Applications:Research Applications:
Gear tooth stress analysis and measurementGear tooth stress analysis and measurement
– Typical component studied in machine design
Finite element modeling and analysis
Stress measurement using polariscope
Machine Design OptimizationMachine Design Optimization
– Improve performance, reduce mass, stress and
cost
Missile design
Optimization theory
Customized Knee Implant:Customized Knee Implant:
– Hinge joint
Design to even out stress, remove areas of stress
concentration
Finite element analysis
Manufacturing

Gear Tooth: IntroductionGear Tooth: Introduction
Gear is a typical component studied in machine designGear is a typical component studied in machine design
In analyzing the stresses in gears one uses stress/strainIn analyzing the stresses in gears one uses stress/strain
and failure theoriesand failure theories
The stresses were measured using a polariscopeThe stresses were measured using a polariscope
Objective:Objective: minimize stress at the root of a gear tooth byminimize stress at the root of a gear tooth by
introducing a stress relief holeintroducing a stress relief hole
Parameters: location (r,Parameters: location (r, θ)θ) and size of holeand size of hole
Analytical model: I-DEAS Master SeriesAnalytical model: I-DEAS Master Series
– Solid Model, FEA, Optimization, .stl file
Experimental analysis to validate analytical model
– Stereolithography model, Polariscope

Gear Tooth: Two Gears MeshingGear Tooth: Two Gears Meshing

Gear Tooth: Solid Model CreationGear Tooth: Solid Model Creation
Involute and gear created in I-DEASInvolute and gear created in I-DEAS
Simplifications: no fillets, one toothSimplifications: no fillets, one tooth
– Pitch Diameter = 360 mm
– Number of teeth = 30
– Pressure angle = 20o
– Addendum = 12 mm
– Dedendum = 15 mm
– Gear thickness = 5 mm
– Circular tooth thickness = 18.85 mm

Gear Tooth: FEAGear Tooth: FEA
Results: original modelResults: original model
– Band of high max principal stress
– Max tensile stress
– Area of concern
Crack propagation
Fatigue failure
begins at a crack
Load
Max
Tensile
Stress

Gear Tooth: FEAGear Tooth: FEA
MeshMesh
– Triangular shell elements
– With and without hole
– Partitions
– Free locals – mesh control
Boundary conditionsBoundary conditions
– Cantilever beam approx.
Load: along 20Load: along 20oo
pressurepressure
lineline

Gear Tooth: OptimizationGear Tooth: Optimization
Objective: Minimize stressObjective: Minimize stress
Design Variables:Design Variables:
– Hole diameter
– Angular location
– Radial location
ConstraintsConstraints
– Displacement restraints
Algorithm:Algorithm: Fletcher-Reeves optimization algorithm
– Gradient based, improved steepest descent method
– Xq
= Xq-1
+ α∗
Sq
Initial search direction is the steepest decent: -∇F(Xq
)
Sq
= -∇F(Xq
)+βqSq-1
βq
= | ∇F (Xq
) |2
/ | ∇F (Xq-1
) |2

Gear Tooth:Gear Tooth: Optimized HoleOptimized Hole
LocationLocation
θ=29o
r = 4 mm
diameter =2 mm

Gear Tooth: StereolithographyGear Tooth: Stereolithography
Model CreationModel Creation
Stereolithography machine SLA-250Stereolithography machine SLA-250
–Laser cured one layer at a time
–Thickness: 0.006 inch (103
layers)
–Material: SL5170
–Ultraviolet oven for 45 min
Models created in 15 hoursModels created in 15 hours
–With and without hole

Boundary
Condition
Holes
Stress Relief Hole
Support Structure

Gear Tooth: ExperimentalGear Tooth: Experimental
SetupSetup
Experimental study to verify FEAExperimental study to verify FEA
A flange with holes for mounting wasA flange with holes for mounting was
added to the models to hold the parts inadded to the models to hold the parts in
place in the polariscopeplace in the polariscope
– Compression force was applied
– Bracket was used to distribute the force
Circular polariscope dark fieldCircular polariscope dark field was usedwas used
– Used to analyze stress in 2D models

Gear Tooth: CircularGear Tooth: Circular
PolariscopePolariscope

Gear Tooth: Isochromatic FringesGear Tooth: Isochromatic Fringes
Extinction of light of a particular wave lengthsExtinction of light of a particular wave lengths
(colored light)(colored light)
Determines the magnitude of the stressDetermines the magnitude of the stress
differencedifference
– n = hc/λ*(σ1- σ2)
n: fringe order
hc/λ: constants
σ1- σ2: stress difference
black yellow red | blue yellow red | green yellowblack yellow red | blue yellow red | green yellow
red | green yellow red | g y r | ...red | green yellow red | g y r | ...

Gear Tooth: Comparison ofGear Tooth: Comparison of
Fringes With and Without HoleFringes With and Without Hole

Gear Tooth:Gear Tooth:
Stress ResultsStress Results
101 kPa 85.7 kPa
(15% decrease)

Deflection ResultsDeflection Results
12.9 nm 13.2 nm
2.3% difference

Concluding RemarksConcluding Remarks
Stresses were analyzed and measured for a gearStresses were analyzed and measured for a gear
– Stresses decreased by 15%.
– Deflection increase of 2.3% has no major effect on the
kinematics and functionality of gear.
Hole was introduced close to the corner ofHole was introduced close to the corner of
maximum tensile stress at an angle of 29 degreesmaximum tensile stress at an angle of 29 degrees
from vertical.from vertical.
Photoelasticity results verified the analysisPhotoelasticity results verified the analysis

Designing parts for performance and massDesigning parts for performance and mass
productionproduction
– Mass reduction
– Stress reduction
– Cost reduction
– Performance improvement
– Machine design components or systems
Missile designMissile design
– Optimization theory and application
– Academic vs. industrial design optimization
Machine Design Optimization:Machine Design Optimization:
Optimization of a MissileOptimization of a Missile

Machine Design Optimization: BasicsMachine Design Optimization: Basics
Optimization VocabularyOptimization Vocabulary
Minimize F(X) Objective function
s.t. gj
(X) ≤ 0Inequality
hk
(X) = 0 Equality constraints
Xi
lower
≤ Xi
≤ Xi
upper
Side
X Design variable vector
Multidisciplinary Design OptimizationMultidisciplinary Design Optimization
– Computational expense
– Organizational complexity
DescriptionDescription
11 Aerodynamic configurationAerodynamic configuration
mass propertiesmass properties
CG locationCG location
22 Aerodynamic coefficientsAerodynamic coefficients
33 Thrust verses timeThrust verses time
Specific ImpulseSpecific Impulse
Nozzle dimensionsNozzle dimensions
44 DimensionsDimensions
Volume, MassVolume, Mass
ConfigurationConfiguration
55 Nozzle exit diameterNozzle exit diameter
power on/offpower on/off
66 Geometric dimensionsGeometric dimensions
Propulsion dimensions,Propulsion dimensions,
Material, WeightMaterial, Weight
77 Single or dual pulseSingle or dual pulse
configurationconfiguration
Propellant weightPropellant weight7
6
4
Propulsion
Analysis
Cost Analysis
Aerodynamic
Analysis
Trajectory
Analysis
1
2
3
5
Geometry
Engine

Machine Design Optimization: BasicsMachine Design Optimization: Basics
Optimization AlgorithmsOptimization Algorithms
– Gradient-based Algorithms
– Genetic Algorithms
MDO FormulationsMDO Formulations
– Discipline communication
ApproximationsApproximations
– Artificial Neural Networks
– Design of Experiment
– Response Surface Approximations
– Taylor Series Approximations

Machine Design Optimization: AlgorithmsMachine Design Optimization: Algorithms
Gradient BasedGradient Based
– Sensitivities (gradients)
from finite difference
– Local minimum
– Basic concept
Xq
= Xq-1
+ α*
Sq
X: design vector
q: iterate
S: Search direction
α: distance to move in direction S
– Unconstrained problem
Gradient is zero
Positive definite Hessian Matrix
– Constrained problem
Khun-Tucker necessary condition
X*
is feasible
λjgj (X*
) = 0 j = 1,m λj ≥0
∇F(X*
) + Σλj∇gj(X*
) + Σλk∇hk(X*
) = 0
λj ≥0
x
)()(
∆
−∆+
=
∆
∆ xuxxu
x
u

Academic vs.Academic vs. IndustrialIndustrial ProblemsProblems
Design GoalDesign Goal
– Maximize range
Key designKey design
parametersparameters
– Mid body diameter
– Mid body length
– Nose length
– Case length
– Web fraction (difference of
the outer and inner radii to the
inner radius)
– Expansion ratio (the ratio
of the exit area to the throat area
of the nozzle)
– Gamma (angle of the
velocity vector)
ConstraintsConstraints
– Weight
– Center of gravity
– Total missile length
– Cost
– Nose finess ratio
– Minimum Mach number

Missile Concluding RemarksMissile Concluding Remarks
Algorithms, Formulations, Approximations andAlgorithms, Formulations, Approximations and
programming language were combined to removeprogramming language were combined to remove
obstacles.obstacles.
Optimization scheme was integrated and tested on aOptimization scheme was integrated and tested on a
highly coupled air-to-air sparrow-like missilehighly coupled air-to-air sparrow-like missile
– Efficient and robust optimization scheme:
Reduced computational time up to 44%
Allows for modifications to the optimization statement
Covers regions in the design space for which a response
cannot be computed
Scheme can be applied to other large-scaledScheme can be applied to other large-scaled
engineering problemsengineering problems

Knee Implant Example cKnee Implant Example c
Knee joint is a hinge jointKnee joint is a hinge joint
Stress analysisStress analysis
Stress concentrationsStress concentrations
Wear of the implantWear of the implant
ManufacturingManufacturing
– Rapid Prototyping
– Investment Casting
Tibia
Fibula
Femur
Patella

Knee Implant Example:Knee Implant Example:
Need for CustomizationNeed for Customization
>0.5 million orthopedic implant surgeries conducted>0.5 million orthopedic implant surgeries conducted
each year in the USeach year in the US
– Number increasing
Increasing life span
Higher activity level
Problems associated with implants are proportionallyProblems associated with implants are proportionally
increasingincreasing
– Use of standard implants leads to removal of valuable bone
material
– Revisions are primarily due to loosening of implants
Poor fit – only a few types and sizes are available
Stress concentrations affect bone remodeling

Current DesignCurrent Design
Cancellous
Bone
Cortical
Bone
Tibial
PlateauStem
Sharp edges
Medial cross section of
femoral component

Current DesignCurrent Design
PProblems with current design:roblems with current design:
– Only 7 different sizes
– Removal of bone
– Doesn’t fit perfectly
– Not used for younger patients
– Sharp edges
– Stress concentrations
– Bone remodeling
– Loosens with time
Tibial component
Femoral component

Design of Customized ImplantDesign of Customized Implant
Designing the customized implantDesigning the customized implant
– Implant should resemble the geometry of the
original knee
– Redistribution of stresses results in variation of
bone mineral density
– Reduce possible relative motion of tibial plate
implant to the tibial bone
Data acquisitionData acquisition
– Computed Tomography data
Modeling of bone and implantModeling of bone and implant

CT-data acquisitionCT-data acquisition
– Scanning device completes a 360o
revolution
– Slices are 1 to 5 mm apart
– Result: Matrix with gray scaled pixels based on
tissue density

Data conversion using Mimics fromData conversion using Mimics from
MaterialiseMaterialise
Density threshold
Investigation of each scanned slice

Scanning the objectScanning the object
Slice distance
Resulting Image SetResulting Image Set

Select the desired regionSelect the desired region
…… and Growand Grow

Data conversion using Mimics from MaterialiseData conversion using Mimics from Materialise

Femoral Component Tibial Component

Initial Stress Analysis of ImplantInitial Stress Analysis of Implant
Finite Element AnalysisFinite Element Analysis
– 0o
, 45o
,90o
gait angle
– Load 3,5,10 times the body weight

45o
gait
90o
gait

Implant Design (Implant Design (σ in MPa)σ in MPa)
Type ofType of
ImplantImplant
X*body weightX*body weight
(85kg * 9.81m/s(85kg * 9.81m/s2)2)
0° gait angle0° gait angle 45° gait angle45° gait angle 90° gait angle90° gait angle
OldOld 33 186186 150150 154154
NewNew 33 158158 115115 130130
OldOld 55 311311 250250 257257
NewNew 55 263263 191191 217217
OldOld 1010 622622 500500 514514
NewNew 1010 525525 383383 435435

ManufacturingManufacturing
Rapid PrototypingRapid Prototyping
–Laser cures one layer at a time
–Thickness: 0.006 inch
Investment CastingInvestment Casting
CAD model to stereolithographyCAD model to stereolithography
modelmodel.
–Eliminates costly low-production-
run wax pattern tooling.

Manufacturing – Investment CastingManufacturing – Investment Casting

Concluding RemarksConcluding Remarks
An implant design has been studied andAn implant design has been studied and
redesigned to increase life of the implantredesigned to increase life of the implant
Initial stress analysis have been performed.Initial stress analysis have been performed.
– Results are favorable for the new implant
Manufacturing of implantManufacturing of implant
– Rapid prototype model
– Investment casting model
Future work:Future work:
– Improve finite element model and analysis
– Parameterize and optimize
Machine design:Machine design:
– Hinge joint, stress analysis, stress concentration,
wear, manufacturing

Overall ConclusionOverall Conclusion
Machine Design OverviewMachine Design Overview
Research Areas and ApplicationsResearch Areas and Applications
– Gear Tooth FEM/FEA and Optimization
– Machine Design Optimization
– Customized Knee Implant: Design, Stress
Analysis and Manufacturing
Research Mission at UNFResearch Mission at UNF

What is machine design

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