what is machine design

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 mechanical Core 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

σσ1σ2σ3

222,1 )

2(

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2( xy

yx

yx

xy

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

Sσσ y

31

FS

S)σ(σ)σ(σ)σ(σ

2

2σ y2

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τ

Compression

test Tension

test

σ1

σ3Sut, Sut

Sut, -Sut

Sut, -Sut

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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 Approach Strain-Life Approach – Low cycle fatigue (<103)– Variations in loads and high

temperatures– Common for service machinery

Fracture Mechanics ApproachFracture Mechanics Approach– Low cycle fatigue– Generally used to determine remaining

life of a cracked part– Paris equation

nKAdN

da)( n,A: empirical values

K: stress intensity factor

t

103 104 106 107105

1.0

0.6

0.8

0.4

Corrected endurance limit:Se=CloadCsizeCsurfCtempCreliabSe‘

Corrected fatigue strengthSf=CloadCsizeCsurfCtempCreliabSf'

Introduction: Introduction: Machine ElementsMachine Elements

Springs Springs FastenersFasteners Bearings Bearings Shafts Shafts 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 Welding Welding

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/strain and In analyzing the stresses in gears one uses stress/strain and

failure theoriesfailure 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 by minimize 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 hole and size of hole Analytical model: I-DEAS Master Series Analytical 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 model Results: original model – Band of high max principal stress– Max tensile stress – Area of concern

Crack propagation Fatigue failure

begins at a crack

Load

MaxTensile 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 20o o pressure pressure 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 + Sq Initial search direction is the steepest decent: -F(Xq) Sq = -F(Xq)+qSq-1

q = | F (Xq) |2 / | F (Xq-1) |2

Gear Tooth:Gear Tooth: Optimized Hole Optimized Hole LocationLocation

θ=29o

r = 4 mmdiameter =2 mm

Gear Tooth: Stereolithography Gear 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: Experimental Gear Tooth: Experimental SetupSetup

Experimental study to verify FEAExperimental study to verify FEA A flange with holes for mounting was A flange with holes for mounting was

added to the models to hold the parts in added 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: Circular Gear Tooth: Circular PolariscopePolariscope

Gear Tooth: Isochromatic FringesGear Tooth: Isochromatic Fringes

Extinction of light of a particular wave lengths Extinction of light of a particular wave lengths (colored light)(colored light)

Determines the magnitude of the stress differenceDetermines the magnitude of the stress difference– n = hc/*(1- 2)

n: fringe order hc/: constants 1- 2: stress difference

black yellow red | blue yellow red | green yellow red | black yellow red | blue yellow red | green yellow red | green yellow red | g y r | ...green yellow red | g y r | ...

Gear Tooth: Comparison of Gear 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)

Gear Tooth: Gear Tooth: Deflection ResultsDeflection Results

12.9 nm 13.2 nm2.3% difference

Gear Tooth: Gear Tooth: 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 of Hole was introduced close to the corner of maximum tensile stress at an angle of 29 degrees maximum 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 mass Designing 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 functions.t. gj (X) 0 Inequality

hk(X) = 0 Equality constraints

Xilower 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 pulse Single or dual pulse configurationconfiguration

Propellant weightPropellant weight 7

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 conceptXq = Xq-1 + *Sq

X: design vector

q: iterate

S: Search direction

: distance to move in direction S

– Unconstrained problem Gradient is zero Positive definite Hessian Matrix

– Constrained problem Khun-Tucker necessary condition

X* is feasiblejgj (X*) = 0 j = 1,m j 0F(X*) + jgj(X*) + khk(X*) = 0j 0

x

)()(

xuxxu

x

u

Machine Design Optimization: Machine Design Optimization: Academic vs. Academic vs. IndustrialIndustrial Problems Problems

Design GoalDesign Goal – Maximize range

Key design parametersKey design parameters– 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

Machine Design Optimization: Machine Design Optimization: Missile Concluding RemarksMissile Concluding Remarks

Algorithms, Formulations, Approximations and Algorithms, Formulations, Approximations and programming language were combined to remove programming language were combined to remove obstacles.obstacles.

Optimization scheme was integrated and tested on a Optimization 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-scaled Scheme can be applied to other large-scaled engineering problemsengineering problems

Knee Implant Example cKnee Implant Example c

Knee joint is a hinge joint Knee joint is a hinge joint Stress analysisStress analysis Stress concentrationsStress concentrations Wear of the implantWear of the implant Manufacturing Manufacturing

– 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 each >0.5 million orthopedic implant surgeries conducted each year in the USyear in the US– Number increasing

Increasing life span Higher activity level

Problems associated with implants are proportionally Problems 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

Knee Implant Example: Knee Implant Example: Current DesignCurrent Design

Cancellous Bone

Cortical Bone

Tibial PlateauStem

Sharp edges

Medial cross section of femoral component

Knee Implant Example: Knee Implant Example: 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

Knee Implant Example: Knee Implant Example: 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

Knee Implant Example: Knee Implant Example: Design of Customized ImplantDesign of Customized 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

Knee Implant Example: Knee Implant Example: Design of Customized ImplantDesign of Customized Implant Data conversion using Mimics from Data conversion using Mimics from

MaterialiseMaterialiseDensity threshold

Investigation of each scanned slice

Scanning the objectScanning the object

Knee Implant Example: Knee Implant Example: Design of Customized ImplantDesign of Customized Implant

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

Knee Implant Example: Knee Implant Example: 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

Knee Implant Example: Knee Implant Example: Initial Stress Analysis of ImplantInitial Stress Analysis of Implant


45o gait

90o gait


Implant Design (Implant Design (σ in MPa)σ in MPa) Type of Type 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 3 3 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

Knee Implant Example:Knee Implant Example:ManufacturingManufacturing

Rapid PrototypingRapid Prototyping–Laser cures one layer at a time–Thickness: 0.006 inch

Investment Casting Investment Casting

CAD model to stereolithography CAD model to stereolithography modelmodel. –Eliminates costly low-production-run wax pattern tooling.

Knee Implant Example:Knee Implant Example:Manufacturing – Investment CastingManufacturing – Investment Casting

Knee Implant Example: Knee Implant Example: Concluding RemarksConcluding Remarks

An implant design has been studied and redesigned to An implant design has been studied and redesigned to increase life of the implantincrease 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 Overview Machine 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

Engineering

sut sut

sut sut

stress analysis

sut uneven

research areasmachine

analysis measuring stress

fatigue failureintroduction

fatigue failure alternating