Unformatted text preview: Machine Design:
Machine
An Overview
An Alexandra Schönning, Ph.D.
Alexandra Presentation Outline
Presentation
Introduction: What is Machine Design?
3 Machine Design: Research Areas
3 Research Applications:
3 – Gear Tooth FEM/FEA and Optimization
– Machine Design Optimization
– Customized Knee Implant: Design, Stress
Analysis and Manufacturing Introduction:
What is Machine Design?
What
3 Core of mechanical
Core
engineering
engineering
–
–
–
– 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 Introduction: Stress and Strain
3 σy Stress and strain τxy – Normal stresses and strains
σx
θ
– Shear stresses and strains
– Principal stresses and strains
– Mohr’s circle and analytical relationships
τ
σ 1, 2 σ3 σ2 σ1 σ σ x +σ y
σ x −σ y 2
2
=
±(
) + τ xy
2
2
τ max σ x −σ y 2
2
=± (
) + τ xy
2 tan(2θ ) = 2τ xy σ x −σ y Introduction: Static Failure
Introduction:
3 Ductile Behavior
– Maximum ShearStress Theory (Tresca/Coulomb/
Sy
σ1 − σ 3 ≤
FS
Guest Theory)
– Distortion Energy Theory (von Mises)
σ eff = 3 Sy
2
(σ1 − σ 2 ) 2 + (σ 2 − σ 3 ) 2 + (σ 3 − σ1 ) 2 ≤
2
FS Brittle Behavior (even and uneven materials)
Suc, Sut – CoulombMohr Theory Sut, Sut Sut, Sut σ1 τ Sut, Sut σ Compression
test σ3 Tension
test uneven
Sut, Sut Introduction: Fatigue Failure
Introduction:
3
3 Alternating and mean stress
StressLife Approach
– High Cycle Fatigue Criteria
– Load amplitude is consistent
– Common for rotating machinery 3 StrainLife Approach
StrainLife
– Low cycle fatigue (<103)
– Variations in loads and high
temperatures
– Common for service machinery 3 σ t
1.0
0.8
0.6
0.4 103 Fracture Mechanics
Fracture
Approach
Approach
– Low cycle fatigue
– Generally used to determine
remaining life of a cracked part
da
– Paris equation dN = A ⋅ (∆K ) n,A: empirical values
K: stress intensity factor
n 104 105 106 Corrected endurance limit:
Se=CloadCsizeCsurfCtempCreliabSe‘
Corrected fatigue strength
Sf=CloadCsizeCsurfCtempCreliabSf' 107 Introduction:
Machine Elements
Machine
Springs
Springs
3 Fasteners
3 Bearings
Bearings
3 Shafts
Shafts
3 Gears
3 Machined Universal
Joint Coiled Machine Design:
Research Areas
Research
3
3
3
3
3
3
3
3
3 Finite Element Analysis
Design Optimization
Biomechanics
Nanotechnology
Fracture Mechanics
Mechanical Material Properties
Composite Materials
Designing for Manufacturing
Welding
Welding Research Applications:
Research
3 Gear tooth stress analysis and measurement
– Typical component studied in machine design
x
x 3 Finite element modeling and analysis
Stress measurement using polariscope Machine Design Optimization
– Improve performance, reduce mass, stress and
cost
x
x 3 Missile design
Optimization theory Customized Knee Implant:
– Hinge joint
x x
x Design to even out stress, remove areas of stress
concentration
Finite element analysis
Manufacturing Gear Tooth: Introduction
Gear
3
3
3
3
3
3 3 Gear is a typical component studied in machine design
In analyzing the stresses in gears one uses stress/strain
In
and failure theories
and
The stresses were measured using a polariscope
Objective: minimize stress at the root of a gear tooth by
introducing a stress relief hole
introducing
Parameters: location (r, θ) and size of hole
Parameters:
θ)
Analytical model: IDEAS Master Series
Analytical
– Solid Model, FEA, Optimization, .stl file
Experimental analysis to validate analytical model
– Stereolithography model, Polariscope Gear Tooth: Two Gears Meshing
Gear Gear Tooth: Two Gears Meshing
Gear Gear Tooth: Solid Model Creation
Gear
3
3 Involute and gear created in IDEAS
Simplifications: 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: FEA
Gear
3 Results: original model
Results:
– Band of high max principal stress
– Max tensile stress
– Area of concern
Crack propagation
x Fatigue failure
x begins at a crack
begins Load
Max
Tensile
Stress Gear Tooth: FEA
Gear
3 Mesh
–
–
–
– Triangular shell elements
With and without hole
Partitions
Free locals – mesh control 3 Boundary conditions
– Cantilever beam approx. 3 Load: along 20o pressure
line
line 3
3 Gear Tooth: Optimization
Gear Objective: Minimize stress
Design Variables:
– Hole diameter
– Angular location
– Radial location 3 Constraints
– Displacement restraints 3 Algorithm: FletcherReeves optimization algorithm
Algorithm:
– Gradient based, improved steepest descent method
– Xq = Xq1 + α∗Sq
x
x
x Initial search direction is the steepest decent: ∇ F(Xq)
Sq = ∇ F(Xq)+β qSq1
β q =  ∇ F (Xq) 2 /  ∇ F (Xq1) 2 Gear Tooth: Optimized Hole
Gear
Location
Location
θ=29o
r = 4 mm
diameter =2 mm Gear Tooth: Stereolithography
Model Creation
Model
3Stereolithography machine SLA250
–Laser cured one layer at a time
–Thickness: 0.006 inch (103
layers)
–Material: SL5170
–Ultraviolet oven for 45 min
3Models created in 15 hours
–With and without hole Stress Relief Hole Support Structure Boundary
Condition
Holes Gear Tooth: Experimental
Setup
Setup
Experimental study to verify FEA
3 A flange with holes for mounting was
flange
added to the models to hold the parts in
place in the polariscope
place
3 – Compression force was applied
– Bracket was used to distribute the force
3 Circular polariscope dark field was used
was
– Used to analyze stress in 2D models Gear Tooth: Circular
Polariscope
Polariscope Gear Tooth: Isochromatic Fringes
Gear
3
3 Extinction of light of a particular wave lengths
Extinction
(colored light)
(colored
Determines the magnitude of the stress
Determines
difference
difference
– n = hc/λ *(σ 1 σ 2)
x
x
x 3 n: fringe order
hc/λ : constants
σ 1 σ 2: stress difference black yellow red  blue yellow red  green yellow
black
red  green yellow red  g y r  ...
red Gear Tooth: Comparison of
Fringes With and Without Hole
Fringes Gear Tooth:
Gear
Stress Results 101 kPa 85.7 kPa
(15% decrease) Gear Tooth:
Deflection Results
Deflection 12.9 nm 13.2 nm
2.3% difference Gear Tooth:
Concluding Remarks
Concluding
3 Stresses 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. 3 3 Hole was introduced close to the corner of
Hole
maximum tensile stress at an angle of 29 degrees
from vertical.
Photoelasticity results verified the analysis Machine Design Optimization:
Optimization of a Missile
3 Designing parts for performance and mass
Designing
production
production
–
–
–
–
– 3 Mass reduction
Stress reduction
Cost reduction
Performance improvement
Machine design components or systems Missile design
– Optimization theory and application
– Academic vs. industrial design optimization Machine Design Optimization: Basics
Machine
3 Optimization Vocabulary
Minimize F(X)
s.t. gj (X) ≤ 0
hk(X) = 0
Xilower ≤ Xi ≤ Xiupper
X 3 Objective function
Inequality
Inequality
Equality constraints
Side
Design variable vector
Design Description
1 Aerodynamic configuration
mass properties
CG location 2 Aerodynamic coefficients 3 Thrust verses time
Specific Impulse
Nozzle dimensions 4 Dimensions
Volume, Mass
Configuration 5 Nozzle exit diameter
power on/off 6 Geometric dimensions
Propulsion dimensions,
Material, Weight 7 Single or dual pulse
configuration
Propellant weight Multidisciplinary Design Optimization
– Computational expense
– Organizational complexity
1 Aerodynamic
Analysis Geom
etry
Engin
e 6 Machine Design Optimization: Basics
Machine
3 Optimization Algorithms
– Gradientbased Algorithms
– Genetic Algorithms 3 MDO Formulations
– Discipline communication 3 Approximations
–
–
–
– Artificial Neural Networks
Design of Experiment
Response Surface Approximations
Taylor Series Approximations Machine Design Optimization: Algorithms
Machine
3 Gradient Based
– Sensitivities (gradients)
from finite difference – Local minimum
– Basic concept ∆u u ( x + ∆x) − u ( x)
=
∆x
∆x Xq = Xq1 + α *Sq
X: design vector
q: iterate
S: Search direction
α : distance to move in direction S – Unconstrained problem
x
x Gradient is zero
Positive definite Hessian Matrix – Constrained problem
x KhunTucker necessary condition X* is feasible
λ jgj (X*) = 0
j = 1,m λ j ≥ 0
∇ F(X*) + Σ λ j∇ gj(X*) + Σ λ k∇ hk(X*) = 0
λj ≥ 0 Machine Design Optimization:
Academic vs. Industrial Problems
Industrial
3 Design Goal
– Maximize range 3 Key design
Key
parameters
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) 3 Constraints
–
–
–
–
–
– Weight
Center of gravity
Total missile length
Cost
Nose finess ratio
Minimum Mach number Machine Design Optimization:
Missile Concluding Remarks
Missile
3 3 Algorithms, Formulations, Approximations and
Algorithms,
programming language were combined to remove
obstacles.
obstacles.
Optimization scheme was integrated and tested on a
Optimization
highly coupled airtoair sparrowlike missile
highly
– Efficient and robust optimization scheme:
x
x
x 3 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 largescaled
Scheme
engineering problems
engineering Knee Implant Example
Knee
3
3
3
3
3 Knee joint is a hinge joint
Knee
Stress analysis
Stress concentrations
Wear of the implant
Manufacturing
Manufacturing
– Rapid Prototyping
– Investment Casting c Femur Fibula
Tibia
Patella Knee Implant Example:
Need for Customization
Need
3 >0.5 million orthopedic implant surgeries conducted
>0.5
each year in the US
each
– Number increasing
x
x 3 Increasing life span
Higher activity level Problems associated with implants are proportionally
Problems
increasing
increasing
– Use of standard implants leads to removal of valuable bone
material
– Revisions are primarily due to loosening of implants
x
x Poor fit – only a few types and sizes are available
Stress concentrations affect bone remodeling Knee Implant Example:
Current Design
Current
Sharp edges Medial cross section of
femoral component Stem Tibial
Plateau Cortical
Bone Cancellous
Bone Knee Implant Example:
Current Design
Current
3 Problems 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 Femoral component Tibial component Knee Implant Example:
Design of Customized Implant
Design
3 Designing 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 3 Data acquisition
– Computed Tomography data 3 Modeling of bone and implant Knee Implant Example:
Design of Customized Implant
Design
3 CTdata 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:
Design of Customized Implant
Design
3 Data conversion using Mimics from
Data
Materialise
Materialise Density threshold
Investigation of each scanned slice Knee Implant Example:
Knee
Design of Customized Implant
Design
Scanning the object
Scanning Resulting Image Set Slice distance Knee Implant Example:
Design of Customized Implant
Design Select the desired region … and Grow
and Knee Implant Example:
Design of Customized Implant
Design
3 Data conversion using Mimics from Materialise Knee Implant Example:
Design of Customized Implant
Design
Femoral Component Tibial Component Knee Implant Example:
Initial Stress Analysis of Implant
Initial
3 Finite Element Analysis
– 0o, 45o, 90o gait angle
– Load 3,5,10 times the body weight Knee Implant Example:
Initial Stress Analysis of Implant
Initial Knee Implant Example:
Initial Stress Analysis of Implant
Initial
45o gait 90o gait Knee Implant Example:
Initial Stress Analysis of Implant
Initial
Implant Design (σ in MPa)
Type of
Implant X*body weight
(85kg * 9.81m/s2) 0° gait angle 45° gait angle 90° gait angle Old 3 186 150 154 New 3 158 115 130 Old 5 311 250 257 New 5 263 191 217 Old 10 622 500 514 New 10 525 383 435 Knee Implant Example:
Knee
Manufacturing
Rapid Prototyping
Rapid
–Laser cures one layer at a time
–Thickness: 0.006 inch
3 Investment Casting
3 CAD model to stereolithography
model.
model
–Eliminates costly lowproductionrun wax pattern tooling. Knee Implant Example:
Knee
Manufacturing – Investment Casting Knee Implant Example:
Knee
Manufacturing – Investment Casting Knee Implant Example:
Knee
Manufacturing – Investment Casting 3
3 Knee Implant Example:
Concluding Remarks
Concluding An implant design has been studied and
An
redesigned to increase life of the implant
redesigned
Initial stress analysis have been performed.
– Results are favorable for the new implant 3 Manufacturing of implant
– Rapid prototype model
– Investment casting model 3 Future work:
– Improve finite element model and analysis
– Parameterize and optimize 3 Machine design:
– Hinge joint, stress analysis, stress concentration,
wear, manufacturing Overall Conclusion
Overall
Machine Design Overview
Machine
3 Research Areas and Applications
3 – Gear Tooth FEM/FEA and Optimization
– Machine Design Optimization
– Customized Knee Implant: Design, Stress
Analysis and Manufacturing
3 Research Mission at UNF ...
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Full Document
 Spring '11
 Staff
 Finite Element Method, Machine Design, Multidisciplinary design optimization, gear, Knee Implant Example, Stress Analysis of Implant

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