What is machine design

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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 Shear-Stress 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 – Coulomb-Mohr 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 Stress-Life Approach – High Cycle Fatigue Criteria – Load amplitude is consistent – Common for rotating machinery 3 Strain-Life Approach Strain-Life – 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: I-DEAS 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 I-DEAS 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: Fletcher-Reeves optimization algorithm Algorithm: – Gradient based, improved steepest descent method – Xq = Xq-1 + α∗Sq x x x Initial search direction is the steepest decent: -∇ F(Xq) Sq = -∇ F(Xq)+β qSq-1 β q = | ∇ F (Xq) |2 / | ∇ F (Xq-1) |2 Gear Tooth: Optimized Hole Gear Location Location θ=29o r = 4 mm diameter =2 mm Gear Tooth: Stereolithography Model Creation Model 3Stereolithography machine SLA-250 –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 – Gradient-based 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 = Xq-1 + 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 Khun-Tucker 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 air-to-air sparrow-like 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 large-scaled 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 CT-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: 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 low-productionrun 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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