Design and Optimization of Multi-Material Material Objects for Enhanced Thermal Behavior Application: Brake Disk Design Vincent Y. Blouin Martin Oschwald Yuna Hu Georges M. Fadel Clemson University 10 th Annual ARC Conference May 19, 004
/7 Outline Background Multi-material objects Brake Disc Temperature Field Transient Heat Transfer Analysis Optimization Problem Methodology Results Conclusion On-going and Future Research
3/7 Multi-material Objects Increased functionality Use specific material properties where needed Tailor properties to meet design goals Increase stiffness-to-weight ratio Possible to create gradient and discrete material distributions
Manufacturability 4/7 The LENS process (Laser Engineered Net Shaping) Computer-driven welding process Laser induces plasma pool Up to 4 powders injected Direct metal deposition Heterogeneous flywheel manufactured using the LENS process (Morvan, 001)
Brake Disc Rotor 5/7
6/7 Issues Vehicle kinetic energy Heat energy supplied to brake disk 90% of heat is stored in disk Energy accumulated in rotor High speed stop: 650 kj (boils liters of water) Temperature rise in rotor Reduced breaking effectiveness (fading) Thermal cracking of rotor (thermal fatigue) Increase wear in pads Rise of braking fluid temperature (vapor lock) Maintain low temperature
Motivation for light weight components 7/7 Legislation Reduce 010 emission levels (HC, CO, NO x ) to 60% of 1996 levels Reduce vehicle mass Replace cast iron brake disks with Al-MMC (Aluminum Metal Matrix Composite) Lotus Elise was the first vehicle with Al-MMC brake disks on front and rear axles Maximum operating temperature is lower Limited to small to medium-size vehicles Can we use multiple materials to reduce weight without compromising thermal characteristics?
Research Goals 8/7 Focus on design methodology Representation technique Optimization technique Multi-criteria aspect Thermal stresses Manufacturability Cost
Expected Material Distribution 9/7 Side view Pads Disk AL ST Transition between ST and AL
Steel vs. Aluminum 10/7 STEEL ALUMINUM Mass density ρ 7500 kg/m 3 70 kg/m 3 Conductivity k 50 W/m o C 190 W/m o C Specific heat C p 475 J/kg o C 880 J/kg o C Volumetric Capacity ρc p 3600 kj/mm 3o C 400 kj/mm 3o C Diffusivity κ = k/ρ/c p 14 mm /s 80 mm /s Thermal Expansion α 13 e -6 / o C 4 e -6 / o C STEEL ALUMINUM t b = 4 sec v o = 75 mph W s = 175 kj z r 310 C 448 C
Transient Heat Equation 11/7 T cρ t = T k r + 1 T r r + r 1 θ T + T + Q z Dirichlet BC (fixed temperature) Neumann BC (heat flux) Cauchy BC (convection) Radiation Heat Source Initial Condition T = T* T q n = k n = h(t T q c q Q r = εβ(t T (0) = T 0 4 ) T 4 ) For optimization, need computational efficiency Developed in-house FE code for transient heat transfer analysis
Neumann BC 1/7 weight distribution G v h Transmitted energy W s = mv 1 1 a F F R L R L F F R F L = L L = L F R R R + hµ mg + L F hµ mg + L F FF q n = W At s b ( t t) b T = k n Linearly decreasing heat flux Energy distribution between front and rear F a = mg
Optimization with EO-Lib 13/7
14/7 Material Representation FE-based representation Element-based material definition Uniform material properties within an element Number of DV s = Number of FE s Group FE s Genotype 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1...
Fitness 15/7 Minimize: Weight (W) Maximum Temperature (T max ) f(x) = α W(x) + 1 α T max (x) Normalization W = W W St St W W Al T max T = T max,al max,al T T max max,st
Results Weight (kg) 16/7 Max Temperature ( o C)
17/7 Effect of Grouping Elements Decrease in CPU-time: 4 times faster Minor differences in material distribution α1 = 0.5 α = 0.5 70 genes 90 genes (grouped by 3) 0.8 0.75 0.760 grouping increases the convergence time Fitness 0.7 0.65 0.766 best individual 90 genes average fitness 90 genes detection of the graded section different regions can be clearly assigned with one material type 0.6 best individual 70 genes average fitness 70 genes 0.55 0 50 100 150 00 Number of generations
Refinement 18/7 Global optimization step Confirmed expected rough distribution Refine transition region Extend the material model to four levels level 1: level : level 3: level 4: 100% AL 67% AL 33% ST 33% AL 67% ST 100% ST
Thermal stresses 19/7 Two types of thermal stresses: Due to non-uniform temperature field Due to non-uniform thermal expansion coefficient Superposition T AL > T ST α > AL α ST
0/7 Thermal Stresses Analysis Flaw in representation technique FE-based material distribution Stresses at interface do not represent reality AL ST Ideally (in-progress) Node-based material distribution Continuous distribution of material properties For now, how to characterize thermal stresses without calculating them? Concerned with CPU
1/7 Thermal Gradient Thermal stresses depend on thermal gradient Quantify thermal gradient at each node by finite difference Largest gradient between adjacent nodes Minimize thermal gradient F TG (x)
Material Distribution Gradient /7 Minimize material gradient F MG (x) avoid abrupt changes in the material distribution Reduce thermal stresses 1 level 1: 100% AL 3 4 1 3 4 1 3 3 4 1 3 4 1 4 level : level 3: level 4: 67% AL 67% ST 33% AL 33% ST 100% ST FVP = FVP + 0.5 FVP = FVP + 1
Fitness 3/7 Fitness function f(x) ( F (x) F (x)) = α1 W(x) + αtmax(x) + α3 TG + MG Thermal gradient Material distribution gradient
Local Optimization Results 4/7 Higher steel concentration lead to lower temperature Higher steel concentration in lower right corner Island/checker-board distribution
5/7 Optimized Brake Disc Design Decrease in weight (30-35%) for acceptable Increase in temperature ( - 5%) Design W (kg) % T max ( o C) % Viol. pairs. AL 0.97 448 0 ST 17 53.70 1.74 1.83 100 65 68 310 36 315 100 105 10 0 3 55 17 53
Conclusion Large number of FE s Large number of DV s Step 1: global optimization (coarse mesh) Step : local optimization (refined mesh) Multi-level graded material model leads to smoother gradients Characterization of thermal stresses (without computing them) Subjectivity is introduced
Work in Progress and Future Research Subjective characterization of thermal stresses Node-based material distribution for continuity Material properties vary within each element Fracture toughness Bring mechanical strength (deformation/stresses) Warping and coning of brake disk rotor Method can be extended to 3D cases Ventilated brake discs Convection and radiation Multi-objective evolutionary algorithm Ranked-based GA Consider different scenarios and material mixtures