Topology and Shape Optimization versus Traditional Optimization Methods

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Topology and Shape Optimization versus Traditional Optimization Methods

  1. 1. Topology and Shape Optimization versusTraditional Optimization MethodsDr.-Ing. Elke Feifel, Dr.-Ing. Dietmar Mandt, Voith TurboPräsentationstitel | Ort oder Vortragender | YYYY-MM-DD 1
  2. 2. OverviewTraction Principles of Railway Vehicles Electric drive (E) Diesel-Electric drive (DE) trolley wire diesel engine generator electric traction electric traction converter motor converter motor Diesel-Hydromechanic drive (DHM) Diesel-Hydraulic drive (DH) diesel diesel engine engine hydrodynamic final transmission drive gearbox final driveTopology and shape optimization versus traditional optimization methods 2
  3. 3. Final Drives Complete wheel sets High Speed Train CRH 3 Metro Pennsylvania EMU Zagreb MoR China USATopology and shape optimization versus traditional optimization methods 3
  4. 4. Final Drives, Values and Objectives  Adapt the speed of the output of an electric motor or transmission to the speed of the wheelset via one ore more gear ratios.  Mechanical power transmission with a minimum of wear, high efficiency and a minimum of noise and vibration.  Low weight and restricted space.Topology and shape optimization versus traditional optimization methods 4
  5. 5. Production Technologies of Spur Gears technologies by hobbing Zahnstange- Bezugsprofil  development in manufacturing Form profile grinding - Fräser - Schleif- methods leads to wider variety technology scheibe in geometry  by modifying tooth root geometry critical stresses can be reduced Source: WZL, RWTH AachenTopology and shape Fingerfräser traditional optimization methods optimization versus 5
  6. 6. Optimization of a Spur Gear  Reduction of stress in root fillet  no collision with tooth of opposite gear dir 1  free-shape optimization in root fillet  most sever load positions dir 2  4 load cases due to 2 directions FLC4 (dir2) FLC2FLC1 FLC3 (dir1)(dir1) (dir2) root fillet Topology and shape optimization versus traditional optimization methods 6
  7. 7. Stress in Root Fillet due to 4 Loadcases LC 1; dir 1 LC 2; dir 1 LC 3; dir 1 LC 4; dir 1 Principle Stress s1 s1,max s1,max Principle Stress s3 s3,max s3,max dir 1 dir 2Topology and shape optimization versus traditional optimization methods 7
  8. 8. Shape Optimization of Root Fillet Optimization task No. Objective Constraints mimimize max. 2 s1 > s1,lim principle stress s1 mimimize max. 3 principle stress s1 mimimize max. 4 equivalent stress svTopology and shape optimization versus traditional optimization methods 8
  9. 9. Shape Optimization of Root Fillet Shape change of optimized contour Original Contour Optimization 2 Optimization 3 Optimization 4Topology and shape optimization versus traditional optimization methods 9
  10. 10. Principle Stress in Root Fillet (LC4) Original Contour  Reduction of tensile Optimization 2 Optimization 3 stress of  35% Optimization 4 sigma_1 (Original Contour) original contour sigma_1 (Optimized Contour 2) sigma_1 (Optimized Contour 4) sigma_1 (Optimized Contour 3) principle stress s1 (LC4) in root fillet optimized contourTopology and shape optimization versus traditional optimization methods 10
  11. 11. Safety Factor of Root Fillet 3.0  fatigue strength considering mean stress 2.5 taken from Smith chart  Minimum safety factors: 2.0  0.87 original contour safety factor SF SFmin=1.17  1.17 optimized 1.5 Original contour No. 3 Contour Optimized  Increase of load capacity 1.0 Contour 3 of  35% SF SFmin=0.87 (Original) 0.5 SF (Optimized Contour 4) 0.0Topology and shape optimization versus traditional optimization methods 11
  12. 12. Safety Factor - Comparison with Bionic Root Fillet 5.0 Safety Factor (Optimized Contour 4) 4.5 4.0 3.5 3.0 2.5 2.0 SFmin=1.17 1.5 optimized root fillet 1.0 („tension triangle“) 0.5 0.0-35 -30 -25 -20 -15 -10 -5 0 node Source: Roth, R.: Developing a Bionic Gear Root Fillet Topology and shape optimization versus traditional optimization methods Contour, VDI-Berichte 2108, 2010. 12
  13. 13. Conclusion – Optimization of Root Fillet  Free shape optimization in root fillet of spur gear leads to reduction of tensile stress and increase of load capacity of more than 35%.  Good agreement with safety factor of bionic root fillet contour based on the method of „tension triangle“  Speed up optimization process by using shape optimization  Shape optimization on fatigue strength instead of optimization on stressesTopology and shape optimization versus traditional optimization methods 13
  14. 14. Spring – Requirements on Design  Specific spring stiffness C0,min  Restriction of design space  Equivalent stress smaller than slim Topology optimization Shape optimizationTopology and shape optimization versus traditional optimization methods 14
  15. 15. Topology Optimization to reduce Stiffness Topology OptimizationNo. Objective Constraints Parameters 1 2 min. minimum1 volfrac < Vlim compliance membersize stress constraint min.2 volfrac < Vlim minimum compliance membersize spring stress constraint3 min. volume stiffness > minimum C0,min membersize 3 4 stress constraint max.4 volfrac < Vlim minimum displacement membersize Topology and shape optimization versus traditional optimization methods 15
  16. 16. Topology Optimization to Reduce Stiffness 1 2  optimization results differ from design exspected  no feasible design 3 4Topology and shape optimization versus traditional optimization methods 16
  17. 17. Topology Optimization optimization results are framework structures members are objected to tension or compression  small strain energy  large stiffness of structure large strain energy required  members subjected to bending  small stiffness of structure modifications of design space to force a structure objected to bending 4 4 4 4 mod1 mod2 mod3 mod4Topology and shape optimization versus traditional optimization methods 17
  18. 18. Design Derived from Optimization Results restrictions on stiffness C0,min fulfilled 4 design good agreement with design mod4 proposal from engineering department allowable stress exceeded no feasible design sv  shape optimization with design derived from topology optimizationTopology and shape optimization versus traditional optimization methods 18
  19. 19. Freeshape Optimization Design proposal: Results of shape optimization: equivalent stress shape change equivalent stress sv > sv,max sv < sv,maxTopology and shape optimization versus traditional optimization methods 19
  20. 20. Conclusion – Optimization of a Spring  OptiStruct optimized design differs strongly from expected design  Topology optimization on minimum compliance has no feasible design  Modifying the design space leads to feasible design proposal which fulfills the requirements  „Intelligent“ solutions might get lost in numerical optimization processTopology and shape optimization versus traditional optimization methods 20
  21. 21. Topology and shape optimization versus traditional optimization methods 21

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