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Topology Optimization of Gear
                                                            Web using OptiStruct

                                                            Sylvester Ashok and Fabian Zender
                                                            Integrated Product Lifecycle Engineering Laboratory
                                                            Daniel Guggenheim School of Aerospace Engineering
                                                            Georgia Institute of Technology




Content in this presentation may not be duplicated, copied, or reproduced, without the permission of the authors or Altair
Overview


• Background
• Introduction
• Problem Setup
• Results
• Conclusion
Background


• A framework has been developed to study and optimize rotorcraft drive
  systems
Background


• One of the biggest problems a designer is faced with is understanding
  what fidelity of analysis is required to obtain the detail of information
  needed.
• The balance between fidelity and detail at different stages of the design
  life-cycle, among different disciplines, is one of the keenly researched
  topics in MDAO.
• Weight saving is critical in aerospace applications
    •   How should topology optimization be treated in drive system design?
Introduction


• Gear web and non-standard gear
  designs can produce up to 30%
  weight saving.
• Gear webs have been designed in
  detailed stages through bench tests
  so far.
• Topology Optimization is a method
  that can be used to study this using
  FEA.
Introduction

                                                                                     σb*= f(x)




weight               Design B               weight
                                                                          Design A



                    Design A                                   Design B
                                     σb *                                            σb *



                     x                                            x
          Analytical sizing result                     Topology optimization result



   Since the design space is discrete, if after topology optimization, design B
   weighs less than design A, topology optimization cannot be considered a
   design refinement, instead must be used to select the optimum design.
Problem Setup



             Parameter   Symbol   Unit   Baseline               Design 2

Power                      P      HP                  700

RPM                        -      RPM                 5000

Gear ratio                 mg      -                   3.3

Diametral pitch            Pd     in-1                 6

Face width                 F       in                  2.4

Pressure angle             φ      deg                  20

Material                   -       -                AISI 9310
Number of teeth            Np      -       23                     24

Tangential load            Pt     lbf    4616.7                  4424.4

Radial load                Pn     lbf    1680.4                  1610.3

Bending Stress (AGMA)      σb     psi     35000                  32951

Weight                     W       lb     7.233                  7.885
Problem Setup


• Radioss run for calibrating load
    •   Gear model brought in from CATIA
    •   Load for FEA application was
        calibrated to obtain analytical
        bending stress value
Problem Setup – Topology Optimization

•   Components
       •      Gear Teeth (blue)
       •      Design Area (red)
       •      Shafthole (blue)


•   Mesh Setup
       •      Shafthole and Design Area: Edge Deviation, 75
              elements per edge
       •      Gear Teeth: QI Optimize, element size 0.06
       •      3D Solid Map, size 0.06


•   Load Setup
       •      Load was distributed across a single line of nodes at
              pitch circle
       •      Inside of Shafthole constrained for 6 DoF


•   Calibrated Load
           Parameter                      Symbol                  Unit      Baseline   Design 2
Tangential load                              Pt                       lbf   6463.4      6194.2
Radial load                                  Pn                       lbf   2352.6      2254.4
Problem Setup – Topology Optimization




                                 Objective: min : F ( x)  Volumedesign

                                 Subject to:    x  X  x  R n | gi ( x)  0,   i  1,..., m
                                 Where,

                                 g1 ( x)  ( f   design )   *
                                 g 2 ( x)  manufacturing constraint (draw)
                                 g3 ( x)  manufacturing constraint (cyclic and symmetry)


  Design            Non-design
Problem Setup – Topology Optimization


• σdesign< 20ksi
• Cyclic Pattern, plane normal to axis of the gear, node (0,0,1.2) and node
  (0,0,0). Instances = multiple of teeth
    •   Ensure cyclic symmetry since single tooth loading is simulated
• Split Draw Constraint, draw direction given by line through center of
  gear (0,0,1.2) and center of front face (0,0,0)
    •   Ensure symmetry through the thickness for simpler manufacturing and ease of
        assembly
Problem Setup – Topology Optimization

• Optimized result only maintains structural integrity within design area
• Optimized result would lead to increased bending stress in gear teeth
Problem Setup – Topology Optimization




Bending Region




                                 Objective: min : F ( x)  Volumedesign

                                 Subject to:    x  X  x  R n | gi ( x)  0,   i  1,..., m
                                 Where,
                                 g1 ( x)  ( f   design )   *
                                 g 2 ( x)   b   b *
                                 g3 ( x)  manufacturing constraint (draw)
                                 g 4 ( x)  manufacturing constraint (cyclic and symmetry)



Design
                    Non-design
Problem Setup – Topology Optimization


• Optimization Responses
   •   Volume – Design region
   •   σb - Tooth bending stress
• Optimization Constraint
   •   σb < 35ksi
• Optimization Objective
   •   Minimize volume (design region)
• Design Variable Constraints
   •   σdesign < 20ksi
   •   Cyclic constraint (number of instances = number of teeth)
   •   Split draw constraint
Problem Setup – Initial Results




                                  N = 23
                                  Cyclic instances = 23
Problem Setup – Initial Results




                                  N = 24
                                  Cyclic instances = 24
Problem Setup – Further Refinement


• Uniform gear web is desired for manufacturing and operation purposes
• Increase number of instance = i * number of teeth, i = 1,2,3…..n
    •   Number of instances for Baseline: 8 * number of teeth = 184
    •   Number of instances for Design 2: 4 * number of teeth = 96
    •   Eliminates holes through thickness
Results - Baseline




                     N = 23
                     Cyclic instances = 184
Results – Design 2




                     N = 24
                     Cyclic instances = 96
Results




                 Baseline                                        Design 2



                            Baseline                           Design 2

     Weight     Before      After      % Difference   Before   After        % Difference



   Gear Teeth   3.777       3.777           -         3.972    3.972             -

   Web          3.243       2.674          18%        3.691    2.731           26%

   Shaft        0.213       0.213           -         0.222    0.222             -

   Total        7.233       6.664          8%         7.885    6.925           12%
Conclusion


• Topology Optimization was used to estimate material removal in the
  gear web.
• For a gear designed to carry a specific torque, 12% weight saving was
  obtained.
• An overdesigned gear does not translate to a lighter gear, post-topology
  optimization, based on preliminary studies.
• Further work is required to understand feature manipulation, application
  for helical gears, and implementation of stiffness criteria.
Questions




            THANK YOU

               Sylvester Ashok
             sylvester_ashok@gatech.edu



                Fabian Zender
                fzender@gatech.edu

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A Method to Integrate Drive System Design - Georgia tech

  • 1. Topology Optimization of Gear Web using OptiStruct Sylvester Ashok and Fabian Zender Integrated Product Lifecycle Engineering Laboratory Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Content in this presentation may not be duplicated, copied, or reproduced, without the permission of the authors or Altair
  • 2. Overview • Background • Introduction • Problem Setup • Results • Conclusion
  • 3. Background • A framework has been developed to study and optimize rotorcraft drive systems
  • 4. Background • One of the biggest problems a designer is faced with is understanding what fidelity of analysis is required to obtain the detail of information needed. • The balance between fidelity and detail at different stages of the design life-cycle, among different disciplines, is one of the keenly researched topics in MDAO. • Weight saving is critical in aerospace applications • How should topology optimization be treated in drive system design?
  • 5. Introduction • Gear web and non-standard gear designs can produce up to 30% weight saving. • Gear webs have been designed in detailed stages through bench tests so far. • Topology Optimization is a method that can be used to study this using FEA.
  • 6. Introduction σb*= f(x) weight Design B weight Design A Design A Design B σb * σb * x x Analytical sizing result Topology optimization result Since the design space is discrete, if after topology optimization, design B weighs less than design A, topology optimization cannot be considered a design refinement, instead must be used to select the optimum design.
  • 7. Problem Setup Parameter Symbol Unit Baseline Design 2 Power P HP 700 RPM - RPM 5000 Gear ratio mg - 3.3 Diametral pitch Pd in-1 6 Face width F in 2.4 Pressure angle φ deg 20 Material - - AISI 9310 Number of teeth Np - 23 24 Tangential load Pt lbf 4616.7 4424.4 Radial load Pn lbf 1680.4 1610.3 Bending Stress (AGMA) σb psi 35000 32951 Weight W lb 7.233 7.885
  • 8. Problem Setup • Radioss run for calibrating load • Gear model brought in from CATIA • Load for FEA application was calibrated to obtain analytical bending stress value
  • 9. Problem Setup – Topology Optimization • Components • Gear Teeth (blue) • Design Area (red) • Shafthole (blue) • Mesh Setup • Shafthole and Design Area: Edge Deviation, 75 elements per edge • Gear Teeth: QI Optimize, element size 0.06 • 3D Solid Map, size 0.06 • Load Setup • Load was distributed across a single line of nodes at pitch circle • Inside of Shafthole constrained for 6 DoF • Calibrated Load Parameter Symbol Unit Baseline Design 2 Tangential load Pt lbf 6463.4 6194.2 Radial load Pn lbf 2352.6 2254.4
  • 10. Problem Setup – Topology Optimization Objective: min : F ( x)  Volumedesign Subject to: x  X  x  R n | gi ( x)  0, i  1,..., m Where, g1 ( x)  ( f   design )   * g 2 ( x)  manufacturing constraint (draw) g3 ( x)  manufacturing constraint (cyclic and symmetry) Design Non-design
  • 11. Problem Setup – Topology Optimization • σdesign< 20ksi • Cyclic Pattern, plane normal to axis of the gear, node (0,0,1.2) and node (0,0,0). Instances = multiple of teeth • Ensure cyclic symmetry since single tooth loading is simulated • Split Draw Constraint, draw direction given by line through center of gear (0,0,1.2) and center of front face (0,0,0) • Ensure symmetry through the thickness for simpler manufacturing and ease of assembly
  • 12. Problem Setup – Topology Optimization • Optimized result only maintains structural integrity within design area • Optimized result would lead to increased bending stress in gear teeth
  • 13. Problem Setup – Topology Optimization Bending Region Objective: min : F ( x)  Volumedesign Subject to: x  X  x  R n | gi ( x)  0, i  1,..., m Where, g1 ( x)  ( f   design )   * g 2 ( x)   b   b * g3 ( x)  manufacturing constraint (draw) g 4 ( x)  manufacturing constraint (cyclic and symmetry) Design Non-design
  • 14. Problem Setup – Topology Optimization • Optimization Responses • Volume – Design region • σb - Tooth bending stress • Optimization Constraint • σb < 35ksi • Optimization Objective • Minimize volume (design region) • Design Variable Constraints • σdesign < 20ksi • Cyclic constraint (number of instances = number of teeth) • Split draw constraint
  • 15. Problem Setup – Initial Results N = 23 Cyclic instances = 23
  • 16. Problem Setup – Initial Results N = 24 Cyclic instances = 24
  • 17. Problem Setup – Further Refinement • Uniform gear web is desired for manufacturing and operation purposes • Increase number of instance = i * number of teeth, i = 1,2,3…..n • Number of instances for Baseline: 8 * number of teeth = 184 • Number of instances for Design 2: 4 * number of teeth = 96 • Eliminates holes through thickness
  • 18. Results - Baseline N = 23 Cyclic instances = 184
  • 19. Results – Design 2 N = 24 Cyclic instances = 96
  • 20. Results Baseline Design 2 Baseline Design 2 Weight Before After % Difference Before After % Difference Gear Teeth 3.777 3.777 - 3.972 3.972 - Web 3.243 2.674 18% 3.691 2.731 26% Shaft 0.213 0.213 - 0.222 0.222 - Total 7.233 6.664 8% 7.885 6.925 12%
  • 21. Conclusion • Topology Optimization was used to estimate material removal in the gear web. • For a gear designed to carry a specific torque, 12% weight saving was obtained. • An overdesigned gear does not translate to a lighter gear, post-topology optimization, based on preliminary studies. • Further work is required to understand feature manipulation, application for helical gears, and implementation of stiffness criteria.
  • 22. Questions THANK YOU Sylvester Ashok sylvester_ashok@gatech.edu Fabian Zender fzender@gatech.edu