Topology optimization of engine and gearbox mount castings

Topology optimization of engine and gearbox mount castings Peter Hougardy, AUDI AG 1 1

Table of contents > Overview AUDI powertrain mounting system > General approach using topology optimization > Examples of engine and gearbox mount castings > Items of influence on topology optimization results > Topology optimization as a standard in product development process > Summary 2 2

AUDI powertrain mounting systems yesterday and today Wanderer W21, built 1933-1934 'conventional' engine mount: a piece of rubber AUDI A5, built since 2007 hydraulic damped, switchable engine mount 3 3

Powertrain mounting system of AUDI A6 with V8-engine 4 4

Engine and gearbox mount castings for AUDI A4, A5 and Q5 21 different aluminum die-cast parts, 4-6 parts assembled in each car -> number of castings per year 3 Mio., total weight 4150 t (cube with edge-length of 11.5m) -> material costs per year 9.5 Mio. 5 5

Overview optimization methods property optimization design variables: thickness, Youngs-modulus, mass,... topology optimization design variables: element void size (0... 1) thick 1 shape optimization design variables: node positions thin beam thickness high topography optimization design variables: node positions perpendicular to surface max 0 void size low stress 0 beadheight 7 7

topology optimization in product development process CAD: design space CAE: meshing of design space and application of forces and constraints 1 2 weight loads material design space manufacturing 5 4 3 CAE: optimization tool removes unnecessary material CAE: analysis and optimization in detail CAD: design with respect to optimization result manufacturing costs assembly... 8 8

Powertrain mounting system of AUDI A4 with 4 cylinder TDI engine torque cross-member 10 10

Development of torque cross-member for 4 cyl. TDI engines in AUDI A4 design space development process using topology optimization result of topology optimization 120% 110% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 100% 100% 100% 43% 45% 113% weight costs of part z-stiffness part for comparison steel welded part AUDI A4 aluminum die-cast stress analysis design weight reduced by approx. 3kg (-57%) stiffness in z-direction increased by 13% costs of part reduced significantly 11 11

Development of torque cross-member for 4 cyl. TDI engines in AUDI A4 comparison of different concepts regarding weight and stiffness option framework U cross section design space 12 12

Development of torque cross-member for 4 cyl. TDI engines in AUDI A4 optimized position of shear center for open profile A A section A-A driving direction A lateral force acting at the shear center causes bending of the profile without torsion. Open profiles have different locations of shear center and center of gravity. center of gravity shear center small torsion due to design space limitations and flexibility of longitudinal member U cross section front open -> bad framework -> better U cross section back open -> optimal 13 13

Powertrain mounting system of AUDI Q5 with 3.2l V6 FSI engine tunnel cross-member 14 14

Development of tunnel cross-member for S tronic gearbox in AUDI A4/A5/Q5 design space development process using topology optimization result of topology optimization 110% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 105% 100% 100% 100% 85% 42% weight costs of part dyn. z-stiffness part for comparison aluminum sand-cast part A4/A5/Q5 aluminum die-cast dynamic stiffness analysis design dyn. stiffness frequency weight reduced by approx. 0.5 kg (-15%) dynamic stiffness increased by 5% costs of part reduced significantly 15 15

Topology optimization of tunnel cross-members regarding dyn. stiffness topology optimization with constraints for static stiffness re-analysis of dynamic stiffness for result of topology optimization analysis of dynamic stiffness for final design dyn. stiffness result of topology optimization final design Static stiffness off tunnel crossmembers is proportional to average of dynamic stiffness. ~ 10% target value minimum dynamic stiffness 'Loss' of approx. 10% in dynamic stiffness of the final design compared to the result of topology optimization. frequency 16 16

Items of influence on optimization results function cost&dates load - fatigue - misuse - car environment - test rig - customer profiles - strength - stiffness - acoustics - weight - crash - development - testing - tools - releases - start of production assembly situation - surrounding stiffness - bolting - contact - elastomer mount - pre tension material know-how - steel - light alloy - plastics - material data - quality geometry - concept - clearance - envelope surface - assembly process - tolerances manufacturing - draw directions - form filling - die-cast - sand-cast - forging - comparison with tests - reference parts - design - optimization software - analysis methods 18 18

Influence of strength: example from the learning period topology optimization of right side engine mount crosss-member for AUDI A4 built until 2007 development process using topology optimization design space result of topology optimization 130% 120% 110% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 100% 100% 100% 85% 62% 125% Gewicht weight% max. max. Spannung stress % z-steifigkeit z-stiffness % part for comparison part A4 until 2007 stress analysis design weight reduced by 160 g (-15%) z-stiffness increased by 25% strength requirements fulfilled 19 19

Influence of strength: example from the learning period strength test of prototype cross-member with optimized geometry reason: initial crack after strength test with forces Fy (transverse direction) optimization without respect to forces Fy, because Fy << Fz loss of robustness regarding Fy due to optimization 20 20

Influence of strength: example from the learning period design modification of crack location from Fy test stress limit exceeded max. stress reduced by ~25% initial crack caused by Fy strength test re-analysis with Fy optimized design investigation: special action: stress limit exceeded at crack location improvement of critical rib geometry general conclusion: number of loadcases for optimization is increased from 4-6 to 20-30 for each part 21 21

influence of surrounding stiffness: example from the learning period strength test of prototype cross-member with optimized geometry initial crack after strenght test with part bolted to longitudinal member and forces Fz reason: different boundary conditions for topology optimization and strength test rig 23 23

influence of surrounding stiffness: example from the learning period strength test rig and boundary conditions in the car for an engine mount cross-member analysis results with car boundary conditions show significantly higher stresses at several locations compared to analysis results with test rig fixture general conclusion: all parts are optimized, analyzed and tested with respect to the boundary conditions in the car 24 24

influence of surrounding stiffness example of system optimization of an engine bracket dynamic stiffness in x-direction dyn. stiffness [db] +5dB engine design stage 1 topology optimization result of an engine bracket +150 Hz frequency [Hz] with engine design stage 1 with engine design stage 2 dynamic stiffness targets for the bracket were not achieved with engine design stage 1 early optimization of engine stiffness single part development has changed to system optimization engine design stage 2 with additional ribs (colored in red) 25 25

gearbox bracket tested by a curious test engineer... if nothing fails during testing you don't learn enough 27 27

comparison of test and analysis results for a gearbox bracket F increased until failure F = 21.7 kn gearbox bracket aluminum die-cast test: max. force F = 21.7 kn required: max. force F > 12 kn location of crack initiation analysis with F = 21.7 kn linear: σ crack-location > 500 N/mm 2 nonlinear: ε plast crack-location > 1.5 % 28 28

Influence of design experience design based on topology result for an engine bracket result of topology optimization stress < limit 1. design stage stress limit exceeded 2. design stage stress < limit high stress thickness 8-12mm thickness 5mm thickness 6mm with additional ribs low 30 30

Influence of design experience design based on topology result for an engine bracket result of topology optimization 1. design stage 2. design stage high stress no stress peak no stress peak stress limit exceeded low direct flow of force z-shaped redirected force flow 31 31

Data needed for topology optimization matrices gearboxes matrices engines DMU-analysis result: 'design space model' FORCE 6 203 1 1.0 0.0 0.0 850. FORCE 6 205 1 1.0 0.0 0.0 13150.0 $ Fz2=14kN (3 LW), Tragfeder Kz=420N/mm FORCE 7 203 1 1.0 0.0 0.0 1400.0 loads FORCE 7 205 1 1.0 0.0 0.0 12600.0 engine mounting loads $ Fz4=-8.5kN (100000 LW), gearbox Tragfeder mountingkz=200n/mm FORCE 8 202 1 1.0 0.0 0.0-7700.0 FORCE 8 204 1 1.0 0.0 0.0-800.0 $ Fz4=-8.5kN (100000 LW), Tragfeder Kz=420N/mm FORCE 9 202 1 1.0 0.0 0.0-8500.0 $ Fz4=8.5kN (100000 LW), Tragfeder Kz=200N/mm FORCE loads 10 203 1 1.0 0.0 0.0 850.0 FORCE differential 10 205 loads 1 1.0 0.0 0.0 7650.0 $ Fz4=8.5kN mounting (100000 LW), Tragfeder torque reaction Kz=420N/mm FORCE 11 203 mounting 1 1.0 0.0 0.0 1400.0 FORCE 11 205 1 1.0 0.0 0.0 7100.0 loads database with load data prepared for analysis matrices car body matrices differential gearboxes surrounding stiffness database with stiffness matrices DESSUB = 6 BEGIN BULK DTPL 1 PSOLID 13 MINMEMB 4.0 DRAW SPLIT 0.0 0.0 0.0 0.0 0.0 OBST parameters 12 DRESP1 1 engine ziel bracketswcomp DRESP1 2 constr VOLFRAC parameters DRESP1 5 disp_z DISP gearbox brackets parameters 3 DRESP1 torque crossmembers 6 mode1 FREQ parameters 1 DRESP1 7 mode2 FREQ 2 parameters mount housings DCONSTR 2 2 0.35 torque brackets DCONSTR 4 3 0.5 DCONSTR 5 4 parameters 0.52857 DCONSTR 11 6 350.0tunnel cross- DCONADD 6 11 members parameters DOPTPRM DESMAX 50 OBJTOL 0.005 MINDENS differential 0.01DISCRETE cross-members optimization parameters archive with data from reference parts Goal: finish topology optimization 3-5 days after DMU-analysis is completed 33 33

Conclusions it is a high risk to optimize a part without understanding the system in detail (loads, boundary conditions, targets,...) topology optimization gives a design proposal which has to be transferred into a feasible design with respect to die-cast process using topology optimization systematically for all castings requires efficient simulation process and data management Advantages using topology optimization systematically averaged weight reduction of 15% compared to non-optimized parts prediction whether part requirements can be achieved before design process in CAD-system is initiated reduction of development time by releasing die-cast tools based on simulation results 35 35

a gearbox mount casting... designed with 900g of aluminum based on a topology optimization 36 36

Powertrain mounting system of AUDI R8 with V8 engine front differential bracket 37 37

Topology optimization of front differential bracket for AUDI R8 (extract from animation) 38 38