Kalibrierung von Materialparametern und Optimierung eines Elektromotors mit optislang

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2 Kalibrierung von Materialparametern und Optimierung eines Elektromotors mit optislang Calibration of material parameters and optimization of an electric motor with optislang M. Schimmelpfennig, Markus Stokmaier, Rene Kallmeyer Dynardo GmbH, Weimar, Germany 2

3 Outline Introduction and Methods in optislang use case 1: Parameter Identification of a Spring Steel Use case 2: Optimization of an electric motor Summary and Outlook 3

4 Outline Introduction and Methods in optislang use case 1: Parameter Identification of a Spring Steel Use case 2: Optimization of an electric motor Summary and Outlook 4

5 Introduction and Methods in optislang optislang is an algorithmic software for sensitivity analysis, optimization, robustness evaluation, reliability analysis robust design optimization (RDO) functionality of stochastic analysis to run real world industrial applications advantages: predefined workflows, algorithmic wizards and robust default settings optislang has a comfortable pre- and post processing that helps the user to set up the analysis and visualize the results 5

6 Introduction and Methods in optislang 6

7 Introduction and Methods in optislang 7

8 Introduction and Methods in optislang optislang inside ANSYS optislang modules Sensitivity + MOP, Optimization and Robustness are directly available in ANSYS Workbench 8

9 Introduction and Methods in optislang CAX-Interfaces the ANSYS Workbench Node optislang Integrations provides the flexibility to extend the process chain ANSYS Workbench can be coupled with different other solvers like MATLAB, SimulationX or Abaqus External geometry or mesh generators can work together with the ANSYS Workbench node 9

10 Outline Introduction and Methods in optislang use case 1: Parameter Identification of a Spring Steel Use case 2: Optimization of an electric motor Summary and Outlook 10

11 Parameter Identification of a Spring Steel Finite element model in ANSYS Workbench Nonlinear material behavior Tensile bar is deformed by a predefined displacement Reaction forces at deformed tensile bar end (1) are monitored depending on deformation between named selection u1 (2) and u2 (3) and saved into the result file file.rst

12 Parameter Identification of a Spring Steel Simulation with initial materials parameters vs. reference (measurements) 12

13 Parameter Identification of a Spring Steel Identification of the material parameters to optimally fit the force-displacement curve to the measurements σ = σ 0 + R 0 ε pl + R (1-e -b εpl ) Unknown material parameters for nonlinear isotropic hardening (NLISO): Young s modulus Yield stress σ 0 Linear hardening coefficient R 0 Exponential hardening coefficient R Exponential saturation parameter b Objective function is the sum of squared errors between the reference and the calculated force-displacement function values 13

14 Parameter Identification of a Spring Steel Generation of a solver chain using ANSYS Workbench and Signal Processing Definition of the input parameters Definition of output and reference signals Sensitivity analysis of signal extraction terms using the given parameter bounds Single objective, unconstrained optimization by minimizing the sum of squared errors 14

15 Parameter Identification of a Spring Steel Curves can be extracted by rst file or text file written by APLD script Sensitivity analysis shows: The reference curve is covered sufficiently by the simulations Parameter bounds seem to be adequate for the calibration 15

16 Parameter Identification of a Spring Steel 16

17 Parameter Identification of a Spring Steel Check also single force_steps values: The influence of the yield stress σ 0 and Young s modulus decreases meanwhile the influence of the exponential hardening coefficient R increases with increasing displacement force_steps[0] force_steps[6] 17

18 Parameter Identification of a Spring Steel Why is the linear hardening coefficient (1) R 0 not important??? The linear hardening coefficient R 0 describes the slope of the asymptotic curve (2), which is zero in this example (3) force_steps[0] force_steps[6] 18

19 Parameter Identification of a Spring Steel Direct Optimization using Downhill Simplex Method Import the best design of the sensitivity analysis as start design 19

20 Parameter Identification of a Spring Steel Very good agreement between simulation and reference is achieved 20

21 Parameter Identification of a Spring Steel 1. Open the parallel coordinates plot: Reduce the range of the objective to the best values and increase the constraint to the value b. 2. The remaining signals are very close 3. The Yield stress σ 0, the Young s modulus and the exponential saturation parameter b show small deviations They can be identified very well with the measurement data 4. The linear hardening coefficient R 0 show larger deviations This can be not identified with sufficient accuracy a. 21

22 Outline Introduction and Methods in optislang use case 1: Parameter Identification of a Spring Steel Use case 2: Optimization of an electric motor Summary and Outlook 22

23 Outline - Optimization of an electric motor The motor simulation ANSYS Maxwell 2D model commutator principle Sensitivity analysis with optislang problem understanding identification of influential parameters identification of tradeoffs Optimization with optislang minimization of torque ripples maximization of the efficiency eta η = P out /P in suitable in this case: ARSM adaptive response surface method 23

24 Optimization of an electric motor Commutator motor: working principle What creates the driving torque? B-field from magnets B-field from coils motor characteristics commutator principle 12 lamellae & coils one current branch U 0 = 12 V fixed outer diameter OD = 78 mm iki/file:kommutator_animiert.gif 24

25 Optimization of an electric motor The model: 2D commutator motor FE-simulation simulation details time: ms in 180 steps Δt = 92.6 μs time integration: Backward Euler ensure that stationary state is reached (not all designs will become stationary at the same time) data extraction: key properties extracted by analyzing only the last cycle access to output variables via Ansys Workbench ParameterSet access to signals via ASCII files 25

26 Model parametrization 26

27 Model parametrisation magnet_coverage: magnet coverage in percent magnet_thickness airgap gapwidth magnet_rounding: as fraction of magnet thickness rotor_borehole: diameter of motor axis HS0 wall_thickness magnet_voffset: for widening of air gap 27

28 Optimization of an electric motor Parametrization needs careful decisions example A: set rotor diameter set magnet thickness motor size dependent example B (used): set motor size set magnet thickness rotor size dependent the bigger the better (in terms of torque & power) magnet takes away space available for rotor and vice versa lost chance to learn about a relevant tradeoff real-world goal conflict well represented 28

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30 Calling Maxwell from optislang 30

31 Optimization of an electric motor Method A: using Ansys Workbench in Maxwell export scalar output variables to Optimetrics parallel design computation with Optimetrics Parametric in the Workbench optislang and Maxwell communicate through the ParameterSet parallel/distributed computation: RSM, PBS, LSF, HPC pack use optislang inside Ansys alternative: optislang full version and a Workbench node 31

32 Optimization of an electric motor Method A: using Ansys Workbench in Maxwell export scalar output variables to Optimetrics parallel design computation with Optimetrics Parametric in the Workbench optislang and Maxwell communicate through the ParameterSet parallel/distributed computation: RSM, PBS, LSF, HPC pack use optislang inside Ansys represented inside the Workbench node alternative: optislang full version and a Workbench node 32

33 Optimization of an electric motor Method B: scripting and ASCII files direct coupling Maxwell and osl Maxwell run batch job run Python script write transient reports into files signal data accessible text file for transporting input parameters optislang text-based batch job node extract signal data with ETK signal data free mathematical computations inside optislang parallel/distributed computation: optislang spawns Maxwell batch jobs 33

34 Optimization of an electric motor Method B: scripting and ASCII files direct coupling Maxwell and osl Maxwell run batch job run Python script write transient reports into files signal data accessible optislang text-based batch job node extract signal data with ETK signal data free mathematical computations inside optislang the batch script Python parallel/distributed computation: optislang spawns Maxwell batch jobs 34

35 Optimization of an electric motor Method B: scripting and ASCII files direct coupling Maxwell and osl Maxwell run batch job run Python script write transient reports into files signal data accessible reading generated stored data optislang text-based batch job node extract signal data with ETK signal data free mathematical computations inside optislang parallel/distributed computation: optislang spawns Maxwell batch jobs 35

36 Optimization of an electric motor Method B: scripting and ASCII files direct coupling Maxwell and osl Maxwell run batch job run Python script write transient reports into files signal data accessible reading generated stored data optislang text-based batch job node extract signal data with ETK signal data free mathematical computations inside optislang parallel/distributed computation: optislang spawns Maxwell batch jobs 36

37 Optimization of an electric motor extract signal data with ETK green area for data analysis FFT amplitudes of the reference signal picture for postprocessing 37

38 Sensitivity analysis 38

39 Initial sensitivity analysis (100 DPs) Good Meta models for responses but bad for the torque ripples parallel coordinates plot: select designs of interest restrict search space restrict some parameters by 20%-30% = reduction of whole search space by 80% airgap magnet edge radius magnet v. offset magnet coverage magnet thickness gapwidth rotor borehole wall thickness hs0 mech. power losses torque ripple amplitude 39

40 2nd sensitivity analysis (limited space 200 DPs) Very good metamodels for responses Medium metamodels for the torque ripples Analyze of the optimization potential Multi-objective approach Correlation analysis 40

41 2nd sensitivity analysis (narrowed space) Correlations equivalent information content 41

42 2nd sensitivity analysis (narrowed space) Correlations 42

43 2nd sensitivity analysis (narrowed space) Correlations 43

44 2nd sensitivity analysis (narrowed space) Correlations 44

45 2nd sensitivity analysis (narrowed space) Correlations no linear correlation for torque ripples Are there nonlinear dependencies? 45

46 2nd sensitivity analysis (narrowed space) Getting more information with coloring 46

47 2nd sensitivity analysis (narrowed space) designs with low torque ripples are scattered 47

48 Optimization 48

49 Optimization problem definition for eta torque or eta P_mech the tradeoff is already well captured in the random sampling optimization = picking 49

50 Optimization problem definition for eta torque or eta P_mech the tradeoff is already well captured in the random sampling optimization = picking but for torque_cv any other goal the nonlinear interactions complicate the situation 50

51 Optimization problem definition options global or local search single- or multi-objective optimization (i.e. SOO versus MOO) on meta model or simulation 51

52 Optimization problem definition options global or local search single- or multi-objective optimization (i.e. SOO versus MOO) on meta model or simulation decisions sensitivity analysis enables problem understanding local search CoP too low for torque ripples optimization on meta model is of limited use MOO requires many more design evaluations than SOO more practical on simulation: SOO search algorithm needs to handle a low number of failed designs ARSM (adaptive response surface method) remaining questions starting point of the search objective function definition 52

53 Optimization: starting point 53

54 Optimization of an electric motor Objective function minimize: (1-eta) + 0.4*torque_cv Constraint: torque

55 Optimization of an electric motor ARSM (adaptive response surface method) objective function and constraint functions treated separately by ARSM good convergence for the objective 55

56 Optimization of an electric motor Reference design 56

57 Optimization of an electric motor parallel coordinates plot select designs of interest restrict search space Best design of the sensitivity 57

58 Optimization of an electric motor parallel coordinates plot select designs of interest restrict search space Best design of optimization (ARSM) 58

59 Optimization of an electric motor reference design 59

60 Optimization of an electric motor sensitivity: best design 60

61 Optimization of an electric motor optimization: final design 61

62 Summary 62

63 Summary - Parameter Identification of a Spring Steel Coupling Mechanical with optislang in Workbench (WB) easy use but only scalar parameters with APDL ASCII files in WB with Signal Processing Sensitivity analysis The reference curve is covered sufficiently by the simulations Parameter bounds seem to be adequate for the calibration Identification of important parameters over the curve (signal) Optimization Direct Optimization using Downhill Simplex Method Import the best design of the sensitivity analysis as start design Very good agreement between simulation and reference is achieved 63

64 Summary - Optimization of an electric motor Coupling Maxwell with optislang via Workbench (node) easy use but only scalar parameters via ASCII files powerful signal processing Sensitivity analysis identification of important parameters and correlations exploring tradeoffs and optimization potentials metamodels: can be used for optimization visualization gain knowledge about nonlinear interactions Optimization ARSM: efficient & robust algorithm for optimization directly on simulation torque ripples reduced by 73%, efficiency increased by 36% play with parametrization and goals fast gain of engineering intuition 64

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