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1
Sensitivity analysis and
optimisation of an electric motor
with ANSYS Maxwell and
optiSLang
Stephanie Kunath,
Markus Stokmaier,
Michael Schimmelpfennig,
Thomas Most
Dynardo GmbH
2Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Introduction:
Dynardo & optiSLang
3Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Dynardo
• Founded: 2001 (Will, Bucher,
CADFEM International)
• More than 50 employees,
offices at Weimar and Vienna
• Leading technology companies
Daimler, Bosch, E.ON, Nokia,
Siemens, BMW are supported
Software Development
Dynardo is engineering specialist for
CAE-based sensitivity analysis,
optimisation, robustness evaluation
and robust design optimisation
• Mechanical engineering
• Civil engineering &
Geomechanics
• Automotive industry
• Consumer goods industry
• Power generation
CAE-Consulting
4Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Full integration of optiSLang in ANSYS Workbench
• optiSLang modules Sensitivity, Optimisation and
Robustness are directly available in ANSYS Workbench
5Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
2ndMultidisciplinary
Optimisation
Adaptive Response Surface, Evolutionary
Algorithm, Pareto Optimization
Robust Design Optimisation with optiSLang
6Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
The motor simulation
7Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Commutator motor: working principle
What creates the driving torque?
https://commons.wikimedia.org/ wiki/File:Kommutator_animiert.gif
B-field from magnets
B-field from coils
Maxwell 2D model setup by Lester Pena-Gomez, CADFEM Germany
8Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
The model: 2D commutator motor FE-simulation
Motor characteristics
• Commutator principle
• 12 lamellae & coils
• One current branch wwww
U0 = 12 V
• Fixed outer diameter www
OD = 78 mm
Maxwell 2D model setup by Lester Pena-Gomez, CADFEM Germany
Desired output quantities
• Torque
• Losses
• Efficiency
• Measures of torque ripples
9Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
The model: 2D commutator motor FE-simulation
Desired output quantities
• Torque
• Losses
• Efficiency
• Measures of torque ripples
Data extraction:
• Key properties extracted
from last cycle
• Access to output variables
via ANSYS Workbench
Parameter Set
• Access to signals via ASCII
files
CV =standard deviation
mean value
10Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Model parametrisation magnet_coverage:
magnet coverage in percent
rotor_borehole:
diameter of motor axis
magnet_voffset:
for widening of air gap
magnet_rounding: as
fraction of magnet thickness
Parametrisation
11Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
airgap
gapwidth
magnet_thickness
wall_thickness
HS0
Parametrisation
12Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity analysis
13Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
Solver
SensitivityEvaluation
• Correlations• Reduced regression• Variance-based
Regression Methods
• 1D regression• nD polynomials• Sophisticated
metamodels
Design of Experiments
• Deterministic• (Quasi)Random
© Dynardo GmbH
Sensitivity Analysis Flowchart
1. Design of Experiments generates a specific number of designs, which are all evaluated by the solver
2. Regression methods approximate the solver responses to understand and to assess its behaviour
3. The variable influence is quantified using the approximation functions
14Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
• Approximation of solver output by fast surrogate model
• Best variable subspace: Reduction of input space
• Best metamodel: Determination of optimal approximation model (polynomials, MLS, …)
• Estimation of prediction qualityby Coefficient of Prognosis (CoP)
DoE
Solver
MOP
Metamodel of Optimal Prognosis (MOP)
© Dynardo GmbH
15Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity study
• Advanced Latin Hypercube Sampling with 9 inputs
• Outputs:
• Power losses P_loss
• Mechanical power P_mech
• Electrical power P_el
• Efficiency eta = Pout/Pin = P_mech/P_el
• torque
• Variation of torque ripples: torque_cv = stddev/ mean
• Normed sum of amplitudes of torque: torque_amps_sum_normed
16Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Metamodelling: CoP matrix
• Very well explainable: eta, P_loss, P_mech, P_el, torque www CoP high
• Less well explainable: size of torque ripples www CoP lower
• 1st insight: 6 out of 9 parameters identified as highly influential
• 2nd insight: there are two subgroups with high and lower total CoP
17Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Metamodelling: Response Surfaces
magnitude oscillation magnitude oscillation
18Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Metamodelling: Response Surfaces
magnitude oscillation
19Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity analysis: understanding relations
• P_mech & torque contain
the same information
20Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity analysis: understanding relations
• P_mech & torque contain
the same information
• P_mech follows P_el until
losses increase
21Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity analysis: understanding relations
• P_mech & torque contain
the same information
• P_mech follows P_el until
losses increase
• eta decreases as losses
increase
22Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Sensitivity analysis: understanding relations
• P_mech & torque contain
the same information
• P_mech follows P_el until
losses increase
• eta decreases as losses
increase
CoP values high because these
relationships get fully captured by the
metamodel
23Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
There is no simple relationship between the torque ripples and the other
output variables.
Sensitivity analysis: understanding relations
24Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Metamodelling: CoP matrix
• Very well explainable: eta, P_loss, P_mech, P_el, torque www CoP high
• Less well explainable: size of torque ripples www CoP lower
High CoP values guideline for parameter reduction
Here: torque ripples are highly nonlinear
influences only partially captured
continuing optimisation with all 9 parameters
25Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Optimisation
26Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
For
or
• the tradeoff is already well
captured in the random sampling,
• little information gain can be
expected from further Pareto-
optimisation
Optimisation problem definition
eta torque
eta P_mech
27Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
For
or
• the tradeoff is already well
captured in the random sampling,
• little information gain can be
expected from further Pareto-
optimisation
However, for
torque_cv other goals
there remains optimisation potential.
Optimisation problem definition
eta torque
eta P_mech
28Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Single-Objective Local Optimisation
Choosing the starting point
• We want to maximise eta and minimise torque_cv while torque > 0.5
29Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
optiSLang Optimisation Algorithms
Gradient-based Methods
• Most efficient method if gradients are accurate enough
• Consider its restrictions like local optima, only continuous variables,and noise
Adaptive Response Surface Method
• Attractive method for a small set of continuous variables (<20)
• Adaptive RSM with default settings is the method of choice
Nature-inspired Optimisation
• GA/EA/PSO imitate mechanisms of nature to improve individuals
• Method of choice if gradient or ARSM fails
• Very robust against numerical noise, non-linearity, number of variables,…
Start
30Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Single-Objective Local Optimisation
Minimise
(1-eta) + 0.4*torque_cv
Constraint:
torque ≥ 0.5
Algorithm:
Adaptive Response
Surface Method (ARSM)
eta: + 2.6%
torque_cv: - 14%
31Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Optimisation result
parallel coordinates plot
• select designs of interest
• restrict search space
sensitivity: best design
eta: + 28%
torque_cv: - 69%
32Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Optimisation result
parallel coordinates plot
• select designs of interest
• restrict search space
optimization: final design
eta: + 31%
torque_cv: - 74%
33Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Optimisation result
reference
design
sensitivity:
best design
34Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Optimisation result
reference
design
optimisation:
final design
35Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Summary
36Sensitivity analysis and optimisation of an electric motor
1st CADFEM ANSYS Simulation Conference, Nov. 2016, Oxford
© Dynardo GmbH
Summary
Sensitivity analysis
• Identification of important parameters and correlations
• Exploring tradeoffs and optimisation potentials
• Metamodels:
can be used for optimisation
visualisation gain knowledge about nonlinear interactions
Optimisation
• ARSM: efficient & robust algorithm for optimisation directly on simulation
• Torque ripples reduced by 74%, efficiency increased by 31%
• Play with parametrisation and goals
fast gain of engineering intuition