Sensitivity analysis and optimisation of an electric motor ... · 1 Sensitivity analysis and optimisation of an electric motor with ANSYS Maxwell and optiSLang Stephanie Kunath, Markus

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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



© 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



© Dynardo GmbH

Full integration of optiSLang in ANSYS Workbench

• optiSLang modules Sensitivity, Optimisation and

Robustness are directly available in ANSYS Workbench



2ndMultidisciplinary

Optimisation

Adaptive Response Surface, Evolutionary

Algorithm, Pareto Optimization

Robust Design Optimisation with optiSLang



© Dynardo GmbH

The motor simulation



© 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



© 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



© 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



© 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



© Dynardo GmbH

airgap

gapwidth

magnet_thickness

wall_thickness

HS0

Parametrisation



© Dynardo GmbH

Sensitivity analysis



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



• 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



© 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



© 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



© Dynardo GmbH

Metamodelling: Response Surfaces

magnitude oscillation magnitude oscillation



© Dynardo GmbH

Metamodelling: Response Surfaces

magnitude oscillation



© Dynardo GmbH

Sensitivity analysis: understanding relations

• P_mech & torque contain

the same information



© Dynardo GmbH




• P_mech follows P_el until

losses increase



© Dynardo GmbH





losses increase

• eta decreases as losses

increase



© Dynardo GmbH





losses increase

• eta decreases as losses

increase

CoP values high because these

relationships get fully captured by the

metamodel



© Dynardo GmbH

There is no simple relationship between the torque ripples and the other

output variables.




© 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



© Dynardo GmbH

Optimisation



© 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



© 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



© Dynardo GmbH

Single-Objective Local Optimisation

Choosing the starting point

• We want to maximise eta and minimise torque_cv while torque > 0.5



© 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



© 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%



© Dynardo GmbH

Optimisation result

parallel coordinates plot

• select designs of interest

• restrict search space

sensitivity: best design

eta: + 28%

torque_cv: - 69%



© Dynardo GmbH

Optimisation result

parallel coordinates plot

• select designs of interest

• restrict search space

optimization: final design

eta: + 31%

torque_cv: - 74%



© Dynardo GmbH

Optimisation result

reference

design

sensitivity:

best design



© Dynardo GmbH

Optimisation result

reference

design

optimisation:

final design



© Dynardo GmbH

Summary



© 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

Documents

Sensitivity analysis and optimisation of an electric motor ... · 1 Sensitivity analysis and optimisation of an electric motor with ANSYS Maxwell and optiSLang Stephanie Kunath, Markus