Sensitivity questions for electric machines and answers ......Sensitivity questions for electric machines and answers via meta-models 9 4th CADFEM ANSYS Simulation Conference Ireland,

1

Sensitivity questions for electric

machines and answers via meta-

models

Markus Stokmaier (Dynardo GmbH),

Bernd Büttner (Dynardo GmbH),

Unai SanAndres (Motor Design Ltd.)

Dublin, October 2017

2Sensitivity questions for electric machines and answers via meta-models

4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin

© Dynardo GmbH

Outline

Intro: Dynardo & optiSLang

Electric machine design =

• topology (machine type & layout)

• resource/space allocation (householding)

• shape tuning

Sensitivity analysis with optiSLang

• design variation

• response surface-based analysis

Motor-CAD & ANSYS Maxwell & optiSLang

• integration, sensitivity, optimization, goal conflicts & trade-offs

exemplary case studies based on Prius IPM machine

• enabling to deal with degrees of freedom

Summary



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Introduction:

Dynardo & optiSLang



© Dynardo GmbH

Dynardo

• Founded: 2001 (Will, Bucher,

CADFEM International)

• More than 60 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,

optimization, robustness evaluation

and robust design optimization

• Mechanical engineering

• Civil engineering &

Geomechanics

• Automotive industry

• Consumer goods industry

• Power generation

CAE-Consulting



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Software Development



© Dynardo GmbH

Full integration of optiSLang in Ansys Workbench

• optiSLang modules Sensitivity, Optimization and

Robustness are directly available in ANSYS Workbench



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• optiSLang’s process integration enables the combination of different

parallel or sequential solvers in one workflow

Combined Integrations



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Process Integration: Maxwell & Motor-CAD

ANSYS Electronics Desktop Motor-CAD



Model CalibrationIdentify important model parameters for the best fit between simulation

and measurement

Design Improvement

Optimize design performance

Design QualityEnsure design robustness

and reliability

Design UnderstandingInvestigate parameter sensitivities,

reduce complexity and generate best possible meta-models

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Workflow of Robust Design Optimization with optiSLang

CAE-Data

MeasurementData

Robust Design



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Electric Machine Design =

Topology + Allocation + Shape



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Electric machine Types and Topologies



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Machine Tuning = Space Allocation

reference

design

sensitivity:

best design



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Machine Tuning = Space Allocation

reference

design

optimization:

final design

• more back iron

• less magnets

• less saturation

• less torque

• increased efficiency



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Allocation and Shaping of Spaces

B-field magnitude



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Allocation and Shaping of Spaces

Title

• a

• b

• c

N

N

S

S

S

N

N S

shortcut paths for field lines

over the bridge field lost

for torque generation

only field lines going

around the coil windings

can be leveraged to

create torque

this plot shows the situation with

zero current we see only the

field lines created by the magnets

this is why the iron

collects and bundles

the field lines

enclosed surface= work performed

= energy dissipated into heat



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Spaces and Shapes Determine Field Lines



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Electric Machine Design Summary

Topology

• Which type of machine? Which layout?

Allocating available space

• space for magnets as source of magnetic field

• space for winding to decrease ohmic losses (coils also generate field)

• space for iron (electrical steel sheet) as “bearer of field lines”

• space usage rotor vs stator

• air pockets: mostly useless, except for intended bottlenecks

Tuning shape details

• control B-field to increase torque/power/efficiency performance

• control B-field noise – vibration – harshness (NVH)

Not to forget

• 3rd dimension, working points, electric control, thermal behaviour

• motor usage and transient drive cycles



© Dynardo GmbH

Sensitivity Questions



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What is Sensitivity Analysis?

x

y

x

y

random scatteringno influence

no correlation

detectable correlation

regression simplest form of model



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Sensitivity questions

• Is the system sensitive to a given parameter?

• How does the dependency look like? Nonlinearity?

• Are parameters interacting? I.e. coupled effects?

• What’s the effort to get to know the effects of many parameters?

• How to deal with information about dozens of parameters?



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Process Integration

optiSLang Drives Design Variations



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Process Integration: AEDT & optiSLang

A) optiSLang inside Workbench B) Direct integration via text files

C) Large-Scale DSO



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A) optiSLang inside Workbench B) Direct integration via text files

C) Large-Scale DSOA2) Workbench inside optiSLang



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Responses can be: scalars, signals, matrices, ...

• computations in AEDT

• computations in optiSLang

RPM, current, load angle, ...

or

slot depth, tooth width, magnet width & angle, ...

Parameters

Responses


scalars, signals, derivates like mean, stddev, FFT, integration, ...



© Dynardo GmbH

Responses can be: scalars, signals, matrices, ...

• computations in AEDT

• computations in optiSLang

RPM, current, load angle, ...

or

slot depth, tooth width, magnet width & angle, ...

Parameters

Responses


mean, stddev, FFT, integration, ...



© Dynardo GmbH

Process Integration: Motor-CAD & optiSLang

A) custom integration

“convencience”

B) self-made Python script

“flexibility”

There are two ways of driving Motor-CAD:

(a) ActiveX and (b) command line call

ActiveX-driven via Python



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Motor-CAD: my first optiSLang trials

varying 1 parameter varying 2 parameters varying 10 parameters



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Sensitivity Analysis

Response Surface-Based Approach



© Dynardo GmbH

What is Sensitivity Analysis?

x

y

x

y

random scatteringno influence

no correlation

detectable correlation

regression simplest form of model



© Dynardo GmbH

When and Why Response Surfaces?

Go from samples to functional relationship

• 1D curve fit

• 2D response surface

• nD response surface

speed

fuel consumption



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• Sensitivity study

• System understanding

• Optimization

• 1D or 2D

• Function with no noise

• Just one response, no conflict

In that case:

interpolation = best fit = all there is to know

optimization = pick best design

Model verification: at a glance



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• Optimization

• Too many dimensions to imagine

• Multiple responses

• Constraints, goal conflicts



© Dynardo GmbH




• Optimization

• Too many dimensions to imagine

• Multiple responses

• Constraints, goal conflicts



© Dynardo GmbH

Validity of Response Surfaces?

speed

fuel consumption

The necessity of expert knowledge

• 1D spline fit is often sufficient and validity obvious at a glance

• nD approach may be efficient & safe if

• expert knowledge used for choosing the right meta-model approach

• expert thinking and investigation involved in model validation



© Dynardo GmbH

Validity of Response Surfaces?

The necessity of expert knowledge

• 1D spline fit is often sufficient and validity obvious at a glance

• nD approach may be efficient & safe if

• expert knowledge used for choosing the right meta-model approach

• expert thinking and investigation involved in model validation

optiSLang avoid the expert knowledge headache

• General purpose meta-modelling

• Validity estimate at a glance (meta-model postprocessing)

• More dimensions meta-model machine stays efficient

• More dimensions still no expert knowledge required

How is it achieved?

• efficient statistical analysis (hidden from user (if desired))

• Measure ratio of explained vs unexplained response variation

• Measure forecast quality instead of fit quality Coefficient of Prognosis



© Dynardo GmbH

optiSLang Sensitivity Methods

Correlations Metamodel of Optimal Prognosis

• One-dimensional • Multi-dimensional

• Single variable • Automatic identification ofimportant variables

• Linear & quadratic • Nonlinear (continuous)

• No interactions • Nonlinear interactions

• No error measure • Prognosis quality as error measure



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Dynardo‘s MOP/CoP Workflow

investigate response by

response based on ALHS sampling

filter variables by importance

generate different and competing

meta-models

calculate forecast quality

using CoP

The winner is …

MOP



Metamodel of Optimal Prognosis (MOP)

• Objective measure of prognosis quality

• Determination of relevant parameter subspace

• Determination of optimal approximation model

• Approximation of solver output by fast

surrogate model without over-fitting

• Evaluation of variable sensitivities

© Dynardo GmbH



© Dynardo GmbH

MOPs of Torque and Eta of an Electric Motor

• Design points with high efficiency have low torque

• MOP = quintessential information about system behavior and physics

• Use case: explore and compare feasible designs; explore goal conflicts



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Case Study

Toyota Prius IPM in Motor-CAD



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Using Motor-CAD‘s Multiphysics Capabilities

EM model

thermal model

n = 3000 RPMI = 50 Atheta = 60°



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Simple 2D Space: Slot Depth vs Tooth Width



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10D Space: Nonlinear Characteristics Captured



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10D Space: Nonlinear Characteristics Captured

Postprocessing benefits:

• check plausibility

• investigate causalities

• quantify trade-offs

after inspection

• e.g. explore design space with optimisation algorithms



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10D Space: Optimisation on MOP

Multiphysics

• electromagnetic model

• thermal steady state

goal is to minimise the winding temperature

thermal model property

constraints with relation to torque and losses

EM model properties



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• using evolutionary algorithm (EA) for global search on 10D MOP

red colour = constraints violated

if there are several harsh constraints then it is not trivial to find constraint-fulfilling designs

best constraint-fulfilling design(a parameter combination found

by “survival of the fittest”)



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• gradient-based method NLPQL for local optimisation

reference design

NLPQL result



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• gradient-based method NLPQL for local optimisation

NLPQL result

interpretation / learning / next steps:

• we understand why the bridge thickness wants to be minimised need to simulate mechanics

• other parameters hitting the limits may trigger us to scan the space beyond

• not only one single working point

• What would be the outcome under different conditions, i.e. other constraints or constraint values?

That’s easy now: just copy & paste

& modify the optimization workflow



© Dynardo GmbH

Case Study

Toyota Prius IPM in Maxwell



© Dynardo GmbH

Maxwell Model of IPM machine

• 1/8th of whole motor

• n = 3000 RPM, I = 50 A, theta = 40°

• 9 varied parameters: tooth width, slot depth,

magnet width/thickness, ...

• eta = P_mech / (P_mech+P_losses)

under load no current



© Dynardo GmbH


• again: global EA and local NLPQL search

• three different single-objective optimisation runs

efficiency

THD of back EMF induced voltage

measure of torque ripples

cogging amplitude

torque

magnet cross section

limits inferred from reference case

i.e. not willing to let the magnets grow more than 10%



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• EA histories



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• best designs after NLPQL fine-tuning and validation simulations



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• best designs after EA+NLPQL optimisation on MOP

response values based on validation simulations

criterion reference best 1 best 2 best 3

eta 98.15 98.23 98.23 98.13

bEMF-THD 4.83e4 4.77e4 4.72e-4 4.66e4

T ripples 4.19e-2 4.31e-2 4.09e-2 2.91e-2

cogging amp. 0.269 0.128 0.196 0.330

T 68.70 73.79 77.51 69.79

magnet CS 57.6 56.39 50.144 52.88

Note that the optimization challenges were chosen for didactic purposes and have only exemplary character. Most importantly the optimizations were conducted considering only one specific working point, a driving point at low torque within the steady-state envelope and far away from peak torque conditions. Realistically, the optimization of a car motor involves at least multiple working points if not whole drive cycles. The real-world challenge would also involve the mechanical aspects, i.e. stability against centrifugal forces and NVH properties.



© Dynardo GmbH


• One more question:

Is there a goal conflict between torque and torque ripples?

• Answer via Pareto-EA on MOP: Yes. This is how it looks like.

• Next what-if: shift of the Pareto front when varying constraint thresholds.



© Dynardo GmbH

Summary



© Dynardo GmbH

Summary I/II

Sensitivity analysis with the response surface approach and MOPs

• identification of important parameters and correlations

• capturing nonlinearity, capturing parameter interaction

• CoP = objective and conservative quality measure for a meta-model

Motor-CAD & ANSYS Maxwell as part of optiSLang workflows

• automation, easy management, templates, wizard-based derivatives

• postprocessing: visualisation, main infos at a glance, investigation when

needed

• graphical programming: create any kind of workflow and roll it out

Answering what-if questions on the meta-model, e.g.

• What’s the best design under the condition of constraint settings A, B, C?

• Pareto: what’s the trade-off under conditions A, B, C?

• multiple working points: what’s the trade-off?

• multi-physics: trade-offs?



© Dynardo GmbH

Summary II/II

Motor-CAD

• slim, fast, analytical models, thermal system simulation, FEA

• takes into account some 3D effects

• lots of predefined machine types and layout options, fully parametrised

• automise it: (a) command line call, (b) ActiveX via Matlab, Python, etc.

ANSYS Maxwell (part of ANSYS Electronics Desktop)

• powerful 2D & 3D FEM solver

• philosophy of physics-based automatic mesh refinement and convergence

• straightforward multi-physics in interaction with other ANSYS solvers

• automise/parallelise it: WB, Python, Optimetrics DSO, Large-Scale DSO, ...

Power up with optiSLang

• enables to deal with the design degrees of freedom you have

Documents

Sensitivity questions for electric machines and answers ......Sensitivity questions for electric machines and answers via meta-models 9 4th CADFEM ANSYS Simulation Conference Ireland,