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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
3Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Introduction:
Dynardo & optiSLang
4Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
5Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Software Development
6Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Full integration of optiSLang in Ansys Workbench
• optiSLang modules Sensitivity, Optimization and
Robustness are directly available in ANSYS Workbench
7Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
• optiSLang’s process integration enables the combination of different
parallel or sequential solvers in one workflow
Combined Integrations
8Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Process Integration: Maxwell & Motor-CAD
ANSYS Electronics Desktop Motor-CAD
9Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
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
© Dynardo GmbH
Workflow of Robust Design Optimization with optiSLang
CAE-Data
MeasurementData
Robust Design
10Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Electric Machine Design =
Topology + Allocation + Shape
11Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Electric machine Types and Topologies
12Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Machine Tuning = Space Allocation
reference
design
sensitivity:
best design
13Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Machine Tuning = Space Allocation
reference
design
optimization:
final design
• more back iron
• less magnets
• less saturation
• less torque
• increased efficiency
14Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Allocation and Shaping of Spaces
B-field magnitude
15Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
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
16Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Spaces and Shapes Determine Field Lines
17Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
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
18Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Sensitivity Questions
19Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
What is Sensitivity Analysis?
x
y
x
y
random scatteringno influence
no correlation
detectable correlation
regression simplest form of model
20Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
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?
21Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Process Integration
optiSLang Drives Design Variations
22Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Process Integration: AEDT & optiSLang
A) optiSLang inside Workbench B) Direct integration via text files
C) Large-Scale DSO
23Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Process Integration: AEDT & optiSLang
A) optiSLang inside Workbench B) Direct integration via text files
C) Large-Scale DSOA2) Workbench inside optiSLang
24Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
Process Integration: AEDT & optiSLang
scalars, signals, derivates like mean, stddev, FFT, integration, ...
25Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
Process Integration: AEDT & optiSLang
mean, stddev, FFT, integration, ...
26Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
27Sensitivity questions for electric machines and answers via meta-models
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© Dynardo GmbH
Motor-CAD: my first optiSLang trials
varying 1 parameter varying 2 parameters varying 10 parameters
28Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Sensitivity Analysis
Response Surface-Based Approach
29Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
What is Sensitivity Analysis?
x
y
x
y
random scatteringno influence
no correlation
detectable correlation
regression simplest form of model
30Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
31Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
When and Why Response Surfaces?
• 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
32Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
When and Why Response Surfaces?
• Sensitivity study
• System understanding
• Optimization
• Too many dimensions to imagine
• Multiple responses
• Constraints, goal conflicts
33Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
When and Why Response Surfaces?
• Sensitivity study
• System understanding
• Optimization
• Too many dimensions to imagine
• Multiple responses
• Constraints, goal conflicts
34Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
35Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
36Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
37Sensitivity questions for electric machines and answers via meta-models
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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
38Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
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
39Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
40Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Case Study
Toyota Prius IPM in Motor-CAD
41Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Using Motor-CAD‘s Multiphysics Capabilities
EM model
thermal model
n = 3000 RPMI = 50 Atheta = 60°
42Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Simple 2D Space: Slot Depth vs Tooth Width
43Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
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10D Space: Nonlinear Characteristics Captured
44Sensitivity questions for electric machines and answers via meta-models
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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
45Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
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
46Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
10D Space: Optimisation on MOP
• 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”)
47Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
10D Space: Optimisation on MOP
• using evolutionary algorithm (EA) for global search on 10D MOP
• gradient-based method NLPQL for local optimisation
reference design
NLPQL result
48Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
10D Space: Optimisation on MOP
• using evolutionary algorithm (EA) for global search on 10D MOP
• 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
49Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
Case Study
Toyota Prius IPM in Maxwell
50Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
51Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
9D Space: Optimisation on MOP
• 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%
52Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
9D Space: Optimisation on MOP
• EA histories
53Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
9D Space: Optimisation on MOP
• best designs after NLPQL fine-tuning and validation simulations
54Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
9D Space: Optimisation on MOP
• 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.
55Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© Dynardo GmbH
9D Space: Optimisation on MOP
• 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.
56Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
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Summary
57Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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?
58Sensitivity questions for electric machines and answers via meta-models
4th CADFEM ANSYS Simulation Conference Ireland, October 12-13 2017, Dublin
© 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
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