Andrew Kasha, PhD Student, Purdue University

Scott Sudhoff, Michael and Katherine Birck Professor of Electrical and Computer Engineering, Purdue University

Multi-Objective Design Optimization of a Surface-Mounted Heterogeneous-Pole Permanent-Magnet (HPM) Machine

SELECT Annual Meeting and Technology Showcase – Logan, Utah – September 27-28, 2016

FLUX DENSITY DISTRIBUTION SHAPING

• Shaping air gap flux can potentially: • Reduce cogging torque • Improve torque density • Improve machine efficiency

• Can be achieved using: • Halbach magnetization • Magnet segmentation • Mixed magnet grades • Physical pole shaping

• The HPM uses mixed grade magnets of disparate shape atop a tiered rotor backiron to achieve FDD shaping

THE SYMMETRIC HPM • The SHPM is a subvariant with:

• Three magnet segments • Constant magnet depth • Identical outer PM

materials • Identical outer magnet

widths • Outer magnets of lower

grade than inner magnet • No rotor backiron tiers • Constant air gap • Symmetric forward and

reverse operation

APPLICATION

• The SHPM can be used to improve torque density of EV propulsion systems

• The topology also has the potential to reduce torque ripple

SHPM ANALYTICAL MODEL

• Improved stator leakage model directly

accounts for flux crossing the slot

• Better predicts the leakage flux

density at the top and bottom of

stator tooth

• Improves the predicted flux density

waveforms in the stator, leading to

better core loss prediction

• Nonlinear model converges even under

saturation and high current density

conditions

• Accounts for DC and AC conduction losses

as well as steel core losses

• Can be used to rapid evaluation of designs

SHPM CROSS-SECTION

MULTI OBJECTIVE OPT. BASED DESIGN

• Choose design variables which fully describe machine

• Establish constraints to ensure performance and viability

• Select metrics for comparing individual designs

• electromagnetic mass

• aggregate loss • Construct fitness function

CASE STUDY

• Constant 2.5 HP • 5:1 speed range • Fixed rotor, stator,

and conductor material

• Aggregate losses evenly weighted at each operating point

• Study repeated 5 times

TOPOLOGY COMPARISON

• Optimization studies for SHPM and SMPM (traditional single surface mounted magnet per pole) were run • SHPM outperforms SMPM in the low mass region • A 10.7% reduction in aggregate losses were

observed for low mass designs

FEA VALIDATION

• Analytical model validated using 2D FEA in Ansys Maxell

• 72 magnetostatic evaluations of machine were performed across a full electrical cycle in 5 degree increments

• Less than 4% error between average torque from FEA and analytical model

• Flux density waveforms in stator show strong agreement between new analytical model and FEA, even at operating points exhibiting high slot leakage

• Maximum average-to-peak torque ripple of 4%

17.86

8.07

3.57

17.29

7.96

3.6

0 2 4 6 8 10 12 14 16 18 20

OP1

OP2

OP3

Torque, Nm

FEM

3.30%

0.63%

-1.11%

FUTURE WORK

• Expansion of analytical model to include generalized HPM

• Development of 3D thermal equivalent circuit (TEC) to predict temperature increase in stator

• Construction of SHPM prototype to validate analytical and TEC models • Redesign SHPM using TEC