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Windings For Permanent Magnet Machines

Yao Duan, R. G. Harley and T. G. HabetlerGeorgia Institute of Technology

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OUTLINE

• Introduction• Overall Design Procedure• Analytical Design Model• Optimization• Comparison • Conclusions

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Introduction

• The use of permanent magnet (PM) machines continues to grow and there’s a need for machines with higher efficiencies and power densities.

• Surface Mount Permanent Magnet Machine (SMPM) is a popular PM machine design due to its simple structure, easy control and good utilization of the PM material

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Distributed and Concentrated Winding

A-A+

C-

C+

B+B-

B+B-

C+

C-

A-A+

Distributed Winding(DW)

Concentrated Winding(CW)

• Advantages of CW Modular Stator Structure Simpler winding Shorter end turns Higher packing factor Lower manufacturing cost

• Disadvantages of CW More harmonics Higher torque ripple Lower winding factor Kw

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Overall design procedureChallenge: developing a

SMPM design model which is accurate in calculating

machine performance, good in computational efficiency,

and suitable for multi-objective optimization

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Surface Mount PM machine design variables and constraints

• Stator design variables Stator core and teeth

• Steel type • Inner diameter, outer diameter, axial

length• Teeth and slot shape

Winding• Winding layer, slot number, coil pitch• Wire size, number of coil turns

• Major Constraints Flux density in stator teeth and cores Slot fill factor Current density

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Surface Mount PM machine design variables and constraints

• Rotor Design Variables Rotor steel core material Magnet material Inner diameter, outer diameter Magnet thickness, magnet pole

coverage Magnetization direction

• Major Rotor Design Constraints Flux density in rotor core Airgap length

Pole coverage

Parallel MagnetizationRadial Magnetization

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Current PM Machine Design Process

• How commercially available machine design software works

• Disadvantages: Repeating process – not efficient and time consuming Large number of input variables: at least 11 for stator, 7 for rotor -- even

more time consuming Complicated trade-off between input variables Difficult to optimize Not suitable for comparison purposes

Manually input design variables

Machine performanceCalculation

Meet specifications and constraints ?

Output

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Proposed Improved Design Process—reduce the number of design variables

• Magnet Design: Permanent magnet material – NdFeB35 Magnet thickness – design variable

** *1

r leakm

r carter

m

B kB g kh

where Bm: average airgap flux densityhm: magnet thicknessBr: the residual flux density. g: the minimum airgap length, 1 mmr: relative recoil permeability. kleak: leakage factor.kcarter: Carter coefficient.

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Proposed Improved Design Process—reduce the number of design variables

• Magnet Design: Minimization of cogging

torque, torque ripple, back emf harmonics by selecting pole coverage and magnetization

Pole coverage – 83% Magnetization direction-

Parallel

75o

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Design of Prototypes

• Maxwell 2D simulation and verification Transient simulation

Concentrated winding Distributed winding

Cogging Toque Peak-to-Peak value 4.0 Nm = 5.0 % of rated 4.3 Nm = 5.38% of rated

Torque ripple Peak-to-Peak value 9.2 Nm = 11.25 % of rated 11.3 Nm = 13.75 % of rated

Rated torque = 79.5 Nm

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Design specifications and constraints

Distributed winding Concentrated winding

Slot number 12, 24, 36 (full pitched) 3, 6 (short pitched)

Number of layers Double Double

Flux density in teeth and back iron

1.45 T (steel_1010) 1.45 T (steel_1010)

Covered wire slot fill factor Around 60% Around 80%

Current density Around 5 A/mm2 Around 5 A/mm2

• Major parameters to be designed: Geometric parameters: Magnet thickness, Stator/Rotor

inner/outer diameter, Tooth width, Tooth length, Yoke thickness Winding configuration: number of winding turns, wire diameter

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Analytical Design Model - 1

• Build a set of equations to link all other major design inputs and constraints –analytical design model With least number of input variables Minimizes Finite Element Verification needed –

high accuracy model

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Analytical design model - 2

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Analytical Design Model - 3

• Motor performance calculation Active motor volume Active motor weight Loss

• Armature copper loss• Core loss• Windage and mechanical loss

Efficiency Torque per Ampere

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Verification of the analytical model -1• Finite Element Analysis used to verify the accuracy of the

analytical model(time consuming)

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Verification of the analytical model - 2

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Particle Swarm Optimization - 1

• The traditional gradient-based optimization cannot be applied Equation solving involved in the machine model Wire size and number of turns are discrete valued

• Particle swarm Computation method, gradient free Effective, fast, simple implementation

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Particle Swarm Optimization - 2

Objective is user defined, multi-objective function• One example with equal attention to weight, volume and efficiency

• Weight: typically in the range of 10 to 100 kg • Volume: typically in the range of 0.0010 to 0.005 m3

• Efficiency: typically in the range of 0 to 1.

*10000 10*(100 *100)obj weight volume eff

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Particle Swarm Optimization - 3

• PSO is an evolutionary computation technique that was developed in 1995 and is based on the behavioral patterns of swarms of bees in a field trying to locate the area with the highest density of flowers.

gbest(t)

Pbest(t)

inertiax(t-1)

v(t)

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Particle Swarm Optimization - 4

• Implementation 6 particles, each particle is a three dimension vector: airgap

diameter, axial length and magnet thickness Position update

x(t-1)

x(t)Vi(t-1)

Vi(t) pg

pi

1 1 , 2 ,* ()* ( ) () * ( )n n best n n best n nv v c rand p x c rand g x

where

: inertia constant

pbest,n: the best position the individual particle has found so far at the n-th iteration

c1: self-acceleration constant

gbest,n: the best position the swarm has found so far at the n-th iteration

c2: social acceleration constant

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Position of each particle

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Output of particles

Iteration No. 0 20 40 60 80 100

gbest Particle No. 6 1 3 2 4 1-6

Weight 37.5 30.3 30.9 31.7 31.4 31.4

10000*Volume 53.3 41.62 40.2 43.0 42.5 42.5

1000*(1-eff) 37.6 51.2 50.2 46.2 46.9 46.9

Efficiency 96.2% 94.9% 95.0%

95.4% 95.3% 95.3%

Objective 128.4 123.1 121.3 121.0 120.9 120.9

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Different Objective functions - 1

• Depending on user’s application requirement, different objective function can be defined, weights can be adjusted

• More motor design indexes can be added to account for more requirement

*10 *10000 10*(100 *100)obj weight volume eff

*10000 5*(100 *100) *10 *10obj weight volume eff WtMagnet TperA

where

WtMagnet: weight of the permanent magnet, Kg

TperA: torque per ampere, Nm/A

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Different Objective Function - 21 *10000 10*(100 *100)obj weight volume eff

2 *10 *10000 10*(100 *100)obj weight volume eff

3 *10000 10*(100 *100) *10 *10obj weight volume eff WtMagnet TperA

From obj1

obj2

Weight 31.4 28.8

10000*Volume

42.5 47.7

1000*(1-eff) 46.9 48.2

Efficiency 95.3% 95.2%

Objective 403.4 384.4

From obj1 obj3

Weight 31.4 31.0

10000*Volume 42.5 43.4

Efficiency 95.3% 95.4%

WtMagnet 0.88 0.92

TperA 3.56 3.58

Objective 94.2 93.8

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Comparison of two winding types

• Objective function

1 *20000 2* (1 )*200 *5 *5obj output volume Weight Eff

WtMagnet TperA

2 *10000 (1 )*1000 *5 *20obj output volume Weight Eff

WtMagnet TperA

obj 1 pays more attention to the weight and volume obj 2 pays more attention to the efficiency and torque

per ampere

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Comparison of optimization Result

• CW designs have smaller weight and volume, mainly due to higher packing factor

• CW designs have slightly worse efficiency than DW, mainly due to short end winding

Objective Function 1 Objective Function 2

CW DW CW DW

Des. 1 Des. 2 Des. 1 Des. 2 Des. 1 Des. 2 Des. 1 Des. 2

Weight / kg 28.5 27.9 30.0 29.4 32.12 32.39 32.02 33.23Volume / m3 0.0031 0.0032 0.003

80.0037 0.0043 0.0041 0.004

80.0047

Efficiency 93.3% 93.3% 94.7% 93.7% 95.1% 94.9% 95.9% 95.9%Torque/Ampere (Nm/Arms)

2.79 2.79 3.54 2.79 3.79 3.74 3.73 3.75

Magnet Weight / kg

0.685 0.780 0.95 0.600 1.48 1.26 1.12 1.04

Obj. Function 122.5 123.2 134.3 134.4 56.38 56.42 52.39 52.17

Conclusion

• Concentrated winding has modular structure, simpler winding and shorter end turns, which lead to lower manufacturing cost

• Before optimization, the torque ripples and harmonics can be minimized by careful design of the magnet pole coverage, magnetization and slot opening

• Analytical design models have been developed for both winding type machines and PSO based multi-objective optimization is applied. This tool, together with user defined objective functions, can be used for analysis and comparison of both winding type machines and different applications

• Optimized result shows CW design have superior performance than convention DW in terms of weight, volume, and have comparable efficiencies.

Acknowledgement

• Financial support for this work from the Grainger Center for Electric Machinery and Electromechanics, at the University of Illinois, Urbana Champaign, is gratefully acknowledged.

Thanks!

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