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					Windings For Permanent Magnet
           Machines

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




                                                 1
OUTLINE

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




                             2
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




                                                       3
 Distributed and Concentrated Winding
                                  Distributed Winding(DW)
• Advantages of CW
     Modular Stator Structure
     Simpler winding
     Shorter end turns
     Higher packing factor
     Lower manufacturing cost
                                 Concentrated Winding(CW)

• Disadvantages of CW                  B+A-
                                  B-          A+
     More harmonics             C+            C-
     Higher torque ripple
                                 C-            C+
     Lower winding factor Kw    A+           B-
                                       A-B+



                                                            4
  Overall design procedure
                         Rated design
                         specifications:                             Challenge: developing a
                            15 KW
                           1800 rpm
                            60 Hz
                                                                   SMPM design model which is
                                                                       accurate in calculating
                                                                   machine performance, good
Concentrated Winding                       Distributed Winding      in computational efficiency,
                                                                       and suitable for multi-
                                                                       objective optimization




     Optimization                              Optimization




      Weight                                     Weight
      Volume                                     Volume
      Harmonics         Comparison               Harmonics
   Torque ripples                             Torque ripples
     Efficiency                                 Efficiency
Inverter requirements                      Inverter requirements

                                                                                              5
   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


                                                     6
Surface Mount PM machine
design variables and constraints
• Rotor Design Variables                      Pole
      Rotor steel core material            coverage
      Magnet material
      Inner diameter, outer diameter
      Magnet thickness, magnet pole
       coverage
      Magnetization direction
• Major Rotor Design Constraints
    Flux density in rotor core
    Airgap length



 Radial Magnetization             Parallel Magnetization




                                                           7
Current PM Machine Design Process
• How commercially available machine design software works


       Manually input               Machine performance
                                        Calculation                Output
       design variables



                           Meet specifications and constraints ?
• 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


                                                                                 8
        Proposed Improved Design Process—
        reduce the number of design variables

•        Magnet Design:
     Permanent magnet material – NdFeB35
     Magnet thickness – design variable
                    Br * kleak
          Bm 
                    * g * kcarter
                 1 r
                         hm

        where
        Bm: average airgap flux density
        hm: magnet thickness
        Br:      the residual flux density.
        g:       the minimum airgap length, 1 mm
        r:      relative recoil permeability.
        kleak: leakage factor.
        kcarter: Carter coefficient.
                                                   9
      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




                                              10
   Design of Prototypes
   •   Maxwell 2D simulation and verification
           Transient simulation                               Rated torque = 79.5 Nm




                                   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



                                                                                             11
  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       1.45 T (steel_1010)         1.45 T (steel_1010)
back iron
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


                                                                                   12
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




                                                        13
      Analytical design model - 2
                                      DiaSGap
                                       Length
                                     ThichMag                   Inductance


                                                                                        DiaSYoke
               Tooth Width
                                     AirGap Flux
              Stator and Rotor                                                          DiaSGap
                                      Density
              Yoke Thickness

                                                   Number of
                                                   turns per                            DiaSRGap
                                                    phase
                                                                              hm        DiaRYoke
                                      Back EMF


                            Output
                            Power


                                       Current                                               Bs0

                                                                                                   Hs0
   Current                                                                         Tw              Hs1
   Desnity                                                                                   Bs1
                                                                                                   Hs2
Slot Fill Factor
                                                                                             Bs2
                                                                                        Rs

                                                     Design
                                                   Parameters




                                         Loss       Weigth           Volume




                                                                                                         14
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


                                         15
Verification of the analytical
model -1
• Finite Element Analysis used to verify the accuracy of the
   analytical model(time consuming)




                                                               16
Verification of the analytical
model - 2




                                 17
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




                                                          18
Particle Swarm Optimization - 2
     Objective is user defined, multi-objective function
       •   One example with equal attention to weight, volume and efficiency

           obj  weight  volume *10000  10*(100  eff *100)
       •   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.




                                                                               19
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.

                              x(t-1)
                                          inertia
                                              gbest(t)

                                            v(t)
                             Pbest(t)



                                                             20
      Particle Swarm Optimization - 4

      •          Implementation
               6 particles, each particle is a three dimension vector: airgap
                diameter, axial length and magnet thickness Vi(t-1)                                 x(t)

               Position update                                                        Vi(t)
                                                                                                       pg
vn   * vn1  c1rand () *( pbest ,n  xn )  c2 rand () *( gbest ,n  xn )
                                                                                               pi

                                                                   x(t-1)
      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
                                                                                                       21
Position of each particle




                            22
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




                                                                     23
Different Objective functions - 1

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

       obj  weight *10  volume *10000  10*(100  eff *100)

• More motor design indexes can be added to account
  for more requirement
obj  weight  volume *10000  5*(100  eff *100)  WtMagnet *10  TperA *10
    where
             WtMagnet: weight of the permanent magnet, Kg
             TperA: torque per ampere, Nm/A
                                                                               24
   Different Objective Function - 2
             obj1  weight  volume *10000  10*(100  eff *100)
             obj 2  weight *10  volume *10000  10*(100  eff *100)
             obj3  weight  volume *10000  10*(100  eff *100)  WtMagnet *10  TperA *10
                  From     obj2                            From obj1    obj3
                  obj1
                                         Weight            31.4         31.0
Weight            31.4     28.8

                                         10000*Volume      42.5         43.4
10000*Volum       42.5     47.7
e                                        Efficiency        95.3%        95.4%
1000*(1-eff)      46.9     48.2
                                         WtMagnet          0.88         0.92
Efficiency        95.3% 95.2%
                                         TperA             3.56         3.58
Objective         403.4    384.4
                                         Objective         94.2         93.8



                                                                                         25
Comparison of two winding types

• Objective function
       obj1   output  volume * 20000  2*Weight  (1  Eff ) * 200
                        WtMagnet *5  TperA *5
      obj 2   output  volume *10000  Weight  (1  Eff ) *1000
                        WtMagnet *5  TperA * 20

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




                                                                      26
    Comparison of optimization Result
                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    33.23
Volume / m3     0.0031    0.0032       0.003    0.0037   0.0043 0.0041          0.004    0.0047
                                       8                                        8
Efficiency      93.3%     93.3%        94.7%    93.7%    95.1%    94.9%         95.9%    95.9%
Torque/Amper    2.79      2.79         3.54     2.79     3.79     3.74          3.73     3.75
e (Nm/Arms)
Magnet Weight   0.685     0.780        0.95     0.600    1.48     1.26          1.12     1.04
/ kg
Obj. Function   122.5     123.2        134.3    134.4    56.38    56.42         52.39    52.17

    •   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

                                                                                                  27
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.


                                                                      28
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.




                                                  29
      Thanks!


Questions and Answers




                        30

				
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posted:11/25/2011
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