REDUCTION OF COGGING TORQUE IN PERMANENT MAGNET MACHINEKrithik Kumar Chandrashekar, Nikhil Kulkarni

What is Cogging Torque and Why reduce it The Torque due to the interaction between the

permanent magnets and stator slots of the machine

Also called ‘No current Torque’ In applications such as servo systems and

spindle drives, the pulsating speed that cogging generates can blemish machined surfaces or reduce position accuracy.

It is also one of the causes of noise and vibration of the machine

Mathematically, Tcog=-1/2*ϕg2* dR/dθ

Φg –Flux In Air gapR – Air Gap Reluctance

An overview of Methods for Reduction Odd number of stator coils and even

number of magnets Skewing stator stack or magnets Asymmetrical Magnet Arrangement Optimizing the magnet pole arc or width Auxiliary Groove on the Permanent

Magnet Any Method will also result in a change

of final torque value(‘with current’)

Base Model

Design Parameter Value

Stator Outer Radius 70mm

Stator Inner Radius 29mm

Rotor Inner Diameter 23.5mm

Magnet Height 4 mm

Stator Slot opening 3mm

Pole Shoe depth 2mm

Pole Width 20 mm

Speed 1800 rpm

Torque ~4-5 Nm

Parameters for the Base Model

Shaping The permanent Magnet Rate of Change of Flux Density reduces

resulting in a reduction of cogging torque Due to the significant amount of reduction

in magnetic material, there is also a drastic reduction in overall torque value

%Reduction in Cogging Torque =89%

Lengthening the Air gap

To keep the air gap flux constant, the magnet height must be increased by a like amount to maintain a constant permanence coefficient operating point.

The results are observed for 0.5 mm increase in air gap.

%Reduction in Cogging Torque =25.13%

Auxiliary Groove To keep the high torque density of the

motor, generally, the auxiliary groove on the PM Pole cannot be too deep and the width of the auxiliary groove should be as small as possible.

The width and depth of the permanent magnet is kept at 2 mm each.

Observe the two additional Peaks.

%Reduction in Cogging Torque =16.6%

Skewed Rotor Skewing attempts to make dR/dθ

zero ever each magnet face.

Simulations Done in Static 3D.

%Reduction in Cogging Torque =16.24%

Skewed Rotor And Stator

This was done in opposing directions.

At +/-2 degrees between each segment .

%Reduction in Cogging Torque =16.6%

Slot less stator• Air gap between the slots is zero• Reduces permanent magnet excitation field• Height of permanent magnet needs to be increased %Reduction in Cogging Torque =43.6%

Asymmetrical Permanent magnets

•Placing the magnets asymmetrically by half slot pitch•Reducing the periodicity of magnetic flux•Minimizes additive effect of flux•%Reduction in Cogging Torque =20.7%

Changing number of stator slots

•Reduces effective air gap between the slots• Reducing saliency of stator•%Reduction in Cogging Torque =42.19%

Odd number of stator slots

• Introducing 7 slots on stator• Number of cycles of cogging torque are double• Less angle of skew is required•%Reduction in Cogging Torque =58.34%

Ncog=q*LCM(NS*NM)/NM

Ncog= 3(4 and 12 slots)Ncog =7(7 slots)

Skewing of stator teeth

•Stator is skewed at an angle of 5°•Each segment at 0.5°•Makes dR/dθ nearly equal to zero •Increases ohmic losses •Adds additional component toAverage torque•%Reduction in Cogging Torque =26.66%

Shifting permanent magnets axially

• Magnets spaced 1mm apart•Easy to fabricate •%Reduction in Cogging Torque =34.79%

Comparison Of Some of The Techniques

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1

2

3

4

5

6

Base 1 2 3 4 5

Cogging

Average

Model Number Average Torque (Nm) Cogging Torque(Nm)

Base Model 5.038 0.2053

1. Slotless 5.024 0.1175

2. Bread Loaf 3.8789 0.0223

3.Assymetry 4.9612 0.1628

4.Airgap Lengthening 4.5717 0.1712

5.Auxillary Groove 4.775 0.1066

Questions