THE 11th INTERNATIONAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTRICAL ENGINEERING

March 28-30, 2019

Bucharest, Romania

Experimental Results Regarding Cogging Torque

Reduction for the Permanent Magnet Synchronous
Motors PMSM
Mihail POPESCU1, Emil TUDOR1, Sergiu NICOLAIE1,
Cristinel Ioan ILIE1, Liviu POPOVICI1, Constantin DUMITRU1
1
INCDIE ICPE-CA Bucharest, Romania
mihail.popescu@icpe-ca.ro, emil.tudor@icpe-ca.ro, sergiu.nicolaie@icpe-ca.ro,
cristinel.ilie@icpe-ca.ro, liviu.popovici@icpe-ca.ro, constantin.dumitru@icpe-ca.ro

Abstract- The goal of this paper is to present some of the methods

for reducing the cogging torque present in permanent magnet II METHODS FOR COGGING TORQUE REDUCTION
synchronous motors PMSM. Some of the methods we analyzed: A. Profile optimization of the magnetic pole
optimal selection of the stator`s pitch number and the poles
number, the optimization of the geometry of the rotor’s pole and
For a PMSM with surface permanent magnet (SPM), the
the skewing of the stator or skewing of the magnetic pole. These optimization can be done by shaping the geometry of the
methods were applied in the design of the 10kW synchronous magnet itself.
generator.
Keywords: cogging torque reduction; stator skewing; PMSM;
surface mounted magnets; design optimization;
I INTRODUCTION
PMSM is a type of synchronous motor that uses permanent
magnets (PM) to produce the necessary rotor flux excitation.
The advantages of PMSM compared to induction motors or
wound rotor synchronous motor are:
- A smaller motor size; Fig. 1. The variation of the radius of the magnet: 0% (a), 25% (b), 50% (c),
- By using PM excitation, the DC supply is no longer 75% (d), 100% (e)
needed;
Doing so, the air gap of the PMSM is variable. In [2], such
- No need for brushes and slip rings;
an experiment is presented, the result being a 50% reduction in
- Better cooling;
cogging torque.
- Low torque ripple;
Modifying the radius of the permanent magnets implies
- The overall efficiency is increased by reducing the
technological difficulties which translates into higher
electrical and the mechanical losses.
manufacturing costs [3].
The cogging torque (CG) of PM motors, (known also as the
parasitic torque) is a specific parameter to these types of
motors and it is a result of the interaction of the permanent 1.8
1.6
magnets with the stator magnetic core. The cogging torque is 1.4
1.2
CA [Nm]

an unwanted phenomenon for the motor’s operational 1

characteristics, especially at low speed, where it affects the 0.8
0.6
starting ability and generates noise and mechanical vibration. 0.4
0.2
At high speed, the cogging torque is filtered by the rotor’s 0
inertial moment. 0 25 50 75 100
The main methods for reducing the cogging torque are: RC [%]
- Profile optimization of the magnetic pole;
- Optimal selection of the poles number and the teeth Fig. 2. Cogging torque for different radius of the pole for the studied motor
number;
- Skewing of the stator stack or skewing of the rotor pole; B. Optimal selection of the poles number and the teeth number
- Increasing of the radial air-gap between the stator and As presented in [4] and in [5], the selection of the design
the rotor [1]. parameters of the PMSM is very important for the resulting
In fact, for a PMSM, there is a direct relation between the magnitude of the cogging torque. A superficial selection of the
stator pitch and the cogging torque and only a slot less stator ratio between the number of the stator teeth and the poles
doesn’t have cogging torque. number can induce a cogging torque two times greater than the
result of a more inspired selection.

978-1-7281-0101-9/19/$31.00 ©2019 IEEE

 The general formula of the cogging torque is [4]: 1.2
1
=∑ , , ,… (1) 0.8

CG [u.r.]
0.6
Where the Nc (the fundamental’s order) is the smallest 0.4
common multiple of Qs - the number of stator slots and 2p - the 0.2
number of poles, θ represents the mechanical angle between
0
the stator and the rotor, Ksk is the skewing factor (axial) 0 20 40 60 80 100 120
between the stator and the rotor. skewing [%]
In order to find the optimal value of Qs and of 2p, the factor
CT is defined to classify the combination between the number
of the stator slots and the number of poles. Lower values of this Fig. 3. Variation of cogging torque with skewing factor
factor means smaller cogging torque values [4].
III EXPERIMENTAL MODEL OF PMSM WITH REDUCED COGGING
= (2) TORQUE

Based on this research we designed a special prototype of a

As an example, we consider the case of a motor with 2p=2
wind generator with a PMSM with surface permanent magnets
poles, where, depending on the number of stator slots, we have
placed on the rotor.
CT=1 for Qs being odd number and CT=2 for Qs being even
number. First conclusion: for PMSM with even number of
stator slots the cogging torque is double the value of a PMSM
with odd number of stator slots.
As described in [5], the results in Table I show how different
values for Qs and 2p produce different values for CT:
TABLE I
THE COMPARISON OF COGGING TORQUE FOR DIFFERENT CONFIGURATIONS
Qs 2p Nc CT CG [%]
72 24 72 24 8.23
36 24 72 12 5.32
36 26 468 0.5 1.72

The second observation is that, for large values of Nc and

small values of slot number or pole number, the amplitude of
the cogging torque will be smaller. The recommendation is that
the stator slot number and the pole number shall be prime with
each other.
C. Skewing of the stator stack or skewing of the rotor pole
Starting from (1), one can calculate the skewing factor (Ksk)
with equation (3), where αsk is the skewing factor with respect Fig. 4. PMSM wind generator - the stator and the motor
to the tooth pitch [4].
For 10 kW required power, the designer choose the
( ⁄ ) following parameters:
= (3) - QS = 36 stator slots;
/
- p = 26 number of poles;
Figure 3 presents the relation between cogging torque and - Nc = 468 (the least common multiple of (36, 26)=468);
the skewing of the stator pole. The minimum cogging torque - CT = 0.5.
was obtained by skewing with one tooth step. As an additional measure the stator was skewed by a factor
of 14% of the tooth pitch.
The magnetic pole is created from 3 magnets which are fixed
using a special adhesive and are protected against centrifugal
extraction by a glass fiber web stretched over them.
 skewed with 14% of the tooth pitch, the research team
proposed increasing the minimum air gap of the generator from
0,5 mm up to 1 mm, with the aim of obtaining a more uniform
magnetic field in the air gap [1].
This generator was analyzed using FEMM (without skewing
the stator) and the predicted reduction in cogging torque would
be 63% when the air gap is increased from 0,5 mm to 1 mm.

Fig. 5. The 14% skewing of the stator

Because the PMSM has to be used as a wind mill generator,

at low wind speeds it’s cogging torque is an important factor
for the initial start of the turbine. Previous work concerning
this wind turbine can be found in reference [6], [7], [8], [9].
The method used for measuring the resistant torque can be Fig. 7. Measuring the cogging torque: the static method
found in [10].
Measurements were made for both of the rotating parts,
generic named “front” and “rear”, by fixing the external rotor
“front” and measuring the static effort needed to start rotating
the motor, in both rotational directions, after that the “rear”
axle was blocked and two new measurements were made.

TABLE II
RESISTANT TORQUE BEFORE THE MAINTENANCE - TRANSMISSION
Torque measurement [Nm]
Nr.
Case Full
1 Rear axle with seal rings 2.7
2 Front axle with seal rings 3.12

TABLE III
RESISTANT TORQUE AFTER THE MAINTENANCE - TRANSMISSION
Torque measurement [Nm]
Nr.
Case Half blocked
1 Front axle (only generator) 1.2
2 Rear axle (only generator) 1.2

TABLE IV
RESISTANT TORQUE BEFORE THE MAINTENANCE- WIND MILL
Fig. 6. Counter-rotating turbine with PMSM generator
Torque measurement [Nm]
After an initial successful test of one year, the generator was Nr.
Case Full
returned to our workshop for maintenance. It was found that 1 Rear axle with seal rings 5.95
the generator had an important resistant torque, which makes 2 Front axle with seal rings 8.75
it less operational at low wind speeds.
The maintenance was conducted to reduce the mechanical TABLE V
friction by changing the main bearing type, some of the seal RESISTANT TORQUE AFTER THE MAINTENANCE – WIND MILL
rings were removed and the radial air gap of the generator was
Torque measurement [Nm]
measured again. Nr.
Case Half blocked
In order to reduce the cogging torque, even if the shape of 1 Front axle (only generator) 3.6
the magnetic poles was type b (see Fig. 1), or the stator was 2 Rear axle (only generator) 6.0
 By decreasing the static friction torque of the bearings and between National R&D Institute for Electrical Engineering
the seal rings an important reduction of the total resistant ICPE-CA and Romanian Ministry of Research and Innovation
torque was obtained. This reduction was amplified with the (MCI).
cogging torque reduction. Table IV and Table V show the REFERENCES
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ACKNOWLEDGMENTS Popescu, "Wind tunnel testing for a new experimental model of
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using a wind mill with double effect, to ensure energetic General Meeting, 2009.
autonomy in specific applications” contract.
The current work presented here was performed under
contract no. 46N/2019 – PN19310202 and 30PFE/2018