Torque Ripple Reduction in Reluctance Synchronous Machines

8/9/2019 Torque Ripple Reduction in Reluctance Synchronous Machines

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Torque Ripple Reduction in Reluctance Synchronous Machines

using an Asymmetric Rotor Structure

Tobias Lange, Burin Kerdsup, Claude Weiss, Rik W. De Doncker

Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Germany.

Keywords: Torque Ripple Reduction, Asymmetric Rotor

Structure, Reluctance Synchronous Machine, Flux Barrier

Placement

Abstract

Reluctance Synchronous Motors combine high efficiency and

high torque density in a limited speed range. This type of ma-

chine is increasingly becoming an alternative to Induction Ma-

chines, especially for pumps and industrial drives. However,

the torque ripple of RSM, caused by the spatial variation of

the machine flux and reluctance, needs to be considered dur-

ing the design process. This paper presents an approach of

torque ripple reduction using asymmetric flux barrier angles

and a flipped rotor structure to compensate certain torque har-

monics by superposition. With the described design process,

the resulting torque ripple is strongly reduced without loosing

average torque.

1 Introduction

In the scope of the german national funded research project

Lufo4 KONKRET, Reluctance Synchronous Machines (RSM)

have been considered as a viable alternative to Induction Ma-

chines (IM). Several publications, such as [1] and [2], showed

a higher torque density or higher efficiency of RSM’s com-

pared to induction machines. Due to continiously decreasing

power electronic costs, the increased reactive power consump-

tion of reluctance synchronous machines can easily be deliv-

ered. The slotted stator and rotor structure of machines causes

a non sinusoidal flux distribution over the stator’s circumfer-ence. Stator slots and rotor teeth interact and produce spatial

flux harmonics, which result in torque ripple. The torque ripple

of the RSM is comparably high, if no further steps for improve-

ment are taken. In this paper a design method for torque ripple

reduction by flux barrier angle adaption is proposed.

2 Overview of Ripple Reduction

Different methods for torque ripple reduction such as skewing

of the rotor or asymmetric barriers over the mechanical circum-

ference are known. Skewing offers good results regarding the

torque ripple, but it also reduces average torque. The optimalmagnetic field vector can not be applied over the stacklength,

because of the skewing and thus active flux and torque is lost.

An alternative was published by [3], where an asymmetrical

arrangement of the barrier ends and the stator teeth results in a

reduction of the overall torque ripple. To avoid mechanical im-

balance, the rotor core lamination is rotated by one pole arc for

each layer. Superposition of the torque harmonics is achieved

which reduces the torque ripple. In [4] a combination of tworotor layouts stacked to one rotor called Romeo and Julia de-

sign was presented. Furthermore, a combination of two differ-

ent barrier designs within one rotor layout called Machaon de-

sign was proposed and evaluated in [5]. Both methods achieve

good results, but also reduced the average torque of the ma-

chine.

3 Design Process

This section presents the design process starting with a com-

mon machine design and completing with the flux barrier angle

optimization for torque ripple reduction. The torque ripple re-duction method is performed after a draft design, evaluation

and geometry adaption, followed by a detailed FEA optimiza-

tion of the machine as shown in Fig. 1.

Fig. 1: Machine design process for torque ripple reduction

The detailed machine design is completed without considera-

1



tion of the torque ripple. Thereafter, the rotor barrier angles

are adapted and varied to obtain the lowest torque ripple. After

choosing the best machine design with asymmetric flux barri-

ers, small improvements can be carried out to finalize the ma-

chine design.

3.1 Geometry Design

The machine design begins with the electric and mechanical

specification and the definition of the dimensional limits. The

design procedure starts with the draft machine design based

on the software for machine design PC-BDC from SPEED

[6] coupled with the finite element analysis SPEED-FEA. The

coupled simulation ensures that saturation effects are consid-

ered during the first design step. The simulation is repeated

with different machine geometry parameters and winding con-

figurations until the desired design demands are met. During

the design variations several barrier shapes and positions, as

well as stator tooth and winding configurations are considered.

Depending on the specification and optimization criteria, such

as high power density or efficiency, the machines are evaluated

and validated to complete the draft design. The draft design

process is followed by a detailed investigation of the machine

in a further finite element analysis. As the saturation effects

had already been taken into account, the results of the draft

design and the detailed FE-analysis match well. Nevertheless,

a further analysis and detailed consideration of the magnetic

properties is necessary to gain the best motor performance.

The torque ripple of the machine was not considered during

the predesign, but will be regarded in the next section.

3.2 Optimization of Barrier Angles

The primary goal of all torque ripple optimizations is to elim-

inate or compensate the flux harmonic effects in the machine.

The flux harmonics are caused by the discrete stator teeth and

slots as well as the rotor teeth of the reluctance motor. As

mentioned in section 2 different methods for torque ripple re-

duction have been proposed in literature. This paper presents a

method where variing the barrier angles leads to a phase shift

of the flux harmonics. Especially the mechanical point sym-

metry is not lost and mechanical imbalance of the rotor can

be avoided. The proposed method eliminates the stator slotharmonics significantly with the help of superposition without

loosing motor performance.

Assuming a 4 pole machine and starting with a barrier angle

of 135◦ as shown in Fig. 2 the barrier angle is increased on

the left and decreased on the right side of the magnetic pole.

Afterwards, one rotor half is flipped by 180◦ and stacked back

onto the rotor shaft as shown in Fig. 3 and 4. Flipping the rotor

layout leads to a phase shift of the flux and torque harmonic

component with the opposite sign. With this knowledge the

rotor barrier angles can be adapted to reach the target of 180◦

phase shift of the slot harmonic between the adapted rotor and

the adapted flipped rotor. To determine the adaption range of the rotor barrier angles θ1 and θ2 in Fig. 3, the following equa-

Fig. 2: Rotor with symmetric flux barrier angles of the exam-

ple machine

tions can be used to find a good starting point for a detailed

calculation. The stator slot pitch δθStator depends on the Sta-

tor slot number N Statorslot:

δθStator = 360◦

N Statorslot(1)

It is desired to compensate the components of the stator slotharmonic in the magnetic flux and the resulting torque. Thus

the adaption of the barrier angles can be limited within one

stator slot pitch to gain the best results. The example shown

in Fig. 3 assumes a 4 pole motor with a symmetric angle

θsymmetric of 135◦.

θ1,max = θsymmetric + δθStator (2)

θ2,min = θsymmetric − δθStator (3)

δθStator ≥ |θ1 − θ2|

2 (4)

The exact barrier angle needs to be determined by detailed fi-

nite element calculations considering the magnetic saturationand the current angle of the preferred operating point. Espe-

cially the placement of the flux barriers within the rotor in-

fluences the resulting angle values. If multiple flux barriers

are used, the inner and outer barriers are kept parallel to each

other. Thereby the leading flux path and saturation behaviour

of the machine is kept nearly constant. The resulting front view

of the example machine with two rotor segments is shown in

Fig. 4 on the left.

4 Results

In this section the method for torque ripple reduction is shownin detail. At the beginning two machines with a rated torque of

2



Fig. 3: Rotor with asymmetric flux barrier angles

Fig. 4: Stacking of asymmetric rotor segments

12 Nm, 4 poles with 4 flux barriers, 24 slot and 36 slot stator

configuration are designed as described in section 3.1. Now

the torque ripple reduction method using angle adaption is car-

ried out for the 24 and 36 slot machines. During the proposed

process for torque ripple reduction, the rotor structures shown

on the left in Fig. 7 and Fig. 10 are investigated. The bar-

rier angles of the 24 slot machine are adapted in the range of

δθStator = ±15◦ and the barrier angles of the 36 slot machine

are in the range of δθStator = ±10◦. It is remarkable that

the total torque ripple is not just dependent on the geometric

positioning of the rotor and stator teeth, but also on the cur-

rent control angle and the magnetic saturation within the ma-

chine. Here the rated operating point is chosen to evaluate the

machine performance. However, higher harmonics of the ro-

tor and stator slots also occur as torque ripple amplitudes, if

the harmonic component with the order of the slot number is

perfectly compensated. The final rotor structure needs to be

considered in a detailed finite element design process to im-

prove the final details. Small modifications to the flux barri-

ers, keeping the previously determined barrier angles constant,

complete the motor design. To evaluate each machine design

the torque ripple is calculated for each barrier angle combina-

tion of θ1 and θ2 as shown in Fig. 5 and Fig. 8.

The result of the 24 slot motor operated at rated torque of

12 Nm is shown in Fig. 5, which contains the contour curves

of equal torque ripple. The ripple amplitude is given in per-

centage values of the rated rotor torque. It is shown that a the

ripple can be reduced to less than 10 % of the average rated

torque. A further improvement would be possible by loosing

average torque. However, in this design process the averagetorque reduction was limited to 6 %.

Fig. 5: Torque ripple as a function of the barrier angles for the

24 slot machine

Choosing the barrier angles θ1 = 143◦ and θ2 = 122◦ for

the minimum torque ripple of 8.7 %, the simulated torque over

one rotor pole pitch of 90◦ is shown in Fig. 6. The upper figure

shows torque ripple of the original rotor without asymmetricbarrier angles. The middle figure shows the torque of each

segment as a solid line and for the flipped rotor segment with

the dashed line. The superposition of the asymmtric rotor is

plotted in the lower figure with the solid line and the average

torque as a dotted line.

Fig. 6: Torque ripple of the 24 slot motor over rotor angle in

degrees

The geometric layout of the motor is shown in Fig. 7. The

left figure shows the machine layout before the torque ripplereduction process and the right figure shows the motor with

3



Fig. 7: Initial and final rotor design of the 24 slot machine

one adapted rotor segment after applying the ripple reduction

method.

Secondly, the method is evaluated for a 36 slot machine with

identical specifications. The machine is operated at rated

torque. The calculated torque ripple plane is shown in Fig. 8.

The non optimized machine has a torque ripple of 14.8 % at

12.3 Nm rated torque. Generally the torque ripple amplitude

of a 36 slot machine is smaller compared to a 24 slot machine,

thus the expected torque ripple reduction is larger than for a 24

slot motor.

Fig. 8: Torque ripple as a function of the barrier angles for the

36 slot machine

Again, the average torque reduction is limited to 6% of the

rated torque. From Fig. 8 the angles for minimum torque ripple

at θ1 = 140.6◦ and θ2 = 127.5◦ are chosen for the resulting

rotor structure in Fig. 10. With the 36 slot machine, the torque

ripple is reduced to 1.5 %. The torque versus rotor pole pitch

of 90◦ is shown in Fig. 9.

The flux barrier angle adaption causes the flux paths change

minimally. Small modifications to improve the magnetic de-

sign should be considered in a final design step as mentioned

before.

Comparing the results of the two proposed motors with 24 slotsand 36 slots, a significant improvement without loosing aver-

Fig. 9: Torque ripple of the 36 slot motor over rotor angle in

degrees

Fig. 10: Initial and final rotor design of the 36 slot machine

age torque can be noted. The torque characteristics of both

machines before and after applying the proposed method of

ripple reduction are listed and compared in Table 1.

24 slot machine 36 slot machine

T orig,avg

T orig,ripple

T avg

T ripple

12.9 Nm

2.9 Nm

12.13 Nm

1.1 Nm

12.4 Nm

1.8 Nm

12.1 Nm

0.2 Nm

Table 1: Average torque and torque ripple of the considered

24 slot and 36 slot motor.

5 Conclusion

In reluctance synchronous motors the stator and rotor flux

harmonics lead to a significant torque ripple at the machine

shaft. This ripple is caused by spatial flux harmonics which

are strongly dependent on the machine geometry. In this pa-

per a method for torque ripple reduction of RSMs has been

proposed. After a common machine design process the torque

ripple reduction process has been carried out. The method is

based on superpostion of rotor segments and requires one ro-

tor layout and cut, which is flipped during the production pro-cess. Additionally, the average torque can be kept constant,

4



while the torque ripple is reduced significantly. Furthermore,

the mechanical balance of the rotor is maintained, because the

flux barrier angle adaption leads to a point symmetric structure.

The method has been shown for two different machines with a

24 and 36 slot stator with distributed windings. The proposed

design process has been verified by a detailed finite elementsimulation.

The project underlying this report was funded by the Fed-

eral Ministry of Economics and Technology, project number

20Y0906A. The responsibility for the content of this publica-

tion lies with the author.

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Torque Ripple Reduction in Reluctance Synchronous Machines