THE 9th INTERNATION

978-1-4799-7514-3/15/$31.00 ©2015 IEEE

Study of TDifferen

SynchronOvidiu Bîrte1, Loránd Sz

Cassio Fa1Technical University of C

2LMS EngineerinOvidiu.Birte@emd.utcluj.ro,

cassio.faria@siemens

Abstract- The use of electric machines as vehicles raises the concern of the vibration generated by the structure. Radial forceelectrical machines have a high contribution This paper presents a coupled finite elementcalculating the radial force, torque ripplacoustic noise in synchronous reluctance mThe knowledge of the modal parameters of (mode shapes and natural frequencies) aspectrum of the radial magnetic force can bedesign SynRMs with minimal noise throughvariations at an early stage. An automatideveloped for designing a synchronous reluenable faster implementation of the geometryinvestigation of electromechanical propertialso the problems related to noise. The automation is demonstrated on modifying thdesign for a SynRM that would apply forelectric vehicles. The effect of the stator gedistribution on acoustic noise can also be model presented in this paper.

Keywords: synchronous reluctance machineradial forces, rotor topologies.

I. INTRODUCTION

The electrical drives are nowadays a advanced automotive applications [1]. Edesigners and researchers in industry,demands to consider many physical effectwhen they bring forth the next generation oconverters, such as electrical machines.particular concern is represented by the nbehavior. In order to be competitive onvehicle requires along being efficient to bquiet.

In electrical machines there are severaelectro-magnetic excitations mechanisms whigh vibration.

The subject is concentrated on the high vthe electromagnetic forces in the electricarotor of electric motors rotates as a resgenerated due to the presence of an electrthe air gap between the rotor and stator.

NAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTMay 7-9, 2015

Bucharest, Romania

E

Torque Ripple and Noisnt Rotor Topologies ofnous Reluctance Mach

zabó1, Member IEEE, Herman Van der Auweraer2, Mearia2, Áron Popp1, Claudia Marţiş1 Member IEEE,

Cluj-Napoca, Memorandumului 28, 400114, Cluj-Napong RTD, Siemens Industry Software NV, Leuven, BelgLorand.Szabo@mae.utcluj.ro, herman.vanderauwerae.com, willanytorpe@gmail.com, claudia.martis@emd

traction in electric and the noise level

es in the stator of to these vibrations.

t method (FEM) for le and predict the

machines (SynRMs). the stator structure and the frequency e effectively used to

h geometrical design c process has been

uctance machine, to y modifications and ies while regarding

practicality of the he rotor geometrical r traction of small eometry or winding

analyzed with the

e, noise, vibration,

common issue in Electrical machine , face increasing ts more accurately of electrical energy One matter of

noise and vibration n today’s market a be comfortable and

al mechanical and which could cause

vibration caused by al machines. The sult of the torque romagnetic field in

The electromagnetic fieldelectromagnetic forces betweeThese electromagnetic forcesorthogonal components, tangentforces in electrical machines arethe effect of driving the electromagnetic forces do not presponsible in the production o[2]. Radial electromagnetic forcvibration and noise, especially wmechanical structure is close texcitation frequencies [3], [4vibration behavior and the smachines it is necessary to havethe resonant frequencies and exc

The variable reluctance syndue to its high efficiency and lpower range can be considered both the induction machines synchronous machines (PMSMs

The choice of such machapplications is generally dmanufacturers based on three frespectively organized by order

The SynRM performance deptopology: only a SynRM with hcan reach high performance [must be designed for maxmaintaining a reasonable sine win the d- and q-axes [8]. It is acogging torques due to interaopenings and the rotor flux barlayers.

SynRMs with adequate desigautomotive applications.

Electromagnetic force distribFinite Element Method (FEM)simulation. Radial force distribstator structure and the vibratio

TRICAL ENGINEERING

se for f a hine

ember IEEE,

oca, Romania gium er@siemens.com, .utcluj.ro

d in the machine creates en the stator and the rotor. s can be divided in two tial and radial. The tangential e producing torque (which has

rotor) while the radial roduce torque but are partially

of audible noise and vibrations ces can cause severe structural when the natural frequency of to the electromagnetic forces

4]. In order to predict the sound radiated from electric e the accurate determination of citing radial forces [5]. nchronous machine (SynRM) lower cost in middle and high as a strong choice to compete and the permanent-magnet

s) [6]. hines for advanced traction determined by automotive

factors: costs, weight and size, of importance.

pends dramatically on the rotor high anisotropy rotor structure [7]. Therefore, the SynRMs ximum saliency ratio, but wave air gap flux distribution also necessary to minimize the ction between the stator slot rriers or nonmagnetic material

gn can also be used in diverse

bution can be calculated using software for electromagnetic bution can be applied to the

on response of the stator or the

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assembled motor can be calculated from a FEM program for structural simulation.

Radial magnetic force on the stator causes the stator and housing to deform in a certain spatial pattern. These spatial patterns are results of the distribution of the magnetic field in the air gap of the motor. They coincide with the magnetic pole generation in the motor for example 2 pole, 4 pole fields etc.

The spatial pattern of the forces also revolves in the structure with frequency which depends on the supply frequency and its harmonics.

In a very simplistic form, the stator can be represented as a cylinder that flexes due to forces applied on it as shown in Fig. 1 [9]. The stator core has several modes of vibration. The core resonant frequency at a particular mode of vibration can be derived from the elasticity theory for a flexural vibration of a cylinder [9].

Since stator is a circular ring it has its own modes of vibration as discussed above. The maximum vibration will occur when the force spatial pattern matches with one of the natural frequency of the stator deformation mode [10]. The odds of intersection of the magnetic force distribution with one of the stator ring frequencies are high when the machine is on variable frequency drive with wide speed range.

The goal and main achievement of the research in this paper was the development of an automatic process for the rapid design of efficient SynRMs both mechanically and noise concerning.

In the study of the SynRMs for noise prediction two FEM software applications have been employed: JMAG Designer and LMS Virtual.Lab [11].

JMAG Designer is the high-speed, high-precision FEM software tool at the core of JMAG software suite for electromechanical equipment design and development. It was used for the electromagnetic (EM) simulation of the SynRM yielding also the distribution of radial forces as a result.

LMS Virtual.Lab is an integrated suite of 3D FEM and multibody simulation software which simulates and optimizes the performance of mechanical systems for structural integrity, noise and vibration, system dynamics and durability. One of its features is Acoustic Harmonic FEM,

which enables the prediction of the noise from the EM loads on the stator [12], [13].

II. ACTIVITY DEVELOPMENT

The main steps for assessing the noise level from the radial force, using the two afore mentioned software applications, are described in the following. These steps of the process are also depicted in Fig. 2.

The procedure is started with constructing a 2D model (considering symmetries) of the machine in JMAG Designer. A transient magnetic analysis needs to be performed on the model over a full rotation. The average torque and torque ripple can be inspected at this point. The distribution of electromagnetic forces on the stator, as vector plot, and the spectral composition of the force at specific points can be visualized. After analyzing the results at this step, decision can be made for the improvement of these features or continuing with the noise and vibration investigation [14].

JMAG has a dedicated tool for the export of the forces to Virtual.Lab. The 2D partial model is converted to a 3D full model. The result of the export is a UNV file which can be processed in Virtual.Lab. The file contains a 3D mesh with the vector loads as time series applied on it.

A 3D structural mesh needs to be created in Virtual.Lab and the vector loads obtained from JMAG are mapped to the structural mesh.

Structural analysis needs to be performed in order to obtain the natural frequencies and mode shapes of the stator. Knowing these modal parameters of the stator and the distribution of forces, an acoustic response can be computed [15]. The results can be visualized in a frequency spectrum or as a sound pressure amplitude map, on a sphere around the stator [16].

Fig. 1. Vibration modes of a stator

Fig. 2. Process for the noise prediction using JMAG and Virtual.Lab

Run the EM simulation for the 2D JMAG model

Export the stator EM forces

Construct the 3D Virtual.Lab model

Run the simulation for the noise evaluation

Import the forces and create the mapping

Examine the results

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The process of evaluating noise from the radial force can be tedious and time consuming, especially when optimization is followed. To minimize the time spent to perform these simulations an automatic process has been created using a Visual Studio script which will read the geometric and the electric parameters via a graphical user interface (GUI) [17]. These parameters can even be obtained from an analytical simulation. The GUI with the design parameters that can be implemented is shown in Fig. 3.

The script will automatically generate the geometry and run the electromagnetic analysis in JMAG and will create the structural mesh in Virtual.Lab.

A 1.5 kW, 3400 r/min SynRM has been studied regarding its behavior when the rotor topology is modified. The outer diameter of the stator is 136 mm, the outer diameter of the rotor is 90 mm and the machine’s active length is 110 mm. Other design parameters can be glimpsed in Fig. 3. The machine was supplied with a sinusoidal three phase current source.

The transformation feature applied to the rotor consisted of modifying the central flux path width (CFP), which is modifying the position of the first barrier and keeping the width of the flux barriers and of the flux paths constant. This is illustrated in Fig. 4, where the closest position of the barriers to the center of the rotor and the furthest position from the center are depicted.

The modification applied to the rotor was implemented by introducing the central flux path width as a sizeable parameter in the script. Thus, ten simulations were performed for ten different geometries and the results were automatically exported to Excel files to visualize and compare the results.

Any of the geometric and electric parameters could be easily implemented to be used as an individual sizeable

parameter, giving the possibility to run multiple EM simulations within a single run of the script itself.

III. RESULTS

Torque ripple for each topology was calculated with (1), where Tmax is the maximum torque, Tmin is the minimum torque and Tave is the average torque. % · 100 (1)

When comparing the results by means of torque ripple and the average torque, a tendency of declining is observed for the average torque with the increase of the central flux path width, while for the torque ripple there is an optimal point at 6 mm width of the central flux path, as shown in Fig. 5.

Fig 3. GUI for the SynRM parameterization

Fig. 4. Rotor geometry transformation for the SynRM a) central flux path width of 1mm (minimum width)

b) central flux path width of 10 mm (maximum width)

Fig. 5. Average torque and torque ripple plotted versus the width of the flux main path

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The study case with the maximum torque ripple and the one with the minimum torque ripple were selected for comparison and further analysis. These correspond to the topologies with 3 mm and 6 mm width of the central flux path. Torque characteristics of the two studied cases are depicted in Fig. 6.

It is noticed that the modification applied to the rotor topology has an effect of reducing the torque ripple by 55% while reducing the average torque by only 2%.

The distribution of forces on the stator is depicted in Fig. 7. The structural analysis performed in Virtual.Lab gives the

natural frequencies and the mode shapes of the stator, as they can be seen in Table I.

For any rotating machine, we can expect to see higher levels in the noise at the frequencies related to the orders of the machine. The orders represent the number of times a phenomenon occurs during one period of mechanical rotation. In electric motors, these orders are directly related to the number of rotor poles, number of stator teeth.

The relation between frequency of this phenomenon and rotational speed is seen in (2):

60 · 2 · · (2)

where n is the rotational speed in r/min, N is the number of the order, p is the number of poles and f is the supply frequency.

Fig. 8 shows the acoustic power generated by the stator when the EM loads are applied on the structure, calculated at a distance of 40 centimeters from the stator. The peaks in the

TABLE I NATURAL FREQUENCIES AND MODE SHAPES OF THE STATOR

Natural frequency

(Hz) Mode shape

Natural frequency

(Hz) Mode shape

1351

6563

2197

7964

3632

8051

4918

9859

Fig. 6. Torque characteristics for the two rotor topologies with central flux path width of 3 and 6 mm, respectively

Fig. 7. Distribution of EM forces on the stator Fig. 8. Acoustic power for the two rotor topologies

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graph correspond to orders given by the geometry of the stator. In the frequency spectrum the orders related to the number of poles (4) and number of teeth in the stator (24) and multiples of that orders are well distinguishable. The order given by the stator poles number is represented by the first peak in the frequency spectrum, appearing at 226 Hz. The order related to the number of teeth in the stator is represented by the highest peak in the above picture, which appears at 1360 Hz.

In Fig. 8 the blue curve represents the acoustic power generated from the stator, for the case with the first topology of the rotor and the orange curve represents the acoustic power generated by the stator from the second case study, the rotor topology with increased central flux path. The reduction in torque ripple of the second topology does not seem to have much effect on the noise through the exciting of the radial modes.

When studying the sound pressure level and the frequency response function, it is observed that the highest levels in the noise are occurring when the natural frequencies of the stator are excited, stimulating the eigenmodes corresponding to these frequencies. This can be seen highlighted in Fig. 9, where the spectral components of the force, the frequency response function (FRF) and the acoustic power are represented in frequency domain [18]. The radial force was measured in JMAG along the central flux path and rotating synchronously with the rotor.

The frequency response function is used as an indicator of the dynamics of a system and is defined as: (3)

It represents the complex ratio between output and input as a function of frequency ω. FRF is a complex function so it has an amplitude | | and a phase . The physical interpretation of the FRF is that a sinusoidal input force, at a

frequency ω, will produce a sinusoidal output motion at the same frequency. The output amplitude will be multiplied by | |, and the phase, between output and input, will be shifted by .

FRF is a function that gives the response for any input at a specific point, using the relation: · (4)

In (4) the output X(ω) can be represented by displacement, velocity or acceleration. The corresponding FRFs are called compliance, mobility and accelerance. For the case pictured in Fig. 9, the FRF was calculated as the ratio between the acceleration of a point and the input force at that point, so it is an accelerance. The accelerance was computed for the input and the response in radial direction. The peaks in the FRF are correspondent to the resonance frequencies of the stator.

Fig. 10 shows the translational displacements of the stator at the frequencies with the highest amplitude, when the electromagnetic loads are applied on the structure.

The translational displacements of the stator around the natural frequencies show that the ovalization and square modes of the stator are excited at their corresponding frequencies.

Fig. 9. Correspondence between noise, resonance and excitation forces

Fig. 10. Translation displacement magnitude a) 1360 Hz; b) 6580 Hz

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The square mode, which yields the highest level of noise, is easier to excite given the distribution of the electromagnetic radial forces in the stator for a 4 poles structure (see Fig. 7).

IV. SUMMARY AND CONCLUSIONS

In this paper a SynRM was studied, through the investigation of rotor topology transformations on the electromechanical parameters and NVH behavior.

The position of the barriers was found to have high influence on the torque and torque ripple.

Two topologies, with the highest and lowest torque ripple were selected for comparison regarding the acoustic response from the EM loads.

The topology with the width of the central flux path of 6 mm gives a good improvement in the torque ripple; however it doesn’t offer the same improvement in the radiated noise.

ACKNOWLEDGMENT

The research discussed in this paper was performed as part of the EC Project “DEsign, Modelling and TESTing tools for Electrical Vehicles” (DeMoTest-EV) project in the frame of FP7 IAPP Marie Curie Actions. Project DeMoTest-EV aims at the development of advanced and extended design, modelling and testing tools for automotive application.

The authors further acknowledge JSOL Corporation for the JMAG® licenses made available and to Siemens Industry Software for the access to LMS Virtual.LAB®.

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