Indian Journal Of Natural Sciences www.tnsroindia.org. © IJONS Vol.6 / Issue 31 / August 2015 International Bimonthly ISSN: 0976 – 0997 RESEARCH ARTICLE Rotor Eccentricity Magnetic Analysis in IPM-Brushless DC Motors Iman dolat shahi1 and Mehrdad jafarboland2* 1Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Isfahan, Iran 2Department of Electrical Engineering, Malek Ashtar University of Technology, Isfahan, Iran Received: 22 Jan 2015 Revised: 21 Mar 2015 Accepted: 22 Apr 2015 *Address for correspondence Mehrdad Jafarboland Departments of Electrical Engineering, Malek Ashtar University of Technology, Isfahan, Iran. E-mail: [email protected] This is an Open Access Journal / article distributed under the terms of the Creative Commons Attribution License (CC BY-NC-ND 3.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. All rights reserved. ABSTRACT Generally BLDC motors have found wide applications such as: electrical vehicles, industries, home appliances, etc. There are many factors which cause torque ripple and acoustic noise in BLDC motors. The unbalanced motor has the major role in the creation of torque ripple and acoustic noise. There are many reasons to the imbalanced air gap, which is the most common fault in asymmetric rotors such as: impacts on the axle or shaft due to the lack of proper design, lack of proper casting or inaccuracy arises in the factory. However, the asymmetry in the rotor which is caused by an imbalanced air gap, causes the differences in air gap flux, so, the vertical and tangential forces will be unbalanced which leads to the production of vibration and acoustic noses. In this paper, a new mapping is used to replace the IPM motor with it’s SPM motor counterpart with the same treatments. For this purpose, the reluctance of the magnetic circuits of the motors in both cases should be equivalent and the dimension of the surface magnet is achieved. Then, Ansoft-Maxwell software is used to simulate the air gap flux density in asymmetric rotor and finally, the asymmetrical solutions in both of the motors are studied. Keywords: air- gap flux density, torque ripple, BLDC motor, rotor eccentricity. INTRODUCTION BLDC motors are generally used and have found wide applications such as: industry machineries, electrical cars, home appliances and etc. There are many factors that cause torque ripple and noise in BLDC motors. If there is an imbalanced air gap in the motor, we can see more and more vibration and noise from motor. Naturally, it is necessary to immediate action to repair or balance the motor [1, 2]. One of the major causes of imbalance in the air gap is the rotor asymmetry from of the main axis. Hence, following the lack of balance in the air gap, air gap flux density becomes unbalanced while, the areas with the lowest air gap has the maximum air gap flux and areas with 9800 Indian Journal Of Natural Sciences www.tnsroindia.org. © IJONS Vol.6 / Issue 31 / August 2015 International Bimonthly ISSN: 0976 – 0997 Iman dolat shahi and Mehrdad jafarboland largest air gap has the minimum air gap flux. So, depending on the asymmetric rotor flux, some components of the motor heat up and even sometimes melt the insulation and cause motor burning. Therefore, identification of these defects prevents future complications and costs [1-3]. The introduction of UMP factor The asymmetry in the axis of the rotor creates a unbalanced magnetic field which leads to asymmetric motor components (or heterogeneous) that briefly is called UMP (Unbalanced magnetic pull). With the creation of the UMP asymmetric rotor and reaction forces in the bearings, the mobility of bearings reduces the lifetime of bearings and increases the mobility of periodic and non- periodic harmonic of the motor. However, two major reasons exist as the root of the UMP, which are: 1. The errors in the windings 2. The occurrence of rotor eccentricity which produces more acoustic noise frequency components [6]. Equations of the magnetic field In this section, we use magnetic field analysis to identify the main sources of UMP in BLDC motors and determine the main frequency components of the rotor eccentricity. Furthermore, brushless DC motors with fractional slots have complex air gap flux and wide frequency range [1, 2]. Air gap flux and UMP factor As previously mentioned, the unbalanced air gap flux causes the unbalanced internal magnetic forces in the motor, So, if FX is assumed to be a force in the X-axis , then [1]: 2r b (y, t) 2 y F L n cos dy X 0 20 r (1) Where, r , is the radius of the contour and y is the linear distance around the contour. It is commonly known that UMP will be generated when there are two air-gap flux waves with pole-pair numbers differing by one as it is discussed with details in [5]. The relative rotational velocities of the waves will dictate as to whether the force is a steady pull or a pulsating force. Multiplying to flux waves together with pole pair differing by one gives [5]: 2 j ( nt nky ) j ( mt mky ) bn ( y,t) Re Bn e Re Bm e 1 j ( n t nky ) j ( mt mky ) j ( n t nky ) j ( mt mky ) ReBn Bm e e B n Bm e e 2 (2) 1 j (( n m )t (n m )ky ) j (( n m )t ( n m )ky ) ReBn Bm e B n B m e 2 2r b ( y,t) 2 F L n (e jky e jky )dy X 4 0 0 2r B B e j (( n m )t (n m )ky ) L n m jky jky Re (e e )dy j (( )t ( n m )ky ) 8 0 n m 0 B n B m e j ( n m )t j ( n m )t rL Bn Bm e n m1 Bn Bm e n m 1 Re 4 j ( n m )t j ( n m )t 0 Bn Bm e n m1 Bn Bm e n m 1 9801 Indian Journal Of Natural Sciences www.tnsroindia.org. © IJONS Vol.6 / Issue 31 / August 2015 International Bimonthly ISSN: 0976 – 0997 Iman dolat shahi and Mehrdad jafarboland For the vertical forces in y axis we have [5]: 2r b ( y,t)2 F L n (e jky e jky )dy Y 0 4 0 2r j ((n m )t (nm)ky ) L Bn Bme Im (e jky e jky )dy j (( )t (nm)ky ) 8 0 n m 0 Bn Bm e (3) j (n m )t j (n m )t rL Bn Bme nm1 Bn Bme nm1 Im 4 j (n m )t j (n m )t 0 Bn Bm e nm1 Bn Bm e nm1 Rotor air-gap flux waves The magnets will produce a trapezoidal shaped rotating flux and this can be put into a complex form [5] where: m m b ( , t ) cos mp ( t ) Re B r e jmp ( r t ) r B r r m (4) m m 2 b ( , t ) m cos mp ( t )(1 cos n ) r B r r m slot s m m B r jmp ( rt ) slot jns jns Re (e )(1 (e e )) m 2 2 Where, m = 1, 3, 5, ... if we include the stator slotting ns and restrict the harmonic number to the stator slot number. Stator air gap flux waves Assume that the winding is balanced 3-phase. However, in a fractional slot machine it should not be assumed that the winding MMF is made with a fundamental pole-pair harmonic with 5th, 7th, 11th,13th, etc windings. We have to take the fundamental harmonic as two for the general case and eliminate harmonics if they are zero according to the method discussed in [6]. Hence: nw b ( , t ) cos( st nw ) (5) s B s m nw nw nw B s j ( s t nw ) B s j ( p r t nw ) b s ( , t ) Re (e ) Re (e ) nw 2 nw 2 where nw is the winding harmonic of the non symmetrical windings Equations (4) and (5) can be used and by putting into (2) and (3), the UMP components and frequencies will be obtained. 9802 Indian Journal Of Natural Sciences www.tnsroindia.org. © IJONS Vol.6 / Issue 31 / August 2015 International Bimonthly ISSN: 0976 – 0997 Iman dolat shahi and Mehrdad jafarboland Rotor Eccentricity situation Rotor eccentricity can be denoted using the method discussed in [7], using permeance modulation. So, the magnet flux wave can be represented as: m Br jm(rt p ) slot jns jns ecc j j br(,t) Re (e )(1 (e e ) (e e )) (6) m 2 2 2 m m m j (mrt(mp1) ) Re (Br e jm(rtp) slot e j(mrt(mpn) ) ecc e ) 2 4 Br 4 Br m Where, ns is the slots number. This equation is for static eccentricity and includes slotting [5]. It can be seen that, eccentricity modulates that MMF to produce air gap flux waves. However, as it is discussed in [5], the eccentricity is restricted to the first permeance harmonic (in a similar way to the slot permeance modulation approximation). Static eccentricity means that the rotor rotates on its own axis but is not centered on the stator bore axis. This could be caused by out of tolerance, misplaced or worn mountings or bearings [5]. On the other hand, the dynamic eccentricity means that the rotor does not rotate on its own axis but does rotate on the stator axis so that the point of minimum air-gap rotates with rotor speed. This could be caused by a bent shaft or out of tolerance manufacturing [5].