Proceedings of the 2017 25th International Conference on Nuclear Engineering ICONE25 July 2-6, 2017, Shanghai, China ICONE25-66807 STUDY ON VIBRATION CHARACTERISTICS OF INDUCTION MOTOR UNDER LOAD CONSIDERING SATURATION OF MAGNETIC CIRCUIT Pu Zhou Shanghai Marine Equipment Research Institute Shanghai, China Zhen Zhen Micropowers Ltd. Shanghai, China Yue Zhang Shanghai Marine Equipment Research Institute Shanghai, China Qiang Wang Shanghai Marine Equipment Research Institute Shanghai, China Hai-jun Feng Shanghai Marine Equipment Research Institute Shanghai, China abroad, the research of induction motors about the influence of the magnetic field saturation often concentrated in the motor performance and the saturation inductance caused by harmonic parameters are always calculated to analyze the performance of the motor changes [2]. For example, Julio C. and T. A. Lipo et al. developed a harmonic equivalent circuit model and introduced the third harmonic of the air-gap magnetic potential into the equivalent rotor circuit to calculate the torque and loss due to saturation harmonics [3]. Liang X, Luy Y researched the saturated harmonics of induction motors and the influence of harmonics on motor current and torque was calculated by adjusting the inductance of rotor side in equivalent circuit [4]. In the design of low-noise motor, in addition to the motor performance, more attention should be paid to the vibration and noise characteristics of the motor. Due to the influence of load characteristics and environmental factors, the saturation coefficient of the magnetic circuit will fluctuate and affect the vibration characteristics of the motor. Based on the principle of T-equivalent circuit, the law of flux density change under the saturated state was analyzed in this paper. Through finite element simulation and bench test, a small induction motor is studied and the vibration characteristics of this motor under saturated magnetic circuit were researched to find the relationship between magnetic saturation and motor vibration. ABSTRACT The variation law of motor vibration with load under saturation of magnetic circuit is one of the focus of motor vibration research. T-type equivalent circuit method is shown to be a suitable engineering analysis way. In this paper, the variation of magnetic flux density under saturation state was analyzed by using a small induction motor, and a physical model of magnetic saturation and motor vibration was established by the way of T-shaped equivalent circuit. Based on the physical model, the vibration mechanism of the motor under the saturated magnetic circuit was analyzed and the motor vibration simulation with different load conditions was carried out by the finite element method. Finally, a vibration test rig for motor under load was built and the simulation results were verified by experiments. The results show that when the motor load is less than the rated load, the amplitudes of the electromagnetic force in the middle and high frequency band change little. When the load is close to or higher than the rated value, the harmonic components of electromagnetic force in the middle and high frequency bands increase, and the amplitudes gradually increases due to the saturation of the magnetic circuit. Therefore, in the low-noise motor design, motor torque performance and vibration noise performance should be considered to optimize the saturation control of the magnetic circuit. KEY WORDS: Induction motor; Magnetic circuit saturation; Vibration under load; Electromagnetic force T-SHAPED EQUIVALENT CIRCUIT THEORY The motor system T-shaped equivalent circuit is shown in Fig.1, where R1 is the stator resistance, R2' is the rotor resistance, X 1 is the stator reactance ， X 2' is the rotor reactance， Rm is the magnetic path loss resistance, X m is the magnetic path reactance, and s is the slip ratio. INTRODUCTION Induction motor is often designed to have a certain degree of magnetic saturation in some special applications in order to improve the electromagnetic torque [1]. At home and 1 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use By defining Z1 = R1 + jX 1 ， Z m = Rm + jX m increase and Fδ will decrease, eventually leading to the increase of the saturation coefficient K s of the magnetic circuit. In addition, K s is related to the magnetic resistance of the magnetic circuit. Fig.2 shows the two most typical relative positions of stator and rotor when the motor is running. When the motor is in position a, due to the stator tooth surface is opposite to the rotor tooth surface, the magnetic reluctance of tooth and yoke is small, as well as K s .When the motor is in position b, because the rotor tooth tip is opposite to the stator tooth surface, K s is obviously larger than the K s in position a. According to the exponential change of the saturation coefficient, the increment of K s in position b is greater than it in position a when the motor load increases. Especially when the motor load exceeds the rated load, the saturation coefficient in position b largely increases. As the motor rotating, the relative position of the rotor keeps changing and experiences a, b, a, b, a, b ... ..., so the motor saturation coefficient volatility increases. ， 1 ' R2 + jX 2' , we have s Z2 = . . I1 =U1 . . 1 1 =U1 Z2Zm Zm Z1 + Z1 + Z Z2 + Zm 1+ m Z2 Z2Zm Z2 + Zm . I 2 =U1 . =U1 (1) Z Z Z1 + 2 m Z 2 + Zm Z 2 Zm (Z1 + Z m )Z 2 + Z1Z m (2) Z2Zm Z2 + Zm I m = U1 Z Z Z1 + 2 m Z m Z 2 + Zm . . . =U1 1 Z1 Z m Z1 + + Zm Z2 (3) When the load increases, the motor slip ratio s will increase, leading to the decrease of Z2. From eqns.3, it can be seen that if the excitation current of the motor Im decreases, the synthetic magnetic potential of the fundamental wave in the air gap space will decrease. Similarly, eqns.1 and eqns.2 show . that when the load increases, the stator current I1 and rotor . current I 2' increase. . R1 I1 . I 2' X1 R2' (a) (b) Fig.2 typical relative positions of stator and rotor To sum up, when the motor load increases, the excitation current decreases, while the magnetic saturation coefficient and its fluctuation increase. As the excitation current is proportional to the amplitude of the magnetic flux density and the fluctuation of the saturation coefficient has great influence on the harmonic component of the flux density, the amplitude of the fundamental flux density will ultimately decrease and the harmonic amplitude will increase if the motor load increases. X 2' . Im Rm 1− s ' R2 s . U1 Xm SIMULATION OF ELECTROMAGNETIC FORCE UNDER DIFFERENT LOAD When the motor is used, the load will change in a certain range, which is often affected by the environment and will cause the change of the rotor winding current, motor speed and other characteristics. These will finally affect the motor's internal radial electromagnetic force. The finite element model of the motor was built and a constant torque load was added in the model, as shown in Fig.3. According to the preliminary calculation result of the motor, the starting torque is about 3.5 Nm. As a result, the load step was taken 0.5 Nm and 8 conditions were calculated ranging in 0 ~ 3.5Nm. Fig.1 T-shaped equivalent circuit The magnetic saturation coefficient [5] is expressed by Ks = Fδ + F j1 + Fi , Fδ （4） where Fδ , Fi and F j1 are the magnetic drop of air gap, stator tooth, and stator yoke, and are positively correlated to . . . . . I1 , I 2' , I m , respectively. When the load increases, I1 , I 2' . will increase while I m will decrease. Therefore, Fi , F j1 will 2 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5 0 5 0 Order 2000 -5 0 1000 Frequency (Hz) Force Amplitude (Pa) Force Amplitude (Pa) 4 x 10 4 x 10 4 2 0 5 （a） （b） Fig.3 Motor section and finite elements division The time-domain results of the air-gap flux density (one point) at different loads are shown in Fig.4. It can be clearly seen from the figure that the radial flux density of the fundamental wave decreases while the load increases, and the fluctuation of the harmonic wave does not change obviously at first, but sharply increases later. 4 2 0 Order -5 0 2000 1000 Frequency (Hz) x 10 4 2 0 5 （c）1 Nm torque 0 Order 4 2 2000 -5 0 1000 Frequency (Hz) x 10 4 2 0 5 （e）2 Nm torque 1 -5 0 2000 1000 Frequency (Hz) Force Amplitude (Pa) Force Amplitude (Pa) -5 0 2000 1000 Frequency (Hz) 4 2 0 Order 0 Order （f）2.5 Nm torque 4 x 10 0 5 2000 1000 Frequency (Hz) 4 Force Amplitude (Pa) Force Amplitude (Pa) 4 0 Order -5 0 （d）1.5 Nm torque x 10 0 5 2000 1000 Frequency (Hz) 4 4 x 10 0 5 -5 0 （b）0.5 Nm torque Force Amplitude (Pa) Force Amplitude (Pa) （a）0 Nm torque 0 Order x 10 2 1 0 5 0 Order -5 0 2000 1000 Frequency (Hz) （g）3 Nm torque （h）3.5Nm Nm torque Fig.5 Radial electromagnetic force of motor under different loads Fig.4 Time - domain result of radial flux density under different loads As the magnitude of the electromagnetic force is proportional to the square of the magnetic flux density, this eventually results in the decrease of the double frequency electromagnetic force of the power supply generated by the fundamental field when the load increases. However, the electromagnetic forces generated by the harmonic magnetic field in the middle and high frequency bands increase. When the load is less than the rated load (~ 2 Nm), the saturation coefficient of stator and rotor is small, so the increment of harmonic forces is not obvious. If the load exceeds the rated value, the harmonic forces increase rapidly. Based on the Maxwell stress tensor method, the magnetic flux density was transformed into the radial electromagnetic force, and then the two-dimensional Fourier transform was performed. The results are shown in Fig.5. In Fig.5, the highest point of electromagnetic force is the second order 50 Hz force generated by the fundamental wave on different conditions, and the magnitude of the force wave decreases with the load increasing. On the other hand, the components of the force in the low frequency band of 0 Hz ~ 300 Hz in each order become complicated with the load increasing, and the amplitudes of the most force increase in different degrees. From the magnetic circuit theory, the amplitude of the flux density is related to magnetic potential and permeability. The magnetic potential is proportional to the excitation current, and the permeability is inversely proportional to the saturation coefficient of the magnetic circuit. As the material magnetization curve is nonlinear, the saturation coefficient changes exponentially with the motor stator current and rotor current changing. VIBRATION TEST OF THE MOTOR UNDER DIFFERENT LOAD In order to validate the correctness of the simulation conclusion, a vibration test rig for motor under loads was built. When the motor is running, there will be some fluctuation of the speed due to the tangential electromagnetic force. When the motor is under load, the load fluctuation will also affect the running speed. In order to minimize the impact of the load fluctuation on the vibration of the motor, a vibration test rig was built shown as Fig.6. From left to right are the magnetic brake load, plum flexible coupling, torque and speed measurement sensors, flange coupling and the measured motor. The tri-direction-force transducers were installed at the motor feet. 3 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Tab.2 Summary of the main transmission force under different conditions (N) Hz 50 400 In addition, the acceleration sensors were arranged around the front bearing, rear bearing and the upper part of the four force sensors (i.e., the four mounting feet of the motor) to measure the vibration acceleration response of the motor. 1 1.5 2 2.5 3 3.5 4.0 0.2 2.6 0.1 2.4 0.2 2.3 0.4 2.1 0.7 1.6 1.3 0.9 2.9 0.7 7.6 SATURATION CONDITION In addition to the electromagnetic force, the induction motor vibration excitation includes the mechanical force of the rotor and the fluid force of the fan. Therefore, the increase of the load does not necessarily make the overall motor vibration increase. In order to study the effect of load on the overall motor vibration with the saturated condition, the vertical vibration response of each measuring point of the motor under different loads were measured. In addition, the same motor was used to drive the measured motor to obtain non-electromagnetic response under the different loads. The vibration responses of each measuring point are shown in Fig. 7 to Fig.9. UNDER SATURATION CONDITION Through a series of load tests, the mechanical characteristics curve of the motor was gotten. Table 1 shows the comparison of results between experiments and simulation. The simulation results of each load case are very close to the actual test results, so the measured forces can be used to verify the conclusions of the simulation. Tab. 1 Comparison of simulation and the measured speed 0 0.5 1 1.5 2 2.5 3 3.5 0.5 INFLUENCE OF LOAD ON MOTOR VIBRATION UNDER INFLUENCE OF LOAD ON MOTOR VIBRATION FORCE Speed (r/min) Simulation measured 1491 1490 1468 1474 1453 1448 1424 1425 1346 1394 1346 1355 1286 1309 1131 1237 0 The results in Table 2 are almost the same as the simulation results, that is, when the load increases, the 50 Hz electromagnetic force (i.e., the double frequency electromagnetic force of the power supply) generated by the fundamental magnetic field is reduced, while the 400 Hz electromagnetic force generated by the harmonic magnetic field increases. This verifies the correctness of the simulation conclusion. Fig.6 The vibration test rig for motor under loads Load (Nm) Nm Error (%) 0.07 -0.41 0.35 -0.07 3.44 -0.66 -1.76 -8.57 Through a series of vibration tests under variable load, each transmission force of the motor foot and the vibration response of the measuring points were gotten. As the motor slip will change the frequency of transmission force, each frequency was conversed in order to facilitate comparison. When the slip is small, it is provided that ft , （5） f = (1 − s ) where f t is the measured frequency, and s is the measured slip ratio. The main transmission forces of each motor feet after the frequency conversion are shown in Table 2. Fig.7 Comparison of vibration responses of motor's front bearing Fig.8 Comparison of vibration responses of motor's rear bearing 4 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Fig.9 Comparison of vibration response of motor's feet Fig.12 The response curves of motor's feet at 50 Hz and 400 Hz From Fig. 7 to Fig. 9, it can be seen that when the induction motor load increases and the rotation speed decreases, the vibration of the machine body caused by the non-electromagnetic force decreases, while the vibration caused by the integrated force basically keeps the same at first, and then gradually increases. At the same time, the 50Hz and 400Hz electromagnetic excitation response curves of each load are shown in Fig. 10 to Fig. 12, the main trend of which is consistent with the simulation results. It can be inferred that when the load of the induction motor is less than the rated load, the overall vibration response of the motor changes little with the increase of the load. It is because that the non-electromagnetic force decreases and the electromagnetic force increases little. When the motor load exceeds the rated load and continues to increase, the electromagnetic force in the middle and high frequency bands increases obviously. It is affected by the saturation of the magnetic circuit, which gradually takes the leading factor. It makes the vibration response of the motor become larger. CONCLUSIONS In this paper, the T-shaped equivalent circuit was combined with the induction motor running rule to study the change mechanism of electromagnetic excitation under different loads and saturation states. The simulation of electromagnetic excitation force of induction motor with finite element method was studied. By building up a motor load test rig, the correctness of the simulation conclusion was verified and the influence of the load on the vibration response of the motor under saturated operating conditions was further analyzed. Through the above study, the conclusions are as follows: 1. The excitation current decreases but the fluctuation of the saturation coefficient increases as the load increases. Therefore, the electromagnetic force amplitudes of the low frequency band such as twice the power frequency are reduced but the electromagnetic force amplitudes of the middle and high frequency bands are increased. 2. When the load of the induction motor is less than the rated load, the non-electromagnetic force decreases and the increment of the electromagnetic force is small as the load increases, and thus the overall vibration response of the motor changes little. 3. The high-frequency electromagnetic force amplitude influenced by the saturation of the magnetic circuit will increase obviously when the motor load exceeds the rated load. It continues to increase and will gradually become the major factor which resulting in motor vibration response increasing. Fig.10 The response curves of motor's front bearing at 50 Hz and 400 Hz Fig.11 The response curves of motor's rear bearing at 50 Hz and 400 Hz 5 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use [3] Moreira J C，Lipo T A. Modeling of Saturated AC Machines IncludingAir Gap Flux Harmonic Components [J]． Industry Applications，IEEE Transactions on，1992，28(2): 343-349. [4] Liang X，Luy Y. Harmonic Analysis for Induction Motors [C] ． Electrical and Computer Engineering ， Canadian Conference on. IEEE，2006: 172-177. [5] CHEN Shi-kun. Motor Design [M]. Second Edition. Beijing: Mechanical Industry Press, 2000: 35-39. . REFERENCES [1] DU Xiao-fei，GUO Nong-sheng，ZHOU Yuan-jun. Simulation Analysis on Magnetic Saturation of Induction Machine [J]. Micromotors, 2014，(47)9: 1-4. [2] Donescu V ， Charette A ， Yao Z ， et al. Modeling and Simulation of Saturated Induction Motors in Phase Quantities ［J］． Energy Conversion，IEEE Transactions on，1999， 14(3): 386-393. . 6 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

1/--страниц