Estimation of Vibrations in Switched Reluctance Motor Drives

This study discusses a simple algorithm for estimat ion and reduction of Vibrations in a Switched Reluctance Motor (SRM) using magnetic circ uit simulation in MATLAB/SIMULINK Environment. A Non-linear model is developed using magnetic circuit equations, wherein non-linearity is added using a inductance profile with back EMF. Dynamic characteristic of the SRM is simulated and the same is being verified experimentally. In this simulation, both current and voltage control techni ques are used to control the SRM. Fast Fourier Transform is used to analyze the electromagnetic torque in Frequency domain, which gives the mechanical and ma gnetic vibration frequencies and their dB magnitude. The complete simulation and experimental results are presented.


INTRODUCTION
The switched reluctance motor is a mechanically rugged machine, due to the simplicity of its construction and stator winding arrangement. It has the capability to run from zero speed to base speed and enter into the field-weakening region [1,2] . The switched reluctance motor is, hence, receiving increased attention in applications where cost reduction and variable speed are required. SRM requires rotor position encoders and has a considerable amount of torque ripple, which causes vibration and acoustic noise.
The vibration in the SRM is due to the control strategies and geometric design of the motor [3][4][5][6][7] . The geometric design approach refers mechanical design related to vibration behavior. The stator part of SRM is particularly designed to avoid resonance frequencies and associated mode shapes excited by a harmonic magnetic force. In dynamic operating conditions control strategies are used to run the motor with reduced vibrations for a better control of the SRM, it is required to predict the vibration frequencies of the SRM at different operating conditions. The existing literature much attention has paid to the mechanical design of stator yoke and pole shape related to vibration behavior. In this geometric design, SRM designed using Finite Element Analysis (FEA) packages has reduced resonance at the operating range of speeds due to harmonic magnetic forces [6][7][8][9][10][11] . The second is vibration is produced in the SRM due to control strategies. It found from current waveform, turn-on and turn-off times of the SRM. In this study, a new algorithm is proposed to estimate vibration produced in the SRM for different control strategies.
In this study a novel method to predict the vibration frequencies SRM from the measured electrical parameters at operating conditions. This method has been developed for the simulation and verified experimentally. In simulation method, a nonlinear model is developed in the MATLAB/SIMULINK environment using inductance profile. Dynamic characteristic of SRM is simulated and the results are verified experimentally with the developed prototype SRM. From the dynamic characteristic of the SRM, electromagnetic torque is found and it is analyzed using time domain to frequency domain analysis tool FFT. Using this tool, vibration frequencies and their magnitudes are found for the SRM in dynamic and transient operating condition. These estimated vibration frequencies for different control strategies are tabulated and compared with the experimental results. Or: where, ϖ is the angular speed of the motor the torque The phase equation can be expressed as: T Mph is generated by on phase can be expressed as: The one phase model of a three phase 6/4 SRM with current loop control is shown in the Fig. 1.

Current Block:
The flux linkage of SRM/phase, which includes the back emf is written as follows: The current-flux linkage-rotor position characteristics of 6/4 SRM are shown in Fig. 2. The complete parameters and dimensions of the SRM are given in appendix-1. The obtained current-flux linkagerotor position characteristics from the MAGNET6.1 are used to model the ANN for SRM model. ANN has two inputs and one output. The inputs are flux linkage and rotor position and output is current. The modeled current block using ANN is shown in Fig. 3.  For dynamic simulation electromagnetic torque produced to be found w.r.t. time. The instantaneous torque produced on SRM can be calculated using equation (6). And it is shown in the Fig. 6.  Figure 7 shows the e.m.f block of the motor. One is a single pulse operation or high-speed operation and another is low speed or current control. The most popular current control strategy is hysteresis current control, wherein actual phase current is allowed to vary between upper and lower bands of the set current values. The current control block is shown in Fig. 8.

Fig. 8: Current Controller
To complete one revolution of the 6/4 pole SRM, it is required to have 12 switching. Figure 9a-d shows the inductance profile for instantaneous current, phase current, phase voltage and torque. Figure 10 shows phase current and voltage during single pulse operation during simulation and Fig. 11 shows phase current and voltage during experimentation on single pulse operation.  Figure 12 and 13 shows the input voltage is for SRM using PWM signal from simulation and experimental setup. In this control current profile is modified and vibration produced SRM is also reduced.

Estimation
Vibration Frequency: Vibration frequency of the SRM is computed from electromagnetic torque produced by it. The electromagnetic torque produced by the motor is a continuous time domain variable. In order to get the vibration frequency, it is necessary to do the frequency transformation. Fourier Transform achieves the frequency transformation of the time domain variable. The Fourier transform, a pervasive and versatile tool, is used in many fields of science as a mathematical or physical tool to alter a problem into one that can be more easily solved. The Fourier transform decomposes or separates a waveform into sinusoids and coincides of different frequency. The sum of sinusoids and coincides of different frequency gives the original waveform. It identifies or distinguishes the different frequency sinusoids and their respective amplitudes. The Fourier transform is defined as: and its inverse transform is defined as: for an input sequence of length of N, the DFT of a continues time signal is given by: and its inverse DFT is given by: If x (n) is real, we can rewrite the above equation in terms of a summation of sine and cosine functions with real coefficients:

Modeling of FT Block:
The FT block available in Simulink is used to analysis the EM torque. The FT block can accept only frame data, which is implemented through the delay line block.

RESULTS
The vibration frequency analysis is done for the different conduction periods (θ ON and θ OFF period) and different loads and the results of the simulation are presented in Table 1. The vibration frequency of the SRM for the single pulse voltage setup with 1N-m load is tabulated in Table 1. The Table 2 presents the same for the PWM control of the input voltage. This analysis is repeated for different load conditions and loop currents. The results are proportional table formed. This analysis shows that vibration of the motor is very less for the conduction period from 12-44 degrees.