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Numerical Modal Analysis of Vibrations in a Three-Phase Linear Switched Reluctance Actuator

, , António Espírito Santo,
Published: 18 April 2017
Modelling and Simulation in Engineering , Volume 2017, pp 1-18; doi:10.1155/2017/3258376

Abstract: This paper addresses the problem of vibrations produced by switched reluctance actuators, focusing on the linear configuration of this type of machines, aiming at its characterization regarding the structural vibrations. The complexity of the mechanical system and the number of parts used put serious restrictions on the effectiveness of analytical approaches. We build the 3D model of the actuator and use finite element method (FEM) to find its natural frequencies. The focus is on frequencies within the range up to nearly 1.2 kHz which is considered relevant, based on preliminary simulations and experiments. Spectral analysis results of audio signals from experimental modal excitation are also shown and discussed. The obtained data support the characterization of the linear actuator regarding the excited modes, its vibration frequencies, and mode shapes, with high potential of excitation due to the regular operation regimes of the machine. The results reveal abundant modes and harmonics and the symmetry characteristics of the actuator, showing that the vibration modes can be excited for different configurations of the actuator. The identification of the most critical modes is of great significance for the actuator’s control strategies. This analysis also provides significant information to adopt solutions to reduce the vibrations at the design.1. IntroductionThe main drawbacks associated with switched reluctance drives (SRD) are the vibrations and the acoustic noise produced in its operation, which are relatively higher than those of the induction machines and permanent magnet synchronous drives. This feature is especially relevant for noise sensitive applications and has received considerable attention over the past two decades. A plethora of studies exists on the analysis of origins and characterization of the mechanical vibrations [1–12], the prediction and mitigation [13–20], and the emitted acoustic noise [11, 20–23]. The majority of published works focuses on the rotational configuration of these type of machines, that is, switched reluctance motor (SRM) drives.When compared to SRM, the linear switched reluctance actuator (LSRA) is a relatively new research and development subject. As a result, the known and published works addressing the vibrations, the force ripple, and the acoustic noise problem for LSRA are relatively scarce [11, 24–28]. Numerous studies identify the primary sources of the acoustic noise as structural vibrations, radiated from the stator, shaft, and bearings and induced by the generated forces. These vibrations vary with the load or the step voltage. Accordingly, several methods have been proposed for either active noise cancellation or new control and optimal driving strategies. For the acoustic noise mitigation, some studies focus on the prediction and characterization of the vibrations. Consequently, several models have been formulated based on the finite element method (FEM), as an alternative to analytical or experimental methods, namely, the hammer test method. Among the reasons that explain the use of FEM are the improvements in computational tools and their performance and also the associated capacity to develop complex mechanical models and achieve high accuracy with the results.The operation of switched reluctance drives is based on the inductance profile of the machine coils,, which is related to the relative positions of its parts and its dimensions. The operation of a three-phase LSRA is based on the same principle as that of SRM and requires the sequential activation of phase coils a, b, and c [29]. If the poles of the stator and the teeth of the translator (or rotor) for any phase are at the unaligned position, the inductance reaches its minimum value. When a phase is activated, the electric current flowing through the coil induces an electromagnetic force that causes the moving parts to move towards the maximum inductance position (minimum magnetic reluctance), that is, to the aligned position. If the movement continues the inductance decreases with the misalignment, due to the increase in the relative displacement towards the minimum inductance. Assuming ideal conditions, the excitation current in the phase coil produces an electromagnetic motoring force that is expressed as [29] (pp. 22)whereis the peak value of the coil excitation current,. At the same time, due to the continuous displacement, regenerative forces,, occur in the regions adjacent to the full alignment position, such that, which are related to the negative variation of the inductance in phase coils b and c, respectively. In general, the regenerative forces superimpose to the motoring force. Repeated activation of the phases in sequence abc moves the translator forward and backwards when the sequence acb is activated. The smoothness of the displacement of the translator depends on the switching positions of the phases, on the duty cycle of the excitation, on the electronics converter topologies, and on the control mode strategies.In real applications, there are imperfections and nonlinearities associated with the inductance profile; besides, the driving currents do not vary linearly either. Moreover, for a given force, the desired excitation current values are achieved by the switching process of the electronics converters and the control strategies, usually modeled by a pulse width modulation signal. The switching regime causes variations to the current that foster ripple in the produced forces. Thus, the nature of the forces generated during the LSRA operation is susceptible to generating vibration whose magnitude can be amplified, especially in the vicinity of the natural frequencies of structural vibrations. The natural modes, the resonant frequencies, and the characteristics of the induced acoustic noise influence or restrict the use of machines, with direct consequences for human well-being and health [30]. On the other hand, the mechanical vibrations are particularly relevant when precise movement is a requirement and can compromise the application of the actuator.The sources of vibrations and the acoustic noise in LSRA are primarily the same as for the rotational configuration, due to their common modes of operation. However, the characteristics of the vibrations in electromechanical linear actuators evidence some unique features. Firstly, the natural modes depend on the structural characteristics of the actuator, which vary according to the relative position of the moving parts. Secondly, while vibrations are usually periodic in rotational configuration, in linear actuators the vibrations are periodic only if the excitation forces and the translation movements are periodic. This phenomenon occurs due to linear displacements in this type of machine, rather than angular movement in the rotational configuration. Also, the vibrations tend to be localized, and the associated displacements depend on the position and the structural configuration. Moreover, the finite length of the machine parts influences the propagation of the mechanical waves along the structure. The reflections at both ends interfere along the actuator structure, forming a stationary wave.The vibrations and the emitted acoustic noise are directly connected with structural aspects of the actuator and its characteristics related to the properties and the dimensions of the materials used. These characteristics dictate the mechanical vibration behavior of the machine and are not an easy issue to deal with from the analytical point of view, in part due to the difficulties encountered in modeling the mechanical structures. Among the structural differences between the rotational and linear configurations of SRD, one can mention the finite length of both the stator and the translator of the latter. On the one hand, the complexity of the mechanical model demands attention to the distribution of masses according to the different positions of the translator. On the contrary, the elastic model denotes results in an increase in complexity, and its analytical solutions are hard to obtain and might be not accurate enough. For these reasons, it is common to use computational simulation tools based on the finite element method (FEM) to model these structures.The FEM is essentially a discretization technique and approximation method for modeling the distributed parameter systems that correspond to its decomposition into several finite elements or building blocks, equivalent to a system discretization technique. When applied to linear systems, the finite element analysis (FEA) allows finding the approximate solutions to the differential equations that describe the physical model [31, 32].This paper presents a simulation study based on the finite element method to obtain the structural vibration modes and frequencies of an LSRA. The focus relies on frequencies within the range up to nearly 1.2 kHz. This band includes the vibration modes considered most relevant and critical to the actuator operation, according to the operation modes as forces profile of the actuator [17, 33]. Moreover, it complements preliminary results of simulations and experiments for frequencies up to 300 Hz [26]. The primary objective of this work is to collect data and establish a framework to characterize the linear actuator fully, regarding the vibrations modes induced due to the regular operation of the machine. Due to the lack of a priori knowledge regarding vibrations, we build a 3D model of the structure and use 3D FEM simulation software to find the natural vibration frequencies. The data obtained support the characterization of the linear actuator focusing on the excited vibrations and mode shapes. The results reveal abundant modes and harmonics and the symmetry characteristics of the actuator. These findings help to identify the vibration modes that can be excited for different configurations of the actuator, according to the position of its moving parts. The gathered
Keywords: switched reluctance motor / modal analysis / vibration / Wave Propagation / Behavior of the Mechanical / Finite element method / finite element analysis / FEM / Machines and Permanent Magnet / phase linear

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