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An investigation of the dynamic electromechanical coupling effects in machine drive systems driven by asynchronous motors

Author links open overlay panel Tomasz Szolc , Robert Konowrocki , Maciej Michajłow , Agnieszka Pręgowska

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Cite https://doi.org/10.1016/j.ymssp.2014.04.004 Get rights and content Highlights

• Analytical model of the driven machine–asynchronous motor system. • Attenuation of vibration resonances caused by the electromagnetic damping. • Increase of the mechanical natural frequencies due to electromagnetic stiffening. • Induction of severe low-frequency torsional vibrations by the asynchronous motor. • Estimation of electromechanical coupling severity using dynamic characteristics. Abstract

In the paper dynamic electromechanical interaction between the rotating machine drive system and the electric driving motor is considered. The investigations are performed by means of the circuit model of the asynchronous motor as well as using an advanced structural hybrid model of the drive system. Using the analytical solutions applied for the electrical and the mechanical systems the electromagnetic stiffness and coefficient of damping, both generated by the electric motor rotationally interacting with the mechanical system of the given dynamic properties, were determined. By means of experimentally validated computational responses obtained for torsional harmonic excitation induced by the driven machine working tool, a modification of dynamic properties of the mechanical system by the electromagnetic flux between the stator and the rotor has been studied. Introduction

Torsional vibrations of drive systems usually result in a significant fluctuation of the rotational speed of the rotor of the driving electric motor. Such oscillations of the angular speed superimposed on the average rotor rotational speed cause more or less severe perturbation of the electromagnetic flux and thus additional oscillations of the electric currents in the motor windings. Then, the generated electromagnetic torque is also characterized by additional variable in time components which induce torsional vibrations of the drive system. According to the above, mechanical vibrations of the drive system become coupled with the electrical vibrations of currents in the motor windings. Such a coupling is often complicated in character and thus computationally troublesome. Because of this reason, till now majority of authors simplify the matter regarding mechanical vibrations of drive systems and electric current vibrations in the motor windings as mutually uncoupled. Then, the mechanical engineers applied the electromagnetic torques generated by the electric motors as ‘a priori’ assumed excitation functions of time or the rotor-to-stator slip, e.g. in [1], [2], [3], usually based on numerous experimental measurements carried out for the given electric motor dynamic behaviors. For this purpose, by means of measurement results, proper approximate formulas have been developed, which describe respective electromagnetic external excitations produced by the electric motor [2]. However, the electricians thoroughly modeled electric current flows in the electric motor windings, but they usually reduced the mechanical drive system to one or seldom to at most a few rotating rigid bodies, as e.g. in [4]. In many cases, such simplifications yield sufficiently useful results for engineering applications, but very often they can lead to remarkable inaccuracies, since many qualitative dynamic properties of the mechanical systems, e.g. their mass distribution, torsional flexibility and damping effects, are being neglected. Thus, an influence of drive system vibratory behavior on the electric machine rotor angular speed fluctuation, and in this way on the electric current oscillations in the rotor and stator windings, cannot be investigated with a satisfactory precision. Currently fast development of machinery driven by electric motors is observed which requires bigger and bigger knowledge about dynamic interaction between the mechanical and electrical parts of the entire system. An importance of the electromechanical coupling effects taken into consideration is particularly significant when possibly exact results are required for investigation of extremely responsible drive systems or for analyses of their sufficiently precise and stable motions as well as in order to elaborate proper active vibration control algorithms. This problem has been already studied for many years and by many authors, but in majority of cases sufficiently accurate electromechanical models are not usually used, e.g. because of the above mentioned far-reaching simplifications of the mechanical system. For example, in [5] an influence of ‘a priori’ assumed rotor angular speed oscillation on the electromagnetic torque fluctuations was investigated by means of the circuit model of the asynchronous motors. In [6] rotor-shaft transient torsional vibrations in the turbogenerator sets caused by network disturbances were considered as coupled with the electric current vibrations in the generator windings. Coupling effects between the geared drive system torsional vibrations and the electric current oscillations in the synchronous motor windings were investigated in [7], where the current flows in the electric machine windings were modeled using Park׳s equations. In the case of synchronous machines the complex torque coefficients method is commonly applied in order to determine the torsional vibration frequency dependent electromagnetic stiffness and damping coefficient, where negative value zones of the latter indicate a probability of dynamic instabilities. Advantages and drawbacks of this approach are described in [8]. A practical application of the complex torque coefficients method has been demonstrated in [9] for the coupled electromechanical vibration analysis of the multi-generator drive system. In [10], [11] the dynamic interaction between the asynchronous or synchronous motors and the drive system was studied, where the motor electromagnetic flux was modeled using two-dimensional finite elements and the drive train was substituted by means of the simple spring-mass model. In these papers the above mentioned electromagnetic stiffness and damping coefficient have also been determined for the synchronous and various asynchronous motors, where the torsional perturbations were excited by the use of ‘a priori’ assumed test impulses of the motor rotor angular speed. Nowadays, a severity of the electromechanical interaction is commonly observed in the case of so called ‘variable speed drives’ (VSD) of large rotating machines driven by synchronous or asynchronous motors controlled by the load commutated inverters. In transient and steady-state operating conditions these devices are responsible for generating additional fluctuating driving torque components which can be a source of unexpected dangerous resonance effects of torsional vibrations. Some results of theoretical and experimental investigations in this field have been reported e.g. in [12], [13]. Coupled electromechanical interactions were also studied in [14] using the circuit model of the stepping motor driving a precise mechanism modeled by means of the advanced hybrid torsional train consisting of torsionally deformable continuous structural macro-elements and discrete dynamic oscillators. As it follows from numerous observations, drive systems of several machines driven by the asynchronous motors commonly indicate diverse sensitivity to resonance effects following from their mechanical eigenvibration properties. It is suspected that for almost complete attenuation of resonance effects at resonant frequencies of excitation induced by the driven machine retarding torque as well as for unexpected severe amplification of torsional vibration amplitudes forced by a non-resonant excitation the above mentioned additional torsional elasticity and viscosity introduced into the mechanical system by the electromagnetic flux generated in the electric motor are responsible. In order to explain such dynamic behavior better, in this paper a qualitative analysis of the electromechanical coupling effects for several rotating machine drive systems driven by various asynchronous motors during their steady-state operation are performed. The investigations are carried out by means of the circuit model of the electric motor and using the advanced structural hybrid model of the rotating machine drive system. Some theoretical results have been confirmed by measurements performed on the real objects. Access through your organization Check access to the full text by signing in through your organization. Access through your organization Section snippets

Modeling of the mechanical system

In order to investigate a character of the electromechanical coupling, the possibly realistic and reliable mechanical model of the drive system is applied. In this paper, similarly as e.g. in [14], [15], [16], dynamic investigations of the entire drive system are performed by means of the one-dimensional hybrid structural model consisting of finite continuous visco-elastic macro-elements and rigid bodies. In this model by the torsionally deformable cylindrical macro-elements of continuously Modeling of the electric motor

From the viewpoint of electromechanical coupling investigation, in the introductory approach, the properly advanced circuit model of the electric motor seems to be sufficiently accurate. The symmetrical three-phase asynchronous motor electric current oscillations in its windings are described by the six circuit voltage equations transformed next into the system of four Park׳s equations in the so called ‘αβ–dq’ reference system [ 3 2 U cos ( ω e t ) 3 2 U sin ( ω e t ) 0 0 ] = [ L 1 + 1 2 M 0 3 2 M 0 0 L 1 + 1 2 M 0 3 2 M 3 2 M 0 L 2 ′ + 1 2 M 0 0 3 2 M 0 L 2 ′

Solution of the problem

From the form of Park׳s equations (5) as well as from formula (6) it follows that the coupling between the electric and the mechanical systems is non-linear in character, particularly for significantly varying motor rotational speeds Ω(t). Such a coupling leads to very complicated analytical description resulting in rather harmful computer implementation. Thus, this electromechanical coupling can be realized here by means of the step-by-step numerical extrapolation technique, which for Computational and experimental examples

The above derived analytical solution for the electromechanical model will be illustrated by means of three examples of various rotating machine drive systems driven by diverse asynchronous motors. Fundamental parameters of these motors are provided in Table 1. In all cases the considerations are going to be focused on the interaction frequency ranges containing the fundamental, first torsional eigenfrequencies. These systems will be studied in steady-state operating conditions under sinusoidal Final remarks

In the paper dynamic electromechanical coupling between the structural model of the rotating machine drive system and the circuit model of the asynchronous motor has been investigated. By means of the analytical–computational approach an interaction between the fundamental torsional eigenmodes and the driving electromagnetic torque was studied in order to determine the frequency zones of greater sensitivity to amplification of torsional vibrations as well as the frequency zones of significant Acknowledgment These investigations have been supported by the Polish National Centre of Research and Development of the Ministry of Science and Higher Education: Research Project PBR-N R03 0012 04.

Recommended articles References (17)

T. Szolc et al. Damage identification in vibrating rotor-shaft systems by efficient sampling approach Mech. Syst. Signal Process. (2009) B.F. Evans, A.J. Smalley, H.R. Simmons, Startup of synchronous motor drive trains: the application of transient... A. Laschet Simulation von Antriebssystemen (1988) P. Schwibinger et al. Improvement of a reduced torsional model by means of parameter identification Trans. ASME, J. Vib., Acoust., Stress Reliab. Des. (1989) L. Harnefors Analysis of subsynchronous torsional interaction with power electronic converters IEEE Trans. Power Syst. (2007) C. Concordia Induction motor damping and synchronizing torques AIEE Trans. Power Appar. Syst. (1952) H. Berger et al. Simulation models for calculating the torsional vibrations of large turbine-generator units after electrical system faults Siemens Forsch. — u. Entwickl. Ber. (1981) T. Iwatsubo, Y. Yamamoto, R. Kawai, Start-up torsional vibration of rotating machine driven by synchronous motor, in:... There are more references available in the full text version of this article. Cited by (66)

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