Mathematical analysis of rotor shaft displacements in asynchronous machines; a critical speed or just a rotation of the orbit axis?

Abstract

This paper presents a mathematical analysis of rotor shaft displacements in asynchronous machines caused by different types of rotor eccentricity. Based on a simplified rotor model, the theoretical coherence between electromagnetic, rotor dynamic, and the specific characteristics of sleeve bearings is shown. The orbits of the rotor mass and the shaft journal are mathematically described for each kind of eccentricity and the shaft displacement with respect to two virtual fixed sensors is derived. Based on this theoretical description and on a numerical example, the paper shows that focusing in a theoretical rotor dynamic analysis only on the calculated amplitudes in direction of two fixed sensor positions, may lead to wrong conclusions concerning the evaluation of resonances. The aim of this paper is, based on a simplified rotor model, to show the mathematical coherence concerning typical rotor eccentricities in asynchronous machines and to demonstrate the necessity to focus not only on the amplitudes relative to two fixed sensor positions, but to also consider the semi-major axis of the calculated orbit and its angular position. The aim of the paper is not to replace a detailed finite element rotor dynamic analysis by a simplified analytical rotor model for predicting the real shaft vibrations. The intension is to prepare the basis for adopting the conclusions, derived from a simplified analytical model, into a more detailed rotor dynamic model -e.g. a finite element rotor dynamic model -and therefore to derive a more precise theoretical analysis of the real shaft displacements.

Theoretical rotor dynamic analysis of two-pole induction motors regarding excitation due to static rotor eccentricity

“…6. This model is a simplified rotor model based on the LAVAL rotor [14], taking in consideration electromagnetic effects [5,9]. In this paper the model is advanced for considering excitation by an oscillating magnetic force F r .…”

“…Therefore it is necessary to consider not only mechanical forces, caused by e.g., mechanical unbalance, but also the electromagnetic forces [1][2][3][4][5][6][7][8][9]. Mechanical unbalance and unbalanced magnetic pull occur with rotary angular frequency Ω-which is called 1x-excitation [1][2][3][4][5][6][7][8][9]. The rotary angular frequency Ω of an induction motor can be described by the electrical supply angular frequency ω 1 , the number of pole pairs p and the fundamental slip s [10].…”

Theoretical Vibration Analysis Regarding Excitation due to Elliptical Shaft Journals in Sleeve Bearings of Electrical Motors

“…The magnetic spring constant c m has a negative reaction, which is shown in Dorrell [7], Smith and Dorrell [8], Schuisky [9], Holopainen [10], Arkkio et al [11], Belmans et al [12], Stoll [13], and Werner [14,15]. This means that a radial movement between the rotor and stator creates an electromagnetic force that tries to magnify the movement.…”

“…Dynamic eccentricity is caused if the rotor is bent or if the rotor core is eccentrically positioned on the rotor shaft due to, for example, tolerances in the punching process of the rotor sheets. In this case a rotating magnetic force occurs, which is called UMP (unbalanced magnetic pull), which has been investigated in many publications as in Dorrell [7], Smith and Dorrell [8], Schuisky [9], Holopainen [10], Arkkio et al [11], Belmans et al [12], Stoll [13], and Werner [14,15].…”

Observer based identification of unbalanced magnetic pull in asynchronous motors

“…There are number of developed and published methods for diagnostics of the motor vibrations [6], [7]. The most of the techniques are primarily dedicated to vibration diagnostics of large machines and using direct measurements of the airgap length, e.g.…”