Abstract
The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.
Highlights
In electrical motors many different kinds of excitation exist, like mechanical unbalance, misalignment of the coupling [1,2,3] and electromagnetic forces—e.g. unbalanced magnetic pull [4,5,6,7,8,9,10,11]—which may cause vibrations
The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and considering the gyroscopic effect
The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings
Summary
In electrical motors many different kinds of excitation exist, like mechanical unbalance, misalignment of the coupling [1,2,3] and electromagnetic forces—e.g. unbalanced magnetic pull [4,5,6,7,8,9,10,11]—which may cause vibrations. In standards and specifications the so called run out of the shaft journals is limited by e.g. the standard IEC 60034-14 [18] and the standard API 541 [19] Due to this form deviation the centre of the shaft journal V changes its position in the sleeve bearings as the rotor rotates, leading to a dynamic displacement on the oil film (Figure 1). The developed rotordynamic model in [12] is more suitable for a stiff rotor design, where only the first bending mode—“V-shape”—of the rotor is of interest For this mode, the influence of the inertias of the mass moments and the gyroscopic effect is usually small for electrical rotors. The here presented rotordynamic model is suitable for flexible rotors
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