Mathematical Multibody Model of a Soft Mounted Induction Motor Regarding Forced Vibrations Due to Dynamic Rotor Eccentricities Considering Electromagnetic Field Damping

The paper presents a mathematical multibody model of a soft mounted induction motor with sleeve bearings regarding forced vibrations caused by dynamic rotor eccentricities considering electromagnetic field damping. The multibody model contains the mass of the stator, rotor, shaft journals and bearing housings, the electromagnetic forces with respect of electromagnetic field damping, stiffness and internal (rotating) damping of the rotor, different kinds of dynamic rotor eccentricity, stiffness and damping of the bearing housings and end shields, stiffness and damping of the oil film of the sleeve bearings and stiffness and damping of the foundation. With this multibody model, the bearing housing vibrations and the relative shaft vibrations in the sleeve bearings can be derived.

Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect

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.

Analysis of Different Vibration Control Strategies for Soft Mounted Induction Motors with Sleeve Bearings Using Active Motor Foot Mounts

The paper presents a theoretical analysis of different vibration control strategies of soft mounted induction motors with sleeve bearings, using active motor foot mounts. After the vibration model is presented, different controllers in combination with different feedback strategies are mathematically investigated. The focus is here on the forced vibrations, caused by dynamic rotor eccentricity—rotor mass eccentricity, magnetic eccentricity and bent rotor deflection. After the mathematically coherences are described, a numerical example is shown, where the forced vibrations caused by bent rotor deflection are investigated, for different control strategies, where the mass matrix, the stiffness matrix and the damping matrix are influenced by different control parameters. The aim of the paper is to show the mathematically coherences and the possibility to influence the vibration behaviour, by different control strategies to optimize the vibration behaviour of soft mounted induction motors.

Influence of the Foundation on the Threshold of Stability for Rotating Machines with Roller Bearings—A Theoretical Analysis

The paper presents a mathematical model for analyzing the threshold of stability for rotating machines, where the rotor is linked to the stator by roller bearings, bearing housings and end-shields and where the stator feet are mounted on a soft foundation. The internal (rotating) damping of the rotor is the only source of instability, which is considered in the paper. After the mathematical coherences of the multibody model are described, a procedure is presented for deriving the threshold of stability. Additionally, a numerical example is shown, where the threshold of stability is calculated for different boundary conditions. It could be demonstrated, that the stiffness of the foundation—even if the foundation stiffness is isotropic—can help stabilizing this kind of vibration system in the same way as orthotropic bearing stiffness or orthotropic bearing housing and end-shield stiffness for a rigid foundation.

Active Vibration Control of Rotating Machines with Active Machine Foot Mounts on Soft Foundations Based on a 3D-Model

The paper presents a simplified 3D-model for active vibration control of rotating machines with active machine foot mounts on soft foundations, considering static and moment unbalance. After the model is mathematical described in the time domain, it is transferred into the Fourier domain, where the frequencies response functions regarding bearing housing vibrations, foundation vibrations and actuator forces are derived. Afterwards, the mathematical coherences are described in the Laplace domain and a worst case procedure is presented to analyze the vibration stability. For special controller structures in combination with certain feedback strategies, a calculation method is shown, where the controller parameters can be directly implemented into the stiffness matrix, damping matrix and mass matrix. Additionally a numerical example is presented, where the vibration stability and the frequency response functions are analyzed.