A Method for Predicting the Influences of Bearing Support Stiffness and Position on the Vibrations of a Flexible Rotor System

The bearing support stiffness and position can greatly affect the vibrations of flexible rotor systems (FRSs). However, most previous works only focused on the effect of the bearing support stiffness on the critical speeds or modal characteristics including the natural frequencies and mode shapes of rigid rotor systems (RRSs). The previous studies missed the combined effects of the bearing support stiffness and position. To overcome this issue, an analytical method of a FRS based on the finite element (FE) method is proposed. Our model considers the bearing support stiffness and rotational inertia of FRS. The frequency equation of FRS is established for solving the critical speeds. The critical speeds and modal deformations of FRS from our model and the numerical model based on a commercial software are compared to verify the effectiveness of the presented method. The effects of the bearing support stiffness and position on the critical speeds of FRS are analyzed. The results show that the critical speeds are positively correlated with the bearing support stiffness. The critical speeds of FRS are also greatly affected by the bearing position. This study can provide some guidance for the optimization design method of bearing support stiffness and position in FRSs.

An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

The support stiffness and positions of the bearings can greatly affect the vibrations of flexible rotor systems. However, most previous works only focused on the effect of the support stiffness of the bearings on the critical speeds of the rigid rotor systems or modal characteristics including natural frequencies and mode shapes, which missed the combine effects of the support stiffness and positions of the bearings. To overcome this issue, an analytical dynamic model of a flexible rotor system based on the finite element (FE) method is proposed. The model considers the support stiffness of the bearings and rotational inertia of the rotor system. The frequency equation of the rotor system is established for solving the critical speeds. The critical speeds and modal deformations of the system from the presented model and the numerical model based on a commercial software are compared to verify the effectiveness of the proposed FE model. The effects of the support stiffness and positions of the bearings on the critical speeds of the flexible rotor system are analyzed. The results show that the critical speeds are positively correlated with the support stiffness. The critical speeds of the flexible rotor system are also greatly affected by the support positions of the bearing. This study can provide some guidance for the optimization design method of the support stiffness and positions of the bearings in the flexible rotor systems.

Robust Optimization of Flexible Rotor Systems With Uncertain Parameters via Interval Analysis Method

Uncertainties in the input parameters are inevitable in any design process. Along with the demands for higher rotational speed and higher efficiency of rotating machinery, parameter uncertainties (e.g. support stiffness, the effective bending stiffness of connecting structures) resulted from the increasing load on rotor systems lead to significant scatter of its dynamic performance. These parameters are “uncertain but bounded” which means the distributions are unknown, but the intervals are always got easier. This paper presents a method to robustly optimize the dynamic performance of flexible rotor systems taking into account parameter uncertainties via interval analysis method. Interval analysis methods for modal properties and dynamic response behavior of rotor systems are developed with the interval variables introduced into the equation of motion. The aim of the robust design method is to optimize the critical speed margins and dynamic load on bearings, in the meanwhile, minimizing the variability of the objective items by the means of reducing their sensitivity to parameter uncertainties. A numerical example is presented, results show that, for the high-speed flexible rotor systems, the optimal choices of design variables could reduce of sensitivity to rotor parameter uncertainties, thus optimizing the variability of dynamic performance, which has important practical significance in engineering.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

Dynamic Analysis of Flexible Rotor Systems Subjected to Time-Varying Base Excitations

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. The objective of this paper is to develop a general model for flexible rotor systems subjected to time-varying base excitations and study the direct effects of angular base motions on the dynamic behaviors of a simple rotor. The model is developed based upon finite element method and Lagrange’s equation. Two groups of Euler angles are introduced to describe the rotation of the rotor and the base, respectively. Six types of base motions are considered in the model. In the numerical simulations, three types of angular base motions (pitching, rolling and yawing) are considered and assumed to be sinusoidal varying with time. The effects of base angular amplitudes, base frequency and rotation speed on the system dynamic behaviors are discussed in detail. It is shown that pitching and yawing have a great influence on the response amplitudes and the shape of the rotor orbits. Especially, resonances occur when the base frequency meets the natural frequencies. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency.