Analysis of dynamic behaviour of rotor-bearing system

Abstract

This paper deals with a non-linear mathematical model for simulation and analysis of a dynamic behaviour of a rotorbearing system. The model is used for the simulation of plane motion of a centre of rotor's cross-section which makes the model convenient for the analysis of vibrations generated in a rolling bearing as well as for the analysis of accuracy of the revolution of rotor supported on a rolling bearing. The model takes into account the following quantities: internal radial clearance, external radial load and unbalanced load. Differential equations of a motion are derived using Lagrange's equations. The contacts between the balls and the rings are considered to be non-linear with a stiffness derived by the Hertzian theory of an elastic contact. The proposed model enables direct determination of local contact deformations which significantly reduces needed computations and CPU time. The results obtained by the model are used to reconstruct phase-space trajectories and Poincaré maps and to calculate the largest Lyapunov exponent in order to establish the stability of rotor-bearing system motion. A computer program is developed based on the mathematical model for the simulation and analysis of a dynamic behaviour of a rotor-bearing system.

Dynamics characteristics of a rotary table motorized spindle with externally pressurized air bearings

“…Rotating speed [rpm] 809 of the rotor are much smaller than the clearance of the air bearings. (3) is mounted on the test stand (4). The spring-loaded method [14] consists of the upper load-applying block (6), the lower load-applying block (9), the load-applying bolt (1), the guide bar (2), and the spring (7).…”

“…According to type of bearing, the rotary table spindle can be classified into three categories: the spindle with rolling bearing, the spindle with fluid bearing and the spindle with air bearing. The rolling bearing spindle [4][5][6] is simple in structure, easy for maintenance, but low in rotation accuracy, limited in working life and moderate in loading capacity. Compared with the rolling bearing spindle, the fluid spindle [7,8] has higher loading capacity, higher rotation accuracy and longer working life, but more complicated construction and higher manufacture cost.…”

Nonlinear Dynamic Analysis of Rotor‐Bearing System with Cubic Nonlinearity

“…A widely used model is that the rotor-bearing assembly is regarded as a spring-mass system where the bearings are modeled to be the massless springs and the rotor is modeled as a mass. For this model, investigators have studied the nonlinear dynamics of the rotor-bearing system caused by rotating speed effects [5][6][7], ball size variation [8][9][10], surface waviness [11][12][13][14][15], the number of balls [16], imbalance [17,18], and internal radial clearance [19][20][21]. In addition to the commonly used two or three degrees of freedom rotor-bearing models, more complex models were presented to research on the dynamic behaviors of the rotorbearing system.…”

Stability characteristics of lubricating film in mill oil-film bearings

“…Up to date, many studies (Shenoy and Pai, 2010;Mishra, 2013;Guha, 2010) have focused on the effects of different factors on the stability of rotor-bearing systems. The analysis methods of stability mainly include the linearization analysis (Guha, 2010), nonlinearization analysis (Jun et al, 2015;Amamou and Chouchane, 2014;Lin et al, 2014;Kushare and Sharma, 2014;Jovanovi c and Tomovi c, 2014) and basis stiffness and damping coefficient from the motion equation (Papadopoulos et al, 2008;Rao et al, 2014). According to the linear rotor dynamics theory, hydrodynamic force is characterized by eight linear stiffness and damping coefficients (Jovanovi c and Tomovi c, 2014).…”