Analytical study of thermal variation impact on dynamics of a spindle bearing system

Abstract

Changes in the thermal status of machine tools spindle-bearing system can have a noticeable effect on the performance of the machine itself, and therefore studying the thermal effect on the performance ball bearing during service is important. For this purpose, a study was carried out where a simple rotating shaft system supported by two angular contact ball bearings was taken into consideration. Heat was generated due to the contact between the balls and rings of the bearing. This thermal effect on the dynamics of the system was studied using a transient thermal model. The system was divided into nodes; each was assumed to be a uniform temperature. Thermal energy balance was used on each node to obtain a set of differential equations. ODE solver in MATLAB was used to solve the resulting system of differential equations. The thermal model considered an initial preload as well as the thermal preload that is caused by the uneven expansion of bearing components. In this research, a 5 DOF nonlinear dynamical system model is integrated with a spindle-bearing thermal model and then utilized to study the impact of preload variations on the spindle-bearing system of a grinding machine. The effect of different system parameters such as speed of rotation, type of bearing, ambient temperature, type of oil, initial preload on temperature output and thermal growth within the system was studied. The study shows that the heat generation rate is directly proportional to the rotational speed of the shaft and higher thermally induced preload is reached at higher speeds. It is also noticed that initial preload has a small effect on the heat generation, thermally induced preload, and temperature of the bearing. Also, the dominant frequency values of the spindle system generally increase with changing thermally induced preload values. This study is useful in predicting the thermal profile as well as preload value resulting in the bearing assembly, which in turn will be used to predict variation in the dynamics of the system.

Effects of the interval geometric deviation and crowning parameters on the automotive differential dynamics

“…Several studies have scrutinized the effects of heat on the dynamic performance of the gear systems. [42][43][44][45] The differential pinion is attached to the driver by means of a pinion shaft that is considered as mass-less and behaves as torsional stiffness denoted by k θ dp . Its expressions can be calculated as follows:…”

A stiffness optimization method for a shaft-bearing-pedestal system based on the dynamics

“…26 is improved to be a comprehensive SBPS model, which can formulate both the shaft and pedestal stiffness. In the dynamic model, some assumptions are made: (a) The Hertzian-based with no friction and hysteretic damping is considered; however, there is hysteretic material damping in practice 33 ; (b) the lubrication oil is ignored and there is no clearances emerge; however, the clearances emerge and a lubricated analysis is required usually, which also provides friction 5 , 34 ; (c) the effect of generated contact temperature is not considered and the isothermal condition is used; however, the contact temperature will be caused in practice 35 ; (d) the defects and ball spin are modelled; (f) the mass of ball is ignored; and (h) the axial load is not considered.…”

Dynamic modeling of rotor-bearing-housing system with local defect on ball bearing using mass distribution and energy methods

“…Alfares et al. 26 integrated a spindle-bearing thermal model with a 5-DOF nonlinear dynamical system model of the grinding spindle supported by a pair of angular contact ball bearings to study the impact of preload variations on the system.…”