The impact of vibration response due to rolling bearing components waviness on the performance of grinding machine spindle system

Abstract

In this research, an analytical model based on a five-degrees-of-freedom nonlinear dynamical system was utilized to investigate the impact of vibration response due to inner race, outer race, and ball bearing waviness on the performance of grinding machine spindle system supported by two angular ball bearings. The waviness of rolling elements is modeled as a sinusoidal function is incorporated along the inner or outer races of bearing and ball surface. The elastic deflection and nonlinear contact force are calculated based on Hertzian contact model, while the shaft has five-degrees-of-freedom motions, three translational and two angular motions. The five–degrees-of-freedom nonlinear governing equations of the spindle system were developed taking into consideration the effect of outer race, inner race, and ball surface waviness, which are included in the kinematic constraints and force equilibrium equations of a ball. The developed model and its results are validated against results found in literature. Results by this paper indicate that the inner race waviness can significantly distort the tolerance and machining quality of grinding spindle-bearing systems more than does waviness in the outer race and ball elements. This is because the inner race waviness generates more complicated vibrations than the outer race and ball waviness. The most severe vibrations caused by the inner race waviness were found to occur when the waviness was of the order that is equal to multiple of number of balls in a bearing set plus or minus one ( $WO = i N_{b} \pm 1$ ).

Keywords

Grinding machine spindle angular-contact ball bearings dynamic analysis and modeling vibration response analysis

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