Formation of bearings parts waviness in centerless mortise grinding on rigid supports

Abstract

The formation of waviness on the working surfaces of bearing parts is associated with fluctuations in the size of the cut layer of metal and changes in the components of the cutting force. Laplace operators were used to model the centerless grinding system based on the construction of the transfer function and the characteristic equation. It was found that the formation of waviness depends on the position of the hodograph of the movement of the vector of the center of the part in the complex plane, which in turn depends on the geometric parameters of the rigid supports of the centerless grinder machine. This makes it possible, based on hodographs and the angular orientation of their asymptotes, to determine the geometric stability of the process depending on the angles of adjustment of the rigid supports of the grinder machine. Two methodological approaches were used to confirm the correctness of the hypotheses. The first one is a multiplication of wave’s hodographs. The second one is regeneration displacement and the coincidence of the combined hodograph of regeneration and waviness displacement mechanisms with the hodograph of infinitely rigid machine displacement. The diagrams which allow choosing geometry of adjustment of rigid support that allows to increase or decrease parameters of certain harmonics are developed. The 3D diagram allows setting the local minima, characterized by acceptable geometric adjustment conditions, providing regulated waviness of the working surfaces of bearing parts.