Study on Correction Algorithm of Time-varying Mesh Stiffness of Helical Gears and Its Influencing Factors

Abstract

Due to the inaccuracy of potential energy method in calculation of time-varying mesh stiffness of helical gears, a stiffness correction algorithm was proposed. Considering the different expressions for the length of contact lines of single tooth on two kinds of situations in which the transverse contact ratio is greater or less than the overlap ratio, a non-uniform cantilever beam model was established when root circle and base circle misaligned, and then the mesh stiffness of helical gears was derived and calculated by using slice-integral method. By comparing with ISO standard and finite element method, the feasibility of the proposed correction algorithm was verified. Meanwhile, a parametric study was conducted to investigate the effects of various parameters, such as helix angle, normal module, tooth number, face width and normal pressure angle on the behavior of mesh stiffness. The calculation and analysis indicate that the relative time of the engaging-in section is related to the proportion values of transverse contact ratio and overlap ratio. Variation of gear parameters affects the fluctuation value of total mesh stiffness and average mesh stiffness by changing the contact ratios and single mesh stiffness. In addition, the fluctuation is little when the transverse contact ratio or overlap ratio is close to an integer, while it fluctuates more intensively when the total contact ratio is close to an integer. Compared with the traditional potential energy method, the precision of correction algorithm in calculating time-varying mesh stiffness of helical gears is obviously improved. It has relatively better practicability in the accurate calculation of stiffness excitation of helical gears.

Keywords: potential energy method,  helical gears,  time-varying mesh stiffness,  contact ratios