Nonlinear vibration of crowned gear pairs considering the effect of Hertzian contact stiffness

Abstract

This study aims to analyze the influence of lead crowning modification of teeth on the vibration behavior of a spur gear pair. Two dynamic rotational models including an uncrowned and crowned gear are examined. Hertzian mesh stiffness is computed using tooth contact analysis in quasi-static state along a complete mesh cycle of teeth mesh. The dynamic orbits of the system are observed using some useful attractors which expand our understanding about the influence of crown modification on the vibration behavior of the gear pair. Nonlinear impact damper consists of non-integer compliance exponents identify energy dissipation of the system beneath the surface layer. By augmenting tooth crown modification, the surface penetration increases and consequently normal pressure of the contact area becomes noticeable. Finally, the results show modification prevents gear pair to experience period doubling bifurcation as the numerical results proved. Using this new method in dynamic analysis of contact, broaden the new horizon in analyzing of the surface of bodies in contact.

Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports

“…In order to achieve this goal, the dynamic models are solved in "RADAU algorithm" numerically [7,20]. The accuracy of this code has been frequently confirmed in several published papers: [7,11,12,20].…”

“…Some researchers are focused on the effect of faults on the dynamic behavior of gear pairs [11][12][13]. Peng et al [14] suggested a new idea of calculating the load transmission error (LTE) by considering the effect of the bearing supports.…”

Spiral Bevel Gears: nonlinear dynamic model based on accurate static stiffness evaluation

“…The LTCA could be carried out using a variety of approaches: FEM, experiments, and analytical solutions (with certain simplifications). By comparing these methods, one can conclude that: i) the experimental method requires a well-equipped laboratory, it is cost and time demanding, moreover, measurements on rotating parts are limited to non-contact surfaces; ii) analytical solutions have been generally developed for spur or helical gear pairs, however, they are not perfectly suitable or precise for gear pairs with complicated geometries, such as a spiral gear pair; iii) nonlinear FEM (including contact analysis) has become increasingly popular in recent years [3,21,22].…”

Spiral Bevel Gears Nonlinear Vibration Having Radial and Axial Misalignments Effects

“…Equation ( 6) is a nonlinear differential equation with time-varying parameters. This governing equation is solved numerically "RADAU scheme", which is an implicit scheme of the Runge-Kutta algorithm; see, e.g., [2,3,22,25,26].…”

“…A wide range of methods has been used to study gear pairs [2][3][4][5][6]. The nonlinear vibration of actual gear pairs, with some likely faults and conditions, has become the main issue among researchers due to vast ranges of applications of the gear systems.…”