Excitation prediction by dynamic transmission error under sliding friction in helical gear system

Abstract

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Keywords

helical gear / time-varying contact line / transmission error / dynamic factor

References

[1] Kubo A. Stress condition, vibration exciting force and contact pattern of helical gears with manufacturing and alignment errors[J]. Journal of Mechanical Design, 1978, 100(1): 77 84

[2] Ozguven H N, Houser D R. Mathematical models used in gear dynamics: A review[J]. Journal of Sound and Vibration, 1988, 121(3): 383-411.

[3] Li C J, Lee H, Choi S H. Estimating size of gear tooth root crack using embedded modeling[J]. Mechanical Systems and Signal Processing, 2002, 16(5): 841-852.

[4] Amabili M, Fregolent A. A method to identify modal parameters and gear errors by vibrations of a spur gear pair[J]. Journal of Sound and Vibration, 1998, 214(2): 339-357.

[5] Ajmi M, Velex P. A model for simulating the quasi-static and dynamic behavior of solid wide-faced spur and helical gears[J]. Mechanism and Machine Theory, 2005, 40(2): 173-190.

[6] Pedrero José I, Pleguezuelos M, Muñoz Marta. Critical stress and load conditions for pitting calculations of involute spur and helical gear teeth[J]. Mechanism and Machine Theory, 2011, 46(4): 425-437.

[7] Fakher C, Tahar F. Analytical modeling of spur gear tooth crack and influence on gear mesh stiffness[J]. European Journal of Mechanics A / Solids, 2009, 28(3): 461-468.

[8] Tamminana V K, Kahraman A, Vijayakar S. A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs[J]. Journal of Mechanical Design, 2007, 129(1): 75-84.

[9] Velex P, Ajmi M. On the modelling of excitations in geared systems by transmissions errors[J]. Journal of Sound and Vibration, 2006, 290(3–5): 882-909.

[10] Velex P, Ajmi M. Dynamic tooth loads and quasi-static transmission errors in helical gears: Approximate dynamic factor formulae[J]. Mechanism and Machine Theory, 2007, 42(11): 1512-1526.