GEARBOX CRITICAL SPEEDS VARIABILITY PREDICTION INDUCED BY MANUFACTURING DISPERSION

摘要

The vibratory and acoustical behaviour of gearboxes results from numerous sources. Among these, it is generally admitted that the main source is the static transmission error under load (STE). This internal excitation is defined as the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfect and rigid (Welbourn, 1979). STE is mainly governed by periodic components at the meshing frequency f{sub}m (f{sub}m=f{sub}(rot)×Z, where Z is the number of teeth) due to (1) the elastic deflections of gear teeth under load (periodic meshing stiffness) and (2) the teeth geometry modifications, manufacturing errors and shaft misalignments. Under operating conditions, STE generates dynamic mesh forces leading to dynamic forces and moments transmitted through bearings, housing vibration and noise. Peak to peak STE is generally chosen as a straightforward indicator of vibratory and acoustic nuisances (Munro, 1991). Further, critical rotation speeds associated with high dynamic mesh forces and high noise levels, correspond to the excitation of some critical modes having a high potential energy stored by the meshing stiffness (Rigaud, 1996). These critical rotation speeds are mainly controlled by the time-average meshing stiffness. At last, considering gearbox manufactured in large number, we observe dispersion of critical speeds and excitation levels mainly due to variability of peak to peak STE and meshing stiffness. Sources of dispersion result mainly from geometry faults authorised by designers who introduce necessary tolerances. We model these uncertain parameters (geometry faults) by random parameters. In this context, the aim of this paper is to deal with some results about variability of peak to peak STE, time-average meshing stiffness and critical speeds. Statistics are obtained from Taguchi's method and compared to Monte Carlo simulations. Sources of variability are teeth profile manufacturing errors, teeth longitudinal manufacturing errors and shaft misalignments.