An analytical study of tooth friction excitations in errorless spur and helical gears

Based upon a Coulomb model, an original analytical analysis of tooth friction excitations in errorless spur and helical gears is presented. Upon averaging the contributions of bending angles at pinion and gear centres and using a constant mesh stiffness per unit of contact length, it is shown that the intensity of tooth friction excitations compared to the excitations caused by time-varying contact lengths depends on three basic functions of time ΔL(τ),FF(τ) and TT(τ). ΔL(τ) represents the normalised variation of contact length between the teeth, while FF(τ) and TT(τ) account for friction excitations in translation and torsion respectively. Their exact analytical expressions are given in the form of Fourier series, valid for all spur and helical gears and, from which contour plots of excitation levels are derived. These performance diagrams enable an easy estimate of the gear set sensitivity to friction excitations as well as the consequences of modifying actual geometric parameters under load. The potentially significant contribution of tooth friction to translational vibrations of pinions and gears is pointed out, particularly in the case of high contact ratio gears.