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A systematic analysis of the influence of tooth shape modifications on the dynamic behavior of single stage narrow-faced helical gears is proposed. Calculations are performed using a 3D model with 36 degrees of freedom including torsional flexural and axial generalized displacements of the gear-shaft-bearing system. Two approximate equations giving the normalized static transmission error [Mathematical Expression Omitted] and load factor RF are deduced. It is shown that, for a given gear set, there exists a unique representation of [Mathematical Expression Omitted] and RF valid over a large range of profile, lead modification amplitudes and transmitted loads. The role of the extent of the profile relief (long, short and intermediate) and the shape of lead modifications (parabolic, elliptic crowning, linear chamfers) is discussed. The paper is concluded by the analysis of the dynamic transmission error of a gear set with various tooth shape modifications selected from static considerations.

Numerical methods for predicting the dynamic behavior of geared equipment are examined. The methods are tested on a simplified 3D lumper parameter model which considers shaft-bearing flexibilities, mesh couplings and time-varying and nonlinear mesh stiffness. Results show the necessity of including a relaxation process in the numerical algorithm to ensure the convergence of spur gears.

This paper presents an analytical expression of the time-varying contact length between perfect involute spur and helical gears. It is shown that contact lengths can be expressed as Fourier series whose numerical expansions correlate very well with the results of numerical time-step simulations based on contact length discretization. Finally, some possible examples of application in gear dynamics are suggested.