An analytical study on the combination of profile relief and lead crown minimizing transmission error in narrow-faced helical gears

• Published in: Mechanism and machine theory 2019-06, Vol.136, p.224-243
• Main Authors: Bruyere, J., Velex, P., Guilbert, B., Houser, D.R.
• Format: Article
• Language: English
• Subjects: Analytical formulae; Face contact ratio; Gears; Lead crown; Mechanics; Physics; Profile modifications; Solid mechanics; Structural mechanics; Transmission error
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2019.03.005

•An original analytical approach to the calculation of the RMS of transmission error is presented.•New closed-form solutions for the combination of profile and lead modification minimising transmission error are proposed.•The specific influence of face contact ratio is highlighted and quantified.•Numerous comparisons with various software codes prove the validity of the new closed-form formulae. Some original analytical developments and results on the formulation of transmission error in solid spur and helical gears are presented, which lead to closed-form formulae defining the optimum combinations of profile relief and lead crown minimising the time-variation amplitudes of transmission error. Extensive comparisons with the results of benchmark software codes prove that the analytical findings are sound and can be used at the initial design stage to define optimum modifications with minimum effort. Some qualitative general trends can also be derived. In particular, it is shown that optimum tooth modifications depend on a limited number of dimensionless parameters, namely the profile and face contact ratios, the normalised depth and extent of profile modifications along with the normalised lead crown amplitude. The influence of the latter is found to strongly depend on a specific function of face contact ratio, which controls the displacement of optimum profile relief either towards the smaller or larger depths of modification at tooth tips. Finally, the analytical formulae (and the numerical simulations) indicate that the optimum modifications are approximately located along a line segment in the relief versus crown amplitude plane.