Mathematical modelling and validation of twist-free lead crowning of spur gears by pulsed electrochemical flank modification process

Abstract

Spur gears are the most commonly used gears in various applications. Their lead crowning helps in mitigating the adverse effects of shaft misalignment and edge contact of their flank surfaces, and improving their operating performance. Conventional contact type processes induce twist-error during lead crowning of spur gears which adversely affects their operating performance and service life. A non-contact process can overcome these problems. Therefore, the present study is focused on development of mathematical model, and innovative cathode gear and experimental apparatus for imparting twist-free lead crowning to spur gears by a non-contact process referred to as pulsed electrochemical flank modification (PECFM) process. The cathode gear provided rotatory motion and spur gear was provided variable reciprocating velocity to ensure lead crowning of the entire flank surfaces of its all teeth. The mathematical model for twist-free lead crowning is developed by equating volumetric material removal based on the spur gear geometry with that given by Faraday’s law of electrolysis. The developed model is validated experimentally by varying applied voltage, pulse-on time, and pulse-off time at four levels each. It found the minimum prediction error for lead crowning model as 0.5%, and minimum and maximum values of imparted lead crowning as 21.5 μm and 46.4 μm respectively. Comparison of topography, microgeometry, and roughness profiles of spur gear flank surfaces before and after their lead crowning confirmed that the developed cathode gear and apparatus through PECFM process not only imparted them twist-free lead crowning but also reduced their arithmetical average roughness and maximum height by 34.3% and 33.6% respectively. They also improved their surface morphology as revealed by their scanning electron microscopy. The outcome of this study will be highly beneficial to the manufacturers and users of spur gears. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.