Optimization of Profile Shift Co-efficient for Highest Contact Ratio in Non-standard Gearing

Abstract

The power transmission in mechanical drives is undoubtedly handled by gears. Tooth profile of a gear characterizes the power transmission. Standard gears mostly employ involute tooth for reasons of simplicity, while non-standard gears employs involute tooth profile shifting either positive or negative to modify the tooth geometry. Profile shifting is practiced in two ways, first known as S-gearing, either S0 or S± without change in tooth-sum while the second known as Altered tooth-sum gearing, aptly called Z± gearing with change in tooth-sum Zs, tooth-sum being the sum of teeth on pinion and gear. In S± gearing the center distance will change while in S0 gearing and Z± gearing the center distance remains unchanged. Altered tooth-sum gearing is a novel method of increasing (Z+) or decreasing (Z-) the tooth-sum of standard gearing either by adding or removing one or more teeth (±Ze) in either pinion or gear or both and eventually distributing the resulting total profile shift co-efficient among the gear pair, thus maintaining the same center distance. In designing Non-standard gearing the amount of profile shift is expressed as ‘Xm’, where ‘X’ is known as Profile shift co-efficient and ‘m’ is module of the gear. This has a significant influence on the gearing in terms of load carrying capacity, contact ratio (CR), load sharing etc. In this study contact ratio of altered tooth-sum gearing is focused, as it affects the tooth load sharing with influence on vibration and noise levels as well. Optimization of the profile shift co-efficient will be meaningful in designing gears to give highest contact ratio. Load sharing is observed to be beneficial in Altered tooth-sum gearing using increased tooth-sum (Z+ gearing), besides this method offering unparallel benefits to gear engineering.