Mathematical Model and Undercutting Analysis of Modified Helical Gears with Smaller Number of Teeth

摘要

This paper proposes a mathematical model for helical gears with smaller number of teeth based on the gear theory and generating mechanism. The unavoidable tooth-profile undercutting of the gears with smaller number of teeth is studied based on the developed mathematical model and the conventional method of tooth-profile shifting. Moreover, an alternative method for lessening the tooth-profile undercutting is also proposed for the gear generation by considering the basic fillet geometry modification with a modified rack cutter. By comparing the results obtained by these two methods, a third method combining the above-mentioned two methods is proposed for the design of helical gears with smaller number of teeth to obtain the gear set that has a higher fillet strength without tooth undercutting.