Mathematical Model and Tooth Undercutting of Curvilinear Gears with Circular-Arc tooth Profiles

Abstract

In this paper, the curvilinear gear with circular-arc tooth profiles is proposed. A mathematical model of the gear is developed based on the theory of gearing. The developed mathematical model of the proposed circular-arc curvilinear gear is then adopted to show the computer graph of gear teeth. Besides, the tooth undercutting is also investigated. Some numerical examples for tooth undercutting analysis of this type of gears are studied and illustrated. The initial tooth undercutting points and tooth undercutting line of the proposed curvilinear gear are investigated. In addition, the minimum number of gear teeth for tooth non-undercutting is also calculated.