Determination of the natural oscillation frequencies of self aligning wheels of an adaptive gear drives with arched teeth

Gears drives are the primary means of transmitting torque in most modern machines. To enhance the performance of these machines, it is essential to improve the load-bearing characteristics of gear drives. One of the promising approaches is the use of cylindrical gears with arched teeth. These gears eliminate axial forces, ensure smooth meshing, and provide higher bending strength compared to straight-tooth gears. When compared to spur and helical gears, curved-tooth gears offer increased durability, reduced vibration, and lower noise levels. However, they require precise installation. Shaft misalignment due to assembly errors, wear, or thermal deformation can negatively affect performance. They demand precise installation. Shaft misalignment resulting from assembly errors, wear, or thermal deformation can adversely affect performance characteristics. The aim of this study is to establish mathematical relationships for calculating the natural frequencies of self-aligning wheels in an adaptive gear drive. The authors of the paper used analytical mechanics methods. They did calculations for a gear system with arched teeth and self-aligning half-wheels operating in parallel. The result is a set of mathematical expressions for determining natural frequencies based on the stiff-ness of elastic elements and the mass properties of the meshing gear and half-wheels.