Linear Gear System Analysis

In 1978, Cornell and Westervelt [36] provided a solution for dynamic model of spur gear systems which was valid for all contact ratios. The dynamic response of the gear system and the tooth loads and stress was obtained in this analysis. This dynamic model assumed two gears as a rigid inertia and the teeth were assumed as variable springs of a dynamic system which were excited by the meshing action of the gear teeth. The influence of various parameters like nonlinearity of the tooth pair stiffness [37] during mashing, the tooth errors and the tooth profile modifications were included in this study. It was concluded finally that damping and system inertia, tooth profile modification and critical speeds of the system affect the dynamic gear tooth load and stresses largely. Two researchers Ramamurti and Gupta (1979) used FEM to study tooth stresses in spur gear. Plane stress condition along with fixed boundary was applied for this analysis. The demerit of this model was the exclusion of consideration of adjacent teeth which was not appropriate. So this model required further correction [38]. It was found that if gear is manufactured by joining the gear teeth with the disk by welding, the stress produced in this condition and that

Two dimensional FEM along with the Lagrangian multiplier technique was used to determine the contact stress. To investigate the friction effect on the mating gears, the static friction coefficient ranged between 0 to 3.0 were used. The actual length of contact was compared with calculated length of contact. The contact stress variation along the contact surface in a direction perpendicular to mating surface gave an idea about the depth of hardening