Wear modelling of bevel gears with biconvex-concave teeth

<ns3:p>To develop a mathematical wear model for bevel gears with biconvex-concave teeth and to confirm the accuracy of the modelling through experimental validation.Analytical relationships between tooth wear and meshing parameters (profile shift coefficients, module, number of gear teeth, gear face width) have been established using mathematical models of meshing and wear for biconvex-concave teeth of bevel gears. In the wear model, the determination of the contact point coordinates of the curves describing the tooth profiles is carried out using a geometric-analytical method. The result of the method is the solution of a transcendental equation with one unknown. The determination of the radius of curvature and the first derivative of the interpolation function was performed using a hypothesis that enabled the application of Hertz's formula for calculating contact stresses in gear teeth. Based on this hypothesis, the contact of profiles with variable curvature is replaced by the contact of two touching circles (cylinders) with radii equal to the curvature radii of the profiles at the contact point. It is assumed that the width of the contact deformation band of the actual profiles and the replacing circles is the same, as well as the distribution law of the contact stresses. The stress-strain state of the tooth was modelled using the finite element method to determine the stiffness of the teeth. Rolling and sliding velocities were determined using known formulas that depend on distance, time, and angular velocity. The experimental determination of wear on biconvex-concave teeth of bevel gears was defined as the difference between the initial coordinates of the points on the lateral surface profile of the teeth and the actual coordinates measured using a laser scanning method.A mathematical wear model for bevel gears with biconvex-concave teeth has been developed, considering wear in the pole of gear meshing and a decrease in the hardness of the contact surface due to the wear of the carburising layer. The models consider changes in the geometric, kinematic and strength parameters of gear meshing caused by alterations in the shape of the lateral profile surface due to wear after each loading cycle. Experimental wear measurements, conducted under production conditions, confirmed the reliability and adequacy of the theoretical models developed. The modelling approach provides sufficient accuracy in calculating the wear of the tooth working surfaces, with the relative error not exceeding 10% and the mean squared error is 0.021 mm.The results of wear modelling for bevel gears with biconvex-concave teeth have been validated by operational data from such gears used in coal shearer drives.The results of tooth wear modelling can be used to increase the service life of bevel gears in coal shearer drives by selecting rational meshing parameters.The selection of rational meshing parameters during tooth wear modelling will increase the durability of gears in coal shearer drives.</ns3:p>