Abstract
Given the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate model. The parameters of the variation function of Kriging model are optimized by using the whale optimization algorithm (WOA), and the explicit mathematical model accuracy between the design parameters and the contact stress of the gear is in turn optimized by the improved Kriging surrogate model. The influence of design parameters on the contact stress of cylindrical gear with arc tooth is analyzed based on the established mathematical model. The proposed algorithm was realized via the programming platform MATLAB; the simulation results indicate that the precision evaluation indexes (the correlation coefficient (R2), root mean square error (RMSE), and the relative maximum absolute error (RMAE)) of the proposed Kriging model are improved, in addition to the error range which is narrowed from (−2, 4) to (0, 3). As the tooth width, modulus, pressure angle, and tooth line radius increased, the contact stress of the cylindrical gear with arc tooth gear declined, which was negatively correlated with the design parameter. The amplitude of contact stress of the cylindrical gear with arc tooth was the largest due to the change of tooth radius, followed by the change of modulus, while the influence of tooth width was less. Finally, the influence of modulus-tooth line radius interaction and pressure angle-tooth line radius interaction on contact stress of cylindrical gear with arc tooth was significant.
Highlights
Gears are widely used in various industries [1], and the involute cylindrical gear is widely used at present
In order to study the influence of design parameters on the contact stress of circular arc tooth line gear, this paper proposes using Kriging surrogate model to establish the mathematical model of contact stress between design parameters
Whale optimization algorithm (WOA) was used for the parameters of the variation function of the traditional Kriging model. e Kriging surrogate model with optimized parameters of the variation function is used to establish the explicit mathematical model between the design parameters and the contact stress of the gear. e influence of design parameters on the contact stress of circular arc tooth line cylindrical gear is discussed based on the established mathematical model
Summary
Gears are widely used in various industries [1], and the involute cylindrical gear is widely used at present. Is new type of gear transmission has the advantages of good meshing performance, high coincidence, no axial force, stable transmission, and so on [2] For this kind of gear, scholars have carried out in-depth research. In order to study the influence of design parameters on the contact stress of circular arc tooth line gear, this paper proposes using Kriging surrogate model to establish the mathematical model of contact stress between design parameters E Kriging surrogate model with optimized parameters of the variation function is used to establish the explicit mathematical model between the design parameters and the contact stress of the gear. E influence of design parameters (tooth width, modulus, pressure angle, and tooth radius) on the contact stress of circular arc tooth line cylindrical gear is discussed based on the established mathematical model Whale optimization algorithm (WOA) was used for the parameters of the variation function of the traditional Kriging model. e Kriging surrogate model with optimized parameters of the variation function is used to establish the explicit mathematical model between the design parameters and the contact stress of the gear. e influence of design parameters (tooth width, modulus, pressure angle, and tooth radius) on the contact stress of circular arc tooth line cylindrical gear is discussed based on the established mathematical model
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