A Calculation Method Of Friction Coefficient Between Gear Teeth Based On The Polynomial Agent Model

The friction of tooth surface has a significant effect on the bending fatigue of tooth root and contact fatigue of tooth surface. The gear friction is the important content of the design of the friction coefficient. However, the fricti on coefficient is uncertain and difficult to measure directly due to the correlation between other factors including the load, lubrication condition, rotation, and roughness of gear tooth etc. In this paper, a pair of spur gears are selected as the research object. The coefficient of friction on gear teeth is calculated based on the multi-island genetic algorithm. To verify the rationality of the genetic algorithm, the calculated results are compared with those of other researchers. The works include the following:(1) The geometric and finite element models of the gear are constructed. Based on the theory of gear meshing, the program code to estab lish the tooth profile is compiled and the geometry coordinates of the key points were extracted, and then it was imported into the finite element software for realizing the parametric modeling. The meshing is divided by selecting the appropriate cell types, setting the real constant and the material parameters. According to the operating condition of the test, the finite element m odel is established.(2) The finite element results of tooth root bending stress are compared with the results of dynamic testing. The linear uniform load is applied to the finite element model and then, the tooth root stresses of the different loading location in dangerous sections along the tooth width are obtained. The signals of the root strain and rotation speed/torque are measured respectively by the gear test bench with electric-closed loading. Then the finite element results are compared with the results obtained by the test. When meshing with two gears, the test result is 10% bigger than the finite element result; the meshing width with single gear of test is larger than theoretical calculation.(3) The friction coefficient of the whole tooth surface is calculated by reverse method. Based on the results of the finite element analysis, the cubic polynomial surrogate model is constructed by the Isight and it is evaluated to be feasible. According to the cubic polynomial surrogate model and the experiment results, the objective function is established and the friction coeffi cient of the upper bound point is figured out by MIGA. According to the same principle of the reverse method, also the friction coefficient of the whole tooth surface can be calculated. The coefficient of friction along the depth direction is verified by the friction calculation formula of other researcher, the results have good consistency.(4) The above method of calculating the friction coefficie nt is applied in the different operating condition. The comparison of the results of the friction coefficient with the same torque in different speed and the ones with the different torque in the same speed are carried out. Without considering the influence factors of the temperature, humidity and the deviations, it is found out that the friction coefficient of the upper bound points with a single pair of teeth in the engagement increases with the increases of the speed and torque.