# Establishment of numerical model for pitting corrosion process of gear in lubrication contact

Based on ABAQUS software, contour integral and MTs criterion are used to simulate the process of pitting corrosion crack propagation of gears with lubrication contact pairs. With the change of meshing position, the radius of curvature on the meshing line will change. In addition, the contact fatigue strength of the tooth surface near the pitch line is the weakest. Therefore, this paper selects the pitch line to study the pitting corrosion of the gear. According to Hertz contact theory, the meshing of two teeth can be simplified as two cylindrical contact models, and then can be further simplified as a plane strain problem according to the conclusion of elasticity. Due to the symmetry principle, the circular section can be simplified as a semicircle, and the contact gap between the two semicircles is the oil film thickness. Therefore, the two-dimensional finite element model in Fig. 1 can be established, which can greatly improve the calculation efficiency. According to the analysis results, the initial crack length A0 = 20 is preset μ m. It is at an angle of 20 degrees to the direction of contact motion, i.e β= twenty °， The y-direction constraint is applied at the bottom of the semicircle, and the x-direction constraint is applied at the center of the semicircle, as shown in Figure 2. The gear is made of quenched alloy steel aisi4130. Its plane strain fracture toughness KIC is 83.8 MPa · M1 / 2, and the critical stress intensity factor of fatigue propagation kth is 8.5 MPa · M1 / 2.

The equivalent contact model is meshed by the discrete method of quadrilateral. Because of the singularity of the stress and strain fields at the crack tip, and other regions are not affected, dividing 36 collapsed quadrilateral elements around the crack tip not only meets the accuracy requirements, but also can simulate the R-1 / 2 stress singularity and R-1 / 2 strain singularity at the crack tip; In other regions of the semicircle, the mesh can be divided sparsely. The corresponding normal and tangential loads are applied to the contact area of the gear pair, and the friction factor f affecting the tangential load is 0.04. The friction coefficient of the part where the pitting crack passes through the oil film and contacts with the opposite tooth surface is 0.1.

The elastohydrodynamic lubrication pressure of gear pair is calculated by using the numerical method of isotherm Contact Elastohydrodynamic Lubrication. The parameters of the studied gear and lubricant, the calculated pressure distribution and film thickness, and the corresponding Hertz contact pressure are shown in Figure 3.

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