Elastohydrodynamic lubrication contact of cylindrical gears

In order to ensure the accuracy of contact analysis, the influence law of micro morphology of tooth surface should be considered in the model. The influence of running in stage on the change of initial surface morphology is particularly prominent. In this stage, the relatively sliding surface is in close contact under the action of external load, and the original roughness peak of the contact surface of cylindrical gear is removed or flattened, which makes the surface roughness smoother, with significant plastic deformation and high wear rate. The research shows that the smoothing of surface roughness peak is mainly due to plastic flow rather than wear.

Due to plastic flow, the original surface of cylindrical gear runs in in a short time and evolves slowly in the later operation process. For the surface morphology in the stable running in period, it is necessary to adopt appropriate methods to simulate the running in process of the surface. Everitt et al. Used the moving average filtering method to treat the shot peening and grinding rough surface, and the peak value was reduced to about 50% ~ 80% of the original height. Compared with the cylindrical gear surface running in test results of Sosa et al. Moving average filtering methods can be divided into one-dimensional and two-dimensional, both of which can effectively reduce the random noise in the measurement process. The one-dimensional moving average low-pass filtering method is used to smooth the surface contour in a single specific direction in order to remove the high-frequency noise that has a slight impact on the measurement results, while the two-dimensional filtering method can more accurately describe the influence of adjacent points on the plane in the running in process, express the effect of running in on the surface smoothness and maintain the main characteristics of the initial morphology. The two-dimensional moving average filtering method is used to simulate the surface morphology characteristics of cylindrical gear after test surface running in, and the morphology characteristics of section are brought into the calculation of oil film thickness of line contact elastohydrodynamic lubrication model, so as to accurately simulate the lubrication behavior of tooth surface.

In order to solve the Reynolds equation, the lubrication region needs to be discretized. The left end of formula is discretized by the central difference method, and the two terms at the right end are discretized by the second-order backward difference method. In order to ensure the good convergence of the iteration, the coefficient matrix needs to be modified, and the specific modification method. The pressure can be obtained through the iterative solution formula. Each iteration needs to update the viscosity, density and oil film thickness based on the pressure distribution of the previous iteration.

The pressure convergence solution and load balance have the following formula:

Where I is the current meshing position point.

The shear stress is calculated by the following formula:

Where G is the ultimate shear modulus, which is calculated as follows:

The ultimate shear stress is calculated as follows:

The surface flash temperature is calculated by the following formula:

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