Influences of fractal characteristics of microscopic morphology of the meshing surface in a planetary gear train on the thermal mixed lubrication performance

With the aim of studying influences of fractal characteristics of microscopic morphology on the meshing surface in a planetary gear train with regard to the thermal mixed lubrication performance, firstly, with the W-M function as the basis, as well as two sets of fractal characteristic parameters for the helical gear meshing surface in both the meshing direction and tooth width direction, a three-dimensional (3D) fractal function model was established to characterize fractal characteristics of microscopic morphology of the meshing surface. Secondly, driven by fractal function, a thermal mixed lubrication model was established with consideration of fractal characteristics of microscopic morphology of the helical gear meshing surface. Meanwhile, by leveraging the solved oil film pressure (OFP) and oil film thickness (OFT), a fractal contact stiffness model for the helical gear meshing surface under thermal mixed lubrication conditions was developed. Ultimately, the research examined how fractal characteristics of microscopic morphology of the meshing surface influence the oil film pressure, oil film thickness, oil film temperature, and contact stiffness within the helical gear meshing surface. Under mixed lubrication conditions, the findings showcase a rise in the fractal dimension ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> ) or a reduction in the characteristic scale parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> ) of the meshing surface brings about uniform OFP and OFT distribution. The growth of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> of microscopic morphology of the meshing surface brings about a reduction in both OFP and oil film temperature. Meanwhile, fluctuations in OFT is reduced. With the reduction of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> of microscopic morphology of the meshing surface, the fluctuations in oil film pressure, oil film thickness, and oil film temperature are diminished. Moreover, an increase in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> of the microscopic morphology of the meshing surface or a reduction in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> leads to an enhancement in the contact stiffness of the meshing surface.