Dynamic Meshing Stiffness Of Transmission Gears Considering Rough Tooth Surface

Gear transmission has the advantages of high efficiency,compact structure,long service life,etc.It is widely used in construction machinery,ships and aircraft.The periodical variation of meshing stiffness of the gear pair is one of the important internal stimuli for the vibration of the gear system.Accurate gear meshing stiffness calculation method can obtain more reasonable results,and can provide a basis for comprehensively evaluating the characteristics of the transmission system and designing vibration reduction and noise reduction..The calculation of gear meshing stiffness generally considers the tooth surface as an ideal smooth surface,and there is a certain gap from the real rough tooth surface.Considering the effect of roughness has important implications for improving the accuracy of the gear meshing stiffness calculation.This paper takes a power split/match gear transmission system as the research object,taking into account the influence of tooth surface contact,first considers the tooth surface as the ideal smooth elastic contact body,and establishes the calculation method of the meshing stiffness of the smooth tooth surface.Considering the contact of rough tooth surface further,the rough flank asperities are regarded as spheres with different heights based on the fractal principle.The normal height of the micro convex body is calculated using the W-M function,various conditions are added to the deformation coordination equation,and iteratively solves the meshing.Stiffness.Based on the calculation method of the rough tooth surface meshing stiffness,the influence of tooth surface roughness,gear structure and load on the gear meshing stiffness is analyzed.(1)A method for calculating the contact stiffness of a smooth tooth surface is established.The finite element method is used to obtain the stiffness matrix of the tooth surface,and the flexibility matrix is obtained by inverting it.The interpolation and the contact flexibility matrix are superposed,and the meshing stiffness of the gear is obtained through the iterative calculation of the deformation coordination equation.The rationality of the method was verified by comparison with literature.Three pairs of helical gears in the power split/convergence gear transmission system are further calculated,and their characteristics are analyzed.(2)A method for calculating the contact stiffness of a rough tooth surface is established.Fractal theory was used to simulate the rough surface.The WM function was used to simulate the normal height of the micro convexity.The flexibility matrix obtained by the finite element method and the contact flexibility matrix considering the roughness were superimposed,and the improved contact deformation coordination equation was iteratively solved to obtain a rough tooth.Surface meshing stiffness.Comparing with the literature,the changing trend of the meshing stiffness of different tooth surfaces is analyzed.The dynamic meshing stiffness calculation considering the roughness is also carried out for three pairs of helical gears.(3)In the tooth surface simulation,the normal height of the roughened surface micro-convex body was simulated using the W-M fractal function.By changing the parameters of the fractal function for comparison and analysis,it was found that the roughness of the surface profile of the object should be considered in combination with the fractal dimension D and the scale factor G.(4)The influence of roughness and other factors on the gear meshing stiffness was studied.By calculating the meshing stiffness of different tooth surface roughness,it is found that the greater the tooth surface roughness value,the smaller the meshing stiffness value.The diameter of the shaft hole,the web structure,and the meshing force are further calculated to calculate the meshing stiffness of the rough tooth surface.The analysis shows that the diameter of the shaft hole increases and the meshing rigidity of the gear increases due to the change of the structural rigidity.The solid gear also has a structure.The influence of the stiffness makes the meshing stiffness larger than that of the web type.Under the other conditions unchanged,the total load increases,and the meshing stiffness also increases.