Meshing Stiffness Analysis Of Nutation Drive With Face Gear Considering Surface Roughness

Nutation drive with face-gears transmission has a series of advantages such as large coincidence degree,strong bearing capacity,high transmission efficiency,smooth transmission,low noise and large reduction ratio,etc.It can be widely used in the shield machine and the main reducer of helicopter.The meshing stiffness of the gear pair is time-varying and periodic,which will cause periodic vibration of the transmission system.Therefore,it is very valuable to study the dynamic meshing stiffness of Nutation drive with face-gear.In this paper,solid modeling,contact trajectory analysis,ABAQUS software simulation,time-varying meshing stiffness calculation and analysis of nutation face-gear are carried out.The main contents are as follows:1.Based on the meshing principle and basic structure of nutation face-gears transmission,a three-dimensional model of nutation face-gears transmission is established,and the contact track of tooth surface in the process of nutation face-gears transmission is calculated by using MATLAB software.The dynamic meshing stiffness of the Nutation drive with face-gears is obtained by the finite element simulation using the finite element software ABAQUS,which provided the basis for the subsequent calculation.The coincidence degree of the Nutation drive with face-gears is calculated by recording the time when the normal force existed on the tooth surface.2.The meshing stiffness of the nutation face-gears is calculated.The bending shear flexibility matrix of the tooth surface is obtained by using the substructure method of ANSYS finite element software without considering the roughness.The bending shear flexibility matrix of the contact position is obtained by interpolation method,and the contact flexibility matrix of the contact point is calculated based on Hertz contact theory.and the two are substituted into the deformation coordination equation for iterative calculation,and the time-varying meshing stiffness of nutation face-gear is calculated.Compared with ABAQUS simulation results,the correctness of the algorithm is verified.The calculation method of dynamic meshing stiffness for nutation face-gears transmission is proposed.3.Based on the calculation of nutation face-gear meshing stiffness,considering the influence of roughness on the tooth surface,the W-M function in M-B model is used to represent the rough contact line of the tooth surface,and the normal height and radius of the microconvex body are calculated,so as to obtain the contact flexibility of the tooth surface contact point.The contact flexibility and the previously obtained flex-shear deformation flexibility are substituted into the improved deformation coordination equation for iterative calculation,and the timevarying meshing stiffness of the nutation face-gear with roughness considered is obtained.Through analysis,it can be seen that the calculation result of meshing stiffness with roughness considered is closer to the real and objective situation.4.The influence of different parameters on the characterization results of W-M function is analyzed,and the variation law of the normal height of the microconvex body with different parameters is explored.The influence of roughness,load and other factors on the meshing stiffness of tooth surface is analyzed.Different tooth surface roughness is obtained by changing fractal parameters,and the influence law of tooth surface roughness on gear meshing stiffness is analyzed.The analysis shows that the stiffness of the nutation face-gear decreases with the increase of the roughness,and the meshing stiffness of the tooth surface can be calculated by further changing the load.It is found that the meshing stiffness of nutation face-gear increases with the increase of load.