A nonlinear dynamic model for analysis of the combined influences of nonlinear internal excitations on the load sharing behavior of a compound planetary gear set

Nonlinear internal excitations, which include meshing stiffness, backlash, and bearing clearance, may cause nonuniform load distribution in compound planetary gear transmission. To quantify the influence of nonlinear internal excitations on load sharing behavior, and to study the combined effects of meshing stiffness, backlash, and bearing clearance on load sharing behavior, this paper develops a nonlinear dynamic model of a Ravigneaux compound planetary gear set with all members possessing translational and torsional vibration degrees of freedom, as an extend dynamic model to the prior research for compound planetary gear set. In detail, the dynamic model is derived on the basis of the second Lagrange equations, and the load sharing coefficients for different meshing pairs are defined and calculated. Single factor analysis is introduced to investigate the influence of each nonlinear internal excitation on load sharing coefficient ( LSC). On the basis of single factor analysis, Taguchi method is incorporated with the nonlinear dynamic model to study the combined effects of nonlinear internal excitation and figure out the most significant control factor affecting LSC among meshing stiffness, backlash, and bearing clearance. The calculation results are evaluated by using signal-to-noise ( S/ N) analysis and ANOVA method. The results indicate that backlash affects the load sharing behavior most significantly, compared with mean value of meshing stiffness and bearing clearance.