Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of 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.
In planetary gear set, load sharing behavior determines the average amplitude of meshing force, so determines the tooth wear. Meanwhile, tooth wear accumulation increases the backlash, so affects the load sharing behavior. As a result, a “two-sides” coupling relation appears between load sharing behavior and tooth wear. In order to reveal this coupling relation, a static tooth wear prediction model for compound planetary gear set is employed to describe the wear distribution along tooth profile and backlash generated by tooth wear accumulation. Then, a “translational-rotational” lumped-parameter dynamic model of compound planetary gear set is built to calculate the eccentric load coefficient for each meshing pair, under the excitation from the backlash generated by tooth wear accumulation, transmission error, and other excitation. Based on the aforementioned two models, a dynamic tooth wear prediction model is put forward to reflect “two-sides” coupling relation between tooth wear accumulation and load sharing behavior in compound planetary gear set. Lastly, in order to improve the reliability, a 3D-diformable model is built to study the influence of tooth wear on load sharing. The results indicated that, with the system running and tooth wear increasing, under the condition of no-initial transmission error, tooth wear accumulation decreases the load sharing at meshing engagement and disengagement, and under the condition of initial transmission error, tooth wear accumulation improves load sharing behavior slightly.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.