;Compared with the parallel axis gear drive, the planetary gear drive, as a power-split mechanism, has the advantages of high power density, coaxial input and output shaft, as well as compact design. Therefore, it is widely applied in various transmissions. But in actual operation, the time-variant mesh stiffness as well as manufacturing and assembly errors will cause the uneven load sharing among multiple planet gears and the jump in variation of contact stress and shared load of contact tooth pairs of the planetary gear set. On the other hand, the deformation of the components in the planetary gear set will also result in uneven load distribution on the tooth flanks. The effective solution in the practice is to apply flank modification to enhance the load capacity and also to improve transmission performance. But the loaded contact characteristics of the drive have to be simulated in advance, so as to proceed suitable flank modification. The goal of the dissertation is thus to propose a loaded tooth contact analysis model for planetary gear drives, so as to simulate and analyze the contact characteristics of the engaged teeth under the real condition.
The equations of the three-dimensional modified flanks, manufactured by profile grinding, are at first derived in the dissertation. Considering the flank modification and the errors, a tooth contact analysis model (TCA) is developed for calculating the variables of the contact points. The transmission errors, the backlashes and the clearances in the planetary gear sets can be analyzed accordingly. The errors, involved in the TCA model, include the tooth thickness error of the planets, the position errors of the pin-hole, the eccentric errors of the carrier, the sun gear and the planet gears, as well as the angular misalignments of the planet pin.
The proposed loaded tooth contact analysis (LTCA) model for planetary gear sets, is based on the influence coefficient method, and involves the influences of the deformation of the teeth, the carrier, the sun gear and the planet pins. The topological conditions of the contact teeth calculated by the TCA model are also involved in the analysis, so as to simulate the Hertzian and Non-Hertzian tooth contact and to analyze the influences of the various manufacturing/assembly errors on the loaded tooth contact.
In order to verify the reliability of the proposed LTCA model, the analyzed results are compared with the finite element method (FEM). The results include the contact stress on the tooth flank along the face-width and the load sharing among each planet gear with the non-floating and floating sun gear. The comparative results show the same trend of contact stress and the difference with less than 10%. This indicates the model is in a good agreement with FEM.
A planetary gear set used in the practice is analyzed by the proposed TCA and LTCA model. The variation of the transmission errors and the backlashes of the planetary gear set is analyzed by applying the developed TCA approach, considering various cases with and without flank modification and errors. The variation of shared loads, contact stress and loaded transmission errors stress during gear meshing, as well as the contact pattern and stress distribution on each engaged tooth flank are analyzed by using the LTCA model. The non-Hertzian contact stresses of tip corner edge contact due to deformation and the face-end edge contact due to misalignment of the planet pin are also simulated. The influence of the errors on the load sharing among planets and the trajectory of the floating sun gear are also analyzed in the dissertation.
The analysis results show that tip corner contact occurs more likely in the planet-annulus gear pairs than sun-planet gear pairs. The contact stress on the flanks of planet-annulus gear pairs distributes more uneven due to the stiffness of the carrier. The stress distributions of the engaged tooth pairs are even and symmetric after flank modification. On the other hand, the eccentric error of the carrier has a larger influence on the load sharing among planet gear and loaded transmission errors.
The proposed LTCA model for planetary gear sets in the dissertation can simulate effectively and efficiently contact characteristics of engaged teeth with or without loading during gear meshing. The results can provide good evidence for designing flank modification of a planetary gear set. It can serve as the model for evaluating the influence of the manufacturing/assembly accuracy on loaded or unloaded transmission errors, backlash, as well as load sharing among planet gears.