Research On Dynamics Of Herringbone Planetary Gear Trains Based On Mesh Phasing

The herringbone planetary gear transmission system is widely used in aviation, aerospace, shipsand other fields. To the herringbone planetary gear transmission system, an effective method ofvibration reduction is the mesh phasing. The main content of this paper is to study the mash phasingof the herringbone planetary gear transmission system.Based on the previous research, this paper deduces the formula for calculating the three meshphase coefficients of the herringbone planetary gear transmission system and then obtains thecondition of no phase difference and the formula of the phase difference coefficient in the herringboneplanetary gear transmission system. Meshing force analysis where the mesh phasing relationships iscongsidered is carried out on the central parts. By the meshing force analysis the relation between thedesign parameters of the planetary gear train and the vibration form of the central parts can beobtained, even if it is a qualitative conclusion.Based on analyzing the mesh phasing relationships in the herringbone planetary gear train, thiswork deduces the formula for the time-varying meshing stiffness in which the mesh phasingrelationships are considered.The error excitation in which the assembly error, the eccentric error andthe tooth profile error are included is analysed detailedly.On the basis of coordinate transformation and the analysis of the relative displacement, thetransverse-torsional coupled dynamic model of the herringbone planetary gear train is established inthe rotating coordinate system according to Newton’s second law of motion, and contains thegyroscopic effect, error excitation, time-varying meshing stiffness excitation and the damp.The modal characteristics of the herringbone planetary gear system is studied; Furthermore, theinfluence of the mesh phasing relationship on modal is researched from many aspects, such as themultiplicity and the change cycle of natural frequency and modes. By solving the dynamic models ofthe herringbone planetary gear transmission system with different meshing phasing relationships bymeans of Fourier series method, the time domain solution and the frequency domain solution can beobtained; moreover, analyses the effects of the mesh phasing relationships on the vibrationcharacteristics of the herringbone planetary gear train. Then according to the mashing force analysisand the dynamics studies this paper obtains the parameter selection principle of the herringboneplanetary gear train.