Investigation Of Dynamic Characteristic Of Planetary Gear Transmission

Planetary gear noise and vibration are primary concerns in theirapplications in the transmissions of marine vessels, aircrafts, automobiles, andheavy machinery.Dynamic analysis is essential to the noise and vibrationreduction.This work analytically investigates some critical issues and advancesthe understanding of planetary gear dynamics.Two parameter models are built for the dynamic analysis of planetary gear.The unique properties of the natural frequency spectra and vibration model aredisserted.The special vibration properties are useful for subsequent research.Taking advantage of the disserted modal properties, the natural frequencyand vibration mode sensitivities to design parameters are closely investigated.The key parameters include mesh stiffness, support stiffness, twiststiffness,component mass,and moments of inertia.The eigensensitivities areexpressed in simple formulae associated with modal strain and kineticenergies.The results indicate each parameter of sun ,ring and carrier ,includingsupport stiffness, twist stiffness,component mass,and moments of inertia,affects one type natural frequency and the infuential extent is disparate todifferent order natural frequency of the same type. Planet design parametersare the most affect parameter and affect most natural frequencies.Meshstiffness affects six different frequencies associated with two rotational modes,two pair of translational modes and two groups of planet modes. Takingadvantage of Taylor formulae and eigensensitivites formulae, the rules ofveering and intersecting are derived to identify changes of natural frequencyunder parameter variations. These results indicate the plots of two same modesveer away and the plots of two different modes intersect with each other in thefigure of natural frequencies versus varying parameter curve. Parametric instabilities are excited by mesh stiffness varity.Using thewell-defined modal properties of planetary gear and the multi-scale method ofinstability analyses of multi-degree of freedom system, the boundary ofstability and instability are derived. The effect of contact ratio and mesh phaseon parametric instability is analytically approached. The results indicateadjusting contact ratio and mesh phasing can suppress or abate some particularinstability.