Research on the mass unbalance response of an inner planetary gear reducer
A new inner planetary gear reducer with three axes is introduced. Three constructions and fixing techniques of the planetary gears are also introduced and compared with each other. Considering the meshing stiffness and damping of the gear pairs and the stiffness of the bearings, the dynamic governing equations of an inner planetary gear reducer with three axes are established based on the lumped mass method and corresponding deformation conditions. According to the different constructions of the reducer, the natural frequency and the mass unbalance response is investigated in frequency field. It is found that the natural frequency of the reducer with different numbers of inner planetary gears has almost the same frequency value. Mass unbalance force can not only result in bending vibrations, but also result in twisting vibrations. When the reducer has three inner planetary gears, the amplitude of the dynamic response is smallest.
Simulation on the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair)
In this paper, an exact vibration model for helical gear pairs, is developed assuming no spacing error and no shaft run-out, in consideration of nonlinear tooth separation phenomenon. Inside the model, a simple modified stiffness function, including the effect of tooth numbers and addendum modification coefficients, is proposed for a helical involute tooth pair. This new stiffness function is verified by comparing its results with theoretical calculation and experiment. The rotational vibration of helical gear pairs with comparative narrow face width is simulated clearly on a 16-bit personal computer using the finite difference method in Fortran. The total contact ratio, including transverse and overlap contact ratios, is changed in the range of 1 ≤ e ≤ 3. As a result, the simulated vibration time waveforms and their frequency characteristics agreed precisely with Umezawa’s calculation and experiment. This simulator is also used to investigate the effect of shaft deviation and pressure angle errors on the vibration of helical gears.
The Meshing Test on Helical Gears under Load Transmission : 3rd Report, The static Behaviours of Driven Gear
This paper deals with the theoretical and experimental studies on the behaviours of a helical gear with the finite width under load transmission. The load distribution along the line of contact on the helical gear teeth was made clear. The stiffness of a pair of the helical gear teeth with the finite width during the whole engagment period was evaluated. The behaviours of a driven gear under loading were made clear with the use of the evaluated stiffness. The theoretical behaviours agreed well with the experimental results. The behaviours of a driven gear under loading were not found for a pair of helical gear with overlap ratio greater than 1.0. On one pair of teeth of helical gears, the behaviours of load transmission changed very gently during the contact in comparison with those of spur gear.