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.
Turbulent boundary layer wall‐pressure fluctuations downstream from an abrupt change in surface roughness
Spectra of wall‐pressure fluctuations beneath a turbulent boundary layer have been investigated immediately downstream from an abrupt change in surface roughness, from slightly rough to very rough. Over the measurable frequency band (400 Hz to 7 kHz), the spectra in the first 150 mm scale on wall variables. This indicates that the motions responsible for the pressure fluctuations measured in this region are very close to the wall. Farther downstream this scaling procedure breaks down. It is suggested that the initially thin internal layer behaves independently of the flow external to it until it has grown appreciably and only then interacts with the outer boundary layer. It was found that, for all frequencies measured, the dimensional spectral level decreases initially then rises to a maximum at 250 mm from the roughness change before decreasing once more. The position of the maximum is close to where the internal layer ceases to have a distinct edge.