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In an aeronautical planetary reducer, the sun gear and the planet gear are mostly solid structures, and the inner ring gear is often fixed on a relatively flexible bracket. For uniform loading, the sun gear, planet wheels or planet carrier take a floating structure. Therefore, in the vibration analysis, the support elasticity should be considered. When the input and output torque are constant, the change of meshing stiffness and the comprehensive meshing error are the main reasons for the planetary transmission vibration. That is, the planetary transmission belongs to the self-excited vibration system in which the parameter excitation and the transmission excitation coexist, so the meshing rigidity of the gear teeth should be dealt with. The gear and the integrated meshing error are analyzed and processed. The meshing stiffness changes periodically due to the change in the number of pairs of teeth that are engaged at the same time. If the change of the single tooth meshing stiffness along the tooth height direction is neglected, the gear tooth comprehensive stiffness is a periodic short waveform, which is expanded into a Fourier series during the meshing period, ie K=K-6Ni=1Aisin(Xit Ui), K- is the average of the meshing stiffness.
The comprehensive meshing error of the gear teeth is a comprehensive reflection of manufacturing error, assembly error and bearing clearance in the direction along the meshing line. The variation of the transmission error and the dynamic load coefficient with the engagement time in one engagement period. Figure 3 shows the maximum value of the dynamic load factor of the gear at different speeds. The dotted line in the figure indicates the dynamic load coefficient between the sun gear and the planetary gear, and the broken line indicates the dynamic load coefficient of the planetary gear and the inner ring gear. Due to the meshing stiffness and the variation of the integrated meshing error, the transmission error and the dynamic load of the planetary transmission cause large fluctuations in the meshing period. When the input speed is 9000r/min, the maximum absolute error of the carrier angle is about 0.3, and the maximum dynamic load coefficient is about 1.34. At the speed of 2000r/min, the planetary reducer generates support resonance; near 4500r/min, the gear is generated. The torsional resonance has a 1/2-resonance peak near 8000 r/min. Planetary transmission is a self-excited system in which both parametric excitation and transmission excitation coexist. In order to study its vibration characteristics, the meshing stiffness and the comprehensive meshing error should be analyzed and processed. The dynamic equation of planetary transmission is a multi-degree-of-freedom coefficient-variable differential equations. When solving by numerical method, the differential step size and initial conditions should be reasonably selected to ensure fast convergence. In the starting process of the aerospace planetary reducer, the support resonance and torsional resonance regions are crossed, so the damping problem should be considered in the structural design. The dynamic load between the planet gear and the ring gear is smaller than the dynamic load between the planet wheel and the sun gear.