Mathematical Modeling of the Elastic Ring Time-Varying Transmission Path for Planetary Gear Condition Monitoring

Purpose The mounted stationary sensor on the ring casing has become a widely accepted way to monitor the planetary gear condition and one challenging aspect of this method is the modulation effect caused by the moving planet gears. It is valuable to study the modulation effect caused by the moving planet gears. Method Different window functions have been proposed to model this modulation phenomenon and there are several drawbacks: the selection of the window function parameters is often arbitrary and subjective instead of basing on the planetary gear physical parameter; the current window function is hard to reflect the impact from the ring gear boundary conditions. Therefore, this paper simulated this modulation phenomenon as moving load dynamic problem to overcome these drawbacks, where the ring casing has been modelled as an axisymmetric flexible structure and the internal meshing forces have been modelled as spatially varying moving loads. Based on the improved hamming window function, this paper related the window function parameters with the planetary gear physical properties and operation conditions and then, quantified the modulation effect with the consideration of moving load speed as well as the ring gear boundary condition. Results For the planetary gear carrier arm rotation speed, the result suggested that the moving speed mainly affect the parameter β and the corresponding value showed a nonlinear decreasing trend when the moving speed increased. For the ring gear rim thickness, similarly, parameter β increased significantly with the increase of the rim value. For the radial support stiffness, parameter β has also been affected most and it shows a decreasing trend when the support stiffness increased. For the sensor location, both parameter α and β shows a periodical change around the ring casing. Conclusion The results suggested that both parameters have been impacted by the rotation speed and boundary conditions, among which parameter β has been impacted most.