Dynamic Characteristics Analysis And Nonlinear Vibration Research On A Planetary Reducer With Small Tooth Number Difference

This research subject stems from the projects “Commission of Science,Technology and Industry for National Defense "Eleventh Five-Year" civilian spacepre-research project-the high performance friction pairs and efficient transmissionmechanism technology under space environment (No. C4220061319)" and “Programfor Changjiang Scholars and Innovative Research Team of Chinese Ministry ofEducation-the innovation design theory, method and technology of high performanceelectric drive system (No. IRT0763)" and “National Natural Science Foundation KeyProject of China-the reliability design theory and methods of new high performancetransmission parts and system (No.50735008)".Working state of reducer system is extremely complex, also the load cases andpower plants are diverse, and for the gear transmission, the factors of the time-varyingmesh stiffness, transmission errors, backlash, and so on, may cause tooth periodical andstrong nonlinear coupled vibration of contact-detachment-contact, which will seriouslyinfluence the smooth and reliability of transmission system. So the researches on itsdynamic characteristics, the backlash nonlinear vibration behaviors and theirinfluencing factors will provide a theoretical basis and experimental reference for thedesign, analysis, and manufacture of high-performance gear system.Aimed at a NN-type planetary reducer with small tooth number difference reducer,firstly, the structure and transmission principle are analyzed, secondly, the naturalfrequencies and mode shapes are analyzed by means of the FE method, then, thenonlinear vibration model and equations of reducer system are established by thelumped mass method, and the equations are solved by numerical method to analyze thenonlinear vibration characteristics and influences of parameters on them, finally, themodal characteristics and vibration response testing is carried out, respectively.The main contents of this paper are as follows:(1) The structure and transmission principle of this reducer are analyzed, thetheoretical speed of each transmission part is calculated under a common operatingcondition, also the theoretical meshing frequency and meshing damping are calculated,the dynamic characteristics parameters such as deformation, stiffness, damping of eachrolling bearing are analyzed in detail.(2) The stiffness calculation formula of single tooth in internal gear pair is deduced. Then, the mesh stiffness of multi-pair of teeth is calculated considering the theoreticalcontact ratio, the time-varying mesh stiffness of two stage transmissions are fitted to8-order Fourier series form, and a sine function, whose angular velocity is meshingangle frequency, is simulated as gear error.(3) The FE modal analysis model of this reducer is established using the ABAQUS,in which the tooth engaging portions are constrained as binding, the bearings aresimulated by spring units. The Lanczos eigenvalue solver is adopted for the free modalsolving of the reducer, the first20orders natural frequencies and mode shapes of thereducer are obtained.(4) Considering the gear meshing stiffness, transmission error, backlash andsupport stiffness and damping, the multi-degree-of-freedom, multi-backlash, variableparameters, bending-torsion coupled nonlinear vibration model of the two-stage gearsystem is established by the lumped mass method, the nonlinear vibration differentialequations of the gear system is deduced by the Lagrange equation. The fourth-orderfifth-grade RKF method is adopted to solve the nonlinear differential equations, the gearvibration displacements, velocity responses, and the vibration displacement-velocityphase portraits, Poincaré sections are analyzed systematically. The elasticity viscousmeshing forces of gear pair, bearing dynamic loads, and vibration accelerationresponses are further calculated, finally, the influences of various parameters on thenonlinear vibration characteristics of the reducer are analyzed.(5) The Hammer free modal experiment on the reducer is carried out by utilizingthe LMS Test. Lab to verify the theoretical analysis results. The three-directionacceleration sensors are adopted to capture the vibration signal of the reducer shell, thevibration frequency can be obtained by the FFT transform, the vibration accelerationstructural noise is analyzed through1/3octave processing, the vibration velocity anddisplacement response can be obtained by integral processing.