Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

Research of Mechanical Resonance Analysis and Suppression Control Method of the Servo Drive System

Transmission mechanisms of the servo drive system are not a pure rigid body, and the existence of the elastic transmission mechanisms will make the system generate mechanical resonance. Aiming at mechanical resonance of the servo drive system, the resonance generation mechanism is analyzed, the four-mass model considering the time-varying meshing stiffness of the gear is established, and the influence of different stiffness parameters on the mechanical resonance of the system is researched in this paper. The composite controller of Model Predictive Control (MPC) with Notch Filter is used to simulate the mechanical resonance suppression of the four-mass servo system considering time-varying meshing stiffness, and it is compared with the mechanical resonance suppression method based on Model Predictive Control. The simulation results show that when the step speed is 200 r/min, the overshoot is reduced from 11.6 r/min to 1.1 r/min, which is reduced by 90.5%. Under the impact load condition, from 10 Nm to 30 Nm, overshoot is reduced from 34.3 r/min to 12.8 r/min, reduced by 62%, and torque oscillation is reduced by 81.5%. Therefore, the composite controller of Model Predictive Control with Notch Filter can suppress the mechanical resonance problem effectively, caused by elastic transmission, and improve the robustness of servo drive system.

Influence of Different Modified Gears on the Vibration and Noise of Electric Vehicle Reducer

The tooth profile crowning modification was applied onto paired gears for reducing the noise of an electric vehicle reducer. The simulated gear contact spots are compared before and after modification, and are validated by a contact spot experiment. Based on the rigid-flexible coupling model of the gear transmission system, the time-varying meshing stiffness, time-varying meshing force, and the vibration and noise of the gear pairs with different modified gears obtained by simulating calculation are analyzed. The results showed that the selection of modified gear has a great influence on the modification effect. In the way of tooth profile crowning, it is not advisable to modify the pinion independently, as it may increase the frequency and degree of meshing impact between the helical gear pair, making the transmission become less smooth; while modifying the wheel and pinion at the same time can effectively reduce the time-varying meshing stiffness and force, and the vibration and noise. Also, the optimized gear modification scheme is verified by the noise test.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.

Nonlinear dynamic analysis of gear system in shearer cutting section under wear failure

Gear wear failure is one of the important failures of the gear system in the shearer cutting section. To reveal the influence mechanism of shearer cutting gear wear on the system dynamic characteristics, considering coupling factors such as time-varying meshing stiffness, dynamic gear clearance, internal error excitation, end load constraint and bearing radial clearance under wear failure, an improved dynamic model of shearer drive gear system is introduced to present an in-depth investigation of uniform wear of gear teeth effect. The dynamic meshing stiffness of gears under different degrees of wear is analysed. Furthermore, the bifurcation diagram is utilized to observe the motion state of the system experiencing different excitation frequencies, support damping as well as terminal loads. It is demonstrated that the gear surface wear could bring a change in gear dynamic transmission error, vibration impact state and amplitude, which is mainly manifested in increasing the unstable area and the vibration amplitude of the gear system, providing a method for monitoring and diagnosing of gear surface faults.

Influence of the Shape of Gear Wheel Bodies in Marine Engines on the Gearing Deformation and Meshing Stiffness

The basic properties of gears must be considered: the shape of their gearing, their load capacity, and the meshing stiffness, which affects the noise and vibration. When designing large gears, it is important to choose the correct shape of the gear body. Large gears used in marine gearboxes must be designed with as little weight as possible. The requirements of sufficient stiffness of the gear wheel body, as well as the meshing stiffness, must be met. This paper is devoted to the influence of spur gear wheel body parameters on gearing deformation and meshing stiffness. The stiffness of the gear is solved on the basis of the deformation of the gearing teeth, which is determined by the finite element method. Examples of the simulation and subsequent processing of results demonstrates how the individual parameters of the gear wheel body influence the stiffness of the gearing teeth. At the same time, the results point to designs of suitable shape and dimensions to achieve the required stiffness of the gearing teeth, but with the lowest possible weight of the spur gear wheel body.