Fault Feature Analysis of Gear Tooth Spalling Based on Dynamic Simulation and Experiments

Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.

Effects of the interval geometric deviation and crowning parameters on the automotive differential dynamics

A differential mechanism is an essential component in the majority of automotive applications. Its vitality stems from the fact that it allows a wheel-drive vehicle to take a curve safely. On the other hand, it can ratchet up the vibration in the wheel-drive vehicle due to the excessive gear tooth deflection from applied torque. Some gear tooth modifications can increase or decrease the level of vibration in the mechanism. So far, very little attention has been paid to the effects of the uncertain geometric deviation of the tooth profile and uncertain crowning parameters on the dynamic performance of the mechanism. This study aims to investigate the impacts of these uncertain parameters on the gear systems’ dynamic performance. To this end, the nonlinear interval model of the differential mechanism is proposed. The mesh stiffness for straight bevel gear is modelled through the potential energy method and slice theory, while bearing stiffness elements are calculated at each time step. A refined computational algorithm is proposed to deal with any gear system with multiple interval variables. The scanning method is used as a reference method in this paper. The main outcomes of this study are that the crowning design can slightly reduce the vibration in the mechanism, and the profile errors can increase its vibration level excessively. Besides, the results derived from the refined algorithm show similarities to those determined by the scanning method, and the study shows that the refined algorithm can handle any gear system with uncertain static or time-varying parameters.

A New Analytical Method for Modeling the Effect of Assembly Errors on a Motor-Gearbox System

The well-known gear tooth defects such as root cracks and flank spalls have been widely investigated in previous studies to model their effects on the time varying mesh stiffness (TVMS) and consequently the dynamic response of motor-gearbox systems. Nevertheless, the effect of assembly errors such as the center distance and the eccentricity has been less considered in past works. Determining the signature of these errors on the system response can help for their early detection and diagnostic to avoid overloading and failure of gears. An original geometric-based method combined with the potential energy method is proposed in this paper to accurately model the effect of these assembly errors on the TVMS of mating spur gear pairs. This is achieved by updating the line of action equation (LOA) at each meshing step using the actual coordinates of gear centers and employing a contact detection algorithm (CDA) to determine the actual contact points coordinates. An electrical model of a three-phase induction machine was then coupled with a dynamic model of a one-stage spur gear system to simulate the effect of assembly errors on the electromechanical response of the motor-gearbox system. The simulation results showed that the center distance error induces a reduction in the TVMS magnitude and the contact ratio, whereas the eccentricity error causes a double modulation of the TVMS magnitude and frequency. In addition, the results showed that assembly errors can be detected and diagnosed by analyzing the system vibration and the motor phase-current.

Nonlinear Dynamic Characteristics of Wind Turbine Gear System Caused by Tooth Crack Fault

Crack in gears impacts the dynamic response of wind turbine multistage gear system, which also influences the safe operation of wind turbine. A translational–torsional nonlinear dynamic model of the multistage gear system is proposed with root crack fault. The model considers the effects of sun gear support, time-varying mesh stiffness, gear backlash and other factors. The mesh stiffness with root crack is analyzed by using potential energy method. Based on the Runge–Kutta method, the system responses are obtained with multiple parameters changing. The nonlinear dynamic features of the cracked and normal system are compared by bifurcation diagram, time series, phase trajectory, Poincaré map, spectrum diagram and corresponding three-dimensional diagrams. The analyses show the effects of input torque, backlash, crack occurrence and evolution on the system dynamic behaviors, and the effect of crack fault on the gear system response is further verified by experiment. The results provide a theoretical basis for the cognition of fault mechanism and fault diagnosis of wind turbine gearbox.

Dynamic Analysis of a Fault Planetary Gear System under Nonlinear Parameter Excitation

In order to facilitate lubrication and avoid the gear stuck due to thermal expansion, there needs to be a gap between the tooth profiles. As a strong nonlinear factor, the backlash will affect the motion state of the planetary gear system. When the gear failures occur, the motion state of the system will accordingly change. In this study, the meshing stiffness of the gear pair with tooth tip chipping fault is calculated by combining the analytic geometry method and the potential energy method. Then, a new nonlinear dynamic model including tooth backlash, time-varying mesh stiffness, and manufacturing error is established to study the dynamic response of the system. The equations of motion are derived by the Lagrangian method and solved by the numerical integration method. Taking the excitation frequency and tooth backlash as the variation parameters, respectively, the dynamic characteristics of the system are analyzed by comparing the global bifurcation diagrams between the health system and the fault system, and the path of the system into chaos is revealed. At the same time, the local characteristics of the system are revealed through the phase diagrams and Poincaré maps. The results show that with the variation of excitation frequency and tooth backlash, the fault system presents a more complex motion state. This study can provide the theoretical support for dynamic design and fault diagnosis of planetary gear transmission systems under the environment of gear fault-prone.

Effect of structural design parameters on nonlinear dynamic characteristics of the gear transmission

The calculation of time-varying meshing stiffness caused by the alternate contacting of the gear tooth is an essential prerequisite to obtain real and effective nonlinear dynamic characteristics of the transmission system, so that the significance of which cannot be overemphasized. Accordingly, this work proposes an improved method to get meshing stiffness with taking fillet-foundation and gear rim deflection into consideration. Compared to the traditional potential energy method, the proposed method has more superior accuracy and performance, and its effectiveness has been further verified by the finite element analytical model. After that, an ideal eight degree of freedoms (DOFs) dynamic model of one stage mass-spring-damper involute spur gear, including lateral and torsional motions, is established to study the dynamic characteristics. Due to the complexity of the gear system operating conditions, we also investigate the influence of various parameters including hub bore radius, transmitting load, and rotation speed on dynamic features, especially in heavy-load and high-speed conditions. From the results, it can be concluded that these parameters will play a prominent role in the spur gear pair dynamic behaviors, providing a certain guidance for gear design.

Coupling effects of manufacturing error and flexible ring gear rim on dynamic features of planetary gear

Manufacturing errors widely exist in and deteriorate the dynamic property of planetary gear train (PGT). To solve this problem, the ring gear is often designed with a thin rim to compensate for the effects of manufacturing errors via the elastic deflections of the rim. Existing dynamic models of the PGT only consider the effects of either the elasticity of the rim of the ring gear or the manufacturing errors. The coupling effects of manufacturing errors and the flexible ring gear are ignored. To understand the dynamic behaviors of the PGT better, a dynamic model of the PGT coupled with typical manufacturing error and flexible ring gear is developed in this study. The tooth contact analysis of the ring-planet mesh, which is calculated based on the potential energy method and uniformly curved Timoshenko beam theory, is studied using the influence coefficient method. A numerical algorithm is proposed to solve the integrated dynamic equations of the PGT. Calculated results show that the dynamic features of the PGT are complex, and the load sharing characteristic is improved when the flexible ring gear is incorporated.

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.

Research on Meshing Stiffness and Vibration Response of Pitting Fault Gears with Different Degrees

In order to study the influence of pitting on meshing stiffness, the normal distribution function is used to simulate the pitting location of pitting gear, and the potential energy method is used to analyze the influence of pitting on meshing stiffness. At the same time, the meshing stiffness of pitting gears with different degrees is analyzed by finite element method, and the validity of the calculation results with potential energy method is verified. On the basis of meshing stiffness, the dynamic model of gear system is established, and the vibration response of pitting gear system with different degrees is analyzed. The results show that with the increase of pitting area, the meshing stiffness decreases; the closer the meshing area of the driving wheel is to the pitting line, the more the meshing stiffness decreases, resulting in the intensification of vibration response and periodic impact; and in the time history diagram, there is a small spurious frequencies near the meshing frequency; in the phase diagrams and the Poincare diagram, trajectory and discrete point aggregation area is gradually increased.

Calculation of optimum profile modification curve for gear pair based on complex potential method

The optimum profile modification curve of a gear pair is usually determined according to the fluctuation minimization of static transmission error (STE). For the calculation of STE, the potential energy method dismisses the correlative tooth deflection induced by gear body elastic coupling effects, and the finite element method requires high calculation cost. In order to simultaneously obtain high calculation accuracy and efficiency, the single tooth deflection is calculated through analytical integration about the Hertz contact pressure based on the conformal map method. The correlative tooth deflection is calculated based on the power series solution of the mixed boundary problem of an elastic annulus. Via combination of deflection compatibility and the force equilibrium condition, a contact analysis model of a spur gear pair is built. Based on the model, the STE is first calculated and compared with the finite element analysis result to verify the model rationality. Then, the optimum profile modification curve which renders constant STE is calculated. For a gear pair with the obtained modification curve, fluctuation of dynamic transmission error also decreases and the optimization effect is verified.