Estimation of a Planetary Gear Mesh Stiffness: An Approach Based on Minimising Error Function

An expert system for fatigue testing of airframes: Gubarev, V.V., Grif, M.G., Metyolkin, N.G., Seryoznov, A.N. and Sklyarov, A.A. Conf. Fatigue and Fracture in Steel and Concrete Structures, ISFF '91, Madras, India, Dec 1991 Vol 2 (Oxford & IBH Publishing Co. Pvt. Ltd, New Delhi, India, 1991) 923–927

Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness

The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.

The traditional method for calculating the time-varying mesh stiffness (TVMS) of cracked gears usually assumes that the root crack is solely located within the gear tooth. Accurate calculation becomes a challenge when the crack propagates into the gear body. In this paper, an improved model for calculating the TVMS of spur gears with crack propagation into the gear body is proposed based on a combined analytical finite element-potential energy method, and the accuracy of the proposed model is verified by the finite element method. A 5-degree-of-freedom (5-DOF) dynamic model with speed fluctuation is developed, taking into account the coupling shaft-bearing stiffness as the support stiffness. Subsequently, a dynamic simulation of a gear system with a gear body crack is conducted. The results indicate that the proposed analytical model can provide relatively accurate mesh stiffness for crack propagation into the gear body. The TVMS decreases as the crack length increases, the decrease in mesh stiffness becomes more significant when considering the influence of the crack on the gear body stiffness. The dynamic response obtained from the proposed dynamic model shows more pronounced pulse characteristics compared to the model that does not consider the influence of shaft stiffness. The low speed and heavy load conditions restrain the speed fluctuation of the gear system. The residual signal is more effective for identifying fault signals than the original signal. The proposed model can provide theoretical and methodological references for diagnosing faults in gear systems with crack propagation into the gear body.

An improved analytical model for gear mesh stiffness calculation

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

This paper investigates the meshing stiffness of beveloid gears in the beveloid rotate vector (BRV) transmission. It is a new kind of transmission evolved from rotate vector (RV) reducer. In the BRV transmission, the beveloid gear is a kind of involute gear with a bevel angle. The BRV transmission have high power density, large transmission ratio and high precision in geared coupled systems. However, there is rare systematic research conducted on the meshing stiffness analysis of the BRV transmission at present. Based on the loaded contact finite element analysis principle, a meshing stiffness analysis model for beveloid gears is established. The influence of different factors such as pitch cone angle, addendum coefficient, load and rim structure parameters of external gear on meshing stiffness are studied. The results show that the pitch cone angle and addendum coefficient have little effect on the shape of the meshing stiffness curve, but they have a significant influence on the amplitude of meshing stiffness. In contrast, the load can affect both the shape and the amplitude of the meshing stiffness curve obviously. Also, the size of scallop-hole and rim thickness have a great impact on the amplitude of the meshing stiffness. The prescribed piece of study can provide a better understanding for gear researchers in order to understand the influence of different parameters on dynamic characteristics analysis of the BRV transmission systems.

A study of effects of tooth surface wear on time-varying mesh stiffness of external spur gear considering wear evolution process

On gear time-varying meshing stiffness calculation considering indexing feeds and processing characteristics of gear shaping processing

In order to accurately describe the complex transmission systems and clarify the effects of internal and external excitation on the vibration characteristics for large complex transmission systems, a dynamics model considering gear meshing error and time-varying meshing stiffness is established at two-stage planetary gears systems. The coupling model is established by matrix set method for two-stage planetary gears and multistage spur gears transmission systems. The random load excitation verified by experiments is the external excitation in the system, and the excitation caused by the time-varying meshing stiffness and meshing error is the internal excitation. The research on the response of the vibration systems shows that the internal excitation caused by gear meshing stiffness and gear meshing error has important influence on the dynamic load behavior of spur gears transmission in complex systems. For the planetary system with heavy external load, the dynamic behavior mainly depends on the external load, and the influence of internal excitation on the dynamic meshing force is less than that of the external excitation for the planetary system. The external excitation mainly affects the low-frequency region of the dynamic meshing force for the system, and the internal excitation affects the high-frequency region of the dynamic force for the system. The frequency influence interval of the internal excitation is much larger than that of the external excitation.

Tooth surface crack is an early fault before spalling, which has an important influence on mesh stiffness and vibration characteristics of the gear system. However, the researches on tooth surface crack are limited as scholars pay little attention to this early fault. In this study, an analytical model of spur gears with tooth surface crack is established. Using the potential energy method, the equations for mesh stiffness calculation of spur gears with tooth surface crack are derived. By adopting the proposed model, the influences of tooth surface crack fault on mesh stiffness of gear tooth are studied. The relationship between tooth surface crack and mesh stiffness of gear tooth under different lengths and depths can be further calculated. This study provides a theoretical basis for the diagnosis of early failure of spalling.

<div class="section abstract"><div class="htmlview paragraph">A new capability to analyze the dynamic interaction of nonlinear hypoid gear mesh characteristics and time-varying bearing stiffness is proposed. Both backlash nonlinearity and time-varying mesh parameters, such as mesh stiffness, mesh point and line-of-action, are included in the nonlinear hypoid gear mesh model. The time-varying bearing stiffness behavior due to the changing orbital position of rolling elements is also modeled. A practical application is studied to reveal the dynamic characteristics of the complex interactions. Dynamic simulation results show that dynamic mesh force is relatively insensitive to the temporal variation in the bearing stiffness. On the other hand, the dynamic bearing loads are affected significantly by the time-varying bearing stiffness, especially in the case of heavy drive torque load without the occurrence of jump response phenomenon. However, for the case of light load condition assuming time-invariant mesh parameters, the dynamic bearing loads are insensitive to time-varying bearing stiffness. The analysis also reveals that the presence of appropriate backlash nonlinearity can stabilize the parametric resonance caused by the time-varying bearing stiffness for the case of light load condition assuming the mesh parameters are time-invariant.</div></div>

Three new models for evaluation of standard involute spur gear mesh stiffness

A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears

Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth