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Meshing power loss is one of the most important parts in power loss calculation of planetary gear set. However, most of the conventional methods assumed the friction coefficient between gears as a constant value in the meshing power loss calculation, and most importantly, the influence of gear tooth surface geometry is usually ignored, for example,...
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... They investigated the dynamic characteristics of the gear system under different roughness and input torque conditions. Wang et al. [6] proposed a new calculation model for meshing power loss in planetary gearsets, considering gear surface roughness based on the elastohydrodynamic lubrication method. ...
In order to explore the time-varying mesh stiffness and dynamic parameters of bevel gears with different surface roughness, the fractal dimension and characteristic scale coefficient are calculated to determine the fractal dimension of tooth surfaces of spiral bevel gears with rough features. Spiral bevel gears with distinct surface roughness are obtained by simulating the gear-cutting process, and after analysis, a dynamic differential equation for spiral bevel gears considering the surface roughness is proposed. By combining the differential equation with finite element analysis (FEA), the time-varying mesh stiffness of spiral bevel gears with various surface roughness is determined. FEA analysis yields the time-varying mesh stiffness under different surface roughness. The vibration velocity and acceleration of spiral bevel gears with different surface roughness are revealed by combining the time-varying mesh stiffness with the dynamic equation. The intricate relationship between gear surface microstructure and its mechanical behavior during engagement is thoroughly analyzed. A comprehensive dynamic parameter model is proposed to capture the influence of microtopological changes on gear dynamics. The results can offer valuable insights for the design and optimization of bevel gears, aiming to enhance their performance and durability.
... Wang et al. 12 proposed a new model for calculating the power loss of planetary gear meshing considering tooth surface roughness and investigated the relationship between tooth surface roughness and the dynamic response. Zhou et al. 13 developed a finite element model of a megawatt wind turbine gear and used the developed model to comparatively study the effects of microstructure, inclusions, and surface roughness on the contact fatigue behavior of the gear. ...
Microscopic roughness is inevitable on the gear meshing surface, which is also a key parameter affecting the dynamic response. The surface roughness exhibits self‐affine characteristics across multiscales. To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads, an experimental setup of spur gear transmission is devised. The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method. The relationships between gear response and fractal parameters are revealed experimentally. Results indicate that a rougher tooth surface, that is, a smaller fractal dimension or larger fractal roughness, corresponds to an intense vibration amplitude. The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads. Under low speed and light load conditions, the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system. With the increase of speed and load, the macroworking conditions gradually become the main factor attributed to vibration amplitude.
... (iii) Due to the coupling effects of the internal and external gear meshing, the dynamic behaviors of planetary gear sets are more complex than parallel-axes gears. The tribo-dynamic characteristics and pitting evolution of planetary gear sets are seldom discussed [42,43]. ...
Considering the coupling effects of the tribology and dynamics, a dynamic pitting evolution model of planetary gear sets is developed. A fast dynamic load distribution algorithm is proposed to obtain the dynamic contact load considering complex pitting topography. Then the mixed elastohydrodynamic lubrication theory is adopted to acquire the tribological parameters. Combing the dynamic load and Zaretsky's fatigue criterion, a contact fatigue model is developed to predict the pitting topography during the degradation process. An iterative algorithm framework is developed to realize the topographical updating in the dynamic pitting prediction. The effectiveness of the proposed model is demonstrated using two experimental examples. The probability distribution of the pitting location is investigated using the proposed model. It is revealed that the gamma distribution is more consistent with the pitting distribution along the involute direction than the normal distribution. Owing to the “competition mechanism” of the pitting and surface wear, the pitting center approaches the pitch point with the increase of the surface roughness. The proposed model is capable of evaluating tribo-dynamic behaviors of planetary gear sets during the life-cycle degradation process of pitting failure. Moreover, it can provide theoretical guidance for the pitting fault mechanism and model-based fault diagnosis.
Power loss and efficiency are pivotal performance metrics significantly impacting the quality of electric-drive axles. This study outlines a numerical method for determining the electric-drive axle system power loss, which includes gear meshing, gear churning, and bearing power losses. Power loss from gear meshing was calculated by analyzing load distribution and friction coefficient. The frictional loaded tooth contact analysis method was employed to ascertain the load distribution during gear meshing. A formula based on a weighting function was utilized to compute the friction coefficient. The finite element method was used to verify the gear load distribution and meshing power loss. Subsequently, empirical formulas were used to calculate the gear churning and bearing power losses. To substantiate the proposed numerical method, an experimental apparatus was employed to measure the power loss and efficiency of an electric-drive axle under various operating conditions. The experimental study demonstrated a strong correlation between the numerical and calculated results. These findings suggest that the proposed method can be an effective tool in predicting the power loss and efficiency of electric-drive axles.
Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.
The lubrication characteristics of a cylindrical gear transmission with a variable hyperbolic circular-arc-tooth-trace (VH-CATT) are important theoretical bases for the tribology design of the gear and its fatigue life prediction. Existing lubrication characteristics studies of it are based on simplified linear contact models, which are limited to one specific meshing position only. Therefore, the mathematical models for tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) are established to calculate most time-varying parameters in a meshing period, such as the kinematic parameters, spatial geometric parameters, and contact parameters, are calculated. Accordingly, a thermo-elastohydrodynamic lubrication (TEHL) model of an elliptical contact of this gear transmission is presented. Using all the proposed mathematical models, the TEHL results with smooth and rough tooth surfaces in a meshing period are analyzed. The obtained results reveal that these models can be used to predict the distribution of the film thickness, pressure, and temperature rise on the smooth and rough tooth surfaces of VH-CATT cylindrical gear transmission in each contact area of a meshing period. And it shows that the time-varying parameters have great influences on lubrication performance. Furthermore, the lubrication mechanism in a meshing period is investigated systematically in VH-CATT cylindrical gear transmission.
