Tooth Friction Research Articles

Analytical investigation on load sharing characteristics and speed difference of coaxial reverse closed differential herringbone gear transmission system with floating gear and errors

To investigate the influence of gear floating on the load sharing characteristics of the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) and the rotational speed difference between the upper and lower rotors, a dynamic Bending-Torsional-Axial-Pendular (BTAP) model of the CRCDHGTS was established using the centralized parameter method, which considers various excitation factors such as gear floating, errors, Time Varying Meshing Stiffness (TVMS), gyroscopic effect, and tooth friction. It considers the interaction between the closed-stage gear set and the differential-stage gear set, treating the herringbone gear as a symmetric helical gear connected through a receding slot. The dynamic model was solved using the Runge-Kutta method to obtain the dynamic meshing forces for each gear pair under single and combined floating modes. The Dynamic Load Sharing Coefficient (DLSC) of the system, which characterizes the Load Sharing Performance (LSP), was deduced. The load sharing characteristics of different floating modes were analyzed, as well as the influence of different floating displacement on the DLSC. The motion path of the gear floating was also determined. Additionally, the impact of manufacturing error and assembly error of each component on the DLSC under combined floating mode was analyzed. Finally, the influence of gear floating on the output rotation speeds of the upper and lower rotors of the system was investigated. The results indicate that both free-floating of the center gear and combined floating can effectively improve the LSP of the system. When the system adopts combined floating mode, the DLSC of inner and outer meshing changes between 0.91 and 1.09, demonstrating a significant improvement in the LSP. The DLSC of the system increases with the increase in error, with the eccentricity error having a greater impact on the DLSC compared to the assembly error. The optimal floating value for the sun gear is between 0.6 mm and 0.8 mm, while for the planetary gear, it is between 0.4 mm and 0.6 mm. The rotational speed difference between the upper and lower rotors can be controlled within 1r/min. These research findings provide a theoretical basis for further analysis of the dynamic stability and reliability of the system.

Tooth friction in spur gear transmission. From local to mean tooth friction loss

In a gear transmission, power losses come from a variety of sources, classified as load-dependent and no-load-dependent losses. No-load-dependent losses are the ones that remain constant regardless of the applied load, such as losses due to drag in rolling element bearings, seals, churning and/or windage for gears. Load-dependent losses include friction losses due to sliding and rolling between gear teeth. These losses are particularly important in some gear transmissions because of their direct impact on overall efficiency and thermal behaviour. Consequently, knowledge of the friction coefficient associated to this loss is of major interest for optimising gears (geometry, surface finish, lubrication, etc.). In this article, a new method is proposed for predicting the mechanical efficiency losses associated with the mean coefficient of friction for pairs of cylindrical gears. It is based on a model developed previously to estimate the instantaneous tooth friction along the plane of action in gears. This model takes into account the lubricant shear and the friction on contacting asperities. The proposed mean friction coefficient is deduced from the instantaneous friction coefficient using specific calculations, particularly at the pitch point. To verify the method, the estimated results are compared with those in the literature calculated for gears and operating conditions common on FZG test rigs.

The investigation of the effect of operating conditions in gearboxes on efficiency

Efficiency is a concept that evaluates the optimal utilization of resources, including time, energy, finances, or materials, in order to accomplish a particular goal or objective. As widely acknowledged, energy losses occur in systems involving relative motion between interacting machine elements due to friction. In the case of a gearbox, these losses can arise from tooth friction in the gear mechanism, friction in sealing elements, friction in roller bearings, and the influence of the lubricant used in the system, all of which are subject to environmental conditions. This study aims to experimentally determine the efficiency of the gearbox under various operating conditions by considering the gearbox as a comprehensive system encompassing all its components. A measurement system was designed in order to obtain the efficiency of a gearbox. Experiments and measurements were carried out via software support. The measurement system contains two torque transducers, electrical resistive load device, an electrical motor with temperature measurement thermocouple, and two stage helical gearbox. In experiments conducted through computer commands, input revolutions were incrementally increased with 400 rpm intervals within the range of 700–2700 rpm. Moreover, experiments were carried out at different lubricant levels in the gearbox. At the same time lubricant temperature was measured and effects to the gearbox efficiency were investigated. Subsequently, different lubricant with distinct viscosity indices were employed. As a result of this experimental design, regime efficiency values were obtained for each case. Thus, power loss of the gearbox system has been determined. These results were examined using a general full factorial design. Analysis of variance (ANOVA) tables were created and the effects of the parameters on the system and the efficiency results were determined by checking whether the parameters were interacting or not. Finally, regression analysis was performed and the regression function was obtained in order to develop a predictive model to estimate the efficiency of a gearbox.

Wear and friction of self-lubricating coatings applied to spur gears in fluid-free aerospace actuation gearboxes

Aerospace actuation gearboxes operate in low-temperature environments where increased lubricant viscosity leads to significant no-load power losses. Replacing fluid lubricants with coatings applied to the gear teeth is one potential approach to improving gearbox efficiency. Here we develop an approach to determining average wear rates of coated gears using a power-recirculating test stand, profile measurements and a model of the tooth contact. Worn gears are inspected using scanning electron imagery, and energy dispersive X-ray and Raman spectroscopy to understand the wear mechanisms and failure modes. Average coefficients of friction are determined at 20°C and −40°C using a power-absorbing test stand and isolation of tooth friction losses by calculation. These methods are then demonstrated on a promising C/Cr composite coating.

Research on Tribo-Dynamic Characteristics of Double Involute Gears Based on Multiphysics Coupling

Abstract In order to accurately obtain the dynamic characteristics of double involute gears (DIGs), according to the characteristics of tooth profile engagement, a tribo-dynamic model of DIGs with multiphysics coupling characteristics is proposed by integrating the thermal elastohydrodynamic lubrication (TEHL) model, the temperature field analysis model and the dynamic model. The influence of different factors on its dynamic behaviors and the difference in dynamic characteristics between DIGs and common involute gears (CIGs) are comparatively analyzed. The results show that the thermal effect and tooth friction can intensify the dynamic response of the gear transmission. The variation of rotational velocity and torque has a significant impact on the dynamic behaviors of DIGs, the change of tooth waist order parameters have little effect on its dynamic characteristics, and the dynamic characteristics between DIGs and CIGs exist difference, but the difference is not obvious. Additionally, the theoretical model is verified through experiments.

Research on the Method of Improving the Precision of Parts in Pearl River Delta Gear Enterprises: Analysis of Gear Transmission Error and Tooth Friction Coefficient Based on the Influence of Tooth Surface Roughness

Tooth surface roughness is an important index to evaluate the quality of gear processing, which affects the gear transmission error and tooth friction coefficient and changes the gear dynamics. Based on the fractal theory, the gear error correction model considering time-varying roughness is derived, and the new model of time-varying roughness and gear error is introduced into the Xu model to construct the friction coefficient model accounting for time-varying roughness and gear error, which has great reference value for improving the accuracy of gear error. The research results show that the root mean square value of gear error increases by 45.39% and 101.08% under comparison Ra = 0.8 μm, Ra = 1.6 μm, and R a = 3.2 μm, respectively, and the root mean square value of time-varying friction coefficient increases by 45.74% and 148.18%, respectively, which provides theoretical method support for precision management and quality management of gear processing in machinery enterprises.

Time-varying mesh stiffness model of a modified gear–rack drive with tooth friction and wear

Time-varying mesh stiffness model of a modified gear–rack drive with tooth friction and wear

Dynamic Analysis of a High-Contact-Ratio Spur Gear System with Localized Spalling and Experimental Validation

The dynamic characteristics and tooth spalling fault features are studied for the high-contact-ratio spur gear bearing system. The bending torsional dynamic model is proposed in this study for the gear bearing system with an ellipsoid spalling fault. This model also considers time-varying meshing stiffness, tooth friction, fractal gear backlash, and comprehensive transmission error. The meshing stiffness of the system is evaluated using the potential energy method. The bifurcation diagram, time-domain waveform, Poincaré map, phase map, frequency spectrum, and related three-dimensional map are used as tools to analyze the system’s dynamic response qualitatively. The results reveal that the system’s motion with ellipsoid tooth spalling defect exhibits rich dynamic behavior. The response of the proposed dynamic model is consistent with experimental results in the frequency domain. Therefore, the developed dynamic model can predict the system’s vibration behavior with localized spalling fault. Hence, it could also provide a theoretical foundation for future spall defect diagnosis of the gear transmission system.

Evaluation of Relation between Friction Coefficient and Oil Film Thickness of Ground Gear

Matsumoto's equation, which determines the ratio of the friction coefficient between boundary lubrication and fluid lubrication by the ratio of the maximum height roughness and minimum oil film thickness, is often used to predict the friction coefficient on gear tooth surfaces. Recently, however, several papers using gears with highly smoothed tooth surfaces have reported discrepancies between the measured friction coefficient of tooth surface and Matsumoto's equation. It seems that the problem of how to determine the boundary lubrication friction coefficient lies behind these discrepancies. In this paper, the coefficient of tooth friction is determined under a wide range of lubrication conditions using ground spur gears, and the experimental results are compared with the calculation results of Matsumoto's equation to reevaluate the relationship between the two. The friction coefficient of boundary lubrication was found to vary with surface roughness of tooth surface.

On the interest of a semi-empirical model for the tooth friction coefficient in gear transmissions

Accurate modelling of friction coefficient is of primary importance in efficiency, vibration and failure analyses of enclosed gear drives. After showing the influence of surface/lubricant interactions on friction, the authors used a semi-empirical model which can take all these aspects into account. Lubricant is modelled as an Eyring–Reynolds fluid and rough surfaces are described with two parameters via a stochastic approach. A specific two-disc machine is used to perform series of friction measurements on smooth and rough discs. Smooth discs allow to operate under full film lubrication and to measure a reference shear stress of lubricant, whereas rough discs reproduce gear tooth roughness and generate a representative value of friction on asperities. The purpose of this present paper is to describe calculations of this physical-based friction coefficient model and to present the experimental process. On the basis of new results, the impact of a surface finishing process is assessed as well as the consequence of calculating friction coefficient based on oil injection instead of local bulk temperature.

Wear simulation of worm gears based on an energetic approach

Wear phenomena in worm gears are dependent on the size of the gears. Whereas larger gears are mainly affected by fatigue wear, abrasive wear is predominant in smaller gears. In this context a simulation model for abrasive wear of worm gears was developed, which is based on an energetic wear equation. This approach associates wear with solid friction energy occurring in the tooth contact. The physically-based wear simulation model includes a tooth contact analysis and tribological calculation to determine the local solid tooth friction and wear. The calculation is iterated with the modified tooth flank geometry of the worn worm wheel, in order to consider the influence of wear on the tooth contact. Experimental results on worm gears are used to determine the wear model parameter and to validate the model. A simulative study for a wide range of worm gear geometries was conducted to investigate the influence of geometry and operating conditions on abrasive wear.

Multi-objective optimization of gear unit design to improve efficiency and transmission error

This study aims to implement multi-objective optimization of a gear unit in order to minimize the power loss and the vibrational excitation generated by the meshing, via a multi-scale approach that extends from gear contact to the complete transmission. All these indicators are closely linked to the macro and micro-geometry definition of the gear pair. The optimization is carried out using a genetic algorithm, namely the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The design variables chosen for the problem are the pressure angle and the helix angle, as macro-geometry characteristics of the gear, and/or the length and the amount of tooth profile modifications, as micro-geometry characteristics of the gear. Constraints are imposed in order to not exceed a maximum bending stress at the tooth root of the gear and to not fall below a minimum total contact ratio. From the results obtained, it is found that the multi-objective optimization with both micro and macro-geometry parameters simultaneously gives different results than those obtained with macro-geometry first and then micro-geometry parameters. In order to study the importance, or not, to take into account the complete gear unit, a comparison is made between the local power loss generated by gear tooth friction and the total power loss in the single stage gear unit in terms of design variables values.

Failure dynamic modelling and analysis of planetary gearbox considering gear tooth spalling

The spalling mechanism and influence of fault evolution are studied for the gear system of wind turbine by analyzing the dynamic responses.The lateral-torsional dynamic model is proposed in this paper for multistage gear system with gear spalling fault, which considers the influences of nonlinear factors such as tooth friction, sun gear support, time-varying mesh stiffness, gear backlash and comprehensive mesh error.Based on the improved energy method, a calculation model of gear spalling fault is performed to analyze the effect of fault on the time-varying mesh stiffness. At the same time, the bifurcation diagram, time series, phase trajectory, Poincaré map, spectrum diagram and related three-dimensional diagramsare used as tools to qualitatively analyze the dynamic response of gear system. The results show that the fault characteristic frequency of sun gear is sensitive at low excitation frequency, which indicates that it is suitable for fault detection. In addition, the dynamic behavior of the system becomes more complex as the spalling becomes deeper.

Analysis of nonlinear dynamic characteristic of a planetary gear system considering tooth surface friction

Based on the lumped mass method, a torsional vibration model of the planetary gear system is established considering the nonlinear factors such as friction, time-varying meshing stiffness, backlash, and comprehensive error. The Runge–Kutta numerical method is used to analyze the motion characteristics of the system with various parameters and the influence of tooth friction on the bifurcation and chaos characteristics of the system. The numerical simulation results show that the system has rich bifurcation behavior with the excitation frequency, damping ratio, comprehensive error amplitude, load and backlash, and experiences multiple periodic motion and chaotic motion. Tooth friction makes the bifurcation behavior of the system fuzzy in the high frequency and heavy load areas, makes the chaos of the system restrained in the low-damping ratio and light load areas, advances the bifurcation point of the system in the small comprehensive error amplitude area, and makes the period window of the chaos area larger in the large-backlash area, which makes the bifurcation behavior of the system more complex.

Analysis of the influence of gear tooth friction on dynamic force in a spur gear

The main objective of this paper is to investigate the influence of tooth friction on the dynamic force of the gearbox. This is one of the most insignificantly investigated aspects of the gearbox work, despite both experimental and theoretical research conducted. For this reason, it is not entirely possible to establish the friction force determining the friction coefficient due to the complexity of the process. Currently, various approaches are taken in calculating dynamic models, among others excluding friction, Coulomb models, models in which the value of the friction coefficient depends on the sliding velocity, and the application of complex elastohydrodynamic models. Due to such different approaches, it was decided to examine the influence of tooth friction on the dynamic force for the stationary work conditions of the gearbox. Moreover, a new gear tooth friction model was developed, based on the Coulomb model of friction and rolling friction. The results were obtained for four friction models and, in the fifth case, without including it. Furthermore, the influence of torsional vibration on the friction lever arm was analysed.

Nonlinear tribo-dynamic model and experimental verification of a spur gear drive under loss-of-lubrication condition

Gearbox is required to serve for ≥ 30 min in helicopter design to improve survivability, when the gear drive loses lubrication due to battle damage. Under such loss-of-lubrication condition, tooth friction, wear and temperature pose serious problems to dynamic performance of gears. Therefore, a nonlinear tribo-dynamic model of spur gear drives is established and experimentally validated in this work. The time-varying friction coefficient is predicted under loss-of-lubrication condition on the basis of computational inverse technique. The temperature rise and tooth wear caused by friction were included by using thermal network model and dynamic wear model. The flexibility of gear shafts and the gyroscopic effect of gear rotors are also considered. The results indicate the gyroscopic effect apparently affects the natural frequency of the gear drive, while friction has negligible effect on the natural frequency but has considerable effect on the nonlinear behavior. The influence of temperature and gyroscopic effect on nonlinear behavior are reflected in the region of middle and high speed, while tooth wear mainly affects the bifurcation at the middle speed. In addition, tooth wear not only aggravates gear vibration but also can change the phase of dynamic transmission error. The analysis and experiment results can be an important reference in reducing friction and wear, restraining nonlinear behavior, and reducing vibration and noise.

Vibration characteristic analysis of gearbox based on dynamic excitation with eccentricity error

In this study, the vibration characteristics of gearbox considering the eccentricity error and the friction excitation of helical gear pair were evaluated theoretically and experimentally. A geometric model of a single-stage helical gear pair with eccentricity error was established to obtain the calculation formula of the length of the dynamic contact line and the friction excitation. The multi-degree-of-freedom dynamic model of the transmission system was established considering the influences of tooth friction, support stiffness and damping, meshing stiffness and damping, static error, and dynamic tooth backlash. Then, the dynamic meshing forces of the system were obtained and applied to the gearbox for vibration response analysis using mode superposition method. A correlation test rig was developed to measure vibration under different operating conditions for verifying the correctness of the simulation models. Comparison between simulation and test was performed to demonstrate the accuracy of the proposed model in predicting vibrations. Results showed that eccentricity greatly influenced the overall vibration characteristics. The relative error between measurement and prediction can be significantly reduced by considering the eccentricity error in the dynamic model of transmission system.

Study on bifurcation characteristics of multi-clearance bending torsional coupling gear transmission based on EHL

In order to study the influence of tooth surface friction on the non-linear bifurcation characteristics of multi-clearance gear drive system, a 6 degree-of-freedom bending torsional coupled vibration model was established. The time-varying mesh stiffness, backlash, support clearance and damping were considered comprehensively in this non-linear vibration model. Loaded tooth contact analysis was used to calculate the time-varying mesh stiffness. Based on the elasto-hydrodynamic lubrication, the time-varying friction coefficient was calculated. Runge–Kutta numerical method was used to solve the dimensionless dynamic differential equation. Using phase diagram, Poincaré diagram, time history diagram, and spectrum diagram, the influence of tooth surface friction on bifurcation characteristics was studied. The results show that the system undergoes a change from 1-periodic motion, multi-periodic motion, to chaotic motion through bifurcation and catastrophe when the speed changes independently. When the friction coefficient of tooth surface changes from 0, 0.05 to 0.09, the chaotic motion of the system is suppressed. Similarly, with the increase in tooth friction, the chaotic motion characteristics are suppressed. Tooth surface friction is the main factor affecting chaotic motion. With the increase in friction coefficient of tooth surface, the chaos characteristic does not change obviously and the vibration amplitude decreases slightly.

Measurement method of tooth friction force for helical gears by laser displacement sensor

Tooth friction force between the mesh teeth is a non-negligible excitation source for gear vibration and noise. However, the accurate measurement of the tooth friction force in mesh is very difficult, especially for helical gears. In this paper, a method for measuring the tooth friction force in helical gears is proposed by using a laser displacement sensor. The tooth friction force is obtained based on the bending deformation and the bending stiffness of the output shaft in the direction of the friction force. System errors of the gearbox are minimized by preload and locking device, and the measurement error is compensated according to the geometric positional relationship of the output shaft with and without the action of the mesh force. Experimental measurement is carried out by using an example of helical gears and compared with theoretical model. Experimental results have been shown that the magnitude and trend of the tooth friction force by measurement are basically the same with the theoretical calculations, which illustrate the effectiveness of the measurement method. It is also observed that both the tooth friction forces from the measurement and the theoretical model change direction twice in one mesh circle.

Influence of surface topography on the friction and dynamic characteristics of spur gears

As an important excitation source of gear dynamic problems, the time-varying friction of tooth surface is closely related to its topography. Considering the friction characteristics of tooth surface is of great significance to improve the calculation accuracy of gear dynamic characteristics. In order to solve the problem that the variation of tooth friction coefficient was simplified too much in the previous gear dynamics research, the time-varying tooth friction coefficient is obtained by fitting the results of twin-disc test in this research. To investigate the influence of tooth surface topography on the friction and dynamic characteristics of spur gears, the relationship between surface topography and friction coefficient under line contact condition is studied using twin-disc tester and analyzed by 3D topography parameters in ISO 25178. The time-varying friction coefficients of spur gears with different tooth surface topographies during meshing are fitted with the experimental results. The influence of time-varying friction coefficient caused by the tooth surface topography on the dynamic characteristics of spur gears under different operating conditions is examined by substituting the fitting curves of time-varying friction coefficient into the multi-degree-of-freedom dynamic model of spur gears. The results show that this influence is mainly embodied in the off-line-of-action direction, which is the direction of friction force acting on the tooth surface. The dynamic characteristics of gears with different surface topography are obviously different under various working conditions. The method presents in this paper simplifies the application of tooth contact analysis in the study of time-varying tooth friction characteristics, which will provide a new way for the gear dynamics research considering the tooth surface topography.