Time-varying Friction Coefficient Research Articles

Nonlinear Dynamics and Meshing State Transition Analysis of Spalling Defect Gears with Multi-Lubrication Conditions

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area.

Dynamic Simulation Analysis of Aviation Gear Transmission Based on Rough Tooth Surface

In order to explore the influence of tooth surface microstructure on the dynamics of aviation gear transmission, this paper describes the profile of aviation gear considering rough surface based on fractal theory. With the help of the established gear fractal contact model, the dynamic parameters such as time-varying friction coefficient, time-varying meshing stiffness and transmission error of rough tooth surface are characterized. The nonlinear dynamic model of aviation gear is established to solve the dynamic response of smooth and rough tooth surface. The dynamic meshing force, dynamic friction force, vibration time domain and frequency domain diagram are obtained, and the corresponding experiments are carried out. The simulation and experimental results show that the fluctuation range of the dynamic simulation results of aviation gear transmission based on rough tooth surface will be larger, and it has a certain degree of disorder, which is closer to the experimental results.

Effect of time-varying friction coefficient on self-excited vibration of floating spline-rotor system

Different lubrication states seriously affect the stability and safety of the aviation power transmission system. This study investigates how time-varying friction coefficients impact the stability of an aviation spline-rotor system using a spline-rotor model that considers uneven stress distribution on the tooth surface. Experimental tests with a high-frequency friction and wear test machine yield time-varying friction coefficients for splines with different lubrication, surface roughness, and materials. A sharp change of friction coefficient for the sample occurs under wear debris lubrication. The average friction coefficient for the sample with roughness 1.6 is lower than those with roughness 0.8 and 3.2. Under the same lubrication conditions, the friction coefficient of Resin matrix composites is smaller than that of metallic materials. Dynamic simulation of the spline-rotor model considering time-varying friction coefficients shows rich self-excited vibration behaviors influenced by lubrication, surface roughness, and materials.

Establishment of the dynamic BTAP model and load-sharing analysis of herringbone gear planetary system with cracks

To reveal the influence of component cracks on the dynamic load-sharing characteristics of the herringbone gear planetary system (HGPS), a 55-DOF bending-torsional-axial-pendular (BTAP) nonlinear dynamic model of the system was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as manufacturing error (ME) and installation error (IE), time-varying mesh stiffness (TVMS), time-varying support stiffness, damping, and friction. The TVMS model of components with cracks was established using the cumulative potential energy method, and the mathematical quantification relationship between different crack parameters and TVMS was studied. Based on the theory of elastohydrodynamic lubrication (EHL), calculate the time-varying friction coefficient and friction force of each gear pair. Using the nonlinear elastic theory of rolling elements and raceways, the time-varying support stiffness of each component is obtained. Using the Runge-Kutta numerical integration method to solve the dynamic differential equations, and analyzed the load-sharing characteristics and sensitivity influence law of the system when the sun gear, planetary gear, and internal gear ring contain cracks respectively. Built a vibration test bench for the HGPS with cracks, and the experimental results were compared with the theoretical results. The results show that as the crack intensifies, the TVMS value decreases at the crack tooth. When the sun gear contains cracks, there will be obvious protruding excitation in the system’s load-sharing curve, and the internal meshing load-sharing characteristics are better than the external meshing load-sharing characteristics. At the same time, as the degree of cracks increases, the system load-sharing characteristics first improve and then deteriorate. At the same crack, as manufacturing and installation errors increase, the load-sharing characteristics of the internal and external meshing pairs deteriorate. When the internal gear ring contains cracks, the dynamic load-sharing coefficients of the internal and external meshing pairs of the system are 7.96 and 4.10, respectively, which have the highest impact on the dynamic load-sharing coefficient and sensitivity of the internal and external meshing pairs of the system. The experimental results are consistent with the theoretical results, verifying the correctness of the model.

A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears

As a critical component of the joint gearbox, spur gear pairs play a crucial role in energy conversion, limiting the performance of a collaborative robot. Accurately assessing their instantaneous efficiency and torque fluctuation is essential for developing high-precision robot joint control models. This study proposes a computational model to predict the instantaneous efficiency and torque fluctuation of spur gears under typical operating conditions. The model incorporates a torque balance model, a load distribution model, and a friction model to reflect the relationship between gear meshing position and efficiency. The instantaneous efficiency and torque fluctuation of gear pairs were compared with the Coulomb friction model with an average friction coefficient and the elastohydrodynamic lubrication model with a time-varying friction coefficient. The effect of gear contact ratio on efficiency is analysed, while the instantaneous efficiency and torque fluctuation of gears are studied under varying operating conditions. The results indicate a maximum efficiency difference of 1.86 % between the two friction coefficient models. Under specific operating conditions, the instantaneous efficiency variation of the gear pair can reach 3.34 %, and the torque fluctuation can reach 5.19 Nm. Finally, this study demonstrates the effectiveness and accuracy of the proposed method through comparative analysis.

Characterization of Microscopic Damage Evolution of Functional Groove in Cageless Bearings

Bearings with partial function grooves as cageless bearings related to magnetic floating bearing protection have characteristics, such as fast offsetting of the impact force caused by rotor fall, and they gradually become important parts of ultra clean and cryogenic transportation systems. However, the functional failure mechanism of the bearing, which is caused by functional groove wear, is not clear. Therefore, this paper establishes a force–motion intrinsic model of particles inside the functional groove, which is based on the discrete element method, which it itself combined with the functional groove damage evolution trend analysis. Then, a hyper-quadratic surface model of inter-particle contact is established to simulate the time-varying friction coefficient of the functional groove by combining particles of different sizes to form particle clusters. Additionally, as the boundary condition, EDEM is used to solve the contact motion state of rolling element rolling through the functional groove for one week to obtain the overlap between particles and contact force change law. The results show that the wide side of the functional groove wears more seriously than the narrow side, and the rolling element leaves the functional groove with more impact than when it enters the functional groove, and the functional groove wears more seriously. In this paper, through the study of local functional groove wear of cageless ball bearing, we propose to characterize the damage extension of functional groove by using the number of particle fracture and motion trend in discrete element method, and this study provides theoretical guidance for the design of cageless bearings.

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.

Dynamic investigation and alleviative measures for the skidding phenomenon of lubricated rolling bearing under light load

The skidding phenomenon occurs during the operation of rolling bearing under the light load owing to the design error, which will intensify the surface damage and lead to noise and abnormal vibration. In this study, a skidding dynamics model of lubricated rolling bearing is established considering the interactions between the roller and races, as well as the cage. The effect of lubricant on the dynamic characteristics of the rolling bearing is characterized as the lubricating oil stiffness, central film thickness, time-varying friction coefficient between the roller and race, passing flow resistances of rollers, and resistance torques. In addition, the nonlinear contact and structure deformations of rollers are formulated. For mitigating the skidding phenomenon of the roller under light load, the effect of roller number, inside radius of the hollow roller, density and viscosity of the lubricant, interference fit, and radial load are analyzed. The results indicate that the skidding phenomenon of the roller is induced by the lesser tangential roller-race friction forces and larger passing flow resistances of rollers. It is helpful to intensify the interactions at the roller-race interface or/and decrease the running resistance by reducing the roller number, decreasing the lubricant density, or choosing the correct viscosity of the lubricant. Besides, the effect of interference fit and increasing radial load is significant on the premise of not changing the design parameters of the rolling bearing.

Study on Work Roll Vertical Vibration Under Periodic Spalling of the Oxide Film

The dynamic effect of work-roll oxide-film periodic spalling on vertical vibration in a hot strip rolling mill was studied. Based on dynamic monitoring test analysis, the friction of the work-roll surface under oxide-film periodic spalling is discussed. Using an average rolling pressure formula, the rolling force under the dynamic vertical vibration and the time-varying friction coefficient were found. A two-degrees-of-freedom dynamic system of the hot strip mill was established, considering the roller system symmetry. Based on the multiscale small-parameter perturbation method, the main resonance characteristic of work-roll vertical vibration has been explored. Using the 1780-mm hot strip mill in Chengde Iron and Steel Co., Ltd., the dynamic characteristics of the system are analyzed when oxide-film periodic spalling occurs on the work roll. The results are consistent with the test data, which show the effect of oxide-film spalling on vertical vibration. The simulation results for resonance characteristics show that the vibration of the system can be effectively reduced by increasing the damping and adjusting the stiffness of the system. In rolling production, it is very important to ensure the stability of the oxide film in order to reduce fluctuation. This study provides a reference for the operation and maintenance of a rolling mill in the strip production process.

Dynamic Response of a Hypersonic Rocket Sled Considering Friction and Wear

The dynamic response of a hypersonic rocket sled was studied by considering the time-varying friction coefficient and the gap caused by wear between the slipper and track. A multibody dynamic model for a hypersonic rocket sled system was established by considering the time-varying mass and moment of inertia, nonlinear aerodynamic loads, engine thrust, track irregularity, and nonlinear contact force. As for the wear calculation, the ductile and shear criteria were used as the material damage criteria, and slipper wear was determined by the number of damaged elements. A rocket sled test was also carried out, and the dynamic response of the sled was measured. The results showed that the computational sliding displacement and velocity of the third-stage sled matched well with the test values. The computational root mean square (RMS) values of the vertical acceleration of the third-stage sled front slipper considering friction and wear matched better with the test values than with the case without considering friction and wear, which underestimated the RMS value by approximately 20.1% at Mach 5. The importance of considering friction and wear and the correctness of the computational method were validated. It is also found that the kinetic friction coefficient decreased with an increase in the product of the pressure and velocity. The wear height of the slipper increased almost linearly with the sliding displacement. The test results showed that the vertical acceleration power spectral density of the third-stage sled front slipper increased with time in the full frequency band below 2000 Hz. This study will guide the design and optimization of hypersonic rocket sleds.

Vibration-Based Fault Diagnosis of Helical Gear Pair With Tooth Surface Wear Considering Time-Varying Friction Coefficient Under Mixed Elastohydrodynamic Lubrication Condition

Abstract Based on “slice method,” the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elastohydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Sliding behavior of high speed ball bearings based on improved nonlinear dynamic model

To accurately predict the dynamic behaviors of high speed ball bearings, an investigation on the sliding behavior of balls at high and low speeds, and light and heavy loads is necessary. However, existing nonlinear dynamic models fail to consider comprehensively key factors such as asperity and hydrodynamic tractions, time-varying friction coefficient and time-varying lubricant mode. In this work, these influencing factors are integrated into the nonlinear dynamic model to make it suitable for the working conditions of high and low speeds and light and heavy loads. The dynamic analysis provides the relation of angular speeds of balls with spin and sliding at light and heavy loads, also it reveals the number of pure rolling point under the combined effect of differential sliding and spin sliding. Research results provide a reliable mathematical model and theoretical bases for further studying the dynamic behaviors of high speed ball bearings.

The Temperature Field of Friction Disc in Wet Clutch Involving the Unconventional Heat Dissipation on the Contact Surface

Wet clutches are widely used in vehicle transmission systems to start and shift. The temperature field of the wet clutch components is influenced by friction and is closely related to the vehicle performance and service life. This work improves the numerical modeling of the temperature field by taking into account groove cooling, local heat dissipation, and the time-varying friction coefficient on the contact surface. An equivalent convection heat transfer coefficient and an equivalent gain coefficient are introduced. The proposed model is more accurate than the traditional model, and its accuracy is verified by bench experiments. The influence of rotational speed difference, oil pressure, and lubrication flow on the temperature field is analyzed. Moreover, the temperature rise characteristics during deformation are measured, which also confirms the abnormal radial and circumferential change of temperature field. These results can guide the accurate simulation of interface temperature and the appropriate control operation of friction components in the wet clutch.

Research on the Nonlinear Dynamics of Micro-segment Gear System with Time-Varying Friction Coefficient

Research on the Nonlinear Dynamics of Micro-segment Gear System with Time-Varying Friction Coefficient

An improved mesh stiffness model for double-helical gear pair with spalling defects considering time-varying friction coefficient under mixed EHL

Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of double-helical gear pair with actual involute, and transition curve is proposed. The nonlinear contact stiffness, improved fillet-foundation stiffness, time-varying friction coefficient with mixed elastohydrodynamic lubrication (EHL) are considered in the model. Based on the improved model, the mesh stiffness of double-helical gear pair under spalling defects are obtained, in which the depth of spalled region is varied along action line, then the influence of spalling length, axial position, and dislocation phase on TVMS are investigated. The results of the improved mesh stiffness model were compared with the finite element method (FEM) results, the resulting coincidence illustrated the superiority of the improved model.

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.

An improved mesh stiffness calculation model of spur gear pair under mixed EHL friction with spalling effect

Based on the “Potential energy method”, the improved mesh stiffness calculation model of spur gear pair with actual involute and transition curve is proposed. Furthermore, the spalling effect, nonlinear contact stiffness, improved fillet-foundation stiffness, time-varying friction coefficient under mixed elasto-hydrodynamic lubrication (EHL) condition are assimilated into the model. Then the results of the improved mesh stiffness model are obtained by numerical simulation, in which the mesh stiffness under mixed EHL friction and the effect of height for spalled area on the mesh stiffness are comprehensively investigated.

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.

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.

Tooth surface friction and its influence on dynamic transmission error of double power input transmission system

According to the meshing characteristics of spur gears and helical gears, calculation formulas of time varying friction stiffness and friction torque coefficient are derived. Based on the theory of the concentrated parameter, considering the influence of the time-varying coefficient of friction, time-varying meshing stiffness and the integrated error of the integrated, a three-dimensional dynamic model for a double power input transmission system with multi degrees of freedom and variable parameters was developed, including the flexional, torsional and axial motions. The Fourier series method is used to solve the equations by transforming the time varying system into a linear time invariant system, and the total system response of the system is obtained after the superposition of each order excitation response. The change law of friction torque coefficient and friction stiffness is obtained too. The results show that the friction stiffness curve of herringbone gear changes gently without mutations, and the direction is constant which what makes the resultant friction force direction be of the friction no unchanged. The tooth surface roughness has a certain influence on the dynamic transmission error. The first and second harmonic order frequencies of the split torque stage gears have an important influence on the dynamic transmission errors.