Oil Film Stiffness Research Articles

Modeling of Multibody Lubrication Dynamics in Cylindrical Roller Bearings

As a typical multibody system, rolling bearing consists of several lubricated frictional pairs which transmit motions and forces among components. In this paper, a multibody lubrication dynamics (MLD) model of cylindrical roller bearings (CRBs) is developed by coupling the bearings dynamics sub-model and several lubrication sub-models of each frictional pairs in real-time. The lubrication sub-models are discretized by using finite difference and solved by numerical iteration methods of Gauss-Seidel with line relaxation and discrete convolution-fast Fourier transform (DC-FFT) technique. What’s more, a parallel algorithm is also designed to enhance the calculation efficiency. Its results are validated by the experimental results in literature, and further compared by the results from other dynamics models. It is revealed that the film formation changes not only friction but also geometrical constraints and pressure distribution, which may introduce additional load inside bearing and increase rolling friction under high-speed conditions. As the dynamic oil film stiffness and damper are took into account by MLD, the cage has a lower whirl frequency and forces. The curve-fitting formulas of EHL film thickness are overestimates the thickness value, and thus change the load distribution and friction between roller and raceway.

TVMS calculation model for gear tooth tip chipping failure with EHL

This paper proposes a calculation method for Time-Varying Mesh Stiffness (TVMS) in the presence of tooth tip chipping defects under elastohydrodynamic lubrication (EHL). A contact stiffness model for tooth tip chipping defects under EHL is established, and an analytical equation for the TVMS of chipping defects under EHL is derived. The torsional stiffness at the chipping defect under EHL is introduced, considering the influence of roughness at the chipping defect on the characteristics of the oil film and its stiffness. The effects of chipping defect size, torsional stiffness of the chipping defect under EHL, roughness, and oil film stiffness on TVMS are analyzed, providing methodological support for improving the calculation accuracy of gear TVMS.

Nonlinear dynamic characteristics analysis method of planetary gear train torsional vibration considering meshing oil film force

Planetary gear train is an important part of automatic transmission. The oil film between teeth is one of the key factors affecting the torsional vibration of planetary gear train. Selecting the appropriate oil film stiffness is of great significance for analyzing the nonlinear dynamic characteristics of planetary gear train. A method for analyzing the nonlinear dynamic characteristics of planetary gear system torsional vibration considering the oil film force between teeth is proposed in this paper. A 3-DOF torsional vibration model of planetary gear train considering oil film is established. In this model, the oil film between teeth is equivalent to a time-varying nonlinear spring-damper element, and nonlinear factors such as backlash and meshing error are also considered. The effects of meshing oil film thickness on oil film stiffness and damping are analyzed, and the torsional vibration characteristics of planetary gear train under different meshing stiffness, meshing damping ratio, and rotational speed are analyzed based on bifurcation diagrams. The results show that in one meshing cycle, the meshing oil film thickness first becomes larger and then becomes smaller. When the meshing oil film thickness increases, the meshing oil film stiffness and the equivalent meshing oil film damping become smaller. The torsional vibration of planetary gear train can be effectively reduced by increasing meshing stiffness, damping ratio, rotational speed within a certain range. This method provides technical support for reducing torsional vibration of planetary gear train and realizing stable transmission of planetary gear train.

Effect of oil film stiffness on vibration of full ceramic ball bearing under grease lubrication

PurposeThis paper aims to understand the vibration characteristics of full ceramic ball bearings under grease lubrication, reduce the vibration of the bearings and improve their service life.Design/methodology/approachThe Hertz contact stiffness formula for full ceramic ball bearings is constructed; the equivalent comprehensive stiffness calculation model and vibration model of full ceramic ball bearings are established. The dynamic characteristic test of full ceramic ball bearing under grease lubrication was carried out by using the bearing life testing machine, and its vibration was measured, and its vibration acceleration root-mean-square was obtained by software calculation and compared with the simulation results.FindingsAt the rotational speed of 12,000 r/min, the root-mean-square value of vibration acceleration is maximum 10.82 m/s2, and the error is also maximum 7.49%. As the rotational speed increases, the oil film stiffness decreases. In the radial load of 600 N, the vibration acceleration root-mean-square is minimum 6.40 m/s2, but its error is maximum 6.56%. As the radial load increases, the vibration of the bearing decreases and then increases, so under certain conditions increasing the radial load can reduce the bearing vibration. With different types of grease, the best preload is also different; low-speed heavy load should be used when the viscosity of the grease is large, and high-speed light load should be used when the choice of smaller viscosity grease is made.Originality/valueIt provides a theoretical basis for the application of full ceramic ball bearings under grease lubrication, which is of great significance for reducing the vibration of bearings as well as enhancing the service life of bearings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0094/

TVMS Calculation and Dynamic Analysis of Cracked Gear considering Oil Film Stiffness

A time-varying meshing stiffness (TVMS) model that includes oil film stiffness in the elastohydrodynamic lubrication (EHL) line contact is proposed for tooth root cracking. This model employs the oil film thickness to estimate the stiffness of the oil film in gear contact by considering the profile variation of the oil film induced by tooth root cracks, to provide the evolution principle of TVMS in EHL line contact to study the effects of oil film stiffness of cracked gear on the TVMS. The results of the analysis reveal that the overall result of TVMS decreases owing to the stiffness of the oil film, whereas the combined TVMS depends mainly on the rotation speed of the gear system because the thickness of the oil film in the tooth crack is affected by the velocity of the entrainment. Furthermore, a six-degree-of-freedom (DOF) dynamic model is introduced to analyze the vibration behavior of the gear system using the combined TVMS results for different crack levels, and the influence of the combined TVMS on the vibration response of the tooth root crack is exhibited from the time-domain analysis, frequency-domain analysis, and statistical indicator analysis.

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Navigating the Dynamics of Squeeze Film Dampers: Unraveling Stiffness and Damping Using a Dual Lens of Reynolds Equation and Neural Network Models for Sensitivity Analysis and Predictive Insights

The squeeze film damper (SFD) is proven to be highly effective in mitigating rotor vibration as it traverses the critical speed, thus making it extensively utilized in the aeroengine domain. In this paper, we investigate the stiffness and damping of SFD using the Reynolds equation and neural network models. Our specific focus includes examining the structural and operating parameters of SFDs, such as clearance, feed pressure of oil, rotor whirl, and rotational speed. Firstly, the pressure distribution analytical model of the oil film inside the SFD based on the hydrodynamic lubrication theory is established, as described by the Reynolds equation. It obtained oil film forces, pressure, stiffness, and damping values under various sets of structural, lubrication, and operating parameters, including length, clearance, boundary pressure at both sides, rotational speed, and whirling motion, by applying difference computations to the Reynolds equation. Secondly, according to the significant analyses of the obtained oil film stiffness and damping, the following three parameters of the most significance are found: clearance, rotational speed, and rotor whirl. Furthermore, neural network models, including GA-BP and decision tree models, are established based on the obtained results of difference computation. The numerical simulation and calculation of these models are then applied to show their validity with all given parameters and the three significant parameters separately as two sets of model input. Regardless of either set of model inputs, these established neural network models are capable of predicting the nonlinear stiffness and damping of the oil film inside an SFD. These sensitive parameters merely require measurement, followed by the utilization of a neural network to predict stiffness and damping instead of the Reynolds equation. This process serves structural enhancement, facilitates parameter optimization in SFDs, and provides crucial support for refining the design parameters of SFDs.

Skidding behavior of lubricated rolling element bearings under the influence of oil film and radial clearances

Skidding is an inevitable phenomenon in rolling element bearing but accelerates the bearing wear and shortens the bearing life. Recognizing skidding behavior under different clearances will benefit to bearing health monitoring. In this study, an improved bearing dynamic model is developed to investigate its vibration characteristics and skidding behavior taking into all bearing structure components, time-varying oil film characteristics and bearing clearances. A novel method is proposed to include time-varying oil film stiffness and thickness under different clearances into the bearing dynamic model. A fast algorithm is adopted through interpolation during the model solving process. Furthermore, vibration responses and skidding behavior under different clearances are analyzed. Finally, a designed synchronous differential encoder (SDE) system tests the skidding behavior of bearings and verifies the proposed model through measuring the angular velocity of cage transformed by distance test. Numerical result shows that both RMS and ball pass frequency of outer race (BPFO) increase with bearing clearances. The slip ratio represents growth with the increase of bearing clearances, which is verified by the designed experiment with good consistency with the simulation. It can be foreseen that this novel dynamic model with SDE system can be well performed for bearing skidding detection and fault detection.

Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing

This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark-β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity.

Sealing performance and optimization design of squamous textured mechanical seal

The work focuses on the optimization of surface texturing and their geometrical characteristics to improve the sealing performance of mechanical seal. The hydrodynamic model is developed to predict the sealing performance of four textures, including dimple, triangle, chevron and squamous textures. Result indicates that the squamous texture exhibits better sealing performance with high ratio of load-carrying capacity to leakage and ratio of oil film stiffness to leakage at various angular speeds and pressures. Furthermore, the functions of squamous texture characteristics with the load-carrying capacity and leakage ratio are revealed by the response surface methodology. And the squamous texture is optimized with high load-carrying capacity and low leakage ratio through the multi-objective optimization algorithm NSGA-II to achieve the Pareto-optimal set.

Dynamics analysis of helical gear considering de-meshing and reverse impact with EHL lubrication condition.

The purpose of this paper was to study the evolution and dynamic characteristics of the helical gear system co-existence response considering the occurrence of de-meshing and reverse impact under lubrication conditions. The double-three tooth alternate meshing model of a helical gear was established, and the time-varying geometric parameters, motion parameters, and load distribution of positive meshing and reverse impact were analyzed, respectively. The variation of oil film parameters and the coupling between oil film stiffness and meshing stiffness of a gear system were studied according to the equivalent lubrication model of a helical gear. Considering the phenomenon that the meshing state changed from positive meshing to de-meshing and reverse impact, the dynamics model was established. The global bifurcation diagram, the attraction domain, the phase portrait, and the Poincaré section were used to analyze the evolution of a coexistence response and dynamic characteristics with helical gear system parameters.

Dynamic analysis of magnetorheological damper incorporating elastic ring in coupled multi-physical fields

The elastic ring assumes a multifunctional role, crucially providing support and reshaping oil-film thickness distribution in applications such as squeeze film dampers, demonstrating its practical efficacy. In this work, a magnetorheological damper (MRD) incorporating an elastic ring is proposed for the first time to improve the performance of damper. The innovative configuration of the elastic ring magnetorheological damper (ERMRD) is fabricated and integrated into a test platform of rotor system. The multi-filed coupling dynamic model of ERMRD is developed involving magnetic field interactions governed by Kirchhoff law, magnetorheological fluid flow dynamics derived from lubrication theory, and the elastic ring deformation based on thin plate theory. The intricate influence mechanisms of elastic ring and excitation current on oil-film characteristic of ERMRD, encompassing oil-film pressure, oil-film force, oil-film stiffness and damping, are investigated in detail. To substantiate the capabilities of ERMRD, it is implemented within the rotor system and a coupled dynamic model is established using Lagrange equation. This is followed by an in-depth analysis of the dynamic response using the Newmark-β method, including a comparative assessment with the conventional MRD. The results reveal that the elastic ring and excitation current influence oil-film pressure distribution in ERMRD from different perspectives, leading the oil-film force to present diverse variation characteristics. Compared to MRD, ERMRD exhibits weaker nonlinearity and superior damping performance.

The Effects Analysis of Contact Stiffness of Double-Row Tapered Roller Bearing under Composite Loads

Double-row tapered roller bearings have been widely used in various equipment recently due to their compact structure and ability to withstand large loads. The dynamic stiffness is composed of contact stiffness, oil film stiffness and support stiffness, and the contact stiffness has the most significant influence on the dynamic performance of the bearing. There are few studies on the contact stiffness of double-row tapered roller bearings. Firstly, the contact mechanics calculation model of double-row tapered roller bearing under composite loads has been established. On this basis, the influence of load distribution of double-row tapered roller bearing is analyzed, and the calculation model of contact stiffness of double-row tapered roller bearing is obtained according to the relationship between overall stiffness and local stiffness of bearing. Based on the established stiffness model, the influence of different working conditions on the contact stiffness of the bearing is simulated and analyzed, and the effects of radial load, axial load, bending moment load, speed, preload, and deflection angle on the contact stiffness of double row tapered roller bearings have been revealed. Finally, by comparing the results with Adams simulation results, the error is within 8%, which verifies the validity and accuracy of the proposed model and method. The research content of this paper provides theoretical support for the design of double-row tapered roller bearings and the identification of bearing performance parameters under complex loads.

Analysis and Multi-target Optimisation of the Characteristics with Stepped Cavity of the Hybrid Bearing

In this paper, the peak pressure, stiffness, flow rate, and temperature rise of the oil film in the stepped cavity of the hybrid bearing are investigated. The pressure and flow equations for the central section of the stepped cavity and the axial section of the deep and shallow cavity are derived using the simplified Navier-Stokes equations and the boundary conditions of a liquid bearing. Using the control variable method, the influence of the geometrical parameters of the stepped cavity and the process parameters on the oil film characteristics was simulated, and the correctness of the pressure and flow equations was verified. The results show that: the spindle speed is positively correlated with the peak oil film pressure and flow rate; the oil film thickness is negatively correlated with the peak oil film pressure and positively correlated with the flow rate; the depth and width of the shallow cavity are correlated with the peak oil film pressure, but the correlation with the flow rate is low; the maximum error between the theoretical calculation and the simulation analysis is less than 7.3%. The pressure equation and the flow equation are used to establish the objective function with the maximum oil film stiffness, load-bearing capacity, and minimum temperature rise, and the ideal point evaluation function method is used to do a multi-target optimization design to optimize the ladder cavity and obtain the optimal oil cavity geometric parameters. And an 8.75% increase in peak pressure and a 4.1% reduction in temperature rise for the same process parameters.

Analysis of spur gearbox dynamics considering tooth lubrication and tooth crack severity progression

A novel tribo-dynamic model of a spur gearbox considering both tooth lubrication and tooth crack is proposed, which integrates an elastohydrodynamic lubrication (EHL) model of a spur gear pair into a gearbox lumped parameter model. The combined stiffness and combined damping of a spur gear pair with a tooth crack are obtained using the oil film stiffness and oil film damping provided by the EHL model and the tooth mesh stiffness and tooth mesh damping calculated by the potential energy method. Effects of tooth lubrication and tooth crack severity progression on combined stiffness, combined damping, and gearbox vibration responses are studied. It is found that considering the tooth lubrication in gearbox dynamic modeling leads to a backward shift of the frequency components induced by tooth crack. A comparison has been made between the proposed tribo-dynamic model and the conventional model of a spur gearbox, and the effectiveness of RMS and Kurtosis for tracking tooth crack severity progression is investigated in the presence of tooth lubrication. The comparison results reveal that the consideration of tooth lubrication overall reflects tooth crack signatures better.

Analytical Research on the Bearing Characteristics of Oil Film Supplied with Constant Oil Flow Hydrostatic Turntables under Fixed Eccentric Load Condition

This study was initiated in view of the phenomenon that hydrostatic turntable rails are prone to scrape damage when the liquid hydrostatic turntable is running under fixed partial load. The existing bias-load hydrostatic turntable oil film bearing characteristics are mainly calculated by using the calculus integration method and CFD fluid simulation method. The calculating formula obtained by the calculus integration method is complex and inefficient. The CFD fluid simulation calculation method requires 3D modeling and meshing of the oil film, which is a tedious and time-consuming process and may not yield convergent calculation results due to improper meshing methods or boundary condition settings. In order to solve the shortage of the above calculation methods, this paper simplifies and equates the uneven thickness of the oil film of each sealing edge of the oil pad of the bias-loaded hydrostatic rotary table to the equivalent uniform thickness of the oil film, and based on this idea, the analytical calculation formula of the oil film bearing capacity, bending moment and stiffness under constant bias-load conditions of the constant-flow liquid hydrostatic rotary table is derived. In this paper, Fluent software was used to numerically simulate the oil film under this working condition, and a hydrostatic turntable test bench was established to conduct an experimental study on the biased load hydrostatic turntable; the experimental data and simulation results were compared with the results obtained from this simplified method of calculating the oil film loading characteristics. The results show that the error of oil film bearing capacity is less than 6% and the error of overturning moment is less than 7%, which has verified the validity of the calculation method. The simplified analytical calculation method proposed in this paper is used to study the influence of tilt displacement rate, lubricant flow rate and turntable speed on the basic performance parameters of oil film, which provides a theoretical basis for the study of oil film load-bearing characteristics under constant bias-load conditions of the constant-flow liquid hydrostatic turntable.

Comprehensive stiffness analysis of the cylindrical roller bearing for aircraft engines considering the radial clearance

PurposeThe rotor system supported by the cylindrical roller bearings is widely used in various fields such as aviation, space and machinery due to its importance. In the study of the dynamic characteristics of the cylindrical roller bearings, it is important to accurately calculate the stiffness of the cylindrical roller bearings. The stiffness of the cylindrical roller bearings is very important in the analysis of the vibration characteristics of the rotor system. Therefore, in this paper, the method of creating a comprehensive stiffness model of the cylindrical roller bearing is mentioned. The purpose of this study is to improve the dynamic stability of the rotor system supported by the cylindrical roller bearing by accurately establishing the comprehensive stiffness calculation model of the cylindrical roller bearings.Design/methodology/approachIn consideration of the radial clearance of the cylindrical roller bearing, the radial load acting on the cylindrical roller bearing was derived, and based on this, a model for calculating the Hertz contact stiffness of the cylindrical roller bearing was created. Based on the load considering the radial clearance, an oil film stiffness model of the cylindrical roller bearing was created under the elastohydrodynamic lubrication (EHL) theory. Then, the comprehensive stiffness was calculated by combining Hertz contact stiffness and the oil film stiffness of the cylindrical roller bearing, and the dynamic parameters are calculated by using the MATLAB program.FindingsWhen the radial clearance of the cylindrical roller bearing is considered, the comprehensive stiffness is larger than when the radial clearance is not taken into account, and the radial clearance of the cylindrical roller bearing is an important factor that directly affects the comprehensive stiffness of the cylindrical roller bearing.Originality/valueIn this paper, based on Hertz contact theory and the EHL theory, the authors investigated the method of creating a comprehensive stiffness model of the cylindrical roller bearing considering the radial clearance. These results will contribute to the theoretical basis for studying the mechanics of cylindrical roller bearings and optimizing their structures, and they will provide an important theoretical basis for analyzing the dynamic characteristics of the rotor system supported by the cylindrical roller bearing.

Study on bearing mechanical and thermal characteristic evolvement rules affected by higher ambient temperature

In this paper, the bearing mechanical characteristics and thermal characteristics as it is running under constant speed (2400 r/min) and constant temperature (100 ℃) adopting bearing mechanical-thermal coupling model built on the basis of quasi-statics and elastohydrodynamic lubrication theory are discussed. Among which, the contact deformation between ball and inner/outer ring has same evolution law, besides, the same as the amplitude. Whose curve shape changes in the form of “circular-oblique D”, its amplitude rearches minimum value at 10thd3h between the location of 120° and 270°. The curve shapes belonging to contact angular between ball and inner/outer ring are similar to “circular”. There is opposite trend of them within the range of 90-300°. The amplitude of contact angular between ball and outer ring is the minimum at 10thd3h and 11thd1h. At the same time, the amplitude of that between ball and inner ring is the maximum. The evolution rules of contact stiffness between ball and inner/outer ring are generally consistent, which are similar to “crab”. But the amplitude of that between ball and outer ring is dominant. The maximum value of them occurs at 10thd3 and 11thd1h. The evolvement tendency of node temperatures maintains stable. Thereinto, the temperature of inner ring equals to that of contact location between ball and inner ring, which is the maximum value. It is obvious that ME, MD, MS, MCB, MCR and MOil devote themselves to heat production, the contribution rates of ME, MS, MCB and MCR are 100 %, the contribution rate of MD ranges from 52.6 % to 65.2 %. However, the amplitudes of friction moments have the opposite trend compared to “heat contribution factor”. The expansion amount owing to heat production is dominant in displacement variation and the effect of clearance on displacement can be ignored, whose evolution rules are contrary. The evolution rules of oil film thickness and oil film stiffness between ball and inner/outer ring are alike. Among which, the oil film thickness between ball and outer ring is dominant, its maximum value emerges at 10thd3h. The curve shapes of oil film stiffness between ball and outer/inner ring are oblique “D”, their amplitudes reach the maximum at 11thd1h-11thd3h.

Meshing Characteristics of Spur Gears Considering Three-Dimensional Fractal Rough Surface under Elastohydrodynamic Lubrication

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.

Five-state engaging model and dynamics of gear-rotor-bearing system based on time-varying contact analysis considering gear temperature and lubrication

Contact behavior of gear teeth plays a key role in modeling and analysis of geared systems. To reasonably evaluate the time-varying contact characteristics of spur gear systems, a new load-dependent time-varying meshing stiffness model incorporating elastic contact stiffness, temperature stiffness and oil film stiffness is developed. Asperity pressure and lubricant pressure are considered for the oil film stiffness. The engagement of the gear pair is decomposed and classified based on the time-varying contact analysis and then five meshing states are obtained. A novel nonlinear dynamic model of the gear-rotor-bearing system with 5-state mesh including time-varying backlash and time-varying meshing stiffness is established by introducing multiple state sub-functions. The effects of gear temperature and load on the meshing stiffness are analyzed. 5-state meshing behavior is identified and characterized by constructing 5 Poincaré maps. The bifurcation and evolution of 5-state meshing behavior are investigated by changing parameters. Distribution of multi-state meshing behavior in two-parameter planes is analyzed to obtain the correlation between multi-parameter and multi-state behavior. The results demonstrate that temperature and load greatly affect the time-varying meshing stiffness, of which the temperature stiffness contributes the most and the oil film stiffness contributes less. The parameters change the system dynamics by affecting the multi-state meshing behavior. The dynamic behavior is highly dependent on the matching and combination of multiple parameters. Diversity of multi-state meshing behavior is clearly revealed. The presented results provide an understanding of the time-varying engaging characteristics and therefore serve as a useful source of reference for engineering in designing and controlling such gear systems.