Time-varying Mesh Research Articles

Effects of periodic long-wave deviations on the dynamic behaviors of spur gear systems

Noise reduction plays a major role in the drive train of motor vehicles operating at higher speeds. Long-wave deviations of gear systems related to manufacturing and assembly errors, such as tooth pitch deviation and geometric eccentricity, exhibit circumferential variations and have been demonstrated to be significant contributors to noise generation. However, a comprehensive and effective model that considers multiple long-wave deviations simultaneously has seldom been studied. To fill this gap, a new numerical model of spur gear systems with long-wave deviations is established, in which the coupling effects of both tooth pitch deviation and geometric eccentricity are taken into consideration. A time-varying mesh stiffness (TVMS) analytical model for spur gear pairs is established, which considers the relationship of errors between pitch deviation and eccentricity. The time-varying contact state of the gear pair under periodic long-wave deviations is also analyzed. A translation-torsion coupled dynamic model is established to investigate the excitation behavior of gear pairs with periodic long-wave deviations. The accuracy of the TVMS and the dynamic model is verified through comparisons with reference and experimental results. Results show that gear pairs with long-wave deviations exhibit periodic fluctuations in TVMS compared to ideal gear pairs, accompanied by phase differences. The mesh stiffness impact phenomenon becomes less pronounced for higher gear precision under lower-load conditions. Conversely, the periodic vibration characteristics induced by eccentricity become less prominent for the lower gear precision level. The excitation behavior of the gear pair with pitch deviation is masked by eccentricity at lower rotational orders, but it still dominates at higher rotational orders. This method can predict the dynamic characteristics of gear transmission systems with periodic long-wave deviations, providing theoretical guidance for reducing the vibration and noise levels.

Time-varying Meshing Stiffness Calculation of Spur Gears with Asymmetric Spalling Defects

Gear systems are subjected to repeated loads during long-term operation, and factors such as insufficient lubricant to increase friction between gears, resulting in elevated temperatures and wear, are highly susceptible to tooth spalling. Tooth spalling is a common form of failure in gear failure. In previous studies, the vibration response of a gear pair with spalling defects at the tooth center near the pitch circle has been investigated. However, the location of the spalling defects offset from the center of the tooth flank is rarely studied. Tooth spalling faults occur in the pitch circle, but not necessarily in the center of the tooth, often formed on both sides of the center of the tooth and torsion in the meshing process. the symmetric and asymmetric rectangular spalling defects are considered, the torsional deformation is introduced. “torsional stiffness” is introduced into the overall TVMS due to the spalling defect. Therefore, it is meaningful to grasp the reasons for the formation of tooth spalling.

Modeling Method of Meshing Stiffness of High Speed Spur Gears

As one of the most important dynamic excitation sources, the gear time-varying mesh stiffness is the key parameter of gear system dynamic model. So how to calculate the gear mesh stiffness accurately is of great importance. Based on Euler beam theory, this paper proposes a primitive calculation algorithm (PCA) to calculate the time-varying mesh stiffness of spur gears. A simplified gear model is developed based on nonlinear strain-displacement relationships, and a finite element program is used to simulate the gear's meshing stiffness. The rationality of this method was verified through finite element analysis. The results indicate that mesh stiffness plays a crucial role in controlling mesh deformation. In view of this, this study lays a theoretical foundation for further analysis of the vibration and noise of gears.

Investigation on meshing characteristics of spiral bevel gear under wear fault evolution with assembly errors

Spiral bevel gears have the advantage of transmitting high torque and power comparing to helical gear and straight bevel gear. However, they are susceptible to wear due to factors such as high loads, poor lubrication, and surface imperfections resulting from machining. In this study, we propose an autonomous model for predicting tooth wear and analyze the meshing characteristics of spiral bevel gear (SBG) pairs under different assembly errors. Concurrently, we establish a finite element model to validate the accuracy of our meshing characteristic analyses. We also compare the distribution patterns of wear depth on the tooth surface with existing literature. Our investigation delves into meshing characteristics, encompassing transmission errors and Time-varying mesh stiffness (TVMS), considering wear evolution under assembly errors. The results demonstrate that the fluctuations in TVMS remain consistent across all four types of assembly errors examined. Gear tooth wear leads to an increase in gear backlash and fluctuations in unloaded transmission error. The meshing stiffness fluctuation of the SBG pair enlarges under wear evolution. Assembly errors result in shifts in the initial contact line and contact pattern, subsequently altering the distribution of wear depth. Different forms of assembly errors may cause a similar effect on the distribution of wear depth and meshing characteristics.

Dynamic responses of the high-speed train with polygonal wheels considering gear transmissions

To examine the influence of polygonal wheels on the dynamic responses of high-speed train, a vehicle-track dynamics model was developed. This model incorporated gear transmissions using multibody dynamics methodology and gear dynamics theory. The effect of gear transmissions on the dynamic responses of the high-speed train was evaluated by comparing the results of the developed model with those of a non-geared traditional model. The dynamic responses of the train were studied by examining the combined effects of wheel polygonal excitation and time-varying mesh stiffness excitation. The results indicated that the vertical wheel-rail contact force and vibration amplitude of the model with polygonal wheels were larger than those of the normal model. Similarly, the geared transmission model exhibited greater contact force and vibration amplitude compared to the non-geared transmission model, attributed to the increased excitation. The evolution of the wheel polygon’s order and wear depth could significantly increase the vertical wheel-rail contact force and the wheel load reduction rate. The safety limits for wheel polygon order and wear depth were established. The model with gear transmissions is more closely aligned with the actual situation and exhibits higher safety performance, providing valuable reference for wheel turning.

Mesh characteristic changes of spiral bevel gear pair with assembly errors during tooth crack propagation

Spiral bevel gears (SBGs) are often used because of their strong carrying capacity and lower vibration. However, this heightened load capacity can sometimes result in the development of tooth surface cracks. This study aims to simulate the three-dimensional propagation of cracks in SBGs under various assembly conditions and explore how the presence of cracks affects mesh characteristics. This paper investigates crack propagation in SBGs by applying principles of fracture mechanics. Employing a combination of finite element software ABAQUS and fracture mechanics software FRANC3D, the study conducts a three-dimensional analysis of crack propagation in SBGs. The study analyzes the impact of crack propagation on the lifespan and mesh characteristics of SBGs, including crack propagation morphology, transmission error, time-varying meshing stiffness (TVMS), gear life, and tooth surface force, under various assembly errors.

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 performance of aerospace face gear-planetary gear transmission system under multi-factors including the effect of temperature

Face gear-planetary gear transmission system combines the advantages of both planetary and face gears. And has enormous advantages in the aerospace field. The meshing of gear teeth generates heat through friction, resulting in thermal deformation and affects nonlinear dynamic characteristics. Exploring the temperature effect on the nonlinear dynamics of the transmission system of face gear-planetary gear is of great significance. Considering the temperature variations effect and time-varying meshing stiffness, tooth side clearance as well as meshing error, a nonlinear dynamic model of the face gear-planetary gear system is established. The nonlinear dynamic characteristics of the system were described by maximum Lyapunov exponent diagram, phase diagram, bifurcation diagram et al. The findings indicate that the effect of temperature variations on the gear system is related to the values of the time-varying mesh stiffness coefficient and mesh damping ratio. When the mesh damping ratio is small, the influence of temperature changes on the bifurcation characteristics of the system is more obvious. As the time-varying mesh stiffness value increases, the temperature rise gradually stabilizes in the range of 15°C to 42°C; Under certain temperature changes, as the meshing damping ratio and time-varying meshing stiffness coefficient increase, the face gear planetary gear system gradually tends to stabilize.

Numerical modeling and analysis of multistage gear transmission system in wind turbine gearbox under load uncertainty

A multistage gear transmission system (MGTS) is widely used in wind turbine gearboxes. Its dynamic responses are closely related to stochastic aerodynamic torque that has a wide interval range between cut-in and cut-out wind speeds. However, most of the dynamic models of MGTS lack attention to dynamic responses caused by uncertainties of multiple parameters under varied input torque. In this study, a dynamic modeling method in conjunction with interval uncertain analysis of MGTS caused by multiple load-related parameters due to varied input torques is proposed. A comprehensive dynamic model of MGTS is developed considering time-varying gear mesh transmission error, load-related gear mesh stiffness and bearing stiffness as well as flexible shafts. The reasonability of simulation is validated, and then the effects of multiple load-related parameters on uncertain dynamic responses are discussed in-depth. Results show that both gear mesh stiffness and bearing stiffness are enlarged with increasing input torque to cause uncertain dynamic responses. These uncertainties would propagate along the flexible shaft and be suppressed by system rigidity. The dominant transverse vibration modes of shafts are sensitive to bearing stiffness, thus, uncertain bearing stiffness has remarkable effects on dynamic responses than gear mesh stiffness.

Simulation and validation of the transmission error, meshing stiffness, and load sharing of planetary spur gear transmissions

Although the load sharing between planets of sequentially phased planetary gear transmissions has been studied in the past, the required solving techniques based on the Finite Element Method result in long time consuming and high computational cost. This limits the possibilities of undertaking extensive studies that take into consideration a high number of cases allowing optimal solutions to be sought or general conclusions drawn. In addition, the determination of the curves of transmission error, time-varying mesh stiffness, and load sharing among tooth pairs in simultaneous contact are also complicated. In this work an analytical model has been developed for the simulation of the time-varying mesh stiffness, quasi-static transmission error, and load sharing ratio between planets and tooth pairs of planetary spur gear transmissions. It is based on similar models for external and internal spur gears previously developed and has been validated by comparison with a hybrid model based on the Finite Element Method and theoretic-experimental correlation.

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

Gear shaping causes processing characteristics on gear tooth surfaces (PCGTS), e.g., gear tooth surface deviation (GTSD) and processing textures (PT), which can affect gear meshing performances. Gear shaping simulation is operated to obtain PCGTS with different indexing feeds. An improved contact stiffness method of gear tooth surfaces is developed based on a wedge-shaped contact form to obtain tooth contact stiffness with PT caused by gear shaping. An improved time-varying meshing stiffness (TVMS) method for gears manufactured by gear shaping is developed to calculate TVMS of gears with GTSD and PT under different indexing feed conditions. Effectiveness of the improved TVMS method is validated using the finite element method. Analysis results of the proposed contact stiffness method of gear tooth surfaces indicate that PT caused by gear shaping can aggravate fluctuations of gear tooth contact stress. Analysis results of the proposed TVMS method for gears also indicate that GTSD of gear tooth surfaces caused by gear shaping can reduce their TVMS. The proposed TVMS method of gears can effectively analyze TVMS of gear tooth surfaces via gear shaping and evaluate processing settings of gear shaping to improve gear meshing performances.

A novel time-varying mesh stiffness model for orthogonal face gear drives considering EHL

PurposeThis study aims to research the time-varying mesh stiffness (TVMS) model for orthogonal face gear drives considering elastohydrodynamic lubrication (EHL) and provide a theoretical basis for understanding the dynamic characteristics of face gear drives.Design/methodology/approachConsidering EHL, a novel model is proposed to calculate the TVMS of orthogonal face gears using the deformation compatibility condition. First, the tooth surface equations of orthogonal face gears are derived according to the tooth surface generation principle. Then, the oil film thickness on the tooth surface of face gears is obtained by solving the governing equations of EHL. Furthermore, the proposed model is used to calculate the TVMS of face gears along the mesh cycle and is verified. Finally, the effects of module, tooth number of shaper cutter and pressure angle on mesh stiffness are analyzed.FindingsThe results indicate that when the contact ratio is greater than 1 and less than or equal to 2, the TVMS of face gears exhibits a phenomenon of double-single tooth alternating meshing where sudden changes occur. As the module increases, the overall mesh stiffness of face gears increases, and the magnitude of the sudden change at the moment of single-double tooth alternating meshing gradually increases. As the tooth number of shaper cutter and pressure angle increase, so does the TVMS of face gears. When the effect of oil film is considered, the calculated TVMS of face gears slightly increases overall and the increase in average oil film thickness leads to a rise in the TVMS. This study provides a theoretical basis for understanding the dynamic characteristics of face gear drives.Originality/valueThis study’s originality and value lie in its comprehensive approach, which includes conducting analysis based on loaded tooth contact, considering the influence of elastohydrodynamic lubrication, proposing a novel analytical–finite–element model, calculating TVMS of face gears, verifying the proposed model and analyzing the effects of typical structural parameters and oil film thickness.

Study on the calculation method of time-varying meshing stiffness of herringbone gear under the influence of crack-pitting coupling

Study on the calculation method of time-varying meshing stiffness of herringbone gear under the influence of crack-pitting coupling

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

Solving time-varying mesh stiffness of spur gears based on improved potential energy method

Meshing stiffness is an important factor in gear dynamics analysis. At present, there are many ways to calculate the meshing stiffness of gears, and we usually use the potential energy method to solve and calculate the meshing stiffness of healthy (faulty) gears. In this paper, the potential energy method, the improved potential energy method and the theoretical calculation method are used to solve the time-varying stiffness of the healthy spur gear pair, and the solution results are compared, which verifies the feasibility of the improved potential energy method to solve the gear meshing stiffness.

Dynamic Characteristics Analysis of the DI-SO Cylindrical Spur Gear System Based on Meshing Conditions

The dual-input single-output (DI-SO) cylindrical spur gear system possesses advantages such as high load-carrying capacity, precise transmission, and low energy loss. It is increasingly becoming a core component of power transmission systems in maritime vessels, aerospace, marine engineering, and construction machinery. In practical operation, the stability of the DI-SO cylindrical spur gear system is influenced by complex excitations. These excitations lead to nonlinear vibration, meshing instability, and noise, which affect the performance and reliability of the entire equipment. Hence, the dynamic performance of the DI-SO cylindrical spur gear system is thoroughly investigated in this research. The impact of excitations and nonlinear factors on the dynamic characteristics was investigated comprehensively. A comparative analysis of the gear system was conducted by establishing a bending–torsional coupling vibration analysis model under synchronous and asynchronous meshing conditions. Nonlinear factors such as periodic time-varying meshing stiffness, meshing damping, friction coefficient, friction arms, load sharing ratio, comprehensive transmission error, and backlash were considered in the proposed model. Then, the effect laws of excitations and nonlinear factors such as meshing frequency, driving load fluctuation, backlash, and comprehensive transmission error were analyzed. The results indicate that the dynamic characteristics exhibited staged stable and unstable states under different meshing frequencies and meshing conditions. At the medium-frequency meshing stage (0.96 × 104~1.78 × 104 Hz), alternating phenomena of multi-periodic, quasi-periodic, and chaotic motion states were observed. Moreover, the root mean square value (RMS) of the dynamic transmission error (DTE) in the asynchronized gear system was generally higher than that in the synchronized gear system. It was found that selecting the appropriate meshing condition could effectively reduce the amplitude of the DTE. Additionally, the dynamic performance could be significantly improved by adjusting control parameters such as driving load fluctuation (0~179 N), backlash (0.8 × 10−4~0.9 × 10−4 m), and comprehensive transmission error (7.9 × 10−4~9.4 × 10−4 m). The research results provide a theoretical guidance for the design and optimization of the DI-SO cylindrical spur gear system.

Dynamic response characteristics of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission system considering wear effect

To illustrate the impact of tooth surface wear on the dynamic response of the cylindrical gear transmission system with variable hyperboloid circular-arc-tooth-trace (VH-CATT), a nonlinear dynamic model of VH-CATT cylindrical gear that considers wear effect was developed in this article. Firstly, according to the analysis conducted through the finite element method, the time-varying meshing stiffness of VH-CATT cylindrical gear is calculated, and the time-varying meshing stiffness considering wear is characterized by introducing wear fault characteristics. Then, the load ratio is introduced to represent the relationship between the error amplitude and the excitation load. By using the error amplitude as the bifurcation parameter, this parameter describes how the excitation load affects the dynamic characteristics of the VH-CATT cylindrical gear. Finally, the bifurcation diagram and maximum Lyapunov exponent of the VH-CATT cylindrical gear transmission system under various wear depths are computed using the fourth-order Runge-Kutta method. At the same time, the response state of the VH-CATT cylindrical gear is verified by phase diagram, Poincaré mapping and time history diagram. The findings indicate that the vibration amplitude of the VH-CATT cylindrical gear system increases as the error amplitude increases. The vibration phenomenon of VH-CATT cylindrical gear transmission system with wear fault is more obvious, and the system enters the bifurcation and chaos effect state in advance. Therefore, the wear of the tooth surface will lead to the decrease of the gear meshing stiffness, which will lead to the increase of the vibration amplitude of the system, resulting in the phenomenon that the dynamic response state of the system is advanced. The research results will provide a theoretical basis for high-quality VH-CATT cylindrical gear transmission and gear nonlinear dynamics research.

Dynamic modeling and failure mechanism study of herringbone gear planetary transmission system for wind turbine under gear cracks

The herringbone gear planetary transmission system (HGPTS) is a common component in the gearbox of wind turbines. Studying the dynamic performance of gear systems is the key to improving their stability. To reveal the influence of cracks on the dynamic characteristics of the HGPTS, using slicing method, we explore the influence of different crack factors on the time-varying meshing stiffness (TVMS) of the system. A 55-degrees of freedom bending torsion axis pendulum dynamic model was constructed using the centralized mass parameter method; in the model, factors such as TVMS of cracks as well as receding groove and errors are considered. The Runge–Kutta method was used to solve the dynamics, and the evolution diagram of the vibration and load distribution characteristics of the system under crack changes was obtained. Vibration tests were conducted on the system studied in this work. The results show that under the influence of cracks, the TVMS of the external and internal meshing pairs of the system will decrease, and as the cracks intensify, the fluctuation of the TVMS will decrease. Cracks can lead to regular impact behavior in the system. A modulation sideband centered on the meshing frequency appears in the vibration response, and the vibration trajectory of the gears will also become disordered, at the same time, under the influence of cracks, there are significant excitation factors in the load-sharing characteristics of the system. As the cracks continue to intensify, the vibration of the system becomes increasingly evident, and the load-sharing characteristics show a trend of first decreasing and then increasing. The vibration test results are in good agreement with the theoretical predictions. The correctness of the established model is verified. The research results can provide reference for the reliability research of wind turbine HGPTS.

Thermal elastohydrodynamic lubrication analysis of the roller enveloping hourglass worm drives considering the roller self-rotation behavior

Elastohydrodynamic lubrication (EHL) plays a crucial role in worm-drive tribology. However, in roller enveloping hourglass worm (REHW) drives, the unique rolling motion of the rollers reduces friction but presents challenges in accurately analyzing the film formation characteristics. To address this, a method for calculating the time-varying meshing characteristic parameters, considering the influence of the roller's self-rotation behavior, is proposed. A thermal EHL numerical model for REHW drives was established based on EHL theory by integrating these parameters. The lubrication characteristics at various meshing instants and contact positions were analyzed, and operational conditions and design parameters were identified to enhance lubrication performance. High-speed and heavy-load REHW drives have demonstrated superior lubrication performance. These findings provide theoretical guidance for optimizing lubrication performance and investigating wear in REHW drives.

A dynamic modelling method for the naval gun under the influence of random wave excitation and servo system

ABSTRACT This paper proposed a mechanical–electrical-hydraulic coupling dynamic modelling method for naval guns coupled with multiple nonlinear factors. The ship's rocking motion equation is derived based on the wave spectrum formula to introduce the influence of random wave excitation into the vibration analysis of naval guns. An efficient gear transmission model of the servo system is developed using a multibody contact-based model to control the computational cost and based on the tooth stiffness theory, the time-varying mesh stiffnesses are considered. The dynamic results show that the ship's rolling motion will have more influence on gun dynamic characteristics than the pitching motion. Though under the control of servo systems, the adverse influence of the ship's rocking motion on cradle motion is basically eliminated. The instantaneous residual disturbances of the cradle increase for the driving torque saturation and the residual disturbances of the cradle will increase gradually with the ship's rocking motion increasing.