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For gear pairs with centre-distance separability, transmission ratios are not affected by centre distance error. Based on space curve meshing theory, the centre distance separability of a line gear pair was studied. A novel line gear pair called the separable and pure rolling parallel shaft line gear pair (SPRPSLG) was proposed, which has centre-distance separability characteristics and pure rolling transmission. The basic design theory of the SPRPSLG pair was established. A design method of the SPRPSLG pair with an eccentric arc tooth profile was given. An SPRPSLG pair example was designed and manufactured using the form milling method. Kinematic experiments and meshing efficiency experiments were conducted. Gear contact spot testing and gear contact simulation analysis were carried out. The SPRPSLG pair was shown to have centre distance separability, which provides a further theoretical basis for the popularization and application of line gears.

The calculation of time-varying meshing stiffness caused by the alternate contacting of the gear tooth is an essential prerequisite to obtain real and effective nonlinear dynamic characteristics of the transmission system, so that the significance of which cannot be overemphasized. Accordingly, this work proposes an improved method to get meshing stiffness with taking fillet-foundation and gear rim deflection into consideration. Compared to the traditional potential energy method, the proposed method has more superior accuracy and performance, and its effectiveness has been further verified by the finite element analytical model. After that, an ideal eight degree of freedoms (DOFs) dynamic model of one stage mass-spring-damper involute spur gear, including lateral and torsional motions, is established to study the dynamic characteristics. Due to the complexity of the gear system operating conditions, we also investigate the influence of various parameters including hub bore radius, transmitting load, and rotation speed on dynamic features, especially in heavy-load and high-speed conditions. From the results, it can be concluded that these parameters will play a prominent role in the spur gear pair dynamic behaviors, providing a certain guidance for gear design.

Gear transmission is an essential element in the motor cars of high-speed trains, as it directly effects the reliability and safety of the vehicle. Based on the classical vehicle–track coupled dyna...

A high-speed-level gear transmission system model of a wind turbine is presented considering a time-varying wind load and an electromagnetic torque disturbance, along with eccentricity, dynamic backlash, and friction force. The auto-regressive model is employed for simulating the time-varying wind load in the realistic wind field as external excitation. A doubly fed induction generator model of the wind turbine is established to calculate the disturbance quantity of electromagnetic torque. The nonlinear differential equations of the system are strictly deduced using Lagrange equation and solved by the fourth-order Runge-Kutta method. The effect of friction on the dynamic response of the high-speed-level gear transmission system is analyzed with the time-varying wind load and the electromagnetic torque disturbance. These results show that the friction force is critical because frequency amplitude and components can be changed by it. The friction force also enlarges vibration displacement. The low-frequency components in the vertical direction are affected gravely by the friction force without electrical disturbance. In addition, sidebands exist in the vicinity of the low-frequency parts as the electromagnetic torque disturbance appears at the output end. The amplitude of the low-frequency component is further increased because of electromagnetic torque disturbance. This shows the frequency characteristics of the slight gear system fault. The study offers some fresh references into the design and diagnosis of the gear system.

In order to study the influence of friction on the nonlinear dynamic characteristics of a planetary gear system, the dynamic model of a planet gear transmission system considering mixed elastohydrodynamic lubrication (EHL) friction, time-varying meshing stiffness, backlash and comprehensive meshing error is established. The Runge–Kutta method is used to solve the dynamic differential equations, and the bifurcation and chaos characteristics of the system are analysed through the bifurcation diagram, largest lyapunov exponent (LLE), Poincaré map, phase diagram, time history curve diagram and fast fourier transform (FFT)spectrum. The results of numerical simulation show that the planetary gear system with mixed EHL friction exhibits rich bifurcation characteristics, and the system experiences short-periodic motion, long-periodic motion, quasi-periodic motion and chaotic motion. The effect of tooth surface friction on the bifurcation characteristics of the planetary gear system is more obvious at high frequency than that at low frequency. Tooth surface friction causes the system to enter chaotic motion in advance.

This study is to systematically analyze the influences of time-varying meshing stiffness (TVMS) and meshing impact on the dynamic characteristics of high-speed gear transmission in the two-stage pure electric vehicle (PEV) gearbox, as well as the effect of tooth surface modification on the vibration control. First, the dynamic model was established, and the TVMS and meshing impact were calculated. Then, the vibration characteristics of single-stage and two-stage helical gear transmission were analyzed under three different excitation conditions, excitation of TVMS, excitation of meshing impact, and excitation of both. The results show that the effect of rotating speed on the system vibration is not significant outside the resonant region under the excitation of TVMS, while the effect of meshing impact becomes the main exciting component with the increasing rotating speed. The vibrations of the two gear pairs interact with each other; the vibration frequency of one gear pair contains both its meshing frequency and the coupling frequency of the other gear pair. Tooth surface modification in the input-stage gear pair can reduce the vibration of both the input- and the output-stage obviously; that is, more attention should be paid to the input-stage gear pair in the modification design of PEV gearbox.

Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.

Reliable lubrication is essential to the life of gear transmission systems. An approach to predict the reliability of gear elastohydrodynamic lubrication (EHL) under a random input torque is propos...

The gear transmission system is a key part to transmit power for the electrical multiple unit (EMU) and to move the train forward. Its dynamic vibrations affect the operation safety and the dynamic...

Based on the planetary gear transmission system considering the coupling effects of friction and elastohydrodynamic lubrication, a torsional dynamic model considering friction, oil film, time-varying meshing stiffness, meshing damping, and gear backlash is established. The Runge–Kutta numerical method is used to solve the vibration equation of the system. The bifurcation diagram and largest Lyapunov exponent are used to analyze the dynamic characteristics of the system under different bifurcation parameters such as the excitation frequency, lubricant viscosity, sun–planet backlash, and planet–ring backlash. The numerical results demonstrate that with the increase of excitation frequency, the system exhibits rich nonlinear dynamic characteristics such as short-period motion, long-period motion, and chaotic motion. With the increase of lubricant viscosity, the chaotic motion of the system is suppressed at low excitation frequency and the periodic motion of the system increases at high excitation frequency. With the increase of sun–planet backlash, the chaotic motion of the system increases at low excitation frequency, and the bifurcation characteristics become complicated at high excitation frequency and enters chaotic motion in advance. With the increase of ring–planet backlash, the system delays into chaotic motion at low excitation frequency and bifurcates from single-period motion to multi-period motion in advance at high excitation frequency.

To improve load capacity and transmission characteristics of crossed-axis helical gear drive, a generation approach of the gear pair with small-angle based on the curve contact element is proposed. Contact principle based on spatial curve meshing relationships is introduced and geometric models of tooth profiles are developed according to a pair of mated conjugate curves. Furthermore, a mathematical model of crossed-axis helical gear drive with small-angle is established. Numerical examples are illustrated for this research using the 10° shaft angle, and the computerized simulation is also developed based on the solid models. According to gear geometry and finite element method, general characteristics including undercutting conditions, sliding ratios and contact stress for tooth profiles are analyzed. Comparisons with crossed-axis involute gears are also carried out. Finally, the gear prototype is processed using the gear milling method and a basic performance test is conducted. Analysis results show that the new gear pair has well contact characteristics. Further studies on the dynamic analysis and precision manufacturing method will be carried out.

With the increasing service life of a gear transmission system, the gear teeth become constantly worn, and the gear clearance increases. The increase in the clearance will produce a series of nonlinear changes that change the stability of the system and can even result in loss of stability. In this paper, dimensionless dynamic equations of a multistage gear transmission system that contains a two-stage fixed-axis gear and a one-stage planetary gear were established. Planetary wear fault was simulated by changes in the gear clearance. System bifurcation diagrams with an increase in the clearance were studied. The frequency characteristics of planetary gears under different excitation frequencies and different degrees of wear were studied. The influence of planetary gear wear on the fixed-axis was discovered. The vibration mechanism and a fault diagnostic method in a multistage gear transmission system were obtained.

This paper considers the wear process of the teeth of straight spur gear transmissions under the conditions of skew of the axes of conjugated wheels. The method for determining the magnitude of wear of tooth profiles, taking the skew angle into account, is based on the dependence of average contact pressure on the skew angle. To determine the contact pressure, the physical and mathematical model of contact interaction of cylindrical elastic bodies is used when they are skewed using the Winkler model of elastic foundation. It is established that the presence of skew angle of teeth of 0.1° increases the wear rate by 3.61 times.

A planetary gear transmission system with multistage face gears combinations as core component can easily realize the variable speed in differential transmission ratios with structural advantages. In order to improve the transmission stability and loading capacity, it is necessary to set up a reasonable kinematic model for multistage face gears pair. This study focuses on the kinematic characteristics of multistage face gears structure with double crown surface by the methods of numerical calculation and experimental verification. The transmission error and efficiency solving models are established by numerical calculation method to analyze the influences of each factor in detail. Then the correctness of the above numerical models are verified with transmission error and efficiency experiment. In addition, the numerical results are compared with the experimental results to further indicate the important influences of the multistage face gears components on the transmission error and efficiency of whole transmission system. The results can provide references for the dynamic and experimental study of multistage face gears in some degree.

Due to changes in the working temperature in a shearer transmission system, it is easy to cause the transmission gear to work abnormally. In this paper, the first gear pair in a cutting transmission system of a permanent magnet semi-direct drive shearer was taken as the research object. The coupling effect of time-varying meshing stiffness, meshing damping, bearing clearance and gear backlash under thermal deformation were fully considered. Then, a three degree of freedom nonlinear dynamic model of the gear pair was established, and a dimensionless analysis was performed. Finally, the Runge-Kutta method was used in the numerical calculations. The motion characteristics of the system were analysed through the gear’s bifurcation diagram of the temperature at different frequencies and the bifurcation diagram of the frequency at different temperatures. The meshing state was analysed at different frequencies and temperatures. For the chaotic motion generated in the system, a periodic resonance excitation was applied to control unstable motion. This study has revealed various specific effects of the temperature on the dynamic characteristics of the system. In addition, the periodic excitation method can effectively control the nonlinear motion in the system and realise the control of the chaos under the temperature effect.

Time-varying mesh stiffness (TVMS), one of the most important parameters in gear dynamics, is usually used to analyze the influence of gear fault in gear transmission systems. In this study, a modified TVMS model is proposed to quantitatively evaluate the influence of the tooth wear on the mesh stiffness. In this model, the potential energy method is employed to calculate the mesh stiffness and the Archard's wear equation is adopted to calculate the tooth wear depth. Furthermore, the analytical expression of the modified mesh stiffness considering the tooth wear is theoretically derived, which can be used for a variety of tooth wear models. The modified TVMS model is applied in a planetary gear set, including the sun-planet mesh and the planet-ring mesh. The results of numerical simulation demonstrate that the tooth wear can result in the reduction of the mesh stiffness; for a planetary gear set, in the initial wear process, the mesh stiffness decreases proportionally when the tooth wear depth increases.

Planetary gear transmission system has been widely used in the field of aerospace equipment, automobiles, ships, etc. High power density design is an important development direction for transmission machinery, but there is a lack of systematic and deepening research in planetary gear transmission system field. Taken the most widely used 2K–H-type planetary gear transmission system as research object, a design method of high power density considering volume and efficiency is put forward. First, the transmission efficiency model of 2K–H-type planetary gear transmission system is built on the basis of calculation of single gear pair meshing efficiency instead of the look-up table method. Second, the volume model of 2K–H-type planetary gear transmission system is built according to the structure of gear. Finally, the smallest volume and the minimum power loss of 2K–H-type planetary gear transmission system are the target of optimization, and the linear-weighted combination method is used to construct target function. Taken a 2K–H-type planetary gear reducer in some machine tool as an example, the optimization is carried out. The results show that the power loss of optimized system is reduced by 11.42%, and the volume of system is reduced by 25.2%.

Tooth modification is critical when designing high-performance gear transmission systems. However, it is difficult to accurately calculate the system deformation and tooth modification amount using the traditional empirical formula. Although the finite element method provides accurate results, it is time consuming and its direct application to tooth modification for multistage geared systems is difficult. This study proposes a novel methodology to define tooth modification in both width and profile directions, which can be used for multistage spur gears. First, a housing-transmission coupled dynamic model is built, and the actual meshing state of each gear pair is obtained from dynamic simulation. Lead and profile modification are then conducted sequentially using the actual meshing state as an input. As the optimal tooth modification parameter is determined by the system dynamic response, and the tooth modification in turn influences the system dynamic response, the “dynamic simulation” and “tooth modification” are repeated iteratively until the modification parameter converges. Taking the drum driving system of a shearer as an example, the optimal tooth modification parameter is obtained after three iterations, and the dynamic factor and maximum tooth contact stress clearly decreased after applying the optimal tooth modification.

Backlash-induced variations may lead to teeth separation and back-side tooth mesh in lightly loaded geared drive. Effects of teeth separation and back-side tooth mesh are considered. The dynamic model of a spur gear pair under multi-state meshing conditions such as teeth separation, drive- and back-side tooth mesh is established based on the gear transmission principle and forces acting on teeth. Time-varying meshing stiffness, time-varying friction, load distribution, comprehensive transmission error and backlash are included in the model. Variations of the dynamic meshing force of the system under different meshing states are analyzed numerically. The dynamic meshing force affects the meshing state of the system significantly. Furthermore, the effects of load, backlash and comprehensive transmission error on meshing states and vibro-impact properties of the system are studied by defining three different Poincare maps, where bifurcation diagrams, top Lyapunov exponent diagrams (TLE), phase portraits are used. Results indicate that the complicated phenomena such as drive-side impact, teeth separation and back-side impact gradually occur with the decrease of the load or the increase of the comprehensive error. However, these phenomena always exist with the increase in backlash. This study provides a theoretical reference for the optimization of gears.

A novel gear transmission with geometric elements constructed tooth pairs having triple contact points is proposed in this study. Based on the equidistance enveloping method, the generation principle and method of the tooth surface are presented. Three types of contact pattern of tooth profiles are generated: convex to convex, convex to plane, convex to concave. A calculation example for convex to concave tooth profiles of gears is provided. Performance experiment is carried out based on the developed gear prototype, and a comparison with involute gear drive is also shown. Theoretical and numerical results demonstrate the feasibility and correctness and it lays the foundation for the design of high performance gear transmission.

The gear transmission system of a high-speed train is the key component, which delivers the traction torque from the motor to the wheelset. It couples with the vehicle system via the suspension system, gear meshing and the wheel–rail interface. The dynamic performance of the transmission system directly affects the operational reliability or even the running safety of high-speed trains. In this study, the effects of wheel polygonalisation and wheel flat on the dynamic responses of the transmission system are investigated through simulations of a novel vehicle dynamics model. This model integrates the flexible gearbox housing, the time-varying mesh stiffness and the nonlinear gear tooth backlash, and the track irregularities to obtain more realistic responses of the traction transmission systems in a vehicle vibration environment, from motors to wheelsets, under the effects of the wheel flat and polygonal wear. The field experimental tests are implemented for a vehicle running along a main high-speed railway line in China. Subsequently, the developed dynamics model is validated with good agreement between the experimental and the theoretical results. The calculated results revealed that wheel flat and wheel polygonal wear caused a high-frequency fluctuation of both the longitudinal creep force and the gear mesh force, causing a violent and complex torsional vibration of the gear transmission system. Moreover, the flexible deformation of the gearbox housing, especially its resonance due to the wheel polygonal wear, contributed to the torsional vibration of the gear transmission system.

A locomotive is usually powered by the electromagnetic torque which is transmitted from the traction motor to the wheelset by gear transmission. In order to investigate the dynamic coupling effects from the gear transmission subsystems on the entire locomotive dynamics system, a comprehensive spatial locomotive dynamics model that considers the dynamic coupling effect of the gear transmissions is developed based on the multibody dynamics theory. In this model, the moved Marker technique is employed to calculate the dynamic mesh force of the gear pairs through which more accurate time-varying gear mesh stiffness excitations could be imported, which is the core of this dynamic model. Then, the established locomotive dynamics model is validated by comparing with the experimental test results. Finally, the dynamic effects of the gear transmissions are revealed by comparing with the results from the traditional locomotive dynamics model without considering the dynamic excitations from the gear transmissions. The results indicate that the gear transmissions have negligible effects on the vibrations of the carbody and the bogie frame, and on the lateral vibrations of the motor and the wheelset. However, the gear transmissions have significant effects on the vertical and, in particular, the longitudinal vibrations of the motor and the wheelset. Thus, it is suggested that the dynamic effects of the gear transmissions are considered in the locomotive dynamics modeling, especially when the vibrations of the motors and the wheelsets are taken into account.

Taking the NW planetary gear transmission of an electric wheel hub as the research object, the mesh model was developed to calculate the mesh parameters using Masta. Then the lump parameter method was used to establish the dynamic model of the NW planetary transmission system considering the time-varying mesh stiffness, transmission error and bearing stiffness. The impacts of the torque load on the dynamic characteristics including the dynamic mesh force, center trajectory, offsets and load sharing coefficients were investigated. Results show that the dynamic mesh force waveform and spectral characteristics of each planetary gear at high and low speeds under the rated and maximum torque load are almost identical. Compared to the peak response at speed 485 rpm and 1770 rpm, both the magnitude and location of the third response at relative high speed about 4300 rpm are increased due to the load increasing. The mean and fluctuation range of the offsets in the radial direction are both larger than the tangential direction. As the load increases, the mean value of the radial offset increases and the magnitude decreases significantly. The mean value of the tangential offset decreases significantly, but the magnitude increases first and then decreases. The load sharing characteristics of the low-speed stage of the NW planetary gear is better than the first stage. With the increase of the load, the load sharing performance of a two-stage planetary transmission gets better and the difference in load sharing between the high-speed and low-speed stages also decreases.

Uncertainty in robot manipulations is a fundamental source of inaccuracy. Most nongeometric uncertainties is caused by the mechanical components of robot manipulators such as gear transmission systems and joints. This study integrates existing uncertainty models for practical applications of both three-degrees-of-freedom serial robot and parallel robot (closed-loop 5R mechanism). We first review the literature on uncertainty and existing methods for improving the precision of robot manipulation. For existing methods for uncertainty modeling: (1) the mathematical model of a harmonic drive considering kinematic error and compliance is derived; (2) joint clearance analysis that includes models of contact force and friction force is presented; (3) Archard’s wear model is used to estimate the effect of joint wear, based on which the geometry of joints is updated. Computer simulation is then used to demonstrate the application of the proposed method for serial and parallel robot manipulators. Simulations are used to examine the behavior of robot manipulators operating under uncertainty, with performance-evaluated positional error and trajectory error. The proposed method can provide some insight into nongeometric uncertainty in robot manipulations. The proposed methodology can be further used to improve the accuracy of robot manipulation under uncertainty by identifying uncertainty parameters.

Nonlinear vibration, a main factor affecting the dynamic stability, widely exists in the transmission system. In addition, geometric eccentricities caused by the manufacturing errors are inevitable in the gear transmission system, which may lead to the excessive nonlinear vibration. In order to suppress the nonlinear vibration under the excitation of the geometric eccentricities, a rigid–flexible gear pair consisting of the ring gear, the composite material, and the hub is proposed in this study. A dynamic model with nine degrees-of-freedom which considers geometric eccentricities is proposed to analyze the nonlinear dynamic characteristics of the rigid–flexible gear pair. Furthermore, the dynamic characteristics of the rigid–flexible gear pair and the rigid gear pair are compared within a wide range of operating conditions. The comparative analysis demonstrates that the rigid–flexible gear pair has better vibration suppression effect on the system.

In this study, we attempt to analyze the influence of different excitation factors on the dynamic behavior of a gear transmission system in a braiding machine. In order to observe nonlinear characteristics, a mathematical model is established with a six-degrees-of-freedom gear system for consideration of multiple excitation factors. Iterative results are used to study the nonlinear characteristics of the gear system with respect to contact temperature, varying levels of friction, and disturbance of yarn tension using bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, Poincare maps, and the power spectrum. The numerical results show that excitation factors such as temperature and surface friction, among others, have considerable influence on the nonlinear characteristics of the gear system in a braiding machine, and the model is evaluated to show the key regions of sensitivity. The analysis of associated parameters can be helpful in the design and control of braiding machines.

This research aims to investigate micro-crack on a failed for helical gear transmission which was to adjust the engine to increased horsepower. The helical gears made are from chromium steel JIS-SCr 420. The spectrophotometer test machine was used to detect chemical composition, Mechanical properties were evaluated by Vickers hardness and microstructural analysis with an optical microscope, which the crack of the surface layer and energy dispersive spectroscopy using a scanning electron microscope. The results showed that the fracture characteristic of the helical gear’s surface was expected to beach marks and break away. It can be seen that the mixing failure area of oxide inclusion with carbide surrounding before the liquid state of material will be solidified which caused the failure cause of this helical gear. The summary analysis results can be accorded with the assumption of this research and which help prolong service life of the component.

Considering flexibility of the support shafts as well as bearing supports, the effect of meshing impact force and meshing stiffness on the dynamic behavior of a gear transmission system in electric vehicle is investigated in this paper using the proposed hybrid user-defined element method. First, a structured grid generation method is introduced to establish accurate mesh models of the pinion and gear teeth. Second, coupling the tooth mesh models and the flexible shafts as well as bearings, two finite element models are, respectively, constructed for the two helical gear pairs of the electric vehicle reduction unit to calculate the meshing impact force. Next, the basic mechanism of meshing impact is explained in detail according to the finite element results, and the impact force is determined as one of the main internal excitations substituted into the dynamic model established by the hybrid user-defined element method. Under 50 N m input torque and 12,010 r/min rotational speed of the input shaft, the simulation results by the hybrid user-defined element method indicate that the example system reaches a steady state and the vibrations primarily occur at the meshing frequencies. With an increment of 600 r/min of the input rotational speed, it is also concluded from the results that (1) the calculated impact force approximately presents linear growth with the increase of the input shaft rotational speed and (2) the root mean square values of the vibration acceleration generally grow with the increase of the speed.

With the rapid development of modern industry, the situation of high speed and heavy load is becoming even more relevant in the gear transmission system. Under the condition of high speed and heavy load, the fault type and frequency of the gear transmission system are gradually increasing. Effective and accurate detection of fault location and fault type is one of the difficult problems in today’s fault diagnosis. In the case of high speed and heavy load, the probability of multi-body fault is greatly increased. However, most of the current fault diagnosis methods are limited to the study of single fault characteristics, and do not take into account the multi body fault. In this paper, the single crack, gear coupling crack, single shaft crack, and gear and shaft coupling crack signal are analyzed by means of the short-time Fourier transform, and the corresponding fault characteristics of different fault types are found out. The modal analysis of the fault state of the gear transmission system is carried out, the structural characteristics of the gear drive are verified, and the influence of the different fault forms on the vibration characteristics of the gear is compared.

Transmission efficiency is the main concern in the design of the lubrication system for a gear transmission system, such as a vehicle axle. This paper presents an optimization method to reduce the churning loss and improve the transmission efficiency in an axle based on the computational fluid dynamics and the response surface method. In this study, the computational fluid dynamics method was applied to simulate the lubrication flow in the axle housing. A numerical model was built for the splash lubrication system that included the entire structure of the hypoid gears, bearings, oil passage, and other parts. The numerical results provided direct visualization of the oil flow inside the axle housing, and the numerical predictions for the oil distribution and churning loss were determined from the numerical result. Furthermore, the influences of the speed, oil level, and oil temperature on the churning loss were investigated. The oil distribution results from the numerical calculations were consistent with the experimental observations, and the error in the predictions for the churning loss was less than 9.3%. The results of this study provide a foundation for subsequent optimization work on the lubrication system of a vehicle axle.

Gear meshing efficiency is an important component of gear transmission efficiency, and the meshing efficiency of gear is directly related to device performance and energy consumption. The gear meshing efficiency can’t be obtained directly from the measurement results of gear test machine. It is rarely reported effective method to calculate the gear meshing efficiency with measured data from gear test machine, which limits the verification of theoretical calculation method of gear meshing efficiency. Therefore, a method for calculating gear meshing efficiency by measured data from gear test machine is proposed in the paper. It is suitable for power closed type gear test machine, and suitable for power open one as well. Firstly, according to the type of gear test machine, the corresponding calculation method of gear transmission efficiency is confirmed. Secondly, the gear transmission efficiency under both unloaded and loaded conditions, the total power under loaded conditions and friction-related losses at the bearings are calculated at a given speed, respectively. Finally, substituting the calculation results of friction-related losses at the bearings, total power under loaded conditions and the gear transmission efficiency both unloaded and loaded conditions into the gear meshing efficiency calculation formula, and gear meshing efficiency by measured data from gear test machine is obtained. An example is presented to verify the proposed method.

A model of a passive vibration absorbers designed for improving the stability of milling tools is presented in this work, the spindle supposed exited backward and upward respectively by the motor through the gearbox and by the cutting forces through the milling tool. First a milling operation is simulated taking into account the tool cutting torque and the gear transmission varying time efforts, then a passive linear absorbers composed by a single mass-spring-damping are implemented in the spindle to study their effect on the dynamic behavior of milling tool. The obtained results show a decreasing of the vibration amplitude of the milling to reach in certain cases 42% compared to the same cutting operation without using absorbers. In addition, the same absorbers prove their efficiency to reduce the cutting time when the feed rate was doubled accompanied by a little improving of the dynamic behavior of milling tool.

Traction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffn...

To reduce the running vibration of spiral bevel gear, an innovative ease-off flank modification method based on the dynamic performance for spiral bevel gear to minimize loaded transmission error (main vibration excitation of gear transmission in low speed range) and meshing impact (main vibration excitation of gear transmission in high speed range) is proposed. First, an innovative wave flank modification method related to high contact ratio, where the concave transmission error is used to replace the parabola transmission error, is proposed to minimize the loaded transmission error of high-contact-ratio spiral bevel gear. Secondly, meshing impact is calculated by considering the base pitch difference generated from loaded deformation. Finally, based on the advanced ease-off technology and wave flank modification method, an optimization model is established to reduce the loaded transmission error and meshing impact of high-speed spiral bevel gear with high-contact-ratio. The numerical results show that compared with optimized second-order spiral bevel gear transmission, the innovative ease-off flank modification method can further reduce the loaded transmission error and meshing impact of high-speed spiral bevel gear with high-contact-ratio, which greatly improves the dynamic performance of high-speed spiral bevel gear in the entire speed range.

To reduce the running vibration of high-contact-ratio (HCR) spiral bevel gear transmissions, an innovative higher-order tooth surface modification (HTSM) method is proposed to reduce the vibration excitation of gear transmission. First, according to the meshing characteristic of HCR spiral bevel gear transmissions, an innovative modification curve is proposed. Second, the auxiliary tooth surface modification (ATSM) method is used to generate the higher-order modified spiral bevel gear. Third, the loaded transmission error (LTE) and meshing impact (MI) of higher-order modified spiral bevel gear transmissions are calculated based on the LTCA method and the impact theory while considering tooth deformation. Last but not least, based on the ease-off technology, an optimization model is built to reduce the LTE and MI of HCR spiral bevel gear transmissions. Through simulation analysis, it is found that compared with the second-order modified spiral bevel gear, the high-order tooth surface modification method can not only effectively reduce the LTE, MI and dynamic load factor (DLF) of HCR spiral bevel gear, but also improve its dynamic performance within full speed range. This study provides an effective way for improving the dynamic performance of HCR spiral bevel gear transmissions within full speed range.

The volume of gear transmission system has been concerned by people. At present, the researchers mainly focus on the optimization algorithm, but there is a lack of research on the volume model of gear transmission system. In the paper, the single-stage spur-gear transmission system is considered and the volume models for different structures of spur gear are built. Firstly, the influence of bottom clearance and the modification coefficient on the spur-gear volume are analysed. The formula of clearance volume is derived. Secondly, volume models of different structure of spur gear are built. In order to illustrate the accuracy of the models, the corresponding three-dimensional models of different structure of spur gear are established. Finally, the design parameters of spur gear are as the optimisation variables, the spur-gears design and transmission requirements are as the constraint conditions, the total minimum volume of single-stage spur-gear transmission system is as the optimisation target, t...

The compound transmission mechanism of curve-face gear is a new type of gear transmission based on the cam mechanism and the curve-face gear pair. It combines the transmission characteristics of the cam mechanism and noncircular bevel gear. When the compound transmission mechanism of curve-face gear is engaged in the meshing transmission, the rotating center of the cylindrical gear is fixed and used as the driving wheel, and the curve-face gear can generate the helical motion around the axis. In this paper, the meshing characteristics and motion laws of the compound transmission mechanism of the curve-face gear are studied based on the theory of screw. Based on the meshing theory of gears, the coordinate system of conjugate surfaces is established, the basic meshing theory and equation are obtained. On this basis, combined with the principle of the cam, the transmission principle is analyzed by the screw theory. The tooth surface equation of the compound transmission mechanism of curve-face gear is deduced based on the meshing theory and the related knowledge of geometry. The motion law of the curve-face gear and the change of the motion law with the change of the basic parameters of the gear pair with different design parameters are calculated and analyzed. An experimental platform is built to verify the law of motion, and the experimental results are compared with the theoretical values. The correctness of the theoretical analysis is verified, which provides a new way for the research of the compound transmission mechanism of the curve-face gear.

This report discusses how a transmission error curve is derived by a coordinate measuring machine, and the result by a coordinate measuring machine is compared with the result by a transmission error measuring machine. A vibration based on a gear pair engagement in fishing reel occurs when a handle of the reel rotates. When this vibration is large, an angler feels uncomfortable. In author’s previous reports, it is known that a rotational feeling depends on the transmission error curve. The result indicates that the rotational feeling can be improved if the accuracy of a tooth flank is improved. In order to reduce the transmission error, the error should be measured in high accuracy. In this research, a measurement method for evaluating the rotational feeling was reported using a face gear pair via a coordinate measuring machine and a transmission error measuring machine. As a result, it was confirmed that the result of measurement by the coordinate measuring machine agrees very well with the result of measurement by the transmission error measuring machine.

Considering the gear manufacturing and meshing theory, a numerical design approach with parabolic modifications was proposed to improve the mesh behaviors of crossed beveloid gear transmission. The generating procedure with parabolic modifications for the crossed beveloid gears with small shaft angle was proposed. And the analytical mesh model with misalignments of crossed beveloid gear transmission was developed. Then the effects of parabolic modifications on contact path and contact ratio were investigated. Also, the misalignments sensitivity was analyzed for the beveloid gears with and without parabolic modifications. Results show that the design situation with a positive parabola coefficient for the pinion and a negative parabola coefficient for the gear is better than other combinations of the parabola coefficients. Both the offset error and shaft angle error tend to deviate the contact path from the theoretical middle region. The parabolic modifications can reduce the sensitivity of contact path to the offset error and shaft angle error for crossed beveloid gear transmission effectively. Both axial pinion and gear position error has little influence on the mesh behaviors for the crossed beveloid gear pair with and without parabolic modifications.

A new design of gear transmission unit with continual variation of gear transmission ratio, for application in wind turbines (WT), has been developed. By variation of transmission ratio the speed of output shaft is 1500 rpm, constant independently of the wind speed. The article contains the presentation of a testing rig and the testing procedure of this design. The testing rig is based on back-to-back connection and power circulation and the testing procedure on simulation of the WT service conditions. The objective of testing process is identification of gearbox operating features and behavior, gearbox reliability and durability.

The connection between a gear pair is commonly treated as constant stiffness in the literature of planetary gear transmission dynamics, leading to inaccurate results. Based on the theory of viscoelastic contact, according to low speed or stationary gear pairs have the characteristics of small relative sliding velocity, viscoelastic contact method is proposed to solve this problem. A hoist equipped with two-stage planetary gear reducer is used as research object to investigate the dynamic properties. The natural frequencies and corresponding vibration modes of this planetary gear transmission system are presented. Accordingly, the natural frequencies are recognized using operational modal analysis under ambient excitation, and the experimental studies are in close agreement with theoretical expectation. In addition, the dynamic behaviours of this planetary gear train are investigated.

The dynamic analysis of a gear transmission system for electric vehicle is analyzed by means of a multibody approach. The architecture of the transmission is constituted of one gear ratio, with the differential integrated in the same gear box. The multibody model of the complete transmission has been created and optimized in order to get the dynamic response of the system. In particular, the frequency response function of the system in terms of rotational speed and loading forces has been determined. Furthermore, the dynamic transmission error has also been determined.

The paper presents the design of a planetary drive with 2 degrees of freedom and simulation of the proposed mechanism in ADAMS software. The mechanism can be used to smoothly change the reduction ratio depending to the applied load on the output shaft. At constant input of motor the proposed mechanism is able to provide variable output speed. The paper is aimed to study the capability of the mechanism to adapt the operation to variable loads. The design constraint has been selected to an application as a reducer of speed on a wind mill. The results of the simulation have been aimed to outline the output parameters of a planetary drive for wind mills.

This paper presents the results of laboratory tests in which evaluation was performed regarding the effect of selected operating factors on the vibroactivity of upper gearbox housings made of three different fiber reinforced polymer composite materials with diverse layouts (cross and random) and types of reinforcing fibers: glass fiber and carbon fiber. The results of tests for composite housings were compared with those for a steel housing. The tests showed that composite housings had a weight lower by more than 60% compared to the steel housing. A multisensor measuring system consisting of vibration acceleration transducers, a directional microphone and a data acquisition card with software was used for the study. Tests of the vibroactivity of upper gear housings were carried out at different loads and rotational speeds of toothed gears. The study showed that composite housings are less sensitive to changes in the rotational speed that steel housings. The tests showed that at a higher rotational speed of the gear transmission, housings made of composite materials had a comparable or lower level of vibration. Tests and analyses of the vibroactivity of housings performed at different loads of the gear allow the conclusion that composite housings, despite a considerably lower weight than steel housings, are less sensitive to changes in the load of the gearing.

The deep-sea geological winch needs to change speed frequently to adapt to the change of cable tension in the process of recovering. The planetary gear mechanism has a compact structure and strong carrying capacity, so adding the planetary gear mechanism between the servo motor and the winch can effectively improve the carrying capacity of the winch. This paper design a planetary gear transmission system with flexible pins and carried out the rigid-flexible coupling dynamics simulation by ANSYS and ADAMS on its load sharing characteristic. Verify the load sharing effect of flexible pin, and provide a reference for the application of planetary gear in deep-sea geological winch.

At present, the mean value of the meshing stiffness and the gear backlash is a fixed value in the nonlinear dynamic model. In this study, wear is considered in the model of the gear backlash and time-varying stiffness. With the increase of the operating time, the meshing stiffness decreases and the gear backlash increases. A six degrees-of-freedom nonlinear dynamic model of a new rigid-flexible gear pair is established with time-varying stiffness and time-varying gear backlash. The dynamic behaviors of the gear transmission system are studied through bifurcation diagrams with the operating time as control parameters. Then, the dynamic characteristics of the gear transmission system are analyzed using excitation frequency as control parameters at four operating time points. The bifurcation diagrams, Poincaré maps, fast Fourier transform (FFT) spectra, phase diagrams, and time series are used to investigate the state of motion. The results can provide a reference for the gear transmission system with wear.

The current research on gear system dynamics mainly utilizes linear spring damping model to calculate the contact force between gears. However, this linear model cannot correctly describe the energy transfer process of collision that often occurs in gear system. Focus on the contact-impact events, this paper proposes an improved gear contact force model for dynamic analysis in helical gear transmission system. In this model, a new factor associated with hysteresis damping is developed for contact-impact state, whereas the traditional linear damping factor is utilized for normal meshing state. For determining the selection strategy of these two damping factors, the fundamental contact mechanics of contact-impact event affected by supporting forces are analyzed. During this analysis, an effect factor is proposed for evaluating the influence of supporting forces on collision. Meanwhile, a new restitution of coefficient is deduced for calculating hysteresis damping factor, which suitable for both separation and non-separation states at the end of collision. In addition, the time-varying meshing stiffness (TVMS) is obtained based on the potential energy approach and the slice theory. Finally, a dynamic analysis of a helical gear system is carried out to better understand the contact force model proposed in this paper. The analysis results show that the contribution of supporting forces to the dynamic response of contact-impact event within gear pair is important. The supporting forces and dissipative energy are the main reasons for gear system to enter a steady contact state from repeated contact-impact state. This research proposes an improved contact force model which distinguishes meshing and collision states in gear system.

The operation effectiveness of multi-bar transplanting mechanisms is low, and the specific changing law of the transmission ratio (the curve of the transmission ratio has twice unequal amplitude [TUA] fluctuation.), which is needed in vegetable pot seedling transplanting, is difficult to fulfill using a planetary gear train with noncircular gears and a single-planet carrier. To address this problem, we propose a noncircular gear pair that comprises an incomplete noncircular gear, rack, partial noncircular gear, and elliptical gear. The structural characteristics and the working principle of the TUA gear pair were analyzed. The pitch curve equation of the noncircular TUA gears was derived from the relationship of the angular displacement of the corresponding pitch curves. The influence of central angle α and eccentricity k on the shape of the pitch curve, angular displacement, and transmission ratio of the TUA gear pair was analyzed. The TUA gear pair was applied to a proposed vegetable seedling pickup mechanism (SPM) considering the design requirements. Finally, the feasibility of the new noncircular TUA gear transmission mechanism was verified by an SPM test.