Effects of time-varying friction coefficient on hypoid gear dynamics

This paper develops a generalized 3-dimensional 14-DOF dynamic model for hypoid gear which considers the time-varying friction coefficient and lubrication situation. We propose a mixed elastohydrodynamic lubrication(EHL) friction model of hypoid gear tooth contact to reflect the realistic lubricant situation in gear transmission system consisted of full film contact and asperity contact. Under the mixed lubrication condition, the effects of time-varying friction coefficient on gear dynamic is analyzed. The load sharing coefficient is used to calculate the instantaneous friction coefficient at each contact point along the contact path. Friction coefficient model based on mixed elastohydrodynamic lubrication(Mixed EHL) is incorporated into the dynamic model to predict the dynamic mesh force and transmission error with constant and time-varying friction coefficient. The simulation results under a wide range of speed and load show that the time-varying friction coefficient has a marginal effect on the dynamic response.     

两级星型五分支传动静态均载分析

为分析两级星型五分支传动系统的均载问题,根据该系统构成功率流动闭环的特点,推导扭转角变形协调条件,结合力矩平衡条件,运用当量啮合误差理论,建立静态条件下的均载力学分析模型,求解得到均载系数,分析制造误差、安装误差、构件浮动对均载特性的影响。结果表明：太阳轮、内齿圈、星轮的误差单独影响均载特性时,内齿圈的误差影响最大,各构件制造误差影响的均载系数随时间做周期变化;太阳轮基于花键间隙浮动和内齿圈径向浮动,改善了均载特性,通过试验验证了理论分析的正确性。     

Intensity Comparative Analysis Based on Ideas Between Involute Gear and Double Involute Gear

Modeler and simulation modules in Ideas software are used to build the finite element models on involute gear and double involute gear with accurate tooth shape, and with the same design parameters and under the same loads, finite element contact analysis has been done. At last, the contact stress and bending stress on the two types gear transmission at the different meshing positions are solved out, and comparative analysis and study have been done. At the same time, that the ladder-shape tooth on the double involute gear how to influence contact stress and bending stress is emphatically analysed. All above offer the theoretical foundation that bring the double involute gear with ladder-shape tooth into the industry.     

Dynamic optimization design of marine gear transmission system

A dynamic model of transmission system for a marine gear is established considering time-varying mesh stiffness, mesh damping and tooth composite error. The solution efficiency is improved by taking contact line length change of gear pair instead of instantaneous gear mesh stiffness change and making mesh damping and tooth surface equivalent to viscous damping. Multi-objective dynamic optimization design is put into practice to improve the marine gear transmission system using vibration acceleration and mass as target function. The results show that the optimization method can effectively reduce the vibration level and mass of marine gear.     

Study on Surface Noise Distribution of Three ring Reducer

The three ring reducer is a kind of gear drive developed in the past decade. Adopting the new conception of "parallel and movable axis" of multiple mechanisms, this kind of gear drive has many characteristics such as large transmission ratio, high efficiency and so on. As the three ring reducer has been invented only for ten years, up to date the design of the gear drive is only made with analogue method, no design theory can be followed, there exist serious vibration and noise in transmission, which limit its wide application in industry. In this paper, the transmission principle of SHQ50 reducer is studied, the surface noise distribution of the reducer, transmission ratio 49.5 , is measured and analyzed by means of sound intensity method. The 3D distribution maps of noise on top of reducer, input side and output side of reducer, and left side and right side of reducer are drawn. With the sound intensity frequency maps of each measuring point, the sources of giving out noise are analyzed. The reducer of low vibration and noise can be designed rightly according to the analysis.     

MODEL EXPERIMENT OF HYPOID GEAR UNDER LOAD

The tooth contact mechanism of hypoid gear under load with similar model experiments is presented and the effect of mounting deflections and tooth deformation on tooth contsct is discussed. Thus, the basis of founding loaded tooth contact analysis calculating method of hypoid gear is brought about.     

Research on analysis of force and contacting stress for the discrete teeth harmonic drives

Mechanical analysis for the discrete teeth harmonic drive gear pair is carried out. The force on discrete teeth is calculated based on the deformation coordination equation,and the contact stress of meshing pair is obtained by Hertz equation. According to transmission periodicity of the discrete gear harmonic wave and the input angle values of continuous sampling wave generator,the distribution of discrete teeth harmonic drive meshing force and contract stress in rigid tooth profile,tooth wave generator and discrete teeth is obtained. By studying the top cutting phenomena in rigid tooth profiles,the change trend of meshing force and contact stress on the contact surface is found,and positions for high meshing force and high contact stress in transmission are also found,in order to provide reference for further intensity and structure optimization design.     

Contact analysis of a new style planetary reducer with a double crank and internal gear board

To address the problems of low carrying capacity and short life of bearings in current ring reducers, a new type of ring reducer is proposed which consists of a two stepped transmission. One is a planetary transmission, and the other is an N type planetary transmission with a low tooth number difference. Based on the analysis of structural features, the transmission principle, and a transmission load situation, a contact finite element model of the new type of ring reducer is set up, and the stress value and the actual pairs of meshing teeth are derived by calculation. Based on gear modification research theory, the second stage transmission gear pairs of the new reducer are modified on its teeth profiles. Results demonstrate that the load capacity of transmission gear pairs have been enhanced greatly.     

Determination of Load Share between Gear Teeth with Contact Finite Element Method

The determination of load share between teeth is a complex problem in gear strength calculation. On the basis of contact finite element method this paper considers the production-assembly error as initial gap to get the finite element model which meets load share between teeth in gear meshing. Through calculating and comparing the result with that from ISO formula to get the load share between teeth which meets the requirements in actual usage.     

Dynamic characteristics of multi-stage planetary gear trains in shield machine cutter drive

A purely torsional dynamic model of multi-stage planetary gear trains is developed to investigate the dynamic characteristics of the transmission system in shield machine cutter drive. In the model,phase difference between mesh stiffness and error among each stage caused by different initial mesh positions is considered,and other factors such as component bearing stiffness,time-varying mesh stiffness and error are considered as well. Inherent characteristic analysis shows there are more unique and diverse vibration modes in multi-stage planetary gear trains than in single-stage planetary gear trains. Through dynamic response analysis,time-domain and frequency-domain response of dynamic meshing force of each stage is obtained. As the frequency of exciting force of medium-speed and high-speed stage is in proximity to the natural frequency of the system,harmonic resonance tends to occur,which needs to be paid great attention to. Dynamic factors of each stage are also computed and prepare the ground for the dynamic optimizing design of planetary gear trains.     

风电齿轮箱传动误差分析及振动噪声预估

针对一级行星两级平行轴风电齿轮传动系统,综合考虑齿轮时变啮合刚度、啮合阻尼、传递误差等因素,建立31个自由度的弯扭轴耦合集中参数动力学模型,采用变步长Runge-Kutta法对系统动力学微分方程进行求解,得出齿轮传动系统各级传动误差;借助软件建立风电齿轮箱刚柔耦合动力学模型,并导入传动误差,采用模态叠加法求得齿轮箱轴承支反力,并将其作为声振耦合模型的边界条件,采用声学有限元法对风电齿轮箱进行振动噪声预估,并与试验结果对比分析,两者吻合良好。     

Pitch error measurement of high-order oval bevel gear on three dimensional measuring machine

Based on the prototype workpiece which is manufactured according to the high-order oval gear envelope method,a measurement method of high-order oval bevel gear is proposed in order to verify the correctness of design and manufacture method for this gear pair. The mathematical model of measurement and evaluation is established according to the spatial gear engagement theory. Then the coordinate point set obtained from three-dimensional measuring machine is analyzed and filtered based on the actual measurement on prototype workpiece. Therefore,the ideal element is available. And then the aberration curve of pitch curve,individual circular pitch error and accumulated error can be obtained after analyzing the point set. Finally,the conclusion that the high-order oval bevel gear pitch error evaluation method is feasible can be obtained because the measurement and analysis result dovetailed basically with the theoretic calculation result.     

Contact Analysis of worm gearing under the Condition of the Errors and the Load

The contact analysis on the double enveloping hourglass worm gearing is very important to control its efficient contact zone and contact quality. Nevertheless, current meshing analysis under the rigid condition cannot really reflect its tooth-surface contact. In this paper, the contact Finite Element Method is used to analyze the tooth contact of double enveloping hourglass worm gearing under the manufacturing error and the elastic deformation caused by the load. The load sharing among the contact tooth pairs and variations of contact zone are investigated. As compared with the result of rigid analysis, the contact zone is obviously shifted. This analysis method can provide a base for the conjugating control of the double enveloping hourglass worm gearing.     

Bending Stress Analysis on Backlash Adjustable Worm Transmission

The full name of variable tooth thickness plane worm gear transmission is. Backlash adjustable plane worm gear with variable tooth thickness enveloping worm transmission, which is a new kind of accurate power transmission that is intervenient between traditional motion transmission and power transmission. Tooth surface equations of the variable tooth thickness plane worm gear transmission are deduced based on the theory of engagement. Basing on the result, the authors create a finite analysis model of backlash adjustable variable tooth thickness plane enveloping worm with perfect tooth shape by using I-DEAS software, and then has done finite element analysis of backlash adjustable variable tooth thickness plane enveloping worm transmission. Finally, the author drew a conclusion about distribution of principal stress and load distribution between teeth, which offer some references for strength and performance analysis of worm transmission.     

Method and Analysis of Time Series Model for Transmission Error

This paper presents the time series model of gear drivetrain error and a compari-son amang several typical time series spectrum estimations.and suggests a time series model suitablefor discribing transmission error.     

Dynamic characteristics research of gear coupling rotor system in gas turbine

Taking the sliding bearing into account, the lateral vibration analysis models of two single rotor were built respectively using the transfer matrix method. The transmission matrix of herringbone gear coupled unit is derived. Using whole transfer matrix method, the lateral torsional coupling analysis model of herringbone gear rotor system is set up, and the vibration characteristics of gear rotor bearing system in gas turbine is analyzed. Through numerical calculation and anlysis, the eigenvalue of gear rotor system, the Logarithmic decrement and the critical speed are obtained. The result shows that the working speed of this gear rotor bearing system is far away from the critical speed, therefore the system is stable and safe.     

Transmission model of higher-order elliptical bevel gearing and motion simulation for interference checking

Higher-order elliptical bevel gear is a typical form of the noncircular bevel gear transmission.Space spherical coordinate system of the bevel gear meshing is set up based on the meshing theory of space transmission.The varying relationship among the pitch curve,tooth profile and mesh lines are analyzed,and the equation of the gear tooth surface is developed with matrix method based on space coordinate transformation.The basic parameters of the noncircular bevel gear such as transmission ratio,modulus and the number of teeth are designed,and detailed analysis of the influence of the eccentricity on the relevant parameters is carried out as well.By using discrete numerical method and three-dimensional software,the mathematical model of the tooth profile and virtual physical model of the noncircular bevel gear are established,and then simulation on its motion and interference checking are performed.Finally,the approach for design,calculation and generation of the tooth profile is obtained and its correction has been verified by experiment.     

The Analysis of Bending Deformation of Cutter Tooth and Gear Tooth During Shaving Process

In this paper,the variation pattern of the contact point on cutter tooth and gear tooth is analyzed during gear shaving process. According to the shaving force measured by dynamometer, the deformation of cutter tooth and gear tooth at the contact point is calculated by appying the three dimension finite element method. The deformation curve of cutter tooth and gear tooth are obtained by analying deformation in shaving domain. It is the basis of studying relation between shaved amount and deformation.     

Gear-bearing coupling dynamics characteristics of wind turbine planetary gear transmission system under variable load

Considering that the transmission system of wind turbine works in complex and changing load environment caused by stochastic wind speed,this paper uses sparse least squares support vector machine(SL-SVM) to simulate wind speed of true wind field,and obtains time-varying wind load caused by stochastic wind speed. The lumped-parameter method is used to develop a dynamic model of planetary gear transmission system of wind turbine coupled with bearing. The model includes the varying wind load,time-vary mesh stiffness of gear pair and time-vary stiffness of rolling element bearing. The numerical method is used to simulate the dynamic performance of planetary gear system of Multibrid Technology Wind Turbine with 1.5 MW rated power. The vibration displacement responses of the transmission system are obtained as well as dynamic meshing force each pair of gear and nonlinear bearing forces. The research can provide a foundation for optimizing dynamic performance and reliable design of gear transmission system of wind generator.     

Numerical simulation of the internal dynamic excitation of a spiral bevel gear transmission

A 3-D geometry model and a static/dynamic finite element (FE) model of a spiral bevel gear transmission are established. Using ANSYS software, the mesh stiffness excitation of a tooth pair is calculated via the static contact FE method. Using LS