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.     

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.     

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。     

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.     

Longitudinal Vibrations of a Single Pile in Saturated Viscoelastic Soil

Based on Biot's theory, the longitudinal vibrations of a single pile in saturated viscoelastic soil are investigated in the frequency domain subject to the harmonic load. By the Novak plane strain model, the control equations for the saturated viscoelastic soil are derived. Regarding the pile as the one-dimensional rod model, the vibration equation of the pile is established. Based on the continuity conditions of the pile and soil, the dynamic stiffness and dynamic damping of the pile top are obtained. It is compared with the solution for Novak, and the influence of different physical parameters of the pile and soil on the longitudinal vibrations of the soil and pile system is examined. It is shown that the dynamic characteristics of the pile in the dry soil as well as the saturated soil have some differences; the resonance effect of dynamic stiffness factor and equivalent damping is obvious weakening with the increase of the ratio of the length to radius of the pile. The resonance effect and natural frequency are increasing when the modulus ratio of the pile to soil increases; the interaction coefficient of the flow-solid and the damping ratio of soil skeleton have few influences on the responses.     

Method for Calculating Steady Vibration Response of Shafting with Local Nonlinearity

A method which is used for calculating steady vibration response of shipping propulsion shafting connecting with a coupling with nonlinear hysteresis characteristics are studied. On condition that the nonlinear dynamic stiffness and hysteresis damping of the coupling be considered, on the basis of GLM(Galerki Levenberg Marquard) method, a method called SSGILM(Separate System Galerkin and Improved Levenberg-Marquardt)to be used for calculating steady vibration response of propulsion shafting with local nonlinear dynamic stiffness and hysteresis damping, is proposed. A simple example is given out and the analyses show that it is effective to calculate steady vibration response of the shafting with local nonlinear dynamic stiffness and hysteresis damping by SSGILM method. From initial response values given arbitrarily, the automatic search algorithm in SSGILM method can converge the given initial response values to the response values accorded with required accuracy quickly; nonlinear dynamic stiffness and hysteresis damping of the coupling have different effect on vibration response of the shafting at different range of frequency. At the area of close nature frequency of the shafting ,displacement amplitude of the shafting is bigger. Beyond the range, the characteristics of the coupling have restraint effect on vibration of the shafting.     

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.     

基于行人动力学模型的人桥竖向动力相互作用

基于行人动力学模型,研究了人桥竖向动力相互作用。行人动力学模型采用以行人步频和体重表示的刚度质量阻尼（SMD）模型,人行桥假定为Euler-Bernoulli梁模型,建立人桥竖向动力相互作用控制方程。采用状态空间法进行非比例阻尼系统瞬时模态的求解,得到系统的时变频率和阻尼比;利用变步长四阶五级Runge-Kutta-Felhberg算法求解时变控制方程,对比分析考虑人桥竖向动力相互作用和只在人行荷载作用下人行桥的动力响应。结果表明：考虑人桥动力相互作用,人行桥自振频率略有降低,阻尼有显著增大;当行人以人行桥的频率行走时,考虑人桥竖向动力相互作用结构的动力响应比不考虑人桥相互作用显著降低。     

Multi-objective dynamic optimization design of high-power wind turbine gearbox

A dynamic model of NGW helical planetary gear transmission for high-power wind turbine gearbox is established by considering these factors as errors of gears and time-varying mesh stiffness by using mass centralized method. Moreover, the random wind velocity is simulated as external seismic excitation making the results more conform to practical condition. And on this basis, this system is optimized for minimum gearbox volume and minimum component torsional acceleration with the restriction of reliability and strength restrain. The result indicates that the optimized parameters make gear transmission lightweight and the dynamic property improved so as to reduing vibration and noised.     

Modeling and Simulation Analysis of the Electromechanical Coupling Facts about Precision Transmission System

Electro-mechanical coupling facts about transmission system influence dynamic characteristic and response characteristic of servo system. The coupling factors of precision transmission system are put forward, and the modelling methods of electro-mechanical system are analyzed. Based on the large-scale precise horizontal machining center, the dynamic chart of servo feed system is gained through analyzing mathematical model of the taehes, and the influence on transmission stiffness and transmission error is simulated in precision transmission system. Through changing parameters in servo feed system, the influence on dynamic characteristic and response characteristic is analyzed, so it provides a mathematical model for parameter optimization.     

Mechanical Performance of a Vertical Seismic Isolation System Employing a Dish Spring

The base isolation technique has been widely used in different countries to reduce seismic disasters during earthquakes. But most of these devices are effective only in horizontal earthquake responses and do not work well in vertical earthquake responses. We propose a vertical seismic isolation system composed of a dish spring and a visco-elastic damper. To study the stiffness and damping performance of this isolation system, a series of tests under static and dynamic loads were performed. The results show that this system is effective in solving problems related to strong vertical bearing capacity and vertical damping of vertical isolation. The system has not only appropriate vertical stiffness and damper performance, but also excellent mechanical performance. In addition, it is compact, easy to manufacture, and can serve as an ideal vertical damping device.     

Junction stiffness analysis and vibration noise prediction of wind power speed-increase gearbox

In order to study the vibration characteristics and radiation noise of wind power speed-increase gearbox, a torsional vibration model of wind power speed-increase gearbox is established based on the analysis of supporting stiffness of bearing and contact stiffness of gear pairs. By solving the vibration differential equation with the help of Matlab, the frequency and corresponding vibration mode are obtained. With taking stiffness excitation, error exaction and meshing impact exaction into account, the dynamic finite element model of speed-increase gearbox is set up, and the dynamic response simulation is carried out. Regarding vibration displacement of the nodes on gearbox surface as boundary condition, an acoustic boundary element model of speed-increase gearbox is built. The surface acoustic pressure of gearbox and the radiation noise of field points are solved by the direct boundary element method. The results show that there is a great difference between torsion frequency and excitation frequency of wind power speed-increase gearbox, and so the resonance doesn't occur. The maximum structural noise and radiation noise mainly appear near the double octave of the gears meshing frequency of high-speed grade.     

The Research on Stiffness of Double Involute Gear with Ladder shape Teeth

The stiffness of the tooth with different profile parameters,meshing stiffness and the coefficients of loading distribution allowing for no error are calculated and analyzed on double involute gear with ladder shape teeth for the first time,and the results are made comparison with traditional involute gear;The stiffness of the double involute gear and the meshing stiffness are both increased,and the coefficients of loading distribution are basically unchanged.The energy integration method is also put forth to solve stiffness approximately by linear approximating the tooth profile curve.     

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.     

Dynamic optimization design of gear transmission system for wind turbine

The differential equation which governs the behavior of the gear transmission system of 1.5 MW wind turbine is established. The external excitation caused by wind speed fluctuation is discussed and the internal excitation due to time varying mesh stiffness and comprehensive error is also analyzed. The calculating formulations of the harmonic balance method of nonlinear dynamic equations are presented. Then, the multi objective dynamic optimization model is developed to minimize the value of vibration acceleration and the overall volume. The optimization of a practical example using mixed discrete combined programming is performed. The result shows that the proposed method of modeling and optimization design can effectively reduce the wind turbines gearbox vibration levels and weight.     

落锤冲击气囊施加均布动荷载的试验方法

在结构构件上施加均布冲击(爆炸)荷载一直是动力试验领域的难题。提出了一种落锤冲击气囊施加均布动荷载的试验装置,和一个双自由度弹簧阻尼冲击加载简化分析模型;给出了该模型的基本力学方程、边界条件和求解方法,并进行了有限元验证;建立了所提出冲击加载试验装置的精细化有限元模型,分析了构件上各受荷区域的荷载均布情况,验证了所提出装置的可行性。基于所建立的简化分析模型,讨论了刚度、荷载作用时间和阻尼比等关键参数,对构件上动荷载的影响,并给出了基本规律。计算结果表明,在选定合适的参数后,落锤冲击气囊试验装置能够较好地模拟构件上的均布动荷载,为实验室中进行爆炸冲击试验提供了一种可能。     

A NONLINEAR PROGRAMMING MODEL AND ITS ALGORITHM FOR TRANSMISSION NETWORK PLANNING

The problem of transmission network planning is studied thoroughly by applying the mathmatical optimal tecqhniue in this paper. A novel approach is put forward for computer aided transmission network planning, which is quite different from what is based on D.C. load flow equations. A nonlinear transmission planning model is set up by regarding A.C. load flow equations as the system model. A practical model which can be solved more easily, and an united algorithm are obtained by applying the SUMT to the nonlinear model. The results of some practical examples indicate that this method can not only make the planning results more accurate, but also provide the voltage qualities and produce planning plans autometically and seek the plans optimally and fast.     

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.     

Robust H control for vehicle seat suspension systems with stochastic disturbance

The paper proposes the design method of robust H controller of vehicle seat suspension system. The dynamic model of seat suspension is developed,and the parameters uncertainties (mass, stiffness, damping) and stochastic vibration are introduced into the model system. Based on stochastic differential theory and Lyapunov functional, a semi controller is designed, and the controller parameters are solved by linear matrix inequality (LMI) which guarantees H performance index. The simulation results in time domain and frequency domain show that the controller designed for parameter uncertainties and stochastic vibration can attenuate the vertical acceleration of suspension system and improve riding comfort of human.     

Numerical Prediction of Frequency of Delaminated Advanced Grid Stiffened plate

The paper aims to investigate natural frequency of delaminated advanced grid stiffened composite plates by hump resonance method.The composite laminated plate element and the rib element are adapted to simulate the laminated plate and the ribs.Based on the composite laminated plate and beam element model considering first-order shear effect,a damping model on the basis of Rayleigh damping model in conjunction with Adams' strain energy method(MSE) and a Hertz nonlinear dynamic contact model to avoid the overlap and penetration phenomenon between the upper and lower sub-laminates at the delaminated region.A numerical analysis method of dynamic response for the delaminated composite plates is carried out by precise time-integration method,and then the natural frequencies are achieved when the dynamic deflections reach the hump peak.For the frequency-domain analysis provided in the former research papers,it is a difficult problem to avoid the embedded phenomenon in the mode shapes at the delamination zone,while in the current time-domain analysis,the embedded phenomenon can be successfully overcome by using nonlinear contact model.By vibration excitation test,the specimens were excited by different excited frequency and the amplitude frequency response characteristics obtained are used to extract the frequency.The extracted frequencies of the narrow delaminated composite plates measured,which agrees well with the predicted natural frequencies.