Analysis and test on vibration and acousticnoise of GWC6066 marine gearbox

The mesh stiffness of gear tooth is simulated by spring elements, the connected bolt between various housings are simplified as bar elements, and the sliding bearing and rolling bearing are simplified as spring dumping elements. Based on them, the gear-shaft-bearing-housing coupled finite element model and boundary element model of GWC6066 marine gearbox are established. Finally, the dynamic response under internal dynamic excitation is analyzed and the vibration severity, structural-borne noise and air-borne noise of the gear system are forecasted. Through the experimental modal analysis of gear system, and the test of vibration response and air pressure, the natural frequencies, vibration severity, structural-borne noise and air-borne noise are obtained. Compared with numerical results, two results show good agreement.     

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 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.     

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.     

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.     

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     

风电增速齿轮箱动力学性能优化方法

建立增速齿轮箱动力学分析有限元模型,利用Lanczos法求得齿轮系统的振动模态;以齿轮副时变啮合刚度激励、齿面综合误差激励和轮齿啮合冲击激励为内部作用激励,采用直接积分法求得箱体表面节点的动态响应。选取箱体上12个主要结构参数作为动力学性能优化的设计变量,齿轮箱体积为状态变量,以齿轮箱表面振动加速度的均方根值最小为动力学性能优化的目标函数,利用零阶与一阶优化算法求得最优设计变量。结果表明：优化前后箱体均不产生共振,且满足静力学条件;优化后目标函数减小37.5%,箱体各计算点的振动响应均有较大幅度的减小,最大减小量为54%。     

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.     

Dynamic analysis of wind turbine gearbox

By inputting reduced matrix of stiffness and mass, a dynamic model including flexible housing, ring gear and carrier for a 3 MW wind turbine gearbox is established based on MASTA. And analysis results show that the kinetic percentage of housing is maximum near the gear mesh frequency and response is maximum at the 1st mesh frequency of HSS gear. The analysis results show certain agreement with vibration test results. This paper can provide reference for avoiding vibration in gearbox design.     

Vibration characteristics of face-gear transmission system with parametric excitation

In order to study the influences of different factors on nonlinear dynamics of face-gear transmission system, a nonlinear dynamic model is presented. This model includes backlash, general transmission error, time-varying meshing stiffness, meshing damping, bearings and external load, etc. Based on numerical analysis theory of nonlinear dynamics, the equations are solved and the bifurcation characteristics with different parameters are obtained. And the calculation results show that increasing the backlash and time-varying meshing stiffness will augment the dynamic load of system, but increasing the mesh damping will reduce the dynamic load effectively.     

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.     

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.     

Dynamic Optimization of System Parameters For the Epicyclic Gear Drive with Internal Tooth

The epicyclic gear drive with internal tooth has been analysed,the formula has been also deduced for computing the inertial force and change of contact force,and the dynamic optimization of system parameters for the force of bearing has been carried,it has given a reliable proof to reduce the dynamic load and prolong the life of bearing of three ring type reducer.     

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.     

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.     

Experimental study on vibration and structure noise of marine gear box with heavy load

The performance requirements of marine gear box are much higher than that of other gear boxes due to its special working conditions. The structure and transmission principle of a high-power marine gearbox are analyzed, and the experimental test is carried out for the analysis and calculation of its vibration characteristics and intensity. Measured by FFT analysis of vibration signals, the main peak is caused by its octave and the engagement frequency of input stage and middle-class transmission. The vibration severity of high-power marine gearbox reached 4.47 mm/s. In addition, the calculated structure noise of the measuring points is at the 1/3 octaves, and the largest structure noise is 131.27 dB which occurred in the frequency of 329 Hz.     

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.     

Influence of Motorcycle Noise on Gear Transmission

The study of motorcycle's acoustic signal shows that gears noise take a great proportion on the whole acoustic of motorcycle.So how to control the noiseof gears is very helpful for reducing the whole motor's acoustic.This paper discusses the engine matching with transmission system in reason,primary transmission and gear geometry design parameter & the mend of tooth body(tooth form & tooth direction) how to influence the acoustic of motorcycle.The study shows that the gear transmission System's matching with engine in reason can notable improve the efficiency of motorcycle.In the meaning time the exactly choosing the primary transmission gear geometry design parameter and the mend of primary transmission gear's tooth body can effectively reduce the acoustic of motorcycle.This paper has engineering practice sense.     

Analysis on new gyratory fixed spindle cycloid drive

The current cycloid reducer drive has the shortage of needing special output mechanism, large volume and high vibration. To solve this problem, a new gyratory fixed spindle cycloid drive is designed. The drive principle of the reducer is introduced. Formula for calculating the basic parameters and tooth profile equation of cycloid gear are derived. On the basis of discussion of the mechanism and the principles of gear connection, a prototype is designed and manufactured. The results of the prototype test on the gear test rig indicate that the transmission efficiency of the new drive may reach 91.9% at rated operating conditions, the biggest vibration velocity effective value is 3.09 mm/s, and the biggest structure noise is 101.6 dB.     

Power Model of Bond Graph and Dynamic Simulation of Hoist System for Multi-Flow Transmission

The double drive hoist reducer developed in the planetary gear is a new generation of energy saving and environment protecting hoist product. The multi flow transmission system theory of hoist is analyzed. With the theory and method of bond graph,a bond graph model with coupled vibration is established for hoist multi flow transmission system for the first time. The state equation of the system is developed and dynamic simulation analysis is also carried out. The internal changing law and relationship of the system for the state variable are got. Therefore, the dynamic properties and gearing features of this system are revealed comprehensively. The research results can provide the dynamic analysis method and design basis for multi flow transmission system of hoist.