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。     

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.     

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 the Comparison of Different Methods of Simplifying Capacity Spectrum

It is necessary to simplify the capacity spectrum into bilinear form so as to get characteristic point of hysteretic bone curve(especially the yield point and the yielded stiffness),ductility and equivalent damping of the structure.Three general methods of calculating yield point and yielded stiffness of equivalent SDOF are introduced and the yield point and the yielded stiffness of three frame structures are compared using above given methods in this paper.The hysteretic bone curves of equivalent SDOF are decided by the equivalent yield force and displacement,the maximum plastic displacements of equivalent SDOF under rare earthquake are calculated,and it is compared with the maximum plastic displacements of member structures using nonlinear dynamic analysis.Finally,the advice of simplifying capacity spectrum is advanced.     

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.     

Error Analysis between Relative Motion Solving Method and Absolute Displacement Direct Solving Method

Under multi-support earthquake excitation, the damping is proportional to the relative velocity in relative motion method, While the damping is proportional to the absolute velocity in method of direct solving absolute displacement, and the damping assuming difference may cause the calculation errors on structural responses. The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model, which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures. Based on probability theory, the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis, and some numerical examples are provided to verify the error analysis. At last, it is pointed out that the calculation errors between the two solving methods decrease with damping ratio, and it is negligible when the damping ratio of structure is less than 5%.     

Calibration of Nonlinear Dynamical Analysis for RC Frame-wall Structure with Slender Coupling Beams Considering Stiffness Reduction

Two 16-storey frame-wall structures with slender coupling beams in regions of Intensity 8(0.2 g),with and without considering the stiffness reduction of the coupling beams,were designed.Nonlinear dynamic response analyses of two typical frame-wall structures subjected to several ground motions were carried out.The analyses were based on the quasi-tridimensional program for nonlinear dynamic response analysis TS-EPA.The analyses led to the following conclusions: Under rare earthquake actions,the coupling beams in framewall structures yield first.This shows that the coupling beam in frame-wall structures is the member at the forefront of earthquake resistance.Comparison of the analytic results of two couples with and without considering the stiffness reduction of the coupling beam found that,in view of the dynamic response to and the requirement for ductility under rare earthquake motions,reducing stiffness causes a minor unfavorable influence on the dynamic response of frame-wall structures.     

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.     

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.     

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.     

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.     

Finite element model of coupled systems for vibration reduction plates with smart constrained layer damping

Considering the relationships of coupling movement and compatible displacement among bonding layer, piezoelectric layer, damping layer, and base structure, a finite element dynamic model of coupled systems for vibration reduction plates is established. The model combined with piezoelectric theory, finite element theory and ADF model of viscoelastic damping material can be suitable for vibration model of complex SCLD structure. The dynamics parameters for clamped-clamped steel plate with partially treated smart constrained layer damping are obtained by theoretical calculation, ANSYS modal analysis and modal experiment. The results show that theoretical values are closer to the test results and ANSYS analysis, and the methods proposed is more accurate and effective.     

Nonlinear Analysis Method for Seismic Responses Considering Pounding between Girders of Curved Bridge with LRBs

A nonlinear constraint-surface impact element (CIE) was developed for simulating the pounding in axial direction between 3D shell-element-mesh bridge girders based on the engineering background of ChaoShan airport. Then, a method, different from the previous literatures, for calculating the stiffness of impact element was proposed based on the flexibility method. The methods proposed were adopted and used to analyze the elevated bridge of ChaoShan airport in GuangZhou for the purpose of investigating comprehensively the earthquake-resistance capability. The bridge girders were modeled by shell elements and CIEs were assigned to the positions of the corresponding expansion joints. Isolating elements were used to simulate LRBs, and typical bilinear LRB hysteresis stiffness model obtained from experiment were adopted to describe the dynamic hysteresis behavior. Pounding forces, dissipation capability of LRBs, lateral displacements of LRBs, pier base shear forces and moments as well as the pounding effect on these cases were investigated, respectively. The proposed methods and analysis results aim at improving the earthquake resistance of the elevated bridge, which provides reference for the similar project.     

刚性连体位置对非对称双塔连体结构动力可靠度的影响

考虑地震动的非平稳性,变化连体位置,对非对称双塔连体结构运用虚拟激励法进行非平稳随机激励下的动力可靠度研究。采用刚度退化的Bouc-Wen模型模拟塔楼各楼层的滞变特性,建立非线性化动力方程。运用混合精细积分法对每一时刻的响应进行求解,得到连体位置变化时非对称连体结构在非平稳随机激励下的时变方差。基于首次超越破坏准则与Markov假定,研究非平稳随机地震激励下连体结构的动力可靠度。运用上述理论,在8度罕遇地震作用下对某非对称双塔连体结构进行随机地震响应与动力可靠度分析。研究结果表明,地震作用下结构的层间位移响应呈现强烈的非平稳性,变化连体位置对连体结构的随机地震响应与动力可靠度将产生显著影响。     

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.     

Practical Method of Form-finding of Semi-rigid Structures

Based on the discussion of the simulation for the cable prestress, the rigidity theory was used to identify the geometrical dimensions of semi-rigid structures in zero state. When the structural geometry in initial state is given, the geometrical dimension in zero state is determined by the initial prestress distribution. The contribution-matrix method is firstly applied to get the initial lack of fit. However, the influencing factor of initial lack of fit on the displacement of control point is linear superposition, that is, the structural response is linear, and it is irreconcilable with the geometry nonlinear of semi-rigid structure. In order to reduce the error of nonlinear structural response, the influencing factor in the contribution-matrix method is revised, and modified contribution-matrix method is put forward. Programs by ANSYS parameter design language APDL are worked out for the form-finding analysis of beam-string structure of a practical project. The numerical results show that the modified contribution-matrix method reduces the errors of the assumption of structural linear response. And it can be applied to the form-finding of semi-rigid structures with small stiffness.     

MODIFYING STRUCTURAL DYNAMIC MODEL USING AN INCOMPLETE SET OF MEASURED COMPLEX MODES

A method is presented in this paper which uses an incomplete set of complex modal parameters identified from the experimental date to modify the structural dynamic model. The method, not requiring iteration and being programed easily,is suitable for the complex structures with general viscous damping in improving the analytical mass, damping and stiffness matrix madel of a structure with a set of minimum changes in the analytical matrics, so as to force the eigensolutions to agree with the test measurement. An example is given to demonstrate the validity of this proposed method.     

Experimental Analysis of Vibration Behavior for Large-span Underground Structure

In this paper, a shaking table test for large-span underground structure is introduced. Based on the test, the frequency of inherent vibration, damping ratio and the dynamic response of the structure are studied. The response of the underground structure for vertical seismic excitation is studied as a key point. With the different imbedding depth, the influence of interaction of soil and structure on the earthquake-resistant capacity of the underground structure is discussed.     

Perturbation Analysis of Complex Modes for Vibration System with Viscous Damping and Its Application

The sensitivity characteristics of the undamped natural frequencies and complex mode shapes of vibration system with the non-proportional viscous damping with respect to structural mass, stiffness and damping modifications are analyzed in this paper using the matrix perturbation of complex modes. The general principles for the selectivity of the design and the most sensitive positions of the structural perturbation modifications are shown thereby. This is of importance to a great computational savings in the dynamic characteristic improvement of large or complex structures. By the dynamic characteristic sensitivity analysis of a test device type RDT-1,the optimal structural design for its especial requirement of dynamic characteristics is obtained easily and the principles presented in this paper are confirmed by the numerical results of perturbation analysis.     

Analysis on Dynamic Properties of Monolayer Cable Net for Point -supported Glass Facade

Monolayer cable net system for point - supported glass facade is a kind of flexible tension structures with relatively strong nonlinearity. Its stiffness greatly depends on the pretension in cables. Yet there are few literatures at present reported on its dynamic properties. The characteristic of modal analysis for flexible pre - stressed structures such as cable structures is expatiated herein. Corresponding program was developed to analyze two important factors such as pretension and geometric nonlinearity for dynamic behaviors of cable net herein. It is demonstrated that large errors are brought about by omitting nonlinearity. There exists apparent nonlinear relationship between vibration frequency and pretension in cables. The influence of pretension and geometric nonlinearity on the dynamic properties of cable net is in coordination with each other.