Dynamics and Control of Grinding Machine with Micropositioning Workpiece Table

To improve the machining precision of a surface grinding machine, a micropositioning workpiece table with high performance was used as auxiliary infeed mechanism to implement nanometer level positioning and dynamic compensation. To better understand the characteristics of the grinding machine modulated with micropositioning workpiece table, the dynamic model of the grinding system was established with modal synthesis and Lagrange's equation methods. The grinding system was divided into five subsystems. For each subsystem, the generalized kinematic and potential energies were obtained. Accordingly the dynamic model of the grinding system was given in the modal domain. The waviness of the grinding process was achieved based on the wheel and workpiece vibration. A nonlinear proportional integral derivative (PID) controller with differential trackers was developed to realize dynamic control. The simulation results show that the machining accuracy of the workpiece can be effectively improved by utilizing the micropositioning workpiece table to implement dynamic compensation. An experimental test was carried out to verify the proposed method, and the waviness of the workpiece can be reduced from 0.46 μm to 0.10 μm.     

A generalized sinusoidal model and its applications

A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period （frequency） of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.     

Nonlinear dynamic analysis of the whole vehicle on bumpy road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of the nonlinear system was verified.Numerical results by 4-order Runge-Kutta method presented the multiform dynamic behavior of the system.     

Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beams with Damage on a Viscoelastic Foundation

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.     

Fault diagnosis of cylindrical grinding machine

Based on experiment modal analysis(EMA) and operation modal analysis(OMA), the dynamic characteristics of cylindrical grinding machine were measured and provided a basis for further failure analysis.The influences of grinding parameters on dynamic characteristics were studied by analyzing the diagnostic signals extracted from racing and grinding experiments.The significant frequency of 38 Hz related to grinding wheel spindle speed of 2 307 r/min showed that the wheel spindle system was in a state of imbalan...     

考虑剪切效应有限变形粘弹性板的动力稳定性

Based on Reddy‘s theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.     

Analytical model of vertical vibrations in piles for different tip boundary conditions: parametric study and applicationsx

In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load.     

Shaking table test of pile-water-pier superstructure

The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier system for developing more reliable design procedures, shaking table model tests of a submerged bridge pier system, including pile groups-cap-pier and inertia mass, were conducted. Since different similitude laws corresponding to different test objectives affected the validity of test results, the similitude law with the aim to consider the effect of hydrodynamic pressure was proposed and confirmed through an actual example. Based on the test results, the effect of water around model on seismic response under seismic excitation input was analyzed and the failure level was judged by observing the variation of basic frequency. The test results indicate that the transfer function of analytical model with water is different from that without water, the natural frequency without water is always higher than that with water, and the first modal shapes are various. It is also concluded that the similitude law is suitable for practical application and the dynamic characteristics and seismic response of the structure system can be changed because of the existence of the surrounding water, which should be paid much attention in the further investigation.     

Transient Responses of Flexible Non—uniform Spinning Shaft with Nonlinear and Asymmetric Supports

In this paper ,a hybrid approach was developed to investigate the transient responses of a multi-span non-uniform flexble spinning shaft with nonlinear and asymmetric supports.The non-uniform spinning shaft with variable parmeters was modeled as a Bernoulli-Euler beam column with sectional constant cross-section properties by the finite element method.The supporting stiffness behavior of the nonlinear supports was described as a piecewise-linear and asymmetric model.The equations of motion in the matrix form of a multi-span non-uniform spinning shaft with nonlinear and asymmetric supports were formulated using Hamilton‘s principle and the assumed mode method.As an example,a spinning rocket with many variable stiffness supports was numerically simulated by the direct integration method.The transient response and dynamic behavior of this rotate-dynamic system are analyzed.     

Translational torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational ? torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.     

Dynamic characteristics analysis of a misaligned rotor-bearing system with squeeze film dampers

In this paper, a dynamic model is established for a two-stage rotor system connected by a gear coupling and supported on ball bearings with squeeze film dampers (SFDs). The nonlinear dynamic behavior of the rotor system is studied under misalignment fault condition. The meshing force of the gear coupling is calculated considering the deformation of the tooth caused by torque transmission and dynamic vibration. The contact force between the ball and race is computed based on the Hertzian elastic contact deformation theory and the elastohydrodynamic lubrication theory. The supported force of SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion are rewritten in non-dimensional differential form, and the fourth-order Runge-Kutta method is employed to solve the nonlinear dynamic equilibrium equations iteratively. To verify the validity of the dynamic model and the correctness of the numerical solution method, the experimental power spectra of the rotor system under various misalignment degrees are compared with the analytical results. The effects of several important parameters, such as the lubrication of the ball bearing, the centralizing spring stiffness, the radial clearance of SFD, and the misalignment of gear coupling, on the dynamic characteristics of the rotor system are investigated and discussed mainly focusing on the system stability. The response spectra, bifurcation diagrams, and Pointcaré maps are analyzed accordingly. These parametric analyses are very helpful in the development of a high-speed rotor system and provide a theoretical reference for the vibration control and optimal design of rotating machinery.     

扁球面网壳在动静荷载作用下的非线性稳定性

根据薄壳非线性动力学理论和拟壳法的思想,给出了扁球面网壳在动、静荷载协同作用下的非线性动力学控制方程.然后利用扁球面网壳的非线性动力学变分方程和协调方程,在夹紧固定的边界条件下,通过Galerkin作用得到一个含二次和三次的非线性动力学微分方程.用Floquet指数方法研究了系统的分岔问题,讨论了平衡点（奇点）邻域的稳定性问题.指出了系统在纯动态作用和在动静荷载协同作用下其平衡位置的变化情况.     

非线性双圆盘转子-密封系统的数值分析

研究目的：求斛双圆盘转了-密封系统的非线性振动特性和运动响应 创新要点：采用有限元法（FEM）和拉格朗目方程求解双圆盘转子-密封系统,进而为研究多级转了系统的非线性振动问题提供有效方法。研究方法：基于有限元法（FEM）和拉格朗目方程。同时利用四阶龙格-库塔法求解系统动特性运动响应情况,利用风岔图、时间历程图、轴心轨迹图、庞加莱映射和幅值谱等分析图研究双圆盘转子-密封系统的非线性振动特性。重要结论：随着转速的增大,双圆盘转子-密封系统呈现丰富的非线性运动形式,包括周期性运动、多周期运动,准周期运动以及混沌运动。在右端圆盘不平衡质量小于34kg、密封间隙范围为0.376mm-0.54mm、密封长度大于0.13m或者密封压差高于0.104MPa的情况下均有利于提高双圆盘转子-密封系统的稳定性。     

基于MLP法的磁浮列车非线性系统的稳定性分析

以磁浮列车的垂向运动为研究对象,研究其非线性系统的稳定性。选取气隙值、电流值为磁浮列车悬浮系统的广义坐标,依据拉格朗日-麦克斯韦方程建立磁浮列车非线性悬浮系统的动力学模型,得到的振动方程是三阶的强非线性负刚度微分方程。应用MLP法求得系统的共振永年项条件,并对初始方程进行了数值计算,得到了磁浮列车在空载、满载、过载情况下的悬浮系统振动时间响应曲线和相图,结果表明:随着列车质量的增加,列车初始位移增加,但列车启动后50 s的时间内,系统振动趋于稳定。     

Nonlinear dynamic analysis of a rotor/bearing/seal system

In this study a new dynamic model of a rotor system is established based on the Hamilton principle and the finite element method (FEM). We analyze the dynamic behavior of the rotor system with the coupled effects of the nonlinear oil film force, the nonlinear seal force, and the mass eccentricity of the disk. The equations of the motion are solved effectively using the fourth order Runge-Kutta method in MATLAB. The dynamic behavior of the system is illustrated by bifurcation diagrams, largest Lyapunov exponents, phase trajectory diagrams, and Poincaré maps. The numerical results show that the rotational speed of the rotor, the pressure drop in the seal, the seal length, the seal clearance, and the mass eccentricity of the disk are the key parameters that significantly affect the dynamic characteristics of the rotor system. The motion of the rotor system exhibits complex types of periodic, quasi-periodic, double-periodic, multi-periodic, and chaotic vibrations. This analysis can be used to guide the design of seal parameters and to diagnose the vibration of rotor/bearing/seal systems.     

基于Hamilton原理的双跨转子系统建模和转子动态特性分析

研究目的：研究双盘双跨转子/轴承/汽封系统在非线性油膜力和非线性汽封力共同作用下的动力学特性,分析了转子转速、密封力、油膜力和联轴器刚度等因素对转子稳定性的影响。创新要点：采用Hamilton原理和有限元方法建立双盘双跨转子/轴承/汽封系统模型,使得双跨多节点的转子系统数值求解更加容易。研究分析转子转速、非线性密封力、非线性油膜力和联轴器刚度等因素对转子稳定性的影响,为大型转子系统的设计提供理论基础。研究方法：采用Hamilton原理和有限元方法建立双盘双跨转子/轴承/汽封系统模型（图1和2）。应用四阶Runge-Kutta法进行数值求解,并采用轴承处、圆盘处的分岔图、时程图、庞加莱映射图、频率图和相轨迹图等来分析转子系统的动态特性。重要结论：1.通过数值计算分析,转子的转速、非线性汽封力、非线性油膜力和联轴器的刚度对双跨转子的稳定性有重要的影响作用。2.随着转速的上升,双跨转子系统从最初的稳定运动,到三倍周期运动,到准周期运动和多倍周期运动交替出现,运动特性相比单跨转子系统要更为复杂。     

水电机组在转子偏心影响下的非线性电磁振动分析

介绍了水轮机组发电机转子在转动过程中的三种偏心:静偏心、振动偏心和转动偏心,建立了转子在不平衡电磁力作用下的非线性振动微分方程。采用数值方法分析了转动偏心和静偏心对轴系电磁振动特性的影响,结果表明,这两种偏心与电磁力呈非线性关系,随着偏心的增大使不平衡磁拉力作用不断加强,机组的横向振动固有频率有所降低,转子和转轮的振幅不断增大,倍频共振时的振幅也显著加大,转子系统展现出非常复杂的非线性动力学特征。     

一类三维动力系统的分岔及混沌分析

对一类三维非线性混沌金融系统进行了动力学特征分析,得到了模型方程的三个平衡点,并对其稳定性进行了讨论.通过数值仿真得到了系统的分岔图及Lyapunov 指数图,进而分析了参数变化对系统稳定性及分岔的影响.该研究对理解各种金融政策的杠杆原理有参考意义.     

Study on pile drivability with one dimensional wave propagation theory

INTRODUCTIONInterestinonedimensionalwavepropagationtheoryforapplicationtounderstandingpiledriv ingismorethanacenturyold .ImportantworkdirectlyrelatedtocurrentapplicationstopiledrivabilitystartedshortlyaftertheSecondWorldWarandcontinuedtothepresent,assuchp…