Wen Bang-chun

Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.

Deflections of Nanowires with Consideration of Surface Effects

The elementary beam model is modified to include the surface effects and used to analyze the deflections of nanowires under different boundary conditions. The results show that compared to deflections of nanowires without consideration of surface effects, the surface effects can enlarge or reduce deflections of nanowires, and nanowire buckling occurs under certain conditions. This study might be helpful for design of nanowire-based nanoelectromechanical systems.

Stability of the Two-span Rotor-bearing System Periodic with Coupling Faults of Crack and Rub-impact

A dynamic model is set up for the two-span rotor-bearing system with coupling faults of crack and rub-impact.Using the continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system,the stability of the system periodic mo- tion is studied by the Floquet theory.The unstable form of the rotor system with crack fault is period-doubling bifurcation,and that with rub-impact fault is Hopf bifurcation.The unstable form of the rotor system with coupling faults is Hopf bifurcation when the depth of crack is smaller.The influence to the response of the system increased along with the depth of crack,the unstable form of the rotor system with coupling faults is period-doubling bifurcation.The conclusions provide theoretic basis reference for the failure diagnosis of the rotor-bearing system.

The sensibility on dynamic characteristics of pre-pressure thin-wall pipe under elastic boundary conditions

Consideration is given to dynamic behavior of cylindrical pressure pipe with elastic boundary conditions. Based on Sanders’ shell theory and Hamilton principle, the system equations are established for integrating the uniform distributed pressure into the elastic boundary condition. In the analytical formulation, the Rayleigh–Ritz method with a set of displacement shape functions is used to deduce mass, damping, and stiffness matrices of the pipe system. The displacements in three directions are represented by the characteristic orthogonal polynomial series and trigonometric functions which are satisfied with the elastic boundary conditions, which are represented as four sets of independent springs placed at the ends including three sets of linear springs and one set of rotational spring. The pressure pipe always suffers a uniform distributed pressure in radial direction. To verify the accuracy and reliability of the present method, several numerical examples with classical boundary condition, including free and simply supported supports are listed and comparisons are made with open literature. Then the influences of boundary restraint stiffness and the distributed pressure on natural frequency and the forced vibration response are studied: The natural frequencies increase significantly as the restraint stiffness or the distributed pressure increases. Compared to the rotational spring stiffness, the stiffnesses of axial, radial, and circumferential springs have more significant effect on natural frequency. And the lower modes are more sensitive on restraint stiffness than higher modes. But the variation of natural frequency with respect to the spring stiffness decreases monotonically with the increasing distributed pressure. The forced vibration response is also affected by the restraint stiffness.

Study on Misalignment-rubbing Coupling Fault of Rotor System Supported by Oil Film Force

针对滑动轴承支撑下的转子系统发生不对中故障进而引起不对中-碰摩耦合故障的诊断问题,基于非线性有限元法,应用短轴承油膜力、等效不对中力矩及Hertz接触理论建立双盘不对中-碰摩耦合故障转子系统动力学模型,并通过增广的拉格朗日方法来处理接触约束条件,以保证转盘和机匣相互接触时满足边界渗透深度在规定的容差范围内。同时,结合试验研究分析了在不同转速条件时,滑动轴承支撑下的耦合故障转子系统的相关动力学特性。研究表明碰摩故障在耦合故障中处于主导地位,不对中故障主要会激发高倍频谱处于从属地位;并且随着转速的提高,系统频率成分以高倍频为主,逐步由拟周期运动进入混沌运动状态,同时由于不对中力矩与碰摩力的作用,油膜失稳现象局部被抑制,一、二阶油膜振荡现象均滞后显现。研究结果可为滑动轴承支撑下耦合故障转子系统故障诊断提供依据。

Identification of noise modes for automobile operational modal analysis

In rotating machinery, the input excitation does not meet the requirement of operational modal analysis (OMA). In this article, an effective and improved method of distinguishing forced harmonic response from measured vibration signal is presented based on the differences of the statistical properties of a stochastic signal and a harmonic signal. It makes the OMA applicable to the situation of existing periodic excitation. In order to prove the effectiveness of the proposed method, a modal experiment of a steel plate excited by a motor is performed. Then, an OMA is performed to solve the vehicle interior noise problem. Combining the projection channel technique with the advanced method, most noise modes, especially harmonic modes are successfully separated. Precise modal parameters of the car are obtained in typical working conditions which provide guidance of the dynamic modification and show that the harmonic identification method has great practical value.

A Comparison Study of PD Control of Joint Velocity in Robot Arms

The PD controller requires measurements of both joint position and velocity. It is necessary to implement position and velocity sensors at each joint. The joint position measurement can be obtained by means of encoder, which gives very accurate measurement. The joint velocity is usually measured by velocity tachometer, which is expensive and often contaminated by noise. Two possible solution are to implement a velocity observers and numerical difference methods. This paper presents a comparison study of performances and characteristics of high-gain observers and LPP numerical difference methods.

A new type of global bifurcation in Hénon map

A simple branch of solution on a bifurcation diagram, which begins at static bifurcation and ends at boundary crisis (or interior crisis in a periodic window), is generally a period-doubling cascade. A domain of solution in parameter space, enclosed by curves of static bifurcation and that of boundary crisis (or the interior of a periodic window), is the trace of branches of solution. A P-n branch of solution refers to the one starting from a period-n (n?1) solution and the corresponding domain in parameter space is named the P-n domain of solution. Because of the co-existence of attractors, there may be several branches within one interval on a bifurcation diagram and different domains of solution may overlap each other in some areas of the parameter space. A complex phenomenon, concerned both with the co-existence of attractors and the crises of chaotic attractors, was observed in the course of constructing domains of steady state solutions of the H?non map in parameter space by numerical methods. A narrow domain of period-m solutions firstly co-exists with (lies on) a big period-n (m?3n) domain. Then it enters the chaotic area of the big domain and becomes period-m windows. The co-existence of attractors disappears and is called the landing phenomenon. There is an interaction between the two domains in the course of landing: the chaotic area in the big domain is enlarged and there is a crisis step near the landing area.

1/3 Pure sub-harmonic solution and fractal characteristic of transient process for Duffing’s equation

The 1/3 sub-harmonic solution for the Duffing’s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.