Papers by Keyword: Longitudinal Vibration

Abstract: The objective of this paper is to present semi-discrete analytical method for the longitudinal vibration of an elastic bar. Using lumped mass finite element method, we first obtain a system of second order ordinary differential equations. In terms of some transform technique we obtain the exact solution to the system, i.e. excellently semi-discrete analytical approximation to the longitudinal vibration. An example is given to illustrate the effectiveness of the proposed method.

Abstract: Aimed at the longitudinal vibration of rope hoisting system with time-varying length, the governing equations are developed employing the Hamilton’s principle considering mutual influence of the rigid motion and deformation of rope. The Galerkin’s method is used to discretize the governing equations. In the mean time, The motions of elevator hoisting system were illustrated to evaluate the proposed mathematical models. The results of simulation show that the modeling methods can represent the longitudinal vibration of rope hoisting system with time-varying length in the paper. The governing equations derived can provide guidelines for further study on flexible hoisting system.

Abstract: Ultrasonic motors adopting longitudinal vibration of bar were widely studied for their considerable thrust, high efficiency and reliability. A novel ultrasonic motor using longitudinal vibration of bar with varying section was proposed in this paper. This ultrasonic motor features with two varying section bars connected by semi-circumferential structure. Elliptical trajectories of particles are formed on top of the semi-circumferential structure outer surface where driving foot located and a mover is pushed to move when the driving foot is pressed onto it. FE model of its stator was built and results of harmonic analysis verified its principle. Testing of prototype shows that this motor was capable of a 10N load with speed 100mm/s.

Abstract: The ball screw drive system is obtained widespread application in the modern machine. Along with the improving of feeding velocity and working precision, its dynamic analysis becomes more and more important. Considering the bearing stiffness and the contact deformation between the worktable and the screw, the drive screw is seen as a bar under elastic supports at both ends and with an internal moving elastic support. Using boundary conditions and matching conditions, the longitudinal vibration frequency equation of the screw is derived and the mode shape of the screw is solved. The vibration frequency is analyzed when the worktable moves from the left to the right end of the screw. The effect of the system parameters on the natural frequency and the mode shape are studied to supply a base for designing the drive system.

Abstract: With the belt driving device which is affected by bi-directional alternating load taken as research object and with the elastic slide between belt and pulley which is caused by elastic deformation of the belt considered, the calculating model of belt instantaneous sliding friction is established. The belt is simplified to elastic body of longitudinal vibration, the mechanical model of the belt longitudinal vibration which is excited by alternating friction is established, and the mathematical model of the wave equation form is established. The numerical simulation model of wave equation is carried out on using the superposition method of mode of vibration. The simulation models of the belt instantaneous sliding velocity and the belt instantaneous sliding efficiency are presented. The factors affecting sliding efficiency are pointed out, such as oscillation amplitude of alternating torque and initial tension of belt. The following conclusions are obtained by the simulating results: (1) load torque fluctuations will lead to lower sliding efficiency; (2) specifically, the sliding efficiency will decrease obviously in the area where the direction of load torque is occurring; (3) on condition that the belt doesn’t skid, the sliding efficiency of the belt reduces with the increase of initial tension, and the sliding efficiency will increase through optimizing the initial tension of belt.