On the gyroscopic and centrifugal effects in the free vibration of rotating beams

This paper addresses the gyroscopic and centrifugal effects on vibrations of rotating Bernoulli–Euler beams. The gyroscopically coupled system is established as a complex eigenvalue problem. It is concluded that there exist three types of velocity-dependent terms that contribute to the natural frequencies with different effects. In particular, the contribution of gyroscopic terms and static and dynamic centrifugal terms to the natural frequencies are discussed for free vibrations of rotating beams with constant angular velocity. On the other hand, the vibrations in different directions coupled through the gyroscopic terms are investigated. Some numerical examples for the elliptic vibration modes in the rotating plane are presented and the results reveal the actual vibration contour of the rotating beams.

Research of Elliptic Ultrasonic Vibration Mechanism

Elliptical vibration cutting is a new processing technology of work piece surface texture generation, the technique based on conventional cutting machine main movement and feed motion of the tool, by changing the structure so that the tip motion to generate ellipse trajectory. This paper designed incentive range vibration frequency as 20~40 KHz, can generate elliptical vibration trajectory in the small space of X/Z axis 16um. Tests prove that, the ultrasonic elliptic vibration cutting mechanism improves the specimen surface texture, smooth discharging of chipping, greatly improving the surface finishes of the work piece.

Effect of Frequency and Amplitude on the Performance of Elliptic Vibration-Assisted Cutting of Fibre-Reinforced Polymer Composites

To effectively machine fibre-reinforced polymer composites using a simple tool, the authors have developed an elliptic vibration-assisted (EVA) cutting technique by applying micro-scale vibrations to a tool tip. This investigation aims to understand the effect of vibration frequency and amplitude on the EVA cutting performance. With the aid of a microstructure-based 3D finite element analysis, this study found that an increased vibration frequency or amplitude can accelerate the fracture of fibres, and reduce cutting forces in both the cutting and normal directions. The fracture mechanism was found to be dominated by the bending of fibres when the vibration frequency or amplitude in the cutting direction was small. With increasing the frequency or amplitude, impact-induced fracture becomes dominant, which reduces subsurface damage. It was found that to promote the performance of EVA cutting, the vibration frequency and amplitude of the cutting tool should be high. However, a too large frequency can bring about severe subsurface damage and bending fracture of fibres beneath the cutting path. A too large amplitude in the cutting direction, however, can accelerate the tool wear, while that in the vertical direction can worsen the fibre-matrix debonding.

Accumulative Drifting Model of Inertial Navigation Platform under Elliptic Vibration

To facilitate the calibration of a precision inertial navigation platform, the drifting of the platform under vibratory testing environment is analyzed, and a simplified drift model is developed which features the accumulative rather than instantaneous impact of the vibration on the platform drifting. When applied to error parameter calibration for the platform, the proposed model entails much less computing load in drifting prediction, and removes the requirement of strict real-time synchronization between the vibration generating device and the drift-predicting programs. The form of vibration can be assumed to be elliptic, a relatively general one which allows the shaker to vibrate sinuoidally in two directions perpendicular to each other and with phase difference of 90 degree. Under certain circumstances, the elliptic vibration can be simplified to a linear or circular one, as is typical in practice. Simulations of the platform drifting error under linear, circular and general elliptic vibration shows that the accumulative model can well serve as an alternative to the conventional one in such test environments, and the merits of the proposed model become more prominent when the frequency of vibration gets higher.

Micromechanical Modelling of Elliptic Vibration-Assisted Cutting of Unidirectional FRP Composites

Fibre-reinforced polymer (FRP) composites have been widely used in industry. However, the machining of FRP products is difficult, because of very different properties of the fibres and matrix. This paper discusses the development and implementation of a microstructure-based three-dimensional finite element model for the elliptic vibration-assisted (EVA) cutting of unidirectional FRP composites. The results showed that the EVA cutting has a good potential to the machining of FRP composites, featured a much reduced cutting force, better surface integrity and controllable chip size.

Effect Mechanism of Elliptic Vibration Assistance on the Cutting of Brittle Materials

A theoretical analysis for the effect mechanism of elliptic vibration assistance on the cutting of brittle materials is presented in this paper. The crack propagation in the chip formation zone in cutting of brittle materials is examined based on an analysis of the geometry and forces in the cutting region. The cutting model shows that the actual undeformed chip thickness is much decreased with elliptic vibration assistance, and the instantaneous rake angle of the cutting tool edge is also in a larger negative value than those in conventional cutting. These two conditions can ensure the compressive stress is much larger than the shear stress during the cutting process. Then the stress intensify factor is suppressed effectively and the shielding effect on the growth of pre-existing flaws is strengthened in the chip formation zone. The removal of brittle material tends to be in ductile mode without fracture. The characteristic examination of cutting force shows that the ratio of thrust force to cutting force with elliptic vibration is increased compared to that of conventional cutting. This can validate that the larger compressive stress can be generated in the chip formation zone with elliptic vibration assistance. The transition depth to brittle machining of silicon carbide with/without elliptic vibration assistance further supports the presented theory.

Simulation and Experiment of New Longitudinal-Torsional Composite Ultrasonic Elliptical Vibrator

A new ultrasonic elliptic vibrator design method was proposed, the ultrasonic elliptic vibration was achieved by the structural curve of the longitudinal and torsional vibrations. The model, harmonic and transient analyses of the new longitudinal-torsional composite ultrasonic elliptical vibrator were performed by using the software ANSYS, the prototype of the new vibrator was tested by using impedance analyzer and PSV-400 laser Doppler vibrometer, the correctness of the finite element simulation results and the feasibility of the new longitudinal-torsional composite ultrasonic elliptical vibrator design methods were verified.