Contours for Planar Cracks Growing in Three Dimensions: Influence of Kinetic Energy

Dynamic steady-state growth in 3D of a semi-infinite plane brittle crack in isotropic elastic solids is considered. Loads cause growth by translating on the crack surfaces at constant, subcritical speed. An analytical solution is obtained and subjected to a criterion for brittle crack growth based on dynamic energy release rate, with kinetic energy included. The result is a nonlinear differential equation for the crack contour, i.e., the curve formed by the crack edge in the crack plane. The equation is studied for the case of compression loading by translating point forces. At large distances from the forces, the crack edge asymptotically approaches the rectilinear and kinetic energy effects can be negligible. A bulge forms around the forces, however, the effect of kinetic energy on its size can be pronounced.

Numerical Analysis and Simulation of Vibration Characteristics of the Rotation Shaft with Mechanical Seal System

This paper make the rigid support Jeffcott shaft-mechanical seal system as the research object. Firstly, it establishes the equivalent stiffness matrix and damping matrix of the rotation shaft with mechanical seal in the fixed-coordinate system, then derives the motion equation of the shaft with mechanical seal and applies the numerical simulation method to analyze and gain the vibration characteristics of the rotation shaft with mechanical seal system. Numerical simulation results show that: when the rotation shaft works at the speed of the subcritical speed, the trajectory of centre will change with the speed of the shaft. When the shaft works at the speed of the second supercritical speed, the trajectory of centre will be a limit circle. When the shaft works at the speed of the subcritical speed, the vibration response appear 1X, 2X, 3X and so on component of the vibration, and when Ω is 1/2, 1/3 and so on, 2X, 3X and so on component of vibration is biggest; when the shaft works at the speed of the second supercritical speed, 2X and 2X above component of the vibration is very small, even to zero, and then the trajectory of the centre is a limit circle. Whenhminis different, amplitude-frequency diagram of the X direction of the rotation shaft is different. Whenhminis bigger ,1X, 2X, 3X component of the vibration is bigger.

Campbell diagrams of weakly anisotropic flexible rotors

We consider an axi-symmetric flexible rotor perturbed by dissipative, conservative and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure in the frequency–speed plane with double eigenfrequencies at the nodes. The diagram is convenient for the analysis of the travelling waves in the rotating elastic continuum. Computing sensitivities of the doublets, we find that at every particular node the unfolding of the mesh into the branches of complex eigenvalues in the first approximation is generically determined by only four 2×2 sub-blocks of the perturbing matrix. Selection of the unstable modes that cause self-excited vibrations in the subcritical speed range is governed by the exceptional points at the corners of the singular eigenvalue surfaces—‘double coffee filter’ and ‘viaduct’—which are sharply associated with the crossings of the unperturbed Campbell diagram with the definite symplectic (Krein) signature. The singularities connect the problems of wave propagation in the rotating continua with that of electromagnetic and acoustic wave propagation in non-rotating anisotropic chiral media. As mechanical examples a model of a rotating shaft with two degrees of freedom and a continuous model of a rotating circular string passing through the eyelet are studied in detail.

Flow Instability and Disk Vibration of Shrouded Corotating Disk System

This paper focuses on the interaction between the flow unsteadiness and disk vibration of shrouded corotating disk system to identify the nature of the flow-induced vibration of disks in the wide range of rotation speed below critical. Special attention is paid to the role of the vortical flow structure on the disk vibration and vice versa. The water test rig for optical measurement and the air test rig for hot-wire and vibration measurements are employed, both being axisymmetric models of 3.5in. hard disk drive. Before investigating fluid-solid interaction, the velocity and vorticity fields between disks are examined by employing a particle image velocimetry, in order to check the flow within our own apparatus to have the same characteristics as those commonly accepted. In the course of this preliminary experiment, it is found that “vortical structures” reported in the previous papers based on the flow visualization are actually “vortices” in the sense that it exhibits closed streamlines with concentrated vorticity at its center when seen from an observer rotating with the structure itself. The measurements of out-of-plane displacement of the disk employing different disk materials reveal that disk vibration begins to occur even in low subcritical speed range, and amplitude of nonrepeatable run out (NRRO) can be uniquely correlated by using the ratio between the rotating speed and the critical speed. The power spectral densities of disk vibration showed that the disk vibrates as a free vibration triggered by, but not forced by, the flow unsteadiness even in the high subcritical speed range. The disk vibration has negligible effect on the vortical flow structure suggesting the soundness of the rigid disk assumption employed in the existing CFD. However, RRO has significant influence on the flow unsteadiness even if the disks are carefully manufactured and assembled. Since the RRO is unavoidable in the real disk system, the flat disk assumption should be considered more carefully.

Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple

This paper investigates the instability of the transverse vibration of a disk excited by two corotating sliders on either side of the disk. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. There are friction forces acting in the plane of the disk at the contact interfaces between the disk and each of the two sliders. The equation of motion of the disk is established by taking into account the bending couple acting in the circumferential direction produced by the different friction forces on the two sides of the disk. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability. Regions of instability for parameters of interest are obtained by the method of state space. It is found that the moving loads produced by the sliders are a mechanism for generating unstable parametric resonances in the subcritical speed range. The existence of stable regions in the parameter space of the simulated example suggests that the disk vibration can be suppressed by suitable assignment of the parameter values of the sliders.

Study on the transient response and wavelet time—frequency feature of a cracked rotor passage through a subcritical speed

The dynamic model in dimensionless form of the transient response of a cracked rotor system is derived, which is based on the simple hinge crack model. By numerical simulation, the transient responses of the uncracked rotor and the cracked rotor are obtained and the subharmonic resonance of the cracked rotor is analysed. The influence of the unbalance, the inhabiting angle and the stiffness variation on the transient response is investigated. The wavelet time-frequency features of the cracked rotor and the uncracked rotor are studied, and the difference between them is discussed. The numerical simulation demonstrates that the wavelet analysis algorithm is valid for the identification of cracked rotor.