A Study on Mode Shape and Natural Frequency of Rotating Flexible Cracked Annular Thin Disk

As an important rotating component, the flexible annular thin disk is widely used in mechanical engineering. Cracks may occur in some weak disk parts, which will greatly shorten the equipment service life and even cause equipment failure. Due to the centrosymmetric structure of the flexible annular disk, two typical cracks are studied in this paper; one is radial crack parallel to diameter, including radial closed crack (RC-crack) and radial opening crack (RO-crack); the other one is vertical crack perpendicular to diameter, including circumferential crack (CF-crack) and tangential crack (TG-crack). The effect of crack parameters, such as crack length, direction, and position, on disk vibration characteristics are studied through theoretical simulation and experimental verification. The research shows that the effect of cracks on vibration characteristic gets more obvious with cracks extending in most cases, RO-crack decreases the natural frequency obviously, and vertical cracks would affect mode shapes. In addition, the bigger the nodal diameter is, the more obvious the effect gets. Meanwhile, the most obvious effect appears in the mode of a nodal diameter locating on the crack. The research possesses some guiding significance in industrial production; by comparing with the vibration characteristics of the flawless disk, the integrity of the rotating flexible disk can be judged to prevent possible equipment damage.

Whirl Analysis of an Overhung Disk Shaft System Mounted on Non-rigid Bearings

Eigenvalues of a simple rotating flexible disk-shaft system are obtained using different methods. The shaft is supported radially by non-rigid bearings, while the disk is situated at one end of the shaft. Eigenvalues from a finite element and a multi-body dynamic tool are compared against an established analytical formulation. The Campbell diagram based on natural frequencies obtained from the tools differ from the analytical values because of oversimplification in the analytical model. Later, detailed whirl analysis is performed using AVL Excite multi-body tool that includes understanding forward and reverse whirls in absolute and relative coordinate systems and their relationships. Responses to periodic force and base excitations at a constant rotational speed of the shaft are obtained and a modified Campbell diagram based on this is developed. Whirl of the center of the disk is plotted as an orbital or phase plot and its rotational direction noted. Finally, based on the above plots, forward and reverse whirl zones for the two excitation types are established.

Nonlinear Vibrations of a Circular Spinning Disk With a Transverse Load

In this paper, we analyze the transverse nonlinear vibration of a rotating flexible disk with a periodically varying rotating speed, subjected to a rotating point force. Based on a small-stretch, moderate-rotation flexible disk theory of the Nowinski and the von Karman type field equations, the nonlinear governing equations of motion are derived for the rotating flexible disk, which are coupled equations among the radial, tangential and transverse displacements. According to the Galerkin approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes are derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, the stabilities of the steady state nonlinear responses are analyzed. Using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including multi-pulse type chaotic motions, periodic and period-n motions for the spinning disk with a varying rotating speed. It is also found that among all parameters the damping and excitation have important influence on the nonlinear responses of the spinning disk with a varying rotating speed.