This paper addresses the rotordynamic instability of an overhung rotor caused by a hydrodynamic moment due to whirling motion through the structural coupling between whirl and precession modes. First, the possibility of instability is discussed based on a vibration model in which the hydrodynamic forces and moments are assumed to be smaller than structural forces with the structural coupling being represented by a structural influence factor. Then, the fundamental characteristics of rotordynamic moment on the backshroud of a Francis turbine runner under whirling motion were studied using model tests and numerical calculations. The runner is modeled by a disk positioned close to a casing with a small radial clearance at the outer periphery. The moment is caused by an inward leakage flow that is produced by an external pump in the model test. The experiments were designed to measure the rotordynamic fluid force moments under various leakage flow rates with various preswirl velocities and various axial clearances between the backshroud and casing. The computation was carried out based on a bulk flow model. It was found that the fluid force moment is generally destabilizing, except for a small region of positive whirling speed ratios.
The fundamental characteristics of rotordynamic fluid force moment on the backshroud of a Francis turbine runner in precession motion were studied using model tests and computations based on a bulk flow model. The runner is modeled by a disk positioned close to a casing with a small axial clearance. An inward leakage flow is produced by an external pump in the model test. The effects of the leakage flow rate, the preswirl velocity at the inlet of the clearance, and the axial clearance on the fluid force moment were examined. It was found that the fluid force moment encourages the precession motion at small forward precession angular velocity ratios and the region encouraging the precession motion is affected by the preswirl velocity. Through the comparisons of the fluid force moment with and without the rotation of the disk, it was found that the normal moment without the disk rotation did not have the effect to encourage the precession motion. Thus, the swirl flow due to disk rotation was found to be responsible for the encouragement of the precession motion.
In order to improve the surface machining quality of slow tool servo (STS) turning in complex surfaces, the optimal method of tool path generation (TPG) was studied. Taking into consideration the problem of large discrete errors and interpolation errors in TPG, equal height discretization method and interpolation algorithm for non-uniform nodes were proposd and the acceleration continuous condition was introduced. Simulation results showed that equal height discretization method could reduce the discrete error by more than 70%. The interpolation errors could be reduced to two orders of magnitude by transforming segment cubic Hermite interpolation into segment cubic spline interpolation. Finally, the processing experiments were performed. The results showed that the form error PV value for the workpiece of the toric surface obtained by equal height discretization method and non-uniformity processing and segment cubic spline interpolation reached 0.002mm. The PV value of the sinusoidal array surface was about 0.009mm, and its surface roughness value was 0.064μm. The results proved this method can effectively reduce the discrete errors and interpolation errors, as well as improve the surface machining quality.
Severe flexural vibration of the rotor shaft of a Francis turbine runner was experienced in the past. It was shown that the vibration was caused by the fluid forces and moments on the backshroud of the runner associated with the leakage flow through the back chamber. The aim of the present paper is to study the self-excited rotor vibration caused by the fluid force moments on the backshroud of a Francis turbine runner. The rotor vibration includes two fundamental motions, one is a whirling motion which only has a linear displacement and the other is a precession motion which only has an angular displacement. Accordingly, two types of fluid force moment are exerted on the rotor, the moment due to whirl and the moment due to precession. The main focus of the present paper is to clarify the contribution of each moment to the self-excited vibration of an overhung rotor. The runner was modeled by a disk and the whirl and the precession moments on the backshroud of the runner caused by the leakage flow were evaluated from the results of model tests conducted before. A lumped parameter model of a cantilevered rotor was used for the vibration analysis. By examining the frequency, the damping rate, the amplitude ratio of lateral and angular displacements for the cases with longer and shorter overhung rotor, it was found that the precession moment is more important for smaller overhung rotors and the whirl moment is more important for larger overhung rotors, although both types of moment due to the leakage flow can cause self-excited vibration of an overhung rotor.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.