EXACT SOLUTIONS FOR THE FREE AND FORCED VIBRATION OF A ROTATING DISK-SPINDLE SYSTEM

• Published in: Journal of sound and vibration Vol. 223; no. 3; pp. 445 - 465
• Main Authors: Parker, R.G., Sathe, P.J.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 10.06.1999; Elsevier
• Subjects: Applied sciences; Drives; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical engineering. Machine design; Physics; Shafts, couplings, clutches, brakes; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Three dimensional model; Equation of motion; Forced vibration; Free vibration; Rotating disk; Dynamic stability; Shaft; Critical speed; Eigenvalue problem; Modeling; Complex variable method; Exact solution
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1998.2097

Spinning disk–spindle systems consisting of an elastic disk mounted on an elastic spindle by means of a three dimensional, rigid clamp extend the rich literature on spinning discs and shafts that are decoupled from each other. This work presents an exact, closed-form solution for the eigensolutions of such systems. The complex eigenfunctions have the classical properties of a gyroscopic system when the individual disk, spindle and clamp deflections for a given eigenfunction are collected in terms of an extended eigenfunction. Eigenvalue perturbations are calculated to determine the sensitivity of the zero speed eigenvalues and the critical speeds to system parameters. Additionally, critical speeds analogous to those of a rigidly supported (classical) spinning disk are examined for the coupled system. Whereas the rigidly supported disk does not experience critical speed instability in the one-nodal diameter eigenfunctions, the coupled system does. The exact solution admits a closed-form modal analysis for the forced response to disk, spindle and clamp excitation. Response is calculated for two examples that demonstrate the strong disk–spindle modal coupling that can exist and the potentially damaging transmission of excitation energy between the disk and spindle.