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The Dynamics of Vertical Gyroscope Rotor with Mass Imbalance and Disk Skewing with an Allowance for Hard Nonlinear Resilient Characteristics

Author Affiliations

  • 1Institute of Mechanics and Machinery Manufacturing named after U. A. Dzholdasbekov, Almaty, Kazakhstan

Res. J. Recent Sci., Volume 5, Issue (3), Pages 1-10, March,2 (2016)


The dynamics of vertical unbalanced gyroscope rotor with hard nonlinear resilient characteristics is considered. For the purpose of investigation of rotor vibrations, its dynamic and mathematical model is constructed. The motion equations are recorded as equations of Lagrange of the 2nd kind. The expressions of amplitude and phase of the main harmonic component are expressed using expansion of solutions to the equations of expressed vibrations as well as harmonic balance to the series of Fourier. The equations as variations, and then the equations of Hill type, are recorded to study hardiness on the basis of motion equations. According to the theory of Floquet, these equations are solved, and the stability criterion is found using the harmonic balance method. We concentrate on study of skewing influence, mass imbalance, disk thickness, size of nonlinear characteristics of the resilient mounting as well as external buffering to amplitude and phase and frequency characteristics as well as area boundaries of variability of the main resonance vibration. On the basis of analysis of research results the particularities of dependencies of the amplitude and phase of the main resonance vibration and instability region boundaries are accentuated and described from the angle between the imbalance lines, disk thickness, external resistance and shaft speed without the hard nonlinear resilient characteristics of the rotor. They can be important for development of optimal control of resonance vibrations, determination of optimal construction parameters, working speed range and rotor balancing methods in the pre-design works. The main working expressions are presented in a compact and non-dimensional form.


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