Onset of chaotic motion in a gyroscopic system

We study forced vibrations of a gimbal gyro occurring if the inner ring is subjected to a perturbing torque that is the sum of the viscous friction torque and a periodic small-amplitude torque. In the absence of the perturbing torque, there exist two steady-state motions of the gimbal gyro, in which the gimbal rings are either orthogonal or coincide. These motions are respectively stable and unstable. We obtain an equation for the unperturbed system, whose separatrix passes through hyperbolic points. The distance between these points (the Melnikov distance) is calculated to find a condition for the intersection of the separatrices of the perturbed system. We find a domain in the parameter space where the distance changes sign, which indicates the onset of chaotic motion.     

Sommerfeld effect in an oscillator with a reciprocating mass

Nonlinear Dynamics - In this paper, the dynamics of a non-ideally driven single-degree-of-freedom vibrating system will be explored in detail. The objective is to describe Sommerfeld effect in a...     

Sommerfeld effect and synchronization analysis in a simply supported beam system excited by two non-ideal induction motors

Nonlinear Dynamics - In this paper, Sommerfeld effect and self-synchronization of two non-ideal induction motors in a simply supported beam system are studied. Based on fully considering non-ideal...     

Attenuation of Sommerfeld effect in an internally damped eccentric shaft-disk system via active magnetic bearings

Meccanica - Eccentric shaft-disk system with internal damping driven by a non-ideal power source exhibits Sommerfeld effect characterized by nonlinear jump phenomena of amplitude and rotor speed...     

EIGENVALUE PROBLEM OF A LARGE SCALE INDEFINITE GYROSCOPIC DYNAMIC SYSTEM

Gyroscopic dynamic system can be introduced to Hamiltonian system.Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gy- roscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system.The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used.The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented,and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem.Therefore,the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved,and two numerical examples were given to demonstrate that the eigensolutions converge exactly.     

Stability boundaries of a spinning rotor with parametrically excited gyroscopic system

Some published papers used Bolotin's method for stability boundaries of spinning rotor with parametrically excited gyroscopic system. However, the original work of the method does not indicate that the method can be used to determine the stability of gyroscopic system. This paper intends to highlight the differences in the results using Bolotin's method. As counter examples, dynamic stability of a special case of the parametrically excited gyroscopic system, a simple gyroscopic rotor under parametric excitation and a rotating Timoshenko shaft subjected to periodic axial forces varying with time are analyzed and discussed by using Bolotin's method and Floquet's method respectively to indicate the differences. The causation of these differences is attributed to the differences in the assumptions of Bolotin's and Floquet's methods as that the assumption of Floquet multipliers in Bolotin's method cannot be satisfied for the gyroscopic system. In this paper it has been shown that the Bolotin's method will result with the enlargement of the instability region for the gyroscopic system, which may contradict the results based upon the Floquet's method.     

Optimal identification of basic direction drifts in the gyroscopic navigation system of a space vehicle

The method developed in the paper permits continuously identifying the gyrostabilizer drift rate in real time of correction of the gyroscopic navigation system on intervals of controlled motion of spacecraft. We present results concerning the practical use of the method for identifying the drift of a three-degree-of-freedom gyrostabilizer.     

On the principle of gyroscopic effect for self-excited rigid bodies

Summary A new method is described whereby the gyroscopic effect for self-excited rigid bodies is studied by means of a differential equation of the second order and the results of other Authors are generalized.

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Sommario Si descrive un metodo di calcolo, che permette di ricondurre la discussione sulla validità dell'effetto giroscopico per i solidi autoeccitati allo studio di una equazione differenziale del secondo ordine e di generalizzare i risultati ottenuti da altri Autori.

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This work has been done under the auspices of the Research Group no. 6 of C.N.R.     

陀螺效应对转子横向振动的影响分析

举例说明了在动力转子系统中陀螺效应对实际模型的影响。着重分析了转子陀螺效应对进动角速度、振型以及临界角速度的影响。并应用状态空间法求解陀螺系统的本征值问题。数值结果表明，在一些工程问题中，陀螺力对于转子系统振动特性的影响是不能忽略的。     

Vibrations of a gyroscopic meridian-plane sensor in a fluid suspension

This article examines a meridian-plane sensor built on the gyrocompass principle. It is assumed that the measurements are made along a curved axis. We therefore used a spherical fluid suspension, which makes it possible to fix the horizontal plane at each measurement point. Most of the information on the theory of gyroscopes that is used in this article can be found in [2–4, 6, 9, 10].S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 90–96, January, 1994.     

Numerical and experimental analysis of a continuous overhung rotor undergoing vibro-impacts

This work aims in obtaining the transient response of an overhung rotor undergoing vibro-impacts due to a defective bearing. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The variation of this system, popularly known as the Jeffcot rotor, has been considered in previous works, but there, the system has been reduced to a single degree of freedom for ease of analysis. In this work the system is modeled as a continuous rotor including gyroscopic effects and the governing partial differential equations are set up and numerically solved. The method of assumed models is used to discretize the system in order to solve the partial differential equations (PDE) by partially decoupling them and solving numerically. These partially decoupled equations are more accurate and less time consuming than the ones produced by finite elements or other numerical schemes. The most important step in the success of this method is the selection of suitable modes for decoupling the system. It is not simply enough to select orthonormal modes for decoupling the PDEs, but care must be taken to select the modes as close to the actual system as possible. Using this method numerical experiments are run and representative results are presented. The different numerical issues involved are also discussed. An experimental setup was also built to run experiments and validate the results. In the setup a defective bearing is introduced at the flywheel end of the shaft to create radial impacts on the shaft. Laser sensor non-contact probes are used to measure the displacement of the shaft a specified locations. Experimental observations show satisfactory qualitative agreement when compared to the numerical integrations.     

On post-resonance backward whirl in an overhung rotor with snubbing contact

Nonlinear Dynamics - Rotordynamic systems are central to many aerospace and heavy-duty industrial applications. The vibrational response of such systems is usually associated with forward whirl...     

Modelling and analysis of a single gimbal gyroscopic energy harvester

This work investigates the non-linear dynamics of a single gimbal gyroscopic energy harvester, excited by a harmonic moment about 1 and 2 axes simultaneously. The governing equations of motion are derived and a numerical model is developed to analyse the forced system response in all three rotational degrees of freedom. Simulations showing the effect of the harmonic forcing frequency and the gyroscopic damping are presented. The results identify the characteristic motion responses and available power of a single gimbal gyroscopic energy harvester including the development of the non-linear responses.