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...     

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.

---

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.

---

---

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

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.     

Orthogonality conditions and analytical response solutions of damped gyroscopic double-beam system: an example of pipe-in-pipe system

The double-beam system is a crucial foundational structure in industry, with extensive application contexts and significant research value. The double-beam system with damping and gyroscopic effects is termed as the damped gyroscopic double-beam system. In such systems, the orthogonality conditions of the undamped double-beam system are no longer applicable, rendering it impossible to decouple them in modal space using the modal superposition method(MSM) to obtain analytical solutions. Based on the complex modal method and state space method, this paper takes the damped pipe-in-pipe(PIP) system as an example to solve this problem. The concepts of the original system and adjoint system are introduced, and the orthogonality conditions of the damped PIP system are given in the state-space. Based on the derived orthogonality conditions, the transient and steady-state response solutions are obtained. In the numerical discussion section,the convergence and accuracy of the solutions are verified. In addition, the dynamic responses of the system under different excitations and initial conditions are studied, and the forward and reverse synchronous vibrations in the PIP system are discussed. Overall,the method presented in this paper provides a convenient way to analyze the dynamics of the damped gyroscopic double-beam system.     

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...     

Static simulation for deflections of a compressor disk by gyroscopic forces

This is a report of an experiment performed on a test disk which was geometrically similar to a typical aircraft gas-turbine compressor disk. A loading stand was constructed which applied static loads simulating centrifugal forces and the gyroscopic moment. The test disk and the loading stand are described. The stresses in the web of the disk and the axial deflections of the disk were measured at several values of gyroscopic moment. Comparisons between the measured values and calculations are given.     

Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects

A rotor driven by an ideal source, i.e., a source capable of delivering unlimited amount of power, becomes unstable beyond a certain threshold spin speed due to non-conservative circulatory forces. The circulatory forces considered in this paper arise out of rotating internal damping. If the drive is non-ideal then the rotor spin speed cannot exceed the stability threshold. This phenomenon is a type of the Sommerfeld effect. In this work, a DC motor driving four-degrees-of-freedom rotor with internal damping and gyroscopic effects is considered and the corresponding steady-state spin frequency and the whirl orbit amplitude are analytically derived as functions of the parameters of the drive and the rotor system.