Calculation of the landing area for a small asymmetric martian probe under the action of the Magnus gyroscopic moment

2018 ◽  
Author(s):  
V. V. Lyubimov
Keyword(s):  
Gyroscopic Moment

INCREASE OF THE ELECTRIC DRIVE LOAD UNDER ACTION OF GYROSCOPIC MOMENT

2016 ◽  
Vol 2016 (6) ◽  
pp. 44-49
Author(s):  
A. Antonov ◽  
◽  
V. Kireyev ◽  
I. Petukhov ◽  
◽  
...  
Keyword(s):  
Electric Drive ◽  
Gyroscopic Moment

Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball

2003 ◽  
Vol 125 (3) ◽  
pp. 487-498 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Centrifugal Force ◽  
Contact Force ◽  
Ball Bearing ◽  
Vibration Frequencies ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Gyroscopic Moment ◽  
Rolling Elements ◽  
Force Contact ◽  
Force Displacement

This research presents an analytical method to calculate the characteristics of the ball bearing under the effect of the waviness in its rolling elements and the centrifugal force and gyroscopic moment of ball. The waviness of rolling elements is modeled by using sinusoidal function, and the centrifugal force and gyroscopic. moment of ball are included in the kinematic constraints and force equilibrium equations to produce the nonlinear governing equations. To improve the convergence of the numerical solution of the nonlinear governing equations, it includes the derivatives of the gyroscopic moment and load-deflection constant of each race in the Newton-Raphson formulation. The accuracy of this research is validated by comparing with the prior research, i.e., (i) the contact force, contact angle in case of considering only the centrifugal force and gyroscopic moment of ball, and (ii) the contact force and vibration frequencies in case of considering only the waviness, respectively. It investigates the stiffness, contact force, displacement and vibration frequencies of the ball bearing, considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

scholarly journals DIGITAL AND PULSE-WIDTH CONTROL OF A SPACE ROBOT WHEN APPROACHING A GEOSTATIONARY SATELLITE

2020 ◽  
Vol 22 (5) ◽  
pp. 74-78
Author(s):  
Ye.I. Somov ◽  
◽  
S.A. Butyrin ◽  
S.Ye. Somov ◽  
◽  
...  
Keyword(s):  
Pulse Width ◽  
Electric Propulsion ◽  
Pulse Width Modulation ◽  
Geostationary Satellite ◽  
Space Robot ◽  
Control Algorithms ◽  
Control Problems ◽  
Guidance And Control ◽  
Gyroscopic Moment ◽  
And Control

The control problems on a space robot during its approach to an information geostationary satellite are considered. The robot motion control system uses an electric propulsion system with 8 engines at the pulse-width modulation of their thrust values and a gyroscopic moment cluster based on 4 gyrodines with digital control. Numerical results are presented that demonstrate the effectiveness of the developed discrete guidance and control algorithms.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Internal Resonance of the Jeffcott Rotor With Nonlinear Spring Characteristics

2001 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Jeffcott Rotor ◽  
Two Degree Of Freedom

Abstract The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model executing lateral whirling motions has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward whirling mode pf and that of a backward whirling mode pb have the relation of internal resonance pf : pb = 1 : (−1). Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. While, in many cases of the practical rotating machinery, such a relationship holds apprximately due to small gyroscopic moment. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with small gyroscopic moment. Especially, the influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance, (b) almost-periodic motions occur, (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment, and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incrrect results.

Dynamic Stability of a Cantilever Shaft-Disk System

1992 ◽  
Vol 114 (3) ◽  
pp. 326-329 ◽  
Author(s):  
Lien-Wen Chen ◽  
Der-Ming Ku
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Beam Theory ◽  
The Finite Element Method ◽  
Disk System ◽  
Stability Behavior ◽  
Gyroscopic Moment ◽  
The Mathematical Model ◽  
Cantilever Shaft

The dynamic stability behavior of a cantilever shaft-disk system subjected to axial periodic forces varying with time is studied by the finite element method. The equations of motion for such a system are formulated using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moment, bending and shear deformation are included in the mathematical model. Numerical results show that the effect of the gyroscopic term is to shift the boundaries of the regions of dynamic instability outwardly and, therefore, the sizes of these regions are enlarged as the rotational speed increases.

Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

2004 ◽  
Vol 126 (4) ◽  
pp. 476-484 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Resonance Phenomena ◽  
Jeffcott Rotor ◽  
The One ◽  
Two Degree Of Freedom

The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model, executing lateral whirling motions, has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward-whirling mode pf>0 and that of a backward-whirling mode pb<0 have the relation of internal resonance pf:pb=1:−1. Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. Furthermore in many practical rotating machines, the effect of gyroscopic moments are relatively small. Therefore, the one-to-one internal resonance relationship holds approximately between forward and backward natural frequencies in such machinery. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with a small gyroscopic moment. The influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance; (b) almost periodic motions occur; (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment; and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us that the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incorrect results.

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