Angular Velocity Free Control Laws of a Rigid Body Motion Using Rotor System with Friction

2005 ◽  
Vol 6 (3) ◽  
Author(s):  
A. El-Gohary
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Control Laws

A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yamin Li ◽  
Hongrui Cao ◽  
Linkai Niu ◽  
Xiaoliang Jin
Keyword(s):  
Rigid Body ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Rotor Systems ◽  
Proposed Model ◽  
Vibration Responses

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

scholarly journals SOME PROBLEMS ABOUT THE MOTION OF A RIGID BODY IN A RESISTIVE MEDIUM

2021 ◽  
Vol 3 (2) ◽  
pp. 6-17
Author(s):  
D. Leshchenko ◽  
◽  
T. Kozachenko ◽  
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Modern Technology ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Body Rotation ◽  
Angular Velocity Vector ◽  
Resistive Medium

The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistive medium. The presence of the velocity of proper rotation of the rigid body leads to the apearance of dissipative torques causing the braking of the body rotation. These torques depend on the properties of resistant medium in which the rigid body motions occur, on the body shape, on the properties of the surface of the rigid body and the distribution of mass in the body and on the characters of the rigid body motion. Therefore, the dependence of the resistant torque on the orientation of the rigid body and its angular velocity can de quite complicated and requires consideration of the motion of the medium around the body in the general case. We confine ourselves in this paper to some simple relations that can qualitative describe the resistance to rigid body rotation at small angular velocities and are used in the literature. In setting up the equations of motion of a rigid body moving in viscous medium, we need to consider the nature of the resisting force generated by the motion of the rigid body. The evolution of rotations of a rigid body influenced by dissipative disturbing torques were studied in many papers and books. The problems of motion of a rigid body about fixed point in a resistive medium described by nonlinear dynamic Euler equations. An analytical solution of the problem when the torques of external resistance forces are proportional to the corresponding projections of the angular velocity of the rigid body is obtain in several works. The dependence of the dissipative torque of the resistant forces on the angular velocity vector of rotation of the rigid body is assumed to be linear. We consider dynamics of a rigid body with arbitrary moments of inertia subjected to external torques include small dissipative torques.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Sign in / Sign up

Export Citation Format

Share Document