Adaptive Virtual Autobalancing for a Magnetic Rotor With Unknown Mass Imbalance: Part II — Dynamic Balancing

1995 ◽  
Author(s):  
Kai-Yew Lum ◽  
Sanjay P. Bhat ◽  
Dennis S. Bernstein ◽  
Vincent T. Coppola
Keyword(s):  
Equations Of Motion ◽  
Magnetic Actuation ◽  
State Equations ◽  
Mass Imbalance ◽  
Unbalanced Rotor ◽  
Statically Unbalanced Rotor ◽  
Multiple Plane ◽  
Control Forces ◽  
Six Degree Of Freedom ◽  
Adaptive Control Algorithm

Abstract In Lum et al. (1995), an adaptive control algorithm for the stabilization of a rigid, statically unbalanced rotor moving in the plane was proposed. The control strategy consisted in emulating a mechanical autobalancer using magnetic actuation so as to directly cancel the effects of static mass imbalance. In this present paper, this strategy is extended to the case of a rigid, dynamically unbalanced rotor in six degree-of-freedom motion. The state equations of the controller are based on the equations of motion of a multiple-plane autobalancer, and the control forces partially emulates the interaction between rotor and autobalancer. It is shown in simulation that the adaptive virtual autobalancing control can achieve stabilization of rotor motion as well as adaptation to changes in imbalance.

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Dynamic Rocking Response and Optimization of the Nonlinear Suspension of a Railroad Freight Car

1980 ◽  
Vol 102 (1) ◽  
pp. 86-93 ◽  
Author(s):  
M. Samaha ◽  
T. S. Sankar
Keyword(s):  
Equations Of Motion ◽  
Sine Wave ◽  
Optimization Techniques ◽  
Model Accuracy ◽  
Frequency Responses ◽  
Optimum Parameters ◽  
Freight Car ◽  
Six Degree Of Freedom ◽  
Railroad Freight ◽  
Rocking Response

A modified mathematical model of a large capacity railroad freight vehicle is presented. The model for this investigation is constructed in such a way to describe the bounce, sway and rocking modes of the system and also to account for most of the vehicle non-linearity effects. Equations of motion of the six degree of freedom nonlinear model are derived assuming that the excitations from the track in vertical and lateral directions are purely periodic in the form of a rectified sine wave. The solution for the time and frequency responses on digital computer are compared with available measured data to investigate the model accuracy. Multivariable optimization techniques are employed to find the optimum suspension parameters that minimizes the maximum car rocking response over the frequency range of interest. The optimum parameters are presented in different forms either for the existing or for stabilized vehicle configuration.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Experimental and numerical investigation of railroad vehicle braking dynamics

2009 ◽  
Vol 223 (3) ◽  
pp. 255-267
Author(s):  
C Mellace ◽  
A P Lai ◽  
A Gugliotta ◽  
N Bosso ◽  
T Sinokrot ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Computer Algorithms ◽  
Coordinate Systems ◽  
State Equations ◽  
Relative Coordinates ◽  
Linear State ◽  
Cartesian Coordinate ◽  
Railroad Vehicle ◽  
Braking Dynamics

One of the important issues associated with the use of trajectory coordinates in railroad vehicle dynamic algorithms is the ability of such coordinates to deal with braking and traction scenarios. In these algorithms, track coordinate systems that travel with constant speeds are introduced. As a result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinates to be effectively used in modelling braking and traction dynamics. One of the objectives of this investigation is to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modelling braking and traction conditions. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of an arc length that represents the distance travelled by the body, and five relative coordinates that define the configuration of the body with respect to its track coordinate system. The independent non-linear state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinate systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The results obtained using the trajectory coordinates are compared with the results obtained using the absolute Cartesian-coordinate-based formulations, which allow modelling braking and traction dynamics. In addition to this numerical validation of the trajectory coordinate formulation in braking scenarios, an experimental validation is also conducted using a roller test rig. The comparison presented in this study shows a good agreement between the obtained experimental and numerical results.

An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

Flow about a fluid sphere at low to moderate Reynolds numbers

1987 ◽  
Vol 177 ◽  
pp. 1-18 ◽  
Author(s):  
D. L. R. Oliver ◽  
J. N. Chung
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Solid Sphere ◽  
Fluid Sphere ◽  
State Equations ◽  
Drag Coefficients ◽  
Low Reynolds Number Flows ◽  
Analytical Series ◽  
Reynolds Number Flows

The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 107 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

Magnetic Field-Induced Nonlinear Vibration of an Unbalanced Rotor

2003 ◽  
Author(s):  
Yuefang Wang ◽  
Ganyun Sun ◽  
Lihua Huang
Keyword(s):  
Magnetic Field ◽  
Potential Energy ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Oscillatory System ◽  
Forced Vibrations ◽  
Electric Motors ◽  
Jump Phenomenon ◽  
Mass Unbalance ◽  
Unbalanced Rotor

The free and forced flexural vibrations are investigated for rotors of electric motors operating in unsymmetrical magnetic fields. The magnetic potential energy reserved in the air-gap is analytically derived and the unbalanced magnetic pull is obtained through the law of energy conservation. With this excitation, the equations of motion of the unbalanced rotor are developed for nonlinear displacements response. For small dynamic eccentricities, the equations of motion are simplified and the rotor is compared to a free Duffing oscillatory system. The analytic solution for forced vibrations subject to residual mass-unbalance excitations is also obtained. Jump phenomenon in the solution is pointed out, and the effects of initial eccentricity and flux density on the natural frequency are also investigated.

Optimal Stabling of Attitude Maneuver for a Special Satellite With Reaction Wheel Actuators

2010 ◽  
Author(s):  
Seyed Hasan Miri Roknabadi ◽  
Mohamad Fakhari Mehrjardi ◽  
Mehran Mirshams
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Low Energy ◽  
Dynamic Equations ◽  
Satellite Motion ◽  
Reaction Wheel ◽  
State Equations ◽  
Time Consumption ◽  
Attitude Maneuver ◽  
Simulation Results

This paper presents an optimal attitude maneuver by Reaction Wheels to achieve desired attitude for a Satellite. At first, Dynamic Equations of motion for a satellite with just three Reaction Wheels of its active actuators are educed, and then State Equations of this system are obtained. An optimal attitude control with the LQR method has exerted for a distinct satellite by its Reaction Wheels. As a result simulation has presented an optimal effort by calculated Gain matrix to achieve desired attitude for chosen Satellite. It shows that satellite becomes stable in desired attitude with a low energy and time consumption. Furthermore equations derivation, coupling of electrical Reaction Wheel equations with dynamic equations of satellite motion, linearizes them and Reaction wheel saturation avoidance approaches are innovative. Simulation results, accuracy of achieving desired attitude and satellite stability support this statement.

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