Spherical Compliant Model for Vibration Estimation and Control

1995 ◽  
Author(s):  
Thomas J. Thompson
Keyword(s):  
Passive Control ◽  
Equations Of Motion ◽  
Spherical Model ◽  
Control Element ◽  
Test Accuracy ◽  
Control Force ◽  
Lumped Mass ◽  
Mass System ◽  
Model Control ◽  
And Control

Abstract Proposed space missions involve large structures which must maintain precise dimensional tolerances during dynamic maneuvers. In order to attenuate disturbances in the many modes of vibration of such structures, active and passive vibration control has been proposed. Passive control is to be achieved by placing viscous or viscoelastic members in a structure to absorb energy, while active control similarly could involve structural members (struts) capable of sensing axial displacement and exerting axial control force. With conventional modal analysis, the effect of a control element on a system is computed by summing its influence on many immutable modes. Since changes in mode shape must be described by this summation, truncation of higher modes results in inaccuracies. The compliant model of vibration to be presented accurately accounts for the effects of locally-acting control elements without inclusion of high-frequency modes. The motion of each spring-mass system representing a structural mode is modified by a control element in series with another stiffness inherent to the structure for that mode and control position. In order to predict the influence of several control elements or dampers on closely-spaced modes, the compliant models for those modes are integrated into a spherical model in which one lumped mass is acted upon by orthogonal modal stiffnesses. In the spherical model, control elements influent the lumped mass from orientations determined by mode participation factors. The resulting equations of motion are stated in standard state-space form. To test accuracy, the compliant model is used to predict eigenvalue shifts due to springs and dampers acting upon an axially-vibrating rod, and the spherical model is used to predict damping accurately in a lumped-mass system with closely-spaced modes.

Passive and Switched Stiffness Vibration Controllers Using Fluidic Flexible Matrix Composites

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Amir Lotfi-Gaskarimahalle ◽  
Lloyd H. Scarborough ◽  
Christopher D. Rahn ◽  
Edward C. Smith
Keyword(s):  
Passive Control ◽  
Axial Strain ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Absolute Error ◽  
Step Response ◽  
Axial Stiffness ◽  
Matrix Composites ◽  
Mass System ◽  
Valve Orifice

This paper investigates passive and semi-active vibration control using fluidic flexible matrix composites (F2MC). F2MC tubes filled with fluid and connected to an accumulator through a fixed orifice can provide damping forces in response to axial strain. If the orifice is actively controlled, the stiffness of F2MC tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the F2MC tube kinematically relates the internal volume to axial strain. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. With a closed valve, however, the high bulk modulus fluid resists volume change and produces high axial stiffness. The equations of motion of an F2MC-mass system are derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. A reduced-order model for operation with either a fully open or fully closed valve motivates the development of a zero vibration (ZV) controller that suppresses vibration in finite time. Coupling of a fluid-filled F2MC tube to a pressurized accumulator through a fixed orifice is shown to provide significant passive damping. The open-valve orifice size is optimized for optimal passive, skyhook, and ZV controllers by minimizing the integral time absolute error cost function. Simulation results show that the optimal open valve orifice provides a damping ratio of 0.35 compared with no damping in closed-valve case. The optimal ZV controller outperforms optimal passive and skyhook controllers by 32.9% and 34.2% for impulse and 34.7% and 60% for step response, respectively. Theoretical results are confirmed by experiments that demonstrate the improved damping provided by optimal passive control F2MC and fast transient response provided by semi-active ZV control.

Theory for an Active Dynamic Vibration Absorber

1991 ◽  
Author(s):  
L. S. Stephens ◽  
K. E. Rouch ◽  
S. G. Tewani
Keyword(s):  
Closed Form Solution ◽  
Control Element ◽  
Vibrational Amplitude ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Lumped Mass ◽  
Dynamic Vibration Absorber ◽  
Mass System ◽  
Dynamic Vibration ◽  
The Impact

Abstract Research in dynamic vibration absorbers has yielded several fundamental designs. Among these are the tuned dynamic absorber, the Lanchester damper, and the impact damper. These designs utilize certain combinations of passive mechanical elements (springs and dampers) to reduce the vibrational amplitude of a system. However, with recent advances in motion sensing and actuating, the design of vibration absorbers that utilize actively actuated elements has become more attractive. This paper develops the theory for using a damped dynamic vibration absorber with an active control element to reduce the vibrational amplitude of a lumped mass system. A control law consisting of a linear combination of velocity and acceleration of the main mass is developed for the active element A closed-form solution is presented for the absorber tuning equation, and numerical methods are used to generate performance curves.

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.

Modeling, Actuation, and Control of an Active Fluid Vibration Isolator

1997 ◽  
Vol 119 (1) ◽  
pp. 52-59 ◽  
Author(s):  
M. J. Panza ◽  
D. P. McGuire ◽  
P. J. Jones
Keyword(s):  
Electrical Power ◽  
Fluid Pressure ◽  
Space Representation ◽  
Vibration Isolator ◽  
Mass System ◽  
Integral Control ◽  
Active Fluid ◽  
State Space Representation ◽  
In Series ◽  
And Control

An integrated mathematical model for the dynamics, actuation, and control of an active fluid/elastomeric tuned vibration isolator in a two mass system is presented. The derivation is based on the application of physical principles for mechanics, fluid continuity, and electromagnetic circuits. Improvement of the passive isolator performance is obtained with a feedback scheme consisting of a frequency shaped notch compensator in series with integral control of output acceleration and combined with proportional control of the fluid pressure in the isolator. The control is applied via an electromagnetic actuator for excitation of the fluid in the track connecting the two pressure chambers of the isolator. Closed loop system equations are transformed to a nondimensional state space representation and a key dimensionless parameter for isolator-actuator interaction is defined. A numerical example is presented to show the effect of actuator parameter selection on system damping, the performance improvement of the active over the passive isolator, the robustness of the control scheme to parameter variation, and the electrical power requirements for the actuator.

The Anchor-Last Deployment Problem for Inextensible Mooring Lines

1975 ◽  
Vol 97 (3) ◽  
pp. 1046-1052 ◽  
Author(s):  
Robert C. Rupe ◽  
Robert W. Thresher
Keyword(s):  
Numerical Model ◽  
Equations Of Motion ◽  
Simultaneous Equations ◽  
Mooring Line ◽  
Integration Scheme ◽  
Lumped Mass ◽  
Mooring Lines ◽  
Concentrated Masses ◽  
Predictor Corrector ◽  
Lagrange’S Method

A lumped mass numerical model was developed which predicts the dynamic response of an inextensible mooring line during anchor-last deployment. The mooring line was modeled as a series of concentrated masses connected by massless inextensible links. A set of angles was used for displacement coordinates, and Lagrange’s Method was used to derive the equations of motion. The resulting formulation exhibited inertia coupling, which, for the predictor-corrector integration scheme used, required the solution of a set of linear simultaneous equations to determine the acceleration of each lumped mass. For the selected cases studied the results show that the maximum tension in the cable during deployment will not exceed twice the weight of the cable and anchor in water.

Torsional Vibrations of a Boiler Feed Pump

1978 ◽  
Vol 100 (4) ◽  
pp. 637-643 ◽  
Author(s):  
A. W. Lees ◽  
K. A. Haines
Keyword(s):  
Flexural Vibration ◽  
Feed Pump ◽  
Lumped Mass ◽  
High Pressure Pump ◽  
Mass System ◽  
Order Of Magnitude ◽  
Vibration Pattern ◽  
Suitable Combination ◽  
Element Technique ◽  
Analytic Models

The paper describes an investigation into the dynamic behavior of a large steam turbine-driven boiler feed pump, following the failure of gearboxes, couplings and bearings. The line consists of a 17 MW turbine driving a four-stage high pressure pump directly and a single-stage booster pump via a 2:1 single-reduction gearbox. Flexural vibration was measured using accelerometers at the bearings and eddy current proximity transducers. The torque transmitted to the gearbox was measured using a four-arm strain gauge bridge mounted in a coupling spacer shaft, the signals being obtained via a telemetry system. The observations showed a complex vibration pattern which was compared with predictions from simple analytic models. A lumped mass system accurately predicted the order of magnitude of oscillatory torque as a function of frequency, given the inevitable errors in gear manufacture. It was shown that the choice of flexible coupling has a crucial effect on the response. The methods of calculation have been generalized to give an accurate model of a system with distributed mass. This is achieved formally using the dynamic Green’s function approach or, for detailed results by a finite-element technique. It was shown that a change of coupling alters the dynamic torque of the system. Hence the effects of a number of changes were calculated and a suitable combination of couplings and gearbox were chosen to implement the practical solution to the problem. The basis for the choice is described and the implications for more general design criteria are discussed.

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