On the Spillover of Steady State Unbalance Response of a Rotating Shaft Under Velocity Feedback

2005 ◽  
Vol 128 (2) ◽  
pp. 143-147 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu
Keyword(s):  
Steady State ◽  
Controller Design ◽  
System Stability ◽  
Feedback Gain ◽  
Beam Model ◽  
Rotating Shaft ◽  
Velocity Feedback ◽  
Reduced Order ◽  
Rayleigh Beam ◽  
Unbalance Response

It has been stated that a uniform rotating shaft in the Rayleigh beam model has only a finite number of critical speeds and precession modes. This paper presents a controller design of optimal sensor/actuator location and feedback gain for steady state unbalance response of a rotating shaft operating in a speed range. For systems under order-limit constraint such that only part of the precession modes can be included in the reduced-order controller design, the system stability can be evaluated. The example of a hinged-hinged rotating shaft is employed to illustrate the controller design of velocity feedback in collocated and noncollocated senor/actuator configuration. Analyses show that the reduced-order controller not only guarantees the closed loop system stability but also effectively suppress the unbalance response.

Vibration Control of a Rotating Shaft: An Analytical Solution

1999 ◽  
Vol 66 (1) ◽  
pp. 254-259 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Feedback Gain ◽  
Beam Model ◽  
Vibration Modes ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Rayleigh Beam ◽  
Sensor Actuator ◽  
Whirl Speed

It has been shown that a rotating shaft in the Rayleigh beam model has only a finite number of whirl speeds and vibration modes when the rotating speed is higher than half of the whirl speed. The system’s unbalanced response can therefore be written analytically by the vibration modes and the generalized coordinates. This paper presents an analytical controller design of optimal sensor/actuator location and feedback gain for minimizing the steady-state unbalanced response. Because all of the critical speeds and vibration modes are included in the controller design, there will be no residual mode, hence no spillover. An example is used to illustrate that the controller design in collocated or noncollocated configuration not only guarantees the closed-loop stability but also effectively suppresses the unbalanced response.

Controller Design of a Distributed Slewing Flexible Structure—A Frequency Domain Approach

1997 ◽  
Vol 119 (4) ◽  
pp. 809-814 ◽  
Author(s):  
S. M. Yang ◽  
J. A. Jeng ◽  
Y. C. Liu
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Controller Design ◽  
System Stability ◽  
Feedback Gain ◽  
Flexible Structure ◽  
Control Law ◽  
Discrete Parameter ◽  
Locus Method ◽  
Beam Experiment

The vibration control of a slewing flexible structure by collocated and noncollocated feedback is presented in this paper. A stability criterion derived from the root locus method in frequency domain is applied to predict the closed-loop system stability of the distributed parameter model whose analytical transfer functions are formulated. It is shown that the control law design requires neither distributed state sensing/estimation nor functional feedback gain; moreover, the spillover problem associated with discrete parameter model can be prevented. Implementation of the noncollocated feedback in a slewing beam experiment validates that the control law is effective in pointing accuracy while suppressing the tip vibration.

scholarly journals Effects of Discrete Damping on the Dynamic Behaviour of Rotating Shaft through Extended Lagrangian Formulation

2016 ◽  
Vol 46 (3) ◽  
pp. 35-64
Author(s):  
Vikas Rastogi
Keyword(s):  
Excitation Frequency ◽  
Continuous System ◽  
Lagrangian Formulation ◽  
Beam Model ◽  
Rotating Shaft ◽  
One Dimensional ◽  
Rotor Shaft ◽  
Rayleigh Beam ◽  
Increase With Increase ◽  
Simulation Results

Abstract The main focus of the paper is touted as effects of discrete damping on the dynamic analysis of rotating shaft. The whole analysis is being carried out through extended Lagrangian formulation for a discrete – continuous system. The variation formulation for this system is possible, considering the continuous system as one-dimensional. The generalized formulation for one dimensional continuous rotary shaft with discrete external damper has been obtained through principle of variation. Using this extended formulation, the invariance of umbra-Lagrangian density through extended Noether’s theorem is achieved. Rayleigh beam model is used to model the shaft. Amplitude equation of rotor is obtained theoretically and validated through simulation results. The simulation results reveal the important phenomena of limiting dynamics of the rotor shaft, which is due to an imbalance of material damping and stiffness of the rotor shaft. The regenerative energy in the rotor shaft, induced due to elasticity/stiffness of the rotor shaft, is dissipated partially through the in-span discrete damper and also through the dissipative coupling between drive and the rotor shaft. In such cases, the shaft speed will not increase with increase in excitation frequency of the rotor but the slip between the drive and the shaft increases due to loading of drive.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

2008 ◽  
Vol 9 (2) ◽  
pp. 300-309 ◽  
Author(s):  
Zi-Li Deng ◽  
Yuan Gao ◽  
Gui-Li Tao
Keyword(s):  
Steady State ◽  
Reduced Order ◽  
Block Diagonal
Sign in / Sign up

Export Citation Format

Share Document