Luis U. Medina

Non-Linear Behaviors in the Motion of a Magnetically Supported Rotor on the Catcher Bearing During Levitation Loss:An Experimental Description

Recent developments improving load capacity foretell the practical implementation of Active Magnetic Bearings (AMB) on industrial level, pushed by the advantages of reduced wear and higher speeds that they make available. However, the possibility of an eventual power failure forces the use of back-up (catcher) bearings, which usually are of the ball bearing type. The back-up bearings present a clearance between the shaft and the inner race, such that there is not contact during normal operation. On a power failure or an emergency stop, the rotor is only supported by the catcher bearings. Thus, the rotor motion within the clearance results on a succession of impacts, contact and non-contact intervals producing a non-linear behavior of the system. The complexity of this non-linear behavior prevents the use of traditional methods for the design of the catcher bearings, calling for the need of extensive experimentation and previous experience in their dimensioning process. Here, the response of a rigid rotor, supported by a pivot on the drive side and a magnetic bearing on the other side, is measured during the emergency stop from several operating speeds. Non-linear analysis tools, such as Poincare Maps and Bifurcation Diagrams, are employed to demonstrate the non-linear characteristics of the motion, which in some conditions is shown to become chaotic with a vibration limit cycle. The rotor motion on the catcher bearings (with the magnetic bearing deactivated) is measured at constant running speeds. The limit cycles and chaotic attractors are described, showing the relation of the non-linear effects to the rotational speed.Copyright

Determining the Effect of Bearing Clearance and Preload Uncertainties on Tilting Pad Bearings Rotordynamic Coefficients

Tilting Pad Journal Bearings (TPJB) are commonly used in high-speed and high-power turbomachines, due to their contributions in avoiding rotor instabilities. Studies related to the estimation of dynamic coefficients have been carried out considering nominal values of the geometric parameters (clearance and preload) for all bearing pads. However, the unavoidable uncertainties on these geometric parameters and, therefore their possible influence on the TPJB rotordynamic coefficients do not seem to have been discussed enough. In a previous work, a numerical study was conducted to examine the influence of preload and bearing clearance variations on a five-pad TPJB rotordynamic coefficient. The current work is an extension of that paper, considering at this time the Design of Experiments framework. By means of a 2k factorial design and ANOVA random effect model, uncertainties on bearing clearance and pad preload values are introduced in a standard numerical model (i.e. finite element model) used to estimate the direct and cross-coupled dynamic stiffnesses of the five pad TPJB. The influence on these dynamic coefficients, due to the variance of the aforementioned geometric parameters, is discussed and presented in graphical form in order to illustrate the sensitivity of the TPJB dynamic coefficients. Results derived from this study show that variations on loaded pads affect the direct dynamic coefficients, and unloaded pads variations influence the cross-coupled dynamic coefficients. This work contributes to the understanding of the sensitivity of TPJB dynamic coefficients to manufacturing tolerances.Copyright

Neural Network Emulation of a Magnetically Suspended Rotor

The use of magnetic bearings in high speed/low friction applications is increasing in industry. Magnetic bearings are sophisticated electromechanical systems, and modeling magnetic bearings using standard techniques is complex and time consuming. In this work a neural network is designed and trained to emulate the operation of a complete system (magnetic bearing, PID controller, and power amplifiers). The neural network is simulated and integrated into a virtual instrument that will be used in the laboratory both as a teaching and a research tool. The main aims in this work are: (1) determining the minimum amount of artificial neurons required in the neural network to emulate the magnetic bearing system, (2) determining the more appropriate ANN training method for this application, and (3) determining the errors produced when a neural network trained to emulate system operation with a balanced rotor is used to predict system response when operating with an unbalanced rotor. The neural network is trained using as input the position data from the proximity sensors; neural network outputs are the control signals to the coil amplifiers.

Asynchronous Dynamic Coefficients of a Three-Lobe Air Bearing

The study of dynamic whirl behavior of air bearings is fundamental for an adequate rotordynamic analysis and future validation of numerical predictions. This work shows the dynamic response of the air film on a three-lobe bearing under asynchronous whirl motion. One-dimensional multifrequency orbits are used to characterize the bearing rotordynamic coefficients. The test rig uses two magnetic bearing actuators to impose any given orbits to the journal. The dynamic forces are measured on the test bearing housing by three load cells. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. The multifrequency excitation is applied at each rotating speed up to 11,000 rpm, allowing the asynchronous characterization of the air film. The experimental procedure requires two linearly independent excitation sets. Thus, vertical and horizontal one-dimensional multifrequency orbits are applied as perturbations. Results show the synchronous and asynchronous dynamic coefficients of the air bearing. Asynchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation. Numerical dynamic coefficients are obtained as the effective coefficient values of the bearing when subject to a given orbit. A full characterization of the asynchronous rotordynamics coefficients of the bearing is presented in three-dimensional maps.

A Neural Network-Based Closed Loop Identification of a Magnetic Bearings System

This paper deals with the identification of a radial-type active magnetic bearing (AMB) system using Artificial Neural Network (ANN). Identification and validation experiments are performed on a laboratory magnetic bearing system. Since the electromechanical configuration is inherently unstable, the identification data is gathered while the AMB is operating in closed loop with a controller in the loop. From this data, the identification procedure generates an open-loop plant model. A NNARX (Neural network autoregressive external input model) structure is proposed and evaluated for emulating the system’s dynamic. The model is implemented by a Neural network, constructed using a multilayer perceptron (MLP) topology, and trained using as inputs the rotor’s displacements and excitation currents. Validation tests are performed under perturbation conditions (impact applied on the rotor). Results show that the neural network based model presented here is a powerful tool for dynamic plant’s identification, and that it could be also suitable for robust control application.Copyright

On Uncertainty Propagation in Mass, Damping and Stiffness Matrices Identification of Mechanical Systems

The accuracy in estimating the mass, damping and stiffness matrices for mechanical systems depends on the error propagation through the stages involved in the parameter identification, i.e. excitation and response measurements, signal processing and modeling stages. Robust algorithms are available to estimate the system’s parameters in the presence of “noisy” measurements. However, uncertainties in the identified parameters of mechanical systems have not been usually reported or have simply been overlooked in the identification strategy. An overall uncertainty occurs for each identified parameter, and it may be defined in terms of error propagation. The recognition of relevant error contributions is the key to accomplishing parameter error estimation in the identification process, a task that may imply subtle aspects. An approach is proposed for uncertainty estimation in mass, stiffness and damping matrices for linearized mechanical systems. This approach is formulated as an extension of the accepted practice for evaluating experimental uncertainty for a scalar measurand. Typical error sources throughout the identification stages are also discussed. The suggested approach may be applied to identify mechanical systems in the frequency domain, and is independent of the algorithm used to estimate the system parameters. Practical limitations of the suggested approach are also discussed.Copyright

A Simple Approach to Determine Uncertainty Bounds on Bearing Rotordynamic Coefficients Identification

The majority of rotordynamic studies concerned with bearing properties identification estimate rotordynamic coefficients without addressing the issue of parameter uncertainties. Uncertainty quantification is required to establish the accuracy and therefore the robustness of the identified parameters. Accuracy on the identification methodology is hampered by measurement noise, experimental and modeling error, and numerical method. The aim of this article is to determine, by means of error analysis, the propagated uncertainty contributions in a parametric frequency-domain identification. The methodology is based on linearly independent excitations for a direct estimation of the bearing rotordynamic coefficients. Errors on measurable excitations and responses are considered in the identification strategy to evaluate uncertainties of the estimated parameters. General formulation using errors-in-variables noise model is presented for system identification, taking into account uncertainty propagation in bearing parameters estimation. Experimental measurements, obtained from a test rig, are employed to estimate rotordynamic coefficients of a three lobe air bearing and the associated uncertainties. Confidence intervals are suggested for the expected bearing coefficients. A Monte Carlo simulation is conducted to study the statistical behavior as a result of simulated stochastic uncertainty propagation for comparison purposes with the experimental evidence. Results are presented graphically to assess the influence of the uncertainty propagation on the bearing properties calculation.Copyright

Asynchronous Dynamic Coefficients of a Three Lobe Air Bearing

The study of dynamic whirl behavior of air bearings is fundamental for an adequate rotordynamic analysis and future validation of numerical predictions. This work shows the dynamic response of the air film on a three lobe bearing under non-synchronous whirl motion. One-dimensional multifrequency orbits are used to characterize the bearing rotordynamic coefficients. The test rig uses two magnetic bearing actuators to impose any given orbits to the journal. The dynamic forces are measured on the test bearing housing by three load cells. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. The multi frequency excitation is applied at each rotating speed up to 11000rpm allowing the non-synchronous characterization of the air film. The experimental procedure requires two linearly independent excitation sets. Thus, vertical and horizontal one-dimensional multi-frequency orbits are applied as perturbations. Results show the synchronous and asynchronous dynamic coefficients of the air bearing. Asynchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation. Numerical dynamic coefficients are obtained as the effective coefficient values of the bearing when subject to a given orbit. A full characterization of the non-synchronous rotordynamics coefficients of the bearing is presented in three dimensional maps.Copyright

Experimental Measurement of a Three Lobe Air Bearing Rotordynamic Coefficients

This work presents direct experimental measurements of air film rotordynamic coefficients on a three lobe bearing. The test rig uses two magnetic bearing actuators to impose desired test orbits to the journal. Tests are conducted at several rotating speeds up to 12,000rpm. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. One-dimensional orbits in the horizontal and vertical axes are applied as excitations at each rotating speed. The experimental results show the behavior of the rotordynamic coefficients of the air film bearing under synchronous and asynchronous excitation. The synchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation coupled with the pressure drop through the feeding holes. The results of this work prove the suitability of the rig to identify both the synchronous and nonsynchronous response of air fluid film bearings.© 2006 ASME

A Simple Kinematic Model for the Behavior of a Magnetically Levitated Rotor Operating in Overload Regime

Currently, the use of magnetic levitation systems has incremented in lieu of the many advantages they present respect to conventional systems. They provide frictionless operation and thus, a wearless life, eliminate the need for lubricants and allow for active vibration control. However, there are some limitations to their use, the dynamic load capacity is restricted by the magnetic properties of the materials used in their constructions and, therefore, their tolerance to large dynamic loads, such as in the case of blade loss or similar sudden failures, is small. For these cases, as well as for the case of bearing power loss, all commercial magnetic suspensions contain a safety backup system, usually consisting of roller bearings that avoid contact between stationary and rotating parts. The present work analyses the behavior of a rotor supported by a magnetic radial bearing on the non-drive end, which is operated in an overload regime. In this regime, a series of impacts occurs between the rotor and the backup bearing, which results on a highly non-linear system that might become unstable depending on the geometry, the control algorithm, the speed and excitation conditions. A non-linear model is proposed. The equations are separated into two regimes, one when the rotor is levitated and one during contact with the backup bearings; the contact is modeled by kinematic conditions. The magnetic bearing forces are estimated using a non-linear model and a PID algorithm is considered as a system’s control strategy. Rigid body theory for planar collision is considered for description of impacts between the backup bearing and the rotor.Copyright