Alexander H. Pesch

Magnetic Bearing Spindle Tool Tracking Through

A method is presented for tooltip tracking in active magnetic bearing (AMB) spindle applications. The proposed tool tracking approach uses control of the AMB air gap to achieve the desired tool position. A μ-synthesis-based controller is designed for the AMBs with the goal of robustly minimizing the difference between the tool reference and estimated tool position. In such a way, the model-based control approach concurrently addresses the tracking problem and the inability to directly measure real-time tool position in the presence of machining disturbances. To ensure the tractability of the control problem, a model of the desired tracking dynamics is included in the plant. The method is demonstrated on a high-speed AMB boring spindle. To confirm the tool tracking capability, characteristic part geometries are traced including stepped, tapered, and convex profiles. Tool tracking is demonstrated for the rotating AMB spindle in the range of 90 μm. Also, static and dynamic external loading is applied to the spindle tool location to confirm the disturbance rejection ability of the closed-loop system.

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This paper presents an experimentally driven model updating approach to address the dynamic inaccuracy of the nominal finite element (FE) rotor model of a machining spindle supported on active magnetic bearings. Modeling error is minimized through the application of a numerical optimization algorithm to adjust appropriately selected FE model parameters. Minimizing the error of both resonance and antiresonance frequencies simultaneously accounts for rotor natural frequencies as well as for their mode shapes. Antiresonance frequencies, which are shown to heavily influence the model’s dynamic properties, are commonly disregarded in structural modeling. Evaluation of the updated rotor model is performed through comparison of transfer functions measured at the cutting tool plane, which are independent of the experimental transfer function data used in model updating procedures. Final model validation is carried out with successful implementation of robust controller, which substantiates the effectiveness of the model updating methodology for model correction.

-Synthesis Robust Control

The purpose of this paper is to present a method for development of the optimal speed-dependent control matrix for a rotor supported on active magnetic bearings (AMBs) with the provision of minimum control power consumption over the operating speed range. The speed dependency of the optimal control matrix is the result of the dynamics of rotating machines. Most of published works on optimal control use a stationary optimal control matrix derived for the non-rotating system and thus neglecting the effect of gyroscopic phenomena. This paper employs the minimum energy consumption condition to derive the speed varying optimal control for rotating AMB rotor system. In the presented approach the control matrix is characterized by a second order polynomial matrix with the angular speed as a variable. This leads to a more compact and lower computational burden for controller implementation. Calculations are performed for a 4-axis AMB rotor test rig. Testing with rotor speed ramps is performed and experimental values for power consumption are presented. These results are compared to results with speed invariant optimal control and PID control.Copyright

Rotor Model Updating and Validation for an Active Magnetic Bearing Based High-Speed Machining Spindle

Robust control techniques have allowed engineers to create more descriptive models by including uncertainty in the form of additive noise and plant perturbations. As a result, the complete model set is robust to any discrepancies between the mathematical model and actual system. Experimental unfalsification of the model set leads to the guarantee that the model and uncertainties are able to recreate all experimental data points. In this work, such a robust control relevant model validation technique is applied to structural health monitoring in order to 1) detect the presence of damage and 2) identify the damage dynamics when used in conjunction with model-based identification. Additionally, the robust control relevant model validation technique allows for a novel quality measure of the identified damage dynamics. Feasibility of the method is demonstrated experimentally on a rotordynamic crack detection test rig with the detection and identification of a change in structure. Further insight is gained from application of the method to seeded damage on a rotor levitated on active magnetic bearings in the form of a local reduction in stiffness.Copyright

Experimental Investigations of Minimum Power Consumption Optimal Control for Variable Speed AMB Rotor

Active magnetic bearings (AMBs) provide support to rotating machinery through magnetic forces which are regulated through active feedback control. As AMBs continue to establish themselves as a proven technology, many classical and modern techniques are being employed to address the design of the control law. The current work studies three of the controller design techniques which are common in the literature for AMB applications: PID, LQG, and μ-synthesis. A controller is designed for an AMB system using each of the three techniques. Details of the design processes are given and the resulting controllers are compared. Finally, the controllers are implemented on the experimental system and the closed-loop characteristics are measured and evaluated. This work provides a common case study to demonstrate the strengths and weaknesses of PID, LQG, and μ-synthesis control methodologies as applied to a specific AMB system.Copyright

Model Validation for Identification of Damage Dynamics

Robust control techniques have enabled engineers to create uncertain models which are able to describe any differences between the model and actual system with uncertainties in a combination of exogenous inputs and plant perturbations. Model validation techniques arose to provide a guarantee that the uncertain model is able to recreate all experimental data. Such model validation techniques have been successfully applied to structural healthy monitoring, invalidating the healthy model when compared to data taken in the presence of damage. Additionally, the technique of model-based identification, originally created to identify the dynamics resulting from unmodeled or under-modeled components in rotordynamic systems, has been employed to identify the difference in dynamics due to the presence of damage. In previous work, the authors detected and identified the change in dynamics in a rotordynamic test rig due to a change in structure. Later, the authors extended the technique to a local change in dynamics due to an approximated crack in a rotor. In the present work, the approach is extended further to identifying the dynamics due to a breathing crack approximation in a similar rotordynamic test setup, with comparison to simulation. Refinement of the model-based identification technique is conducted to account for any errors between the healthy model and data, allowing for a finer look at the contribution due to the damage. doi: 10.12783/SHM2015/64

A Case Study in Control Methods for Active Magnetic Bearings

Robust control techniques have allowed engineers to create model sets which are robust to deviations from the actual system through the use of model uncertainty in the form of both additive noise and plant perturbations. To ensure the quality of the uncertain model, experimental unfalsification is employed to guarantee that the model set is able to recreate all experimental data points. In previous work, such a robust control relevant model validation technique was employed to identify the presence of damage on a rotordynamic test rig. Additionally, model-based identification was employed to model the overall change in dynamics due to the damage, as well as to provide a novel quality measure for the identified damage dynamics. In the present work, the technique is extended to include a rotordynamic model. This advancement allows for locating the damage source and to determine the local change in dynamics at the damage location. The method is demonstrated experimentally on a rotordynamic test rig through the identification of a wire EDM cut in the shaft and determination of the local change in dynamics, including axial position along the shaft.

A Combined Model-Based Identification and Model Validation Approach for Damage Identification

Oil whip is a self-excited vibration in a hydrodynamic bearing which occurs when the rotation speed is above approximately twice the first natural frequency. Because of this, the oil whip phenomenon limits the operational speed of a rotor system on hydrodynamic bearings. Below the oil whip threshold, the related phenomenon of oil whirl can cause large vibrations at frequencies below half the rotation speed.A method is presented for stabilizing oil whip and oil whirl in a hydrodynamic bearing with an active magnetic bearing (AMB). The AMB controller is designed with μ-synthesis model-based robust control utilizing the Bently-Muszynska fluid film bearing model, which predicts the unstable phenomena. Therefore, the resulting AMB controller stabilizes the natural instability in the hydrodynamic bearing. Rotor speed is taken into account by use of a parametric uncertainty such that the method is robust to changes in running speed.The proposed method is demonstrated on an experimental hydrodynamic bearing test rig. Details of the test rig and implementation of the AMB controller design are presented. Waterfall plots for the controlled and uncontrolled system are presented which demonstrate the improved stability limit.Copyright

Model Validation for Damage Identification and Determination of Local Damage Dynamics

The hybrid system approach is used to minimize losses in the AMB system by switching controllers and bias current. The method is validated with experimental results at steady state and rotating system. With high bias orbits of the rotor are reduced while in the absence of disturbance the losses are minimized with low bias. The switching rules based on inner variables of the control system are proposed.

Stabilizing Hydrodynamic Bearing Oil Whip With μ-Synthesis Control of an Active Magnetic Bearing

A structural change quantification methodology is proposed in which the magnitude and location of a structural alteration is identified experimentally in a rotor system. The resonance and antiresonance frequencies are captured from multiple frequency response functions and are compared with baseline data to extract frequency shifts due to these features. The resulting expression contains sufficient information to identify the dynamic characteristics of the rotor in both the frequency and spatial domains. A finite element model with carefully selected tunable parameters is iteratively adjusted using a numerical optimization algorithm to determine the source of the structural change. The methodology is experimentally demonstrated on a test rig with a laterally damaged rotor and the frequency response functions are acquired through utilization of magnetic actuators positioned near the ball bearings.Copyright