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 spin dle 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 cut ting tool plane, which are independent of the experimental transfer function data used in model updating procedures. Final model validation is carried out with successful imple mentation of robust controller, which substantiates the effectiveness of the model updat ing methodology for model correction.
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.
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 spin dle 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 cut ting tool plane, which are independent of the experimental transfer function data used in model updating procedures. Final model validation is carried out with successful imple mentation of robust controller, which substantiates the effectiveness of the model updat ing methodology for model correction.
A method is presented for tool tracking in active magnetic bearing (AMB) spindle applications. The method uses control of the AMB air gap to achieve the desired tool position. The reference tracking problem is transformed from the tool coordinates into the AMB control axes by bearing deflection optimization. Therefore, tool tracking can be achieved by an off-the-shelf AMB controller. The method is demonstrated on a high-speed AMB boring spindle with a proportional integral derivative (PID) control. The hypothetical part geometries are traced in the range of 30 lm. Static external loading is applied to the tool to confirm disturbance rejection. Finally, a numerical simulation is performed to verify the ability to control the tool during high-speed machining.
A rotor supported on active magnetic bearings (AMBs) is levitated inside an air gap by electromagnets controlled in feedback. In the event of momentary loss of levitation due to an acute exogenous disturbance or external fault, reestablishing levitation may be prevented by unbalanced forces, contact forces, and the rotor's dynamics. A novel robust control strategy is proposed for ensuring levitation recovery. The proposed strategy utilizes model-based µ-synthesis to find the requisite AMB control law with unique provisions to account for the contact forces and to prevent control effort saturation at the large deflections that occur during levitation failure. The proposed strategy is demonstrated experimentally with an AMB test rig. First, rotor drop tests are performed to tune a simple touchdown-bearing model. That model is then used to identify a performance weight, which bounds the contact forces during controller synthesis. Then, levitation recovery trials are conducted at 1000 and 2000 RPM, in which current to the AMB coils is momentarily stopped, representing an external fault. The motor is allowed to drive the rotor on the touchdown bearings until coil current is restored. For both cases, the proposed control strategy shows a marked improvement in relevitation transients.
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.
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