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.
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