Gabriele Barbaraci

Active magnetic bearing design study

The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of vane is large enough to host an AMB. As this substitution could offer some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The journal ratio is the geometrical parameter introduced to develop the present analysis. The variation of journal ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on shaft when it is tested by disturbance rejection and reference tracking input in order to analyze the differences on dynamic behavior of the shaft on its suspended sections. Results show that the displacement pattern of the suspended sections remains unchanged, confirming that the reaction load, produced by pole expansion, remains the same varying the journal ratio.

Performances comparison for a rotating shaft suspended by 4-axis radial active magnetic bearings via µ-synthesis, loop-shaping design, and sub(H) ∞ with uncertainties

The control systems applied on active magnetic bearing are several. A perfect levitation is characterized by maintaining the operating point condition that is characterized by the center of stator coincident with the geometric center of shaft. The first controller implemented for this purpose is PID controller that is characterized by an algorithm that leads the amplifier to produce control current until the operating point condition is not reached, this is obtained by an integration operator. The effect of an integrator is essential but not necessary for a centered levitation for example in the robust control characterized by a dynamic model depended on plant of system so that it depends on angular speed as LQR controller does. In LQR there is not integrator so there is not a perfectly centered section of shaft with center of stator. On contrary PID controller does not depend on angular speed and it can be easily implemented according some simple rules. Predictive control is another interesting controller characterized by a multiple controller operating in different condition in order to get the minimum of cost function, but also in this case the angular speed is introduce for the same reason discussed before.

Axial active magnetic bearing design

The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of the vane is large enough to host an AMB. As this substitution could give some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The coil ratio is the geometrical parameter introduced to develop the present analysis. The variation of coil ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on the shaft when it is tested by a step response and performing frequency response parameterized with coil ratio. Results show that the displacement carried out by the step response is always the same, when the journal ratio and frequency response are varied, confirming that the reaction load, produced by pole expansion, remains the same when the coil ratio varies. The simulations and results are performed by finite element method magnetic and MATLab software.

An estimator algorithm for the rotation time of magnetization vector in nuclear magnetic resonance for imaging (NMRI)

The purpose of this paper is to propose a useful method to investigate the rotation time of the magnetization vector in the nuclear magnetic resonance for imaging (NMRI) system. The ninety degrees rotation of the magnetization vector is the first step in order to establish the free induction decay that radiates electromagnetic energy inside the NMRI chamber. The estimator involved in this research is called Luenbergers observer which is a state estimator of a dynamical system. The Blochs equation is a dynamical system characterized by a radio frequency (RF) impulse located inside the dynamic matrix, which means the system is not linear. The observer algorithm involved in this paper estimates each vectors component of the Blochs dynamic model characterized by the magnetizations along the x, y and z direction which are axles located inside the NMRI chamber where the z axis has the same direction of the uniform magnetic field. The result is compared with one shown in the literature which results coincident with estimation. The estimator has been calculated in a closed form except in some cases where the symbolic expression makes the mathematical characterized by a high computational burden. The expression of the solutions is calculated by using the Heaviside expansion once the poles of the dynamical systems characterizing the Blochs differential equations system are known. A set of simulations is carried out by using different configurations of the observer that have been calculated formerly without considering the RF pulse and subsequently with its introduction showing how the Blochs dynamical system is affected by the skew symmetric matrix which is typical of a gyroscopic dynamical system. This likelihood produces a time estimation of the rotation vector which is slightly higher than the estimated value offered in the literature.

Optimal Damping Constant Investigation on a Quarter-Car

This paper shows an investigation on optimal damping constant performed in the frequency domain. The optimal damping constant is meant as that value that minimizes the acceleration of all connected bodies characterizing a two degree of freedom system sketching a quarter car. The connected bodies are sprung and unsprung mass respectively for quarter of chassis and tire, this last keeps the contact with the ground and it is connected with the sprung mass through a shock absorber characterized by spring and fluid damper. Optimal damping constant was determined by imposing analytical conditions on the expression of acceleration of two masses. Afterwards, the variation of acceleration and position in function of frequency for the obtained value of damping constant is plotted numerically in two ways using Wolfram Mathematica and MSC Adams software.

Influence of Uncertainties on PD Tuning

The aim of this work is to present a method for tuning the parameters of PD controller under the influences of the uncertainties, in order to stabilize the position of a rotor supported by active magnetic bearings (AMBs). The uncertainties are relative to mass, transverse and polar moment of inertia of the rotor. The introduction of the uncertainties is due to an incomplete modeled dynamic of the system or in the case the system being subjected to a parametric variation. The presence of the uncertainties produces a set of differences among the values of the output. Poles displacement method is used to reach the asymptotically stability condition characterized by a periodic oscillation during the transient response as a consequence of the impulse input. In this way we carried out some particular condition under graphical representation which helps making a prevision when the phenomena of instability occurs. In the present approach the poles displacement is obtained by imposing respectively the condition on the real part, which must be negative, and in the discriminant of a second degree equation, which must be less than zero, both depend on the uncertainties and the angular speed of the rotor. All calculations are performed through a 4-axis AMB rigid rotor to validate the PD controller method rule introduced in this work.