Koichi Matsuda

Optimal Number of Stator Poles for Compact Active Radial Magnetic Bearings

We present a method for finding the optimal number of stator poles for active radial magnetic bearings that minimizes the stator outside diameter. We use magnetic circuit analysis to determine the number of turns of wire to generate the worst case load capacity within limits of coil currents and flux densities. Using the analysis, we developed six types of magnetic bearing for a given value of journal diameter. We found that 3-pole bearings yield the smallest outside diameter among the six types of bearing for a journal diameter less than 50 mm; however, all the bearings have almost the same outside diameter for a journal diameter larger than 200 mm. For an infinite-length bearing, the stator diameter is a linear function of the product of numbers of poles and coil turns. We applied a linear controller design method to a heteropolar 3-pole magnetic bearing that has nonlinear coupling between the orthogonal components of bearing force. With this controller, we successfully levitated a slender-rotor system and rotated it at 3571 rpm.This paper treats the optimal number of stator poles for active radial magnetic bearings in a sense of minimizing the stator outside diameter. The magnetic circuit analysis is used to determine the number of turns of wire to generate the worst case load capacity within limits of coil currents and flux densities. Owing to the analysis, six types of magnetic bearing are designed for a given value of journal diameter. The designed stator outside diameters show that 3-pole bearings are the smallest among the six types of bearing for a smaller value of journal diameter than 50 mm, and, however, all the bearing have almost the same outside diameter when a journal diameter is larger than 200 mm. For an infinite-length bearing, the stator diameter is a linear function of the product of numbers of poles and coil turns. A linear controller design method is applied to a heteropolar 3-pole magnetic bearing that has nonlinear coupling between the orthogonal components of bearing force. A slender-rotor system is successfully levitated by the designed controller and rotated at the speed of 3571 rpm.

Self-Sensing Three-Pole Magnetic Bearing Using a Kalman Filter

Self-sensing active magnetic bearing is designed by a new approach. The approach aims to solve the observer bias problem by introducing a Kalman filter. In order to verify the validity of the approach, a Kalman filter is designed for a three-pole homopolar magnetic bearing and used to estimate the radial displacement and velocity of the rotor. The electric current is driven by a linear power-amplifier circuit to flow through the coils, and the coil terminal voltage is passed through an analog first-order low-pass filter with a cut-off frequency of 100 Hz. The designed Kalman filter uses the filtered coil-voltage and the controller inputs as an input for calculating the estimate. The unobservable bias is estimated as an unknown state, and the Kalman-filter estimates are numerically simulated by the measured input/output data. The results show that the bias is successfully estimated to overlap the estimated displacement to its measurement

Optimal Clearance Configuration of Fluid-Film Journal Bearings for Stability Improvement

This paper aims to optimize a clearance configuration of fluid-film journal bearings. In order to improve stability of a rotating-machinery system, a performance index is given by summing the squared values of the attitude-angles over a region of eccentricity. A Fourier series is used to represent an arbitrary clearance configuration of a bearing, and the problem is to find the Fourier coefficients to minimize the performance index. The problem is numerically solved by a kind of the conjugate gradient method to yield a unique clearance configuration. The optimal clearance configuration is computed for various ratios of length to diameter of a bearing. A rigid-rotor system is used to verify that the designed bearing improves the system stability compared with that of a full circular bearing and to show that this optimization is more effective for shorter bearings.

Stability-Optimized Clearance Configuration of Fluid-Film Bearings

The whirl instability occurs at higher rotating speeds for a full circular fluid-film journal bearing, and many types of clearance configuration have been proposed to solve this instability problem. A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of the full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary clearance configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The designed bearing has a clearance configuration similar to that of an offset two-lobe bearing for smaller length-to-diameter ratios. It is shown that the designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed for a wide range of eccentricity ratio. The load capacity of the designed bearings is nearly in the same magnitude as that of the full circular bearing for smaller length-to-diameter ratios. The whirl-frequency ratios of the designed bearing are very sensitive to truncating higher terms of the Fourier series for some eccentricity ratio. The designed bearings successfully enhance the stability of a full circular bearing and are free from the whirl instability.

An approach to designing a magnetic-bearing system for smaller rotating machines

This paper presents a design of a magnetic-bearing system well suited for a smaller rotating machine. The system contains two 3-pole active radial bearings and an optimal passive axial bearing. The effects of number of stator poles are investigated on the rotor outside diameter for an outer-rotor type of radial bearing, and the investigation reveals that 3-pole bearings yield the smallest rotor outside diameter for a stator-core diameter less than 50 mm. The structural configuration of the axial bearing is also optimized to have the largest support stiffness. Those radial and axial bearings are integrated in a homopolar configuration to yield a smaller magnetic-bearing system.

ATTITUDE CONTROL OF A SPACE ROBOT USING THE NONHOLONOMIC STRUCTURE

This paper treats the attitude control of a space robot using the fact that a free-flying space robot can reorient its attitude only by moving the manipulators. We solve an optimal control problem formulated in a more general way than those of the problems to have been solved so far. That is, our approach can afford to solve the case where the initial and final postures of the manipulators are different and where the solution could not be a smooth and continuous function of time. The optimal control problem is discretized by the rectangular rule into a mathematical programming problem to be solved by the periodically preconditioned conjugate gradient-restoration algorithm. A space-robot model with a multi-link manipulator is used to exemplify the present approach.

Reaction disturbance cancellation for a magnetically levitated ladder arm of clean-room robot

This paper treats a disturbance cancellation problem for minimizing the effects of reaction forces on position accuracy of a clean-room robot applied with magnetic bearings. The robot is composed of a main body and a ladder arm, and moves without friction at joints owing to magnetic support. The support stiffness is, however, weaker than the conventional bearings, and the ladder arm moves in reaction to rotary motion of the main body. A feedforward controller is designed to compensate the effects of the reaction forces, and implemented successfully to reduce the transverse displacements of the ladder arm when the main body rotates.

Stability-optimized clearance configuration of fluid-film journal bearings

A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of a full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The whirl-frequency ratio is inversely proportional to the stability threshold speeds of a Jeffcott rotor. The short bearing approximation is used to simplify a mathematical model that describes a pressure distribution developed in a fluid-film bearing. The designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed subject to the short-bearing assumption and significantly reduces the size of the unstable region for a finite-length bearing with a small length-to-diameter ratio.Copyright

Image-processing approach to vibration isolation of a scanning electron microscope

We propose a new approach to estimating a pointing error of the electron probe of a scanning electron microscope. The approach is formulated to estimate the pointing errors using a specimen image. Specimen images are numerically simulated by a mathematical model and identified with measured images of the specimen using a least-squares procedure to determine the pointing errors. The pointing errors are estimated by the proposed approach and used to design a controller for vibration isolation of a scanning electron microscope. Acceleration sensors are located at the root of the specimen chamber and are used to detect any environmental disturbance into the microscope. The designed controller is based on a transfer function from the sensor outputs to the pointing errors, and the transfer function is determined by sinusoidal excitation tests for the microscope. The controller is implemented as a digital filter on a PC and is used to move the electron probe to cancel the pointing errors using image-shifting coils. The pointing errors are successfully reduced by the controller in a lower frequency region that contains the first four natural frequencies.

New method of vibration isolation of scanning electron microscope

This paper presents a new image-processing approach to estimating a pointing error of the electron probe of a scanning electron microscope. An environmental disturbance causes a pointing error of the probe that is reflected upon a specimen image in a microscope. The new approach uses the deteriorated specimen image to estimate the pointing errors of the probe. The microscale is used as a specimen in this experiment, and a simple mathematical model is used to simulate a microscale image. The mathematical model is obtained by using the surfcace tilt and shadowing contrast of the microscale and by approximating the delta and step functions to differentiable functions. Simulated microscale images are identified by a least-squares procedure with measured images to estimate the pointing error of the probe. The estimated pointing errors are used to design a controller for vibration isolation of a scanning electron microscope. The designed controller is based on a transfer function from acceleration sensor outputs to the pointing errors. An acceleration sensor is situated close to the specimen stage in the microscope chamber to detect the stage motion. Sinusoidal excitation tests are performed to determine the transfer function. The sensor outputs are passed through the designed controller to compute the inputs into the image-shifting coils, and the coils move the electron probe to cancel the pointing errors. The performance of the designed controller is verified by comparing specimen images with and without control when the microscope vibrates. The comparison shows the pointing errors are significantly reduced in a region of lower frequencies.