Spherical Rotor Research Articles

Modeling and Analysis of Drift Error from Stator of A MSSG with Double Spherical Envelope Surfaces

For the newly developing magnetically suspended sensitive gyroscope (MSSG) with double spherical envelope surfaces, it is necessary to analyze the causes of drift error to improve sensing accuracy. This paper builds the models of disturbing torques generated by stator assembly and process errors based on the geometric construction and running regularity of the MSSG, and further reveals the generation mechanism of the drift error. Then the drift error from a single stator magnetic pole is calculated quantitatively with the established model, and the key factors producing the drift error are further discussed. It is proposed that the main approaches in reducing the drift error from stator are guaranteeing the rotor envelope surface to be an ideal spherical and improving the controlling precision of rotor displacement. The common problems associated in a gyroscope with a spherical rotor can be effectively resolved by the proposed method. This analysis provides a reference for the structure optimization and error compensation of a MSSG.

Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.

The Shell-Like Spherical Induction Motor for Low-Speed Traction: Electromagnetic Design, Analysis, and Experimental Tests

This paper analyzes the electromechanical characteristics of a novel shell-like spherical induction machine with multiple degrees-of-freedom (DOF), formed by a shell stator and a spherical hollow rotor. The shell-like induction machine is evaluated using n -harmonic analytical models for its electromechanical characteristics. The electromechanical model includes the distribution of the copper windings in the stator slots, incorporating the currents harmonic content to describe its spatial distribution. The distribution of the magnetic potential vector and the components of the magnetic flux density are computed using the real source-current distribution. A small prototype was built to validate the analytical model. To do so, experimental tests were done to the magnetic flux density and the torque. The shell-like induction motor is concretized as traction motor in an electric wheel-chair. Its results are compared with a finite-element analysis tool.

Study on spherical stator for multidegree-of-freedom ultrasonic motor

A multidegree-of-freedom ultrasonic motor (MDOF-USM) has excellent features such as high torque at a low speed and a self-holding force, compared with other types of MDOF motor. Therefore, the MDOF-USM has been considered for applications in robot joints, multidimensional systems, and spacecraft. In previous research, the MDOF-USM consisting of a spherical rotor and a stator vibrator of various shapes has been mainly studied. In contrast, the MDOF-USM consisting of a spherical stator and a rotor of various shapes is proposed in this paper. The excitation methods for vibration modes and mode rotation using piezoelectric plates and multilayered piezoelectric actuators were examined. Furthermore, a stator support method that does not significantly affect the vibration of the sphere was devised. From the results of experiments using the fabricated prototype stator, the generation of vibration mode and mode rotation were confirmed. Therefore, the possibility of the realization of the MDOF-USM using a spherical stator was indicated.

Sandwich-Type Multi-Degree-of-Freedom Ultrasonic Motor With Hybrid Excitation

A sandwich-type multi-degree-of-freedom (MDOF) ultrasonic motor with hybrid excitation is proposed in this paper. The motor adopts pair combination of three resonance modes to drive the sphere rotations around three coordinate axes. When the sphere rotates around any axis, all piezoelectric ceramics of the proposed motor are excited for the vibration of the motor. The final structure parameters of the motor are confirmed by way of finite element method, and the elliptical motion trajectories of the driving areas are verified. At last, the prototype is fabricated and tested. The prototype achieves no-load speeds of 109.8 r/min, 107.9 r/min, and 290.8 r/min in the YOZ, XOZ, and XOY driving modes, respectively. The proposed motor employs only four pieces of lead zirconate titanate ceramics to achieve the MDOF rotations of a spherical rotor.

Satellite Attitude Control System Using a Spherical Reaction Wheel

A reaction wheel is generally capable of providing single axial torque. Three separated devices were indispensable for controlling three-axis attitude of a satellite. The proposed system, which is called spherical reaction wheel, enables three-dimensional rotation of a spherical rotor and provides three-dimensional torque so that mounting only one proposed device can be sufficient to control three-axis attitude of a satellite. Furthermore, the system reduces size and weight of an attitude control system in comparison with the conventional system. To confirm the validity of the proposed device as an attitude control system, we conduct experiments concerning attitude control of a small satellite model with PID controller.

Closed-loop magnetic bearing and angular velocity control of a reaction sphere actuator

This article presents the first closed-loop magnetic bearing and angular velocity experimental results of a reaction sphere actuator for satellite attitude control. The proposed reaction sphere is a permanent magnet spherical actuator whose rotor is supported by magnetic bearing and can be torqued electronically about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-pole stator with electromagnets. The electromechanical model of the reaction sphere is summarized together with procedures to estimate the rotor magnetic state, the back-EMF voltage, and the rotor angular velocity, which are all fundamental ingredients for controller design. Dynamic controllers are developed to levitate the rotor inside the stator (magnetic bearing) and to control the rotor angular velocity. The magnetic bearing is based on a state-space controller with reduced-order displacement velocity estimator whereas the angular velocity controller is a simple proportional controller with a dedicated angular velocity estimator. The developed control algorithms are experimentally validated using the developed laboratory prototype showing the ability of simultaneously levitating the rotor while rotating it about a given arbitrary axis.

A novel two-degree-of-freedom spherical ultrasonic motor using three travelling-wave type annular stators

In order to promote the tolerance and controllability of the multi-degree-of-freedom (M-DOF) ultrasonic motor, a novel two-degree-of-freedom (2-DOF) spherical ultrasonic motor using three traveling-wave type annular stators was put forward. Firstly, the structure and working principle of this motor were introduced, especially a spiral spring as the preload applied component was designed for adaptive adjustment. Then, the friction drive model of 2-DOF spherical motor was built up from spatial geometric relation between three annular stators and the spherical rotor which was used to analyze the mechanical characteristics of the motor. The optimal control strategy for minimum norm solution of three stators’ angular velocity was proposed, using Moore-Penrose generalized inverse matrix. Finally, a 2-DOF prototype was fabricated and tested, which ran stably and controllably. The maximum no-load velocity and stall torque are 92 r/min and 90 mN·m, respectively. The 2-DOF spherical ultrasonic motor has compact structure, easy assembly, good performance and stable operation.

Supersymmetry and eigensurface topology of the spherical quantum pendulum

We undertook a mutually complementary analytic and computational study of the full-fledged spherical (3D) quantum rotor subject to combined orienting and aligning interactions characterized, respectively, by dimensionless parameters $\eta$ and $\zeta$. By making use of supersymmetric quantum mechanics (SUSY QM), we found two sets of conditions under which the problem of a spherical quantum pendulum becomes analytically solvable. These conditions coincide with the loci $\zeta=\frac{\eta^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $\eta$ and $\zeta$ parameters. The integer topological index $k$ is independent of the eigenstate and thus of the projection quantum number $m$. These findings have repercussions for rotational spectra and dynamics of molecules subject to combined permanent and induced dipole interactions.

Analysis of Electrostatic Suspension Kinematic Characteristics of Hollow Be Rotor

The hollow Be rotor is a spherical rotor with high accuracy, it has been grinded by the four-shaft-ball lapping machine. The rotor is a hollow sphere with non-uniform wall structure and there are errors between geometric center and mass center. Analyze the affect of eccentric distance and harmonic coefficients to the working condition of the rotor, establish the kinematic balance equation of rotor that is solved by Matlab software, and draw the rotor motion law with the change of time. The results indicate that with the decrease of eccentric distance of the rotor, the influence of damped motion decrease significantly. The influence on the damped motion of the rotor can be negligible when the eccentric distance is less than or equal to 0.051μm. The larger the harmonic coefficients, the faster the rotor attenuate.

Digital image processing method for static balance measurement of incomplete spherical rotor with air suspension

Measurement and calibration of mass imbalance for rotors are often indispensible as mass imbalance will cause undesired vibration and present serious problems accordingly. In this study, a new method based on digital image processing (DIP) to measure the mass imbalance of a special rotor with air suspension is introduced. By hunting the trace of tilt angle through several identification points on the rotor by DIP, the corresponding oscillating period will be determined, which in turn contributes to the calculation of mass imbalance. Two-dimensional monochrome charge-coupled device (CCD) and peripheral component interconnect (PCI) image board are applied in the experiment to capture the rotor's image, and several user interfaces are developed for image processing and curve fitting as well. Besides, the system error analysis and the comparison of experimental results with that of other related work are provided, which prove the effectiveness and accuracy of this DIP method.

Development of a spherical reaction wheel actuator using electromagnetic induction

A spherical reaction wheel is a novel three-axis induction motor consisting of a spherical rotor and electromagnets. The electromagnets allow the rotor to levitate and to rotate about any desired axis without mechanical contact. A benefit of the actuator is to control the satellite for three-axis attitude using the single spherical reaction wheel. In this study, a prototype model of the spherical reaction wheel with a single rotating axis is developed, and a feasibility study on the actuator is conducted. The actuator system is designed through electromagnetic field analyses of the spherical rotor in order to evaluate the levitation force and torque. Dynamic performance tests are carried out under electromagnetic rotation and levitation conditions, and torque-speed characteristics are investigated. Using the test data, torque modeling and velocity control simulations are also performed. Finally, closed loop speed control tests are conducted on the experimental model. The model shows that the maximum torque and speed are 0.7 N m and 13,500 rpm, respectively, and the speed control error is less than 4%.

Rotor Design Optimization for a Reaction Sphere Actuator

This paper presents the rotor design optimization for a reaction sphere (RS) actuator. The RS is a permanent-magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The RS is composed of an 8-pole permanent-magnet (PM) spherical rotor and of a 20-coil stator. Due to the highly complex geometry of the spherical rotor, consisting of eight bulk PM poles with truncated spherical shape adjusted on the back-iron structure with truncated octahedral shape, a pure analytical approach for the optimization problem is not practicable. Therefore, given a set of specifications, the optimization of design parameters is performed using finite-element simulations to minimize the rotor magnetic flux density distortion with respect to the fundamental harmonic. The resulting optimized rotor is fully compliant with design specifications. Finally, experimental measurements on the manufactured rotor are reported showing a strong correspondence with the specified flux density values.

A curved ultrasonic actuator optimized for spherical motors: Design and experiments

Multi-degree-of-freedom angular actuators are commonly used in numerous mechatronic areas such as omnidirectional robots, robot articulations or inertially stabilized platforms. The conventional method to design these devices consists in placing multiple actuators in parallel or series using gimbals which are bulky and difficult to miniaturize. Motors using a spherical rotor are interesting for miniature multidegree-of-freedom actuators. In this paper, a new actuator is proposed. It is based on a curved piezoelectric element which has its inner contact surface adapted to the diameter of the rotor. This adaptation allows to build spherical motors with a fully constrained rotor and without a need for additional guiding system. The work presents a design methodology based on modal finite element analysis. A methodology for mode selection is proposed and a sensitivity analysis of the final geometry to uncertainties and added masses is discussed. Finally, experimental results that validate the actuator concept on a single degree-of-freedom ultrasonic motor set-up are presented.

Miniaturized high-precision piezo driven two axes stepper goniometer.

A miniaturized inertial stepper goniometer with two orthogonal axes (θ and φ axes) has been realized using four shear piezo based actuators arranged in a tetrahedral configuration tangent with a polished sapphire spherical rotor. The measured sensitivity is about 11.5 microdegree (μ°) per Volt. The smallest angular step size, achieved with a minimal peak-to-peak voltage Upp of 200 V is about 0.6 millidegree (m°). The crosstalk between both axes is below 10%. Our specific design is used to accurately position a glass fiber, but the concept can be utilized for many different applications as well.

球状リアクションホイールによる三軸姿勢制御

The principal function of a control system for a small vehicle is to generate or counteract its angular momentum. A straightforward approach to exerting control torque is to use three separate flywheels with motors in a mutually orthogonal arrangement. This paper describes the development of a three-dimensional reaction wheel using a spherical rotor that can reduce the number of flywheels from three to one. Therefore, the proposed system can be applied to a small satellite with space and weight limitations. The system consists of the spherical rotor, three piezoelectric actuators as the stator, and optical sensors. The spherical rotor can rotate around arbitrary axes without a very complex mechanism using gears, links, and special mechanism. A feedback control system is designed to control the angular velocity vector of the spherical rotor. The performance of the proposed system is verified through preliminary experiments.

Design of a noncontact spherical bearing based on near-field acoustic levitation

Based on near-field acoustic levitation, a noncontact bearing with a spherical rotor was proposed to explore its potential application for novel supporting bearing of suspended gyro. The stator of the noncontact bearing has a hollow bowl-shaped configuration, in order to produce acoustic levitation force for a spherical object. Two orthogonal flexural standing waves were piezoelectrically generated and led to a traveling wave in the stator, and then the induced high-intensity sound in the air gap between the stator and spherical rotor could apply levitation force and even driving force for the spherical rotor. In this article, finite element model of a bowl-shaped piezoelectric stator was built, and the dynamic analysis and parametric optimization for the stator have been conducted. The prototypes were manufactured and vibration parameters of the stators were experimentally obtained. The test system for the noncontact spherical bearing was built, and its levitation and driving characteristics were measured. The spherical rotor successfully achieved levitation and noncontact rotation based on near-field acoustic levitation and the experimental results preliminarily indicate the feasibility of near-field acoustic levitation for suspended gyro.

A Novel Method on Real-Time Measurement of 2-DOF Motions of Spherical Ultrasonic Motor

Spherical ultrasonic motor (SUSM) is utilized primarily in the assembly sectors, precision machining and active tracking devices. The controllability and accuracy of the SUSM are much concerned in those practical uses. So the sensors which measure the motion of the stator are usually used to build up a closed loop control system. These sensors can detect the position and speed of the ball stator. However, the traditional contact positional detection device which contains photoelectric encoders has the disadvantages of low measuring precision. A novel contactless method which based on an optical sensor, is introduced in the paper. A further illustration including principles of the method, the model of 2-DOF motion of the spherical ultrasonic motor rotor, a set of experiment test-bed to verify the feasibility of the method are presented in the article. The experiment turns out an expectant result and shows the method feasible and significant for application.

Force and Torque Analytical Models of a Reaction Sphere Actuator Based on Spherical Harmonic Rotation and Decomposition

This paper presents an analytical model for the force and torque developed by a reaction sphere actuator for satellite attitude control. The reaction sphere is an innovative momentum exchange device consisting of a magnetic bearings spherical rotor that can be electronically accelerated in any direction making all the three axes of stabilized spacecrafts controllable by a unique device. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Force and torque analytical models are derived by solving the Laplace equation and applying the Lorentz force law. The novelty consists in exploiting powerful properties of spherical harmonic functions under rotation to derive closed-form linear expressions of forces and torques for all possible orientations of the rotor. Specifically, the orientation of the rotor is parametrized using seven decomposition coefficients that can be determined noniteratively and in a linear fashion by measuring the radial component of the magnetic flux density from at least seven different locations. Therefore, force and torque models for all possible orientations of the rotor are expressed in closed form as linear combination of mutually orthogonal force and torque characteristic matrices, which are computed offline. The proposed analytical models are experimentally validated using a developed laboratory prototype.

A novel orientation measurement using optical sensor for spherical motor

The measurement of spherical rotor orientation is crucial to the close-loop control of spherical motors. This paper presents a novel method for the measuring of three-degree-of-freedom (DOF) rotor orientation of spherical motors using optical sensors. The spatial orientation of spherical rotor is output in the form of ZXZ Euler angles. Firstly, the structure of the measuring system composed of optical sensors and the patterns on the rotor surface are presented, and the operational principle of recognizing intersection points between the optical ring detectors and the latitude/longitude on the rotor surface is illustrated. The analytical model of input-output characteristic is established for the measuring system of three-DOF rotor orientation. Afterwards, the effect of parameters of the optical ring detectors on the linearity, sensitivity, resolving power and measuring range of the measuring system is analyzed using the analytical model. Finally, the feasibility of the measurement is validated through experiments of prototype measuring system. The analysis is expected to be a basis for the design parameter optimization of the orientation measuring system of a PM spherical motor.