Ph.D. Thesis Summary

Precision Control of a Spherical Rotor with a Self-Pressurized Air Film Bearing

Dan Ezenekwe

December 1998

High precision motion actuators are in increasing demand in today’s advanced manufacturing processes. Conventional single axis electromechanical actuators, which are typically connected via mechanical linkages, are still commonly used in many of these applications. Such configurations are usually bulky; susceptible to reduced accuracy due to backlash, friction and deformation at the linkages; and usually result in poor quality products and/or wastes from damages. Current precision multi degree-of-freedom (DOF) orientation motion devices are often expensive, complex in design or have sophisticated control scheme, are often fragile and present maintenance challenges. A device which promises to meet these demands is an electromagnetic spherical motor offering three (DOF) motion in one joint. Developed at Georgia Tech. by Lee et al., the variable reluctance (VR) spherical motor has attractive features that include relative simplicity of design, ease of manufacturing, compactness and isotropic properties.

From conceptualization to prototype construction, the VR spherical motor has already presented many interesting challenges to researchers. Although the principle of actuation has been demonstrated, its performance is susceptible to mechanical friction, which undercuts the versatility of its applications especially at low speeds. For these reasons, this research investigates a method for design, characterization, analysis and control of a non-contact bearing system for fine motion application of the VR spherical motor.

To characterize and model the innovative spherical bearing system, a practical design is proposed and an analytical methodology to realize the design is developed. The design configures the bearings in regular patterns in relation to the electromagnetic pole system of the motor. An optimal bearing arrangement is desirable to maximize the output force of the system. Yet, the symmetric and isotropic properties of the motor are preserved; the manufacturability of the motor is not jeopardized; and the analytical kinematics and dynamic models for the system remain feasible.

The innovative approach to rotor support presents new modeling and controls challenges associated with the rotor dynamics under the influences of the electromagnetic and air bearing forces. The spherical air bearing models developed in this thesis represent the first detailed analysis of the non-contact bearing system in relation to the kinematics and dynamics of the VR spherical motor. Both the forward and the inverse kinematics have been developed, which determine the relationship between the rotor displacement vector and the air-gaps at specified points on the spherical stator.

In addition, both the electromagnetic and the air bearing force models are derived for the 1-D and 3-D system dynamics in quadratic form. To illustrate the primary difference, a number of interesting point-bearing configurations and setups are compared. The passive air bearing system is shown to be stable and pressure forces effective in regulating the rotor around the equilibrium point. The electromagnetic levitation system, which is dynamically open-loop unstable, is stabilized by the more dominant air bearing system when superposed. It is expected that practical implementation of the air bearing system on a prototype VR spherical motor will facilitate the implementation of a proposed reaction-free levitation scheme for the electromagnetic system.

Unlike other techniques found in the literature, the air bearing design methodology, which has been developed allows the desired dynamic characteristics to be achieved by back-calculating the design parameters from given performance specifications. The design and analysis provides a stability analysis to give insight to the differences of the system geometric parameter and to provide guidance to design parameter selection. Both provide the information required in constructing an improved VR spherical motor design. The concept feasibility of the theoretical model has been demonstrated by simulation. The results show that the rotor can be regulated to within sub-millimeter motion precision. The concepts and theories presented are the engineering basis for characterization and design of this class of actuators.

The contributions of this thesis to the general engineering knowledge are summarized as follows:

The modeling and design of a spherical air bearing system that is capable of eliminating frictions in spherical actuators is established. The system is expected to provide an effective means to evaluate a spectrum of design configurations.
The kinematic and dynamic analyses of the rotor displacement geometry for multi air-bearing support mechanism have been presented. Both the forward and the inverse kinematics are formulated in closed form for control design and simulations.
The research has explored methods of integrating point bearings to control the translation of the rotor of spherical actuators so as to preserve the motor electromagnetic system and yet increase the torque output by eliminating mechanical friction.
A pressure-flow relationship that will be an essential basis for the development of the bearing system forces and dynamics will be formulated. Both the electromagnetic and the air bearing forces will be developed and represented in quadratic forms for optimal control purposes.
Both active and passive methods of regulating the rotor displacement that could be applied to other servo-devices have been explored analytically.
A first known method of design of spherical air bearings as applied to spherical actuators has been established. A practical air bearing design methodology that will guarantee achievement of desired dynamic characteristics has been presented.