COMPLEX DYNAMIC MODEL (CDM) OF THE USM

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Background

The information in this section provides an introduction to the subject areas central to this thesis. To begin, force-feel systems, their beginnings and their progression into modern applications are discussed. Next, a review of research examining rotary ultrasonic motors in force-feel systems is presented, and an abbreviated history of the various USM modeling efforts follows. The chapter is concluded with a summary and a short discussion of how the work of this thesis aims to determine whether USMs are fit to be the sole actuator to provide controlled torque and displacement in a force-feel system.

Force-Feel Systems

Force-feel systems fall under the umbrella of haptic feedback systems, or systems capable of providing force feedback and tactile feedback. Force feedback is the simulation of hardness,weight and inertia, and tactile feedback is the simulation of contact geometries, smoothness, slippage and temperature [2]. Haptic feedback is especially important in virtual reality simulations to provide a user a feel for the virtual environment, but it has been equally important for increasing the control of by-wire systems. Without actuators providing feedback forces to the user, the virtual reality interface remains solely an input device to the computer just as a control stick lacking a feel-system is just an input to the aircraft [3]. The feel-systems considered in this thesis require only force feedback, so tactile feedback is given no further consideration.Originally used on a robotic tele-operation system for nuclear environments in 1954,advancements in force feedback research extended its use to systems including electromechanical arms for virtual molecular docking, active control sticks for both flight simulators and fly-by-wire aircraft and feedback gloves for the handling of virtual reality objects. By the late 1990s, inexpensive haptic joysticks were even available for computer games [2]. Regardless of application, one of the most important goals of feel-system design is its transparency, a term describing the lack of forces exerted by the system on the operator’s hand when no forces exist in the virtual reality environment or on the surfaces that the input device controls. A systems backdrivability is the quantification of its transparency and is maximized in cases of low actuator inertia and static friction [3]. The result is minimal resistance to operator inputs. Good backdrivability increases the range of feedback forces that can be output by the feel-system by allowing small forces, originally masked by friction or gear forces, to be felt. Prior to determining an actuators backdrivability, the actuator’s speed and torque capabilities,including ranges and maximum continuous outputs, must be obtained. These are manufacturer specifications and easily acquired. Speed and torque controllability must also be proven; a task typically involving both modeling and experimental validation. With respect to ultrasonic motors, speed and position control are clearly possible, as they are the most widely used actuator in present day auto-focusing camera lenses. Whether the output torque of a USM can be controlled remains a point of speculation requiring a full analysis of its operating characteristics through motor modeling for confirmation.

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USMs in Force-Feel Systems

Design and modeling have been major research areas since the USMs introduction in the 1980s. With respect to design, increasing the motor’s load carrying capability is generally of most concern, as the torque range of commercially available USMs is only a fraction of that covered by DC motors. In terms of modeling, considerable research has gone into developing schemes that predict motor outputs as a function of its inputs. It would seem that given the large body of knowledge covering those subjects that further research would tend towards the application of USMs as engineering solutions, but it is not the case. Clearly, accurate position and speed control laws have been developed for USMs, as they are being used in innovative designs as positioning actuators. However, few publications exist that examine the USM as a source of controllable torque. Some of the more recent pertaining to force-feel systems include:2000: Researchers at the University of Paderborn suggested the USM be applied in an active control stick feel-system citing its high torque density and high torque capability at low rotational speeds as beneficial to a fly-by-wire aircraft control systems. A torque  control algorithm was formulated in order to control the motor torque which generated restorative feedback forces to the control stick to return it from a forward or backward sweep [4].2006: Researchers at the Polytech’Lille/USTL in France expanded on the active control stick application by exploring a torque control method in which the motor torque was considered a function of the ideal and actual rotor speeds [5]. 2007: Researchers at the National University of Singapore developed a haptic knob composed of a USM and an active powder brake coupled by a differential gear. The USM acted as velocity source while the brake acted as a clutch allowing torque control of the system [6].

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ABSTRACT
ACKNOWLEDGEMENTS 
TABLE OF CONTENTS 
LIST OF FIGURES 
LIST OF TABLES 
1 INTRODUCTION
1.1 MOTIVATION
1.2 OBJECTIVES
1.3 OUTLINE 
1.4 CONTRIBUTIONS
2 BACKGROUND
2.1 FORCE-FEEL SYSTEMS
2.2 USMS IN FORCE-FEEL SYSTEMS
2.3 USM MODELING
2.3.1 Finite Element Models
2.3.2 Equivalent Circuit Models
2.3.3 Complex Dynamic Models
2.4 SUMMARY
3 COMPLEX DYNAMIC MODEL (CDM) OF THE USM 
3.1 CDM: CONTACT MECHANICS
3.1.1 Half-Contact Length, xo
3.1.2 Stick-points, xs
3.1.3 Torque generation (Steady State)
3.1.4 Torque generation (Transient)
3.2 CDM: SUBSYSTEMS
3.2.1 Stator
3.2.2 Rotor (Vertical)
3.2.3 Rotor (Angular)
3.3 CDM: MODELING DIFFICULTIES
3.4 CDM: OUTPUTS 
3.5 CDM: CONCLUSIONS
4 CONTRIBUTION 1: REDUCED DYNAMIC MODEL (RDM)
4.1 RDM: DEVELOPMENT
4.2 DYNAMICS OF THE STATOR-ROTOR COMBINATION 
4.3 RDM: PSEUDO-XO
4.4 RDM: PSEUDO-XS 
4.5 RDM: IN SIMULINK
4.6 RDM: VALIDATION 
4.7 RDM: CONCLUSIONS 
5 CONTRIBUTION 2: FORCE-FEEL CAPABILITIES OF USMS
5.1 BDCS VERSUS USMS IN FORCE-FEEL
5.2 USING THE SIMULINK MODELS FOR ANALYSIS
5.3 CASE 1: CONSTANT-FORCE FEEL
5.3.1 Constant-Force feel, Resistive Motor Loading
5.3.2 Constant-Force feel, Additive Motor Loading
5.4 CASE 2: LINEAR SPRING FORCE
5.4.1 Linear Spring Force-Feel, Resistive Loads
5.4.2 Linear Spring Force-feel, Resistive Loads, Simulation results
5.4.3 Linear Spring Force-feel, Additive Loads
5.4.4 Linear Spring Force-feel, Additive Loads, Simulation results
5.5 CONCLUSIONS
6 CONCLUSIONS AND FUTURE WORK
6.1 SUMMARY
6.2 FUTURE RESEARCH 
REFERENCES
APPENDIX A
APPENDIX B 

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