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

Electromagnetic fields and interactions in 3D cylindrical structures : modeling and application

The demand for more efficient and compact actuation systems results in a search for new electromagnetic actuator configurations. To obtain actuators that meet these challenging specifications, accurate modeling of the electromagnetic fields is often a prerequisite. To date, analytical modeling techniques are widely used to predict electromagnetic fields in classical rotary and linear machines represented in two dimensional coordinate systems. This thesis presents the extension of an analytical modeling technique to predict the 3D field distribution in new cylindrical actuator configurations. One specific technique that is used to analyze and design electromagnetic devices is based on Fourier series to describe sources and the resultingmagnetic fields. In this research, the harmonic modeling technique is extended to describe electromagnetic fields due to presence of permanent magnets in regular and irregular shaped 3D cylindrical structures. The researched modeling technique can be applied to current-free cylindrical problems exhibiting periodicity or a soft-magnetic boundary in the axial direction. The cylindrical structure can posses either circumferential slots, axial slots or rectangular cavities. The assignment and a method to solve the various boundary conditions are discussed in a generic manner to enable model application to a wide range of 3D cylindrical structures. The magnetic field solutions are provided, and the model implementation is presented in matrix form. Model validation is presented by means of a comparison of the magnetic fields in a cylindrical structure with a rectangular cavity calculated using the analytical model and a finite element model. To calculate the magnetic interactions, e.g., attraction and cogging forces due to permanent magnets, the Maxwell stress tensor is analytically evaluated. The harmonic magnetic field solution is used in this evaluation resulting in compact force equations describing the 3D force components between concentric cylinders

A Magnetic Actuated Fully Insertable Robotic Camera System for Single Incision Laparoscopic Surgery

Minimally Invasive Surgery (MIS) is a common surgical procedure which makes tiny incisions in the patients anatomy, inserting surgical instruments and using laparoscopic cameras to guide the procedure. Compared with traditional open surgery, MIS allows surgeons to perform complex surgeries with reduced trauma to the muscles and soft tissues, less intraoperative hemorrhaging and postoperative pain, and faster recovery time. Surgeons rely heavily on laparoscopic cameras for hand-eye coordination and control during a procedure. However, the use of a standard laparoscopic camera, achieved by pushing long sticks into a dedicated small opening, involves multiple incisions for the surgical instruments. Recently, single incision laparoscopic surgery (SILS) and natural orifice translumenal endoscopic surgery (NOTES) have been introduced to reduce or even eliminate the number of incisions. However, the shared use of a single incision or a natural orifice for both surgical instruments and laparoscopic cameras further reduces dexterity in manipulating instruments and laparoscopic cameras with low efficient visual feedback. In this dissertation, an innovative actuation mechanism design is proposed for laparoscopic cameras that can be navigated, anchored and orientated wirelessly with a single rigid body to improve surgical procedures, especially for SILS. This design eliminates the need for an articulated design and the integrated motors to significantly reduce the size of the camera. The design features a unified mechanism for anchoring, navigating, and rotating a fully insertable camera by externally generated rotational magnetic field. The key component and innovation of the robotic camera is the magnetic driving unit, which is referred to as a rotor, driven externally by a specially designed magnetic stator. The rotor, with permanent magnets (PMs) embedded in a capsulated camera, can be magnetically coupled to a stator placed externally against or close to a dermal surface. The external stator, which consists of PMs and coils, generates 3D rotational magnetic field that thereby produces torque to rotate the rotor for desired camera orientation, and force to serve as an anchoring system that keeps the camera steady during a surgical procedure. Experimental assessments have been implemented to evaluate the performance of the camera system

Extended analytical charge modeling for permanent-magnet based devices : practical application to the interactions in a vibration isolation system

This thesis researches the analytical surface charge modeling technique which provides a fast, mesh-free and accurate description of complex unbound electromagnetic problems. To date, it has scarcely been used to design passive and active permanent-magnet devices, since ready-to-use equations were still limited to a few domain areas. Although publications available in the literature have demonstrated the surface-charge modeling potential, they have only scratched the surface of its application domain. The research that is presented in this thesis proposes ready-to-use novel analytical equations for force, stiffness and torque. The analytical force equations for cuboidal permanent magnets are now applicable to any magnetization vector combination and any relative position. Symbolically derived stiffness equations directly provide the analytical 3 £ 3 stiffness matrix solution. Furthermore, analytical torque equations are introduced that allow for an arbitrary reference point, hence a direct torque calculation on any assembly of cuboidal permanent magnets. Some topics, such as the analytical calculation of the force and torque for rotated magnets and extensions to the field description of unconventionally shaped magnets, are outside the scope of this thesis are recommended for further research. A worldwide first permanent-magnet-based, high-force and low-stiffness vibration isolation system has been researched and developed using this advanced modeling technique. This one-of-a-kind 6-DoF vibration isolation system consumes a minimal amount of energy (Ç 1W) and exploits its electromagnetic nature by maximizing the isolation bandwidth (> 700Hz). The resulting system has its resonance > 1Hz with a -2dB per decade acceleration slope. It behaves near-linear throughout its entire 6-DoF working range, which allows for uncomplicated control structures. Its position accuracy is around 4mum, which is in close proximity to the sensor’s theoretical noise level of 1mum. The extensively researched passive (no energy consumption) permanent-magnet based gravity compensator forms the magnetic heart of this vibration isolation system. It combines a 7.1kN vertical force with <10kN/m stiffness in all six degrees of freedom. These contradictory requirements are extremely challenging and require the extensive research into gravity compensator topologies that is presented in this thesis. The resulting cross-shaped topology with vertical airgaps has been filed as a European patent. Experiments have illustrated the influence of the ambient temperature on the magnetic behavior, 1.7h/K or 12N/K, respectively. The gravity compensator has two integrated voice coil actuators that are designed to exhibit a high force and low power consumption (a steepness of 625N2/W and a force constant of 31N/A) within the given current and voltage constraints. Three of these vibration isolators, each with a passive 6-DoF gravity compensator and integrated 2-DoF actuation, are able to stabilize the six degrees of freedom. The experimental results demonstrate the feasibility of passive magnet-based gravity compensation for an advanced, high-force vibration isolation system. Its modular topology enables an easy force and stiffness scaling. Overall, the research presented in this thesis shows the high potential of this new class of electromagnetic devices for vibration isolation purposes or other applications that are demanding in terms of force, stiffness and energy consumption. As for any new class of devices, there are still some topics that require further study before this design can be implemented in the next generation of vibration isolation systems. Examples of these topics are the tunability of the gravity compensator’s force and a reduction of magnetic flux leakage

A Spherical Magnetic Dipole Actuator for Spacecraft Attitude Control

Spacecraft generally require multiple attitude control devices to achieve full attitude actuation because of the limited control authority a single, traditional device can provide. This work presents a new momentum-exchange device that has the potential to replace traditional attitude control systems with a single actuator, in turn providing mass, volume, and power savings. The proposed actuator consists of a spherical dipole magnet enclosed in an array of coils that are fixed to the spacecraft body. Excitation of the coils as prescribed by the control law accelerates the dipole magnet in such a manner as to produce a desired reaction torque for orienting the spacecraft. The coils also control the magnet's position inside the spacecraft body via a separate control law, which is necessary because of the non-contact nature of the device. Analytical force and torque models are developed and are used in an attitude regulation maneuver. Simulations conducted so far indicate that full attitude control is possible from a single device despite the axisymmetric field of the magnetic dipole rotor, which was anticipated to cause control issues. Finally, the single actuator system is compared to a cluster of three reaction wheels, illustrating how this device can provide mass, volume, and power savings