The objective of the thesis is to develop the torque model method for SWM and position control using open-loop control. The torque model requires an understanding of the SWM design as well as the analysis of the magnetic fields. In previous research, the torque model of SWM was demonstrated to summarize the interaction between each permanent magnet and the electromagnet since the magnetic circuit is linear.
The experiment and other simulations were conducted to check the validity of the simplified torque model. To demonstrate that the coupling model and the principle of position control were correct, the experiment was conducted with position control in open-loop control. Moreover, the experiment results show that the SWM properly controls the position using the proposed torque model and position control mechanism.
Figure 1.1 Examples of multi-degree-of-freedom manipulators (a) 6DOF serial manipulation (KUKA Robotics Corporation) (b) 6DOF parallel manipulation (Hydra Power system) Figure 2.1 SWM design. Figure 3.5.1 extended distributed multipole (eDMP) cylindrical coil geometry (a) PM modeling, (b) EM modeling (c) Dipole moment. Figure 3.5.2 Simulation data and torque function using internal PM only Figure 3.5.3 Simulation data and torque function using internal and external PM.
Introduction
Among them, the magnetic field analysis is an indispensable research topic in SWM control for torque calculation. Existing techniques for analyzing electromagnetic fields include analytical solutions to the Laplace equation, numerical methods, and various computational methods such as lumped parameter analysis, and so on. Many researchers use various other calculation methods, such as finite element, finite difference of boundary elements and mesh-free methods and so on.
These methods provide a good prediction of the magnetic fields for accurate calculation of the magnetic torque. However, these approaches have difficulties in achieving both accuracy and short computation time for efficient design and robust control of the actuators. So they are still not real tools for the real-time control, which requires the higher accuracy and the less calculation time.
The experiment and other simulations are conducted to verify the validity of the simplified torque model.
Design of Spherical Wheel Motor
The two stator pole planes have an angle s between the XY plane as shown in Fig. During this study, the numbering systems of rotor poles and stator poles are established as shown in Fig. 2.1.2. Similarly, the first two EMs are located in the right half of the XZ plane in the absolute frame.
As shown in the previous section, the design of EM is composed of two coils representing two different sizes of cylinder coils. The number of turns is calculated with the areas divided by the thickness of the coil (the standard of the wire is 0.4 mm, current is 1A and material is copper). The two columns of the PMs are located plane to xz plane of COMSOL frame.
The position of EM lies along the right half plane of the xz plane, which is the midpoint between the 1st ~ 3rd PMs and the 4th ~ 6th PMs. The first case of the simulation results is the graphs in the first column; some 6 PMs with any type of coil. In the first case, Type C has the largest maximum torque value and Type A has the smallest torque value.
The order of each volume corresponds to the torque value for the same angles; VTypeC VTypeB VTypeA. But there are three differences; Type C is not used for the first case, the coil current in the second case is 0.5 A (the simulation is 1 A), and the rotation angle range is changed. According to the first column graphs of the simulation results, it is clear that Type C has the largest torque value because the diameter of Type C (which is closest to PM) is different.
Then the Type B shows the next largest maximum torque in both the simulation and the experiment. Based on that, the coil Type A is selected; Although Type A and Type B show the same value, the Type A can easily be manufactured as a Type B.
Torque Model
The magnetic torque between jth EM and the kth PM can be written in an xyz frame which is a rotor frame. From the design, SWM can be divided into repeating 10 sections, each of which is composed of two columns of PM pairs. Based on this constraint, the shape of the section can be changed to the trapezoidal shape created by adjacent 4PMs, as shown in Figure 3.2.1 (a).
Simply, the section can be made with the four permanent magnets, and this section always includes one EM or not. Based on the section and the location of EM, the number of torque terms can be reduced from nsnr to 2ns 4ms. 3.2.1; j is the angle between the projection of sj on x yi i plane from the xi axis and j is the angle between sj and x yi i plane;.
An important thing in this equation is the determination of the angle j which means that the jth EM is in the ith section. Based on this, the unit cross product vector can be represented by two components y zj, j. Then, the value of hi can be calculated using the formula of the distance between the location of.
In section 3.4 the linking model is simplified by using a simplified cross-unit product term. COMSOL is the program that is one of the popular programs for analyzing magnetic fields based on the FE method. Then the magnetic field can be expressed as a combination of a finite number of dipole moments.
The design parameters can be calculated by minimizing the error between the predetermined magnetic field and the field written in Equations 3.28 and 3.29. Lorentz force F and torque at the origin, TO can be calculated based on PM and EM dipole moments interaction, comparing the torque of two types of stator coils. The error is calculated by following the following equation: where the x is the comparison value, such as experiment, DMP and simplified model data; And.
Because the purpose of the simplified model is the real-time control by reducing the calculation time.
Position Control
Therefore, when the desired angle is input to the control mechanism, the current changes discontinuously. The holding torque vector for this experiment is a vector designed to indicate the y-axis rotation. Using this torque matrix with hold torque input, the currents are calculated using pseudo-inverse because the torque matrix is 3×1 matrix, the two torque matrices are 3×4 matrix and the current matrix is 4×1 matrix.
Experiment
The coils are manufactured as follows: the start wire and the end wire are located on the same side of the coil, the thickness is 26 AWG, the small coil is wound in the counterclockwise direction, and the large coil is wound in the clockwise direction to connect . The angle increased clockwise, but in the case of the actual z-direction rotation, the angle increased counterclockwise. On the other hand, the values of the up and down key buttons can be changed intermittently; the torque magnitude value increases or decreases by 5N/mm and the alp and bet value increases or decreases by 0.1 degree.
The first case and the second case are when only one steering position angle is changed; one of them is azimuthal angle and the other is reversed polar angle. The results of the first case are shown in Fig 5.2.1 that only the azimuthal angle is changed from 0° to 10°. The results show that the blue lines increased gradually and the changes are proportional to the desired angle of entry.
For a more accurate analysis, the line separation angle is measured for each case. The results of the second case are presented in Fig. 5.2.2 with a change in the polar angles from 0° to 6° with intervals of two degrees. The results of the first experiment and the second experiment show that the measured values of the separation angle generally vary in proportion to the desired angles, given that they are open-loop controls with no external torque due to gravity.
Fig 5.2.3 shows the results when the desired polar angle is 2° and the azimuth angle is 10°. The values of separation angles from the home position are 11° in the first figure, 3° in the second figure, and 0.5° in the third figure. The values of separation angles from the home position are 5° in the first image, 4° in the second image and 1.5° in the third image.
To verify the suitability of the simplified rotation model, the experiments are continued with different desired angles. This phenomenon may be caused by the existence of different equilibrium points at the same current state due to multiple poles in the stator PM.
Conclusion
Kwan Design Concept Development of a Spherical Space for Robotic Applications," IEEE T-Robotics and Automation, Vol. Jewel, & D Howe, 2003, "Design and Control of a New Three-DOF Spherical Permanent Magnetic Actuator," IEEE/ ASME Trans Lee, “Distributed Multipole Models for the Design and Control of PM Actuators and Sensors,” IEEE/ASME Trans.
Sun, “Orientation measurement based on magnetic inductance by the extended distributed multi-pole model,” Sensors, vol. First of all, I would like to express my thanks and respect to my advisor Professor Dr. Discuss. It was especially a great honor to be able to do research on SWM, the subject of his research.
During this study I was able to develop different thoughts while studying according to his previous research and I was able to produce good results based on this. Their advice allowed me to fill in the gaps, without this advice it would have been difficult to finish the study. Last, but certainly not least, I would also like to thank people whose names I did not mention, but who nevertheless were a great support for me in my learning process.
