# Three-Dimensional Active Magnetic Levitation Actuating and Control System for Curved Pipes
## 8 Analysis of Influencing Factors
When the running speed of the mechanical arm is 10 mm/s, 15 mm/s, and 20 mm/s, the ball has a large fluctuation due to inertia, and the fluctuation trajectory covers the original motion trajectory of the magnetic ball during the descending motion, indicating that the operation of the mechanical arm has a great impact on the levitating motion of the magnetic ball. When the operating speed of the mechanical arm is 20 mm/s, the two steps are almost connected, and the motion trajectory of the target position is a wavy curve of large amplitude. Moreover, it takes a long time to stabilize, and it is impossible to reach a stable state within the allowed time range. When the running speed is 5 mm/s, the fluctuation range of the first step of the magnetic ball is within \(\pm\)0.100 mm, and the fluctuation range of the second step is within \(\pm\)0.150 mm. The operation of the mechanical arm has little influence on the motion of the ball. The fluctuation is in a controllable range and does not cause the ball to touch the inner wall of the pipe during levitation. In the process of right-angle bending, the rotating motion made by the two-dimensional maglev actuating system driven by the mechanical arm will have a certain impact on the levitation stability of the magnetic ball. Figure 23 shows the fluctuation responses of levitating motion of the magnetic ball at different rotation speeds of the mechanical arm. The rotation speed of the mechanical arm is set at \(5^{\circ}/\)s, \(10^{\circ}/\)s, \(15^{\circ}/\)s, and \(20^{\circ}/\)s, respectively. Figure 22: Fluctuation responses of descending levitating motion of the magnetic ball at different horizontal speeds of the mechanical arm. (**a**) The speed of the mechanical arm is 5 mm/s. (**b**) The speed of the mechanical arm is 10 mm/s. (**c**) The speed of the mechanical arm is 15 mm/s. (**d**) The speed of the mechanical arm is 20 mm/s. It can be seen from the curve that the magnetic ball has a large irregular fluctuation in the horizontal Y-axis direction. As the rotation speed of the mechanical arm increases gradually, the trajectory fluctuation becomes larger and larger, and the irregular noise in the trajectory becomes more and more obvious. Due to the sudden rotation of the two-dimensional maglev atuating system, the position of the magnetic pole of the electromagnetic actuators changes. The relative position of the magnetic ball is delayed due to inertia, and then the magnetic pole of the ball rotates, resulting in irregular position changes of the ball. The fluctuation of the magnetic ball indicates that the operation of the mechanical arm has an impact on the stability of the system. However, since the rotation axis of the mechanical arm coincides with the axis of the vertical actuators of the two-dimensional maglev atuating system, the fluctuation of the magnetic ball is relatively less influenced by the rotation of the mechanical arm than the horizontal operation of the mechanical arm and the vertical position change of the magnetic ball during the operation of the mechanical arm. When the rotating speed of the mechanical arm is \(5^{\circ}/\)s and \(10^{\circ}/\)s, the fluctuation of the horizontal Y-axis of the ball is within \(\pm 0.010\) mm, and the influence on the levitation stability of the system is very low. When the mechanical arm operates at \(15^{\circ}/\)s and \(20^{\circ}/\)s, the horizontal Y-axis fluctuation of the ball exceeds \(\pm 0.040\) mm, which is four to eight times the fluctuation effect of the rotation speed of \(5^{\circ}/\)s. Through a comparative test, it is verified that when the rotation speed of \(5^{\circ}/\)s is adopted by the mechanical arm to rotate the two-dimensional maglev atuating system, the levitating motion of the magnetic ball is stable, and the fluctuation is within the allowable range.