# Development of a 3-DOF Cylindrical Ultrasonic Motor Based on Non-Standard Modes
## 5 Experiments and Discussion
Figure 18 illustrates the relationship between voltage frequency and motor speed in different directions. In the experiment, the applied voltage amplitude is set as 420 V\({}_{\text{p-p}}\). The fixed preload applied by the permanent magnet in the stator to the rotor is 21 N. The motor is unloaded. The \(x\) and \(y\) motions are driven by bending and longitudinal vibrations, so the output performance is similar. The \(z\) motion is a combination of bending vibrations. The drive frequency band in the \(z\)-axis direction differs from those in the \(x\) and \(y\) directions. When the frequency increases, the motor speed increases and then decreases. As shown in Figure 18a, the maximum speed is 36 r/min at 64.44 kHz in the \(x\) direction. The motor obtains a top rate of 37 r/min in the \(y\) direction at 64.64 kHz. Figure 18b illustrates that the maximum motor speed of 77 r/min in the \(z\)-axis direction is obtained at 66.02 kHz. The drive control of the multi-DOF cylindrical ultrasonic motor differs from the previous two-phase drive ultrasonic motor. The cylindrical motor's \(x\)- and \(y\)-axis motions require both longitudinal and bending ceramics to be excited, and the \(z\)-axis motion requires bending ceramics to be excited. Therefore, the frequency range of the drive motion is within the frequency range of the longitudinal and bending modes. The speed change of the proposed motor is related to the frequency and amplitude of the applied voltage. The actual drive frequency of the proposed motor is slightly lower than the simulated values, around 1-1.5 kHz lower. The possible reasons for this phenomenon are: 1. errors in the machining and assembly of the motor components caused frequency variations; 2. the used stator material parameters differ from the simulated parameters; 3. the node boundary conditions are partially idealized during the simulation, and the stiffness and mass matrices differ from the actual ones; 4. interference caused by two sets of piezoelectric ceramics being excited at the same time. Figure 19 shows the speed as a function of voltage amplitude. The voltage frequency is fixed at 62 kHz in the \(x\)- and \(y\)- directions. In the \(z\)-axis direction, the fixed frequency is 64.7 kHz. The speed is approximately linearly related when the voltage amplitude is in a particular range. In the \(x\) direction, the motor stops when the amplitude is less than 245 V\({}_{\text{p-p}}\), and the speed enters saturation when the amplitude is greater than 440 V\({}_{\text{p-p}}\). In the \(y\) direction, the maximum motor voltage at speed 0 is 230 V\({}_{\text{p-p}}\), and the minimum amplitude at which speed enters saturation is 456 V\({}_{\text{p-p}}\). The motor speed enters the saturation zone at voltages greater than 460 V in the \(z\)-axis direction. Figure 18: Relationship between rotation speeds and frequency: (a) \(x\) and \(y\) direction, and (b) \(z\) direction. Figure 20 shows the relationship between load and speed. The voltage amplitude is set to 420 V. The voltage frequencies in the \(x\), \(y\), and \(z\) directions are 62 and 64.7 kHz, respectively. The load is replaced by weights applied to the rotor using a rope with a pulley. With increased load, the speed gradually decreases until 0. The maximum motor load is around 20 mN on the \(x\)- and \(y\)-axes. The output torque is approximately 25 mNm in the \(z\)-axis direction. It can be seen from the experiment that the maximum speed of the motor on the \(x\)- and \(y\)-axes can reach 37 r/min, and the speed on the \(z\)-axis can reach 77 r/min. The load capacity of the motor reaches 20-25 mNm. The lower speed makes the motor easier to control, and is more suitable for precision motion occasions, such as robot arm motion, Vientiane conveyor, etc. Considering the overall size of the motor, the motor has excellent load capacity and can easily drive loads such as robot joints.