## 5 Experiments
### Mechanical Output Performance Experiments  
An experimental platform has been designed and fabricated to verify the correctness of the theory and analysis. Figure 8 shows the three-dimensional model and section view of the experimental platform. It consists of the stator installation platform, the slider guide rail, the load installation sliding table, and the data acquisition. By altering the inertia load and preload, the slider's displacement and velocity curves could be measured from the data acquisition, and the maximum initial acceleration could be easy to calculate via the velocity curves. Eventually, the output thrust could be figured out by multiplying the acceleration by the inertia load.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & **Vibration Test** & **The Finite Element** & **Absolute Deviation** & **Relative Deviation** \\  & **(kHz)** & **Simulation (kHz)** & **(kHz)** & **(\%)** \\ \hline Mode A & 24.429 & 24.640 & 0.211 & 0.86 \\ Mode B & 24.476 & 24.653 & 0.177 & 0.72 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between the finite element simulation and the prototype working frequency.  
Figure 8: Experimental platform structure diagram: (**a**) The 3D model of general linear ultrasonic motor experimental platform; (**b**) The side-view of general experimental platform. 1. thrust spring; 2. stator mounting plate; 3. Motor; 4. motor mounting bracket; 5. friction material installation plate; 6. load sliding table; 7. guide rail installation pedestal; 8. inertia load block; 9. guide rail sliding block; 10. reading head; 11. grating scale; 12. experimental platform pedestal.  
Figure 7: Mode A and B vibration modes and vibration velocity response spectra: (**a**) Mode A vibration mode and vibration velocity response spectrum (the side face of the horizontal transducer is the test surface); (**b**) Mode B vibration mode and vibration velocity response spectrum (the side face of the vertical transducer is the test surface).  
The motor's mechanical output characteristics could be tested on the manufactured experimental platform illustrated in Figure 9a. As shown in Figure 9b, the non-loaded optimal operating frequency is 24.55 kHz. While improving the output thrust, the speed is also guaranteed to reach the best state, so the exciting frequency is set as 24.55 kHz in the latter experiment. When the exciting voltage is 150 V\({}_{\text{rms}}\), on the condition of no force load and a 15 kg inertia load, the motor output thrust and velocity curves are presented in Figure 10a and in Figure 10b, respectively.  
According to the above measured results, when the exciting voltage is 150 Vrms, the proposed LUSM non-loaded maximum velocity is 0.83 m/s and the maximum output thrust can even reach 56 N. A comparison between the proposed T-shape piezoelectric motor and a previous one with a similar principle [15] is listed in Table 5. The maximum power of the modified motor is nearly six times that of the previous motor when the preload is 80 N with a 15 kg inertia load. Hence, the proposed LUSM output thrust characteristic has a huge enhancement.  
Figure 10: The mechanical output performance of the prototype: (**a**) Plot of the no-load speed and force under the voltage of 150 V\({}_{\text{rms}}\); (**b**) Plot of a 15 kg inertia load speed and force under the voltage of 150 V\({}_{\text{rms}}\).  
Figure 9: The real image of experimental platform and the speed curve: (**a**) The real image of experimental platform; (**b**) The speed curve of optimal operating frequency.