# An Eight-Zonal Piezoelectric Tube-Type Thread Ultrasonic Motor Based on Second-Order Bending Mode
## 1 Introduction  
Ultrasonic motors are novel energy-conversing devices based on the principles of an inverse piezoelectric effect, resonant displacement amplification, and friction drive effect [1; 2; 3]. Since the prototype of the first ultrasonic motor was reported in the 1970s, it has attracted extensive attention worldwide for the merits of high power density, fine positioning accuracy, power-off self-locking, quick response, free electromagnetic interference, light weight, compact structure, and so on [3; 4; 5]. Based on the research so far, ultrasonic motors have been successfully applied in some commercial products in the fields of precise positioning, biomedical instruments, aeronautics and astronautics, and so forth [3; 6; 7; 8].  
In view of the different vibration waveform combinations for generating periodic rotary or linear movement, ultrasonic motors can be classified into three categories: traveling-wave type, standing-wave type, and composite type [9]. However, for the purpose of high torque output, a cylindrical traveling-wave type motor might be superior to flat ones in millimeter- and sub-millimeter-order diameters [10]. In 2000, [PERSON] et al. [11] proposed a cylindrical miniature ultrasonic motor (\(\O 1.4\) mm \(\times\) 5 mm) based on a lead zirconate titanate (PZT) thin film (0.25 mm). However, the maximum rotary speed and torque were only 680 rpm and 0.67 uNm at 20 Vpp driving voltage due to the thin-film deposition structure. In 2002, [PERSON] et al. [12] fabricated a cylindrical-type ultrasonic motor(\(\O\O 2.4\ mm\times 10\ mm\)), which consisted of a metal tube and two piezoelectric plates bonded on its surface, based on two first-order bending modes. The maximum output torque was up to 1.8 mNmN at 120 Vpp driving voltage. In addition, in 2006, [PERSON] et al. [13] proposed a cylindrical rotary motor based on a PZT tube stator that was divided into four exciting electrode parts. Then, in 2014, [PERSON] et al. [14] fabricated a screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator. At 300 Vpp, the maximum thrust force, velocity, and efficiency were approximately 4.2 N, 9.5 mm/s, and 5.6%, respectively. Later, in 2016, [PERSON] et al. [15] reported a single-phase driven screw-thread-type cylindrical ultrasonic motor based on an asymmetric stator design and piezoelectric plate bonding structure. When the driving voltage was 200 Vpp, the maximum no-load velocity was 4.1 mm/s and the stall force was 1.6 N. The cylindrical traveling-wave-type motor has been studied for decades, and various tube-shaped piezoelectric motors based on the first-order bending modes [16; 17] have been proposed and experimentally researched. However, few researchers have dealt with the coupling of high-order bending modes.  
In this study, we proposed an eight-zonal piezoelectric tube-type threaded ultrasonic motor based on two second-order bending modes. Experimental results show that the threaded motor could output a stall force of about 5.0 N and a linear velocity of 4.9 mm/s with no load at the driving voltage of 40 Vpp, thus, realizing the purpose of reducing the driving voltage and improving the output performance.