# A High-Thrust Screw-Type Piezoelectric Ultrasonic Motor with Three-Wavelength Exciting Mode
## 2 Structure and Operating Principle  
### The Structureof the Screw-Type Ultrasonic Motor  
The structure of the screw-type piezoelectric ultrasonic motor with a three-wavelength exciting mode is shown in Figure 1. The motor comprised of a stator that is a metal elastomer bonded with twelve rectangular piezoelectric plates on its external surface at 30 degree spacing, and a screw output shaft with external threads that engage with the internal threads of the stator. The material of the metal elastomer is brass. The stator is deformed by converse piezoelectric effect, and an elliptical deformation motion is generated at the contact point between a stator and a screw output shaft. The frictional effect enables the elliptical deformation motion of the stator to drive the external threads of the screw output shaft to rotate, so the screw output shaft implements the linear motion. The three-dimensional model of the motor is shown in Figure 1a. In the design process, the different dimensions parameters have the great influence on the vibration mode of the motor, such as the variable \(L\), \(d\), and so on. The variable \(L\) is defined by the length of the stator along to the axial direction, and the value of \(L\) is equal to 36 mm in this paper. The variable \(d\) is defined by the pitch diameter of the inner thread of the stator. In this paper, a combined circumferential-axial vibration mode of the stator is excited, which includes the first and the third bending vibration modes along the axial and circumferential directions, respectively. A three-wavelength traveling wave can be synthesized by this combined vibration mode. The three-wavelength traveling wave is used to drive the screw output shaft by frictional force between the stator and screw output shaft. The designed stator includes the twelve piezoelectric plates and the metal elastomer. By calculation, the volume ratio of twelve rectangular piezoelectric plates and metal elastomer is about 1:25. The influence of the twelve piezoelectric plates can be ignored. The stator is approximated as a homogeneous material. In addition, the three-wavelength traveling wave is located at the thread pitch diameter of the metal elastomer. Thus, the main dimension relationships of the designed stator are supposed to satisfy the following calculation process. The detailed calculation process of the first bending vibration mode of the stator along the axial direction is as follows:  
\[L=\lambda \tag{1}\]  
The detailed calculation process of the third bending vibration mode of the stator along the circumferential direction is as follows:  
\[\pi d=3\lambda \tag{2}\]  
According to the above equations, the design principle of the motor can be obtained, and the main dimensions are supposed to satisfy the following calculation equation:  
\[L=\frac{\pi d}{3} \tag{3}\]  
where the \(\lambda\) is the wavelength of the bending vibration mode of the stator, the \(L\) is the length of the stator along to the axial direction, and the \(d\) is the pitch diameter of the thread of the stator. According to the design principle, the main design dimensions of the motor can be calculated, as shown in Figure 1b.The dimension parameters of the stator are designed as follows: The dimension of the thread used in elastomer is M 36\(\times\)1.5, which means that the thread type is common metric triangular thread, and the nominal diameter and thread step are 36 mm and 1.5 mm, respectively. The length of the elastomer in axial direction is 36 mm, and the outside diameter of the elastomer is 46 mm. The inner diameter of the hollow cylinder of elastomer is 39 mm. In addition, the length, width and thickness dimensions of rectangular piezoelectric plates are 16 mm, 6 mm, 1 mm respectively. According to references [30,31], the length of piezoelectric plates is relative to the force factor. Under  
Figure 1: Structure of the proposed piezoelectric ultrasonic motor: (**a**) the three-dimensional model of the motor; (**b**) the main structure parameters of the stator (unit: mm).