1 Vol.:(0123456789) Scientifc Reports | (2023) 13:11910 | https://doi.org/10.1038/s41598-023-39111-8 www.nature.com/scientificreports A novel spherical ultrasonic motor with wire stators and measuring torque and preload via a new method Seyed Hassan Jahantab * , Yousef Hojjat * , Behzad Ghavami Namin & Mohammad Shirkosh The present study introduces a multi-degree-of-freedom (MDOF) ultrasonic motor, which is capable of driving a spherical rotor using spiral wire stators and a piezoelectric stack actuator. Wire stators and piezoelectric stack actuators enable the proposed motor to be smaller and simpler, lower in power consumption, and have diferent modes at diferent frequencies. In this motor, two wire stators are used to drive the spherical rotor and rotate it in diferent directions. The eigenfrequency and frequency domain analyses were carried out using the fnite element method (FEM) to evaluate the MDOF capability of the motor in diferent vibration modes. It has been demonstrated that the piezoelectric stack actuator can provide MDOF motions through its vibration modes. The resonant frequency obtained by the frequency domain approach agreed with the impedance analyzer test. Rotational speed, torque, and preload force were experimentally investigated. Using shear stress caused by viscous fuid in contact with the spherical rotor, a new torque calculation method was developed. Based on the buoyancy force exerted on the immersed rotor, the preload force was measured. The experimental results indicated that the maximum rotational speed of the spherical rotor was 306 rpm, and the maximum torque was 4.7 μN m. Ultrasonic motors are one of the main applications of the inverse piezoelectric efect. Tey turn the undulatory vibrational and progressive motions of the stator (the friction between rotor and stator) into a rotary or linear motion. In recent years, high-tech applications require small, accurate, light, and low-noise actuators capable of functioning in electromagnetic environments. Ultrasonic motors are developed to address such needs. Spherical ultrasonic motors (SUSMs) have been researched and developed to beneft from the advantages of ultrasonic motors while no complex design change is required 1–7 . Some advantages of ultrasonic motors are as follows: (1) high positioning accuracy, (2) short responding time, (3) noiseless performance, (4) high energy density, (5) simple structure, (6) high efciency in strong mag- netic felds, and (7) low power consumption 8–13 . Te advantages have made ultrasonic motors a proper choice for many applications such as precise positioning, robot joints 14 , the inspection of limited-access pipes 15 , and medical applications for tiny mechanisms 16 , especially in diagnostic methods such as angioscopy, in which a spherical ultrasonic micro-motor is used to move the camera in any direction for physicians to see inside the blood vessels 17–19 . Various designs have been proposed for SUSMs, each of which has specifc advantages and disadvantages regarding their potential applications and expected performance. One of such designs is SUSMs with their stator being a sandwich transducer operating in a bending mode 20–24 . Providing the proper actuation of piezoelectric material, the bending of various planes leads to rotation around diferent axes; however, there has been no report on simultaneous rotations around diferent axes. Toothed stators are a highly fexible design enabling the spherical rotor to rotate around diferent axes; however, it is challenging for such designs to apply the preload equally 8,25,26 . Multi-degree-of-freedom (MDOF) SUSM with four toothed piezoelectric plates, allowing for equal exertion of preload force on the rotor, was examined in another approach and correlation between rotor rotation rate and preload was also investigated 27 . Each toothed stator requires a set of at least three individual phases for excitation voltage, which may complicate the driving circuit for a higher degrees of freedom. Another SUSM design, called sandwich SUSMs, uses circular piezoelectric plates divided into several zones. Each zone must be separately excited to rotate the spherical rotor. In aforementioned study, a piezoelectric disk was adopted, and loading (the force between the rotor and stator), diferent contact surfaces, optimal voltage and frequency, OPEN Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran. * email: s.jahantab@modares. ac.ir; yhojjat@modares.ac.ir