Design and evaluation of a novel light arc-shaped ultrasonic motor

Ultrasonic motors can be classified into two types, namely, traveling-wave and standing-wave ultrasonic motors. Due to a series of advantages including low velocity, high torque, and self-locking when power off, ultrasonic motors have now been successfully applied in many domains including medicine, optics, and aerospace.^1–4 For the motor application in pan/tilt/zoom (PTZ), so far electromagnetic motors are generally used on the market, which have higher speed but larger weight and smaller torque, sometimes could be a large load to the PTZs.^5,6 Besides, the surrounding magnetic field will also have a certain impact on the output performance to the motor.^7,8 Later, people applied traveling wave type ultrasonic motor to PTZs according to their needs.^9,10 Scholars have conducted a great deal of research on the applications of ultrasonic motors in PTZ. In general, rotating traveling-wave ultrasonic motors are used in PTZs, which have lower output torques compared to standing-wave motors with same weights. Since the output torque of an ultrasonic motor is highly dependent on the volume, the motor can hardly be further miniaturized, satisfying also a certain torque requirement.^11–14 Ultrasonic motors belong to a multidisciplinary research area, in which the design of the driving mechanism is most critical. Zhao et al., from Nanjing University of Aeronautics and Astronautics, designed a small rotating ultrasonic motor with a diameter of 30 mm and a weight of 50 g. Its output torque reached up to 0.15 N·m and the rotating speed was as high as 250 rpm.¹⁵ With the aim of increasing torque, Kursawa et al. paralleled 3 V-shaped linear ultrasonic motors and used the parallel structure in a precision driving system of large telescopes.¹⁶ In 2013, Jeong et al. designed a small V-type beam-structure ultrasonic moto with a velocity of 235 rpm, a maximum torque of 0.02 N·m, and a mass of approximately 20 g.¹⁷ 

In order to satisfy the requirements of small PTZs, this study proposes a novel in-plane arc-shaped motor. Based on the inverse piezoelectric effect of piezoelectric ceramics, the motor was driven to produce an elliptical motion. Moreover, the developed motor possessed several advantages, including light weight, small volume, simple structure, and high torque. In the present paper, the motor structure was initially designed according to the requirements of micro-PTZ applications, and the related driving principle was analyzed. Moreover, a finite-element model of the motor was developed, the operating mode was determined, and the relation between amplitude and critical size of the stator was analyzed. Finally, the mechanical properties of the developed prototype, including vibration characteristics, output characteristics, and output torque were examined.

Fig. 1 shows the structure of the motor. The motor was designed according to the superposition principle of longitudinal-flexural composite modes. The motor was fabricated from phosphor bronze, with a radian angle of 60°. Both two sides of the motor were attached with the piezoelectric ceramic plates (PZT-8). The piezoelectric ceramic plate on the one side included four excitation areas, while the piezoelectric ceramic plate on the other side included only one excitation area. The ceramic plate was polarized along its thickness direction. Specifically, the four excitation areas included two phases and the opposite piezoelectric ceramic plates included one phase. The ceramic plates were arranged in the direction opposite to the excitation direction, so as to excite the first-order flexural-vibration and the second-order longitudinal-vibration mode on the stator substrate. The AC excitation signal with same frequency and amplitudes and a phase difference of 90° was applied on the two-phase piezoelectric ceramic. In-plane longitudinal-vibration mode and bending mode with spatial and temporal phase differences of π/2 were excited by the inverse piezoelectric effect of the piezoelectric ceramic. The coupling of the two modes can produce an elliptical motion trajectory around the two driving feet, which can drive the rotation of the rotor. The application of reverse voltage on the piezoelectric ceramic can drive the reverse rotation of the rotor.

Fig. 2 displays the operating mode of the motor in a cycle. A voltage with a phase difference of +90° was applied on the two signal channels. In phase (a), the motor was driven to move. At that moment, both bending vibration displacement and longitudinal vibration velocity reached the maxima. In the phases from (b) to (d), two driving feet of the motor generated an up-to-down elliptical motion by turns. The bending vibration velocity and longitudinal vibration displacement reached the maxima in phases (b) and (d). After the application of a certain pre-pressure, the driving feet came into contact with the rotor, the rotor was driven by the friction force, and rotated under the action of the elliptical motion of the stator. The motor could produce reverse rotation if the phase difference between the two signal channels was adjusted to -90°.

Both the natural vibration model and modal frequency of the stator and the motion trail of the center-of-mass point on the motor driving feet can be calculated through finite element analysis. Based on the principle of minimum potential energy, the fundamental dynamic equation of the motor can be written as:^18–20 

where M, K, T, S, and C represent the mass, stiffness, electro-elasticity, capacitance, and resistance matrices, respectively, q and φ are the motor’s displacement and potential vectors, respectively, and Q denotes the electric charge vector at the electrode. The displacements of the motor driving feet under different excitation voltages were calculated according to Eq. (1). When the frequencies of two-phase excitation voltage V₁ = V₃sin(ωt + $φ1$⁠) and V₂ = V₃sin(ωt + $φ2$⁠) are close to the frequencies of first-order longitudinal vibration and second-order bending vibration, the motor will simultaneously excite the first-order longitudinal vibration and the second-order bending vibration.

Displacement response of the first-order longitudinal vibration mode:

Displacement response of the second-order bending vibration mode:

u_x, u_y are the tangential and normal displacement of the two driving feet, U_x, U_y are the first-order longitudinal vibration amplitudes and the second-order bending vibration amplitudes. According to the displacement response of forced vibration of the first-order longitudinal vibration and the second-order bending vibration, it can be calculated:

By using the trigonometric function relation, the parametric equation (4) can be transformed into the form in cartesian coordinate system:

When the phase difference is $Δφ$=90°, The trajectory of each point on the driving foot is a standard ellipse.

The stator elastomer of the designed motor was fabricated by QSn-6.5 and a PZT-8 piezoelectric ceramic plates were also used. Table I lists the material properties of the motor components.

In order to satisfy the coincidence of two-phase modal frequencies, the structural parameters that significantly affect the operating frequency were selected through sensitivity analysis. As it can be seen in Fig. 1, the stator was characterized by 5 structural parameters. Under different application scenarios, some structural dimensions of the stator and some size parameters of the piezoelectric ceramic were fixed, and simultaneously, the driving feet were arranged on the peak of the second-order bending vibration wave. There existed 5 structural parameters in the optimization design, namely, the outer diameter d₁, the inner diameter d₂, the radian s, the thickness L, and the height of the driving foot h. The sensitivities of these parameters were analyzed by means of an analytical method. The corresponding sensitivity can be calculated by:

Where w represents the variable of modal frequency corresponding to the modes generated in different sizes, pi denotes the structural dimension variable or material parameter variable. Fig. 3 displays the calculated sensitivities of main design variables of the model transducer, from which it can be observed that both the inner and outer diameters of the motor imposed significant effects on the modal frequency.

According to the sensitivity analysis results, the motor size was adjusted for further modal analysis. The motor with the dimensions of Table II had a weight of approximately 2 g, and the frequencies corresponding to the first-order longitudinal-vibration mode and the second-order bending vibration mode were 130.34 kHz and 130.35 kHz, respectively, with a frequency difference of 10 Hz. Subsequently, a harmonic response analysis was performed on the motor at from 120 kHz to 135 kHz, and the frequency variation curves versus vibration amplitude were plotted (Fig. 4). The maximum vibration amplitudes of the motor in the tangential and normal directions were 0.67 μm and 0.49 μm, respectively. As shown in Fig. 5, when the regulating frequency was set as the maximum superimposed value of the vibration amplitudes in the tangential and normal directions, the driving feet of the motor moved along an in-plane elliptical path. The output power of the motor was also measured. The output power of the motor was simulated using ANSYS, based on the material parameters listed in Table I, and the maximum output power was 20 W.

The clamping quality of the motor affects significantly the motor’s output performance. In this study, a bolt with a rubber gasket on the top was used for clamping at the nodes of the motor convex platform. The pre-pressure on the bottom of the stator was adjusted by regulating the bolt in order to ensure a reasonable contact between the stator driving feet and the rotor. The rubber gasket was used to provide the clamping fixture with certain flexibility and reduce the effect of the fixture on the mode. As it can be observed in Fig. 6, the motor performance was tested using a signal generator and an amplifier.

The relation between the test frequency and the motor vibration was examined using a three-dimensional (3D) laser Doppler vibration meter (Fig. 7). Firstly, a scanning frequency test was performed on the motor. The motor voltage was adjusted to 80V_pp, and a sinusoidal signal was transmitted to the motor through the power amplifier controlled by the main control computer. The motor was scanned in the frequency range of 20∼150 kHz and the frequency response curve of the motor was measured and is presented in Fig. 8. It can be observed that the resonant frequency of the motor in practical operation was 126.25 kHz, which was 1.66 kHz lower than the theoretically calculated value (127.91 kHz). The inconsistency between the theoretical value and the measured resonant frequency during the actual operation of the motor can be attributed to the error in the establishment of the theoretical model and the simplified geometry of the stator used in the simulation. Next, the motor frequency was adjusted to 126.25 kHz for a fixed-frequency experiment. Subsequently, the motor’s first-order longitudinal vibration mode and second-order bending-vibration were acquired. The measured vibration model of the motor displayed in Fig. 9. At an excitation voltage of 80V_pp, the measured amplitude was 0.6 μm. The vibration mode of the stator indicated that the measured vibration modes of the stator fit are in accord with the finite element simulation results.

The motor performance was also tested. In this study, the torque of the motor was measured by hanging weights. Reflective markers were attached on the side of the rotor and the rotating speed was measured using a photoelectric non-contact laser velocimeter (SW826). During the experiment, the pre-pressure between the rotor and the stator was regulated by adjusting the bolt. As shown in Fig. 10, a single sinusoidal AC signal with a phase difference of π/2 was input to the two phases of the piezoelectric ceramic plates and the voltage was set as 200V_pp. According to the experimental results, at a driving frequency of approximately 126.5 kHz, the motor exhibited a stable output performance. Then, the torque of the motor and the variation rules of the non-load speed at this frequency were investigated in detail.

The relation between voltage and motor rotating speed was tested in a voltage range of 0∼400 V_pp, and the obtained characteristic curve is shown in Fig. 11. When the driving frequency was constant, the rotating speed of the motor and the input voltage exhibited an almost linear relationship. As the voltage increased to 400V_pp, the maximum rotating speed of the motor reached up to 230 rpm. When the excitation voltage was maintained at 200V_pp, the variation of the motor’s no-load speed with the driving frequency was tested, as the results are shown in Fig. 12. It can be observed that the variation curve was similar to the amplitude/frequency characteristics of the structure in the resonant frequency band. This was due to the fact that the output speed of the motor increased with the vibration amplitude when the motor operated around the resonant frequency. At a driving frequency of 126.5 kHz, the maximum rotating speed of the motor was 120 rpm.

Fig. 13 displays the starting characteristic curves of the motor tested with an encoder. An excitation signal at a frequency of 126.5 kHz was applied on the motor and the voltage was set as 200V_pp. The rotor rotated clockwise at a phase difference of π/2, and performed a counterclockwise rotation at a phase difference of −π/2. The motor required approximately 30 ms to go from the starting to stable operation.

The motor torque under single-stator and double-stator configuration was tested by hanging weights. Firstly, the motor torque was measured with a single-stator. In order to accurately measure the maximum output torque of the motor, the driving frequency of the motor was set to 126.5 kHz, and the driving voltage of the motor was increased from 20 V_pp to 200 V_pp. Fig. 14 illustrates the test results, where it can be easily observed that the motor torque and voltage have an approximate linear relation. The maximum torque was 2.6×10^-2 N·m. Afterwards, the motor torque in the double-stator configuration was tested likewise. Theoretically, the output torque under the double-stator configuration should be double of the value under the single-stator configuration; however, the actual measured output torque was 1.5 times that of the single-stator. The main reasons for this difference are described below. Firstly, due to the manufacturing error and the limitations in the manufacturing technology, two motors cannot be completely same. An installation error also existed in the placement of the piezoelectric ceramic. Secondly, the slip loss caused by the discordance of the contact points between stators and rotor, and the slight difference in resonance characteristics of each stator may both affect the mechanical output characteristics.²¹ Thirdly, the pre-pressure exerted by the two stators during the installation process cannot be exactly the same, which may also lead to some loss of the output energy.²² Therefore, it is impossible for the two stators to output their maximum torque at the same time. That is, the final output torque of the motor should be a vector sum but not be a double superposition.

Aiming at addressing the existing application problems of ultrasonic motors on micro PTZ, this study designed a light flexible ultra-sonic motor, systematically investigated its driving principle, and performed size optimization and finite-element calculations. The total mass of the motor is approximately 2 g. Scanning-frequency and fixed-frequency experimental results demonstrated that the vibration characteristics of the designed motor were in good consistency with the design scheme, which confirmed the feasibility of the operating principle. Moreover, the mechanical properties and output torque of the designed motor were tested. When the excitation voltage is 200 V_pp and the working frequency is 126.5 kHz, the maximum output torque of the single stator motor is 2.6×10^-2 N·m, the maximum idle speed is 120 rpm, and the maximum output torque of the double stator motor is about 1.5 times of that of the single stator. Both rotating speed and torque of the motor as desired. The comparison results of the output torque under single-stator and double-stator configurations indicated a certain energy loss in the torque output, i.e., the output efficiency was slightly lower than the theoretical value.

The research is funded by The National Basic Research Program of China (973 Program, Grant No. 2015CB057501).