Introduction

1.1. Application of Piezoelectric Materials to USMs

Piezoelectric materials are essential to ultrasonic motor technology due to its ability to convert electrical energy into mechanical energy. They involve coupling of mechanical parameters (T, S) to electrical parameters (E, D) and forms electromechanical equations of piezoelectric elements. The direct piezoelectric effect is described in equation (1) while the inverse piezoelectric effect is described in equation (2).

$${D_m=d_{mj}{T}_j+\mathsf{\epsilon }}_{mn}^T E_n (\mathrm{m}, \mathrm{n}=1,2,3,)$$

(1)

$$S_i=s_{ij}^E{T}_j+d_{ni}{E}_n(\mathrm{i}, \mathrm{j}=1,2,\dots ,6)$$

(2)

$$\left[\begin{array}{c}{D}_1\\ D_2\\ D_3\end{array}\right]=\left[\begin{array}{ccc}{d}_{11}& d_{12}& d_{13}\\ d_{21}& d_{22}& d_{23}\\ d_{31}& d_{32}& d_{33}\end{array} \begin{array}{ccc}{d}_{14}& d_{15}& d_{16}\\ d_{24}& d_{25}& d_{26}\\ d_{34}& d_{35}& d_{36}\end{array}\right] \left[\begin{array}{c}{T}_1\\ T_2\\ T_3\\ T_4\\ T_5\\ T_{\begin{array}{c}6\\ \end{array}}\end{array}\right]+0;(E_n=0)$$

(3)

$$\left[\begin{array}{c}{S}_1\\ S_2\\ S_3\\ S_4\\ S_5\\ S_{\begin{array}{c}6\\ \end{array}}\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}{d}_{11}\\ d_{12}\\ d_{13}\end{array}\\ d_{13}\\ d_{15}\\ d_{16}\end{array} \begin{array}{c}\begin{array}{c}{d}_{21}\\ d_{22}\\ d_{23}\end{array}\\ d_{24}\\ d_{25}\\ d_{26}\end{array} \begin{array}{c}\begin{array}{c}{d}_{31}\\ d_{32}\\ d_{33}\end{array}\\ d_{34}\\ d_{35}\\ d_{36}\end{array} \right] \left[\begin{array}{c}{E}_1\\ E_2\\ E_3\end{array}\right]+0;(T_i=0)$$

(4)

Where the symbol ε represents dielectric constant, D indicates electric displacement, E specify the electric field strength, d express piezoelectric constant, S denote the stress vector, s is the elastic compliance, and T represents the strain vector of piezoelectric material. Equation (3) represents the matrix form of coupling equation of direct piezoelectric effect, while equation (4) represents the matrix form of coupling equation of inverse piezoelectric effect. The mechanism of both direct and inverse piezoelectric effects is graphically shown in Figure 2. Where a generation of electric field in response of mechanical stress or external force is shown in Figure 2 (a) while the external electrical field applied to piezoelectrical material produce a structural deformation is shown in Figure 2(b). A symbol F indicates the applied force while E represents applied electric field.

Figure 2. Polarization produces in Piezoelectric material: a) Direct piezoelectric effect, b) Converse piezoelectric effect.

Figure 2. Polarization produces in Piezoelectric material: a) Direct piezoelectric effect, b) Converse piezoelectric effect.

Doping or swapping additives allows for a wide range of adjustments to the piezoelectric characteristics. The particular goals of the devices must be taken into consideration while determining the necessary characteristics of piezoelectric materials. For instance, the material must have a low permittivity and a modest high-frequency dielectric loss in order to be employed in high/ultra-high-frequency applications. The material's acoustic impedance and coupling coefficient are often put under strain in the context of energy transducer applications. A material that has great frequency stability and high mechanical quality factor (Q_m) values can be used as standard frequency oscillators. To meet the requirements of the delay line application, the materials must be frequency stable, and the sound velocity in materials must also be taken into account. Ceramics employed in the electro-acoustic area must possess a significant permittivity, electromechanical coupling factor k_p value, and elastic compliance coefficient however, dielectric loss have little effect on the devices. For hydroacoustic transducer applications, if employed as receivers, the material must have high k_p value, a big piezoelectric coefficient of g₃₃ or g₃₁, and compliance constant, with a large permittivity, however its Q_m value is not strictly required. On the other hand, if piezoelectric material is used as a power emitter in hydroacoustic transducers, it is necessary that it has a little dielectric loss (tanθ), a high dielectric constant, great Q_m under a range of electric field, large piezoelectric constant, and high k_p value. Filters require materials that possess exceptional durability and resistance to temperature fluctuations. Additionally, these materials should exhibit high Q_m and low tanθ. The specific value of k_p needed for the filters depends on their bandwidth. High-voltage generators and igniters necessitate materials with high values of g₃₃ and k₃₃, a high permittivity, a high Q_m, and a low tanθ. Hence USMs are highly dependent on the characteristics of the piezoelectric materials that are employed in their fabrication. Table 1 shows a list of commonly used piezoelectric materials in ultrasonic motor, including their most notable characteristics, advantages and disadvantages. In modern times, the properties of piezoelectric ceramics may be finely tuned throughout a broad spectrum through the use of doping and substitution techniques, allowing them to be tailored for many application scenarios [38,39,40].

1.2. Piezoelectric USMs:

Piezoelectric USMs leverage the inverse piezoelectric effect and the frictional coupling to transform electric inputs to mechanical outcomes. Based on their vibration states, they can be classed as resonant and non-resonant. Non-resonant piezoelectric motors often achieve efficiencies near the nanoscale magnitude; however, their highest velocity is barely tens of millimeters/second [41,42]. Resonant piezoelectric motors achieve significantly greater velocities and exceeding one meter/second [43,44,45,46,47,48]. The resonant piezoelectric motor can be referred to as piezoelectric ultrasonic motors (USMs) because it operates at a frequency that is usually greater than 20kHz to prevent damaging individual hearing. As a solid-state actuator, the USMs offers advantages over electrostatic motors, electromagnetic motors, electro-conjugate fluid motors, and thermal mechanical motors in terms of simplicity of design, rapid response, a substantial output torque at a small size, and freedom from electromagnetic interference [49,50,51]. In the previous decade, several unique USMs have been suggested to implemented in many fields such as invasive surgical procedures, handling medications, optical focusing systems, microrobots, and aeronautical devices.

Table 2. Advantages of piezoelectric USMs over other traditional motors.

Table 2. Advantages of piezoelectric USMs over other traditional motors.

Feature	Piezoelectric Ultrasonic Motor	Electromagnetic Motor	Electrostatic Motor	Thermal Mechanical Motor	Electro-Conjugate Fluid Motor
Voltage(I/P)	Lower voltage	Lower voltage	High voltage required	Moderate voltage	Moderate voltage
Size & Weight	Compact and lightweight	Bulky due to magnets and coils	Can be bulky and heavy	Can be bulky	Can be complex
Suitable Environment	Works in air and vacuum	Affected by magnetic fields	Limited by air breakdown	Sensitive to temperature	Sensitive to leaks
Noise	Silent operation	Can be noisy (brushes/gears)	May generate noise	May generate noise	May generate noise
Electromagnetic Interference (EMI)	No EMI	Generates EMI	May generate EMI	No EMI	No EMI
Low-Speed Torque	High torque at low speeds	Torque decreases at low speeds	Limited torque at low speeds	Limited torque at low speeds	Generally lower torque
Response Time	Very fast response time	Can be slow depending on design	Slower response time	Slowest response time	Slower response time
Motor Complexity	Simple design	Complex design with moving parts	Complex design	Complex heating/cooling system	Complex fluid dynamics
Temperature	Stable performance across a wide range	Performance may be affected	Performance may be affected	Performance may be affected	Performance may be affected
Motor Efficiency	High efficiency, especially at low speeds	Varies depending on design	Lower efficiency	Lower efficiency	Lower efficiency

1.3. Basic Operating Principle of USMs:

Ultrasonic piezoelectric motor is comprised of two primary components: stator and rotor. The stator is the immobile part that contains the piezoelectric components. The stator design can change based on the exact type of ultrasonic motor such as standing wave or traveling wave. While the rotor is the mobile part that works with the stator to produce rotational or linear movement[52]. The USMs universal working concept is to convert the spiraling driving foot motion to the movement of the rotor via the friction interaction that occurs between the rotor and its stator, demonstrated in figure 3. The pushing element of the circular motion moves the runner with the friction force, while the pressing element shifts the force that are normal within the driving foot and the runner on a periodic basis. The pushing and pressing elements are parallel and perpendicular to the runner’s traveling trajectory respectively. In figure 3, from point P to Q, the normal and frictional forces increase, and driving foot's horizontal speed exceeds the runner speed causing the driving foot accelerates the runner. The normal force drops in the direction Q to R, and the flow of friction force drive backwards, and driving foot's horizontal speed falls than the runner speed. As a result, driving foot accelerate down the runner. The friction and normal forces rise from R to P, where the runner's speed decreases further. Hence in this manner, the circular motion behavior of driving foot causes to move the runner periodically. Therefore, the pressing and pushing elements of the circular movements have the predominant impact on the motor's thrust and speed, respectively[53].

Figure 3. Basic operation of USM.

Figure 3. Basic operation of USM.

Classification of USMs

Figure 4. Classifications of USMs.

Figure 4. Classifications of USMs.

Traveling Wave Motor.

When a traveling wave propagates through the stator, it causes elliptical motions on its surface. Figure 5 depicts the basic working concept of a traveling wave USMs where the driving foot is the point at which the stator and the runner make contact. The vertical amplitude of the traveling wave and driving foot are coincides. The driving foot's horizontal amplitude is related to the slope angle generated thru the moving wave and its distance among the stator's neutral layer and driving foot. A horizontal and vertical elements of driving foot are connected precisely as a traveling wave's slope angle and amplitude are. The stator's driving foot alternately drives the runner/rotor with its elliptic movements as the traveling wave spreads onward. Hence the runner moves against the other direction as the traveling wave moves. By overlapping of two standing waves a traveling wave is formed. The vibration superposition principle states that two standing waves should have identical vibrational structure, frequency, and amplitude, having a wavelength of one quarter variance in space and a distinction in phase of ± π/2 over a period. The equations of vibration for traveling and standing waves are presented in equations. (5) to (7).

(5)

(6)

(7)

The mathematical representation of the standing waves is shown in equations (5) and (6), while the traveling wave is described in equation (7); symbol t denotes time; ζ is wavelength, ϖ indicates the angular frequency, and k symbolize standing wave’s amplitude. It demonstrates that the traveling wave motor requires two sinusoidal stimulating impulses of the identical frequency with a phase alteration of +π/2 or -π/2. Furthermore, the two sinusoidal waves will stimulate the identical stator vibrational mode alongside an identical amplitude however, separated by a distance ζ/4 in space. Changing the difference in phase between the excited signals causes the traveling wave to flow in the other way, reversing the direction of runner's moving. Therefore, the traveling wave motor can achieve bidirectional motion. The driving foot can regulate the magnitude of the elliptical movement thru varying the exciting signals voltages at the same time. It is worth noting that changing the voltage levels of both exciting signals would result in additional standing waves formed in the stator, that will have an influence on the circular driving foot’s motion. The structure of elliptical movement remains constant since the amplitudes of vibrations of pressing and pushing both components are connected; this restricts the adaptability of modifying the traveling wave motor's output torque and speed.

Figure 5. Operating principle of TUSMs.

Figure 5. Operating principle of TUSMs.

Some performance analysis of the various state-of-the-art TUSMs are numerically illustrated in Table 3 where motion and type of stator, size of piezoelectric element, driving voltage, rotational velocity and speed, frequency, preload force and generated torque are shown for various proposed motors.

2.2. Standing Wave USMs

The driving foot's elliptical motion is created by generating a standing wave (also known as a mode shape) in the stator of ultrasonic piezoelectric motor[85]. The basic working mechanism of the standing wave ultrasonic motor is graphically demonstrated in figure 6. Despite the driving foot's pushing and pressing components are produced by the same exciting sinusoidal signal, the elliptical movement can be obtained due to the stator's damping ratios along the distinct directions of these component. As a small difference between the damping ratios, the motion trajectory typically degenerates into an almost straight line-like flat ellipse[86,87]. The oscillating driving foot’s direction is consistently diagonal to the forward motion of the runner(rotor), ensuring that both components are sufficiently powerful to propel the runner. The runner's movement direction is governed thru the driving foot’s vibrational direction. In figure 6, one may be clearly observed that driving foot's position and the stator's mode shape determine the direction of vibration for the standing wave motor. Both stator design and exciting frequency dictate the mode shapes. The driving foot goes diagonally when seen from the bottom left to the top right if it is positioned on the antinode's right side. Conversely, the driving foot will experience vibrations that travel from the right side of bottom to the left top, causing the runner to drive towards the left. In contrast to the generation of traveling waves in the stator of the TUSMs, the stator of the SUSMs may readily produce standing waves despite its geometry. The SUSMs may utilize rotors as runners for linear motion and sliders for rotational motion. Therefore, several linear SUSMs [88,89,90] and rotary SUSMs[91,92,93] were proposed in state of the art, each exhibiting different vibration patterns in the stators. The SUSMs can further categorized into two types based on their output motions: unidirectional and bidirectional SUSMs. Some performance analysis of the various state-of-the-art SUSMs are numerically demonstrated in table 4 where vibrator, shape of stator, driving voltage, rotational velocity and speed, frequency, force are shown for various proposed motors. Figure 7 show the V-shaped standing wave ultrasonic piezoelectric motor represented by Xiandi et al [94] , where figure 7(a) shows the physical prototype photo of standing wave transducer, figure 7(b) shows the excitations appeared in motor, figure6(c) illustrates the excitation signals followed by the vibration direction, figure 7(d) represents the driving tip’s elliptical trajectory evolution along the phase difference, figure 7(e) demonstrates the ultrasonic testing setup, and figure 7(f) represents the complete experimental setup for standing wave ultrasonic motor.

Figure 6. Basic operating principle of SUSMs.

Figure 6. Basic operating principle of SUSMs.

Table 4. Performances analysis of various SUSMs.

Table 4. Performances analysis of various SUSMs.

Reference	Year	Vibrator	Stator shape	Voltage	Velocity/Speed	Frequency	Force
[95]	2023	-	V-shaped	90V	0.2m/s	32.2kHz	10N
[94]	2023	linear	V-shaped	80Vrms	0.23m/s	33kHz	20N
[96]	2023	linear	V-shaped	150V	-	39.1kHz	-
[97]	2021	linear	V-shaped	400Vrms	0.53m/s	39kHz	30N
[98]	2020	linear	V-shaped	350Vrms	1.27m/s	38.6kHz	80N

* Vrms is the root mean square voltage.

2.3. Hybrid Modes USMs

Hybrid modes USMs (HUSMs) are USMs that use two distinct modes of operation to mimic elliptical motion of the driving foot, working mechanism of HUSMs is graphically demonstrated in figure 8. Where the driving foot oscillates in distinct ways in modes A and B. Based on the concepts of vibration superposition and Lissajous curves, the driving foot’s elliptical motion can be accomplished through stimulating modes A and B with two sin impulses at the identical frequency and with a specified phase variation (ϕ). To reverse the direction of rotation of the elliptical trajectory, flip the phase difference of the excited signals to -ϕ. Hence, varying the phase difference allows the HUSMs to achieve bidirectional movements. Furthermore, the two exciting signals can separately change the pressing and pushing components of elliptical movement, which are subject by modes A and B, correspondingly. Therefore, the electrical voltage levels of the exciting signals may be used to modulate the HUSMs output speed and thrust with great versatility.

Table 5 numerically illustrates the performance of various state of the art presented HUSMs, contains the vibration or motion patterns, stator type, presented prototype dimensions, applied voltage, obtained velocity and speed, operating frequency, and force. A hybrid mode ultrasonic piezoelectric motor is shown in figure 9 presented by Ziang et al[99] , where figure 9(a) demonstrates the hybrid motor ovel all configuration, figure 9(b) illustrations that when longitudinal PZT plates are powered by phased voltages, the longitudinal traveling waves (LTW) travels in a pair of arms oriented over the x-axis, causing another arms pair (the passive arms) to produce bending vibration. Figure 9(c) describes the mesh structure relating to the LTWs, figure 9(d) shows the elliptical motions by bending standing waves (BSWs) in the xz and yz planes, and figure 9(e) illustrates the mesh shapes occurred by BSWs in vertical directions.

Figure 7. V-shaped vibrator of standing-wave linear ultrasonic motor: (a) proposed physical prototype motor, (b) motor in excitation mode, (c) the vibration following direction, (d) driving tip’s elliptical trajectory progress along the phase difference, (e) testing ultrasonic motor prototype, and (b) complete experimental testing setup. [94].

Figure 7. V-shaped vibrator of standing-wave linear ultrasonic motor: (a) proposed physical prototype motor, (b) motor in excitation mode, (c) the vibration following direction, (d) driving tip’s elliptical trajectory progress along the phase difference, (e) testing ultrasonic motor prototype, and (b) complete experimental testing setup. [94].

Figure 8. Basic working principle of HUSMs.

Figure 8. Basic working principle of HUSMs.

Figure 9. Hybrid mode ultrasonic piezoelectric motor: (a) the hybrid motor ovel all configuration, (b) when longitudinal PZT plates are powered by phased voltages, the longitudinal traveling waves (LTW) travels in a pair of arms oriented over the x-axis, causing another arms pair (the passive arms) to produce bending vibration, (c) the mesh structures related to the LTWs, (d) the elliptical motions by bending standing waves (BSWs), and (e) the mesh shapes occurred by BSWs in vertical directions.[99].

Figure 9. Hybrid mode ultrasonic piezoelectric motor: (a) the hybrid motor ovel all configuration, (b) when longitudinal PZT plates are powered by phased voltages, the longitudinal traveling waves (LTW) travels in a pair of arms oriented over the x-axis, causing another arms pair (the passive arms) to produce bending vibration, (c) the mesh structures related to the LTWs, (d) the elliptical motions by bending standing waves (BSWs), and (e) the mesh shapes occurred by BSWs in vertical directions.[99].

Table 5. Performances analysis of various HUSMs.

Table 5. Performances analysis of various HUSMs.

Reference	Year	Motion/Vibration	Stator structure	Prototype Size	Voltage	Velocity/Speed	Frequency	Force
[100]	2022	Longitudinal Bending	tuning fork	-	320Vpp	88.67mm/s	80.2kHz	99mN
[101]	2022	Bending Longitudinal	-	45.7*30mm	180Vp	1103mm/s	30.2kHz	392mN
[102]	2020	Transverse-Shear	disk	2*10*4mm	300Vpp	169.4mm/s	24.7kHz	7.5N
[103]	2020	Longitudinal-torsional	cylinder	10*10*55mm	400Vpp	483rpm	56kHz	22N
[104]	2019	Bending-Bending	planar	20*44*30mm	400Vpp	300µm/s	40Hz	1.47N
[99]	2023	Longitudinal Bending	disk	68*68*28mm3	250V	877mm/s	27.4kHz	40.2N
[105]	2019	Longitudinal- Bending	disk	40*112*38mm	400Vpp	124.2mm/s	1.4kHz	105N

2.4. Multi-DOF Piezoelectric Ultrasonic Motor

The further functions associated with the concurrent management of numerous degrees of freedom (DOF) inside a single mechanism of USMs provided the investigators with a particularly extensive area of exploration[106,107]. Various multi-DOF-USMs are being described [108,109]who follow the core fundamentals of operation of the SUSMs, TUSMs, and HUSMs for the purpose of offering qualities such as nanometric resolution, self-braking, high controllability, rapid response time, and other similar characteristics. Several stators can work together to provide multi-DOF-USMs movements for the runner. The next sub-sections discuss three distinct categories of multi-DOF-USMs, including: Spherical, rotary-linear, and planar USMs, where rotary-linear and planar USMs have just two DOF while spherical USMs have two or three DOF.

2.4.1. Spherical USMs

S. Toyama invented one of the first ‘spherical' USMs in 1991 [110], which was later enhanced [111]. The drive was designed for machine assembly, laser cutting, and use as an individual joint in robots. Recent advancements in MEMS technology and active piezoelectric materials have led to the development of expert spherical USMs. A bonded type longitudinal-bending mode spherical shape 2-DOF HUSM is presented to meet the needs for accurate movement along with control in a limited space for underwater and space applications [112]. The motor comprises a pyramid-shaped piezoelectric active elements mover and a friction base with a curved spherical shape that serves as the stator, where the prior loading force is generated by a tension spring underneath the piezoelectric mover. Functioning modes include the mover's bending and longitudinal vibrations. The geometry parameters were optimized using FEA of the motor. Where the experimental findings showed that the highest velocity of rotation in both x and y directions approached to 414 deg/s when the voltage used for excitation is 550 Vpp. Moreover, results also showed that the highest peak forces for the proposed spherical based 2-DOF HUSM in x and y directions are 5.25 N and 5.34 N, correspondingly, where the excitation voltage is 525 Vpp. Mizuno et al [107] presented spherical shaped stator base multi-DOF USMs utilizing rotational mode vibrational motion of the stator shown in figure 10(a), where 24 multilayer piezoelectric actuators are embedded on the surface of stator. Other highlighted spherical shape multi-DOF USMs are presented in [113,114,115].

2.4.2. Rotary-linear USMs

Linear and rotary are the two distinguished classes of USMs however, some multi-DOF USMs may produce both linear and angular motion [116,117]. A linear-rotary moment based USM is presented [118] for optical beam luminous flux density control. The motor features a single stator made of a piezoelectric bimorph disc and a carbon fiber cylindrical tube, attached in the center. The disk is perpendicular to its flat surface. Quadrilateral waveguides are generated in the inner circumference of a disc, aligning with the tangential direction of the cylindrical tube outer surface. This waveguide arrangement converts the radial vibrations of the bimorph disc into rotational oscillations of the cylindrical tube. The USM has two vibration modes: second out-of-plane bending and first radial. The carbon-based tube has a ring-shaped rotor that may be moved or rotated using the inertial principle. Another highlighted USM named precise linear-rotary positioning stage (LRPS) is presented by Chang et al [119] for optical focusing graphically shown in figure 10(b). This motor achieved both linear and rotational motions along and around the vertical directions respectively. Furthermore, an experimental study was conducted on the prototype of LRPS to evaluate its performance illustrated in figure 10(c). The experiment demonstrated that it could perform linear motion with a stroke of 5 mm and rotational motion with a stroke of 360˚. The resolutions for upward and downward linear movements were 82.32 and 86.26 nm, respectively. The resolutions for clockwise and anticlockwise rotating rotations were 3.90 and 3.85 μrad, respectively.

2.4.3. Planar USMs

The paper [120] describes a planer motion-based USM called twin coil spring-based soft actuator, which is powered by two flexible USMs. Each USM consists of a small metallic stator and an elastic, extended coil spring. It can travel forward and backward with extensibility and bend left and right with flexibility. The motor's basic operating concept is based on two vibrational modes: the first mode repeats contraction and expansion symmetrically around the central cross-section, while the second mode is asymmetrical. The model has been experimentally examined, and it has demonstrated strong response characteristics, high sensor linearity, and resilience while maintaining flexibility and controllability in planer motion. Wentao et al[121] presented a bonded-type planer multi-DOF USMs which operates in both torsional and bending hybrid modes containing PZT plates. Its working principle is shown in figure 10(d), where the vibrations displacement occurred in all four directions. Another prominent study on planer type USM based on two-mode X-Y direction motion is represented [122].

Figure 10. Multiple degree of freedom USMs: (a) Spherical stator bases multi-DOFUSMs [107], (b) Optical focus precise linear-rotary positioning stage (LRPS) prototype containing two piezoelectric actuators [119], (c) Experimental setup for LRPS [119], (d) Planer ultrasonic motor bending in four directions [121].

Figure 10. Multiple degree of freedom USMs: (a) Spherical stator bases multi-DOFUSMs [107], (b) Optical focus precise linear-rotary positioning stage (LRPS) prototype containing two piezoelectric actuators [119], (c) Experimental setup for LRPS [119], (d) Planer ultrasonic motor bending in four directions [121].

Finite Element Modeling of USMs

A finite element modeling (FEM) is important computational method for analyzing and forecasting USMs behavior. Before building actual prototypes, engineers can use it to realistically replicate the motor's efficiency under various operating situations. This method conserves resources as well as time during the design and implementation phase.

Figure 11. Steps of 3D Finite element modeling of USMs in multiphysics software.

Figure 11. Steps of 3D Finite element modeling of USMs in multiphysics software.

The initial step of FEM is system modeling that includes to define geometry dimensions, material properties, mesh generation, boundary conditions and loading conditions. Once the system modeling is completed then analysis and results are carried out through simulations, which may include strain and stress distribution, model analysis and performance prediction. Torque/speed study under loading and unloading conditions, displacements, efficiency, and noise generations are the characteristics observed in performance prediction step. Various commercial software like COMSOL multiphysics, Anysis, ADINA, and Abaqus offers FEM features and tools to analysis the piezoelectric devices effectively. However, FEM for USMs still have some challenges, like careful consideration of material characteristics, boundary conditions, and non-linearities such as friction in the contact region are necessary to create an accurate FEM model. Furthermore, to execute simulations, sophisticated models with precise meshing may need a large amount of processing power and time. To make sure the model correctly depicts behavior in the actual world, experimental testing is required to validate the FEM results.

The first FEM of USMs was performed by Yamabuchi and Kagawa[123] in 1989 in order to analyze the piezoelectric elastic structures and represent the study to understand qualitatively characteristics of the ultrasonic motor. Later in 1992, Maeno et al. shed light on the mechanical properties of the ring type ultrasonic motor by FEM code MSCINASTRAN to determine the real ring-type stator's vibration mode [124]. In 1996, another study was presented to looked at how the piezoceramic's shape affects the stator's vibration by FEM [125]. Where a detailed geometry was considered to compute the electrical excitation and mechanical vibration in the stator of USM. In last two decades a lot of work has been done on FEM of USMs to get more advance, efficient and optimized designs. The highlighted work includes model analysis to demonstrate the elliptical vibration process [14,103,126,127]. The major steps of FEM of USMs are graphically demonstrated in Figure 11 and design and modeling figure were taken from the FEM study presented by Yang et al.[128] .

Fabrication Methods of USMs

Micro and Nano Fabrication Methods of USMs

Techniques for fabricating micro and nanoscale materials provide benefits for intricate designs and downsizing. A major essential techniques are thin-film deposition, micromachining, and lithographie galvanoformung abformung(LGA). Several considerations influence the choice of micro or nano manufacturing technique, notably the necessary performance of the motor, the size and complexity of the desired feature, the material's suitability to the piezoelectric film, and the volume and cost of production [130,131]. The techniques, advantages and considerations of these nano/micro fabrication methods are listed in table 6.

A thin-film deposition method utilizing processes like chemical vapor deposition (CVD), sputtering, and electrohydrodynamic jet printing (EHJ printing), in order to directly deposit a thin film of piezoelectric materials onto a printing surface. Atoms that form a thin layer on the substrate are ejected using sputtering processes, which use a high-energy laser to target the piezoelectric material. Precursor chemicals are introduced using CVD, and they react and break down on the substrate to generate the appropriate piezoelectric layer. Piezoelectric ink with suspended particles is applied onto the substrate by EHJ Printing using an electric field. Micromachining entails the use of several methods, including Reactive ion etching (RIE), photolithography, and deep reactive ion etching (DRIE), for removing material from a substrate to produce the required USMs geometries. Figure 12 shows the basic steps of micro machining fabrication process for thin-film micro motor. Zhou et al. presented a MEMS (Microelectromechanical systems) technology based on silicon wafer consist of metal decomposition, etching, and sputtering [132]. Another highlighted MEMS technology-based fabrication was presented by Yang et al. for thin film piezoelectric micromotor[133].

Figure 12. Basic steps of micro machining fabrication process for thin-film micro motor.

Figure 12. Basic steps of micro machining fabrication process for thin-film micro motor.

The first miniature tube ultrasonic motor was fabricated by Uchino[134,135,136], the motor was fabricated in three different designs by reducing its size, the total length of tube ultrasonic motor of 1^st design was 10mm, 2^nd design was 6mm and 3^rd design was 4mm shown in Figure 13. Kohei et al utilized the micromachining technology to produce a small stator of dimensions of (0.41 mm × 0.41 mm × 0.25 mm). The success of the stator manufacturing process is attributed to a micromanipulator that can regulate a small quantity of glue in a sub-milligram order [137]. Another highlighted miniature ultrasonic motor was fabricated by Shunsuke et al for-focus systems[138].

Figure 13. Miniature tube USMs presented by Uchino in various dimensions[135].

Figure 13. Miniature tube USMs presented by Uchino in various dimensions[135].

Table 6. List of various techniques for micro/nano fabrication methods along with their advantages and considerations.

Table 6. List of various techniques for micro/nano fabrication methods along with their advantages and considerations.

Method	Techniques	Considerations	Advantages
Thin-Film, Deposition	⮚ CVD, ⮚ Sputtering, EHJ Printing	Cost, Performance of thin films, Dedicated apparatus	Complex designs, Miniaturization, Remove the need of bonding process
LGA	⮚ X-ray lithography, ⮚ Electroplating, molding	Expert tools, Complex process, limited materials	Good quality surface, Raised proportions of aspects of metal structures
Micromachining	⮚ RIE, ⮚ Photolithography, ⮚ DRIE	Surface roughness, Multi-step process, residual stress	Intricate characteristics, Combines thin-film deposition processes

"Lithographie Galvanoformung Abformung," (LGA) is the German acronym that translates to "X-ray lithography, electroplating, and molding." A high-resolution resist design is made on a substrate using X-ray radiation in this procedure. A thick coating of metal is electroplated onto the patterned resist. Following that, the resist is removed, revealing a metallic mold with a high aspect ratio. The USMs stator with exact characteristics may then be created by casting molten metal into the mold.

Characterizations of USMs

Dynamic Characterization

In dynamic characterization usually frequency response and resonance analysis based techniques are applied to study important characteristics of USMs. The assessment of frequency response determines the motor's reaction to varying driving frequencies. By employing frequency sweep techniques and examining output torque or fluctuations in speed, it may be quantified. Resonant frequencies of the motor are identified using resonance analysis, which is important since they might affect stability and performance. Vibration patterns or changes in electrical impedance are measured using these approaches. Shunsuke et al. performed the characterization of thin hollow linear ultrasonic motor for lens focus systems and studies transient response, force and velocity characteristics of motor shown in figure 16. [138]

Figure 14. Various characterization methos of USMs.

Figure 14. Various characterization methos of USMs.

Figure 15. The micromotor's transient reaction (a) experiments and least minimal approach for hard PZT, (b) the torque derived from the angular velocity curve approximation for hard PZT, (c) experiments and the least minimal approach for PMN-PT, (d) the torque derived from the angular velocity curve approximation for PMN-PT.[137].

Figure 15. The micromotor's transient reaction (a) experiments and least minimal approach for hard PZT, (b) the torque derived from the angular velocity curve approximation for hard PZT, (c) experiments and the least minimal approach for PMN-PT, (d) the torque derived from the angular velocity curve approximation for PMN-PT.[137].

Figure 16. Characterization of hollow ultrasonic miniature motor for lens used in focus systems.[138].

Figure 16. Characterization of hollow ultrasonic miniature motor for lens used in focus systems.[138].

Table 7. Equipment and techniques used for various characterization of USMs.

Table 7. Equipment and techniques used for various characterization of USMs.

Characteristic	Equipment	Technique
Torque	Torque meter, Load Cell [130,134]	Static or Dynamic Load Application, [132] Pre-Load mechanisms Custom test configuration
Speed Velocity	Tachometer, Laser doppler vibrometer, [133] encoders	Transient characterization method [130,135] Direct Measurement, Frequency Sweep Techniques
Efficiency	Power Supply, Load Cell, Tachometer, Multimeter	Calculation of Mechanical Output Power / Electrical Input Power, Frequency Sweep Techniques Torque*angular speed/ Input power [136]
Vibration	Accelerometer, Laser Scanner Vibrometer	Measurement of Vibration Levels and Patterns [131]
Strain	Strain Gauge, Digital Image Correlation, Interferometry	Non-contact optical method High-precision technique
Temperature	Thermocouple or Thermistor	Monitoring Temperature Distribution
Noise	Sound Level Meter	Measurement of Acoustic Noise
Electric parameters	Multimeter	Direct measurement of current and voltage
Friction and Wear	Tribometer	Simulation of Operating Conditions
Piezoelectric coefficient	Berlincourt Meter, d33 Meter, Laser Interferometry	Quasi-static method
Holding Force	Load Cell	Measurement of Maximum Static Load
Frequency Response	Signal Generator, Power Amplifier, laser Doppler vibrometer, Spectrum Analyzer	Inputting Varying Frequency Signals and Measuring Response
Resonance	Signal Generator, Power Amplifier, laser Doppler vibrometer, Spectrum Analyzer	Identification of Resonant Frequencies and Mode Shapes, Frequency Sweep Techniques
Impedance	Impedance analyzer[138], LCR meter, Network analyzer, Oscilloscope	Direct Measurement, Vectorial Measurements, S-Parameters[139]
Displacement Angular acceleration	linear variable differential transformer, Laser Triangulation sensor, laser displacement sensor, laser interferometer, linear encoder	Measurement of Linear or Angular Displacement[131] Newton second law[135]
Quality factor	Bode plot	Bode plot[131]

Applications of USMs

Surgical Robots Based on USMs

USMs serve an important role in minimally invasive surgery. The noteworthy advantages of these surgeries include a decrease in post-operative discomfort, diminished risks during and after surgery, shorter hospital stays, faster healing, fewer cuts and scars, less immune system stress, and shorter surgical times and total expenses [168,169]. A broad range of nano and microscale medical ultrasonic robots have been revealed in last decade to approach and transcend the level of biological tools used for general surgeries in the pancreas, liver, intestines, gallbladder ducts, cardiovascular, spinal, and genital areas. Furthermore, various research investigations are being undertaken in oncological surgeries, such as urology, and lung surgery. Moreover, some of these models dealt with detecting tumoral lesions and establishing resection margins, while others were meant to assess the viability of ultrasound-guided surgeries. A few studies also assessed the robotic drop-in probe, the consistency of the hepatic tissue, and the circulatory flow in the pulmonary vein [170]. A millimeter-scale rolling microrobot is designed for gastrin testimonial tracks and arteries. Driven by a micro ultrasonic motor and a micro planetary gear train, it can produce 60 µNm torque and 4500 rpm speed. The prototype measures 14 mm in length, 10 mm in width, and 7 mm in height, and weighs 640 mg. Experiments showed that the microrobot maintains speed on slopes with high friction coefficient, even on low friction slopes [171].

Figure 17. Various application of USMs.

Figure 17. Various application of USMs.

Laparoscopic Surgery

Electromechanical rotatory USMs based on piezoelectric material are commonly employed in laparoscopic single-site operations owing to their tiny wound size, wide field of vision (FoV), ease of repetitive high positioning precision, small dimension, and fast response [172,173]. The authors describe a novel three degree of freedom laparoscopic surgical robot (LSR) powered by a double-leg ultrasonic motor (DUM) containing piezoelectric ceramic active plates in order to induced longitudinal and bending coupling vibrations. The two-stage, three-order bending vibrations can form a traveling wave that drives the DUM rotor. A genetic algorithm-II is used to optimized the DUM stator, leading to increased moving stability and driving efficiency. The mechanical properties of DUM have been investigated experimentally. The maximum no-load rotational speeds are 333.75 and 335.77 rpm for clockwise and counterclockwise rotation respectively, with maximum output torques of 2 and 1.6 N mm. The experimental platform is designed to demonstrate that LSR may alter its posture to get a proper surgical FoV, demonstrating that the use of DUM in LSR has substantial benefits and potential [174]. Katsuhiko et al. suggested a soft actuator with a cylindrical cam mechanism that converts linear to rotating movement for laparoscopic surgery. In laparoscopic surgery, a tiny rotating actuator was mounted on the edge of a forceps manipulator, resulting 3Nmm torque with a 70° angle of rotation. The actuator has the benefit of being easily sterilized and disposable [175].

Neurosurgery

For conducting robotic neurosurgery, the ultrasonic piezoelectric motor is noticeably favorited part of the system, especially in microsurgery and stereotactic procedures. It shows several benefits, including nonferrous material, tiny size, strong holding torque, and quiet operation. A researcher develops magnetic resonance (MR) conditional parallel robot consists of a 3-degree-of-freedom translational and remote center of motion (RCM) modules by using the actuation capabilities of USMs [176]. A model evaluation based on genetic algorithm is performed in order to obtained maximize dexterity then prototype fabrication and experimental verification is carried out. The RCM module's orientation stability was measured to be 0.055±0.0016°, with an absolute orientation inaccuracy of 2.05±0.019°. The robot's impact on the signal-to-noise ratio in images obtained from MR imaging is less than 4%, demonstrating a high potential application in MR-restricted neurosurgery. Another flexible surgical robot that uses beacon total focusing technique (b-TFM) to enable high-accuracy ultrasonic position sensing and strong magnetic steering is presented [177]. This robot demonstrates the ability to drive nimbly. A 1 mm x 1 mm PZT patch inserted on the tip of the robot which determine the robot's location. The ultrasonic position sensing system used in the model oversee the entire navigation process, with a maximum error of 0.8 mm at a steering radius of 100 mm. Moreover, USMs have proven frequently employed in MRI-guided robotic systems to increase accuracy by legitimate the system's uncertainties and nonlinearities due to its MR safety properties [178,179]. For example, the positioning accuracy can be effectually reduced to sub-degree level thru particularly developed controllers [180,181].

Cardiovascular Surgery

A hollow ultrasonic motor (HUM) is successfully utilized in Master-slave vascular interventional robotic systems for minimally invasive cardio surgery. The goal of the vascular interventional robotic system using a hollow ultrasonic motor, is to provide physicians the ability to carry out intricate vascular procedures precisely and dependably. The proposed slave robot is made up of a linear movement platform and a hollow drive mechanism which relies on a traveling wave ultrasonic motor. The stator of HUM, optimized by an evolutionary algorithm for superior quality and larger amplitude of traveling waves, which are beneficial to the drive efficiency, eliminates the need for a redundant transmission mechanism and maintains beneficial co-axiality due to its property of a high positional precision, and fast response. The overall Master-slave vascular interventional robotic systems feature High kinematic accuracy, little hysteresis, and excellent cooperative performance [158].

Table 8. Importance of various characteristics of ultrasonic motor in various applications.

Table 8. Importance of various characteristics of ultrasonic motor in various applications.

Characteristic	Importance	Fields	Applications
High Precision & Resolution	Allows precise and intricate motions, allowing for accurate placement and providing manipulation at the micrometer scale.	Minimally invasive surgery	Instrument control
		Aerospace	Antenna pointing, Telescope adjustment
		Biomedical engineering	Drug delivery, Microfluidic devices
		Industrial automation	Robotic assembly, Laser cutting
Fast Response & Speed	Enables fast operating and swift adjustments in position through the use of speedy start-stop and motion functions.	Industrial automation	Assembly lines, Material handling
		Biomedical engineering	Pumps, Microfluidic devices
Silent Operation	Essential for locations that are sensitive to noise by producing minimum noise.	Minimally invasive surgery	Improved Patient Comfort, Quieter surgical environment, Improved Communication and Collaboration of surgical teams
		Biomedical engineering	Medical pumps, Diagnostic Equipment, Implantable Devices
		Aerospace	Minimizing acoustic disturbances, Microgravity Experiments,
No electromagnetic interference (EMI)	Ensures optimal performance in the proximity of delicate electronic devices while preventing electromagnetic interference (EMI) disturbances.	Biomedical engineering	Implantable devices
		Industrial automation	Environments with sensitive electronics, Medical Device Production and Assembly, Applications Requiring Sparks or Flammable Materials
		Aerospace	Safeguarding sensitive Electronics, Compatibility with scientific Equipment, Reduced Risk of Signal Interference
Compact Size & Lightweight	Enables the reduction in size of instruments and decreases the total weight.	Minimally invasive surgery	Surgical tools
		Aerospace	Spacecraft design
		Biomedical engineering	Implantable devices
Harsh Environment Tolerance	Capable of functioning in harsh conditions such as severe temperatures, radiation, and vacuum, making it indispensable for space operations.	Aerospace	Satellite components, Deployment mechanisms
Low Power Consumption	Conserves energy and prolongs battery lifespan in circumstances with limited resources.	Aerospace	Spacecraft design
		Biomedical engineering	Implantable devices

Piezoelectric USMs Trends and Future Developments

Conclusions

References

1. L. Capineri and A. Bulletti, “Ultrasonic Guided-Waves Sensors and Integrated Structural Health Monitoring Systems for Impact Detection and Localization: A Review,” Sensors, vol. 21, no. 9, p. 2929, Apr. 2021. [CrossRef]
2. M. Mazalan, A. Noor, Y. Wahab, S. Yahud, and W. Zaman, “Current Development in Interdigital Transducer (IDT) Surface Acoustic Wave Devices for Live Cell In Vitro Studies: A Review,” Micromachines (Basel), vol. 13, no. 1, p. 30, Dec. 2021. [CrossRef]
3. H. X. Cao, V. Du Nguyen, J.-O. Park, E. Choi, and B. Kang, “Acoustic Actuators for the Manipulation of Micro/Nanorobots: State-of-the-Art and Future Outlooks,” Micromachines (Basel), vol. 15, no. 2, p. 186, Jan. 2024. [CrossRef]
4. D. Mandal and S. Banerjee, “Surface Acoustic Wave (SAW) Sensors: Physics, Materials, and Applications,” Sensors, vol. 22, no. 3, p. 820, Jan. 2022. [CrossRef]
5. Z. Guan et al., “A self-powered acoustic sensor excited by ultrasonic wave for detecting and locating underwater ultrasonic sources,” Nano Energy, vol. 104, p. 107879, Dec. 2022. [CrossRef]
6. A. Čeponis, V. Jūrėnas, and D. Mažeika, “Low Profile Triangle-Shaped Piezoelectric Rotary Motor,” Micromachines (Basel), vol. 15, no. 1, p. 132, Jan. 2024. [CrossRef]
7. Y.-H. Wang, S. C.-S. Tsai, and F. C.-F. Lin, “Reduction of Blood Loss by Means of the Cavitron Ultrasonic Surgical Aspirator for Thoracoscopic Salvage Anatomic Lung Resections,” Cancers (Basel), vol. 15, no. 16, p. 4069, Aug. 2023. [CrossRef]
8. J. Zhang, Y. Wang, T. Liu, K. Yang, and H. Jin, “A Flexible Ultrasound Scanning System for Minimally Invasive Spinal Surgery Navigation,” IEEE Trans Med Robot Bionics, vol. 3, no. 2, pp. 426–435, May 2021. [CrossRef]
9. D. Zhang et al., “Diagnostic Value of Multi-Mode Ultrasonic Flow Imaging Examination in Solid Renal Tumors of Different Sizes,” J Clin Med, vol. 12, no. 2, p. 566, Jan. 2023. [CrossRef]
10. J. Qian et al., “Ultrasound-Assisted Enzymatic Protein Hydrolysis in Food Processing: Mechanism and Parameters,” Foods, vol. 12, no. 21, p. 4027, Nov. 2023. [CrossRef]
11. Y. Li et al., “An Ultrasound–Fenton Process for the Degradation of 2,4,6-Trinitrotoluene,” Int J Environ Res Public Health, vol. 20, no. 4, p. 3102, Feb. 2023. [CrossRef]
12. M. Salimi et al., “Experimental and Numerical Investigation of the Use of Ultrasonic Waves to Assist Laser Welding,” Materials, vol. 17, no. 11, p. 2521, May 2024. [CrossRef]
13. J. Qiu, Y. Yang, X. Hong, P. Vasiljev, D. Mazeika, and S. Borodinas, “A Disc-Type High Speed Rotary Ultrasonic Motor with Internal Contact Teeth,” Applied Sciences, vol. 11, no. 5, p. 2386, Mar. 2021. [CrossRef]
14. D. Xu, W. Yang, X. Zhang, and S. Yu, “Design and Performance Evaluation of a Single-Phase Driven Ultrasonic Motor Using Bending-Bending Vibrations,” Micromachines (Basel), vol. 12, no. 8, p. 853, Jul. 2021. [CrossRef]
15. A. Zameer, S. Naz, and M. A. Z. Raja, “Parallel differential evolution paradigm for multilayer electromechanical device optimization,” Modern Physics Letters B, Mar. 2024. [CrossRef]
16. S. Naz, A. Zameer, M. A. Z. Raja, and K. Muhammad, “Weighted differential evolution heuristics for improved multilayer piezoelectric transducer design,” Appl Soft Comput, vol. 113, p. 107835, Dec. 2021. [CrossRef]
17. A. Zameer, S. Naz, M. A. Z. Raja, J. Hafeez, and N. Ali, “Neuro-Evolutionary Framework for Design Optimization of Two-Phase Transducer with Genetic Algorithms,” Micromachines (Basel), vol. 14, no. 9, p. 1677, Aug. 2023. [CrossRef]
18. S. Naz, A. Usman, A. Zameer, K. Muhammad, and M. A. Z. Raja, “Efficient multivariate optimization of an ultrasonic transducer with genetic parallel algorithms,” Waves in Random and Complex Media, pp. 1–25, Sep. 2023. [CrossRef]
19. S. Naz, M. A. Z. Raja, A. Mehmood, A. Zameer, and M. Shoaib, “Neuro-intelligent networks for Bouc–Wen hysteresis model for piezostage actuator,” The European Physical Journal Plus, vol. 136, no. 4, p. 396, Apr. 2021. [CrossRef]
20. S. Naz, M. A. Z. Raja, A. Mehmood, and A. Z. Jaafery, “Intelligent Predictive Solution Dynamics for Dahl Hysteresis Model of Piezoelectric Actuator,” Micromachines (Basel), vol. 13, no. 12, p. 2205, Dec. 2022. [CrossRef]
21. Z. Zheng et al., “Micro-Electro-Mechanical Systems Microphones: A Brief Review Emphasizing Recent Advances in Audible Spectrum Applications,” Micromachines (Basel), vol. 15, no. 3, p. 352, Feb. 2024. [CrossRef]
22. A. C. Hatfield and T.-B. Xu, “Transparent Piezoelectric LiNbO3-based Surface Acoustic Wave for Dust Mitigation in Space Environment,” in AIAA SCITECH 2023 Forum, Reston, Virginia: American Institute of Aeronautics and Astronautics, Jan. 2023. [CrossRef]
23. G. Ali and F. Mohd-Yasin, “Comprehensive Noise Modeling of Piezoelectric Charge Accelerometer with Signal Conditioning Circuit,” Micromachines (Basel), vol. 15, no. 2, p. 283, Feb. 2024. [CrossRef]
24. Q.-T. Lai, Q.-J. Sun, Z. Tang, X.-G. Tang, and X.-H. Zhao, “Conjugated Polymer-Based Nanocomposites for Pressure Sensors,” Molecules, vol. 28, no. 4, p. 1627, Feb. 2023. [CrossRef]
25. S. Bouhedma, J. Bin Taufik, F. Lange, M. Ouali, H. Seitz, and D. Hohlfeld, “Different Scenarios of Autonomous Operation of an Environmental Sensor Node Using a Piezoelectric-Vibration-Based Energy Harvester,” Sensors, vol. 24, no. 4, p. 1338, Feb. 2024. [CrossRef]
26. C. Chen, T.-B. Xu, A. Yazdani, and J.-Q. Sun, “A high density piezoelectric energy harvesting device from highway traffic — System design and road test,” Appl Energy, vol. 299, p. 117331, Oct. 2021. [CrossRef]
27. Q. Qiao, X. Wang, W. Liu, and H. Yang, “Defect Detection in Grouting Sleeve Grouting Material by Piezoelectric Wave Method,” Buildings, vol. 14, no. 3, p. 629, Feb. 2024. [CrossRef]
28. I. Izadgoshasb, “Piezoelectric Energy Harvesting towards Self-Powered Internet of Things (IoT) Sensors in Smart Cities,” Sensors, vol. 21, no. 24, p. 8332, Dec. 2021. [CrossRef]
29. Z. Abdullah, S. Naz, M. A. Z. Raja, and A. Zameer, “Design of wideband tonpilz transducers for underwater SONAR applications with finite element model,” Applied Acoustics, vol. 183, p. 108293, Dec. 2021. [CrossRef]
30. L. Shams and T.-B. Xu, “Underwater communication acoustic transducers: a technology review,” in Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2023, Z. Su, M. P. Limongelli, and B. Glisic, Eds., SPIE, Apr. 2023, p. 8. [CrossRef]
31. S. Naz, M. A. Z. Raja, A. Kausar, A. Zameer, A. Mehmood, and M. Shoaib, “Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach,” Math Comput Simul, vol. 196, pp. 88–113, Jun. 2022. [CrossRef]
32. A.Kausar, C.-Y. Chang, M. A. Z. Raja, A. Zameer, and M. Shoaib, “Novel design of recurrent neural network for the dynamical of nonlinear piezoelectric cantilever mass–beam model,” The European Physical Journal Plus, vol. 139, no. 1, p. 16, Jan. 2024. [CrossRef]
33. F. Qian, T.-B. Xu, and L. Zuo, “Piezoelectric energy harvesting from human walking using a two-stage amplification mechanism,” Energy, vol. 189, p. 116140, Dec. 2019. [CrossRef]
34. J. Lin, P. Yuan, R. Lin, X. Xue, M. Chen, and L. Xing, “A Self-Powered Lactate Sensor Based on the Piezoelectric Effect for Assessing Tumor Development,” Sensors, vol. 24, no. 7, p. 2161, Mar. 2024. [CrossRef]
35. J. Wang et al., “Design and Analysis of a Cardioid Flow Tube Valveless Piezoelectric Pump for Medical Applications,” Sensors, vol. 24, no. 1, p. 122, Dec. 2023. [CrossRef]
36. J. Wallaschek, “Piezoelectric Ultrasonic Motors,” J Intell Mater Syst Struct, vol. 6, no. 1, pp. 71–83, Jan. 1995. [CrossRef]
37. M. Hunstig, “Piezoelectric Inertia Motors—A Critical Review of History, Concepts, Design, Applications, and Perspectives,” Actuators, vol. 6, no. 1, p. 7, Feb. 2017. [CrossRef]
38. chunsheng zhao, Ultrasonic motors: technologies and applications. . Springer Science & Business Media., 2011. Accessed: May 17, 2024. [Online]. Available: https://books.google.com/books?hl=en&lr=&id=gVbGGkT5emgC&oi=fnd&pg=PR4&dq=ultrasonic+motors+technologies+and+applications+by+chunsheng+zhao&ots=4R_kqVr56E&sig=mPLMjASJ2kyu5IWkW4iA2c6vVqQ#v=onepage&q=ultrasonic%20motors%20technologies%20and%20applications%20by%20chunsheng%20zhao&f=false.
39. A.Shuaibu Ahmad, M. Mukhtar Usman, S. Bello Abubakar, and A. Yusuf Gidado, “Review on the application of Piezoelectric materials in the development of ultrasonic motors,” Journal of Advanced Research in Applied Mechanics Journal homepage, vol. 33, no. 1, pp. 9–19, 2017, [Online]. Available: www.akademiabaru.com/aram.html.
40. K. Spanner and B. Koc, “Piezoelectric Motors, an Overview,” Actuators, vol. 5, no. 1, p. 6, Feb. 2016. [CrossRef]
41. D. Xu, Y. Liu, S. Shi, J. Liu, W. Chen, and L. Wang, “Development of a Nonresonant Piezoelectric Motor With Nanometer Resolution Driving Ability,” IEEE/ASME Transactions on Mechatronics, vol. 23, no. 1, pp. 444–451, Feb. 2018. [CrossRef]
42. M. V. Golub, S. I. Fomenko, P. E. Usov, and A. A. Eremin, “Elastic Waves Excitation and Focusing by a Piezoelectric Transducer with Intermediate Layered Elastic Metamaterials with and without Periodic Arrays of Interfacial Voids,” Sensors, vol. 23, no. 24, p. 9747, Dec. 2023. [CrossRef]
43. Y. Wang, S. Wu, W. Wang, T. Wu, and X. Li, “Piezoelectric Micromachined Ultrasonic Transducers with Micro-Hole Inter-Etch and Sealing Process on (111) Silicon Wafer,” Micromachines (Basel), vol. 15, no. 4, p. 482, Mar. 2024. [CrossRef]
44. A. U. H. Mohsan et al., “Design and Effect of Resonant Ultrasonic Vibration-Assisted Laser Cladding (R-UVALC) on AlCrFeMnNi High-Entropy Alloy,” Materials, vol. 17, no. 5, p. 969, Feb. 2024. [CrossRef]
45. L. Gou et al., “Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane,” Micromachines (Basel), vol. 15, no. 2, p. 279, Feb. 2024. [CrossRef]
46. A. Wellendorf, L. von Damnitz, A. W. Nuri, D. Anders, and S. Trampnau, “Determination of the Temperature-Dependent Resonance Behavior of Ultrasonic Transducers Using the Finite-Element Method,” Journal of Vibration Engineering & Technologies, vol. 12, no. 2, pp. 1277–1290, Feb. 2024. [CrossRef]
47. Y. Liu, M. Hafezi, and A. Feeney, “A cascaded Nitinol Langevin transducer for resonance stability at elevated temperatures,” Ultrasonics, vol. 137, p. 107201, Feb. 2024. [CrossRef]
48. M. Taşlıyol, S. Öncü, and M. E. Turan, “An implementation of class D inverter for ultrasonic transducer mixed powder mixture,” Ultrason Sonochem, vol. 104, p. 106838, Mar. 2024. [CrossRef]
49. V. Ruiz-Díez, J. Hernando-García, J. Toledo, A. Ababneh, H. Seidel, and J. L. Sánchez-Rojas, “Bidirectional Linear Motion by Travelling Waves on Legged Piezoelectric Microfabricated Plates,” Micromachines (Basel), vol. 11, no. 5, p. 517, May 2020. [CrossRef]
50. C. Peng, H. Wu, S. Kim, X. Dai, and X. Jiang, “Recent Advances in Transducers for Intravascular Ultrasound (IVUS) Imaging,” Sensors, vol. 21, no. 10, p. 3540, May 2021. [CrossRef]
51. W. Li, M. Ge, R. Jia, X. Zhao, H. Zhao, and C. Dong, “Design and Analysis Method of Piezoelectric Liquid Driving Device with Elastic External Displacement,” Micromachines (Basel), vol. 15, no. 4, p. 523, Apr. 2024. [CrossRef]
52. K. Uchino, “Piezoelectric ultrasonic motors: overview,” Smart Mater Struct, vol. 7, no. 3, pp. 273–285, Jun. 1998. [CrossRef]
53. K. Uchino, S. Cagatay, B. Koc, S. Dong, P. Bouchilloux, and M. Strauss, “Micro Piezoelectric Ultrasonic Motors,” J Electroceram, vol. 13, no. 1–3, pp. 393–401, Jul. 2004. [CrossRef]
54. S. Ueha, Y. Hashimoto, M. Kuribayashi, and E. Mori, “Ultrasonic Power Measurement Using Standing Wave Ratio,” Jpn J Appl Phys, vol. 24, no. S1, p. 169, Jan. 1985. [CrossRef]
55. Siyuan He, Weishan Chen, Xie Tao, and Zaili Chen, “Standing wave bi-directional linearly moving ultrasonic motor,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 45, no. 5, pp. 1133–1139, Sep. 1998. [CrossRef]
56. Y. Liu, S. Shi, C. Li, W. Chen, L. Wang, and J. Liu, “Development of a bi-directional standing wave linear piezoelectric actuator with four driving feet,” Ultrasonics, vol. 84, pp. 81–86, Mar. 2018. [CrossRef]
57. X. Dong, M. Hu, L. Jin, Z. Xu, and C. Jiang, “A standing wave ultrasonic stepping motor using open-loop control system,” Ultrasonics, vol. 82, pp. 327–330, Jan. 2018. [CrossRef]
58. X. Hou, H. P. Lee, C. J. Ong, and S. P. Lim, “Development and numerical characterization of a new standing wave ultrasonic motor operating in the 30–40kHz frequency range,” Ultrasonics, vol. 53, no. 5, pp. 928–934, Jul. 2013. [CrossRef]
59. L. Wang, C. Shu, Q. Zhang, and J. Jin, “A novel sandwich-type traveling wave piezoelectric tracked mobile system,” Ultrasonics, vol. 75, pp. 28–35, Mar. 2017. [CrossRef]
60. S. Kondo, H. Yamaura, D. Koyama, and K. Nakamura, “Traveling wave type ultrasonic linear motor using twin bending bars,” Phys Procedia, vol. 3, no. 1, pp. 1053–1058, Jan. 2010. [CrossRef]
61. D. Sun, S. Wang, S. Hata, J. Sakurai, and A. Shimokohbe, “Driving mechanism and experimental realization of a cylindrical ultrasonic linear microactuator,” Microelectron Eng, vol. 86, no. 4–6, pp. 1262–1266, Apr. 2009. [CrossRef]
62. M. K. Kurosawa, “State-of-the-art surface acoustic wave linear motor and its future applications,” Ultrasonics, vol. 38, no. 1–8, pp. 15–19, Mar. 2000. [CrossRef]
63. K. Asai, M. K. Kurosawa, and T. Higuchi, “Novel power circulation methods for a surface acoustic wave motor,” in 1999 IEEE Ultrasonics Symposium. Proceedings. International Symposium (Cat. No.99CH37027), IEEE, 1999, pp. 667–670 vol.1. [CrossRef]
64. M. Kurosawa, M. Takahashi, and T. Higuchi, “Ultrasonic linear motor using surface acoustic waves,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 43, no. 5, pp. 901–906, Sep. 1996. [CrossRef]
65. M. Kurosawa, M. Takahashi, and T. Higuchi, “Ultrasonic linear motor using surface acoustic waves,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 43, no. 5, pp. 901–906, Sep. 1996. [CrossRef]
66. M. Kuribayashi, S. Ueha, and E. Mori, “Excitation conditions of flexural traveling waves for a reversible ultrasonic linear motor,” J Acoust Soc Am, vol. 77, no. 4, pp. 1431–1435, Apr. 1985. [CrossRef]
67. M. Guo, S. Pan, J. Hu, C. Zhao, and S. Dong, “A small linear ultrasonic motor utilizing longitudinal and bending modes of a piezoelectric tube,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 61, no. 4, pp. 705–709, Apr. 2014. [CrossRef]
68. K. Asumi, R. Fukunaga, T. Fujimura, and M. Kuribayashi Kurosawa, “High speed, high resolution ultrasonic linear motor using V-shape two bolt-clamped Langevin-type transducers,” Acoust Sci Technol, vol. 30, no. 3, pp. 180–186, 2009. [CrossRef]
69. M. Kuribayashi Kurosawa, O. Kodaira, Y. Tsuchitoi, and T. Higuchi, “Transducer for high speed and large thrust ultrasonic linear motor using two sandwich-type vibrators,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 45, no. 5, pp. 1188–1195, Sep. 1998. [CrossRef]
70. A. Endo, N. Sasaki, and Y. Tomikawa, “Linear type ultrasonic motor using two-dimensionally positioned piezoelectric elements,” Ferroelectrics, vol. 112, no. 1, pp. 165–170, Dec. 1990. [CrossRef]
71. K. Uchino, K. Kato, and M. Tohda, “Ultrasonic linear motors using a multilayered piezoelectric actuator,” Ferroelectrics, vol. 87, no. 1, pp. 331–334, Nov. 1988. [CrossRef]
72. Z. Xue, K. T. Chau, W. Liu, and T. W. Ching, “Design, Analysis, and Implementation of Wireless Traveling-Wave Ultrasonic Motors,” IEEE Trans Power Electron, vol. 39, no. 4, pp. 1–11, Apr. 2024. [CrossRef]
73. S. Guo, L. Wang, J. Jin, and Y. Yang, “A general structural design method, dynamics modeling and application study for built-in sandwich annular traveling wave piezoelectric transducers,” Mech Syst Signal Process, vol. 199, p. 110476, Sep. 2023. [CrossRef]
74. C. Jiang, Z. Zhao, D. Lu, Z. Xu, and L. Jin, “Contact analysis and performance evaluation of ring type traveling wave ultrasonic motors based on a surface contact model,” Ultrasonics, vol. 127, p. 106851, Jan. 2023. [CrossRef]
75. T. Yang, B. Cao, Y. Chen, X. Li, J. He, and W. Su, “Optimization of three-dimensional traveling wave drive for a PZT thin-film micro-motor based on stiffness tuning of the supporting structure,” Ultrasonics, vol. 134, p. 107066, Sep. 2023. [CrossRef]
76. Y. Zhang et al., “Laser-induced microtextured stators coupling with flexible rotors for low-voltage driving rotational piezoelectric motors,” Chemical Engineering Journal, vol. 467, p. 143361, Jul. 2023. [CrossRef]
77. G. Wang et al., “Improving output performance of ultrasonic motor by coating MoS2 on the stator,” Tribol Int, vol. 186, p. 108608, Aug. 2023. [CrossRef]
78. K. Murai, D. Kong, H. Tamura, and M. Aoyagi, “Hollow cylindrical linear stator vibrator using a traveling wave of longitudinal axisymmetric vibration mode,” Ultrasonics, vol. 129, p. 106910, Mar. 2023. [CrossRef]
79. C. Jiang, X. Wu, D. Lu, Z. Xu, and L. Jin, “Contact modeling and performance evaluation of ring type traveling wave ultrasonic motors considering stator teeth,” Ultrasonics, vol. 117, p. 106518, Dec. 2021. [CrossRef]
80. X. Ma, J. Liu, J. Deng, Q. Liu, and Y. Liu, “A Rotary Traveling Wave Ultrasonic Motor With Four Groups of Nested PZT Ceramics: Design and Performance Evaluation,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 67, no. 7, pp. 1462–1469, Jul. 2020. [CrossRef]
81. N. Chen and D. Fan, “A teeth-discretized electromechanical model of a traveling-wave ultrasonic motor,” Mechanical Sciences, vol. 11, no. 2, pp. 257–266, Jul. 2020. [CrossRef]
82. J. Li, S. Zeng, S. Liu, N. Zhou, and T. Qing, “Tribological properties of textured stator and PTFE-based material in travelling wave ultrasonic motors,” Friction, vol. 8, no. 2, pp. 301–310, Apr. 2020. [CrossRef]
83. S. Zeng, J. Li, N. Zhou, J. Zhang, A. Yu, and H. He, “Improving the wear resistance of PTFE-based friction material used in ultrasonic motors by laser surface texturing,” Tribol Int, vol. 141, p. 105910, Jan. 2020. [CrossRef]
84. X. Liu, J. Song, H. Chen, G. Zhao, J. Qiu, and Q. Ding, “Enhanced transfer efficiency of ultrasonic motors with polyimide based frictional materials and surface texture,” Sens Actuators A Phys, vol. 295, pp. 671–677, Aug. 2019. [CrossRef]
85. L. Kang et al., “Design of precision driving control system for standing-wave ultrasonic motor,” in Eighth Symposium on Novel Photoelectronic Detection Technology and Applications, S. Zhu, Q. Yu, J. Su, L. Chen, and J. Chu, Eds., SPIE, Mar. 2022, p. 592. [CrossRef]
86. Q. Pan, Y. Wang, A. Wan, C. Li, M. Zhao, and R. Li, “Development of a novel single-mode miniature standing wave ultrasonic motor,” Smart Mater Struct, vol. 32, no. 12, p. 125015, Dec. 2023. [CrossRef]
87. Y. Deng, G. Zhao, X. Yi, and W. Xiao, “Contact modeling and input-voltage-region based parametric identification for speed control of a standing wave linear ultrasonic motor,” Sens Actuators A Phys, vol. 295, pp. 456–468, Aug. 2019. [CrossRef]
88. Z. Chen, X. Li, P. Ci, G. Liu, and S. Dong, “A standing wave linear ultrasonic motor operating in in-plane expanding and bending modes,” Review of Scientific Instruments, vol. 86, no. 3, Mar. 2015. [CrossRef]
89. Y. Shi and C. Zhao, “A new standing-wave-type linear ultrasonic motor based on in-plane modes,” Ultrasonics, vol. 51, no. 4, pp. 397–404, May 2011. [CrossRef]
90. Siyuan He, Weishan Chen, Xie Tao, and Zaili Chen, “Standing wave bi-directional linearly moving ultrasonic motor,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 45, no. 5, pp. 1133–1139, Sep. 1998. [CrossRef]
91. I. Grybas, R. Bansevicius, V. Jurenas, A. Bubulis, J. Janutenaite, and G. Kulvietis, “Ultrasonic standing waves-driven high resolution rotary table,” Precis Eng, vol. 45, pp. 396–402, Jul. 2016. [CrossRef]
92. M. Shafik and L. Makombe, “A Standing Wave Piezoelectric Ultrasonic Motor Using a Single Flexural Vibration Ring Transducer,” Applied Mechanics and Materials, vol. 415, pp. 126–131, Sep. 2013. [CrossRef]
93. X. Lu, J. Hu, L. Yang, and C. Zhao, “A novel dual stator-ring rotary ultrasonic motor,” Sens Actuators A Phys, vol. 189, pp. 504–511, Jan. 2013. [CrossRef]
94. X. Jin, Y. Zhang, H. Fu, J. Ji, X. Hua, and Y. Fu, “Low-voltage driving linear piezoelectric motors having textured sliders of surface multi-connected vesicle-like microarray,” Int J Mech Sci, vol. 241, p. 107984, Mar. 2023. [CrossRef]
95. Q. and P. Q. and Z. Y. and D. X. and F. H. and J. J. and W. P. L. and F. C. and L. J. and Y. Z. Peng, “ Crocodile-Skin-Inspired Surface Microstructures for Friction Regulation of Piezoelectric Motors.,” SSRN, Oct. 2023.
96. Q. Peng et al., “Mechanical Characteristics Regulation of V-Shaped Standing-Wave Ultrasonic Motors With Minimal Quantity Lubrication,” Tribology Transactions, vol. 66, no. 2, pp. 222–237, Mar. 2023. [CrossRef]
97. L. Zhou, Z. Yao, S. Dai, Y. He, and H. Xu, “Modeling and verification of life prediction of a V-shaped linear ultrasonic motor,” Review of Scientific Instruments, vol. 92, no. 4, Apr. 2021. [CrossRef]
98. X. Li, Z. Yao, R. Li, and D. Wu, “Dynamics modeling and control of a V-shaped ultrasonic motor with two Langevin-type transducers,” Smart Mater Struct, vol. 29, no. 2, p. 025018, Feb. 2020. [CrossRef]
99. J. Wu et al., “A two-DOF linear ultrasonic motor utilizing the actuating approach of longitudinal-traveling-wave/bending-standing-wave hybrid excitation,” Int J Mech Sci, vol. 248, p. 108223, Jun. 2023. [CrossRef]
100. H. Qu, C. Liu, L. Zhang, J. Qu, and B. Song, “A Longitudinal-Bending Hybrid Linear Ultrasonic Motor and Its Driving Characteristic,” Shock and Vibration, vol. 2022, pp. 1–14, Jan. 2022. [CrossRef]
101. Z. Ding, W. Wei, K. Wang, and Y. Liu, “An Ultrasonic Motor Using a Carbon-Fiber-Reinforced/Poly-Phenylene-Sulfide-Based Vibrator with Bending/Longitudinal Modes,” Micromachines 2022, Vol. 13, Page 517, vol. 13, no. 4, p. 517, Mar. 2022. [CrossRef]
102. D. Lu, Q. Lin, B. Chen, C. Jiang, and X. Hu, “A single-modal linear ultrasonic motor based on multi vibration modes of PZT ceramics,” Ultrasonics, vol. 107, p. 106158, Sep. 2020. [CrossRef]
103. L. Yang, W. Ren, C. Ma, and L. Chen, “Mechanical simulation and contact analysis of the hybrid longitudinal-torsional ultrasonic motor,” Ultrasonics, vol. 100, p. 105982, Jan. 2020. [CrossRef]
104. J. Deng, Y. Liu, J. Liu, D. Xu, and Y. Wang, “Development of a Planar Piezoelectric Actuator Using Bending–Bending Hybrid Transducers,” IEEE Transactions on Industrial Electronics, vol. 66, no. 8, pp. 6141–6149, Aug. 2019. [CrossRef]
105. Y. Liu, L. Wang, Z. Gu, Q. Quan, and J. Deng, “Development of a Two-Dimensional Linear Piezoelectric Stepping Platform Using Longitudinal-Bending Hybrid Actuators,” IEEE Transactions on Industrial Electronics, vol. 66, no. 4, pp. 3030–3040, Apr. 2019. [CrossRef]
106. J. Leng, L. Jin, Z. Xu, and X. Zhu, “Development of a 3-DOF Cylindrical Ultrasonic Motor Based on Non-Standard Modes,” Applied Sciences, vol. 13, no. 18, p. 10096, Sep. 2023. [CrossRef]
107. A. Mizuno, H. Kajiwara, H. Tamura, and M. Aoyagi, “Study on Multidegree-of-Freedom Ultrasonic Motor Using Vibration Mode Rotation of Metal Spherical Stator,” Actuators, vol. 11, no. 1, p. 27, Jan. 2022. [CrossRef]
108. Z. Li, Z. Guo, H. Han, Z. Su, and H. Sun, “Design and characteristic analysis of multi-degree-of-freedom ultrasonic motor based on spherical stator,” Review of Scientific Instruments, vol. 93, no. 2, Feb. 2022. [CrossRef]
109. J. Leng, L. Jin, X. Dong, H. Zhang, C. Liu, and Z. Xu, “A multi-degree-of-freedom clamping type traveling-wave ultrasonic motor,” Ultrasonics, vol. 119, p. 106621, Feb. 2022. [CrossRef]
110. S. Toyama, S. Hatae, and M. Nonaka, “Development of multi-degree of freedom spherical ultrasonic motor,” in Fifth International Conference on Advanced Robotics ’Robots in Unstructured Environments, IEEE, 1991, pp. 55–60 vol.1. [CrossRef]
111. S. Toyama, S. Sugitani, Zhang Guoqiang, Y. Miyatani, and K. Nakamura, “Multi degree of freedom spherical ultrasonic motor,” in Proceedings of 1995 IEEE International Conference on Robotics and Automation, IEEE, pp. 2935–2940. [CrossRef]
112. R. Liu, L. Wang, J. Jin, and H. Zhao, “A Novel 2-Dof Ultrasonic Motor Design, Simulation, and Experimental Investigation,” in 2022 16th Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA), IEEE, Oct. 2022, pp. 77–81. [CrossRef]
113. Z. Huang, S. Shi, W. Chen, L. Wang, L. Wu, and Y. Liu, “Development of a novel spherical stator multi-DOF ultrasonic motor using in-plane non-axisymmetric mode,” Mech Syst Signal Process, vol. 140, p. 106658, Jun. 2020. [CrossRef]
114. Z. Li, Z. Wang, P. Guo, L. Zhao, and Q. Wang, “A ball-type multi-DOF ultrasonic motor with three embedded traveling wave stators,” Sens Actuators A Phys, vol. 313, p. 112161, Oct. 2020. [CrossRef]
115. V. Jūrėnas, G. Kazokaitis, and D. Mažeika, “Design of Unimorph Type 3DOF Ultrasonic Motor,” Applied Sciences, vol. 10, no. 16, p. 5605, Aug. 2020. [CrossRef]
116. X. Yang and W.-L. Zhu, “Design, Analysis, and Control of an XY Parallel Nanomanipulator With Multiple Actuation Modes,” IEEE Transactions on Industrial Electronics, vol. 67, no. 9, pp. 7639–7648, Sep. 2020. [CrossRef]
117. J. Deng, Y. Liu, S. Zhang, and J. Liu, “Modeling and experiments of a nano-positioning and high frequency scanning piezoelectric platform based on function module actuator,” Sci China Technol Sci, vol. 63, no. 12, pp. 2541–2552, Dec. 2020. [CrossRef]
118. D. Mazeika, S. Borodinas, P. Vasiljev, R. Bareikis, A. Struckas, and V. Jurenas, “2DOF LINEAR-ROTARY TYPE ULTRASONIC MOTOR.”.
119. Q. Chang, Y. Liu, J. Deng, S. Zhang, and W. Chen, “Design of a precise linear-rotary positioning stage for optical focusing based on the stick-slip mechanism,” Mech Syst Signal Process, vol. 165, p. 108398, Feb. 2022. [CrossRef]
120. Y. Sato, A. Kanada, and T. Mashimo, “Self-Sensing and Feedback Control for a Twin Coil Spring-Based Flexible Ultrasonic Motor,” IEEE Robot Autom Lett, vol. 5, no. 4, pp. 5425–5431, Oct. 2020. [CrossRef]
121. W. Wei et al., “A linear ultrasonic motor driven by torsional/bending vibrations,” Sens Actuators A Phys, vol. 357, p. 114404, Aug. 2023. [CrossRef]
122. H.-K. Guo, Y.-H. Hsu, and C.-K. Lee, “Control of a multi-direction piezoelectric linear motor using a gyroscopic feedback control,” in Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2024, M. P. Limongelli, C. T. Ng, and B. Glisic, Eds., SPIE, May 2024, p. 19. [CrossRef]
123. T. Yamabuchi and Y. Kagawa, “Numerical simulation of a piezoelectric ultrasonic motor and its characteristics,” J. Jpn. Soc. Simul. Technol, vol. 8, no. 3, pp. 69–76, 1989.
124. T. Maeno, T. Tsukimoto, and A. Miyake, “Finite-element analysis of the rotor/stator contact in a ring-type ultrasonic motor,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 39, no. 6, pp. 668–674, 1992.
125. J. W. Krome and J. Wallaschek, “Finite Element Models for the Piezoelectric Actuation in Ultrasonic Traveling Wave Motors,” J Intell Mater Syst Struct, vol. 7, no. 2, pp. 157–161, Mar. 1996. [CrossRef]
126. Z. Yin, C. Dai, Z. Cao, W. Li, Z. Chen, and C. Li, “Modal analysis and moving performance of a single-mode linear ultrasonic motor,” Ultrasonics, vol. 108, p. 106216, Dec. 2020. [CrossRef]
127. W. Ren, M. Yang, L. Chen, C. Ma, and L. Yang, “Mechanical optimization of a novel hollow traveling wave rotary ultrasonic motor,” J Intell Mater Syst Struct, vol. 31, no. 8, pp. 1091–1100, May 2020. [CrossRef]
128. L. Yang et al., “Design and Dynamic Simulation of a Novel Traveling Wave Linear Ultrasonic Motor,” Micromachines (Basel), vol. 13, no. 4, p. 557, Mar. 2022. [CrossRef]
129. J. Li, F. Che, J. Deng, W. Chen, J. Liu, and Y. Liu, “A linear ultrasonic motor with a hollowed and symmetrical stator,” Int J Mech Sci, vol. 262, p. 108718, Jan. 2024. [CrossRef]
130. T. Kanda, A. Makino, T. Ono, K. Suzumori, T. Morita, and M. K. Kurosawa, “A micro ultrasonic motor using a micro-machined cylindrical bulk PZT transducer,” Sens Actuators A Phys, vol. 127, no. 1, pp. 131–138, Feb. 2006. [CrossRef]
131. P. Marter, M. Khramova, F. Duvigneau, R. J. Wood, D. Juhre, and R. Orszulik, “Bidirectional motion of a planar fabricated piezoelectric motor based on unimorph arms,” Sens Actuators A Phys, vol. 377, Oct. 2024. [CrossRef]
132. T. Yang et al., “A PZT Thin-Film Traveling-Wave Micro-Motor With Stator Teeth Based on MEMS Technology,” Journal of Microelectromechanical Systems, vol. 33, no. 2, pp. 236–247, Apr. 2024. [CrossRef]
133. W. Zhou et al., “A Piezoelectric Microultrasonic Motor With High Q and Good Mode Match,” IEEE/ASME Transactions on Mechatronics, vol. 26, no. 4, pp. 1773–1781, Aug. 2021. [CrossRef]
134. S. Cagatay, B. Koc, P. Moses, and K. Uchino, “A piezoelectric micromotor with a stator of φ = 1.6mm and l = 4mm using bulk PZT,” Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, vol. 43, no. 4 A, pp. 1429–1433, 2004. [CrossRef]
135. K. Uchino, S. Cagatay, and B. Koc, “Ultrasonic Motors,” 2003. [Online]. Available: https://www.researchgate.net/publication/279377213.
136. S. Cagatay, B. Koc, and K. Uchino, “A 1.6-mm, Metal Tube Ultrasonic Motor,” 2003.
137. K. Kikuchi, M. Hussain, and T. Mashimo, “Fabrication and characterization of a submillimeter-scale ultrasonic motor,” Sens Actuators A Phys, vol. 360, p. 114524, Oct. 2023. [CrossRef]
138. S. Izuhara and T. Mashimo, “Design and characterization of a thin linear ultrasonic motor for miniature focus systems,” Sens Actuators A Phys, vol. 329, p. 112797, Oct. 2021. [CrossRef]
139. B. Delibas and B. Koc, “Single crystal piezoelectric motor operating with both inertia and ultrasonic resonance drives,” Ultrasonics, vol. 136, p. 107140, Jan. 2024. [CrossRef]
140. N. Chen, J. Zheng, X. Jiang, S. Fan, and D. Fan, “Analysis and control of micro-stepping characteristics of ultrasonic motor,” Frontiers of Mechanical Engineering, vol. 15, no. 4, pp. 585–599, Dec. 2020. [CrossRef]
141. Z. Li, Z. Wang, L. Zhao, and P. Guo, “Characteristic analysis and experimental study of spherical ultrasonic motor with multi-degree-of-freedom,” Journal of Applied Science and Engineering, vol. 23, no. 4, pp. 619–626, Dec. 2020. [CrossRef]
142. X. Li, Z. Wen, B. Jia, T. Cao, D. Yu, and D. Wu, “A Review of Application and Development Trends in Ultrasonic Motors,” ES Materials & Manufacturing, 2020. [CrossRef]
143. L. Zhang, H. Zheng, S. Huang, W. Zhang, F. Li, and D. Liu, “A life test of ultrasonic motors under different torque loads and the analysis of the characteristics of wearing surfaces,” Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 234, no. 5, pp. 770–777, May 2020. [CrossRef]
144. “Ultrasonics: Fundamentals, Technologies, and Applications - Dale Ensminger, Leonard J. Bond - Google Books.” Accessed: May 31, 2024. [Online]. Available: https://books.google.com/books?hl=en&lr=&id=EVnqEAAAQBAJ&oi=fnd&pg=PP1&dq=+ultrasonics+motors+in+Semiconductor+Manufacturing&ots=TIGXh-YtVV&sig=7PVusgeNkbYOJfIhcFwA8ANCvNU#v=onepage&q&f=false.
145. K. Guo, J. Lu, and H. Yang, “Simulation Analysis of a Sandwich Cantilever Ultrasonic Motor for a Dexterous Prosthetic Hand,” Micromachines 2023, Vol. 14, Page 2150, vol. 14, no. 12, p. 2150, Nov. 2023. [CrossRef]
146. K. Asumi, R. Fukunaga, T. Fujimura, and M. K. Kurosawa, “Miniaturization of a V-shape transducer ultrasonic motor,” Jpn J Appl Phys, vol. 48, no. 7 PART 2, p. 07GM02, Jul. 2009.
147. T. Kimmel, S. Stall, D. Porada, C. Kunkel, and A. Kessler, “Comparison of ultrasonic devices for the pretreatment of textiles before washing and analysis of action,” J Eng Fiber Fabr, vol. 18, Jan. 2023.
148. C. Dils, S. Hohner, and M. Schneider-Ramelow, “Use of Rotary Ultrasonic Plastic Welding as a Continuous Interconnection Technology for Large-Area e-Textiles,” Textiles 2023, Vol. 3, Pages 66-87, vol. 3, no. 1, pp. 66–87, Jan. 2023. [CrossRef]
149. N. M. Zashchepkina, V. G. Zdorenko, N. R. Tierentyeva, O. M. Markina, M. O. Markin, and K. M. Bozhko, “Ultrasonic method of quality control for textile materials,” Archives of Materials Science and Engineering, vol. Vol. 97, no. nr 1/2, pp. 39–49, 2019. [CrossRef]
150. J. A. Gallego-Juarez, E. Riera, V. Acosta, G. Rodríguez, and A. Blanco, “Ultrasonic system for continuous washing of textiles in liquid layers,” Ultrason Sonochem, vol. 17, no. 1, pp. 234–238, Jan. 2010. [CrossRef]
151. K. Rapouch and Mrázek M, “Use of ultrasound for cleaning of components of historical vehicles in Technical Museum”. [CrossRef]
152. F. I. Alzarooni, A. K. Alkharji, A. A. Alsuwaidi, and E. R. Almajali, “Design and implementation of an automated dry solar-panel cleaning system,” 2020 Advances in Science and Engineering Technology International Conferences, ASET 2020, Feb. 2020. [CrossRef]
153. T. Kimmel, C. Kunkel, M. Ait Sghir, and A. Kessler, “Potential of ultrasonics for energy saving in the household washing process,” Energy Effic, vol. 16, no. 5, pp. 1–11, Jun. 2023.
154. J. Huang and D. Sun, “Performance Analysis of a Travelling-Wave Ultrasonic Motor under Impact Load,” Micromachines (Basel), vol. 11, no. 7, p. 689, Jul. 2020. [CrossRef]
155. X. Liu, G. Zhao, and J. Qiu, “Improving the performance of ultrasonic motors in low-pressure, variable-temperature environments,” Tribol Int, vol. 160, p. 107000, Aug. 2021. [CrossRef]
156. E. T. K. Chiang, T. Urakubo, and T. Mashimo, “Lift Generation by a Miniature Piezoelectric Ultrasonic Motor-Driven Rotary-Wing for Pico Air Vehicles,” IEEE Access, vol. 10, pp. 13210–13218, 2022. [CrossRef]
157. J. Zhou et al., “Development of a Δ-Type Mobile Robot Driven by Three Standing-Wave-Type Piezoelectric Ultrasonic Motors,” IEEE Robot Autom Lett, vol. 5, no. 4, pp. 6717–6723, Oct. 2020. [CrossRef]
158. Q. Lu, Z. Sun, J. Zhang, J. Zhang, J. Zheng, and F. Qian, “A Novel Remote-Controlled Vascular Interventional Robotic System Based on Hollow Ultrasonic Motor,” Micromachines (Basel), vol. 13, no. 3, p. 410, Mar. 2022. [CrossRef]
159. S. Izuhara and T. Mashimo, “Design and characterization of a thin linear ultrasonic motor for miniature focus systems,” Sens Actuators A Phys, vol. 329, p. 112797, Oct. 2021. [CrossRef]
160. K. Kikuchi, M. Hussain, and T. Mashimo, “Fabrication and characterization of a submillimeter-scale ultrasonic motor,” Sens Actuators A Phys, vol. 360, Oct. 2023. [CrossRef]
161. A. Antoniou et al., “Robotic system for magnetic resonance guided focused ultrasound ablation of abdominal cancer,” The International Journal of Medical Robotics and Computer Assisted Surgery, vol. 17, no. 5, p. e2299, Oct. 2021. [CrossRef]
162. X. Bai, M. Hu, T. Gang, and Q. Rong, “A Submerged Optical Fiber Ultrasonic Sensor Using Matched Fiber Bragg Gratings,” Sensors, vol. 18, no. 6, p. 1942, Jun. 2018. [CrossRef]
163. J. Tian, X. Dong, S. Gao, and Y. Yao, “Multipoint fiber-optic laser-ultrasonic actuator based on fiber core-opened tapers,” Opt Express, vol. 25, no. 24, p. 29737, Nov. 2017. [CrossRef]
164. M. Giannakou et al., “Magnetic resonance image–guided focused ultrasound robotic system for transrectal prostate cancer therapy,” The International Journal of Medical Robotics and Computer Assisted Surgery, vol. 17, no. 3, p. e2237, Jun. 2021. [CrossRef]
165. C. Damianou, M. Giannakou, G. Menikou, and L. Ioannou, “Magnetic resonance imaging-guided focused ultrasound robotic system with the subject placed in the prone position,” Digit Med, vol. 6, no. 1, pp. 24–31, Jan. 2020. [CrossRef]
166. A. Mustafa, T. Sasamura, and T. Morita, “Robust Speed Control of Ultrasonic Motors Based on Deep Reinforcement Learning of a Lyapunov Function,” IEEE Access, vol. 10, pp. 46895–46910, 2022. [CrossRef]
167. Y. J. Mon, “Vision Robot Path Control Based on Artificial Intelligence Image Classification and Sustainable Ultrasonic Signal Transformation Technology,” Sustainability 2022, Vol. 14, Page 5335, vol. 14, no. 9, p. 5335, Apr. 2022. [CrossRef]
168. J. Sun, D. Zhou, Y. Liu, J. Deng, and S. Zhang, “Development of a Minimally Invasive Surgical Robot Using Self-Helix Twisted Artificial Muscles,” IEEE Transactions on Industrial Electronics, vol. 71, no. 2, pp. 1779–1789, Feb. 2024. [CrossRef]
169. J. Li, H. Liu, J. Li, Y. Yang, and S. Wang, “Piezoelectric transducer design for an ultrasonic scalpel with enhanced dexterity for minimally invasive surgical robots,” vol. 234, no. 7, pp. 1271–1285, Dec. 2019. [CrossRef]
170. M. Pavone et al., “Ultrasound-guided robotic surgical procedures: a systematic review,” Surg Endosc, vol. 38, no. 5, pp. 2359–2370, May 2024. [CrossRef]
171. R. Y. Hutama, M. M. Khalil, and T. Mashimo, “A Millimeter-Scale Rolling Microrobot Driven by a Micro-Geared Ultrasonic Motor,” IEEE Robot Autom Lett, vol. 6, no. 4, pp. 8158–8164, Oct. 2021. [CrossRef]
172. J. Li, Z. Sun, H. Yan, and J. Chen, “Design of a Magnetically Anchored Laparoscope Using Miniature Ultrasonic Motors,” Micromachines 2022, Vol. 13, Page 855, vol. 13, no. 6, p. 855, May 2022. [CrossRef]
173. X. Li, T. Stritch, K. Manley, and M. Lucas, “Limits and Opportunities for Miniaturizing Ultrasonic Surgical Devices Based on a Langevin Transducer,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 68, no. 7, pp. 2543–2553, Jul. 2021. [CrossRef]
174. Q. Lu, Z. Sun, H. Yan, J. Zhang, J. Zhang, and J. Yang, “A novel laparoscopic surgical robot (LSR) based on double-leg ultrasonic motor (DUM),” J Intell Mater Syst Struct, vol. 34, no. 11, pp. 1276–1288, Jul. 2023. [CrossRef]
175. K. Fukushima et al., “A pneumatic rotary actuator for forceps tip rotation,” Sens Actuators A Phys, vol. 333, p. 113222, Jan. 2022. [CrossRef]
176. Y. Qin, Y. Shi, L. Wang, H. Wang, and J. Han, “Design, Modeling and Optimization of a Magnetic Resonance Conditional 3-RRR Spherical Parallel Robot for Neurosurgery,” IEEE Trans Med Robot Bionics, vol. 6, no. 2, pp. 556–566, May 2024. [CrossRef]
177. F. Ju et al., “A Flexible Surgical Robot with Hemispherical Magnet Array Steering and Embedded Piezoelectric Beacon for Ultrasonic Position Sensing,” Advanced Intelligent Systems, vol. 6, no. 3, Mar. 2024. [CrossRef]
178. S. Manjila, B. Rosa, K. Price, R. Manjila, M. Mencattelli, and P. E. Dupont, “Robotic Instruments Inside the MRI Bore: Key Concepts and Evolving Paradigms in Imaging-enhanced Cranial Neurosurgery,” World Neurosurg, vol. 176, pp. 127–139, Aug. 2023. [CrossRef]
179. B. Li, L. Yuan, C. Wang, and Y. Guo, “Structural design and analysis of pneumatic prostate seed implantation robot applied in magnetic resonance imaging environment,” The International Journal of Medical Robotics and Computer Assisted Surgery, vol. 18, no. 6, Dec. 2022. [CrossRef]
180. M. Li, “Design and stability analysis of a nonlinear controller for MRI-compatible pneumatic motors,” Proc Inst Mech Eng C J Mech Eng Sci, vol. 238, no. 1, pp. 3–17, Jan. 2024. [CrossRef]
181. A. L. Gunderman, M. Azizkhani, S. Sengupta, K. Cleary, and Y. Chen, “Modeling and Control of an MR-Safe Pneumatic Radial Inflow Motor and Encoder (PRIME),” IEEE/ASME Transactions on Mechatronics, pp. 1–12, 2023. [CrossRef]
182. X. T. Wankhede SP, “ The Roles of Piezoelectric Ultrasonic Motors in Industry 4.0 Era: Opportunities & Challenges.. ,” in Piezoelectric Actuators-Principles, Design, Experiments and Applications, Hu Huang and Jianping Li, Eds., IntechOpen, 2021, ch. 8.
183. X. Li et al., “A Design Method of Traveling Wave Rotary Ultrasonic Motors Driving Circuit under High Voltage Using Single-Sided Hertzian Contact Forced Oscillator Model,” Micromachines (Basel), vol. 14, no. 1, p. 64, Dec. 2022. [CrossRef]
184. C.-P. Lee, M.-C. Tsai, and Y.-K. Fuh, “Tiny Piezoelectric Multi-Layered Actuators with Application in a Compact Camera Module—Design, Fabrication, Assembling and Testing Issues,” Micromachines (Basel), vol. 13, no. 12, p. 2126, Dec. 2022. [CrossRef]
185. X. Xin, X. Gao, J. Wu, Z. Li, Z. Chu, and S. Dong, “A ring-shaped, linear piezoelectric ultrasonic motor operating in E01 mode,” Appl Phys Lett, vol. 116, no. 15, Apr. 2020. [CrossRef]
186. R. Niu, H. Zhu, and C. Zhao, “A four-legged linear ultrasonic motor: Design and experiments,” Review of Scientific Instruments, vol. 91, no. 7, Jul. 2020. [CrossRef]
187. X. Ma et al., “A novel rotary ultrasonic motor based on multiple Langevin transducers: design, simulation, and experimental investigation,” Smart Mater Struct, vol. 33, no. 5, p. 055001, May 2024. [CrossRef]
188. X. Ma, J. Liu, J. Deng, Q. Liu, and Y. Liu, “A Rotary Traveling Wave Ultrasonic Motor With Four Groups of Nested PZT Ceramics: Design and Performance Evaluation,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 67, no. 7, pp. 1462–1469, Jul. 2020. [CrossRef]
189. S. Guo, L. Wang, J. Jin, and Y. Yang, “A general structural design method, dynamics modeling and application study for built-in sandwich annular traveling wave piezoelectric transducers,” Mech Syst Signal Process, vol. 199, p. 110476, Sep. 2023. [CrossRef]
190. Z. Xue, K. T. Chau, W. Liu, and T. W. Ching, “Design, Analysis, and Implementation of Wireless Traveling-Wave Ultrasonic Motors,” IEEE Trans Power Electron, vol. 39, no. 4, pp. 4601–4611, Apr. 2024. [CrossRef]
191. Y. Zhang et al., “Laser-induced microtextured stators coupling with flexible rotors for low-voltage driving rotational piezoelectric motors,” Chemical Engineering Journal, vol. 467, p. 143361, Jul. 2023. [CrossRef]
192. L. Yang et al., “A novel traveling wave rotary ultrasonic motor with piezoelectric backup function,” J Intell Mater Syst Struct, vol. 34, no. 20, pp. 2414–2427, Dec. 2023. [CrossRef]
193. Z. Wen, X. Li, T. Cao, B. Wang, R. Liu, and D. Wu, “A Low-Voltage Cylindrical Traveling Wave Ultrasonic Motor Incorporating Multilayered Piezoelectric Ceramics,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 69, no. 6, pp. 2129–2136, Jun. 2022. [CrossRef]
194. Y. Liu, Y. Xiong, L. Hua, L. Yang, and W. Zeng, “Mechanical characteristic analysis of a separable stator fabricated by fine-blanking process with numerical and experimental methods,” The International Journal of Advanced Manufacturing Technology, vol. 112, no. 9–10, pp. 2435–2445, Feb. 2021. [CrossRef]
195. T.-B. Xu, “Review on PMN-PT Relaxor Piezoelectric Single Crystal materials for cryogenic actuators,” in AIAA SCITECH 2022 Forum, Reston, Virginia: American Institute of Aeronautics and Astronautics, Jan. 2022. [CrossRef]
196. T.-B. Xu, L. Tolliver, X. Jiang, and J. Su, “A single crystal lead magnesium niobate-lead titanate multilayer-stacked cryogenic flextensional actuator,” Appl Phys Lett, vol. 102, no. 4, Jan. 2013. [CrossRef]