Displacement Resolution Research Articles

Research on variable stiffness asymmetrical resonant linear piezoelectric actuator based on multi-modal drive

In this paper, a linear piezoelectric motor with variable stiffness and asymmetric resonance is proposed, which is driven by a single harmonic signal. Working in the resonant state improve the output performance of the motor. Motor control is relatively simple and can realize reverse movement under the driving of second-order single harmonic signal. At the same time, the new motor can obtain different operating speed and step distance by changing the clamping position in front and back to meet the requirements of different loads and different working conditions and has strong applicability. By experiment, the first-order optimal operating frequency of the motor prototype at three different stiffness adjustment positions is 88 Hz, 90 Hz and 92 Hz respectively. Under the excitation of 240 Vp–p first-order resonance signal, the corresponding output speed of the motor prototype is 16.116 mm s−1, 20.457 mm s−1 and 25.015 mm s−1 respectively, and the corresponding displacement resolution is 0.18 mm, 0.22 mm and 0.27 mm respectively. When the stiffness adjustment positions is 2 mm, the maximum load of the motor prototype reaches 450 g. The second-order optimal operating frequency at the stiffness adjustment positions 1 mm is 601 Hz. Under the excitation of a 240 Vp–p second-order resonant signal, the reverse output speed of the motor prototype is 13.126 mm s−1, and the corresponding displacement resolution is 0.02 mm.

Optical Interferometric MEMS Accelerometers

AbstractLaser interferometry is one of the most accurate measurement technologies whose displacement resolution can reach the femtometer (fm) level. With the development of Micro‐Electro‐Mechanical Systems(MEMS) technology, many excellent optical interferometric MEMS sensors have emerged, which play an essential role in intelligent manufacturing, aerospace, and many other fields. Among them, optical interferometric MEMS accelerometers develop rapidly due to their high sensitivity, low noise, and anti‐electromagnetic interference advantages. Lots of research in optical interferometric chip design, micro‐nano fabrication process, signal demodulation algorithm, and range extension technology are performed, and different types of MEMS accelerometers based on the optical interferometric principles are developed, which have been demonstrated and applied in the fields of disaster monitoring, equipment operation and maintenance, and resource exploration. This paper reviews the development status of optical interferometric MEMS accelerometers, mainly focusing on the critical problems and solutions that need to be solved in the development process of optical interferometric accelerometers, and finally introduces the typical application scenarios.

Design, simulation, and experimental investigation on a novel multi-drive pattern three-degree-of-freedom rotary piezoelectric motor

Three-degree-of-freedom (3-DOF) rotary piezoelectric motors often suffer from low positioning accuracy, complex excitation signals, and uneven preloading, limiting their application in precision drive systems. To address these issues, this study proposes a novel multi-drive pattern 3-DOF rotary piezoelectric motor, comprising a sandwich-type hollow cylindrical stator, a spherical rotor, and a pre-tightening structure. The proposed motor can operate in both inertial and traveling wave drive patterns. In the inertial drive pattern, the first-order and the third-order bending vibration modes of the stator are simultaneously excited by a sawtooth wave signal, generating a saw-tooth displacement on its driving feet to rotate the rotor around the x or y-axis. In the traveling wave drive pattern, two mutually orthogonal first-order bending vibration modes of the stator are simultaneously stimulated by two sinusoidal signals, generating a traveling wave on its driving feet to rotate the rotor around the z-axis. Initially, finite element analysis is used to simulate the operating principle of the stator and determine its geometric dimensions. Subsequently, a prototype of the sandwich-type hollow cylindrical stator is fabricated, and its vibration characteristics are tested to confirm the validation of the proposed operating principle and the correctness of the finite element simulation. Finally, a prototype of the proposed 3-DOF rotary piezoelectric motor is assembled, and its mechanical output characteristics are experimentally evaluated. Experimental results indicate that when the excitation voltage is 200 Vpp, the no-load rotary velocities of the motor prototype in three rotation directions are 79 r min−1, 76 r min−1, and 101 r min−1, respectively, start/stop response times are 10 ms/8.6 ms, 13.4 ms/6.2 ms, and 15.5 ms/7.7 ms, respectively, and the angular displacement resolutions are 7.4 μrad, 8 μrad, and 11.4 μrad, respectively. The proposed motor exhibits high mechanical integration, 3-DOF rotation, few excitation signals, adjustable pre-tightening force, and high positioning accuracy advantages, holding the potential applications in fields such as robotic technology and space pointing mechanisms.

Modeling and controlling a rotary piezo actuator

In this study, a novel piezo rotary stick–slip actuator was designed and investigated. This approach employs two piezo actuators to deform a flexible mechanism in order to generate a variable stick-and-slip force that drives the rotor. The compliant mechanism is composed of the bridge amplifiers and lever mechanism. They are arranged in sequence to amplify the piezo actuator's displacement. Hence, the operating range of the actuator, which includes rotation speed and resolution, can be increased. To optimize the fundamental dimensions of the actuator, the method of finite elements was investigated. The mechanical structure is detailed, the operating principle is elucidated, and a dynamic model is developed. From experimental data, the dynamic model of the structure is identified. The actuator achieves an angular displacement resolution of 0.028 degree at an applied voltage of 45 V and an operating frequency range up to 140 Hz, allowing it to be employed in applications requiring high precision positioning. Besides, the closed-loop control scheme is proposed to control the actuator in both directions. The simulation and experimental results have demonstrated that the position of the stick–slip actuator can be effectively controlled through this proposed controller. This is expected to increase the potential application of the stick–slip actuator in industrial practice.

An integrated modeling method for piezo-actuated compliant mechanisms

Piezo-actuated compliant mechanisms are widely employed in precision positioning and micro/nano manipulation due to their advantages of compact structure, high displacement resolution, and fast response. However, it is still challenging to accurately analyze the designed mechanisms due to the complicated coupled electromechanical behaviors of piezoelectric actuators and compliant mechanisms, which prevents further performance improvement by configuration design and optimization. A novel modeling method is developed in this paper for the kinetostatic and dynamic analyses of piezoelectric actuators and their comprised systems with compliant mechanisms. The electromechanical model of piezoelectric actuators is derived from linear piezoelectric vibration theory and further simplified as a practical equivalent model in the form of dynamic stiffness matrices. With the proposed actuator model, an integrated modeling method based on the dynamic stiffness matrix method is proposed for analyses of the piezo-actuated compliant mechanism with complicated configurations of piezoelectric actuators and flexible structures. Two case studies, including a piezoelectric actuator and a fast scanning stage, are analyzed to verify the effectiveness of the proposed approach. Both finite element analysis and experimental results validate that the presented modeling method can be used to resolve the kinetostatics and dynamics of complex piezo-actuated compliant mechanisms efficiently and effectively.

Touch, press and stroke: a soft capacitive sensor skin

Soft sensors that can discriminate shear and normal force could help provide machines the fine control desirable for safe and effective physical interactions with people. A capacitive sensor is made for this purpose, composed of patterned elastomer and containing both fixed and sliding pillars that allow the sensor to deform and buckle, much like skin itself. The sensor differentiates between simultaneously applied normal force and shear using summation and differences of signals from four deformable capacitors. Cross talk from shear to normal force is less than 2.5%, and between shear axes is less than 10%. Normal and shear stress sensitivity is 0.49 kPa and 0.31 kPa respectively, with a minimum displacement resolution of 40 μm. In addition, finger proximity is detectable at a range of up to 15 mm. The operation is demonstrated on a simple gripper holding a cup. The combination of features and the straightforward fabrication method make this sensor a candidate for implementation as a sensing skin for humanoid robotics applications.

Integrated heterodyne laser Doppler vibrometer based on stress-optic frequency shift in silicon nitride

We demonstrate a compact heterodyne Laser Doppler Vibrometer (LDV) based on the realization of optical frequency shift in the silicon nitride photonic integration platform (TriPleX). We theoretically study, and experimentally evaluate two different photonic integrated optical frequency shifters (OFSs), utilizing serrodyne and single-sideband (SSB) modulation. Both OFSs employ stress-optic modulators (SOMs) based on the non-resonant piezoelectrical actuation of lead zirconate titanate (PZT) thin-films, deposited on top of the silicon nitride waveguides with a wafer-scale process. To improve the modulation bandwidth of the SOMs we investigate a novel configuration of the electrodes used for the actuation, where both electrodes are placed on top of the PZT layer. Using this top-top electrode configuration we report frequency shift of 100 kHz and 2.5 MHz, and suppression ratio of the unwanted sidebands of 22.1 dB and 39 dB, using the serrodyne and the SSB OFS, respectively. The best performing SOM structure induces 0.25π peak-to-peak sinusoidal phase-shift with 156 mW power dissipation at 2.5 MHz. We use the SSB-OFS in our compact LDV system to demonstrate vibration measurements in the kHz regime. The system comprises a dual-polarization coherent detector built in the PolyBoard platform, utilizing hybrid integration of InP photodiodes (PDs). High quality LDV performance with measurement of vibration frequencies up to several hundreds of kHz and displacement resolution of 10 pm are supported with our system.

Microwave Absolute Distance Measurement Method with Ten-Micron-Level Accuracy and Meter-Level Range Based on Frequency Domain Interferometry.

A microwave absolute distance measurement method with ten-micron-level accuracy and meter-level range based on frequency domain interferometry is proposed and experimentally demonstrated for the first time. Theoretical analysis indicates that an interference phenomenon occurs instantaneously in the frequency domain when combining two homologous broad-spectrum microwave beams with different paths, and the absolute value of the distance difference between the two paths is only inversely proportional to the period of frequency domain interference fringes. The proof-of-principle experiments were performed to prove that the proposed method can achieve absolute distance measurement in the X-band with standard deviations of 15 μm, 17 μm, and 26 μm and within ranges of 1.69 m, 2.69 m, and 3.75 m. Additionally, a displacement resolution of 100 microns was realized. The multi-target recognition performance was also verified in principle. Furthermore, at the expense of a slight decrease in ranging accuracy, a fast distance measurement with the single measurement time of 20 μs was achieved by using a digitizer combined with a Fourier transform analyzer. Compared with the current microwave precision ranging technologies, the proposed method not only has the advantages of high precision, large range, and rapid measurement capability, but the required components are also easily obtainable commercial devices. The proposed method also has better complex engineering applicability, because the ten-micron-level ranging accuracy is achievable only by using a simple Fourier transform without any phase estimation algorithm, which greatly reduces the requirement for signal-to-noise ratio.

Ultra-Low Frequency High-Precision Displacement Measurement Based on Dual-Polarization Differential Fiber Heterodyne Interferometer

Picometer displacement measurement in the ultra-low frequency band below 1 Hz is highly demanded in the fields of geophysics and space exploration for the applications of hydrophones, geophones, drag-free space controllers, and so on. In this work, high-precision displacement detection in ultra-low frequency is achieved by proposing and demonstrating a dual-polarization differential fiber heterodyne interferometer. By injecting two orthogonal polarized lights into the dual-polarization differential fiber heterodyne interferometer, two optical interferences can be co-existed in a monolithic interferometer with a fully identical optical fiber path. Through the difference of the two optical interferometric phases, the light source noise and the fiber link noise can be well suppressed. Meanwhile, a pull-push type displacement sensing module is designed to double the displacement sensitivity as well as suppress the common-mode noise derived from the environmental fluctuation. Through the calibration experiment, the displacement sensitivity is obtained as 0.01634(±0.00022) rad/nm, which is consistent with the theoretical calculation. The displacement resolutions of 1.8 pm/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 0.1 Hz and 0.25 pm/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 1 Hz are achieved in the experiment, which is the superior displacement measurement level for this frequency band in the existing optic displacement sensors to our knowledge. The proposed fiber optic displacement sensor with ultra-high resolution in low frequency can be of great use in scientific research and precision engineering.

Monitoring the Opening of Rapid Palatal Expansion (RPE) in a 3D-Printed Skull Model Using Fiber Optic F-P Sensors.

We present a novel method for the online measurement of multi-point opening distances of midpalatal sutures during a rapid palatal expansion (RPE) using fiber optic Fabry-Perot (F-P) sensors. The sensor consists of an optical fiber with a cut flat end face and an optical reflector, which are implanted into the palatal base structure of an expander and is capable of measuring the precise distance between two optical reflective surfaces. As a demonstration, a 3D-printed skull model containing the maxilla and zygomaticomaxillary complex (ZMC) was produced and a miniscrew-assisted rapid palatal expander (MARPE) with two guide rods was used to generate the midpalatal suture expansion. The reflected spectrums of the sensors were used to dynamically extract cavity length information for full process monitoring of expansion. The dynamic opening of the midpalatal suture during the gradual activation of the expander was measured, and a displacement resolution of 2.5 μm was demonstrated. The angle of expansion was derived and the results suggested that the midpalatal suture was opened with a slight V-type expansion of 0.03 rad at the first loading and subsequently expanded in parallel. This finding might be useful for understanding the mechanical mechanisms that lead to different types of expansion. The use of a fiber optic sensor for mounting the rapid palatal expander facilitates biomechanical studies and experimental and clinical evaluation of the effects of RPE.

Design and evaluation of a stick-slip piezoelectric actuator with flexure hinge mechanism inspired by the earthworm.

In this work, a new bionic piezoelectric actuator inspired by the earthworm is proposed, fabricated, and tested. The operating principle of the actuator imitates the crawling motion of the earthworm. The piezoelectric stack is embedded in the stator with a flexure hinge mechanism. One side of the stator is inspired by the earthworm body. Then the elongation of the piezoelectric stack is transmitted to the driving tip to produce oblique displacement under such a stator. The vertical and horizontal components are used to press and drive the slider, respectively. The principle of the proposed actuator is described in detail. The static deformation is investigated by the FEM method. A dynamic model of the actuator is developed to further reveal the motion characteristics of the slider via theoretical analysis. Finally, the output characteristics of the proposed BPA are tested. The experimental results show that the actuator achieves a maximum output speed of 12.72 mm/s at a voltage of 100V and a frequency of 710Hz. The maximum output force is 3 N under a locking force of 2 N. Besides, the displacement resolution is tested at 87nm at a frequency of 710Hz, which indicates that the developed actuator can be applied in the field of precision actuation.

A Resonant-Type Thin Plate Piezoelectric Actuator Inspired by Koala's Locomotion

Imitating the behavioral traits or structures of biological organisms can provide new ideas and operating principles for designing micro actuators. Inspired by the locomotion of koalas, a lightweight self-locomotion piezoelectric actuator (SLPA) is developed. Based on the hybrid of the longitudinal and bending vibration modes, the proposed SLPA is able to obtain linear locomotion. The configuration of the SLPA is designed based on a thin metal plate with miniature size of 19.5×19.5×1.1mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The operating principle is verified through the finite element analysis (FEA) simulation. The experimental results show that the prototype achieves maximum speed of 61.68 mm/s and slope angle of 20° when the excitation frequency and voltage are 19.75 kHz and 50 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-p</sub> , which demonstrates the validity of the proposed SLPA climbing on slopes and the effectiveness of the proposed operating principle. Furthermore, the step displacement resolution of 2.2 μm is obtained by the proposed SLPA under the resonant working state. Finally, a simple optical focusing system is established to verify the feasibility of potential application of micro piezoelectric actuator.

A 3-DOF Piezoelectric Micromanipulator Based on Symmetric and Antisymmetric Bending of a Cross-Shaped Beam

A three degrees of freedom (3-DOF) piezoelectric micromanipulator (PEMMR) based on symmetric and antisymmetric bending of a cross-shaped beam is proposed in this work. Different from typical scheme of combining piezoelectric stack actuator (PSA) and flexible mechanism in previous micromanipulation devices, this work only utilizes eight piezoelectric ceramic plates to construct actuation units and further to realize 3-DOF motions; it overcomes the disadvantages of complex structure, high capacitance and relatively high cost of traditional micromanipulation devices constructed on PSAs. The structure design and motion principle are presented, and the finite element analysis (FEA) method is used to simulate output motions and analyze output characteristics; then a prototype is fabricated and an experimental system is established to implement experiments. The experimental results show that the prototype achieves operating range of 99.28 μm×99.09 μm×24.19 μm, displacement resolution of 15.74 nm, output force of 57.76 mN and force resolution of 0.067 mN, which successfully verifies the design and analysis. The static capacitance of the PEMMR is only about 13.34 nF per axis. Furthermore, a preliminary application experiment is implemented, in which the non-contact posture adjustment of microsphere with diameter of 500 μm in liquid is successfully achieved by the developed PEMMR.

Unified digital image correlation under meshfree framework

AbstractThe implementation of digital image correlation (DIC) involves several different problems, such as image prefiltering, image intensity gradient calculation, image intensity interpolation at subpixel positions, shape function construction and strain calculation. This paper offers a unified insight into the nature of several key problems in DIC technique. We treat all the problems involved in the former mentioned key steps as fundamentally the same problem, that is, reconstructing an analytical description from a discrete and noisy sampling of a signal, such as discrete image intensity and displacement at some scattered nodes. From the reconstructed analytical description, the gradient and physical value at subpixel or integral pixel position can be analytically calculated without extra error. Here, we solve all these problems using the same mathematical tool, the meshfree method, leading to a unified DIC (U‐DIC) method. This method introduces errors solely during the steps involving the determination of the continuous description. However, it effectively avoids errors in the remaining steps. It holds the best balance between spatial resolution and measurement resolution for both displacement and strain measurements compared to 28 state‐of‐the‐art DIC algorithms based on the benchmark tests on DIC Challenge 2.0. It also holds all the unique advantages of the advanced meshfree DIC (MF‐DIC) compared to conventional local DIC and global DIC. The novel concept and excellent balance between spatial resolution and measurement resolution make U‐DIC an attractive replacement for conventional DIC methods. Additionally, the consistency of the implementation procedures in U‐DIC can simplify the parameter selection in DIC, which is of potential for the standardization of DIC technique.

A New Vision Measurement Technique with Large Field of View and High Resolution.

The three-dimensional (3D) displacement resolution of conventional visual measurement systems can only reach tens of microns in cases involving long measuring distances (2.5 m) and large fields of view (1.5 m × 1.5 m). Therefore, a stereo vision measurement technology based on confocal scanning is proposed herein. This technology combines macroscopic visual measurement technology with confocal microscopic measurement technology to achieve a long measuring distance, a large field of view, and micron-level measuring resolution. First, we analyzed the factors affecting the 3D resolution of the visual system and developed a 3D resolution model of the visual system. Subsequently, we fabricated a prototype based on the resolution model and the proposed stereo vision measurement technology. The 3D displacement resolution measurement results in the full field of view show that the displacement resolutions of the developed equipment in the x-, y-, and z-directions can reach 2.5, 2.5, and 6 μm, respectively.

Iraqi Kurdistan People's Displacement and UN Resolution 688 between the US and Iran

Iraqi Kurdistan People's Displacement and UN Resolution 688 between the US and Iran

Acoustic Michelson interferometer based on a phononic crystal

A practical and highly sensitive acoustic Michelson interferometer with a small form factor is introduced. It involves two different types of phononic crystals composed of steel rods in water acting as a medium for self-collimated waves and mirrors for the reference and sample beams, as well as a beam splitter formed by modified scatterers arranged diagonally. Finite-element method simulations are employed to demonstrate its operation around 200 kHz. Equifrequency contour analysis reveals self-collimation of ultrasonic waves between 190 and 210 kHz. Introduction of the beam splitter and mirror phononic crystals is not detrimental to self-collimation where outgoing waves from the two interferometer arms interfere such that the output intensity varies in a cosine squared manner. Consequently, maximum sensitivity is achieved when the movable mirror displacement is either zero or half of the interferometer phononic crystal period. On small intervals in these ranges, micrometer-scale displacement resolution is achievable, as the output intensity drops by 0.2% per micrometer. Thus, displacements smaller than a percent of the wavelength are easily resolvable. Nanoscale resolution can be obtained with a scaled down interferometer design. Moreover, application to liquid concentration sensing by considering ethanol–water binary mixture is demonstrated. A percent increase in weight fraction of ethanol up to 10% in the mixture leads to an intensity drop as high as 2%. Thus, significantly higher sensitivities compared to sensing schemes based on resonance frequency shift are attainable. The proposed approach can be adapted for surface acoustic waves in strain measurement or biosensing.

Parametrically Driven Inertial Sensing in Chip‐Scale Optomechanical Cavities at the Thermodynamical Limits with Extended Dynamic Range

AbstractRecent scientific and technological advances have enabled the detection of gravitational waves, autonomous driving, and the proposal of a communications network on the Moon (Lunar Internet or LunaNet). These efforts are based on the measurement of minute displacements and their corresponding force transduction, which enables acceleration, velocity, and position determination for navigation. State‐of‐the‐art accelerometers use capacitive or piezoresistive techniques and micro‐electromechanical systems (MEMS) via integrated circuit (IC) technologies to drive transducers and convert their output for electric readout. In recent years, laser optomechanical transduction and readout have enabled highly sensitive detection of motional displacement. Here the theoretical framework is further examined for the novel mechanical frequency readout technique of optomechanical transduction when the sensor is driven into oscillation mode. Theoretical and physical agreements are demonstrated, and the most relevant performance parameters are characterized by a device with a 1.5 mg Hz−1 acceleration sensitivity, a 2.5 fm Hz−1/2 displacement resolution corresponding to a 17.02 µg Hz−1/2 force‐equivalent acceleration, and a 5.91 Hz nW−1 power sensitivity, at the thermodynamical limits. In addition, a novel technique is presented for dynamic range extension while maintaining the precision sensing sensitivity. This inertial accelerometer is integrated on‐chip and enabled for packaging, with a laser‐detuning‐enabled approach.

Stability and Resolution of a Conventional Displacement Measuring Heterodyne Interferometer Using a Single Phase-Locked Loop

Stability and Resolution of a Conventional Displacement Measuring Heterodyne Interferometer Using a Single Phase-Locked Loop

Development of a Novel Piezoelectric Actuator Based on Stick-Slip Principle by Using Asymmetric Constraint.

In this work, a novel piezoelectric actuator based on the stick-slip principle is proposed. The actuator is constrained by an asymmetric constraint approach; the driving foot produces lateral and longitudinal coupling displacements when the piezo stack is extended. The lateral displacement is used to drive the slider and the longitudinal displacement is used to compress the slider. The stator part of the proposed actuator is illustrated and designed by simulation. The operating principle of the proposed actuator is described in detail. The feasibility of the proposed actuator is verified by theoretical analysis and finite element simulation. A prototype is fabricated and some experiments are carried out to study the proposed actuator's performance. The experimental results show that the maximum output speed of the actuator is 3680 μm/s when the locking force is 1 N under the voltage of 100 V and frequency of 780 Hz. The maximum output force is 3.1 N when the locking force is 3 N. The displacement resolution of the prototype is measured as 60 nm under the voltage of 15.8 V, frequency of 780 Hz and locking force of 1 N.