Linear Displacement Measurement Research Articles

The Experimental-Numerical Study of Aviation Autocannon Mechanisms

The objective of this research was to investigate the displacement, velocity, and acceleration of selected components and mechanisms of the GSh-23 aviation autocannon (specifically, the bolt and the connecting lever of the feeding mechanism). During the research implementation, measurements of linear and angular displacements of the chosen mechanisms of the GSh-23 aviation autocannon were carried out on a purpose-built research platform. This platform enables the movement of the weapon mechanisms without the use of ammunition, utilising compressed air instead. Parts and mechanisms were carefully selected for the study, allowing their motion to be recorded by a high-speed camera without the need for disassembling crucial weapon components. The results of measuring kinematic quantities using the high-speed camera and TEMA software were employed to validate a numerical model of the weapon mechanisms in MSC ADAMS software. The displacement and velocity characteristics obtained from the simulation were reasonably consistent with the experimentally obtained characteristics.

Research on precision linear displacement measurement method based on closed loop phase-shift control of single alternating light field

Abstract A high-precision linear displacement measurement method based on the digital phase shift of a single light source is proposed. In this method, the light intensity of a four-channel sinusoidal transmission surface with a 90° difference in the spatial phase is modulated by a single channel alternating light, and four-channel alternating light intensity signal with the same time phase can be obtained. Two channels of standing wave signals with a time difference of 90° are obtained through micro-control digital phase shift processing. After differential amplification, an electric travelling wave signal containing position information of measurement object is synthesized by these two standing wave signals. By measuring the phase difference between the travelling wave and the reference signal, the high precision linear displacement can be measured. The principle of displacement measurement based on the modulation of a single-alternating light field and the principle of digital phase-shift of micro-control are introduced in detail. The feasibility of the method is verified through experiments. Finally, the sensor is optimized by analyzing the causes of error, and the measurement accuracy of ±0.2 μm is achieved within the 100 mm range with a 0.6 mm grating period.

Biomechanics of biting in loggerhead shrikes: jaw-closing force, velocity and an argument for power.

Differences in the physical and behavioral attributes of prey are likely to impose disparate demands of force and speed on the jaws of a predator. Because of biomechanical trade-offs between force and speed, this presents an interesting conundrum for predators of diverse prey types. Loggerhead shrikes (Lanius ludovicianus) are medium-sized (∼50 g) passeriform birds that dispatch and feed on a variety of arthropod and vertebrate prey, primarily using their beaks. We used high-speed video of shrikes biting a force transducer in lateral view to obtain corresponding measurements of bite force, upper and lower bill linear and angular displacements, and velocities. Our results show that upper bill depression (about the craniofacial hinge) is more highly correlated with bite force, whereas lower bill elevation is more highly correlated with jaw-closing velocity. These results suggest that the upper and lower jaws might play different roles for generating force and speed (respectively) in these and perhaps other birds as well. We hypothesize that a division of labor between the jaws may allow shrikes to capitalize on elements of force and speed without compromising performance. As expected on theoretical grounds, bite force trades-off against jaw-closing velocity during the act of biting, although peak bite force and jaw-closing velocity across individual shrikes show no clear signs of a force-velocity trade-off. As a result, shrikes appear to bite with jaw-closing velocities and forces that maximize biting power, which may be selectively advantageous for predators of diverse prey that require both jaw-closing force and speed.

Design and Parameter Optimization of Zero Position Code Considering Diffraction Based on Deep Learning Generative Adversarial Networks

Absolute measurement has consistently been the primary focus in the development of precision linear and angular displacement measurements. The scheme design of binary zero position codes is an important factor for absolute measurement. Designing and optimizing high-bit zero position codes with over 100 bits face considerable challenges. Simultaneously, the working parameters of zero position codes [unit code width (b), distance (d), and yaw angle (α)] remarkably affect their post-installation performance, particularly in absolute positioning and limit code application in multi-degree-of-freedom measurement schemes. This study addresses these challenges by proposing a design method for zero position codes that considers diffraction based on generative adversarial networks and aims to explore a design with increased efficiency and accuracy as well as optimization for high-bit zero position codes. Additionally, the tolerance range of zero positioning performance for each working parameter is examined. By leveraging the adversarial network structure, this study generates the optimization of a 150-bit code and processes the tests of the zero position code by using simulation results. The following working parameter ranges for code design are recommended on the basis of theoretical and experimental results: b greater than 10 μm, d and α within 1000 μm and 3490 μrad, and avoidance of intervals with sharp changes in the full width at half maximum. The proposed code design and parameter optimization lay a solid foundation for research and engineering applications in absolute measurement field and have considerable potential for generalization and wide applicability.

Combined Displacement and Angle Sensor with Ultra-High Compactness Based on Self-Imaging Effect of Optical Microgratings

In this paper, an ultracompact combined sensor for displacement and angle-synchronous measurement is proposed based on the self-imaging effect of optical microgratings. Using a two-grating structure, linear and angular displacement can be measured by detecting the change of phase and amplitude of the optical transmission, respectively, within one single structure in the meantime. The optically transmitted properties of the two-grating structure are investigated in both theory and simulation. Simulated results indicate that optical transmission changes in a sinusoidal relationship to the input linear displacement. Meanwhile, the amplitude of the curve decreases with an input pitch angle, indicating the ability for synchronous measurement within one single compact structure. The synchronous measurement of the linear displacement and the angle is also demonstrated experimentally. The results show a resolution down to 4 nm for linear displacement measurement and a maximum sensitivity of 0.26 mV/arcsec within a range of ±1° for angle measurement. Benefiting from a simple common-path structure without using optical components, including reflectors and polarizers, the sensor shows ultra-high compactness for multiple-degrees-of-freedom measuring, indicating the great potential for this sensor in fields such as integrated mechanical positioning and semiconductor fabrication.

Estimation of the sensitivity of optical measurements using a holographic interferometer

Various interferometers used for high-precision spectroscopic measurements are considered, and the choice of a holographic interferometer based on the spatial-spectral method of holographic interferometry is justified, with the help of which the movements of the phase center of a coherent light flux in a wide dynamic range are measured in real time and measurement information is recorded digitally. On the basis of mathematical relations proposed by the authors in previous publications and based on the results of experimental studies, the sensitivity of a holographic interferometer to spatial displacements of phase centers (focus points) of light streams – point light sources forming a holographic interferogram is numerically estimated. The dependence of the level of the normalized intensity of the luminous flux in the central region of the holographic interferogram on the movement of the actual point light source along the normal to the plane of the Fourier hologram is established. Based on the results of mathematical modeling, it is shown that the sensitivity of the holographic interferometer to the movements of a real point light source along the normal to the plane of the Fourier hologram depends on the parameters of the optical scheme of the holographic interferometer when exposing the hologram and during measurements. At the same time, the sensitivity of the holographic interferometer to the indicated displacements of a real point light source can only be evaluated experimentally. It is proposed to increase the sensitivity of the holographic interferometer by using a thin collecting lens in its optical scheme. For the first time, a mathematical relation was obtained and investigated for the gain coefficient of the light flux phase with a spherical wavefront, which makes it possible to numerically estimate the increase in sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry with known parameters of a thin collecting lens in an optical scheme. It is shown that the sensitivity of a holographic interferometer to the movements of an imaginary point light source along the normal to the plane of the Fourier hologram is 2.86 times greater than its sensitivity to the same movements of a real point light source. It is established that the sensitivity of a holographic interferometer with a volumetric Fourier hologram and a thin collecting lens in its design can be increased by at least an order of magnitude compared to the sensitivity of known optical interferometers. The results of assessing the sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry to the movements of point sources of real and imaginary light fluxes, as well as the obtained ratio for the gain of the light flux phase gain by a thin collecting lens will be useful for high-precision measurements of linear and angular displacements of objects, as well as for the construction of photonic device designs. Based on the results of the study, an experimental sample of an acousto-electric converter was developed and manufactured on the basis of a holographic interferometer, which has high sensitivity in wide dynamic and frequency ranges and is intended for use in acoustic location of unmanned aerial vehicles.

A Dual-Beam Differential Method Based on Feedback Interferometry for Noncontact Measurement of Linear and Angular Displacement

A dual-beam differential method for noncontact measurement of linear and angular displacement is reported in this paper. Compared to other optical sensors, the system based on the frequency-modulated feedback interferometry has higher sensitivity for non-cooperative targets and a wider range with respect to the angle measurement. Performance of the proposed method is evaluated via testing a prototype system. The experimental results show that the prototype has a stability of 35 nm and 0.15“ over 1 hour with a resolution of 1 nm and 0.02” respectively. The linearity is 5.58×10^-6 in the range of 100 mm and 1.34×10^-4 in the range of 360°. The experiments for PZT deformation measurement and rotary motor monitor indicate that the proposed method possesses considerable potential for high-precision metrological applications, such as lathe calibration and motor control.

Optical Grating Diffraction and Optical Beat Frequency Principle-Based Ultrahigh Resolution Displacement Measurement System

This research presents a novel displacement measurement system that combines optical grating diffraction, the optical Doppler principle, and the optical beat frequency principle. The system utilizes a double-frequency laser device, an interferometer, a measuring grating, and an electrical signal processing unit. By dividing the laser into reference light and measuring light and analyzing the beat frequency signal generated by the interaction of the measuring light and the reference light, the system achieves precise linear displacement measurements in two directions. The system offers sub-nanometer-grade or even higher resolution and accuracy, simultaneous measurement of horizontal large-stroke displacement and horizontal displacement, and exhibits advantages such as environmental insensitivity, high measurement accuracy, compact size, and lightweight. The proposed system finds potential applications in ultraprecise workpiece platform position measurement systems, contributing to the overall performance improvement of lithography machines.

A novel magnetic circuit and structure for magnetic levitation ruler

The single axis linear displacement measurement system of CMM is composed of grating ruler, servo motor and linear motion mechanism. Although the measuring accuracy of grating ruler is high, the accuracy of servo motor and linear motion mechanism is low. Therefore, the complex structure limits the measurement accuracy of the linear displacement measurement system. This paper introduces a novel linear displacement measurement system named magnetic levitation ruler. According to the working principle of grating ruler and the characteristics of magnetic levitation technology, the magnetic circuit design and structural design of magnetic levitation ruler are completed in this paper. The mover core of the magnetic levitation ruler is in the stable working magnetic field provided by the stator yoke. The horizontal control coil wound on the mover core can obtain more stable ampere force to improve the control accuracy of the mover core displacement. Therefore, the mover core can be moved in step mode, and the length of each step is fixed. Each step is the minimum scale of the magnetic levitation ruler. Therefore, the mover core can implement displacement measurement while moving in a linear motion. This paper analyzes the working principle of levitation, horizontal motion, and displacement measurement of magnetic levitation ruler, and determines the structural materials and parameters of magnetic levitation ruler with the help of finite element analysis software. The simulation results show that the levitation force of the magnetic levitation ruler is proportional to the current passing through the levitation coils, and the thrust of the horizontal control coil is less disturbed by the magnetic field. Compared with the linear displacement measurement system with rotational servo motor or permanent magnet synchronous linear motor as the core, the magnetic levitation ruler has stable magnetic field, strong controllability, high integration, and is easier to achieve high-precision control.

Confocal probe based on the second harmonic generation for measurement of linear and angular displacements.

A measurement method based on a confocal probe on the second harmonic generation that can measure linear and angular displacements in the focusing point is proposed. In the proposed method, a pinhole or an optical fiber placed in front of the detector in conventional confocal probes is replaced by a nonlinear optical crystal, which is utilized as a medium generating second harmonic wave whose light intensity changes by the linear and angular displacements of a target under measurement. The feasibility of the proposed method is verified by theoretical calculations and experiments with the newly designed optical setup. Experimental results have demonstrated that the developed confocal probe has a resolution of 20 nm and 5 arc-seconds for measurement of linear and angular displacements, respectively.

Method of determining thermal diffusivity on the basis of measurements of linear displacements

An innovative, relatively simple method of non-stationary determination of thermal diffusivity with the use of linear displacement measurements is proposed. This method is dedicated mostly to materials with an extensive internal structure (porous building materials, i.e. concrete, ceramics, wood, etc.), where the thermal parameters should take into account the heterogeneity of the structure (relatively large samples are required). The main difference between the proposed method and the methods known from the literature is that in order to determine the thermal diffusivity, it is only necessary to measure changes in the length of the sample during cooling or heating. This is an alternative to methods based on direct or indirect measurement of the surface temperature of the sample. The proposed method was tested on samples made of plexiglass. The obtained results were compared with the reference results obtained from measurements with the use of commercial measuring equipment (Netzsch HFM 446), which allows to determine the thermal conductivity coefficient and specific heat with high accuracy. Good agreement of the obtained results was obtained. The uncertainty analysis of the proposed method showed that it is at the level of 3%, which is sufficient in the case of building materials.

A new approach to linear displacement measurements based on Hall effect sensors

Since displacement is a vital variable to be considered in many industrial applications, displacement sensing devices have been extensively studied both theoretically and experimentally. There have been also many studies on Hall effect-based displacement measurement, but for many systems linearity still remains a problem. This paper discusses different approaches to calculate the magnetic field due to a cylindrical permanent magnet and proposes a new setup geometry with 2-Hall effect sensors and a permanent magnet between them to overcome the linearity problems. Furthermore, theoretical and experimental studies of the discussed displacement sensor were presented by focusing on the linear range and the sensitivity of the system. These parameters were investigated for different sensor-to-sensor distances. As this value decreases, it is found that sensitivity increases, and yet the linear range decreases as well. For the 25.5 mm sensor-to-sensor distance linear range was determined as around 3 mm, and the sensitivity and maximum error in displacement measurement was calculated as 351 mV/mm and 0.029 mm, respectively. We believe that by using the results of our study, it is possible to develop Hall sensor-based approaches that can be used for sensitive displacement measurements in a certain range and can meet the needs of researchers and industry in many applications.

Error Compensation for Low-Density Circular Gratings Based on Linear Image-Type Angular Displacement Measurements

The image-type angular displacement measurement method based on linear image recognition has garnered attention because of its higher frequency response, strong fault tolerance, and high robustness. In the small-size image angular displacement measuring device, due to the limited pixel size, the circular grating cannot place more lines when realizing single-channel absolute coding recognition on a small diameter grating disk. This leads to larger errors in angular displacement measurement when the line density of the grating disk is low. To improve the measurement accuracy of small-scale displacement, the present work aimed to reduce this error by studying the error compensation method involving low-density grating disks. First, the mechanism of linear image-type angular displacement measurements is described, and a measurement algorithm based on linear scan images is proposed. Second, the measurement error model for low-density grating disks is established according to the proposed measurement algorithm. Third, a simplified error compensation algorithm based on a harmonic model is developed. Finally, simulations and experiments are performed to verify the performance of the proposed algorithm. Simulation results show that the developed harmonic compensation algorithm can effectively reduce the error caused by the low-density circular grating. When the proposed error compensation algorithm is applied to a grating disk with a 62 mm diameter and 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^N</i> lines, the measurement accuracy is improved from 8.14” to 4.78”. The proposed error compensation algorithm can significantly improve the accuracy of linear image-type angular displacement measurements involving low-density grating disks, and the results presented herein laid a foundation for improving the accuracy and engineering applicability of angular displacement measurement technology.

Linear Displacement and Straightness Measurement by Fabry-Perot Interferometer Integrated with an Optoelectronic Module

This research develops a three degrees of freedom (DOF) measurement system by integrating Fabry-Perot interferometer and photoelectronic inspection module to determine linear displacement, horizontal and vertical straightness geometric error parameters simultaneously. The interferometer and the photoelectronic inspection module in a three DOF measurement system share the same light source, and the two structures are used to measure linear displacement and straightness errors. The experimental results are utilized to calculate the relevant error parameters according to ISO standards and numerical analysis. They show that after the machine error compensation, the positioning deviation of the system is reduced from 55 μm to 19 μm, corresponding to the reduction of 65%. The accuracy is promoted from 65 μm to 31 μm, about the improvement of 52%. The horizontal and vertical straightness errors of the machine are 4.30 μm and 5.71 μm respectively.

A New Image Grating Sensor for Linear Displacement Measurement and Its Error Analysis.

To improve the accuracy of the current vision-based linear displacement measurement in a large range, a new type of linear displacement sensing system, namely, image grating, is proposed in this paper. The proposed system included a patterned glass plate attached to the moving object and an ultra-low distortion lens for high-accuracy image matching. A DFT local up-sampling phase correlation method was adopted to obtain the sub-pixel translation of the patterns onto the target plate. Multiple sets of stripe patterns with different designs were located on the glass plate to expand the measurement range, based on the principle of phase correlation. In order to improve the measurement accuracy, the main errors of the image grating system were analyzed, and the nonlinear error compensation was completed based on the dynamic calibration of the pixel equivalent. The measurement results, after the error compensation, showed that the total error of the proposed system was less than 2.5 μm in the range of 60 mm, and the repeatability was within 0.16 μm, as quantified by standard deviation.

Solving Phase Ambiguity in Interferometric Displacement Measurement With Millimeter-Wave FMCW Radar Sensors

The frequency-modulated continuous-wave (FMCW) radar sensor is subject to phase ambiguity in measuring large displacement of over half a wavelength, which is particularly severe in the millimeter-wave FMCW radar sensor due to its short wavelength. The state-of-the-art linear phase demodulation techniques were mostly developed for single tone quadrature continuous-wave (CW) radars such as the Modified differentiate and cross-multiply (MDACM) algorithm. This paper presents a novel linear interferometric displacement measurement technique which can synthesize the quadrature <inline-formula> <tex-math notation="LaTeX">${I}/{Q}$ </tex-math></inline-formula> signals across slow time from a single-channel FMCW radar. In this way, the linear phase demodulation technique developed for the CW radar can now be leveraged for the FMCW radar. The theoretical analysis and working principles are discussed. Exhaustive experiments are performed to validate the proposed technique. It is demonstrated that the displacement motions as large as 10 times of the wavelength can be precisely extracted from a single channel FMCW radar with micrometer accuracy and without any phase ambiguity.

High-precision displacement measurement algorithm based on a depth fusion of grating projection pattern.

Displacement measurement based on an image recognition algorithm has more advantages in the field of displacement measurement. Due to the uncertainty of image location, the accuracy of the displacement measurement algorithm studied in the previous stage is limited. To improve the accuracy of image-type displacement measurement, a high-precision displacement measurement algorithm based on depth fusion of the grating projection pattern is proposed. First, a line-scan image sensor and parallel light source are placed on both sides of the calibration grating. The marking pattern on the calibration grating is projected onto the image sensor through illumination of the parallel light source to realize the projection imaging. Then, the centroid algorithm is used to calculate the centroid of each line in the collected image, and the mean value of the centroid group is determined. Finally, a linear function is used to fit multiple centroids to calculate the endpoints of the subdivision region, and the subdivision operation is carried out according to a ratio algorithm. To test the performance of the proposed algorithm, a linear displacement measurement device with a 250 mm range and an angular displacement measurement device with a 100 mm diameter grating are both used for experiments. After testing, the linear measurement accuracy of the proposed algorithm is improved from 4.63 to 1.26 µm, and the angular displacement measurement accuracy is enhanced from 8.87 to 2.88''. The research in this paper provides a theoretical basis for high-performance displacement measurement.

A Novel Self-Correction Method for Linear Displacement Measurement Based on 2-D Synthesis Mechanism

With increased range, the accuracy of longer-range linear displacement measurement is difficult to guarantee. According to the analysis, it is inevitable that there will be a certain margin between the direction of the calibration grating and the direction of the reading head, which will impact the longer-range linear displacement measurement. In order to eliminate this measurement error, a self-correction method based on 2-D synthesis is herein proposed. First, we describe the principle of absolute linear displacement measurement based on image recognition. Then, the error model is established, which caused by the included angle between the calibration grating and the reading head. Third, a method is proposed for obtaining the vertical offset of the calibration grating by using the vertical image sensor. Finally, we reach an error self-correction method based on 2-D synthesis. In order to test the feasibility of the proposed method, a linear displacement measuring device with a range of 200 mm was developed. After experiment, the maximum absolute error was reduced from 4.34 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.03~\mu \text{m}$ </tex-math></inline-formula> with the proposed error correction in the long range of 200 mm. The proposed algorithm does not depend on the assembly and installation position, and can realize self-correction of errors. So the method could lay the groundwork for improving larger range linear displacement measurement technology.

Precise-robust position measurement of a linear motor based on the extended speed-up robust features algorithm and sawtooth stripe pattern.

To improve the accuracy and robustness of linear motor mover position detection, a linear motor displacement measurement method is proposed based on the extended speed-up robust features algorithm and sawtooth stripe image. First, a sawtooth stripe image is constructed as the target image. To optimize the target image with strong robustness, the spatial frequency and image standard deviation are introduced as the image quality evaluation indices. Second, a line scan camera fixed on the linear motor is used to capture the target image signals in real time. The sequential sawtooth stripe signals are preprocessed by filling sampling to improve the matching rate of feature points. To satisfy the real-time requirement of mover position detection, the singular value decomposition is used to reduce the dimension of the preprocessed image. Subsequently, an improved speed-up robust features algorithm is used to achieve sub-pixel displacement measurement. Finally, the actual displacement of the mover can be calculated by the calibration coefficient of the measurement system. Simulation and comparative experiments show that the proposed sawtooth stripe image has better robustness, in contrast with the fence image and aperiodic sinusoidal image in references. It is also demonstrated that the proposed method has higher accuracy and anti-interference performance than other methods under different conditions.

Novel nano-scale absolute linear displacement measurement based on grating projection imaging

There is urgent demand for new absolute Linear Displacement Measurement (LDM) technology with high resolution and high precision, during the development of high-end numerical control technology. In previous research, we found that displacement measurement based on the image processing method performs well, however, the volume increases when using an imaging lens, and the system is susceptible to factors such as virtual focus. In this paper, the lensless LDM image optical path is established based on grating projection imaging, then the absolute grating coding method is operated based on M−sequence pseudo-random coding. A linear displacement subdivision algorithm is then deployed based on the digital image recognition algorithm. An LDM device with a measuring range of 250 mm was designed to test the performance of the proposed method. The device shows a measurement resolution of 1 nm and measurement accuracy of 1.76 μm in the range of 250 mm. This work lays a foundation for further research on high performance LDM technology.