Vibration Error Research Articles

Sowing Depth Monitoring System for High-Speed Precision Planters Based on Multi-Sensor Data Fusion

High-speed precision planters are subject to high-speed (12~16 km/h) operation due to terrain undulation caused by mechanical vibration and sensor measurement errors caused by the sowing depth monitoring system’s accuracy reduction problems. Thus, this study investigates multi-sensor data fusion technology based on the sowing depth monitoring systems of high-speed precision planters. Firstly, a sowing depth monitoring model comprising laser, ultrasonic, and angle sensors as the multi-sensor monitoring unit is established. Secondly, these three single sensors are filtered using the Kalman filter. Finally, a multi-sensor data fusion algorithm for optimising four key parameters in the extended Kalman filter (EKF) using an improved sparrow search algorithm (ISSA) is proposed. Subsequently, the filtered data from the three single sensors are integrated to address the issues of mechanical vibration interference and sensor measurement errors. In order to ascertain the superiority of the ISSA-EKF, the ISSA-EKF and SSA-EKF are simulated, and their values are compared with the original monitoring value of the sensor and the filtered sowing depth value. The simulation test demonstrates that the ISSA-EKF-based sowing depth monitoring algorithm for high-speed precision planters, with a mean absolute error (MAE) of 0.083 cm, root mean square error (RMSE) of 0.103 cm, and correlation coefficient (R) of 0.979 achieves high-precision monitoring. This is evidenced by a significant improvement in accuracy when compared with the original monitoring value of the sensor, the filtered value, and the SSA-EKF. The results of a field test demonstrate that the ISSA-EKF-based sowing depth monitoring system for high-speed precision planters enhances the precision and reliability of the monitoring system when compared with the three single-sensor monitoring values. The average MAE and RMSE are reduced by 0.071 cm and 0.075 cm, respectively, while the average R is improved by 0.036. This study offers a theoretical foundation for the advancement of sowing depth monitoring systems for high-speed precision planters.

Source and mask optimization for stability of reticle and wafer stages

The relative motion of the reticle stage and wafer stage caused by vibration during the scanning exposure process of the lithography machine is an important factor that affects the imaging quality under limited lithography ability. In this paper, the influence of the vibration of the lithography stage system on the lithography imaging quality is studied. The lithography model including the vibration error of the stage is taken into account in the framework of source and mask optimization (SMO). For the 193-nm immersion lithography machine, combined with different design patterns with a line width of 40 nm and different vibration states of the stage when the lithography machine is exposed, the SMO joint optimization research is carried out, and the robustness of the stage under the limit process after SMO optimization is explored. The research results show that the contrast and relative light intensity change of the limit design figure under the influence of moving standard deviation (MSD) will greatly affect the linewidth at the light intensity threshold and then affect the process window (PW). The SMO including MSD allows the MSD to change in the range of 0-6 nm without changing the PW.

Adaptive light intensity aided wavelength tuning for phase‐shifting interferometric measurement system

AbstractIn phase‐shifting interferometric measurement system, using wavelength‐tuned phase‐shifting technology to measure optical surface can improve vibration errors. However, the wavelength‐tuned phase‐shifting interferometry is greatly challenged by nonlinear distortion between wavelength‐tuned light intensity and voltage modulation, which has a certain impact on phase calculation accuracy. To address this issue, an adaptive light intensity‐aided interferometric measurement scheme is proposed in this study. To improve the adjustment time of voltage response, an improved fuzzy single‐neuron adaptive proportional differential integral constant amplitude control algorithm is built. By exploiting the online detection and feedback control of light intensity, the stable output of light intensity is integrated into phase‐shifting measurement system. Experiment results verify that the improvement of light intensity fluctuation range, root mean square, and peak‐to‐valley measurement repeatability can be achieved with the proposed scheme.

Speed Sensor-less Control of Induction Motor based on Super-helical Sliding Mold

Background: With the continuous progress of technology and the development of shield enterprises, higher requirements are put forward for speed estimation and system stability in the sensorless control system of induction motors in shield machines. Method: In order to solve the problems of velocity observation error and sliding mode vibration of the induction motor velocity observation method based on sliding mold observer, an improved superhelical sliding mold observer is proposed by combining the currently known invention patents and the information based on the induction motor control. Result: The open square of the current error value is introduced into the continuous function of the sliding variable of the observer, and two different functions are used in the boundary layer to replace the sign function, which reduces the sliding mode noise and vibration problems, and the stability of the observer is proved by the Lyapunov stability theory. After that, a phase-locked loop alternative model-referenced adaptive algorithm is used as the rotational speed observation link, which solves the problem that the conventional model-referenced adaptive algorithm relies on the current-modeled magnetic chain observer. Conclusion: The improved super-helical sliding mode observer and phase-locked loop control method effectively reduce the system vibration and speed estimation error of the motor under different speeds and loading conditions, and the observed currents are smoother, which improves the stability of the system. Simulation and experimental results under different working conditions show the effectiveness of the proposed method.

Adaptive composite learning control of a flexible two‐link manipulator with unknown spatiotemporally varying disturbance

AbstractThis article presents a novel adaptive composite learning (ACL) control strategy combining reinforcement learning and a disturbance observer (DOB) to address vibration issues in a flexible two‐link manipulator (FTLM) system affected by unknown spatiotemporally varying disturbances. Based on the assumed mode method, the FTLM system is initially transformed into an ordinary differential equation model, while effectively capturing the elastic deformation and vibration characteristics of the flexible link. A composite learning controller, based on the actor‐critic algorithm and DOB, is then developed to achieve trajectory tracking and vibration suppression in the FTLM system. The DOB in the controller compensates for unknown disturbances resulting in reduced system error. It is noting that the proposed optimal control strategy is continuously gathering system experience and evaluating the current policy's effectiveness. The stability and robustness of the closed‐loop system incorporating the composite controller are analyzed using Lyapunov's direct method, and the semi‐global uniform ultimate boundedness of the tracking and vibration errors are also demonstrated. To validate the effectiveness and superiority of the proposed ACL controller, comparative simulations and experiments are conducted on the Quanser experimental platform.

Near-field beamforming method based on motion model analysis for UAVs communication

This study presents a near-field beamforming method for the moving swarm composed of unmanned aerial vehicles (UAVs) to address the challenges of position errors that hinder effective beamforming. Firstly, a model with positional errors in moving UAVs was developed. The sources and characteristics of UAVs’ position errors were analyzed and classified into low-frequency motion errors and high-frequency vibration errors, and their effects on UAVs array beamforming were analyzed using coordinate transformation and decomposition. Secondly, a parameter estimation algorithm was proposed based on the Fast Fourier Transformation (FFT) and the Least Square (LS) method to estimate the unknown parameters of the UAV's low-frequency motion errors. Lastly, a near-field beamforming algorithm for UAVs was proposed based on the Interpolation Kalman filter (IKF). The effectiveness of the proposed model and algorithms was verified through simulations, which provided a theoretical basis for the near-field beamforming under the existence of the UAVs position errors.

An Airborne Arc Array Synthetic Aperture Radar Vibration Error Compensation Method

Compared to conventional radars, arc array synthetic aperture radar (SAR) enables wide-area observation under ideal conditions. However, helicopters carrying arc array SAR platforms are generally smaller in size and more sensitive to vibration, which has a greater impact on the imaging quality. In this paper, the vibration error of the arc array SAR platform is investigated, and a vibration error model of the arc array SAR platform is established. Based on the study of the vibration error model, a vibration phase estimation and compensation algorithm based on the delayed conjugate multiplication method is proposed. In the first step, distance pulse pressure processing is performed on the echo signal. In the second step, the pulse pressure signals and their delays in the same distance unit are subjected to conjugate multiplication, and the phase of the signal after conjugate multiplication is extracted. The extracted phase is then amplitude- and phase-compensated to estimate the vibration phase. In the third step, the vibration phase is compensated in the azimuthal direction of the distance pulse pressure signal, and the pairwise echo is eliminated, which completes the compensation of the airborne arc array SAR vibration platform.

SAL vibration estimation and compensation based on triangular interferometric signals.

Synthetic aperture Ladar (SAL) is an extension of synthetic aperture technology in the optical frequency band. Owing to the short wavelength of lasers, the system has high-resolution, high-data-rate, and refined imaging capabilities, which has potential in high-resolution observation fields such as ground observation and space target observation. However, the short wavelength of lasers also makes SAL severely sensitive to vibrations even on the micron order which cause azimuth defocusing and range cell migration. To address this problem, we establish a de-chirp signal model under vibration environment, and propose a vibration error estimation and compensation method using triangular interferometric signals. According to the symmetrical characteristics of triangular frequency modulated continuous wave (T-FMCW) and the time-frequency information introduced by the azimuthal vibration phase, we use a two-stage interferometry method to estimate instantaneous frequency introduced by the vibration errors that cause range cell migration. For the scenarios without obvious range cell migration, we use a one-stage interferometry method to estimate the instantaneous frequency. Subsequently, we establish a vibration compensation filter using the estimated instantaneous frequency to compensate for the vibration errors. We use two experiments to verify the effectiveness and superiority of the proposed method. The results show that the proposed method effectively eliminates range cell migration and azimuthal phase errors introduced by vibration errors, producing SAL imaging results with higher resolution than the conventional spectral correlation method.

Force servo nano-precision diamond cutting of freeform surfaces on a micro-precision machine

This paper presents force servo single point diamond cutting of freeform surfaces with nano-precision on a micro-precision machine. For nanometric machining accuracy, traditional diamond cutting based on position servo, requires accurate machine axial motions by ultra-precision machine with high cost, or utilizes a fast tool servo to compensate for machine slide vibration and motion error of common machines that is a complicated procedure. In this paper, nanometric machining accuracy was achieved on a micro-precision machine by force servo diamond cutting, in which the tool can be driven to trace the workpiece surface to compensate for the machine slide vibration, machine motion errors and workpiece incline errors accurately and automatically. For highly sensitive and stable force controlling, force servo nanocutting mechanism (FSNM) based on flexible structures was designed with force sensing resolution down to submillinewton level, and a damping controller was developed to suppress the resonant vibration of the FSNM. For extending application of force servo cutting from fabrication of only discontinuous microstructures to continuous freeform surfaces, referring force maps were developed by considering the real material removal volume of each cutting point. Force servo cutting was then validated by fabricating freeform surfaces with surface form errors of less than 10 nm on silicon spherical surfaces based on the micro-precision machine. The works discussed in this paper provide an effective technique for the fabrication of complex and continuous microstructured and freeform surfaces with nano-precision by common machines only with micron even tens of microns precision.

Vibration errors compensation method based on self-feature registration for the 3-D dynamic measurement of metallic sealing ring forming surface

The formed surface quality of metallic sealing ring of aero-engine affects the aircraft service performance directly. However, existing inspection methods, such as the final destructive inspection and the line laser scanner section profile measurement, only evaluate the formed quality from a 2-D view, that is, single or multiple radial formed section profiles. The lack of geometric information of 3-D surface is not conducive to the comprehensive monitoring of forming quality and process planning. Therefore, based on the line laser scanners, this paper mainly proposes a vibration errors compensation method based on self-feature registration. Aiming at the problem of rigid transformation of the measurement profile caused by random vibration during the rotary motion of metallic sealing ring, the feature of measurement profile in stationary scene (MPSS), that is, the medial axis, is used as the reference for the correct pose of measurement profile. The principle of finding the correct pose of measurement profile in rotary motion scene (MPRMS) is to minimize the distance between the medial axes. Next, based on the rotary motion information of metallic sealing ring and the geometric information of measurement system, a 3-D reconstruction matrix is built, so as to convert each measurement profile to the base coordinate system in turn, and finally a 3-D dynamic measurement method for the metallic sealing ring forming surface is built. The effectiveness of the proposed method is verified through simulation experiment and real measurement.

Nonlinear vibrational analysis and linearization error investigation in size-dependent resonant pressure microsensors

Dynamic and vibrational behavior of nonlinear resonant pressure micro sensors is studied in this paper using a proposed dynamic model. The basic part of the device is a microplate deflects due to external pressure in presence of electrostatic actuation. The frequency changes because of the microplate deformation is used to estimate the external pressure. For modeling of the micro sensor, the nonlinear governing equation of size dependent microplate in polar coordinate system and based on the modified couple stress theory is presented. Assuming specified number of Taylor expansion terms for electrostatic force, the linear and nonlinear ODE is obtained and nonlinear equation is solved both with multiple time scales method (MTS) and finite difference numerical method. Results indicate that considering finite terms of Taylor expansion (1 term for linear and three terms for MTS method) is the source of error in estimation of pressure or system stability. Using sufficient terms of Taylor Expansion, the error in linear and MTS solutions is vanished. Therefore, the limited values of microplate vibrational amplitude is extracted to increase the accuracy of the sensor in linear action. The effect of size dependency, applied voltage on nonlinear behavior and linearization error is also studied.

The machinability of titanium alloy thin-wall parts in cooling minimum quantity lubrication (CMQL) environments

The machining of thin-wall components made of titanium alloys is challenging because the poor machinability of the material leads to severe problems such as accelerated tool wear and poor surface quality, while the weak rigidity of the thin-wall structure results in unavoidable vibration and surface form errors. To address these issues, this paper investigated the mechanisms and performance of cooling minimum quantity lubrication (CMQL) in milling titanium thin-wall parts. To verify the efficiency of CMQL, different cooling/lubrication strategies, including conventional flood cooling, minimum quantity lubrication (MQL) and CMQL with different temperature levels, were investigated. The cutting force, tool wear state, chip formation, surface integrity, and surface form errors were compared and analysed in detail. The experiment results show that MQL is inadequate at higher spindle speeds due to its ineffective cooling capacity and weakened lubrication ability. In contrast, CMQL has demonstrated its feasibility and superiority in milling titanium thin-wall parts under all conditions. The outcomes indicate that a lower temperature level of CMQL is advantageous to producing better wear resistance and lower thermomechanical loads, and the CMQL (− 15 ºC) machining environment can remarkably improve the overall machining performance and control the surface form errors of the machined thin-wall parts. At the spindle speed of 3000 rpm, the surface roughness measured under CMQL (− 15 °C) condition is reduced by 16.53% and 23.46%, the deflection value is decreased by 54.74% and 36.99%, while the maximum thickness error is about 53.51% and 20.56% smaller in comparison to flood cooling and MQL machining. In addition, CMQL is an economical and sustainable cooling/lubrication strategy; the outcomes of this work can provide the industry with useful guidance for high-quality machining of thin-wall components.

Automatic vibration control method for grasping end of flexible joint robot

Because flexible robots have flexible components such as reducers, there are problems of accuracy deviation and end vibration in the process of external interference and trajectory tracking. This leads to the proposal of a Sliding Mode Control Approach Based on RBF Neural Network (SMC-RBF) parameter optimization. This method is mainly applied to reduce the end vibration and running position error of flexible robot. Firstly, the Newton-Euler method is used to establish the dynamic model of robot considering joint flexibility. At the same time, the experiment optimizes the Sliding Mode Control (SMC) method through RBF neural network. The experiments verify the control methods of the two-joint flexible robot and the six-joint flexible robot respectively. In the control of two-joint robot, the maximum tracking curve error of SMC is only about 0.25 rad under the interference of pulse signal; And the recovery time is only about 1 s. In the control of 6-joint robot, the maximum error of RBF-sliding mode control method on XYZ axis is 0.7 mm, 0.25 mm and 1.25 mm respectively; The error on three axes is smaller than that of traditional PD control method. The results demonstrate that the tracking error of the improved mode control is small, the chattering phenomenon of the robot system is weakened as well.

Research on registration error compensation of large-scale measurement field based on neural network.

The combination of large tooling size, environmental vibration, and equipment errors at the aircraft assembly site leads to errors in the enhanced reference system (ERS) point measurement information. ERS point errors directly reduce the accuracy of the assembly measurement field. This paper proposes ERS point error prediction and registration compensation based on the neural network to address this problem. First, the effects of equipment measurement errors and environmental vibration factors on the measurement field are studied. The ERS point error prediction model based on the neural network is established. On this basis, model evaluation is used to assess the prediction model of this paper. Then, a measurement field registration compensation model is constructed based on the neural network error results for ERS point compensation analysis. Finally, an experimental validation platform was built to predict the ERS point errors and compensate for the constructed measurement fields using the method in this paper. The experimental results show that, compared with the conventional method, the maximum registration errors in the X, Y, and Z directions are reduced from 0.0812, -0.0565, and -0.2810 to -0.0184, -0.0010, and 0.0022mm, respectively, after compensation in this paper. The method proposed in this paper can not only predict the ERS point error state and provide a reference for designers but also guide the selection of appropriate ERS points when constructing the measurement field. The compensation method in this paper effectively reduces the measurement field registration error.

Development of Automated Test Equipment to Improve the Measurement Uncertainty of Seismic Acceleration Sensors: Focusing on Tilting-Type Equipment

This study developed an automated seismic acceleration sensor test equipment to improve the high measurement uncertainty of existing test equipment with the tilting method. The equipment was developed by setting the legal standards for seismic acceleration sensor test equipment and the problems of existing test equipment as performance indicators. The problems with the existing test equipment, which was manually operated, included measurement error owing to handling vibration, occurrence of angle error according to the observation field, and measurement method without considering hysteresis. The developed equipment satisfied the legal standards, and the problem of measurement error owing to handling vibration and angle error according to the observation field of view was improved by attaching a servo motor and precision level to the measurement equipment. Hysteresis control has been improved by adding the delay time control function of dedicated software (S/W). The developed automated seismic acceleration sensor test equipment can be used for the testing of seismic acceleration sensors, and the operating software reduced measurement uncertainty in the testing of seismic acceleration sensors.

Effects of tooth root cracks on vibration and dynamic transmission error responses of asymmetric gears: A comparative study

Gears are significant machine elements used in various industrial applications. An undetected fault in a gear transmission system may lead to a fatal breakdown and, thus, severe economic losses or even human casualties. From this standpoint, the present study developed a numerical method to detect root crack damages in symmetric and asymmetric involute spur gears. To achieve this end, the single tooth stiffness values were calculated for healthy and cracked (25%-50%-75%-100%) gears, and then the time-varying mesh stiffness was obtained. A six-degree-of-freedom dynamic model of a single-stage gear mechanism was developed to collect vibration and Dynamic Transmission Error (DTE) signals. The efficacy of vibration and DTE responses in fault detection was compared through six statistical indicators. The results indicate that the vibration signals were more effective than DTE in detecting tooth root cracks. It was observed that the statistical indicator changes significantly increase with the increment of the drive side pressure angle from 20° to 30° for the backup ratios where the root crack propagates along the tooth, thus making fault detection easier. The findings could provide significant outputs for a better understanding of the influence of tooth asymmetry on gear dynamics characteristics and early fault diagnosis.

Wave propagation behaviors of a low-symmetry reentrant chiral structure with mass inclusion in a single material

This work proposed a low symmetry characteristics metamaterial in a single material. The structural configuration of the metamaterial is composed of the reentrant structure, chiral structure and mass inclusion. The wave propagation characteristics are investigated in terms of the Bloch-Floquet wave propagation theorem. Firstly, the band diagram of the metamaterial is analyzed. The wave behaviors of the structure are changed due to the low symmetry characteristics. The irreducible Brillouin zone (IBZ) of the proposed structure is changed. The band diagram in the whole IBZ is analyzed to get the accurate distributions of the bandgaps. Some extremum values of the dispersion surface are deviated from the boundary of the IBZ. The formation mechanisms of bandgaps are illustrated based on the analysis of the vibration mode shapes. Then, the phase velocity and group velocity of the elastic wave are calculated, showing the strong anisotropic properties. Moreover, the effects of the geometrical parameters on the bandgaps are investigated. The locations and width of the bandgaps can be tuned for by the rational design. The existence of bandgaps of the metamaterial are validated by a finite element model. Finally, a metamaterial beam sample with seven cells is made and experiment test are conducted for the vibration attenuation performance and error analysis. The proposed structure can be used for vibration attenuation in the fields of underwater vehicles.

Feasibility study of an enhanced heterodyne dispersion interferometer

Interferometry is the commonly exploited technique for electron density measurements in magnetically confined fusion plasma experiments. Reliable electron density measurements are fundamental both for machine protection and for plasma physics understanding. In the last years, attention was drawn on the dispersion interferometer concept, because of its robustness and simplicity. Nevertheless, the heterodyne version of this configuration, which has several advantages over the homodyne scheme, loses one of the main benefits of the dispersion interferometer technique, that is its inherent insensitivity to vibration errors. In this paper, two methods are proposed and theoretically investigated to reduce the vibration noise in the electron density measurements performed with heterodyne dispersion interferometers.

Two-Stage Time-Varying Vibration Compensation for Coherent LiDAR Based on the Adaptive Differential Evolution Method

Coherent LiDAR, which is based on triangular frequency modulated continuous wave (T-FMCW), is a promising technology for high-resolution imaging, because it can achieve long-range and high-precision measurements using low power. However, owing to the short wavelength of laser, the system is extremely sensitive to time-varying vibration. Most vibration compensation methods perform well in the scenes that contain strong scatterers using enough data. However, they lose validity in scenes without strong scatterers and sufficient observation time. To address this problem, we develop a second-order vibration error model for coherent LiDAR that divides the Doppler frequency shift caused by time-varying vibrations into quadratic and primary errors. Based on the vibration error model, we propose a two-stage time-varying vibration compensation method using the adaptive differential evolution (ADE) algorithm. In the first stage, we iteratively determine the optimal quadratic vibration coefficients that minimize the spectral entropy of the compensated dechirp signals using the ADE algorithm. Subsequently, we compensate for the quadratic errors using the estimated quadratic vibration coefficients. In the second stage, we use the frequency spectrum cross-correlation method to estimate the primary vibration coefficients and compensate for the primary errors. We perform experiments in the scene containing a point target and the scenes containing multi-component targets and distributed targets without strong scatterers. The results indicate that the proposed method can effectively compensate for time-varying vibration errors using only one-period T-FMCW data in different scenes. Further, the results of the proposed method are more accurate and stable than the Doppler frequency shift method.

Compensation for High-Frequency Vibration of SAR Imaging in the Terahertz Band Based on Linear Chirplet Transform and Empirical Mode Decomposition

SAR in THz band is very important and valuable in the field of radar signal processing, and it is much sensitive to the high-frequency vibration of the platform due to the short wavelength. In this article, the high-frequency vibration is characterized as a multicomponent SFM signal, and the parameters estimation method based on the linear chirplet transform and empirical mode decomposition is proposed to compensate for the high-frequency vibration errors. This method can extract the instantaneous frequency of the received signal with high precision, and the focused SAR image can be obtained consequently. Results of simulated and real measured data are provided to illustrate the effectiveness of the novel algorithm proposed in this article.