Research on the Dynamic Model of Spindle Rotation Induced Error Compensation System of Boring and its Simulation

In this paper we address the dynamics of compensation cutting process from both Laplace s frequency domain and the time domain of the first time, using the two computer aided analyzing softwares: MATLAB and SIMULINK. Theoretical analysis and simulation experiments firstly show that not only the systematical stiffness of workpiece, spindle and tools, but also the regenerated coefficient affects the compensation displacement effect. The results show that the SREC is practicable in reality to decease the spindle induced errors in many engineering applications such as hard boring through simulation and the preliminary experiment results.

Research on dynamic error compensation for an armored K type thermocouple

A new method was proposed, in which a high-power CO2 laser modulated by high frequency was used as the driv- ing source to heat up a surface-temperature sensor. The continual beam and the pulsed beam sent out by the same laser could be used in the same system to carry on the static calibration of the radiation thermometer and the dynamic calibration of the temperature sensor to be checked. The frequency-response characteristics of high-speed radiation thermometer surpassed that of the temperature sensor, therefore it could be used as the reference value to calibrate the latter and let system error be cor- rected. Differences in the environment of the sensor installing and the error caused by the change of thermo-physical proper- ty could be avoided. Thus, the difficult problem of traceable dynamic calibration of temperature was solved. In experiment, to obtain the frequency characteristics of the thermocouple and the dynamic performance of the K type thermocouple, which could compensate the dynamic characteristics of the sensor, the sensor was dynamically corrected by using the method, and then the mathematical model was established.

Motion Error Compensation of Multi-legged Walking Robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot＇s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot＇s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.

Modeling Approach of Regression Orthogonal Experiment Design for Thermal Error Compensation of CNC Turning Center

The thermal induced errors can account for as much as 70% of the dimensional errors on a workpiece. Accurate modeling of errors is an essential part of error compensation. Base on analyzing the existing approaches of the thermal error modeling for machine tools, a new approach of regression orthogonal design is proposed, which combines the statistic theory with machine structures, surrounding condition, engineering judgements, and experience in modeling. A whole computation and analysis procedure is given. Therefore, the model got from this method are more robust and practical than those got from the present method that depends on the modeling data completely. At last more than 100 applications of CNC turning center with only one thermal error model are given. The cutting diameter variation reduces from more than 35 μm to about 12 μm with the orthogonal regression modeling and compensation of thermal error.

Precision Metrology of Micro Work-pieces on Their Tribological Performance with Error Compensation Method

The frictional properties of micro bearings have strong influence on the performance of the whole system because of tiny scale of micro-electromechanical system (MEMS). To develop micro bearings with low friction,it is important to evaluate the friction behaviors on the micro bearing. The testing system and the principle to evaluate the tribological performance of micromachining work-pieces under the load of mill Newton scale is introduced in paper "A new approach to measure the friction coefficient of micro journal bearings" of Yao et al,. But as the tribological force is faint in micro scale, the measured force is influenced a lot by the testing error. As the equation of that of Yao’s paper is very sensitive to the measured force, the tested result is influenced remarkably by testing error. So it is hard to get precision result. To solve this problem, the test system with new compensation method is introduced to precisely evaluate tribological performance under mill scale. The new metrology method is developed by means of the error compensation from two sets of testing data. The data are the force collected respectively when the friction counterparts rotate in CW(clockwise) and CCW(counter-clockwise) direction. So we deduce the equation of friction coefficient respctively on the condition of journal running in CCW and CW direction. As condition of measuring those two friciton coefficients are alike except the running direction of journal, and then the friction coefficient should be the same because this difference of direction has no influence on the fricition coefficients. Considering this, we unite the both equation, make the data measured in different subtract each other in the equation, and then a new equation can be gotten. This new equation enhances the metrology precision of friction coefficient theoretically thanks to the counteracting of error values in the equation. Using this method we testing the friction of high speed steel journal with hard alloy bearing. The result shows the new compensation method has better precision and repetition than CW and CCW method thanks to the error resistance.

Research on Positioning Error Compensation for Micro Milling Machine Tool

Micro milling has many advantages in fabricating three-dimensional(3D) structure in micrometer scale. The micro milling machine tool with high positioning accuracy is of great importance for getting micro structure with high profile precision and good surface quality. Meanwhile, the method of position error compensation is a good way to improve the accuracy of the micro milling machine tools. In this paper,a software method is adopted to compensate the positioning error and improve the positioning accuracy. According to error cancellation theory,the compensation values are generated and compensation tables are built to adjust the positioning error in the NC system based on Industrial Motion and Automation Control( IMAC). The positioning accuracy of linear motor is ± 0. 3 μm without backlash after compensation. In order to verify the effectiveness of compensation on the machining performance,concave spherical surfaces are processed on the micro milling machine tool. The experimental results show that the profile radius error of the spherical surface machined with compensation decreases more than 60%.

Low-order Wavefront Error Compensation for Multi-field of Lithography Projection Objective Based on Interior Point Method

Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation model between wavefront error and degree of movable lens freedom is established.Converting over-determined system to underdetermined system,the compensation is solved by Interior Point Method(IPM).The presented method is compared with direct solve the over-determined system.Then,other algorithm GA,EA and PS is compared with IPM.Simulation and experimental results show that the presented compensation method can obtained compensation with less residuals compared with direct solve the over-determined system.Also,the presented compensation method can reduce computation time and obtain results with less residuals compare with AGA,EA and PS.Moreover,after compensation,RMS of wavefront error of the experimental lithography projection objective decrease from 56.05 nm to 17.88 nm.

Periodic Error Compensation for Quartz MEMS Gyroscope Drift of INS

In order to improve the navigation accuracy of an inertial navigation system （INS）, composed of quartz gyroscopes, the existing real-time compensation methods for periodic errors in quartz gyroscope drift and the periodic error term relationship between sampled original data and smoothed data are reviewed. On the base of the results, a new compensation method called using former period characteristics to compensate latter smoothness data （UFCL for short） method is proposed considering the INS working characteristics. This new method uses the original data without smoothing to work out an error conversion formula at the INS initial alignment time and then compensate the smoothed data errors by way of the formula at the navigation time. Both theoretical analysis and experimental results demonstrate that this method is able to cut down on computational time and raise the accuracy which makes it a better real-time compensation approach for periodic error terms of quartz micro electronic mechanical system （MEMS） gyroscope＇s zero drift.

Kinematic Calibration and Forecast Error Compensation of a 2-DOF Planar Parallel Manipulator

Due to large workspace,heavy-duty and over-constrained mechanism,a small deformation is caused and the precision of the 2-DOF planar parallel manipulator is affected.The kinematic calibration cannot compensate the end-effector errors caused by the small deformation.This paper presents a method combined step kinematic calibration and linear forecast real-time error compensation in order to enhance the precision of a two degree-of-freedom(DOF) planar parallel manipulator of a hybrid machine tool.In the step kinematic calibration phase of the method,the end-effector errors caused by the errors of major constant geometrical parameters is compensated.The step kinematic calibration is based on the minimal linear combinations(MLCs) of the error parameters.All simple and feasible measurements in practice are given,and identification analysis of the set of the MLCs for each measurement is carried out.According to identification analysis results,both measurement costs and observability are considered,and a step calibration including step measurement,step identification and step error compensation is determined.The linear forecast real-time error compensation is used to compensate the end-effector errors caused by other parameters after the step kinematic calibration.Taking the advantages of the step kinematic calibration and the linear forecast real-time error compensation,a method for improving the precision of the 2-DOF planar parallel manipulator is developed.Experiment results show that the proposed method is robust and effective,so that the position errors are kept to the same order of the measurement noise.The presented method is attractive for the 2-DOF planar parallel manipulator and can be also applied to other parallel manipulators with fewer than six DOFs.

Thermal Error Compensation for Telescopic Spindle of CNC Machine Tool Based on SIEMENS 840D System

In this paper, eddy current sensors and thermocouple sensors were employed to measure the thermal field and thermal deformation of a spindle of a telescopic CNC boring-milling machine tool, respectively. A linear regression method was proposed to establish the thermal error model. Furthermore, two compensation methods were implemented based on the SIEMENS 840D system by using the feed shaft of z direction and telescopic spindle respectively. Experimental results showed that the thermal error could be reduced by 73.79% when using the second compensation method, and the thermal error could be eliminated by using the two compensation methods effectively.

Non-Exchangeable Error Compensation for Strapdown Inertial Navigation System in High Dynamic Environment

Strapdown non-exchangeable error compensation technology in high dynamic environment is one of the key technologies of strapdown inertial navigation system.Mathematical platform is used in strapdown inertial navigation system instead of physical platform in traditional platform inertial navigation system,which improves reliability and reduces cost and volume of system.The maximum error source of attitude matrix solution is the non-exchangeable error of rotation due to the non-exchangeable of finite rotation of rigid bodies.The rotation non-exchangeable error reaches the maximum in coning motion,although it can be reduced by shortening the correction period and increasing the real-time calculation.The equivalent rotation vector method is used to modify the attitude to reduce the coning error in this paper.Simulation experiments show that the equivalent rotation vector method can effectively suppress the non-exchangeable error and improve the accuracy of attitude calculation.

Technical Research for Detector of Grain Moisture Content Based on Error Compensation

According to the existing method including testing the frequency and establishing the relationship between moisture content and frequency, a corresponding instrument was designed. In order to further improve the accuracy and rapidity of the system, a new approach to describe the relationship between the measurement error and the temperature was proposed. The error band could be obtained and divided into several parts（based on the range of temperature） to indicate the error value that should compensate the grain moisture content for the changes in temperature. By calculating the error band at the maximum and the minimum operating temperatures, as well as by determining the error compensation value from the error band based on the measurement moisture content, the final effective result was derived.

Thermal Error Compensation of the Wear-Depth Real-Time Detecting of Self-Lubricating Spherical Plain Bearings

The spherical plain bearing test bench is a necessary detecting equipment in the research process of self?lubricating spherical plain bearings. The varying environmental temperatures cause the thermal deformation of the wear?depth detecting system of bearing test benches and then a ect the accuracy of the wear?depth detecting data. However, few researches about the spherical plain bearing test benches can be found with the implementation of the detect?ing error compensation. Based on the self?made modular spherical plain bearing test bench, two main causes of ther?mal errors, the friction heat of bearings and the environmental temperature variation, are analysed. The thermal errors caused by the friction heat of bearings are calculated, and the thermal deformation of the wear?depth detecting sys?tem caused by the varying environmental temperatures is detected. In view of the above results, the environmental temperature variation is the main cause of the two error factors. When the environmental temperatures rise is 10.3 °C, the thermal deformation is approximately 0.01 mm. In addition, the comprehensive compensating model of the thermal error of the wear?depth detecting system is built by multiple linear regression(MLR) and time series analysis. Compared with the detecting data of the thermal errors, the comprehensive compensating model has higher fitting precision, and the maximum residual is only 1 μm. A comprehensive compensating model of the thermal error of the wear?depth detecting system is proposed, which provides a theoretical basis for the improvement of the real?time wear?depth detecting precision of the spherical plain bearing test bench.

Laser Interferometer Based Measurement for Positioning Error Compensation in Cartesian Multi-Axis Systems

Accuracy is one of the most important key indices to evaluate multi-axis systems’ (MAS’s) characteristics and performances. The accuracy of MAS’s such as machine tools, measuring machines and robots is adversely affected by various error sources, including geometric imperfections, thermal deformations, load effects, and dynamic disturbances. The increasing demand for higher dimensional accuracy in various industrial applications has created the need to develop cost-effective methods for enhancing the overall performance of these mechanisms. Improving the accuracy of a MAS by upgrading the physical structure would lead to an exponential increase in manufacturing costs without totally eliminating geometrical deviations and thermal deformations of MAS components. Hence, the idea of reducing MAS’s error by a software-based alternative approach to provide real-time prediction and correction of geometric and thermally induced errors is considered a strategic step toward achieving the full potential of the MAS. This paper presents a structured approach designed to improve the accuracy of Cartesian MAS’s through software error compensation. Four steps are required to develop and implement this approach: (i) measurement of error components using a multidimensional laser interferometer system, (ii) tridimensional volumetric error mapping using rigid body kinematics, (iii) volumetric error prediction via an artificial neural network model, and finally (iv) implementation of the on-line error compensation. An illustrative example using a bridge type coordinate measuring machine is presented.

The Error Compensation of Inclinometer Based on Polynomial Fitting

In order to reduce the influence of nonlinear characteristic and temperature on the measuring accuracy of inclinometer, the application of polynomial fitting principle to compensate the measuring error of inclinometer is studied. According to the analysis of the experimental data of inclinometer, a polynomial model of the nonlinear error and the measured value is constructed, and then the relation between the coefficient of the polynomial model and the temperature is obtained by fitting, and finally the function of the measurement error of inclinometer on the measured inclination and temperature is obtained. The results show that this method is feasible and effective, which can not only reduce the influence of temperature, but also correct its nonlinear error.

Kinematic error modeling and error compensation of desktop 3D printer

Desktop 3D printers have revolutionized how designers and makers prototype and manufacture certain products.Highly popular fuse deposition modeling(FDM)desktop printers have enabled a shift to low-cost consumer goods markets,through reduced capital equipment investment and consumable material costs.However,with this drive to reduce costs,the computer numerical control(CNC)systems implemented in FDM printers are often compromised by poor accuracy and contouring errors.This condition is most critical as users begin to use 3D-printed components in load-bearing applications or to perform mechanical functions.Improved methods of low-cost 3D printer calibration are needed before their open-design potential can be realized in applications,including 3D-printed orthotics and prosthetics.This paper applies methodologies associated with high-precision CNC machining systems,namely,kinematic error modeling and compensation coupled with standardized test methods from ISO230-4,such as the ballbar for kinematic and dynamic error measurements,to examine the influence and feasibility for use on low-cost CNC/3D printing platforms.Recently,the U.S.Food and Drug Administration's"Technical considerations for additive manufactured medical devices"highlighted the need to develop standards specific to additive manufacturing in regulated manufacturing environments.This paper shows the benefits of the methods described within ISO230-4 for error assessment,alongside applying kinematic error modeling and compensation to the popular kinematic configuration of an Ultimaker 3D printer.A Renishaw ballbar QC10 is used to quantify the Ultimaker's errors and thereby populate the error model.This method quantifies machine errors and populates these in a mathematical model of the CNC system.Then,a post-processor can be used to compensate the printing code.Subsequently,the ballbar is used to demonstrate the dramatic impact of the error compensation model on the accuracy and contouring of the Ultimaker printer with 58%reduction in overall circularity error and 90%reduction in squareness error.

A New Method of Error Compensation for Numerical Control System

This paper presents a method of rapid machine tool error modeling, separation, and compensation using grating ruler. A robust modeling procedure for geometric errors is developed and a fast data processing algorithm is designed by using the error separation technique. After compensation with the new method, the maximum position error of the experiment workbench can be reduced from 400 μm to 15 μm. The experimental results show the effectiveness and accuracy of this method.

Stock Price Prediction Using Predictive Error Compensation Wavelet Neural Networks

:Machine Learning(ML)algorithms have been widely used for financial time series prediction and trading through bots.In this work,we propose a Predictive Error Compensated Wavelet Neural Network(PEC-WNN)ML model that improves the prediction of next day closing prices.In the proposed model we use multiple neural networks where the first one uses the closing stock prices from multiple-scale time-domain inputs.An additional network is used for error estimation to compensate and reduce the prediction error of the main network instead of using recurrence.The performance of the proposed model is evaluated using six different stock data samples in the New York stock exchange.The results have demonstrated significant improvement in forecasting accuracy in all cases when the second network is used in accordance with the first one by adding the outputs.The RMSE error is 33%improved when the proposed PEC-WNN model is used compared to the Long ShortTerm Memory(LSTM)model.Furthermore,through the analysis of training mechanisms,we found that using the updated training the performance of the proposed model is improved.The contribution of this study is the applicability of simultaneously different time frames as inputs.Cascading the predictive error compensation not only reduces the error rate but also helps in avoiding overfitting problems.

Event-triggered predefined-time control for full-state constrained nonlinear systems: A novel command filtering error compensation method

In this paper, a command filter-based adaptive fuzzy predefined-time event-triggered tracking control problem is investigated for uncertain nonlinear systems with time-varying full-state constraints. By designing a sliding mode differentiator, the inherent computational complexity problem within the predefined-time backstepping framework is solved. Different from the existing command filter-based finite-time and fixed-time control strategies that the convergence time of the filtering error is adjusted through the system initial value or numerous parameters, a novel command filtering error compensation method is presented,which tunes one control parameter to make the filtering error converge in the predefined time, thereby reducing the complexity of design and analysis of processing the filtering error. Then, an improved event-triggered mechanism(ETM) that builds upon the switching threshold strategy, in which an inverse cotangent function is designed to replace the residual term of the ETM,is proposed to gradually release the controller's dependence on the residual term with increasing time. Furthermore, a tan-type nonlinear mapping technique is applied to tackle the time-varying full-state constraints problem. By the predefined-time stability theory, all signals in the uncertain nonlinear systems exhibit predefined-time stability. Finally, the feasibility of the proposed algorithm is substantiated through two simulation results.

Process planning and contour-based error compensation for precision grinding of miniature scalpels

Miniature scalpels are mainly used in microsurgeries such as ophthalmic and cardiovascular surgeries.The size of a miniature scalpel is only a few millimeters,and the precision of the blade shape is high,which makes production of miniature scalpels extremely difficult.This study proposes a new sharpening process for grinding miniature scalpels on a four-axis machine tool.A post-processing algorithm for a four-axis grinding machine based on a kinematics model is established.We then propose a corresponding parameter calibration method for the parameters used in the kinematics model.Because of possible errors in the parameter calibration,a contour-based error compensation method is proposed for accurate adjustments to the edge shape following grinding.This can solve the problem of large deviations between the actual edge shape after grinding and the ideal edge shape.The effectiveness of the proposed process planning and error compensation method is verified experimentally,and the grinding process parameters of the miniature scalpel are optimized to improve its surface processing quality.The sharpness of the optimized miniature scalpel is less than 0.75 N,and the blade shape is symmetrical,which meets the technical requirements of miniature scalpels.