MODELING AND COMPENSATION TECHNIQUE FOR THE GEOMETRIC ERRORS OF FIVE-AXIS CNC MACHINE TOOLS

One of the important trends in precision machining is the development ofreal-time error compensation technique. The error compensation for multi-axis CNC machine tools isvery difficult and attractive. The modeling for the geometric error of five-axis CNC machine toolsbased on multi-body systems is proposed. And the key technique of the compensation―identifyinggeometric error parameters―is developed. The simulation of cutting workpiece to verify the modelingbased on the multi-body systems is also considered.

Error Compensation of Thin Plate-shape Part with Prebending Method in Face Milling

Low weight and good toughness thin plate parts are widely used in modem industry, but its flexibility seriously impacts the machinability. Plenty of studies locus on the influence of machine tool and cutting tool on the machining errors. However, few researches focus on compensating machining errors through the fixture. In order to improve the machining accuracy of thin plate-shape part in face milling, this paper presents a novel method for compensating the surfacc errors by prebending the workpiece during the milling process. First, a machining error prediction model using finite element method is formulated, which simplifies the contacts between the workpiece and fixture with spring constraints. Milling fbrces calculated by the micro-unit cutting force model arc loaded on the error prediction model to predict the machining error. The error prediction results are substituted into the given formulas to obtain the prebending clamping forces and clamping positions. Consequently, the workpiece is prebent in terms of the calculated clamping forces and positions during the face milling operation to reduce the machining error. Finally, simulation and experimental tests are carried out to validate the correctness and efficiency of the proposed error compensation method. The experimental measured flatness results show that the flatness improves by approximately 30 percent through this error compensation method. The proposed mcthod not only predicts the machining errors in face milling thin plate-shape parts but also reduces the machining errors by taking full advantage of the workpiece prebending caused by fixture, meanwhile, it provides a novel idea and theoretical basis for reducing milling errors and improving the milling accuracy.

Modeling and Compensation Technology for the Comprehensive Errors of Fixture System

Error modelling and compensating technology is an effective method to improve the processing precision.The position and orientation deviation of workpiece is caused by the fixing and manufacturing errors of the fixture.How to reduce the position and orientation deviation of workpiece has become a technical problem of improving the processing quality of workpiece.In order to increase machining accuracy,an implementation scheme of fixture system comprehensive errors（FSCE） compensation is proposed.A FSCE parameter model is established by analyzing the influence of contact points on the position and orientation of workpiece.Meanwhile,a parameter identification method for FSCE parameter model is presented by using the 3-2-1 deterministic positioning fixture,which determines the model parameters.Moreover,a FSCE compensation model is formulated to study the compensation value of the cutting position.By using RenishawOMP60 Probe and combining vertical machining centre（SKVH850） equipment with SKY2001 Open CNC System,on-machine verification system（OMVS） is built to measure FSCE successfully.The processing error can be reduced by analyzing the cutting position of the tool with the homogeneous transformation of space coordinate system.Finally,the compensation experiment of real time errors is conducted,and the cylindricality and perpendicularity errors of hole surface are reduced by 30.77% and 28.57%,respectively.This paper provides a new way of realizing the compensation of FCSE,which can improve the machining accuracy of workpiece largely.

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.

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.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

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.

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.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

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.

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.

ERROR COMPENSATION OF COORDINATE MEASURING MACHINES WITH LOW STIFFNESS

A technique for compensating the errors of coordinate measuring machines (CMMs) with low stiffness is proposed. Some additional items related with the force deformation are introduced to the error compensation aquations. The research was carried on a moving colunm horizontal arm CMM. Experimental results show that both the effects of systematic components of error motions and force deformations are greatly reduced, which shows the effectiveness of proposed technique.

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.

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.

Time-varying baseline error correction method for ground-based micro-deformation monitoring radar

In recent years, ground-based micro-deformation monitoring radar has attracted much attention due to its excellent monitoring capability. By controlling the repeated campaigns of the radar antenna on a fixed track, ground-based micro-deformation monitoring radar can accomplish repeat-pass interferometry without a space baseline and thus obtain highprecision deformation data of a large scene at one time. However, it is difficult to guarantee absolute stable installation position in every campaign. If the installation position is unstable, the stability of the radar track will be affected randomly, resulting in time-varying baseline error. In this study, a correction method for this error is developed by analyzing the error distribution law while the spatial baseline is unknown. In practice, the error data are first identified by frequency components, then the data of each one-dimensional array(in azimuth direction or range direction) are grouped based on numerical distribution period, and finally the error is corrected by the nonlinear model established with each group.This method is verified with measured data from a slope in southern China, and the results show that the method can effectively correct the time-varying baseline error caused by rail instability and effectively improve the monitoring data accuracy of groundbased micro-deformation radar in short term and long term.

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%.

A Rapid Method for Compensating Output Error of Electromagnetic Tracker

Some methods which use an optical tracker(OT) as a standard reference of electromagnetic tracker(EMT) were proposed in order to compensate the output error of electromagnetic tracker. Usually,they use a magneto-optic tool to collect the outputs of OT and EMT simultaneously,and then compare the output of OT with that of EMT to compensate the error of EMT. Although the outputs of EMT and OT can be matched each other by using a time stamp which denotes when the acquirement command is sent,but the accuracy will decrease if the tool moves faster for the errors of the time stamp itself. A rapid method for compensating EMT output error is proposed. A particular scan mode of the magneto-optic tool is designed for collecting EMT and OT outputs,and a data registration method is proposed to match the outputs of EMT and OT. The simulated results show that the output error of EMT can be decreased efficiently and the accuracy of the compensation can be improved by about 15% compared with that of the existing methods.

Machining Complex Oriented Compensation System for Generalized Kinematic Errors

This paper puts forward a machining complex oriented compensation strategy for the generalized kinematic errors (GKEs). According to this strategy, the error map, which is constructed by using the off line measuring information of the machined workpiece, is not oriented for the machine tool but for the machining complex to compensate the GKEs. The error map is derived by the proposed predictive learning control algorithm (PLCA), which is supported by the information model of machining complex. Experimental results show that the machining complex oriented GKEs compensation strategy and the information model based PLCA is effective.

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.