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.

Temperature Variable Optimization for Precision Machine Tool Thermal Error Compensation on Optimal Threshold

Machine tool thermal error is an important reason for poor machining accuracy. Thermal error compensation is a primary technology in accuracy control. To build thermal error model, temperature variables are needed to be divided into several groups on an appropriate threshold. Currently, group threshold value is mainly determined by researchers experience. Few studies focus on group threshold in temperature variable grouping. Since the threshold is important in error compensation, this paper arms to find out an optimal threshold to realize temperature variable optimization in thermal error modeling. Firstly, correlation coefficient is used to express membership grade of temperature variables, and the theory of fuzzy transitive closure is applied to obtain relational matrix of temperature variables. Concepts as compact degree and separable degree are introduced. Then evaluation model of temperature variable clustering is built. The optimal threshold and the best temperature variable clustering can be obtained by setting the maximum value of evaluation model as the objective. Finally, correlation coefficients between temperature variables and thermal error are calculated in order to find out optimum temperature variables for thermal error modeling. An experiment is conducted on a precise horizontal machining center. In experiment, three displacement sensors are used to measure spindle thermal error and twenty-nine temperature sensors are utilized to detect the machining center temperature. Experimental result shows that the new method of temperature variable optimization on optimal threshold successfully worked out a best threshold value interval and chose seven temperature variables from twenty-nine temperature measuring points. The model residual of z direction is within 3 μm. Obviously, the proposed new variable optimization method has simple computing process and good modeling accuracy, which is quite fit for thermal error compensation.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

Bayesian networks modeling for thermal error of numerical control machine tools

The interaction between the heat source location, its intensity, thermal expansion coefficient, the machine system configuration and the running environment creates complex thermal behavior of a machine tool, and also makes thermal error prediction difficult. To address this issue, a novel prediction method for machine tool thermal error based on Bayesian networks (BNs) was presented. The method described causal relationships of factors inducing thermal deformation by graph theory and estimated the thermal error by Bayesian statistical techniques. Due to the effective combination of domain knowledge and sampled data, the BN method could adapt to the change of running state of machine, and obtain satisfactory prediction accuracy. Ex- periments on spindle thermal deformation were conducted to evaluate the modeling performance. Experimental results indicate that the BN method performs far better than the least squares (LS) analysis in terms of modeling estimation accuracy.

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.

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.

Pre-Compensation for Continuous-Path Running Trajectory Error in High-Speed Machining of Parts with Varied Curvature Features

Parts with varied curvature features play increasingly critical roles in engineering, and are often machined under high-speed continuous-path running mode to ensure the machining efficiency. However, the continuous-path running trajectory error is significant during high-feed-speed machining, which seriously restricts the machining precision for such parts with varied curvature features. In order to reduce the continuous-path running trajectory error without sacrificing the machining efficiency, a pre-compensation method for the trajectory error is proposed. Based on the formation mechanism of the continuous-path running trajectory error analyzed, this error is estimated in advance by approximating the desired toolpath with spline curves. Then, an iterative error pre-compensation method is presented. By machining with the regenerated toolpath after pre-compensation instead of the uncompensated toolpath, the continuous-path running trajectory error can be effectively decreased without the reduction of the feed speed. To demonstrate the feasibility of the proposed pre-compensation method, a heart curve toolpath that possesses varied curvature features is employed. Experimental results indicate that compared with the uncompensated processing trajectory, the maximum and average machining errors for the pre-compensated processing trajectory are reduced by 67.19% and 82.30%, respectively. An easy to implement solution for high efficiency and high precision machining of the parts with varied curvature features is provided.

A Method for Identification and Compensation of Machining Errors of Digital Gear Tooth Surfaces

In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are analyzed directly from the real tooth surfaces.The topography data of the part are off-line measured in the post-process.A comparison is made between two models:CAD model of DGTS and virtual model of the physical measured surface.And a matching rule is given to determine these two surfaces in an appropriate fashion.The developed error estimation model creates a point-to-point map of the real surface to the theoretical surface in the normal direction.A“pre-calibration error compensation”strategy is presented.Through processing the results of the first trail cutting,the total compensation error is predicted and an imaginary digital tooth surface is reconstructed. The machining errors in the final manufactured surfaces are minimized by generating this imaginary surface.An example of ma- chining 2-D DGTS verifies the developed method.The research is of important theoretical and practical value to manufacture the DGTS and other digital conjugate surfaces.

IMPROVING ACCURACY OF CNC MACHINE TOOLS THROUGH COMPENSATION FOR THERMAL ERRORS

A method for improving accuracy of CNC machine tools through compensation for the thermal errors is studied. The thermal errors are obtained by 1 D ball array and characterized by an auto regressive model based on spindle rotation speed. By revising the workpiece NC machining program, the thermal errors can be compensated before machining. The experiments on a vertical machining center show that the effectiveness of compensation is good.

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.

Thermal Error Modeling Method with the Jamming of Temperature-Sensitive Points'Volatility on CNC Machine Tools

Aiming at the deficiency of the robustness of thermal error compensation models of CNC machine tools, the mechanism of improving the models＇ robustness is studied by regarding the Leaderway-V450 machining center as the object. Through the analysis of actual spindle air cutting experimental data on Leaderway-V450 machine, it is found that the temperature-sensitive points used for modeling is volatility, and this volatility directly leads to large changes on the collinear degree among modeling independent variables. Thus, the forecasting accuracy of multivariate regression model is severely affected, and the forecasting robustness becomes poor too. To overcome this effect, a modeling method of establishing thermal error models by using single temperature variable under the jamming of temperature-sensitive points＇ volatility is put forward. According to the actual data of thermal error measured in different seasons, it is proved that the single temperature variable model can reduce the loss of fore- casting accuracy resulted from the volatility of tempera- ture-sensitive points, especially for the prediction of cross quarter data, the improvement of forecasting accuracy is about 5 μm or more. The purpose that improving the robustness of the thermal error models is realized, which can provide a reference for selecting the modelingindependent variable in the application of thermal error compensation of CNC machine tools.

Key point selection in large-scale FBG temperature sensors for thermal error modeling of heavy-duty CNC machine tools

Thermal error is one of the main factors that influence the machining accuracy of computer numerical control(CNC)machine tools.It is usually reduced by thermal error compensation.Temperature field monitoring and key temperature measurement point(TMP)selection are the bases of thermal error modeling and compensation for CNC machine tools.Compared with small-and medium-sized CNC machine tools,heavy-duty CNC machine tools require the use of more temperature sensors to measure their temperature comprehensively because of their larger size and more complex heat sources.However,the presence of many TMPs counteracts the movement of CNC machine tools due to sensor cables,and too many temperature variables may adversely influence thermal error modeling.Novel temperature sensors based on fiber Bragg grating(FBG)are developed in this study.A total of 128 FBG temperature sensors that are connected in series through a thin optical fiber are mounted on a heavy-duty CNC machine tool to monitor its temperature field.Key TMPs are selected using these large-scale FBG temperature sensors by using the density-based spatial clustering of applications with noise algorithm to reduce the calculation workload and avoid problems in the coupling of TMPs for thermal error modeling.Back propagation neural network thermal error prediction models are established to verify the performance of the proposed TMP selection method.Results show that the number of TMPs is reduced from 128 to 5,and the developed model demonstrates good prediction effects and strong robustness under different working conditions of the heavy-duty CNC machine tool.

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.

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.

Error compensation for precision machine tools

As one of the ways to improve the machining accuracy of machine tools, error compensation is reviewed from different view points, and the main barriers to further improvement of efficiency of error compensation are analyzed in detail and the vista of the error compensation in precision and ultra precision machines is discussed.

STUDY ON THE FEEDFORWARD COMPENSATION OF THE MOTIONERRORS OF NC MACHINE TOOLS

A feedforward compensation naethod of the motion errors of NC machine tools imple- mented with software is proposed , with which the motion errors can be compensated whithout changing the original computer control systems of the NC machine tools. The experimental results show that the circular interpolation profile machining errors decrease by a factor of 2/3 after com- pensated.

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.

CNC Thermal Compensation Based on Mind Evolutionary Algorithm Optimized BP Neural Network

Thermal deformation error is one of the most important factors affecting the CNCs’ accuracy, so research is conducted on the temperature errors affecting CNCs’ machining accuracy;on the basis of analyzing the unpredictability and pre-maturing of the results of the genetic algorithm, as well as the slow speed of the training speed of the particle algorithm, a kind of Mind Evolutionary Algorithm optimized BP neural network featuring extremely strong global search capacity was proposed;type KVC850MA/2 five-axis CNC of Changzheng Lathe Factory was used as the research subject, and the Mind Evolutionary Algorithm optimized BP neural network algorithm was used for the establishment of the compensation model between temperature changes and the CNCs’ thermal deformation errors, as well as the realization method on hardware. The simulation results indicated that this method featured extremely high practical value.

Numerical Investigation of Thermal Behavior of CNC Machine Tool and Its Effects on Dimensional Accuracy of Machined Parts

The dimensional accuracy of machined parts is strongly influenced by the thermal behavior of machine tools (MT). Minimizing this influence represents a key objective for any modern manufacturing industry. Thermally induced positioning error compensation remains the most effective and practical method in this context. However, the efficiency of the compensation process depends on the quality of the model used to predict the thermal errors. The model should consistently reflect the relationships between temperature distribution in the MT structure and thermally induced positioning errors. A judicious choice of the number and location of temperature sensitive points to represent heat distribution is a key factor for robust thermal error modeling. Therefore, in this paper, the temperature sensitive points are selected following a structured thermomechanical analysis carried out to evaluate the effects of various temperature gradients on MT structure deformation intensity. The MT thermal behavior is first modeled using finite element method and validated by various experimentally measured temperature fields using temperature sensors and thermal imaging. MT Thermal behavior validation shows a maximum error of less than 10% when comparing the numerical estimations with the experimental results even under changing operation conditions. The numerical model is used through several series of simulations carried out using varied working condition to explore possible relationships between temperature distribution and thermal deformation characteristics to select the most appropriate temperature sensitive points that will be considered for building an empirical prediction model for thermal errors as function of MT thermal state. Validation tests achieved using an artificial neural network based simplified model confirmed the efficiency of the proposed temperature sensitive points allowing the prediction of the thermally induced errors with an accuracy greater than 90%.

A stepwise camera calibration method incorporating compensation for eccentricity error

In visual measurement,high-precision camera calibration often employs circular targets.To address issues in mainstream methods,such as the eccentricity error of the circle from using the circle’s center for calibration,overfitting or local minimum from fullparameter optimization,and calibration errors due to neglecting the center of distortion,a stepwise camera calibration method incorporating compensation for eccentricity error was proposed to enhance monocular camera calibration precision.Initially,the multiimage distortion correction method calculated the common center of distortion and coefficients,improving precision,stability,and efficiency compared to single-image distortion correction methods.Subsequently,the projection point of the circle’s center was compared with the center of the contour’s projection to iteratively correct the eccentricity error,leading to more precise and stable calibration.Finally,nonlinear optimization refined the calibration parameters to minimize reprojection error and boosts precision.These processes achieved stepwise camera calibration,which enhanced robustness.In addition,the module comparison experiment showed that both the eccentricity error compensation and the camera parameter optimization could improve the calibration precision,but the latter had a greater impact.The combined use of the two methods further improved the precision and stability.Simulations and experiments confirmed that the proposed method achieved high precision,stability,and robustness,suitable for high-precision visual measurements.