Error Model Of Machine Tool Research Articles

Recent Patents on Thermal Characteristic Analysis and Modeling of Machine Tools

Abstract: Modern machining machines are becoming more sophisticated and automated, but the problems of thermal deformation caused by machining have also come to the fore. CNC machine tools are used in high-speed, high-feed rate machining conditions, so the impact of thermal deformation factors will lead to a more prominent loss of accuracy. In this context, the design and manufacture of future CNC machine tools need to take further account of the errors caused by thermal deformation and the accompanying loss of accuracy. The principle of thermal characterisation and thermal error modeling of machine tools is to measure and reasonably analyse the machine tool at different temperature points and make corrections to the analysis data in order to get a value as close as possible to the real value and improve machining accuracy. Several representative patents and studies on thermal characterisation and thermal error modeling of machine tools at home and abroad are reviewed. This study presents a selection and summary of a large number of recent patents and studies on machine tool thermal characterisation and thermal error modeling, focusing on the selection of the machine tool thermal error measurement point area, thermal error modeling methods, spindle thermal displacement compensation, and other aspects, and discusses the future trends in the mainstream methods for reducing the thermal error of machine tools. The analysis and modeling of thermal errors in machine tools have an integral influence on further improvements in machining accuracy and efficiency in the future.

Modeling and compensation of enhanced volumetric error of machine tools containing crosstalk errors

The error compensation method is an economical and effective method to improve the machining accuracy of machine tools. Conventional volumetric error modeling of machine tools is based on the rigid body kinematics model using 21 terms of geometric errors and assumes the geometric error of one axis is independent of other axes. However, if the error motion does not satisfy this assumption in serial machine tools, it may significantly influence the overall machine tool accuracy. This paper reveals the existence of mutual crosstalk of angular errors in coupling axes by experiments with equipping the five-degree-of-freedom (5-DOF) embedded sensor module in each axis. A new on-machine measurement method is proposed for detecting crosstalk errors of the coupling axes covering the whole coupling area. It is confirmed that the position-dependent geometric errors (PDGEs) of each axis should be modified by two-dimensional dependence. Therefore, extended from the normal volumetric error model (NVEM) that is commonly used nowadays, a novel enhanced volumetric error model (EVEM) that contains crosstalk's PDGEs is proposed. The real-time error compensation controller (RECC) embedded in CNC system kernel has been developed in collaboration with the vender by writing in the application function. The effectiveness and feasibility of the EVEM and RECC are verified by non-cutting and cutting experiments. Through comparison tests with laser interferometer on body diagonals, the accuracy improving rate of EVEM is about 10 % higher than NVEM. The real-cutting tests on the ISO10791 sample are verified by a CMM and the results show the accuracy improvement of EVEM is better than NVEM by about 20 %.

Robust thermal error estimation for machine tools based on in-process multi-point temperature measurement of a single axis actuated by a ball screw feed drive system

In machine tools, thermal errors account for 70 % of the total machining errors. The latest improvements in sensor technology have enabled the robust estimation of thermal displacement using the multi-point temperature data of an entire structure. The complex geometry and constant motion of a feed drive system make the direct measurement of temperature difficult because of the sensor power supply and data transmission. In this study, a wireless multi-point temperature sensor system was developed, and the temperature of a ball screw was measured. The ball screw was developed with a built-in temperature sensor array and was installed in an actual machining center. Thermal error measurement tests were conducted, wherein the temperatures of 277 points on the structure and 25 points on the Z-axis ball screw were measured during machine operation. Using finite element analysis (FEA) with multi-point temperature mapping of the drive system, the difference between the relative displacement of the tool center point (TCP) along the Z-axis, measured by an eddy current sensor, and the value estimated by the FEA was calculated to be less than 10 μm. However, the Z-axis ball screw temperature distribution contributed little to the accuracy of thermal displacement estimation along other axes. Therefore, a superposition of the thermal displacements of the structure and drive system provided TCP relative displacement, suggesting the effect of temperature-dependent geometric errors on the volumetric error model of machine tools.

Thermal error modeling of machine tool based on dimensional error of machined parts in automatic production line

Thermally induced error has proven to be the major source of machining error for the machine tool working in a non-temperature-controlled workshop. Current research on thermal error modeling and compensation is implemented based on the measured thermal deformation of machine tool, and the data is obtained referring to spindle idling rather than metal cutting condition, resulting in the disadvantages of the established model with low adaptability to varying conditions. In this paper, a modeling and compensation method based on the dimensional error of the machined parts is proposed to address the issue and verified through machine tools in an automatic production line. Compared with the modeling based on thermal deformation, the method formulates a more direct relations between temperature rise and machining error. The thermal error modeling is carried out by measuring the dimension deviation of the inner hole diameter of the motor end cover and the screened representative temperature variables. Meantime, considering the temperature coefficient in model is difficult to converge when modeling with the single-day data, the unified modeling with the multi-day data is realized by improving the conventional multiple linear regression model. Finally, the generalized model used for thermal error compensation in x direction of the machine tool is obtained. The real-time compensation of the thermal error based on the established model is realized with the machine tool machining in mass production. The verification results show that this error modeling and compensation method can reduce the machining error of the end cover by more than 52%, irrespective of experiencing various complicated working conditions. Stability and robustness of the modeling are also validated through application on the other machine tool with the same configuration and real machining over seven days.

Improved exponential model for thermal error modeling of machine-tool spindle based on fruit fly optimization algorithm

Establishing a robust thermal error model is crucial for thermal error compensation of machine tools. In this paper, an improved exponential model for thermal error modeling was proposed. First, the improved exponential model is established by combining the exponential model and the temperature-dependent model. Second, the improved fruit fly optimization algorithm is used to determine the parameters. Finally, two strategies are used to select the optimal sensor location from six potential ambient temperature sensors. The ambient temperature data is proved to be effective in improving the robustness of the model. The average root mean square error of the proposed model, the exponential model without ambient temperature, and the linear model are 1.18 μm, 1.79 μm, and 2.70 μm, respectively. The modeling results show that the proposed model has high accuracy and strong robustness, which is suitable for workshop environment and variable conditions in thermal error modeling of machine tools.

Enhancing machining accuracy reliability of multi-axis CNC Indexed by: machine tools using an advanced importance sampling method

The purpose of this paper is to propose a general precision allocation method to improve machining performance of CNC machine tools based on certain design requirements. A comprehensive error model of machine tools is established by using the differential motion relation of coordinate frames. Based on the comprehensive error model, a reliability model is established by updating the primary reliability with an advanced importance sampling method, which is used to predict the machining accuracy reliability of machine tools. Besides, to identify and optimize geometric error parameters which have a great influence on machining accuracy reliability of machine tools, the sensitivity analysis of machining accuracy is carried out by improved first-order second-moment method. Taking a large CNC gantry guide rail grinder as an example, the optimization results show that the method is effective and can realize reliability optimization of machining accuracy.

Applying Integrated Grey System Theory and Sensor Technology to Study Influence of Cutting Conditions on Thermal Error Modeling of Machine Tools

Applying Integrated Grey System Theory and Sensor Technology to Study Influence of Cutting Conditions on Thermal Error Modeling of Machine Tools

Thermal Error Modeling for Machine Tools: Mechanistic Analysis and Solution for the Pseudocorrelation of Temperature-Sensitive Points

The temperature-sensitive point is the input variable of the thermal error compensation model of computer numerical control (CNC) machine tools. At present, the most commonly used selection method is to measure the multipoint temperature and thermal error of the machine tool synchronously and select several temperature measurement points with the highest thermal error correlation as temperature-sensitive points according to the measurement data. This study reveals that this method sometimes has obvious mis-selection and causes the model to fail. The reason is that the weak correlation temperature measurement point away from the machine tool heat source amplifies the volatility of the correlation evaluation result, owing to the small overall change. If the calculated result exceeds the true strong correlation temperature measurement point, it will be incorrectly selected as the temperature-sensitive point. This scenario has been termed herein as the pseudocorrelation problem. With the gradual popularization of thermal error compensation technology for CNC machine tools, pseudocorrelation will seriously affect the mass production pass rate. Therefore, the study analyzes and rigorously proves the mathematical mechanism of this problem, and the temperature measurement point preselection algorithm based on the correlation coefficient volatility determination factor (CCVDF) is proposed to eliminate potential pseudocorrelation temperature points before selecting temperature-sensitive points. After 1000 random simulation experiments, the failure rate of Z-direction thermal error modeling after preselection decreased from 5.1% to 0.5%, and the Y-direction error decreased from 33.7% to 1.5%. This algorithm can greatly improve the qualification rate of large-scale equipment of thermal error compensation technology.

The selection of temperature-sensitivity points based on K-harmonic means clustering and thermal positioning error modeling of machine tools

In the thermal error compensation technology of CNC machine tools, the core is to establish a mathematical model of thermal error with high predictive accuracy and strong robustness. The prerequisite for the error model is to select the optimum temperature-sensitivity points, which can inhibit the multi-collinearity problem among temperature points and improve the predictive accuracy and robustness of the error model. In this paper, K-harmonic means (KHM) clustering is introduced for the first time to select the temperature-sensitivity points in the field of error modeling. In statistical numerical experiments, it is verified that KHM clustering is very stable and requires relatively small number of iterations to converge comparing with the common clustering methods such as K-means (KM) clustering and fuzzy C-means clustering (FCM). Then, the effect of KHM clustering on the selection of temperature-sensitivity points is validated in the actual experiments. Multiple linear regression model combined with KHM clustering (MLR-KHM) is adopted to construct the thermal error model of positioning error. The experimental results demonstrate that the predictive accuracy and robustness of MLR-KHM error model can conform with the requirements of the error compensation.

Thermal error modeling and compensation of a heavy gantry-type machine tool and its verification in machining

In order to derive a thermal error model that can better reflect the physical model of the machine tool to improve the model’s robustness and also has an explicit and simpler expression for real-time thermal error compensation, a new thermal error model of a heavy gantry-type machine tool was established. Firstly, multi-body system (MBS) was used to transform the thermal error modeling of the machine tool into the thermal error modeling of the discrete parts of the machine tool. Then, as for the thermal error modeling of the slider-ram structure, by analyzing the characteristic of the thermal expansion of a one-dimensional rod, power function was considered to better reflect that relationship in which the index number can represent the distance between heat source and the temperature measurement location. Then, its thermal error model was expressed as the superposition of two power functions according to the thermal superposition principle and the distribution of the heat sources. As for the thermal error modeling of gantry structure, it was simplified to a frame with −3 DOF. And its thermal error model was derived by virtual work principle (VWP). Then, the whole thermal error model of the machine tool was embedded into the Simens840d NC system and S7-300 programmable logic controller to establish a thermal error compensation system. Finally, the error model and compensation was verified by machining a rhombus-shaped workpiece of which different zones reflect the thermal error in different directions. And the workpiece was measured by a CMM. The results show that the average thermal error can be reduced from around 101 to 13.5 μm after the compensation, indicating the effectiveness of the thermal error modeling and compensation for the practical application.

A Temperature Sensor Clustering Method for Thermal Error Modeling of Heavy Milling Machine Tools

A clustering method is an effective way to select the proper temperature sensor location for thermal error modeling of machine tools. In this paper, a new temperature sensor clustering method is proposed. By analyzing the characteristics of the temperature of the sensors in a heavy floor-type milling machine tool, an indicator involving both the Euclidean distance and the correlation coefficient was proposed to reflect the differences between temperature sensors, and the indicator was expressed by a distance matrix to be used for hierarchical clustering. Then, the weight coefficient in the distance matrix and the number of the clusters (groups) were optimized by a genetic algorithm (GA), and the fitness function of the GA was also rebuilt by establishing the thermal error model at one rotation speed, then deriving its accuracy at two different rotation speeds with a temperature disturbance. Thus, the parameters for clustering, as well as the final selection of the temperature sensors, were derived. Finally, the method proposed in this paper was verified on a machine tool. According to the selected temperature sensors, a thermal error model of the machine tool was established and used to predict the thermal error. The results indicate that the selected temperature sensors can accurately predict thermal error at different rotation speeds, and the proposed temperature sensor clustering method for sensor selection is expected to be used for the thermal error modeling for other machine tools.

The tool following function-based identification approach for all geometric errors of rotary axes using ballbar

This paper proposes a tool following function-based identification approach (TFFIA) for geometric errors of two rotary axes for one five-axis machine tool. It is comprehensive to identify all geometric errors of rotary errors. Firstly, synthetic error formulas of ballbar originate from the geometric error model of machine tools in order to consider the influences of 21 errors of three translational axes. It makes the approach more reasonable and precise. Secondly, the structures of three measurement patterns of TFFIA are described. Thirdly, in each pattern, errors of rotary axes affecting the accuracy of the sensitive direction are identified. As the result, the identification equations of all 20 errors coincide with the geometric properties of errors. Moreover, the impacts of setup errors of ballbar are eliminated with least square method to improve the precise of TFFIA. According to the structures of three patterns, only three installation of workpiece ball of ballbar are needed in the whole identification of two rotary axes to obtain the required ballbar readings. It greatly shortens the measurement time. Twenty geometric errors of two rotary axes are calculated with identification equations and ballbar readings. Finally, TFFIA is applied to a SmartCNC500 five-axis vertical machining center. The corresponding comparisons are proposed to verify the effectiveness and accuracy of TFFIA.

Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction

This paper presents geometric error compensation of CNC machine tools based on workpiece model modification and the numerical solution of equation set. Firstly, the nominal cutter position is introduced to the geometric error model of machine tool as the compensation goal according to the kinematics of three-axis machine tools. With the polynomials of basic error components, the polynomials of the geometric error model are established, which are the functions about movements of all axes and nominal NC code. The accurate compensation is represented as solution of corresponding simultaneous equations. The high-efficiency numerical calculation can obtain the compensated NC code. Secondly, the polynomial equations about points of workpiece are established based on the simple relationship between workpiece model and NC codes. The compensated points are calculated using numerical solution. STL is chose as the format of reconstructed workpiece model. In order to obtain the precise workpiece model with compensated points, one conversion approach from CAD model to STL model is proposed. The number of points calculated with isoparametric method can control the precision of STL. The reconstructed STL model is inputted to CAM software to generate processing file for machining. The input of the proposed compensation is CAD model of workpiece rather than NC codes and CL data. It makes the compensation convenient and suitable for different three-axis machine tools. Finally, the experiments are carried out on Carver800T CNC machine tool to testify the effectiveness of proposed geometric error compensation.

A novel linear virtual temperature constructing method for thermal error modeling of machine tools

When a thermal error model of a machine tool is established, selecting the appropriate temperature measurement point is a very difficult problem. This paper proposes a novel method for constructing a linear virtual temperature. The proposed method can overcome the problem of selecting the temperature measurement point. First, temperature-thermal expansion hysteresis characteristics are used to divide the temperature measurement points into two groups. Each temperature variable is then chosen through a principal component analysis (PCA). Finally, using two temperature-variable weights and the correlative coefficient thermal displacement as the maximum optimal indexes, two temperature-weighted coefficients are calculated, and a linear virtual-temperature variable related to the thermal error linearity is then formed. In establishing the proposed thermal error model, the linear virtual temperature formed can serve as a system input variable. The proposed method was tested on a three-axis milling machine to determine the spindle Z-axial thermal error, and the results show that the root mean square error (RMSE) is reduced by 11 % and the sum of the squares of the error (SSE) is reduced by 39 % in comparison with a direct application of a temperature variable when establishing such a model. In the proposed method, only two temperature measurement points are used to establish a model, through which the complexity in determining the optimal measurement points through a traditional method, along with the number of temperature measurement points required, is greatly reduced.

Review on Thermal Error Modeling of Machine Tools

Review on Thermal Error Modeling of Machine Tools

Fluctuation prediction of machining accuracy for multi-axis machine tool based on stochastic process theory

Geometric error has significant influence on the processing results and reduces machining accuracy. Machine tool geometric errors can be interpreted as a deterministic value with an uncertain fluctuation of probabilistic distribution. Although, the uncertain fluctuation can not be compensated, it has extremely profound significance on the precision and ultra-precision machining to reduce the fluctuation range of machining accuracy as far as possible. In this paper, a typical 3-axis machine tool with high precision is selected and the fluctuations in machining accuracy are studied. The volumetric error modeling of machine tool is established by multi-body system (MBS) theory, which describes the topological structure of MBS in a simple and convenient matrix form. Based on the volumetric error model, the equivalent components of the errors for the three axes are established by reducing error terms. Then, the fluctuations of equivalent errors and the machining accuracy in working planes are depicted and predicted using the theory of stochastic process, whose range should be controlled within a certain confidence interval. Furthermore, the critical geometric errors that have significant influence on the machining accuracy fluctuation are identified. Based on the analysis results, some improvement in the machine tool parts introduced and the results for the modified machine show that the prediction allow for reduction in errors for the precision and ultra-precision machining.

Error Model of Machine Tool Based on Cutter Contacting Point Vector Chain

Error modeling and analysis can improve the manufacturing precision and the error compensation accuracy of machine tool. According to the surface of the parts topography information, this paper puts forward a kind of error model of machine tool based on cutter contacting point vector chain. Based on analyzing the cutter contacting point of one tool path which is on the surface of the parts, Based on analyzing action rules of a single cutter contacting point error, the cumulative rules of errors and calculation methods were introduced detailedly, and an application demonstration is given.

A new error measurement method to identify all six error parameters of a rotational axis of a machine tool

This paper presents a new error measurement method, a Dual Optical Path Measurement Method (DOPMM), to identify error parameters of the rotational axis of a machine tool along its error sensitive directions. The method development was carried out on a motorized rotary stage equipped with a Doppler laser instrument. An error measurement experiment and a machining experiment were conducted on a five-axis machining center with a titling rotary table. It was found that the DOPMM can identify all of the six volumetric error parameters with the simple algebraic operations. Compared with the existing ball bar tests, which need a mathematical error modeling of machine tools to separate the error parameters, the identified process of DOPMM is more simple and easier to understand. And the operation of machine tools during the measurement is much easier than that of the existing ball bar tests. The experimental results showed that the part precision can have a significant improvement of 68% when the identified error parameters are used for error compensation. Hence, the measurement method established in this study is sensible and efficient, and could be used for the error compensation on a wide range of machine tools to improve their machining precision.

The Error Analysis of Ultra-Precision Diamond Turning Machine Based on Tool Swing Feeding

In the respect of ultra-precision manufacturing of axisymmetric surface, the machine tool with tool swing feeding has less interpolation error sources compared to the conventional ultra-precision diamond turning machine tool. The installation errors of machine tool greatly affect the manufacturing accuracy of parts. Therefore, based on the multi-body dynamics theory , the structure characteristics of this machine tool, and the parts' relative positions of machine tool, in this paper we established the space geometric model and the integrated error model of machine tool integrated with the actual installation error of machine. The analysis results of the error model show that the relationship between the depth of axis (tool shaft and main shaft of machine) parallelism and the profile error is linear function; when the installation error of swing arm was lower than 150′′,the profile error of parts was less than λ/10.

Identification, development and testing of thermal error compensation model for a headstock assembly of CNC turning centre

In CNC machine tools, transient temperature variation in the headstock assembly is the major contributors for spindle thermal error. The compensation of thermal error is critical for ensuring the accuracy of machine tool. The performance of an error compensation system depends largely on the accuracy and robustness of the thermal error model. In the present work, a robust thermal error model is developed for minimizing the error in lateral direction of the spindle which significantly influences the geometrical accuracy of the workpiece. Analysis-of-variance (ANOVA) is applied to the results of the experiments in determining the percentage contribution of each individual temperature key point against a stated level of confidence. Based on the analysis of existing approaches for thermal error modeling of machine tools, an approach of LASSO (least absolute shrinkage and selection operator) is proposed in order to avoid the multi collinearity problem. The proposed method is an innovative variable selection method to remove redundant or unimportant temperature key points in the linear thermal error model and minimize the residual sum of squares. The predictive error model is found to have better robustness and accuracy in comparison to the combination of grey correlation and step wise linear regression for error compensation of CNC lathe. Keywords: Analysis Of Variance (ANOVA), CNC Machine Tool, Grey Correlation Analysis (GCA), Headstock Assembly, LASSO Regression, Mean Absolute Deviation (MAD), Mean Square Error (MSE), Robustness, Standard Deviation (SD), Thermal Error.