Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

Fast calibration and modeling of thermally-induced machine tool errors in real machining

Calibration and modeling of thermally induced errors is a critical part of enhancing machine accuracy by software error compensation. In most applications, parametric thermal errors of a machine tool are calibrated and modeled individually by air-cutting experiments. Calibrating thermal errors individually is time-consuming and may neglect thermal interaction among thermal sources. The accuracy of the air-cutting model in real machining is also questionable. In this report, thermal errors of multiple machine axes in real cutting were calibrated simultaneously by a quick set-up measurement system consisting of on-machine probes and artifacts. Characteristics of thermal errors in real cutting under different cutting conditions, cutting paths and workpiece materials were investigated. It was found that thermal errors in real machining were distinct from those in air cutting.     

Modelling geometric and thermal errors in a five-axis cnc machine tool

The total volumetric error within the workspace of a machine tool is induced by the propagation of both scalar and position dependent geometrical errors, as well as time-variant thermal errors. This paper presents a compact volumetric error model which can be used as a basis for a practical compensation scheme. The broad objective is to increase the achievable accuracy of an industrial five-axis CNC machine tool. In place of using Denavit-Hartenberg (D-H) transformations, the method used here directly considers the shape and joint transformations for inaccurate links and joints using small angle approximations and then finds the total volumetric error in the workspace as a function of all the possible errors.The development of the model shows that angular deviations are independent of translational errors. However, the tool point deviations are dependent on both translational and rotational errors. The model has been used for the design and testing of a compensation strategy. The simulation studies indicate that CNC compensation for errors in X, Y and Z axes is possible. However, the capability of the CNC compensation for pitch, roll and yaw errors is dependent on the positioning of the rotary axes on the machine tool. This is shown by an example using the compensation scheme developed.     

基于敏感度分析的机床关键几何误差元素辨识与评定

为了正确识别和判定机床关键几何误差元素对机床精度设计的影响,以PCV-620立式加工中心为研究对象,采用多体系统理论建立机床空间误差模型,从而得到机床几何误差元素与机床精度之间的关联函数。对空间误差模型进行灵敏度分析,获得机床各运动方向的局部灵敏度系数,完成机床关键几何误差元素的初步辨识。以局部灵敏度系数为基础,提出一种与局部灵敏度系数和工作空间中任意位置处的几何误差元素值相关的全局灵敏度系数计算方法,将其作为机床关键几何误差元素的辨识和评定标准,分析得到PCV-620立式加工中心的关键几何误差元素包含3项定位误差、3项垂直度误差和5项直线度误差。     

Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools

In order to investigate the effect of thermal expansion on the ball screw feed drive system of a precision boring machine tool, theoretical modeling of and experimental study on thermally induced error along with heat generation characteristics are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure and collect the thermodynamic data with the feed drive system operating at different speeds. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. Relationships between the thermal error and axial elongation are established to characterize the thermal error distribution considering the thermal expansion coefficient as a temperature-variant parameter. It turns out that the thermal error varies with different working positions through the ball screw length and working time nonlinearly, and there definitely exists certain transform from the thermal expansion to the thermal error obtained by measurement. In addition, regression analysis is employed to carry out the theoretical modeling of thermal error with the temperature data of the critical heat generation points. The relations between temperature rise and thermal error are formulated directly while taking the thermal expansion as an implicit variable. Experiments under a different condition are preformed and the proposed methods for thermal error modeling prove to be effective and accurate enough to be used in the machining process as well.     

Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools

Fixe-axis capabilities on machine tools are becoming increasingly common. However, the problem of modeling the propagation of errors of individual axes through the kinematic chain, and their effect on the position and orientation errors of the cutting tool in the machine's work space has not been addressed. To increase the accuracy capabilities of such machines it is crucial to be able to study this propagation and develop approaches to minimize their effects on the errors at the tool tip. This paper discusses an approach to model the effects of the positioning errors of a machine's axes on the accuracy (positioning and orientation) of the cutting tool in its work space. Computer programs are developed for implementing the models and generating error contours or maps showing the variation of the different components of a machine's volumetric errors in its work space. This is a useful tool that can be used in machine tool design for the budgeting of errors and for optimization of a machine's accuracy.     

Adaptive compensation of quasi-static errors for an intrinsic machine

An adaptive compensation strategy for quasi-static error correction in intrinsic machines is proposed and tested. The proposed methodology consists of systematic modelling of the machine forward kinematics, including quasi-static errors, as well as direct modelling of the inverse kinematics using nonlinear regression analysis. The result is a model which is a hybrid of physical modelling and regression analysis modelling. In addition, the methodology includes a compensation strategy of the machine contouring errors using the state observer technique for on-line adaptive compensation. A CMM is chosen as a test bed for validation of the proposed methodology. Systematic modelling is carried out in two stages for the forward and inverse kinematics. Regression based models are verified using two different tests. The statistical analysis of variance technique (ANOVA) is used to select the best model in addition to model testing using an independent set equal to approximately 10% of the fitting data. The obtained models are then employed in two compensation strategies; one for the measurement error correction, and another one for the contouring error correction by motion command modification in the forward control path. For contouring tests, the CMM behavior at different thermal states is estimated using experimentally obtained Effective Coefficient of Thermal Expansion (ECTE). Simulations of the machine in contouring selected trajectories are carried out over a range of thermal states. Results obtained show an improvement in the CMM performance to a level close to the machine resolution. The CMM performance is tested using the standard ASME B.89.1.12M-1990 evaluation test, as well as a novel modified version of the test accounting for a thermally varying environment. Machine errors are significantly reduced using the proposed methodology.     

Error compensation in machine tools — a review: Part I: geometric,cutting-force induced and fixture-dependent errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

扩大并联机床工作空间方法的研究

在计算并联机床工作空间时,由于其约束条件较多,因此在一定程度上影响了它的加工能力,为了扩大它的工作空间,在机床的工作台上安装一个转台,这就涉及到从刀位文件中进行转台转角分解的问题。采用传统的分解方法,住往产生章动角超出机床工作空间的问题。因此,针对机床坐标系和工件坐标系的关系,采用一致坐标系转台转角分解和非一致坐标系转台转角分解方法来解决这个问题。非一致坐标系转台分解是在一致坐标系转台转角分解的基础上进行二次分解,在工件定位时设定初始角,使章动角回到机床的工作空间内,从而达到扩大并联机床工作空间的目的。     

Error compensation in machine tools — a review: Part II: thermal errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

Geometric and force errors compensation in a 3-axis CNC milling machine

This paper proposes a new off line error compensation model by taking into accounting of geometric and cutting force induced errors in a 3-axis CNC milling machine. Geometric error of a 3-axis milling machine composes of 21 components, which can be measured by laser interferometer within the working volume. Geometric error estimation determined by back-propagation neural network is proposed and used separately in the geometric error compensation model. Likewise, cutting force induced error estimation by back-propagation neural network determined based on a flat end mill behavior observation is proposed and used separately in the cutting force induced error compensation model. Various experiments over a wide range of cutting conditions are carried out to investigate cutting force and machine error relation. Finally, the combination of geometric and cutting force induced errors is modeled by the combined back-propagation neural network. This unique model is used to compensate both geometric and cutting force induced errors simultaneously by a single model. Experimental tests have been carried out in order to validate the performance of geometric and cutting force induced errors compensation model.     

数控机床热误差补偿建模综述

热误差建模技术是决定热误差补偿能否有效进行的关键,对提高数控机床的加工精度至关重要。介绍数控机床热误差建模的国内外研究状况,阐述国内外常用的几种主要的热误差建模方法,即人工智能法、统计分析法、灰色系统法等,探讨各种方法的特点,指出目前研究存在的问题,并展望未来的发展。     

A displacement measurement approach for machine geometric error assessment

It is complicated and time-consuming to evaluate the performance of a machine tool. In this research, a displacement method is proposed to shorten the measurement time and to simplify the measurement. By measuring the positioning errors along the 15 lines in the machine work zone, a total of 21 geometric error components can be determined. Among the 15 lines, seven of them are mandated by the ANSI/ASME standard for the performance evaluation of CNC machining centers. Therefore, only eight additional positioning error measurements are necessary to evaluate the machine's performance. The results from the experimental tests show that the method is feasible and accurate. This method shortens the calibration time and is beneficial, particularly to the reconfigurable machining system, which needs frequent calibration.     

Computer-aided accuracy enhancement for multi-axis CNC machine tool

A computer-aided error compensation scheme has been developed to enhance the accuracy of multi-axis CNC machine tools by compensating for machine geometric and thermal errors in software way. Stationary geometric errors including the coupling effect of linkage errors between machine slides are calibrated off line. Dynamic thermal errors are predicted on line by an artificial neural network model. Because machine errors are variant with the cutting time and slide positions, a PC based compensation controller has been developed to upgrade commercial CNC controllers for real-time error compensation. The real-time compensation capability is achieved by digital I/0 communication between the compensation controller and CNC controller without the need of any hardware modification to the machine servo-drive loops. The compensation scheme implemented on a horizontal machining center has been proven to improve the machine accuracy by one order of magnitude using a laser interferometer and cutting test.     

Analysis of thermal errors in a high-speed micro-milling spindle

Thermally induced errors account for the majority of fabrication accuracy loss in an uncompensated machine tool. This issue is particularly relevant in the micro-machining arena due to the comparable size of thermal errors and the characteristic dimensions of the parts under fabrication. A spindle of a micro-milling machine tool is one of the main sources of thermal errors. Other sources of thermal errors include drive elements like linear motors and bearings, the machining process itself and external thermal influences such as variation in ambient temperature. The basic strategy for alleviating the magnitude of these thermal errors can be achieved by thermal desensitization, control and compensation within the machine tool.This paper describes a spindle growth compensation scheme that aims towards reducing its thermally-induced machining errors. The implementation of this scheme is simple in nature and it can be easily and quickly executed in an industrial environment with minimal investment of manpower and component modifications.Initially a finite element analysis (FEA) is conducted on the spindle assembly. This FEA correlates the temperature rise, due to heating from the spindle bearings and the motor, to the resulting structural deformation. Additionally, the structural deformation of the spindle along with temperature change at its various critical points is experimentally obtained by a system of thermocouples and capacitance gages.The experimental values of the temperature changes and the structural deformation of the spindle qualitatively agree well with the results obtained by FEA. Consequently, a thermal displacement model of the high-speed micro-milling spindle is formulated from the previously obtained experimental results that effectively predict the spindle displacement under varying spindle speeds. The implementation of this model in the machine tool under investigation is expected to reduce its thermally induced spindle displacement by 80%, from 6 microns to less than 1 micron in a randomly generated test with varying spindle speeds.     

A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test

This paper proposes a machining test to parameterize error motions, or position-dependent geometric errors, of rotary axes in a five-axis machine tool. At the given set of angular positions of rotary axes, a square-shaped step is machined by a straight end mill. By measuring geometric errors of the finished test piece, the position and the orientation of rotary axis average lines (location errors), as well as position-dependent geometric errors of rotary axes, can be numerically identified based on the machine׳s kinematic model. Furthermore, by consequently performing the proposed machining test, one can quantitatively observe how error motions of rotary axes change due to thermal deformation induced mainly by spindle rotation. Experimental demonstration is presented.     

Thermal behavior of a machine tool equipped with linear motors

Development of a feed drive system with high speed and accuracy has been a major issue in the machine tool industry. Linear motors can be used as efficient tool to achieve the high speed and accuracy. However, a high speed feed drive system with linear motors, in turn, can generate heat problems. Also, frictional heat is produced at the ball or roller bearing of LM block when driven at high speed. It can affect the thermal deformation of the linear scale as well as that of the machine tool structure.In this paper, important heat sources and resulting thermal errors in a machine tool equipped with linear motors were investigated when it was operated at high speed. The thermal deformation characteristics were identified through measuring the thermal error caused from thermal deformation of the linear scale and the machine tool structure. The dominant thermal error components were identified from the thermal error analysis using finite element method. It was shown that the proposed analysis scheme is efficient in identifying the dominant thermal error components and its magnitudes such as the thermal expansion and movement of the linear scale, thermal deformation of the machine tool slide.     

A systematic optimization approach for the calibration of parallel kinematics machine tools by a laser tracker

Parallel kinematics machine has attracted attention as machine tools because of the outstanding features of high dynamics and high stiffness. Although various calibration methods for parallel kinematics machine have been studied, the influence of inaccurate motion of joints is rarely considered in these studies. This paper presents a high-accuracy and high-effective approach for calibration of parallel kinematics machine. In the approach, a differential error model, an optimized model and a statistical method are combined, and the errors of parallel kinematics machine due to inaccurate motion of joints can be reduced by this approach. Specifically, the workspace is symmetrically divided into four subspaces, and a measurement method is suggested by a laser tracker to require the actual pose of the platform in these subspaces. An optimized model is proposed to solve the kinematic parameters in symmetrical subspaces, and then arithmetical mean method is proposed to calculate the final kinematic parameter. In order to achieve the global optimum quickly and precisely, the initial value of the optimal parameter is directly solved based on the differential error model. The proposed approach has been realized on the developed 5-DOF hexapod machine tool, and the experiment result proves that the presented method is very effective and accurate for the calibration of the hexapod machine tool.     

Durability evaluation of software error correction on a machining center

Machine tool software error correction has been successfully demonstrated in laboratories for at least the last 20 years. However, no results could be found that evaluate the durability of such an approach. To be cost beneficial for industry, the time consuming measurement procedure needs to be as infrequent as possible. This study attempts to quantify the durability of such an approach on a commercial 3-Axis machining center. A traditional correction model is created and implemented inside the control system along with a first order thermal correction of the scales. Measurements are made with the Laser Ball Bar, which minimizes data collection to less than 30 min. The compensation system was evaluated over a 9 month period in which the machine experienced normal machining and common mishaps (tool crash). The results show that during this 9 month period, the compensation system was still capable of significantly reducing the machine's inherent errors.     

Assessment of machine tool trunnion axis motion error, using magnetic double ball bar

A method is proposed in this paper to assess the axis motion errors of a trunnion-type A-axis using the magnetic double ball bar (DBB) as the measuring instrument. The proposed method consists of five DBB tests with a single setup for all of the tests and the exclusive motion of the trunnion axis during data acquisition. The single setup helps to reduce non-productive time by limiting the intervention of the operator within the machine workspace whereas the exclusive trunnion axis motion prevents the data from being contaminated by other axes motion errors within each test. Simulations show that setup errors cause eccentricities and radius changes of the ball bar data when viewed on a polar plot. Finally, the proposed method is applied to a VL30 Mitsui-Seiki vertical machine tool to identify its trunnion axis motion errors. The results show the effectiveness of the proposed method as well as its ease of use and the short time required.