Linear Position Error Research Articles

Positioning errors and accuracy of CNC machine tools

Abstract Computerized numerically controlled (CNC) machine tools are a solid foundation for modern industrial manufacturing. These machines provide linear and angular displacements in three or five axes. The accuracy of moving and positioning the tooltip relative to the work part's surface determines the final product's accuracy. Errors due to machine positioning can be linear or angular or both. This work studies the positioning errors of a vertical turning center CNC machine type. This machine has three axes, two linear X (horizontal) and Z (vertical), and one rotation axis “C”. The travel of the spindle carrying the cutting tool along the X-axis is 1400mm, and the travel of the carriage holding the spindle along the Z-axis is 1300mm divided into six latches. The machine rotary table which carries the work part can rotate 360°. A highly precise laser interferometer system determines the linear positioning errors in both the X and Z axes. The angular positioning errors for the “C” rotation axis are determined accurately by an autocollimator system. The positioning error measurements are carried out based on ISO 230-2 as a measurement standard of positioning deviation, accuracy, and repeatability. The collected error measurements in linear displacements and angular rotation are analyzed, interpreted, and compared with manufacturer specifications and ISO 13041-4 allowable tolerances.

Linear Motion Error Evaluation of Open-Loop CNC Milling Using a Laser Interferometer

Abstract The usage of computerised numerical control (CNC) machines requires accuracy verification to ensure the high accuracy of the processed products. This paper introduces an accuracy verification method of an open-loop CNC milling machine using a fringe counting of He–Ne laser interferometry to evaluate the best possible accuracy and functionality. The linear motion accuracy of open-loop CNC milling was evaluated based on the number of pulses from the controller against the actual displacement measured by the He–Ne fringe-counting method. Interval distances between two pulses are also precisely measured using the He–Ne interferometry. The linear motion error and controller error can be simultaneously evaluated in sub-micro accuracy. The linear positioning error due to the micro-stepping driver accuracy of the mini-CNC milling machine was measured with the expanded uncertainty of measurement and was estimated at 240 nm. The experimental results show that linear motion error of the open-loop CNC milling can reach up to 50 μm for 200 mm translation length.

Measurement of Machine Tool Two-Dimensional Error Motions Using Direction-Regulated Laser Interferometers

The volumetric accuracy of a machine tool generally changes with time. Its periodic check, performed at a user’s site in a semi-automated manner, can be a key to ensure a sufficient volumetric accuracy in the long term. A laser interferometer can only measure the linear positioning error motion of a linear axis. This paper proposes a scheme to identify all the two-dimensional (2D) error motions of two linear axes in a plane based on a set of distance measurements using only a laser interferometer. Unlike conventional tracking interferometers, the proposed scheme requires only a numerically controlled rotary table on which a laser interferometer is mounted. It regulates the laser beam direction based on the command target position in an open-loop control manner. This paper presents an algorithm to identify 2D error motions of two linear axes by performing only a single tracking test, in addition to the direct measurement of linear positioning error motions of two linear axes. The experimental comparison of the estimated error motions with their direct measurements is presented. The uncertainty analysis is also presented.

Workshop-suited geometric errors identification of three-axis machine tools using on-machine measurement for long term precision assurance

In this paper we present a novel methodology for fast geometric errors identification of three-axis machine tools (MTs) using on-machine measurement. For this purpose, a new design of a three-dimensional artifact is proposed. The artifact allows to identify the linear positioning error and the two straightness errors of any linear axis of MTs with cartesian kinematics and the perpendicularity error between the axes. The prerequisite for the measurement is that the roll, pitch and yaw errors of all axes have already been measured and are negligibly small. The presented methodology is especially suitable for regular control of the machine accuracy in order to ensure the precision of the machining in the long term.As part of this work, an artifact was made of thermo-invariant material (Invar) and calibrated with an accurate coordinate measuring machine (CMM). This artifact was used to identify the geometric errors of an MT with three linear axes, with the raw data being collected using a 3D touch trigger probe. The measured errors were compared with results from laser interferometer and ballbar measurements. Moreover, the measurement uncertainty of presented methodology was analysed and compared with those of the laser interferometer and ballbar.

Efficient uncertainty estimation of indirectly measured geometric errors of five-axis machine tools via Monte-Carlo validated GUM framework

Whether using a machine tool as a machining or a measuring system, its accuracy has a key role in ensuring product quality. As a result, conducting periodic geometric calibration of a machine tool to quantify and to compensate for the machine's geometric errors is highly desirable. The measured geometric errors must be accompanied by uncertainty estimates, reflecting the lack of exact knowledge of the value of measurands. Indirect calibration approaches, as opposed to direct ones, have gained considerable attention recently because they can be automated and take considerably less time to conduct. However, the uncertainty of the indirectly measured error parameters is more challenging to estimate because of the complexity of the used mathematical models and the large number of machine error parameters identified simultaneously. The use of uncalibrated artifacts also adds to the wariness towards such approaches. In this paper, two different approaches are used to evaluate the uncertainty of machine geometric errors identified by the scale and master ball artefact (SAMBA), an indirect approach relying on the on-machine probing of uncalibrated and calibrated artifacts. First, a simulator of an adaptive Monte Carlo method (MCM) determines the uncertainty of machine tool geometric errors. A multivariate sample generator draws at random the input vectors from a joint probability distribution function (PDF) obtained through experimental replications over 15 days. Supplement 2 to the Guide to the expression of uncertainty in measurement (GUM) specifies the conditions where an adaptive MCM validates the GUM uncertainty framework (GUF). Adhering to the instructions given by this standard, the validity of GUF, a much faster uncertainty evaluation method, is examined. Results show that the adaptive MCM procedure, which takes 24 h to run, validates the alternative GUF approach, which takes a computation time of only 10 min. A maximum disagreement of 1% between the geometric errors from experimental replications and their estimates identified by the adaptive MCM implies that the marginal means of the estimated output joint PDF in the adaptive MCM well represent the average of the output quantities. High dependencies of the linear terms (slopes) of the linear positioning errors of prismatic axes X, Y, and Z on the SAMBA scale bar length cause high correlations between these errors with correlation coefficients up to 0.965. The largest standard uncertainty estimated for the angular geometric errors is 1.26 μrad (associated with the out-of-squareness error of axis Z relative to axis X, EB0Z) and that for the translational geometric errors is 1.03 μm (associated with the distance between the spindle axis and axis B along axis X, EX0S). Axis X is estimated to have the largest standard uncertainty (6.1 μm/m) of the linear terms (slopes) of the linear positioning errors among the machine's prismatic joints.

A novel scheme to measure 2D error motions of linear axes by regulating the direction of a laser interferometer

In the standardized accuracy test procedures for machine tools, error motions of a linear axis, i.e. the linear positioning, straightness, and angular error motions, are separately measured in a different setup with a different measuring instrument. This paper presents a novel scheme to measure all the two-dimensional (2D) error motions of two linear axes by using a laser interferometer only. The proposed test consists of (1) direct measurement of the linear positioning deviation of two linear axes, and (2) the distance measurement to the retroreflector, positioned by the two linear axes on a rectangular path, by continuously regulating the laser beam direction of a laser interferometer. It requires a laser interferometer only; lower implementation cost is its major practical advantage. As an experimental case study, the proposed scheme is applied to a large-sized machine tool. The uncertainty analysis is also presented.

Impact of Model Complexity in the Monitoring of Machine Tools Condition Using Volumetric Errors

The scale and master ball artefact (SAMBA) method allows estimating the inter- and intra-axis error parameters as well as volumetric errors (VEs) of a five-axis machine tool by using simple ball artefacts and the machine tool’s own touch-trigger probe. The SAMBA method can use two different machine error models named after the number of model parameters, i.e., the “13” and “84” machine error models, to estimate the VEs. In this study, we compare these two machine error models when using VE vector directions and values for monitoring the machine tool condition for three cases of machine malfunctions: 1) a C-axis encoder fault, 2) an induced X-axis linear positioning error, and 3) an induced straightness error simulated fault. The results show that the “13” machine error model produces more focused concentrated VE directions but smaller VE values when compared with the “84” machine error model; furthermore, although both models can recognize the three faults and are effective in monitoring the machine tool condition, the “13” machine error model achieves a better recognition rate of the machine condition. This paper provides guidelines for selecting machine error models for the SAMBA method when using VEs to monitor the machine tool condition.

Generation of a 3D error compensation grid from ISO 230-1 error parameters obtained by a SAMBA indirect calibration and validated by a ball-bar spherical test

Tool path deviation reduces machined parts quality. To enhance machine tool accuracy, compensation tables are provided in most controllers to automatically apply small corrections to axis commands. A model-based approach, considering the ISO 230-1 machine geometric error parameters, is proposed to generate the table entries. The error parameters are estimated using model-based indirect calibration results from a scale and master balls artifact probing (SAMBA) test. Two models are used, one with primarily the axis alignment errors and scale errors and the other including many error motions. The 3D grid error compensation is generated with a minimal optimum mesh grid dimension to achieve a preset precision considering the estimated model error parameters. The efficiency of the table is evaluated using a 3D ball-bar test consisting of various circular trajectories along several meridians and the equator before and after applying the table-based error compensation. It is shown that the volumetric errors due to out-of-squareness errors and linear axis linear positioning errors can be compensated using a 2 × 2 × 2, 8 nodes, grid. However, when including error motions, the optimum grid dimension depends on the specific error values of the machine. For the tested machine, a 19 × 19 × 19 for 6859 nodes grid was required, with which the out-of-sphericity of the tool trajectory relative to the workpiece frame is improved by over 82%.

Model Free Adaptive Iterative Learning Control for Tool Feed System in Noncircular Turning

The linear motor tool feed system is an important part in noncircular turning. In this paper, the compact form dynamic linearization based model-free adaptive iterative control scheme (CFDL-MFAILC) and the full form dynamic linearization based model-free adaptive iterative control method scheme (FFDL-MFAILC) are designed for a complex nonlinear tool feed system. Theoretical analysis shows that the proposed scheme guarantees the output tracking error monotonic convergence along the iteration axis, and the FFDL-MFAILC is a complement and improvement to the CFDL-MFAILC. The designed control schemes are compared with PID and iterative learning feedforward and model-free adaptive predictive control feedback combination scheme (ILC-MFAPC) by simulations and experiments. Simulation results show that the proposed scheme can greatly decrease linear motor position error as iteration time increase, and has better position control advantages then other algorithms, the FFDL-MFAILC has faster convergence speed and smaller steady-state error than the CFDL-MFAILC. Experiment results prove that the proposed scheme is effective in linear motor tool feed system position control.

Performance Analysis of Linear Variable Reluctance Resolvers Based on an Improved Winding Function Approach

Linear variable reluctance (LVR) resolvers have substantial benefits that make them suitable for linear motion control drives. The optimal design of LVR resolvers needs an accurate modeling that is usually achieved by a three-dimensional (3-D) time-stepping finite element method (TSFEM). However, the 3-D TSFEM is a very time-consuming method and is unsuitable for cousage with optimization algorithms. So, in this paper an accurate analytical model based on an improved winding function method is proposed. The proposed model is used to calculate the inductances, air-gap flux density, induced voltages, and linear position error. The distinguished feature of the proposed model is the direct usage of the turn function in calculating the inductances. The conventional modified winding function (MWF) method uses the Fourier Seri of the turn function. So, the proposed model is much faster and more accurate than the models based on the conventional MWF method. The results of the proposed model are verified with those of the 3-D TSFEM. Then, the proposed model is used for design optimization of the sensor. Also, two methods are proposed for compensating the longitudinal end effect. Finally, the experimental prototype is used to evaluate the developed analytical model and the optimization process.

Comparison of Direct and Indirect Methods for Five-axis Machine Tools Geometric Error Measurement

Geometrical error (GE) is a key criterion for machine tools performance evaluation. GE measurement methods can be classified as direct and indirect methods. As an indirect GE measurement method, the scale and master ball artefact (SAMBA) method can estimate the GE of linear and rotary axes by probing series of master balls and a scale bar artefact installed on the machine tool pallet. The purpose of this study is to research the performance of direct and indirect GE measurement methods (i.e. laser interferometer and SAMBA method) in linear positioning error measurement such as EXX and EYY. These errors of the X- and Y-axis are separately measured on a five-axis machine tool with the two methods. The results reveal that the SAMBA method yields similar results as the laser test in error shape and range. However, there are some minor differences which are discussed.

Mathematical Approach for Geometric Error Modeling of Three Axis CNC Vertical Milling Machine

The aim of this paper overviews about to find out the errors that come from three axis CNC vertical milling machine. The errors come from, the CNC milling machine can be modelled into mathematical models and later on these error models will be used to analyse the errors in the measured data. Many errors from CNC machine tools have given significant effects toward the accuracy and repeatability of manufacturing process. There are two error sources come from CNC machine tools such as tool deflection and thermal distortions of machine tool structure. These errors later on will contribute to result in the geometrical deviations of moving axis in CNC vertical milling machine. Geometrical deviations of moving axis such as linear positioning errors, roll, pitch and yaw can be designated as volumetric errors in three axis machine tool. Geometrical deviations of moving axises happen at every axis in three axis CNC vertical milling machine. Geometrical deviations of moving axises in linear and angular movement has the amount of errors up to twenty one errors. Moreover, this geometrical errors play the major role in the total amount of errors and for that particular reason extra attention towards the geometrical deviation errors will be needed along machining process. Each of geometrical error of three axes vertical machining center is modeled using a homogeneous transformation matrix (HTM). The developed mathematical model is used to calculate geometrical errors at each axis and to predict the resultant error vector at the interface of machine tool and workpiece for error compensation.

Research on Precision Experimental Table for CO<sub>2</sub> Laser Machining Microfluidic Chip

In order to experiment study of CO2 laser machining polymer-based microfluidic chip, a laser micro-processing precision experimental table was built. A servo feed system directly driven by linear motor was designed to achieve high speed and high position accuracy. Dual-CPU open CNC system used Industrial Personal Computer(IPC) as master computer and PMAC controller as slave computer was constructed to ensure system real-time control. In order to increase position accuracy of precision table, a forecast model of the linear motor position error was put forward based on LSSVM and error compensation was processed. Research results indicated that the use of radial basis function of the LSSVM could improve linear motor position accuracy.

Eliminating Linear Positioning Bias with Polynomial Approximation in AGPS Method

An AGPS (assisted global positioning system) positioning method was researched with polynomial approximation in this paper. Linear positioning errors were found through the analysis of an AGPS positioning algorithm with mobile station (MS) clock error. These errors were engendered to induce a bias of reference moment. The value of an objective function can be quadratically related to the deviation of reference time. Thus, the objective function curve was fitted with three reference time values, and the lowest point of curve to amend the reference time is determined. This method can eliminate linear positioning error.

A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table

For calibrating an angular rotary table, either a high precision standard table or a laser interferometer and related optics are normally employed at high cost. This paper establishes a novel, simple and low cost technique to calibrate the 4-degrees-of-freedom (DOF) errors of a rotary table (three angular position errors and one linear position error) for a 360° full circle by employing one reference rotary table, one 1 dimensional (1D) grating and two 2 dimensional (2D) position-sensing-detectors (PSD). With this technique, no highly accurate reference rotary table, but with good repeatability is needed. After two full circle tests, the 4-DOF errors of both the target rotary table and the reference rotary table could be obtained. The system calibration, stability test, system verification and full circle test were completed. The angular stability of this system was less then 2 arc sec, while the displacement stability was less than 1.2 μm.

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.

Thermal error analysis for a CNC lathe feed drive system

The development of high-speed feed drive systems has been a major issue in the machine tool industry for the past few decades. The resulting reduction in the time needed for tool changes and the rapid travel time can enhance productivity. However, a high-speed feed drive system naturally generates more heat and resultant thermal expansion, which adversely affects the accuracy of machined parts. This paper divides the feed drive system into two parts: the ball screw and the guide way. The thermal behavior model for each part is developed separately, in order to estimate the position errors of the feed drive system caused by thermal expansion. The modified lumped capacitance method (MLCM) and genius education algorithm (GEA) are used to analyse the linear positioning error of the ball screw. Thermal deformation of the guide way affects straightness and introduces angular errors, as well as affecting linear positioning. The finite element method is used to estimate the thermal behavior of the guide way. The effectiveness of the proposed models is verified through experiments using a laser interferometer.

A method of measuring moving characteristics of precision mechanical‐translation stages using ultrasonic plane waves and applying it to a line‐focus‐beam acoustic microscopy system

AbstractA method of measuring moving characteristics of precision mechanical‐translation stages using ultrasonic plane waves is presented. The moving characteristics are obtained by analyzing the phase variation of ultrasonic waves reflected from a reflector set on the translation stage. The resolution is 4 nm at an ultrasonic frequency of 225 MHz; higher resolution is expected at higher frequencies. The method is demonstrated for a line‐focus‐beam (LFB) acoustic microscopy system. Measurement errors of the phase velocity of leaky surface acoustic waves, caused by the positioning errors of the z‐stage, are investigated both theoretically and experimentally. The linear positioning and straightness errors of the z‐stage are estimated at 225 MHz and these effects on velocity measurements are successfully removed using the measured moving characteristics.

Calibration And Rationalisation Of AManufacturing Facility

Within the machine shop at Micro Metalsmiths Ltd. in North Yorkshire five Matchmaker FMS 3 machine tools are used to perform finishing operations on a wide range of non-ferrous castings. These five machine tools have a central role within the company's manufacturing strategy, and non-availability of any of the machines had a severe effect on production of selected batches. This was because, although these machines all shared a common axis configuration with similar drive and feedback devices, the Production Management team had little confidence in the ability to switch jobs between the machines, due to the differing errors on them. As part of the Teaching Company Scheme between the University of Huddersfield and Micro Metalsmiths Ltd. the errors on this particular group of machines were calibrated. A two-fold exercise to reduce the linear positioning errors and the circularity errors was then undertaken. In order to complete this exercise a measurement procedure was devised, which could then be used to carry out the subsequent measurements required for the continued monitoring of the machine tool's accuracy. It was envisaged that the initial re-calibration work and the following monitoring of the errors would enable batches of any component to be produced on any of the five machine tools with confidence that the scrap rate would not be adversely affected. Transactions on Engineering Sciences vol 23, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533