Master Ball Research Articles

Five-Axis Machine Tool Volumetric and Geometric Error Reduction by Indirect Geometric Calibration and Lookup Tables

Abstract Modern CNC machine tools provide lookup tables to enhance the machine tool’s precision but the generation of table entries can be a demanding task. In this paper, the coefficients of the 25 cubic polynomial functions used to generate the LUTs entries for a five-axis machine tool are obtained by solving a linear system incorporating a Vandermonde expansion of the nominal control jacobian. The necessary volumetric errors within the working volume are predicted from the machine’s geometric errors estimated by the indirect error identification method based on the on-machine touch probing measurement of a reconfigurable uncalibrated master ball artifact (RUMBA). The proposed scheme is applied to a small Mitsubishi M730 CNC machine. Two different error models are used for modeling the erroneous machine tool, one estimating mainly inter-axis errors and the other including numerous intra-axis errors. The table-based compensation is validated through additional on-machine measurements. Experimental tests demonstrate a significant reduction in volumetric errors and in the effective machine error parameters. The LUTs reduce most of the dominant machine error parameters. It is concluded that although being effective in correcting some geometric errors, the generated LUTs cannot compensate for some axis misalignments such as EB(OX)A and EB(OX)Z. The root-mean-square of the translational volumetric errors is improved from 87.3, 75.4, and 71.5 µm down to 24.8, 18.8, and 22.1 µm in the X-, Y-, and Z-directions, respectively.

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.

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%.

Optimal calibration strategy for a five-axis machine tool accuracy improvement using the D-optimal approach

An optimisation process is proposed to design a measurement strategy for the indirect calibration of a five-axis machine tool using the SAMBA (Scale and Master Balls Artefact) method. The DETMAX algorithm is applied to select optimised artefact positions and lengths, and rotational machine axes angular positions, based on a comparison of maximised observability indices values. Simulation outcome produces probing sequences that offer a better estimation of axis location errors and error motions within a limited processing time. Different optimised calibration scenarios are then conducted simultaneously in a nested experimental test to ensure a fair selection of the probing strategy within the same operational conditions. Observability index results supported by uncertainty analysis suggest that a one master ball, for axis location errors, and four master balls, for axis location errors and error motions, probing sequences are the most efficient strategies for a number of measurement depending on the number of machine error model unknown parameters.

Five-Axis Machine Tool Coordinate Metrology Evaluation Using the Ball Dome Artefact Before and After Machine Calibration

Now equipped with touch trigger probes machine tools are increasingly used to measure workpieces for various tasks such as rapid setup, compensation of final tool paths to correct part deflections and even verify conformity to finished tolerances. On five-axis machine tools, the use of data acquired for different rotary axes positions angles brings additional errors into play, thus increasing the measurement errors. The estimation of the machine geometric error sources, using such methods as the scale and master ball artefact (SAMBA) method, and their use to calibrate machine tools may enhance five-axis on-machine metrology. The paper presents the use of the ball dome artefact to validate the accuracy improvement when using a calibrated model to process the machine tool axis readings. The inter-axis errors and the scale gain errors were targeted for correction as well the measuring tool length and lateral offsets. Worst case and mean deviations between the reference artefact geometry and the on-machine tool measurement is reduced from 176 and 70 µm down to 31 and 12 µm for the nominal and calibrated machine stylus tip offsets respectively.

Five-axis machine tool fault monitoring using volumetric errors fractal analysis

Detecting machine tool condition deterioration affecting its accuracy is a constant challenge for industrial machine maintenance. Machine tool volumetric errors (VEs) exhibit complex variations due, for example, to normal thermal variations, wear or faults and defective components. A monitoring technique based on the fractal analysis of VEs, estimated with the scale and master ball artefact method, is studied. Different fractal parameters from the VE vectors are compared with magnitude based quantities for the detection of abnormal machine states. Results using both actual data with real and pseudofaults and synthetic data from simulated faults using ISO230-1 error parameters are presented.

Quantitative assessment of machine tools condition through fractal analysis of volumetric error vector similarity measures

The volumetric error state of machine tools is related to the quality of the machined parts and the machine tool condition. Volumetric error vectors (VEs) of machine tools can be estimated using methods such as R-test, laser trackers and the scale and master ball artefact (SAMBA) method. During one measurement, a series of volumetric error vectors can be acquired. Herein, volumetric error vector features extracted using vector similarity measures (VSMs), such as the Module, the Cosine, the Area and the Volume measures, are subsequently processed by fractal analysis for quantitative assessment of the machine tool volumetric error state. Although VEs have recently been processed directly using fractals, this paper documents the first attempt to process VEs, extracted by VSMs, using fractal analysis. The proposed method is validated using VEs measured from the machine tool in its normal state and faulty state with real and pseudo-faults. In addition, simulated faults caused by the change of ISO230-1 error parameters are also applied. The results reveal that the performance of the proposed method in machine tools state representation is related to VSMs. Fractal analysis of VEs features extracted by the Area and Volume measures performs better than fractal analysis of Modu and Cosine measure in VEs condition evaluation. However, for the same fault, the change revealed by fractal analysis of VE coordinates are clearer than the change revealed by the fractal analysis of VE features extracted by VSMs.

Application of the adaptive Monte Carlo method in a five-axis machine tool calibration uncertainty estimation including the thermal behavior

Calibration of the geometry of five-axis machine tools needs to be performed periodically since the machine accuracy has a direct impact on machined parts. Because mechanical adjustment and a software correction may be done using calibration results, the measurement results must be evaluated. In this paper, the scale and master ball artefact (SAMBA) method is evaluated through the estimation of the uncertainty of the identified machine geometric error parameters. This approach has the multi-input multi-output (MIMO) model and an iterative solution that makes it challenging to apply commonly used uncertainty calculation methods The Guide to the Expression of Uncertainty in Measurement Supplement 2 (GUM S2) gives the opportunity to estimate the uncertainty of a MIMO model through the adaptive Monte Carlo method (MCM). In order to include all the uncertainty sources, the input uncertainty is estimated from the repeated calibration tests performed in different thermal conditions (with and without the warm-up cycle). The uncertainty is calculated for each of the identified machine geometric error parameters along with their covariance. The correlation between the output variables and the impact of the machine state, before and during the repeated calibration, are analyzed. The results demonstrate that the machine tool geometry variations occur even without the warm-up cycle performed before the calibration. Moreover, machine performance has an impact the calibration results.

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.

Axis Location Errors and Error Motions Calibration for a Five-axis Machine Tool Using the SAMBA Method

Positioning accuracy is one of the most important factors influencing a machine tool's ability to manufacture parts meeting the required tolerances. Thus, regular check-ups followed by geometric compensation or mechanical adjustments are necessary to prevent accuracy degradation on such machines. This paper presents an enhanced measurement strategy to extend the capability of the Scale and Master Balls Artefact (SAMBA) method to the estimation of not only the axis location errors but also error motion parameters modeled as ordinary polynomials. This indirect measuring method uses on-machine probing of a scale enriched uncalibrated master balls artefact to gather observations of the machine volumetric behaviour. The analysis of the kinematic model and its associated Jacobian matrix which characterizes the sensitivity of the volumetric errors, as detected by the SAMBA method, to the axis location errors and error motions provide the mathematical basis for the probing strategy design. The simulation and experimental results presented demonstrate the contribution of the applied strategy in enriching substantially the machine tool error model.

2つの非接触変位計を用いた工作機械の運動精度測定装置の開発

Recently, some evaluation techniques have been proposed for five-axis machining centers. In those techniques, the simultaneous three-axis control motions in which the one rotary axis and two linear axes are controlled can detect the positional and angular deviations, and the simultaneous five-axis control motions for cutting the cone frustum of NAS 979 can evaluate various errors. Generally, ball bar instruments are used for the measurement of the displacement between the spindle and the table in those simultaneous multi-axis control motions. Also in the method using a master ball and a linear variable differential transformer, R-test instruments are a possible substitute for ball bar instruments. However, the displacement sensors of those instruments are the contact types. In this study, the measuring instrument for measuring the simultaneous multi-axis control motions is developed in order to avoid collision between the instrument and the five-axis machining center. The proposed measuring instrument consists of a master ball and two noncontact LED/CCD optical micrometers. One micrometer is mounted perpendicular to the other on the base plate. The base plate is fixed on the table and the master ball attached to the spindle is set in the intersection area of the LED light. The measurements of the simultaneous three-axis positioning and the circular motion were carried out on a three-axis machining center. The proposed measuring instrument can precisely measure the motion trajectory in three dimensions.

Five-axis machine tool calibration by probing a scale enriched reconfigurable uncalibrated master balls artefact

On-machine probing of a reconfigurable uncalibrated master balls artefact enriched with a ball bar artefact provides sufficient data to estimate all axis to axis location errors and some axis component errors of a five-axis machine tool. Numerical simulations supported by experimental trials are presented in the case of a five-axis horizontal machining centre using artefacts with up to 26 balls for estimation of ten location errors, including the spindle translational errors, and all three linear axes positioning linear error terms. Volumetric error prediction capability, the impact of data selection on parameter estimation and thermal effect tracking are addressed.

Dynamic R-Test for Rotary Tables on 5-Axes Machine Tools

Conventional methods using a touch-trigger probe in combination with a master ball to calibrate 5-axes machine tools cannot measure dynamically and therefore are unable to detect or capture the observed dynamic machine tool behaviour as described in this paper. For a dynamic measurement the R-test is required. The R-test continuously measures the X, Y and Z displacement of the tool relative to the work piece while at least two linear axes and a rotary axis are operated simultaneously. In this paper dynamic R-test measurements are described addressing a ‘dynamical backlash error’ of the rotary axis for which the clockwise measurement result significantly differs from the counter clockwise measurement. Verification with a ball bar measurement proves this is not caused by the machine's linear axes. The dynamical backlash error is caused by a rotation dependent synchronisation error between the rotary axis and two linear axes.

Design of Motion Accuracy Measurement Device for NC Machine Tools with Three Displacement Sensors

To measure motion accuracy, including that of the rotary axis of five-axis machining center that have been widely introduced into production sites recently, a device with three displacement sensors combined to measure the center position of the master ball was invented and will be added to the International Standard. Such measurement devices are not difficult to produce in principle, but the commercially available products are expensive. This study discusses a threedimensional (3D) coordinate measurement device with multiple displacement sensors, discussing it in terms of the test standards of the machines to which the device has been applied and in relation to devices which have been studied, developed, and released. Our measurement device is then designed and produced, and its measurement accuracy is confirmed.

Reduced configuration set for the multi-step method applied to machine and probe error separation on a CMM

This paper presents a refinement and further analysis of an application of the multi-step method for the separation of machine and probe errors on a CMM using multiple redundancy probing of the machine’s own master ball. The objective is to reduce the amount of data required and so minimize the test time in order to reduce the industrial cost of such periodic verifications.

Automated Detection and Classification of Non-Wet Solder Joints

Non-wet solder joints in processor sockets are causing mother board failures. These board failures can escape to customers resulting in returns and dissatisfaction. The current process to identify these non-wets is to use a 2D or advanced X-ray tool with multidimension capability to image solder joints in processor sockets. The images are then examined by an operator who determines if each individual joint is good or bad. There can be an average of 150 images for an operator to examine for each socket. Each image contains more than 30 joints. These factors make the inspection process time consuming and the output variable depending on the skill and alertness of the operator. This paper presents an automatic defect identification and classification system for the detection of non-wet solder joints. The main components of the proposed system consist of region of interest (ROI) segmentation, feature extraction, reference-free classification, and automatic mapping. The ROI segmentation process is a noise-resilient segmentation method for the joint area. The centroids of the segmented joints (ROIs) are used as feature parameters to detect the suspect joints. The proposed reference-free classification can detect defective joints in the considered images with high accuracy without the need for training data or reference images. An automatic mapping procedure which maps the positions of all joints to a known Master Ball Grid Array file is used to get the precise label and location of the suspect joint for display to the operator and collection of non-wet statistics. The accuracy of the proposed system was determined to be 95.8% based on the examination of 56 sockets (76 496 joints). The false alarm rate is 1.1%. In comparison, the detection rate of a currently available advanced X-ray tool with multidimension capability is in the range of 43% to 75%. The proposed method reduces the operator effort to examine individual images by 89.6% (from looking at 154 images to 16 images) by presenting only images with suspect joints for inspection. When non-wet joints are missed, the presented system has been shown to identify the neighboring joints. This fact provides the operator with the capability to make 100% detection of all non-wets when utilizing a user interface that highlights the suspect joint area. The system works with a 2D X-ray imaging device, which saves cost over more expensive advanced X-ray tools with multidimension capability. The proposed scheme is relatively inexpensive to implement, easy to set up and can work with a variety of 2D X-ray tools.

Evaluation Method to Determine Radial Error of Spindle Units on Simulation Turntable

Many errors including radial error influence the accuracy of simulation turntable, which is a crucial equipment in hardware-in-the-loop simulation system. The aim of this paper is to propose a new method of radial error motion separation of rotating spindle on a simulation turntable. Based on transformation matrix and small angle approximation, gesture transformation matrix with various error items is achieved. As a result of this analysis, form errors of master ball are corrected and the eccentricity from the rotation error of a spindle is separated. This radial error analysis is carried out when this measurement result is applied to a simulation turntable. Furthermore, this study also permits the user to know how to minimize some error sources of the spindle system.

Volumetric distortion assessment of a five-axis machine by probing a 3D reconfigurable uncalibrated master ball artefact

Abstract In this paper, a method is proposed that uses an artefact assembled in situ and exploiting the on-machine probing capability to perform a rapid volumetric distortion assessment of a five-axis machine. The 3D reconfigurable uncalibrated master ball artefact (RUMBA) is an assembly of the machine pallet and an adjustable number of master balls located within the machine working and probing envelop. The artefact design philosophy allows flexibility in the number and positions of the balls thus conferring the reconfigurability attribute. Reconfigurability allows adaptation of the artefact to the machine topology and geometry and its construction around a fixture and workpiece to reduce disruption to machine production. On the down side, the artefact is uncalibrated as its construction concept hinders precise knowledge of its geometry. During a test, combinations of all the machine axes are used to move and probe the master balls. A mathematical model is developed in order to identify the setup errors of each master ball and the probe. Simultaneous identification of the rotary axes’ linear offset with the setup errors is proposed to improve the parameter estimation and volumetric distortion prediction. The machine contribution to the volumetric distortion is then computed from the ball centre data excluding the setup errors. Tests are conducted in a laboratory on a horizontal machining centre. The results show that the proposed mathematical procedure is capable of removing the influence of the uncalibrated artefact geometry, excluding scale, and that the proposed design is suited to the machine environment.

Identification of Motion Error Sources on Five-axis Machine Tools by Ball-bar Measurements (1st Report)

The inclusion of the application of the double ball bar (DBB) measurement to the accuracy calibration of five-axis machine tools into the revision of ISO standards is currently under the discussion. This paper presents the modified DBB measurement device, referred to as “DBB5” in our study, where master balls are supported from the 45°direction to the spindle axis. It can perform all the circular tests on XY, YZ, and ZX planes without changing the setup. This paper first presents the classification of motion error components of a five-aixs machine tool into location and component errors. Experimental application examples of the DBB5 to the calibration of location and component errors assciated with rotary axes on a five-axis machine tool are then presented.