An improved machine tool volumetric error compensation method based on linear and squareness error correction method

The article is devoted to increasing the volumetric accuracy of multi-axis machine tools. Based on the model of measurement and calculation of the volumetric geometric error of machine tools presented by the authors, a method has been developed which allows to signifi cantly improve the accuracy of the movement of the operating unit of a three-axis metal-cutting machine tool to a given point. The astatic law and the calculation of the coordinate correction according to the differential geometric model of the volumetric error are used to control the movement of the operating unit. The developed method is implemented programmatically and allows to perform the correction in the control program represented in G-code. As a result of experiments on software correction of volumetric errors according to the developed method, conducted at the State Engineering Centre of the Moscow State University of Technology “STANKIN” on a threeaxis CNC machine tool, a signifi cant reduction (up to 90 %) of geometric volumetric errors was shown. The developed method can be used to improve the accuracy of metal-cutting machine tools by creating postprocessors that calculate corrections to the coordinates set in the control system based on the results of interferometric measurements.Keywords: volumetric accuracy, interference measurements, three-axis machine tools, machine tool accuracy, geometric errors, astatic control law, mathematical modelling, differential geometry

A three-point method based on sequential multilateration is applied to measuring the geometric error components (GECs) of three-axis machine tools (MTs). To meet the accuracy requirement of geometric error mapping, a sequential multilateration scheme is developed for high-accuracy point measurement by introducing four additional targets into the measuring system, and the uncertainty of point measurement is verified by simulation. Three independent targets fixed on the MT’s spindle assembly move along with each axis step by step and their coordinates at each step can be determined by the distance data acquired by laser tracker at all steps based on sequential multilateration. Then the volumetric errors of the three target points can be obtained by comparing the actual coordinates and the corresponding desired coordinates, and nine equations can be established by substituting volumetric errors into the error model of linear axis, so that the six GECs of each axis can be obtained by solving these equations. The three squareness errors can be determined by computing the angles between the average lines of the three axes which are achieved by linear curve fitting. Experiments are conducted to measure these 21 GECs, and the volumetric errors in the three-axis MT’s workspace, which are determined by these measured GECs based on the error model of three-axis MT, are compensated. Finally, the positioning errors of the MT with compensation and without compensation are evaluated by laser interferometer, respectively, the experimental results of which demonstrate that the positioning errors are significantly reduced by the error compensation.

In this paper, we study basic properties of linear network error correction codes, their construction and error correction capability for various kinds of errors. Our discussion is restricted to the single-source multicast case. We define the minimum distance of a network error correction code. This plays the same role as it does in classical coding theory. We construct codes that can correct errors up to the full error correction capability specified by Singleton bound for network error correction codes recently established by Cai and Yeung. We propose a decoding principle for network error correction codes, based on which we introduce two decoding algorithms and analyze their performance. We formulate the global kernel error correction problem and characterize the error correction capability of codes for this kind of error.

Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools

The volumetric accuracy of machine tools is significantly impacted by thermal errors, making the evaluation of volumetric accuracy a significant challenge for the manufacturing industry. Several technical solutions have been implemented, both at the industrial and research level, to address this issue. However, considering thermal errors in the volumetric error characterization adds complexity to the process and remains an open topic of research in the field.In this study, a novel volumetric error characterization technique based on simulated Thermal Modal Analysis is proposed for a three-axis machine tool. This approach involves analyzing the impact of thermal modes of the machine tool's structural elements on the volumetric error, providing a characterization that incorporates the physical meaning of the structure. This simulated characterization will serve as a foundation for future experiments that combine it with other techniques to achieve a comprehensive understanding of volumetric errors.

Machine tool geometric inaccuracies are frequently corrected through the use of compensation tables available in machine tool controllers. Each compensation table contains a set of values that determine the incremental change in the commanded position of an axis given the current positions of the axes. While a five-axis machine tool, for example, can have at most 25 compensation tables, most machine tool controllers limit the number of compensation tables that can be implemented and provide constraints on the combinations of compensation tables that can be utilized. This work presents an artificial intelligence-based methodology to select and populate the optimal set of machine tool compensation tables when these limitations and constraints exist. Using data from an industrial five-axis machine tool to construct a kinematic error model, simulation results for the proposed methodology and a heuristic based on the impact of individual compensation tables when selecting six compensation tables are compared, and the proposed methodology is found to outperform the heuristic. The proposed methodology and a solution based on a full set of compensation tables are experimentally implemented on the machine tool and the mean volumetric error resulting from the proposed methodology is found to be only 25 μm less than the volumetric error resulting from the full set of tables. The proposed methodology is then implemented in two more simulation studies where constraints are imposed on which combination of compensation tables could be used and which type of compensation tables could not be utilized. The resulting mean volumetric error was 7.0 and 28.3 μm greater, respectively, than the unconstrained solution.

The measurement of six-degrees-of-freedom (6-DOF) errors of rigid bodies can show the real and accurate spatial pose of those rigid bodies. It plays a major role in precision calibration, spacecraft docking, machining, assembly, etc. In this paper, a four parallel laser-based simultaneous measurement (FPL-SM) method is proposed for measuring 6-DOF errors of rigid bodies with translational motion. First, a FPL-SM device is introduced. Its four laser heads form a rectangle, which is perpendicular to the movement direction of the measured linear displacement. Second, identification formulas for all geometrical errors in rigid bodies with translational motion are presented based on the relative positions of the four lasers. Based on the readings of the four lasers, angular errors and corresponding straightness errors are calculated for the direction of motion around the other two linear motions. As the two parallel sides of the rectangle are in different planes, the straightness errors of the two planes are different. The rolling angular error in the direction is expressed as the difference between the straightness errors of the two planes divided by the distance between the two planes. Six fundamental errors for rigid bodies with translational motion are obtained by four lasers in a single setting of the device. For multiple rigid bodies with mutually perpendicular translational motion, the squareness error is calculated by fitting to the actual direction of motion. Finally, experiments were carried out on the SmartCNC_DRDT five-axis machine tool and 21 geometric errors were determined for three translational axes. Error compensation was carried out using the generated machine tool geometric error data to verify the effectiveness of the proposed FPL-SM method. In addition, geometric errors and thermal errors of the Z axis of the GTI-2740 machine tool are measured based on the FPL-SM method.

Accuracy enhancement of five-axis CNC machines through real-time error compensation

Geometric error measuring, modeling, and compensation for CNC machine tools: A review

We use a terahertz echo pulse as a transfer standard to correct linear time-base errors of a terahertz spectrometer. With this calibration technique, the linear error of the translate stage is corrected and the spectral repeatability of the spectrometer is improved. This calibration technique is able to correct each ‘shot’ of the terahertz pulse and can realize on-line calibration of the terahertz spectrum. The average of multiple measurements of carbon monoxide gas absorption lines was corrected and the deviation was reduced by a factor of 2.5 using this technique. This on-line calibration technique needs no additional optical components and causes no performance degradation of the terahertz spectrometer. It provides a simple and alternative method to the conventional interferometric technique and allows for accurate measurement of spectral properties of specimens in the terahertz region.

The accuracy of high speed five-axis machine tool is mainly determined by the contour accuracy of machine tools. The contour accuracy evaluation and improvement of 5-axis machine tools have always been concerned. In order to simplify the calculation of five-axis contour error considering the synchronization between tool tip position and tool orientation, a novel five-axis contour evaluation index TCCE(Two-point Cutter location Contour Error) is proposed in this paper, which is based on the tool axis trajectory surface. The calculating method of the proposed index by NC servo encoder input from 5-axis machine tools is introduced. Finally, the experiment is performed to evaluate the trajectory accuracy and servo matching performance of the machine tool with the proposed contour error evaluation index and the calculating method.

Geometric errors of a machining center can cause great influence on machining accuracy, and these geometric errors should be identified and compensated in the actual working conditions. Taking a three-axis vertical machining center as example, 21 geometric errors of the machine tool were solved. By using the 12-line method based on a laser interferometer, identification principle of the positioning errors, straightness errors, pitch errors, yaw errors, roll errors and squareness errors are presented, and all of the 21 geometric errors of the machining center were identified. Geometric errors having great influence effect on machining accuracy can be identified. The research results provide guidance for analyze of geometric errors of machining center.

Stereo vision (SV) is a widely used measurement technology, while accuracy is one of its most critical properties. Currently, modeling the volumetric error of the SV system is a way to improve measurement accuracy. This article proposes an accurate volumetric error modeling method for submeter SV systems. An analytical expression of the volumetric error considering the effect of random error is developed at first. To accurately evaluate the measurement error of SV systems, a platform consisting of a laser tracker and a robot is established, and an error evaluation method is proposed. Since the random error is coupled with the measurement error and impacts the accuracy of the volumetric error model, we propose an error decoupling method to separate the random error from the measurement error by only a single measurement. Finally, the accuracy of the proposed method is verified through simulations and experiments.

The ability to assess the accuracy of machine tools is required by both tool builders and users. Builders must have this ability in order to predict the accuracy capability of a machine tool for different part geometry`s, to provide verifiable accuracy information for sales purposes, and to locate error sources for maintenance, troubleshooting, and design enhancement. Users require the same ability in order to make intelligent choices in selecting or procuring machine tools, to predict component manufacturing accuracy, and to perform maintenance and troubleshooting. In both instances, the ability to fully evaluate the accuracy capabilities of a machine tool and the source of its limitations is essential for using the tool to its maximum accuracy and productivity potential. This project was designed to transfer expertise in modern machine tool accuracy testing methods from LLNL to US industry, and to educate users on the use and application of emerging standards for machine tool performance testing.

This study realizes face- and body-diagonal length tests using a double ball-bar (DBB) to measure squareness errors at the full working volume of machine tools (MTs). Each test consists of two steps: 1) length measurement at diagonal paths formed using machine commands, and 2) squareness error calculations. For each diagonal path, the machine receives sequential commands according to two nominal coordinates, and tool-tip positions are fixed on the workpiece table. Then, the distance between the two positions is measured using a DBB, which is not calibrated for initial length. The actual tool-tip coordinates are modeled using nominal coordinates and squareness errors. The relationship between the measured lengths and squareness errors is derived using the actual tool-tip coordinates to calculate the squareness errors. The two realized methods are applied to a MT, and verified by comparing the measurement lengths without and with compensation for the measured squareness error. The main advantages of the methods are 1) robust results, unaffected by set-up errors, 2) flexible measurements for various machine tools having different working volumes using a DBB with extension bars only, and 3) cost-effective measurements using the DBB, and the need for only a short time (~5 min) to complete measurements.