Errors Of Machine Tools Research Articles

An Optimal Method for Improving Volumetric Error Compensation in Machine Tools Based on Squareness Error Identification

This paper proposes a new method to identify the squareness errors of machine tools and gives an optimal method to improve the volumetric compensation accuracy based on the identified squareness errors. The volumetric error model based on screw theory is proposed and the effects of the squareness errors on the volumetric errors have been analyzed to clarify the possibility of improving volumetric error compensation by proper and accurate squareness errors. Then the identification method of the squareness errors is deduced in theory considering a 3-axis horizontal machine tool. With the identified squareness errors, an optimal method to improve volumetric error compensation in machine tools has been proposed. Experiments have verified that the 3 identified squareness errors are in accordance with the measured squareness errors within the accuracy range. Moreover, compared with the traditional measurement of squareness errors not considering the PDGEs, the proposed method is more effective and shows error compensation improvement in the volumetric error compensation process.

Geometrical theory of cutting stock with torus end mills in five-axis CNC machining and its applications in machining simulation

We have established the geometric theory of cutting stock with flat end mills in five-axis CNC machining and an accurate and efficient approach to 3D geometric modeling of un-deformed chips in this machining (Chang et al. Comput Aided Des 88:42–59, 2017). The work has laid a theoretical foundation for geometrical and physical simulation for five-axis milling. However, fillet and ball end mills are more popular than flat end mills. The equations of the instantaneous cutting edges of a fillet end mill are more complicated in the geometric theory, and the boundary of the area covered by the cutting edges is more difficult to determine. Therefore, this article is to formulate the instantaneous cutting edges and their critical points in five-axis milling and to illustrate how to use the boundary construction diagram to determine the boundary with two examples of the geometric and the physical simulations. This work is verified with the valid results of the examples, and the results indicate that this model can take into account the errors of cutter and machine tool. Therefore, the geometric theory is viable, and its application on the five-axis milling simulation is feasible for high-performance machining.

Calculation and Compensation Method for Fixture Errors in Five-Axis CNC Machine Tools

Computer-Aided Design and Applications is an international journal on the applications of CAD and CAM. It publishes papers in the general domain of CAD plus in emerging fields like bio-CAD, nano-CAD, soft-CAD, garment-CAD, PLM, PDM, CAD data mining, CAD and the internet, CAD education, genetic algorithms and CAD engines. The journal is aimed at all developers and users of CAD technology to ptovide CAD solutions for various stages of design and manufacturing. The journal publishes all about Computer-Aided Design and Computer-Aided technologies.

Rapid Measurement and Identification Method for the Geometric Errors of CNC Machine Tools

Error compensation technology offers a significant means for improving the geometric accuracy of CNC machine tools (MTs) as well as extending their service life. Measurement and identification are important prerequisites for error compensation. In this study, a measurement system, mainly composed of a self-developed micro-angle sensor and an L-shape standard piece, is proposed. Meanwhile, a stepwise identification method, based on an integrated error model, is established. In one measurement, four degrees-of-freedom errors, including two-dimensional displacement and two-dimensional angle of a linear guideway, can be obtained. Furthermore, in accordance with the stepwise identification method, the L-shape standard piece is placed in three different planes, so that the measurement and identification of all 21 geometric errors can be implemented. An experiment is carried out on a coordinate measuring machine (CMM) to verify the system. The residual error of the angle error, translation error and squareness error are 1.5″, 2 μm and 3.37″, respectively, and these are compared to the values detected by a Renishaw laser interferometer.

Real-time thickness compensation in mirror milling based on modified Smith predictor and disturbance observer

Thickness of large thin-walled parts is difficult to keep constant since the time-varying disturbances during machining, such as the deformation of the workpiece and the machine tool errors. Mirror milling is an effective means to machine such parts. It reduces the deformation and acquires the wall thickness of the cutting area online via the support head arranged symmetrically with the cutter. However, the delay of thickness measurement makes the closed-loop system unstable and difficult to achieve satisfactory control of thickness. In this work, a novel online thickness error measurement and compensation method based on modified Smith predictor (MSP) and disturbance observer (DOB) is proposed for mirror milling. While previous researches have only realized open-loop thickness control by compensating for deformation, the proposed method achieves stable real-time closed-loop control and is not sensitive to the source of wall thickness error. Firstly, an online measurement system is built to obtain the thickness and local deformation of the workpiece. The measured deformation data and the geometrical pose of the machine tool are used to estimate the wall thickness to reduce the delay of thickness acquisition. Then, a DOB based on thickness estimation is constructed to observe and eliminate the external disturbances. Since there is small delay in the thickness estimation, the proposed DOB can obtain faster disturbance rejection. Furthermore, MSP-DOB compound controller is proposed, in which MSP is used to stabilize the closed-loop system by eliminating the thickness measurement delay and improve the accuracy by compensating for the internal disturbances. Simulations and cutting experiments are both conducted. The wall thickness accuracy is improved from [-0.101,0.065] (unit: mm) to [-0.065,0.048] (unit: mm) in the experiments, thus verifying the validity of the proposed method.

Investigation of rotary axes geometric performance of a five-axis machine tool using a double ball bar through dual axes coordinated motion

The accuracy of coordinated motion involving multiple axes of five-axis machining is critical to surface finish quality and geometric tolerances. However, the lack of existing criteria to benchmark such accuracy causes severe problems in maintaining machining accuracy. Therefore, this paper proposes a novel method to identify the geometric performance of rotary axes of a five-axis machine tool with a tilting head and a rotary table using a double ball bar (DBB). A new measuring trajectory only involving two rotary axes simultaneous movement is presented. A DBB was employed to sample the complex motion, causing a semi-conical surface in a 3D space formed by the DBB poses. The asynchronisation between the resultant speed of the spindle tool cup during the B- and C-axes coordinated motion and the DBB sampling rate has been resolved, enabling the true reflection of machine tool error conditions. Simulation models were built to compare with the testing results, suggesting the estimation of PIGEs of both rotary axes. Disagreements in the simulation and experimental results were analysed and possible reasons causing such disagreements were given. The results show that the compensation of the PIGEs diagnosed with the proposed method will significantly enhance the coordinated motion of the B- and C-axes and result in geometric accuracy improvement due to the promotion of the geometric and kinematic behaviour of the target five-axis machine tool.

A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece

In the acceptance process of newly developed five-axis machine tools (FAMTs), it is urgent for machine tool builders to understand the main causes of machining defects on S-shaped test piece. This paper proposes a novel causation analysis method based on error spatial morphology of S-shaped test piece to decouple the key geometric error parameters causing contour errors of test piece. Firstly, based on multi-body system (MBS) theory, tool axis surface error model of a FAMT is set up. In order to eliminate the effect of theoretical error on contour error of S-shaped test piece, the optimized tool path is planned based on the three-point tangential method. Then, the NC instruction is calculated, and error spatial model is established to characterize contour error of the test piece by considering tool setting position. As a basis, error spatial morphologies of test piece are drawn and the relationships between geometric error parameters and error spatial morphologies are analyzed. In order to decouple the key geometric error parameters affecting contour error of test piece, the causation analysis method of local error and global error are presented. After repairing the local and global key error parameters of the test piece obtained from these two analysis methods respectively, the local machining errors are reduced by more than 80%, and the global machining error is not beyond the tolerance. Finally, the cutting experiments of S-shaped test piece on the FAMT XKAS2525 × 60 are implemented. Error detection results of the cutting test piece are basically the same as that shown in error spatial morphologies of test piece, which verifies the correctness of error spatial model for the test piece. After compensating the global key error parameters obtained from the causation analysis method of global error in CNC system, the detection results of re-cutting test piece under the same conditions indicate the test piece has very few points that are not within the tolerance range, and detection results after compensation and global repaired results are almost similar, which verifies the feasibility and correctness of the proposed analysis method. Therefore, it is obvious that the presented method bridges between geometric characteristics of S-shaped test piece, geometric errors of machine tool, and machining defects of test piece and provides a comprehensive error analysis method in the acceptance and performance testing of FAMTs by using the S-shaped test piece. Thus, this study is of great significance for improving the accuracy evaluation method and enhancing the design accuracy of FAMTs.

Geometric accuracy evaluation during coordinated motion of rotary axes of a five-axis machine tool

This paper presents a novel method to identify Position Independent Geometric Errors (PIGEs) of a five-axis machine tool with a tilting head and a rotary table using a Double Ballbar (DBB). A newly defined measuring trajectory only involving both rotary axes coordinated motion is proposed. The DBB is used to capture conic deviations that are used to generate error trace patterns. The asynchronisation between the resultant speed of the spindle tool cup during the B- and C-axes coordinated motion and the DBB capture speed has been resolved, enabling the true reflection of machine tool error conditions. The testing results are compared with simulation results established using the Homogeneous Transformation Matrices (HTMs) in conjunction with the rigid body kinematics. Different PIGEs were both estimated and measured using the simulation model and the proposed testing method respectively. Disagreements in the simulation and experimental results are analysed. The residual error after compensation of the PIGEs accounts for 8.76% of the total error budget, which might be due to thermal errors and kinematic errors. Experimental results show that the compensation of the PIGEs diagnosed in this paper will significantly enhance the coordinated motion of the B- and C-axes. Since the measurement involves both axes moving simultaneously, it can not only reflect the PIGEs of each rotary axes, but also assesses the geometric and kinematic coordination between the two rotary axes, which could comprehensively reflect the geometric accuracy of the five-axis machine tool.

Influence and error transfer in assembly process of geometric errors of a translational axis on volumetric error in machine tools

The geometric errors of a translational axis are important factors influencing the volumetric error of machine tools. Error relationship in the assembly process of a translational axis quantitatively remains an open problem. In the paper, the slide guideway, forming the translational axis, has been decomposed into three key parts as the base, slider and carriage. New error transfer relationship model has been proposed in the assembly process. Volumetric error model of the horizontal machine tool is established and influence of the assembly error parameter on the volumetric error is analyzed with the two error models. Measurement experiments for the slide guideway has been carried out and the error transfer model has been verified. The proposed error transfer relationship model, as well as the error effects analysis method, provides important theoretical guide basis to optimize manufacture and assembly of a translational axis in a scientific and reasonable way.

A Method for Simultaneously Measuring 6DOF Geometric Motion Errors of Linear and Rotary Axes Using Lasers.

A novel method for simultaneously directly measuring six-degrees-of-freedom (6DOF) geometric motion errors of CNC machine tools was proposed, and a corresponding measurement system was developed. This method can not only be applied for measuring a linear axis, but also for a rotary axis. A single-mode fiber was used to separate the measuring unit from the laser source in order to ensure system thermal stability and measurement accuracy. The method has the advantages of high efficiency and good accuracy, and requires no complicated decoupling calculation. The positioning error of the linear axis and radial motion error of the rotary axis are measured by laser interferometry and other 5DOF geometric motion errors by laser collimation. A series of experiments were performed to verify the feasibility and effectiveness of the developed measurement system.

An identification method for crucial geometric errors of gear form grinding machine tools based on tooth surface posture error model

The identification for crucial geometric errors of gear form grinding machine tools is essential for the later error accurate compensation, but complicated and difficult. To reveal the mapping rules between geometric errors and machining errors, the tool posture error model (TPEM) was first constructed but it failed to consider the effects of grinding process. Hence, the tooth surface posture error model (TSPEM) was established based on the discretization of the grinding trajectory and the calculation of the grinding contact lines. Then the improved Sobol method was performed to analyze the error sensitivity and identify the crucial errors and sensitive components by considering the stochastic and intercoupling characteristics of geometric errors. To validate the effectiveness of the proposed method, the identified results were compared with that of the Morris method and the modification experiment of crucial errors was conducted. It shows that the tooth surface errors in the δy-direction are reduced by 68.75% for the TSPEM and 43.36% for the TPEM and that the TSPEM is more effective for the identification of crucial geometric errors.

Analysis of friction error in CNC machine tools based on electromechanical characteristics

Friction is a kind of inherent and nonlinear disturbance in feed systems, which inevitably deteriorates motion accuracy at velocity reversal. Position error caused by friction is integrally effected by three aspects of feed drives, including command, control, and mechanical subsystems. Unfortunately, the traditional analyses hardly consider all mentioned aspects. Especially, no research has been reported on control characteristic at reverse motion. The purpose of this paper is to reveal the generation mechanism of friction error of a feed drive based on the commercial computer numerical control with three-loop control structure and velocity feedforward and proportional–proportional–integral controllers. Firstly, the generation process of the friction error at velocity reversal is profoundly investigated. Based on it, a simplified control model is conducted to explain transition from presliding to sliding regimes. It is the bond of analyzing friction error from command, control, and mechanical subsystems. Subsequently, the processes of presliding, acceleration, and adjustment stages are analyzed. Moreover, analytical formulas are derived to predict the durations of three stages and describe the shape of friction error. Then, the contour errors of linear and circular motion caused by friction can be predicted online. Experiments are introduced to verify the effectiveness of the proposed methods and formulations.

Fv-SVM-Based Wall-Thickness Error Decomposition for Adaptive Machining of Large Skin Parts

Large skin parts play an important role in the aerospace industry. The wall thickness of the machined pocket in the skin part needs to be strictly controlled to ensure the transport capacity and structural strength. The wall-thickness accuracy is generally decreased by various factors, such as the shaping error of the workpiece blank, fixing error, machine tool error, and deformation caused by cutting force or internal stress. These factors are usually inevitable and stochastic due to the extremely weak rigidity and easy-to-deflect characteristics of the large skin parts. To ensure the wall-thickness accuracy, a fuzzy v-support vector machine (Fv-SVM)-based wall-thickness error decomposition method is proposed. The wall-thickness errors, which are monitored in the cutting process, are decomposed into spatial-related errors and time-related errors. The Fv-SVM-based decomposition method with the principle of spatial statistical analysis is a data-driven approach for intelligent manufacturing. The data-driven method can consider all factors that affect the wall-thickness accuracy, while the model-driven method usually only considers one factor, such as the workpiece deformation or fixing error. After decomposition, the spatial-related wall-thickness error is offline compensated, and the time-related wall-thickness error is compensated by using a real-time strategy. The novel method can be applied to complex tool paths. The cutting experiment of rectangular pockets in a large skin panel was conducted to verify the effectiveness of the proposed method. The wall-thickness accuracy can be improved to 0.05 mm for the workpiece with only 2 mm thickness.

The Method of Geometric Error Measurement of NC Machine Tool Based on the Principle of Space Vector’s Direction Measurement

To achieve the quick and accurate calibration of the geometric errors of NC machine tool, a new method with laser tracker on the basis of space vector’s direction measurement principle is proposed in the paper. A series of measuring points are mounted on the moving part of the machine tool, and then adjacent measuring points are connected to form a space vector respectively. Due to the motion error of the machine tool, the direction of the vectors composed will be changed. Meanwhile, the deviation of vector’s direction only relates to angular displacement error rather than linear displacement error. Based on the characteristic, the change of vectors’ direction is measured by laser tracker based on the multi-station and time-sharing measurement during the motion of machine tool, and then the angular displacement errors and linear displacement errors of each axis can be accurately identified successively, which reduces the complexity of error identification. By establishing the mathematical model of geometric error measurement of machine tool based on the principle of space vector’s direction measurement, the base station calibration algorithm by measuring the motion of the designed precise turntable, the measuring point determination algorithm and geometric error separation algorithm are derived respectively, and the accuracy of these algorithms are verified by simulations. In addition, the results of the experiments show the feasibility of the proposed method.

Error identification and verification of cycloid gear profile surfaces in precision forming grinding

ABSTRACT This paper presents an error identification method for directly related geometric errors of 4-axis forming grinding machine tool and some processing-induced errors from actual teeth profiles of a machined cycloid gear. Based on the developed 4-axis geometric error model, we build up an overall error model of cycloid gear-tooth profiles by forming grinding, which includes some directly related geometric errors of the machine tool and processing-induced errors. Error separation or identification methods are developed in correspondence with the form grinding process and are verified by some non-cutting identification or measurement techniques, including multi-lateration laser measurement technique and a laser rotary axis calibrator. The experiment results demonstrate that the separated geometric errors based on the machining test approach reach a better accuracy. In order to further improve the machining accuracy of the cycloid gear, two identified geometric errors and tooth-shaped error can be utilised for error compensation in the future.

Machining Based Geometric Error Estimation Method for 3-Axis CNC Machine

Computer numerical control (CNC) machine tool plays an extremely significant role in any manufacturing industry due to its automation and high accuracy. Keeping the CNC machine tool at its highest performance to meet the demand of high accuracy machining is always significant. To maintain the accuracy of a machine tool over the time, it is important to measure and compensate the geometric error, one of the main error source of machine tool, especially when the machine get old. There are totally 21 geometrical errors in a 3-axis machine tool including three translational errors and three rotational errors for each axis and three perpendicular error (Squareness) within three axes of the machine. This paper presents an economical and simple method for measuring the geometric error of a 3-axis CNC machine tool based on the machining of actual samples. Three samples for each axis will be machined following a design cutting path. The samples will then be measured using a coordinate measuring machine (CMM). The collect data will be used for estimating the geometric errors. The volumetric errors will be then computed and verified through machining of 3D geometries.

PARAMETERIZATION OF ENVIRONMENTAL INFLUENCES BY AUTOMATED CHARACTERISTIC DIAGRAMS FOR THE DECOUPLED FLUID AND STRUCTURAL-MECHANICAL SIMULATIONS

Thermo-elastic effects contribute the most to positioning errors in machine tools especially in operations where high precision machining is involved. When a machine tool is subjected to changes in environmental influences such as ambient air temperature, velocity or direction, then flow (CFD) simulations are necessary to effectively quantify the thermal behaviour between the machine tool surface and the surrounding air (fluid). Heat transfer coefficient (HTC) values effectively represent this solid-fluid heat transfer and it serves as the boundary data for thermo-elastic simulations. Thereby, deformation results can be obtained. This two-step simulation procedure involving fluid and thermo-structural simulations is highly complex and time-consuming. A suitable alternative for the above process can be obtained by introducing a clustering algorithm (CA) and characteristic diagrams (CDs) in the workflow. CDs are continuous maps of a set of input variables onto a single output variable, which are trained using data from a limited number of CFD simulations which is optimized using the clustering technique involving genetic algorithm (GA) and radial basis function (RBF) interpolation. The parameterized environmental influences are mapped directly onto corresponding HTC values in each CD. Thus, CDs serve as look-up tables which provide boundary data (HTC values along with nodal information) under several load cases (combinations of environmental influences) for thermo-elastic simulations. Ultimately, a decoupled fluid-structural simulation system is obtained where boundary (convection) data for thermo-mechanical simulations can be directly obtained from CDs and would no longer require fluid simulations to be carried out again. Thus, a novel approach for the correction of thermo-elastic deformations on a machine tool is obtained.

A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision.

Periodic health checks of contouring errors under unloaded conditions are critical for machine performance evaluation and value-added manufacturing. Aiming at breaking the dimension, range and speed measurement limitations of the existing devices, a cost-effective knowledge-driven approach for detecting error motions of arbitrary paths using a single camera is proposed. In combination with the PNP algorithm, the three-dimensional (3D) evaluation of large-scale contouring error in relatively high feed rate conditions can be deduced from a priori geometrical knowledge. The innovations of this paper focus on improving the accuracy, efficiency and ability of the vision measurement. Firstly, a camera calibration method considering distortion partition of the depth-of-field (DOF) is presented to give an accurate description of the distortion behavior in the entire photography domain. Then, to maximize the utilization of the decimal involved in the feature encoding, new high-efficient encoding markers are designed on a cooperative target to characterize motion information of the machine. Accordingly, in the image processing, markers are automatically identified and located by the proposed decoding method based on finding the optimal start bit. Finally, with the selected imaging parameters and the precalibrated position of each marker, the 3D measurement of large-scale contouring error under relatively high dynamic conditions can be realized by comparing the curve that is measured by PNP algorithm with the nominal one. Both detection and verification experiments are conducted for two types of paths (i.e., planar and spatial trajectory), and experimental results validate the measurement accuracy and advantages of the proposed method.

Identification of inherent position-independent geometric errors for three-axis machine tools using a double ballbar with an extension fixture

This paper presents a double ballbar method with an extension fixture to identify the position-independent geometric errors of three-axis machine tools with respect to their entire workspace by conducting face- and body-diagonal length tests. To extend the length of the double ballbar to the required nominal length in the face- and body-diagonal directions, an extension fixture is designed and manufactured using a fused-deposition-modeling 3D printer to ensure that it is lightweight. Inherent position-independent geometric errors can be calculated from measured lengths by using homogeneous transformation matrices, which are multiplied under the assumption of small values, to determine the volumetric error produced by a machine tool. The relationships between the position-independent geometric errors, roll-pitch-yaw errors, and measured lengths can be derived according to the definition of the straightness errors, based on the end-point of the reference straight line. Finally, the position-independent geometric errors, with analysis of measurement uncertainties, can be identified by substituting the values of the roll-pitch-yaw errors, measured by a multi-axis calibrator, into the derived relations. The results can then be validated by re-measuring the face- and body-diagonal lengths with error compensation. The main advantage of the proposed approach is that it can be used to identify the inherent position-independent geometric errors of machine tool workspaces. This could contribute to reducing volumetric errors in machine-tool workspaces by allowing compensation for measurement errors, thus making machine tools more effective.

Identification of integrated geometric errors of rotary axis and setup position errors for 5-axis machine tools based on machining test

As a fundamental error source, geometric errors of 5-axis machine tools have a negative influence on a machine tool’s motion accuracy. Large numbers of efficient and robust geometric error measurement and compensation methods have been developed by existing researches to improve the performance of the machine tools during the automatic machining of the workpiece. However, influence of the geometric errors on workpiece clamping is hard to measure and evaluate in most of the clamping processes since manual operations are involved. It is important to identify both geometric errors and setup position errors to control the entire machining process, standing from the perspective of a manufacturer. In this study, a position-dependent geometric error and setup position error identification method is investigated based on machining test. A kinematic model for a 5-axis machine tool with tilting rotary table is constructed while considering both geometric errors of the two rotary axes and setup position errors. Machining patterns and calculation algorithm are designed to analytically calibrate these errors. Experimental demonstration is conducted to validate the feasibility of the proposed measurement method.