Geometric Error Compensation Research Articles

Study on the analytical verification method of geometric error models

Abstract Geometric error compensation is a widely used and effective approach for enhancing the accuracy of Coordinate Measuring Machines (CMMs) and Computer Numerical Control (CNC) machines. The research in this field primarily focuses on the challenging task of developing geometric error modelling techniques. Currently, there are several well-established methods for modelling geometric errors. However, there is scarce availability of methods that can validate the established geometric error models. Therefore, this article proposes an analytical validation method for geometric error models based on the error transformation equation. The principle of the method is elaborately explained, and its correctness is verified through specific model verification example. The method proposed in this article enables rapid and accurate model correction and iteration, effectively reducing the economic and time costs of model validation in the current geometric error compensation process. Therefore, the method provides guidance for standardising the modelling process and could be widely applied to various structural forms of measurement and machining systems.

Active prediction compensation strategy: A new positioning compensation technique for improving the accuracy of the dual ball screw feed mechanism under load

The dual ball screw feed mechanism (DBSFM) is commonly employed in high-end machining applications. However, its accuracy is challenging to enhance due to variations in the axial stiffness of the dual actuators under load, making geometric error compensation (GEC) difficult. To address this, our research establishes a comprehensive error model that integrates geometric error and load-induced error (LIE) to improve feeding accuracy. The axial stiffness matrix of the DBSFM is identified using motor current information, and an active prediction error matrix is defined based on the geometric error model, milling force model, and axial stiffness matrix. We propose and analyze the active prediction compensation (APC) strategy as a new method to enhance accuracy under load. Experimental validation using a gantry-type machine tool demonstrates that the APC strategy can reduce the positioning error of the DBSFM to ±2 μm under load, representing significant improvements over the established GEC method. Specifically, the APC strategy achieves a 53.07% and 57.04% enhancement in accuracy along the two axes. This work illustrates the effectiveness of the APC strategy in reducing positioning errors and improving feeding accuracy in DBSFM machining processes.

Geometry accuracy control in abrasive water jet taper hole machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates

AbstractThe primary factors affecting the geometric accuracy of abrasive water jet (AWJ) machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates are the cutting front drag and kerf width deviation caused by energy dissipation. Firstly, this study comprehensively analyzes the influence of the coupling relationship between cutting front drag and kerf width deviation on the geometric accuracy of hole machining. Secondly, a gradient distribution theory for jet traverse speed with cutting depth is proposed for taper hole machining characteristics. Finally, a general geometric error model applicable to both straight and taper hole machining of ultra‐thick CFRP laminates using AWJ is established, along with a geometric error compensation method. A series of experiments validate the accuracy of the proposed geometric error model and compensation method. The novelty of this research lies in unifying the geometric error models for straight and taper hole machining of ultra‐thick CFRP laminates by considering the gradient distribution of jet traverse speed. The proposed error compensation method reduces the high degree of freedom required for machine tools. This study provides a general geometric error model and compensation strategy for AWJ hole machining of ultra‐thick CFRP laminates, which has significant engineering value for achieving 3D controllable AWJ machining of complex ultra‐thick CFRP components.Highlights The high geometric precision taper holes machining technique is a necessary prerequisite for achieving precise machining of complex trajectories in ultra‐thick CFRP with abrasive water jet. The influence of the coupling relationship between cutting front drag and kerf taper on the geometric accuracy of hole processing is comprehensively analyzed. A model considering the gradient distribution of traverse speed during taper holes machining was established, and a geometric error model considering this gradient distribution of traverse speed was developed. A taper holes machining geometric error compensation method with high engineering applicability was proposed. Geometric error prediction experiments and error compensation experiments were conducted, and the results proved the accuracy of the geometric error model and error compensation method.

Geometric error compensation method of five-axis CNC machine tool based on improved genetic algorithm

Geometric error compensation method of five-axis CNC machine tool based on improved genetic algorithm

Simultaneous compensation of geometric and compliance errors for robotics with consideration of variable payload effects

In order to satisfy the high accuracy requirements of robotic applications, it is necessary to consider not only the geometric errors but also the compliance errors which are caused by the self-gravity of the link and the external payloads. A general error model is developed based on the modified Denavit-Hartenberg (DH) model. For the parameters in the error model, there is a coupling between the compliance coefficients and the link parameters, making it difficult to use only the compliance coefficients to compute the compliance errors due to external payloads. As the external payload for the robot manipulator varies, the parameter identification of the model should be conducted again. In this paper, a novel algorithm using a variable payload method is proposed to first identify the compliance coefficients using different payloads and end effector position information. Second, the kinematic parameter errors and link parameters are identified with the given compliance coefficients. Then, the algorithm generates a modified trajectory using the calibrated DH tables for the precision compensation. Simulation and experimental results demonstrate that the positioning accuracy can be improved by 80 % to 90 % even under different payloads. The root mean square, mean, maximum, and standard deviation of the residual errors by using the proposed algorithm could outperform the conventional kinematic algorithm.

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.

Geometric Error-Based Multi-Source Error Identification and Compensation Strategy for Five-Axis Side Milling

Based on a multi-source error model, this paper discusses the principle of error element identification and uses the mirror bias method to compensate the geometric errors of a process system. Firstly, a nine-line measurement method to determine the geometric error of the linear feed axes of machine tools is introduced, and the geometric error identification model based on the “nine-line method” is established. Then, using a ballbar mounted in the axial, tangential, and radial directions of the machine, the geometric error elements of the rotation axis are identified by three simple measurements in each direction. Subsequently, for the more common flat vise clamping workpiece in actual production, the workpiece position error is identified by using the traditional process of dimensional chain, and the workpiece attitude error is identified by fitting the angle between the positioning plane and the horizontal plane by the least squares method. Finally, based on the tool position points and tool axis vectors obtained from the multi-source error model, the error compensation value is solved using inverse machine tool kinematics to offset the machining error by mirroring the error value of the same size, and based on the “S-shaped specimen” to compensate the processing experiments, after compensation, the processing error is reduced by 30~45%, verifying the effectiveness of the compensation method.

A Technique for Integrated Compensation of Geometric Errors and Thermal Errors to Improve Positional Accuracy of Hole Machining in Large-Size Parts

A Technique for Integrated Compensation of Geometric Errors and Thermal Errors to Improve Positional Accuracy of Hole Machining in Large-Size Parts

An approach for crucial geometric error analysis and accuracy enhancement of gantry milling machines based on generalized correlation sensitivity

Geometric errors in gantry milling machines with long-span beams and large travel can seriously degrade workpiece accuracy. Sensitivity analysis and compensation of geometric errors with coupling and fluctuation can significantly improve the machining performance of machine tools. An accuracy enhancement approach for gantry milling machines is proposed in this paper. Firstly, the geometry error analytic fluctuation eigenfunctions are established by using the high-order Fourier series fitting. Secondly, a non-linear generalized correlation analysis model is proposed to identify the crucial errors that significantly affect the machining accuracy. Thirdly, the motion commands compensated for geometric errors are calculated. Specifically, compared to traditional inverse kinematics, the proposed error compensation process is simple and suitable for most machine tools with orthogonal linear axes. Finally, comparative cutting experiments are performed. The accuracy of the test piece is improved by approximately 34.7 % with error compensation. The effectiveness of the proposed method is validated.

Efficient Method for Identifying Key Errors Based on 21-Geometric-Error Measurement of Three Linear Axes of Machine Tools

Key errors of machine tools have a significant impact on their accuracy, however accurately and quickly measuring the geometric errors of machine tools is essential for key error identification. Fortunately, a quick and direct laser measurement method and system for 21 geometric errors of three linear axes of machine tools were proposed previously, which enables the measurement of all 21 geometric errors via a one-step installation and a three-step automated measurement process. Based on this, to efficiently identify the key error factors, this paper first utilizes the 21 geometric errors obtained from the proposed measurement system to evaluate the contribution of each error to the volumetric errors of machine tools, leading to the building of a 21-geometric-error sensitivity analysis model. Then, experiments are carried out on the vertical machining tool TH5656, and all 21 geometric errors are obtained in 5 min. After this, the volumetric error distribution in the machining workspace is mapped according to the relationship between the geometric errors and the machining errors, and the key error factors affecting the manufacturing and machining accuracy of the TH5656 are ultimately determined. Thus, this new method provides a way to quickly identify key errors of the three linear axes of machine tools, and offers guidance for the machine tool configuration design, machining technology determination, and geometric error compensation.

Research on geometric error compensation of ultra-precision turning-milling machine tool based on macro–micro composite technology

Research on geometric error compensation of ultra-precision turning-milling machine tool based on macro–micro composite technology

High-precision robotic kinematic parameter identification and positioning error compensation method for industrial robot

Abstract A method based on laser tracing multi-station measurement technology is proposed in this paper. The method identifies the robotic kinematic parameters and compensates for the absolute positioning errors of industrial robots to improve the absolute positioning accuracy further. The position coordinates of industrial robots are typically measured using laser tracking devices. In this study, the measurement accuracy of an industrial robot is further enhanced using laser tracer multi-station measurement technology. Additionally, the least absolute shrinkage and selection operator (LASSO) algorithm was used to identify the robotic kinematic parameters. Compared with the commonly used least squares algorithm, the LASSO algorithm improved the parameter identification accuracy and the compensation effect on absolute positioning errors. A position error model was established based on the parameters of the modified Denavit–Hartenberg model of an industrial robot. Using the LASSO algorithm, the robotic kinematic parameters were accurately identified, and the original data in the controller were replaced to compensate for the geometric errors of the industrial robot. In the compensation experiments, after implementing the geometric error compensation, the average absolute positioning error of the industrial robot decreased by 41.15%, demonstrating a significant improvement in the absolute positioning accuracy.

A layerwise geometric error compensation procedure for additive manufacturing

PurposeThe purpose of this paper is to provide a new procedure for in-plane compensation of geometric errors that often appear in the layers deposited by an additive manufacturing (AM) process when building a part, regardless of the complexity of the layer geometry.Design/methodology/approachThe procedure is based on comparing the real layer contours to the nominal ones extracted from the STL model of the part. Considering alignment and form deviations, the compensation algorithm generates new compensated contours that match the nominal ones as closely as possible. To assess the compensation effectiveness, two case studies were analysed. In the first case, the parts were not manufactured, but the distortions were simulated using a predictive model. In the second example, the test part was actually manufactured, and the distortions were measured on a coordinate measuring machine.FindingsThe geometric deviations detected in both case studies, as evaluated by various quality indicators, reduced significantly after applying the compensation procedure, meaning that the compensated and nominal contours were better matched both in shape and size.Research limitations/implicationsAlthough large contours showed deviations close to zero, dimensional overcompensation was observed when applied to small contours. The compensation procedure could be enhanced if the applied compensation factor took into account the contour size of the analysed layer and other geometric parameters that could have an influence.Originality/valueThe presented method of compensation is applicable to layers of any shape obtained in any AM process.

Optimal proportion compensation method of key geometric errors for five-axis machine tools considering multiple-direction coupling effects

Five-axis machine tools are subject to highly coupled geometric errors that significantly affect their machining accuracy. Existing geometric error compensation methods do not consider the coupling effects between errors, resulting in insufficient error compensation efficiency and accuracy. To solve this problem, an optimal proportion compensation method for key geometric errors of five-axis machine tools was proposed, considering multiple direction coupling effects. The key geometric errors were identified using the improved Sobol method based on the volumetric error model. The coupling effects of the geometric errors were analyzed based on the overlapping terms of the key errors in multiple directions, and the coupling situation was classified into four types. The compensation sequence and proportion value in each direction were developed according to the coupling type; i.e., the key errors were compensated to the proportion value instead of the traditional compensation to zero. Taking the S-shaped specimen as an example, the experimental verification indicated that the number of geometric error items that had to be compensated by our method was reduced by 44.4 % compared to the traditional key geometric error compensation method. Additionally, the compensation accuracy was increased by 58.9 %, thus proving the effectiveness of the proposed method.

Uncertainty assessment of machine tool squareness error identification using on-machine measurement

Identification and compensation of geometric errors in the machine tool are widely performed to increase machining accuracy. Periodic verification of the geometric errors, as introduced in ISO 230-2, helps monitor the machine tool accuracy during continued manufacturing operation and detect accuracy degradation early on. While interferometry-based error identification techniques are commonly applied, on-machine measurement (OMM), with its increasing availability to machine tools, can be used to identify geometric errors as an alternative to traditional interferometry-based techniques. As geometric errors also contribute to OMM error, assessment of the uncertainty of error identification is essential to ensure the reliability of the identification. This work presents a method to evaluate the uncertainty in the OMM-based geometric error identification process by Monte Carlo simulation. The error ellipse model, which represents OMM errors with better accuracy, is utilized to improve the identification uncertainty. The squareness errors, as position-independent geometric errors that contribute to machining inaccuracy, are taken as an example to demonstrate the presented method. The influence of the artifact setup errors on the error identification is also investigated. A series of experiments are conducted to evaluate the uncertainty of the OMM-based identification method. The geometric error obtained with the presented method is found to deviate by less than 10% from that obtained with an interferometry-based commercial instrument. The uncertainty obtained from the proposed Monte Carlo simulation method matches well with the uncertainty results obtained by the Guide to the Expression of Uncertainty in Measurement method and repeated measurements.

Hierarchical Error Compensation Method for Two-Degree-of-Freedom Manipulator Positioning Error in Hybrid Robots

In this paper, taking a two-degree-of-freedom parallelogram serial manipulator of a hybrid robot as an example, a hierarchical error compensation method that combines geometric and non-geometric error compensation is proposed. First, we establish the geometric kinematic modeling and error model and use the Levenberg-Marquardt (L-M) method to identify the geometric error parameters. Then, we use the grid interpolation method to compensate for non-geometric errors, thereby improving the overall positioning accuracy of the manipulator. Finally, a simulation is presented to verify the correctness and effectiveness of the proposed method. The results show that the positioning accuracy is improved from 4.8568 mm to 0.0036 mm, and the attitude error is improved from 0.9437° to 0.0105°.

Geometric error modeling and compensation for high precision composite optical measurement systems

Composite optical measurement systems are widely used in the field of precision measurement due to their combination of inspection with high accuracy, speed, wide range, real-time, and other advantages. Whereas errors are prevalent in measurements, in order to improve detection accuracy, the systems must be compensated for geometric errors in three-dimensional space. Aiming at the complex situation of multi-probes and multi-zooms in the composite optical measurement system, the current error modelling methods are difficult to be directly applied, so this paper establishes a unified three-dimensional volumetric error model based on the theory of multi-body system and combined with the principle of geometric optics, performs the error verification through the direct measurement method, and finally realises the compensation of geometric error in the continuous space of the whole measurement range. Eventually, the accuracy of the proposed error model and the effectiveness of the error compensation method were verified by a laser interferometer and standard objects to be measured, and the integrated geometric error of the system was decreased by 76.55%, which effectively improved the accuracy of the system. The error modelling and compensation method proposed in this paper provides a new idea for the error compensation of the zoom measurement system, and at the same time, it is universal for the measurement systems of different structures and motion forms, which can be widely used in the field of precision measurement.

Position-independent geometric error compensation of a non-orthogonal five-axis machine tool using a simplified algebraic algorithm

Geometric errors are the key error sources that affect the machining quality of a five-axis machine tool. In the case of a non-orthogonal five-axis machine tool (NOFAMT), the modelling and compensation of geometric errors can be quite complex. This paper proposes a simplified modelling algorithm to derive the analytical expressions for the position-independent geometric error (PIGE) compensation of a NOFAMT without generating higher-order error terms. First, the geometric error modelling was conducted based on the homogeneous transformation matrix (HTM). Then, algebraic expressions for PIGE compensation were obtained according to the actual inverse kinematics and a simplified algorithm. By using the simplified algorithm, the efficiency of deriving algebraic expressions for geometric error compensation can be greatly enhanced. The PIGE compensation’s numerical control (NC) codes can be directly computed using these algebraic expressions. Finally, the effectiveness and efficiency of the new algorithm were verified by numerical analysis and virtual machining. The detailed results were compared with those obtained using the differential method, and both sets of results showed the same trend.

A novel geometric error compensation method for improving machining accuracy of spiral bevel gear based on inverse kinematic model

A novel geometric error compensation method for improving machining accuracy of spiral bevel gear based on inverse kinematic model

Geometric Error Calibration of XYZ-3RPS Hybrid Kinematic Machine via Binocular Vision

Abstract To improve the motion accuracy of an XYZ-3RPS hybrid kinematic machine (HKM), a geometric error calibration method via binocular vision measurement is studied. First, to separately calibrate the series kinematic mechanisms (SKMs) and parallel kinematic mechanisms (PKMs), the geometric error identification equations (GEIEs) of the XYZ SKM and 3RPS PKM are derived, respectively. By analyzing the different influence principles of the geometric errors on the position and attitude of the 3RPS PKM, a constraint function is added to the GEIE of the PKM to improve the calculation accuracy. Moreover, the geometric error compensation strategy is based on the structural characteristics of the XYZ-3RPS HKM. In addition, based on the principle of binocular vision measurement, two calibration plates, called dynamic and static calibration plates, are designed as markers to define the coordinate systems, enabling the acquisition of full positions and attitudes. Furthermore, a marker transformation method and an in-situ adjustment method are designed to determine the positions and attitudes of the HKM required for calibration such that the marker is always at the center of the field of view of the camera to improve measurement accuracy. Finally, the effectiveness of the calibration method is verified through prototype experiments.