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Machines
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Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools
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Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Machines Testing and Maintenance".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 9940

Special Issue Editors

Dr. Guoqiang Fu

E-Mail Website
Guest Editor
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Interests: precision enhancement of multi-axis machine tools and precision machining, including thermal error modeling and correction, cutting error control based on signal processing and intelligent control; CNC tool path generation and optimization
Prof. Dr. Jianzhong Fu

E-Mail Website
Co-Guest Editor
1. The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
2. Key Lab of 3D Printing Process and Equipment of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
Interests: intelligent manufacturing technology; intelligent CAD/CAM/CNC; 3D printing technology and equipment

Special Issue Information

Dear Colleagues,

CNC machine tools represent the core competitiveness of a country’s manufacturing industry. They play an important role in national defense, aerospace, and automobile manufacturing. With the development of intelligent manufacturing, the demands regarding the accuracy of CNC machine tools have been increasing. Many factors influence the machining accuracy of CNC machine tools, including geometric errors, thermal errors, cutting force deformation errors, servo tracking errors, and so on. Error measurement, analysis, and compensation is one of the important ways to enhance the accuracy of the CNC machine tools.

The objective of this Special Issue is to discover the most recent and significant developments in error measurement, error analysis, error modeling, and compensation for CNC machine tools. This Special Issue encourages and welcomes original research articles with a significant contribution to numerical, theoretical, and experimental analysis. Review articles related to these application areas are also invited.

Potential topics include, but are not limited to:

Geometric errors of machine tools;
Thermal errors of machine tools;
Error measurement and identification;
Error modeling;
Error compensation;
Data acquisition and measurement methods;
Machine learning and intelligent error modeling.

Dr. Guoqiang Fu
Prof. Dr. Jianzhong Fu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • CNC machine tools
  • error measurement and identification
  • error modeling
  • error compensation

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Published Papers (7 papers)

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Research

17 pages, 5289 KiB  
Article
Multi-Objective Optimization Design of Dual-Spindle Component Based on Coupled Thermal–Mechanical–Vibration Collaborative Analysis
by Xiaoliang Lin, Yiming Xie, Xiaolei Deng, Jing Tian, Yue Han and Peng Wang
Machines 2024, 12(12), 885; https://doi.org/10.3390/machines12120885 - 5 Dec 2024
Viewed by 712
Abstract
To comprehensively improve the thermal, static and dynamic characteristics and achieve lightweighting for CNC machine tools, this paper proposes a multi-objective joint optimization method based on coupled thermal–mechanical–vibration collaborative analysis. The dual-spindle component of a CNC machine tool is taken as the parameterized [...] Read more.
To comprehensively improve the thermal, static and dynamic characteristics and achieve lightweighting for CNC machine tools, this paper proposes a multi-objective joint optimization method based on coupled thermal–mechanical–vibration collaborative analysis. The dual-spindle component of a CNC machine tool is taken as the parameterized model. According to the theories of thermal characteristics, statics, and dynamics, the solution of thermal-mechanical coupling deformation and the solution of vibration characteristics under prestress are repeatedly conducted, that are working collaboratively with each process of parameters sensitivity computing, selection of design variables, central composite design, and multi-objective joint optimization. The response surfaces of the objective functions are established. The optimal parameter combination for improving CNC machine tool performance is effectively obtained. And the multiple objectives of improving the thermal, static and dynamic characteristics, as well as lightweighting, are achieved. The results show that the mass of the optimized component is reduced by 10.1%; the first-order natural frequency is increased by 3.9%; the coupling deformation of the end face of the left spindle seat is reduced by 5.3%; and the coupling deformation of the end face of the right left spindle seat is reduced by 9.0%, while the temperature of the component hardly increases. This indicates that this method can comprehensively improve the performance of CNC machine tool components and provide a reference for the multi-objective joint optimization design of CNC machine tools. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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19 pages, 3670 KiB  
Article
Modal Parameter Identification of Electric Spindles Based on Covariance-Driven Stochastic Subspace
by Wenhong Zhou, Liuzhou Zhong, Weimin Kang, Yuetong Xu, Congcong Luan and Jianzhong Fu
Machines 2024, 12(11), 774; https://doi.org/10.3390/machines12110774 - 4 Nov 2024
Viewed by 1051
Abstract
Electric spindles are a critical component of numerically controlled machine tools that directly affect machining precision and efficiency. The accurate identification of the modal parameters of an electric spindle is essential for optimizing design, enhancing dynamic performance, and facilitating fault diagnosis. This study [...] Read more.
Electric spindles are a critical component of numerically controlled machine tools that directly affect machining precision and efficiency. The accurate identification of the modal parameters of an electric spindle is essential for optimizing design, enhancing dynamic performance, and facilitating fault diagnosis. This study proposes a covariance-driven stochastic subspace identification (SSI-cov) method integrated with a simulated annealing (SA) strategy and fuzzy C-means (FCM) clustering algorithm to achieve the automated identification of modal parameters for electric spindles. Using both finite element simulations and experimental tests conducted at 22 °C, the first five natural frequencies of the electric spindle under free, constrained, and dynamic conditions were extracted. The experimental results demonstrated experiment errors of 0.17% to 0.33%, 1.05% to 3.27%, and 1.29% to 3.31% for the free, constrained, and dynamic states, respectively. Compared to the traditional SSI-cov method, the proposed SA-FCM method improved accuracy by 12.05% to 27.32% in the free state, 17.45% to 47.83% in the constrained state, and 25.45% to 49.12% in the dynamic state. The frequency identification errors were reduced to a range of 2.25 Hz to 20.81 Hz, significantly decreasing errors in higher-order modes and demonstrating the robustness of the algorithm. The proposed method required no manual intervention, and it could be utilized to accurately analyze the modal parameters of electric spindles under free, constrained, and dynamic conditions, providing a precise and reliable solution for the modal analysis of electric spindles in various dynamic states. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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17 pages, 11316 KiB  
Article
Thermal Error Transfer Prediction Modeling of Machine Tool Spindle with Self-Attention Mechanism-Based Feature Fusion
by Yue Zheng, Guoqiang Fu, Sen Mu, Caijiang Lu, Xi Wang and Tao Wang
Machines 2024, 12(10), 728; https://doi.org/10.3390/machines12100728 - 15 Oct 2024
Viewed by 1258
Abstract
Thermal errors affect machining accuracy in high-speed precision machining. The variability of machine tool operating conditions poses a challenge to the modeling of thermal errors. In this paper, a thermal error model based on transfer temperature feature fusion is proposed. Firstly, the temperature [...] Read more.
Thermal errors affect machining accuracy in high-speed precision machining. The variability of machine tool operating conditions poses a challenge to the modeling of thermal errors. In this paper, a thermal error model based on transfer temperature feature fusion is proposed. Firstly, the temperature information fusion features are built as inputs to the model, which is based on a self-attention mechanism to assign weights to the temperature information and fuse the features. Secondly, an improved direct normalization-based adaptive matrix approach is proposed, updating the background matrix using an autoencoder and reconstructing the adaptive matrix to realize domain self-adaptation. In addition, for the improved adaptive matrix, a criterion for determining whether the working conditions are transferrable to each other is proposed. The proposed method shows high prediction accuracy while ensuring training efficiency. Finally, thermal error experiments are performed on a VCM850 CNC machine tool. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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16 pages, 6063 KiB  
Communication
Drifted Uncertainty Evaluation of a Compact Machine Tool Spindle Error Measurement System
by Yubin Huang, Xiong Zhang, Kaisi You, Jihong Chen, Hao Zhou and Hua Xiang
Machines 2024, 12(10), 695; https://doi.org/10.3390/machines12100695 - 1 Oct 2024
Viewed by 1014
Abstract
The accurate measurement of spindle errors, especially quasi-static errors, is one of the key issues for the analysis and compensation of machine tool thermal errors in machining accuracy. To quantitatively analyze the influence of the measurement system’s own drift on the measurement results, [...] Read more.
The accurate measurement of spindle errors, especially quasi-static errors, is one of the key issues for the analysis and compensation of machine tool thermal errors in machining accuracy. To quantitatively analyze the influence of the measurement system’s own drift on the measurement results, a drifted uncertainty evaluation method of the precision instrument considering the time drift coefficient is proposed. This study also produced a high-precision compact spindle error measurement device (with a displacement measurement error of less than ±1.33 μm and an angular measurement error of less than ±1.42 arcsecs) as the research object to verify the proposed drift uncertainty evaluation method. A method for evaluating the drift uncertainty of the measurement system is proposed to quantitatively evaluate the system error and drift uncertainty of the measurement device. Experiments show that the drift uncertainty evaluation method proposed in this paper is more suitable for evaluating the uncertainty changes in measurement instruments during long-term measurements compared to traditional methods. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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16 pages, 3561 KiB  
Article
Thermal Error Prediction for Vertical Machining Centers Using Decision-Level Fusion of Multi-Source Heterogeneous Information
by Yue Han, Xiaolei Deng, Junjian Zheng, Xiaoliang Lin, Xuanyi Wang and Yong Chen
Machines 2024, 12(8), 509; https://doi.org/10.3390/machines12080509 - 29 Jul 2024
Cited by 1 | Viewed by 1190
Abstract
To address the limitations in predictive capabilities of thermal error models built from single-source, single-structure data, this paper proposes a thermal error prediction model based on decision-level fusion of multi-source heterogeneous information to enhance prediction accuracy. First, an experimental platform for multi-source heterogeneous [...] Read more.
To address the limitations in predictive capabilities of thermal error models built from single-source, single-structure data, this paper proposes a thermal error prediction model based on decision-level fusion of multi-source heterogeneous information to enhance prediction accuracy. First, an experimental platform for multi-source heterogeneous information acquisition was constructed to collect thermal error data from different signal sources (multi-source) and different structures (heterogeneous). Next, based on the characteristics of the multi-source and heterogeneous data, relevant features were extracted to construct the feature set. Then, using the feature information set of the multi-source and heterogeneous data, thermal error prediction sub-models were established using Nonlinear Autoregressive models with exogenous inputs (NARX) and Gated Recurrent Units (GRUs) for a vertical machining center spindle. Finally, the entropy weight method was employed to assign the weights for the linear-weighted fusion rule, achieving decision-level fusion of multi-source heterogeneous information to obtain the final prediction result. This result was then compared with experimental results and the prediction results of single-source models. The findings indicate that the proposed thermal error prediction model closely matches the actual results and outperforms the single-source and single-structure data models in terms of Root-Mean-Square Error (RMSE), Coefficient of Determination (R2), and Mean Absolute Error (MAE). Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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18 pages, 5290 KiB  
Article
The Grinding and Correction of Face Gears Based on an Internal Gear Grinding Machine
by Zhengyang Han, Chuang Jiang, Xiaozhong Deng, Congcong Zhang, Longlong Geng and Yong Feng
Machines 2024, 12(8), 496; https://doi.org/10.3390/machines12080496 - 23 Jul 2024
Viewed by 1469
Abstract
This paper presents a method of calculating and correcting grinding face gears on an internal gear grinding machine. The generating principle of face gears is studied, and the feasibility of grinding motion on an internal gear grinding machine is analyzed. Then, the motions [...] Read more.
This paper presents a method of calculating and correcting grinding face gears on an internal gear grinding machine. The generating principle of face gears is studied, and the feasibility of grinding motion on an internal gear grinding machine is analyzed. Then, the motions that need to be followed for grinding are analyzed based on the gear machine tool structure. Four main error sources causing tooth surface deviation in the grinding movements are proposed. The mathematical modeling of the grinding of face gears containing proposed error sources on an internal gear grinding machine is accurately established. The influence of the error sources on the topological deviations of the tooth surface is explored. A sensitivity matrix is established for the influence of various error factors on the tooth surface deviations. The correction values of each error factor are obtained in the case of existing tooth surface deviations. Finally, a virtual machining experiment is conducted, which proves the accuracy of the proposed method for characterizing grinding and realizing corrections. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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16 pages, 2697 KiB  
Article
Kinematic Parameter Identification and Error Compensation of Industrial Robots Based on Unscented Kalman Filter with Adaptive Process Noise Covariance
by Guanbin Gao, Xinyang Guo, Gengen Li, Yuan Li and Houchen Zhou
Machines 2024, 12(6), 406; https://doi.org/10.3390/machines12060406 - 12 Jun 2024
Cited by 2 | Viewed by 1509
Abstract
Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of [...] Read more.
Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of high-order system information. To address this issue, we propose an unscented Kalman filter (UKF) with adaptive process noise covariance for robot kinematic parameter identification. The kinematic model of a typical 6-degree-of-freedom industrial robot is established. The UKF is introduced to identify the unknown constant parameters within this model. To mitigate the reliance of the UKF on the process noise covariance, an adaptive process noise covariance strategy is proposed to adjust and correct this covariance. The effectiveness of the proposed algorithm is then demonstrated through identification and error compensation experiments for the industrial robot. Results indicate its superior stability and accuracy across various initial conditions. Compared to the conventional UKF algorithm, the proposed approach enhances the robot’s accuracy stability by 25% under differing initial conditions. Moreover, compared to alternative methods such as the extended Kalman algorithm, particle swarm optimization algorithm, and grey wolf algorithm, the proposed approach yields average improvements of 4.13%, 26.47%, and 41.59%, respectively. Full article
(This article belongs to the Special Issue Error Measurement, Analysis, and Compensation Technology for CNC Machine Tools)
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