Thermal Error Modeling Research Articles

An interval prediction approach for quantifying the thermal error uncertainty of ball screw system

The ball screw system is one of the most core components of CNC machine tool, and its thermal positioning error directly affects the machining accuracy of parts. Establishing a data-based thermal error model is currently a popular method to predict this thermal error. Uncertain disturbances are unavoidable in reality. However, most of the existing thermal error models are deterministic, which cannot consider the uncertainty and generally can only provide the predictive value. To quantify the uncertainty of thermal error from the ball screw system, this paper proposes an interval prediction method, in which gated recurrent unit (GRU) neural network is embedded into the model and prediction interval (PI) evaluation indexes are used to determine the model parameters. Both the temporal and spatial characteristics of thermal error in the ball screw system are taken into account by the proposed method. The experimental data has verified that the proposed method can effectively generate PIs for the thermal error of ball screw system.

Thermal Error Transfer Prediction Modeling of Machine Tool Spindle with Self-Attention Mechanism-Based Feature Fusion

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.

Feed shaft thermal expansion error modeling based on principal component regression

In order to further improve the prediction accuracy of the thermal error model of the feed shaft of the gear grinding machine, this paper proposes a feed shaft thermal expansion error modeling method based on principal component regression. The feed shaft positioning error is decoupled by linear fitting to obtain the thermal expansion slope parameter, the position correlation of the feed shaft thermal expansion error is eliminated, and a regression model of the thermal expansion slope parameter and the temperature of all measuring points is established based on the principal component regression algorithm. Different from the traditional method, the principal component regression model does not require additional screening of temperature sensitive points, and the root mean square error mean and standard deviation of the group experimental prediction results can reach 2.0 μm/m、0.9μm/m, which has higher accuracy and stability than conventional methods.

A method for temperature sensor and model selection for machine tool thermal error modelling using ANFIS and ANN

AbstractThermal errors account for a significant part of the dimensional errors of components produced by precision machine tools. These errors are commonly compensated using predictions from temperature-based empirical models. The accuracy and robustness of these predictions are affected by the locations of temperature sensors used to obtain the model’s input data. Methods for sensor selection found in literature are often difficult to replicate and automate because they require tuning of several hyperparameters. This work presents a sensor and model selection approach that uses proper orthogonal decomposition (POD) and QR pivoting to select a subset of sensors that have been preinstalled in the machine tool as possible model inputs. These sensors are then sorted according to their correlation with the thermal error being modelled. The final set of inputs and thermal error model structure is chosen using Bayesian Information Criterion (BIC) to limit model overfitting. The approach was tested by modelling the Y-axis thermal error measured from air-cutting experiments performed under different spindle speeds and feed rates. This enabled determination of the structure and the choice inputs for Adaptive Neuro Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN) thermal error models. The accuracy of these models was compared to that of models trained using inputs selected by conventional approaches: the least absolute shrinkage and selection operator (LASSO), fuzzy c-means clustering (FCM), and principal component regression (PCR). The presented approach had better or comparable results to the conventional approaches while using fewer inputs. The presented approach is also well suited for automation compared to conventional approaches that require expert input.

Machine tool thermal error measurement and prediction via wireless microscope

A novel method is proposed to measure the thermal errors of a three-axis machine tool by taking images of unique custom-designed fiducials attached to a worktable using a wireless microscope mounted to the spindle. Multiple fiducials are applied for the measurement of different thermal errors at various worktable locations. In addition, a least-squares thermal error model within the work volume is proposed in which the model parameters are determined from various fiducial measurements, and the use of various fiducials for the thermal error model is analyzed. The results show the method can measure thermal errors within four times the positioning resolution of the machine tool, with most of the errors being smaller in magnitude than twice the positioning resolution. Further, the results show the thermal error model depends on the location of the fiducials used to construct the model. The unique numbering system for the fiducial patterns also allows for the measurement of large planar thermal errors, which is advantageous for machine tools that undergo significant thermal drift.

Thermal image-driven thermal error modeling and compensation in CNC machine tools based on deep attentional residual network

Thermal image-driven thermal error modeling and compensation in CNC machine tools based on deep attentional residual network

Recent Patents on Thermal Characteristic Analysis and Modeling of Machine Tools

Abstract: Modern machining machines are becoming more sophisticated and automated, but the problems of thermal deformation caused by machining have also come to the fore. CNC machine tools are used in high-speed, high-feed rate machining conditions, so the impact of thermal deformation factors will lead to a more prominent loss of accuracy. In this context, the design and manufacture of future CNC machine tools need to take further account of the errors caused by thermal deformation and the accompanying loss of accuracy. The principle of thermal characterisation and thermal error modeling of machine tools is to measure and reasonably analyse the machine tool at different temperature points and make corrections to the analysis data in order to get a value as close as possible to the real value and improve machining accuracy. Several representative patents and studies on thermal characterisation and thermal error modeling of machine tools at home and abroad are reviewed. This study presents a selection and summary of a large number of recent patents and studies on machine tool thermal characterisation and thermal error modeling, focusing on the selection of the machine tool thermal error measurement point area, thermal error modeling methods, spindle thermal displacement compensation, and other aspects, and discusses the future trends in the mainstream methods for reducing the thermal error of machine tools. The analysis and modeling of thermal errors in machine tools have an integral influence on further improvements in machining accuracy and efficiency in the future.

Modeling of machine tool thermal error based on factor extraction

Abstract In the process of modeling thermal errors in machine tools, optimizing the extraction of temperature information affects the prediction accuracy of the thermal error model. This paper proposes a thermal error modeling method based on factor extraction. Firstly, the temperature measurement points are optimized to determine the optimal number using finite element, fuzzy clustering, and correlation methods. Then, the common deformation factors in the machine tool temperature information are extracted through factor analysis, and they are used as independent variables for thermal error modeling. Finally, the method was applied to establish a model for thermal error model for a certain model of precision machine tool, and a regression model of the machine tool was obtained after factor extraction optimization, the effectiveness and feasibility of the proposed method in this paper were verified by comparing it with experimental data. The method proposed in this study provides a reference for modeling thermal errors in various types of machine tools in the future.

Multi-verse optimizer for thermal error modeling approach of spindle system based on thermal image

Since the spindle thermal error of CNC machine tools has a significant impact on machining precision, this paper introduces a unique approach for modeling spindle thermal error. Several key steps are involved in the proposed approach. First, the Fluke thermal imaging camera is employed for acquiring thermal image information of the spindle system. Second, the Gaussian filter is employed to denoise the thermal image sequence. Next, the temperature values at the measurement points are extracted from the thermal image sequence according to the mapping relationship between the grayscale value and the temperature value. Subsequently, critical temperature points are identified from thermal images using the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the correlation coefficient method. Finally, the multi-verse optimized NARX neural network is employed to investigate the nonlinear prediction of thermal deformation. The research is conducted on the VMC-850E vertical machining center as the subject of study. The performance of the model is validated under conditions of idle spindle and 5000 r/min, comparing prediction results against traditional algorithms. The findings demonstrate that the non-contact measurement method based on thermal imaging successfully establishes the thermal error model, achieving a prediction accuracy of 0.1517 μm for the MVO-NARX model.

Thermal error modeling method of truss robot based on GA-LSTM

PurposeThe selection of sensitive temperature measurement points is the premise of thermal error modeling and compensation. However, most of the sensitive temperature measurement point selection methods do not consider the influence of the variability of thermal sensitive points on thermal error modeling and compensation. This paper considers the variability of thermal sensitive points, and aims to propose a sensitive temperature measurement point selection method and thermal error modeling method that can reduce the influence of thermal sensitive point variability.Design/methodology/approachTaking the truss robot as the experimental object, the finite element method is used to construct the simulation model of the truss robot, and the temperature measurement point layout scheme is designed based on the simulation model to collect the temperature and thermal error data. After the clustering of the temperature measurement point data is completed, the improved attention mechanism is used to extract the temperature data of the key time steps of the temperature measurement points in each category for thermal error modeling.FindingsBy comparing with the thermal error modeling method of the conventional fixed sensitive temperature measurement points, it is proved that the method proposed in this paper is more flexible in the processing of sensitive temperature measurement points and more stable in prediction accuracy.Originality/valueThe Grey Attention-Long Short Term Memory (GA-LSTM) thermal error prediction model proposed in this paper can reduce the influence of the variability of thermal sensitive points on the accuracy of thermal error modeling in long-term processing, and improve the accuracy of thermal error prediction model, which has certain application value. It has guiding significance for thermal error compensation prediction.

Predicting and compensating for small-sample thermal information data in precision machine tools: A spatial-temporal interactive integration network and digital twin system approach

The thermal errors in ball screws present complex spatial-temporal characteristics and exhibit persistent long-term memory, significantly affecting the machining accuracy of the whole machine tool in applications. Deep learning has emerged as a promising approach to predict these errors using thermal data. However, the scarcity of extensive thermal datasets, typically due to the prohibitive costs and time required for experimental acquisition, hampers the comprehensive exploitation of spatial-temporal and long-term memory attributes. Moreover, the current thermal error compensation system does not support the deployment of deep learning-based thermal error models due to its weak real-time performance. These limitations lead to suboptimal prediction accuracy and inadequate error compensation. Addressing this challenge, a novel spatial-temporal interactive integration network is proposed, and this is a sophisticated model that synergistically blends a time memory gate and a spatial-temporal fusion gate within an advanced attention-based spatial-temporal graph convolutional framework. Our network ingeniously leverages spatial data to anchor long-term memory while employing temporal data for selective memory feature extraction, facilitating a refined integration of spatial-temporal features. Concurrently, the integration of gated recurrent units and a time attention layer meticulously extracts and enhances temporal features, bolstered by our innovative time memory gate, which is adept at handling small-sample scenarios and refining thermal error predictions. Critically, the digital twin system for thermal error compensation is constructed to improve the system’s real-time performance. The integration of this network into the digital twin system marks a pivotal advancement in thermal error compensation. Our empirical results underscore the system's remarkable robustness and superior predictive accuracy, demonstrating a significant reduction in positioning and machining errors (over 90% and 80% respectively) even with constrained thermal data inputs. These advancements not only delineate a substantial leap in predictive accuracy but also underscore our contribution to reducing operational costs and enhancing the efficacy of machine tools.

Correction to: Integrated thermal error modeling and compensation of machine tool feed system using subtraction‑average‑based optimizer‑based CNN‑GRU neural network

Correction to: Integrated thermal error modeling and compensation of machine tool feed system using subtraction‑average‑based optimizer‑based CNN‑GRU neural network

Study on thermal error modeling of high-speed motorized spindle considering bearing inner ring temperature

In addressing the challenge of unattainable temperature data at critical heat source points in bearings, this study solves for the temperatures of the bearing inner ring and rollers by merging thermal resistance network calculations with experimental data, referencing finite element simulation outcomes. The impact of temperature data from various positions within bearings on model accuracy is assessed using a BP prediction model. Subsequently, the training dataset of the thermal error model is optimized to enhance its predictive performance. To further boost the predictive capabilities of the model, a whale optimization algorithm is employed to optimize the BP neural network, which is then compared against both the conventional BP model and the GPR model. The findings reveal that a model optimized with the input of inner ring temperatures and the WOA algorithm achieves an accuracy rate of 97.748 %, outperforming both the BP model and the GPR model. This study provides a new idea for the field of thermal error modeling of motorized spindle.

Thermal error modelling and compensation of CNC lathe feed system based on positioning error measurement and decoupling

Thermal error modeling and compensation considering of the measured positioning error decoupling for the lathe with a slant bed is proposed. Due to the complex coupling factors of thermal error, the current compensation methods exhibit limited applicability and generalization. The linear fitting method is used to decouple geometric error and thermal error from the positioning error. The motion heating and non-motion heating experiments of X-direction feed system were carried out to investigate the principle of thermal error generation and the impact factors. The multiple linear regression model of the thermal error was established based on the analysis of the thermal error measurement results. To verify the effectiveness of the proposed model, the thermal error at two working conditions was predicted, and then the error compensation was carried out. The results show that the positioning error is reduced by more than 84% and 92% with the present method compared with that without compensation. This research provides effective method for the generation principle and compensation of thermally induced errors of lathe with a slant bed.

Spindle unit thermal error modeling and compensation based on digital twin

Spindle unit thermal error modeling and compensation based on digital twin

Thermal error modeling of electric spindles based on cuckoo algorithm optimized Elman network

Thermal error modeling of electric spindles based on cuckoo algorithm optimized Elman network

A novel adaptive deep transfer learning method towards thermal error modeling of electric spindles under variable conditions

Thermal error modeling (TEM) plays a vital role in maintaining the machining accuracy of electric spindles. Recently, deep learning (DL) techniques have obtained promising achievements in this area. However, DL techniques have certain limitations. The data acquired from variable working conditions present large distribution discrepancies, the DL-based model established on one working condition fails to obtain satisfactory prediction accuracy in another working condition. Moreover, existing studies focus solely on using temperature features to build prediction models, neglecting the full use of multi-sensory information. To address these issues, this paper proposes a novel adaptive deep transfer learning method towards TEM of electric spindles, which takes full advantage of the temperature, current, and power sensory information. Firstly, finite element simulation is employed to analyze the thermal characteristics of the electric spindle and determine the locations for temperature measurement points. Then, the convolutional long short-term memory network (C-LSTMN) is constructed, where the spatial features from multi-sensory information between inputs and prediction patterns are captured by convolutional layers, these features are further processed by long short-term memory network (LSTMN) to extract temporal features. Subsequently, the multi-kernel joint maximum mean discrepancy (MK-JMMD) measure is developed to minimize the distribution discrepancies between the source and target domains, thus the prediction model initially established on the source domain can be adaptive to effectively predict on the target domain. Finally, with unavailable thermal error data in the target domain, the proposed method is validated through 12 transfer tasks using datasets from four working conditions with other comparison methods. The results demonstrate that the proposed method overcomes the challenges of unavailable labeled thermal error samples and outperforms advanced methods.

Adaptive thermal error prediction for CNC machine tool spindle using online measurement and an improved recursive least square algorithm

Establishing models for predicting and compensating for spindle thermal errors is cost-effective and necessary to improve the accuracy of machine tools for smart manufacturing. However, the prediction performance of existing methods deteriorates significantly with dynamic working conditions of machine tools because training from static conditions leads to the inability to adapt to dynamic conditions. Therefore, an adaptive thermal error modeling method using online measurement and an improved recursive least square algorithm is proposed to fill this research gap, which updates the thermal error model adaptively to ensure that dynamic working conditions are learned in real time. Particularly, Spearman's rank correlation coefficient method is first adopted for temperature-sensitive point selection to capture the nonlinear relationship between temperature and thermal error variables. Furthermore, a variable-forgetting factor-based recursive least square (VFF-RLS) algorithm is proposed to improve the prediction performance, in which the proposed variable forgetting factor is adaptively updated according to real-time thermal error data collected by online measurement. The experimental results showed that the proposed VFF-RLS method can maintain a high prediction accuracy of 1.75 μm and robustness of 0.16 μm on both constant and dynamic working conditions. The effectiveness of the VFF-RLS method is validated by verification experiments.

Integrated thermal error modeling and compensation of machine tool feed system using subtraction-average-based optimizer-based CNN-GRU neural network

Integrated thermal error modeling and compensation of machine tool feed system using subtraction-average-based optimizer-based CNN-GRU neural network

Thermal error modelling of gear measuring instrument based on principal component regression

As gear measuring instruments (GMI) are frequently used at the production site, the influence of temperature on their accuracy and stability becomes non-negligible. The existing standards and technologies only consider the error modelling and compensation problem when the GMI is in a uniform temperature field and is not suitable for the production site environment with a large temperature change rate and large temperature gradient. The paper delves into the problems of GMI thermal error modelling at the production site. First, the temperatures of the GMI and its surroundings were measured using multiple temperature sensors. The parallelism thermal errors between centres and the Z-axis (referred to as parallelism thermal errors) and the y-direction spatial thermal errors (referred to as spatial thermal errors) were also measured by the probe and laser interferometer synchronously. Then, the models of them were established based on principle component regression (PCR). As evidenced by the experimental results, the fitting determination coefficient of the models are both greater than 97%, and the prediction determination coefficient is greater than 90%, demonstrating that the models are precise and robust.