Thermal Error Research Articles

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.

Research on electric spindle thermal error prediction model based on DBO-SVM

Research on electric spindle thermal error prediction model based on DBO-SVM

A Novel Methodology for Measuring Ambient Thermal Effects on Machine Tools.

Large machine tools are critically affected by ambient temperature fluctuations, impacting their performance and the quality of machined products. Addressing the challenge of accurately measuring thermal effects on machine structures, this study introduces the Machine Tool Integrated Inverse Multilateration method. This method offers a precise approach for assessing geometric error parameters throughout a machine's working volume, featuring a low level of uncertainty and high speed suitable for effective temperature change monitoring. A significant innovation is found in the capability to automatically realise the volumetric error characterisation of medium- to large-sized machine tools at intervals of 40-60 min with a measurement uncertainty of 10 µm. This enables the detailed study of thermal errors which are generated due to variations in ambient temperature over extended periods. To validate the method, an extensive experimental campaign was conducted on a ZAYER Arion G™ large machine tool using a LEICA AT960™ laser tracker with four wide-angle retro-reflectors under natural workshop conditions. This research identified two key thermal scenarios, quasi-stationary and changing environments, providing valuable insights into how temperature variations influence machine behaviour. This novel method facilitates the optimization of machine tool operations and the improvement of product quality in industrial environments, marking a significant advancement in manufacturing metrology.

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.

Feature correlation method for image reconstruction evaluation in under-sampled scanning probe microscopy

We introduce an advanced feature-correlation approach for evaluating the accuracy of data completion in scanning probe microscopy (SPM). Our method utilizes characteristic patterns from conventional SPM images and their reconstructions via data interpolation. We develop a refined comparative evaluation algorithm based on correlation coefficients. This algorithm provides a precise assessment by effectively addressing SPM-specific distortions such as thermal drift, feedback error, and noise limitations often overlooked by traditional metrics such as peak signal-to-noise ratio and structural similarity index measure. The effectiveness of our approach is demonstrated through its application in high-resolution and extensive scanning tunneling microscopy assessments.

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

Modelling and onsite testing on dynamic thermal responses of built environment in passive solar rooms on Tibetan plateau

It of great importance in assessing built thermal environment level and evaluating corresponding indoor air conditioning demand for energy conservation in construction sectors. Nevertheless, because of the unique meteorological features in plateau area, classical building performance simulation approach contributes to thermal performance evaluation errors since most design codes or standards relies on low attitude regions. In this paper, a modified and improved dynamic thermal design model is put forward for built environment and energy consumption estimation for passive buildings for plateau buildings. Moreover, the simplified experiment is set up to monitor dynamic thermal responses for modelling building. The testing validation illustrate that the onsite measurement accuracy level is quite acceptable for engineering applications with less than 30% relative change range coefficient. Besides, the experiment data demonstrates that window-to-wall ratios, architectural orientation, thermal insulation coefficients, have substantial impacts for solar heat gains in plateau buildings. The study renders building design guidance for energy conservation in high altitude plateau areas.

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.

Novel correction procedure for compensating thermal contraction errors in the measurement of the magnetic field of superconducting undulator coils in a liquid helium cryostat.

Superconducting undulators (SCUs) can offer a much higher on-axis undulator field than state-of-the-art cryogenic permanent-magnet undulators with the same period and vacuum gap. The development of shorter-period and high-field SCUs would allow the free-electron laser and synchrotron radiation source community to reduce both the length of undulators and the dimensions of the accelerator. Magnetic measurements are essential for characterizing the magnetic field quality of undulators for operation in a modern light source. Hall probe scanning is so far the most mature technique for local field characterization of undulators. This article focuses on the systematic error caused by thermal contraction that influences Hall probe measurements carried out in a liquid helium cryostat. A novel procedure, based on the redundant measurement of the magnetic field using multiple Hall probes at known relative distance, is introduced for the correction of such systematic error.

Post-process updating of model parameters to approximate thermal errors of machine tools operating in different configurations

Machine tool (MT) thermal errors induced by external and internal heat sources (e.g. changing environment, friction and power losses in MT components) are an important element in machined workpiece inaccuracies. In the past few decades, indirect software compensation techniques have been used to address thermal errors on account of their economic and ecological aspects. Many slightly different approaches are described in the literature. If thermal error models are properly identified based on experiments with sufficiently varying input parameters, they usually work within similar calibration and verification conditions. As the sensory equipment of machines increases, models can be adapted to regions with higher thermo-mechanical system nonlinearity and inhomogeneity through the introduction of deformation feedback from direct measurements into model structures. However, adaptive functionalities require discrete interruptions of the MT's work cycle, which threaten the integrity of the machined surface and complicate the model structure and thus also implementation and industrial deployment possibilities. In this research, a novel approach of automatic post-process adaptation suitable for repetitive manufacturing, which takes advantage of transfer functions (TF), is proposed for thermal error reduction. The method respects basic heat transfer mechanisms in the MT structure by combining linear parametric models, requires a minimum of additional gauges, and feedback from direct measurements is obtained only during technological pauses in the production process. Post-process adaptation is solved retrospectively by updating model parameters using the heuristic method of genetic algorithms (GA). First, the approach was tuned on a case study of a heavy-duty milling machine with a horizontal headstock for a configuration with an exchangeable spindle head and a configuration with a change in the position of the headstock in the workspace, both of which were different from the initial model's calibration range. Subsequently, the developed approach was applied to repeated production on a medium-sized milling centre. Another goal of the paper is to emphasize the need for quality input information for modelling efforts and the industrial applicability of scientific results.

Data-driven thermal error modeling based on a novel method of temperature measuring point selection

Data-driven thermal error modeling based on a novel method of temperature measuring point selection

Research on High-speed Electric Spindle Cooling Devices and Thermal Error Compensation Technology

Background: When computerized numerical control (CNC) machine tools are working, the electric spindle generates serious heat, which can easily cause the thermal elongation of the spindle and generate thermal errors. Designing cooling devices to control the generation of thermal errors in the spindle and utilizing thermal error compensation techniques for error compensation are essential for improving machining quality and productivity. Objective: By summarizing the current status of research on cooling devices and compensation technology of electric spindles in recent years, some conclusions have been drawn in this work to propose the future research direction. Methods: By reviewing patents on cooling devices and thermal error compensation technology of high-speed electric spindles published in recent years, we have explored the ideas for the improvement of existing cooling devices and compensation technology. Results: Some problems of the patents on current cooling devices and thermal error compensation technology are analyzed, and future research directions are proposed, respectively. Conclusion: As spindle power and speed continue to increase, the existing spindle cooling device and compensation technology also need to be continuously improved. Designers use intelligent technology to monitor the temperature changes during the work of the spindle and fast and accurate control of the cooling system so that the high-speed spindle cooling device tends to be intelligent. Aiming at the thermal error generated in the spindle working process, the designer enhances the error compensation effect by continuously improving and upgrading the key steps in the thermal error compensation technology, which in turn improves the spindle machining accuracy.

A study on the thermodynamic characteristics of a mechanical A/C swing angle milling head

Several studies have evaluated the thermal error modeling and structural characteristics of the swing angle milling head; however, few studies have reported the thermodynamic characteristics of the swing angle milling head. Therefore, based on the thermodynamic theory, the thermodynamic characteristics of the mechanical A/C swing angle milling head of the five axis CNC gantry milling machine are evaluated, and the relevant heating calculation results are obtained. The temperature field distribution and thermodynamic characteristics of the swing angle milling head were simulated and analyzed by using ANSYS Workbench finite element software. In addition, the accuracy and rationality of the finite element simulation results of this study are verified based on the experimental conclusions of other relevant scholars that the maximum temperature of the gear is also mainly distributed near the pitch line of the tooth surface. The research results indicate that the maximum heat generation area inside the swing angle milling head is mainly concentrated on the pitch line of the bevel gear tooth surface of the main spindle execution component, with a maximum temperature of 43.559°C. The maximum thermal deformation is located at the tip of the swing angle milling head, with a maximum thermal deformation of 1.8353 × 10−5 m, this study can provide important theoretical reference and data support for the structural optimization and thermal deformation control of subsequent swing angle milling heads.

Thermal error modeling of motorized spindle and application of miniature radiator in motorized spindle

Thermal error modeling of motorized spindle and application of miniature radiator in motorized spindle

Thermal Error Measurement and Compensation with Torque Limit Skip in Swiss-type Lathe Manufacturing

This paper presents a new methodology for the measurement of thermal errors of Swiss-type lathes. The basis of the proposed method is the torque limit skip function integrated in the lathe’s control which stops the motion of a linear axis if the torque on the corresponding axis servo is exceeded. The skip signal is triggered via a slow contact between a bar in the lathe’s spindle and an artefact in the lathe’s tool holder. Experimental results indicate that when a sufficiently low torque override limit is applied, the axis positioning repeatability under the repeated application of the torque limit skip is within ±1μm. The relative change in position of the axis after the skip measured over several hours is the thermal error which can be compensated. The proposed measurement technique offers significant advantages over conventional thermal error measurement with a touch-trigger probe or linear displacement sensors: if available on the machine’s control, it does not require any specialized installation, can be used during production, and delivers comparable results without high additional equipment costs.

The active cooling method for improving the accuracy of rotary tables of five-axis machines

This study investigated the application of an active cooling method to improve the accuracy of rotary tables in five-axis machines. The active cooling method stabilizes temperatures and optimizes the thermal environment around rotary tables. Multiple physical coupling analyses were performed to optimize thermal error and cooling performance through simulations and experiments. Flow control reduced deformation by approximately 53.5% and 84.1% through flow difference and temperature control, respectively. Following the ISO 230-3 experimental method, variable speed tests were conducted for durations of 10, 15, and 30 min. The results demonstrated that flow control effectively lowered spindle and bearing temperatures, thus mitigating thermal deformation. In the 10-minute variable speed experiment, decreasing the average temperature from 0.5 to 2 °C resulted in a 37.3% increase in Z-axis accuracy. In the 15-minute and 30-minute variable speed experiments, temperature reductions of 0.5 to 1 °C corresponded to Z-axis accuracy increases of 40.1% and 52.12%, respectively. The temperature decreases from 0.5 to 2.5 °C, resulting in a substantial 54.5% increase in Z-axis accuracy. The flow control at 80 rpm after 240 min in the 30-minute variable speed experiment exhibited superior temperature and deformation performance compared to the experiment without flow control. Results indicated that the cooling control method significantly improves the accuracy of five-axis machines, providing practical benefits for industrial applications.