Changes In Thermal State Research Articles

Viscosity and structure correlation mechanism of Fe[sbnd]Cr[sbnd]C melt based on MD simulation

The viscosity of FeCCr melt affects the mass transfer behavior during steelmaking processes. Reasonable regulation of viscosity can improve production efficiency. There is a close relationship between melt viscosity and structure. Therefore, it is of great theoretical significance to analyze the correlation between viscosity and structure of chromium-containing iron melt for the optimization of the whole metallurgical process. This study experimentally investigated the viscosity of FeCCr melt and utilized molecular dynamics simulation to analyze the formation and growth behavior of atomic clusters, revealing the correlation mechanism between structure and viscosity. As the Cr content increased from 11 % to 13 %, the melt viscosity increased by 10.05 %. At a temperature range from 1773 K to 1473 K, the viscosity reached a maximum of 15.5 mPa·s, representing a 40.9 % increase. Simulation results indicated that CrC clusters within the melt act as intermediaries, connecting with CrFe and FeC clusters to form FeCrC clusters. The key influence of increased Cr content on viscosity lies in promoting the generation of FeCrC multicomponent clusters, while the key influence of temperature reduction lies in promoting cluster growth. With the increase in Cr content, the number of clusters at 1773 K increased from 154 to 175, and the average volume of clusters increased from 212 Å3 to 224 Å3. When the temperature decreased from 1773 K to 1473 K, the number of clusters increased by 51.2 %, and the average volume of clusters increased by 18.75 %. In comparison, the thermal state change had a greater impact on clusters, where temperature reduction led to rapid cluster growth, reduction of free volume within the melt, and ultimately resulted in increased viscosity due to the combined effects.

AutoTherm: A Dataset and Benchmark for Thermal Comfort Estimation Indoors and in Vehicles

Thermal comfort inside buildings is a well-studied field where human judgment for thermal comfort is collected and may be used for automatic thermal comfort estimation. However, indoor scenarios are rather static in terms of thermal state changes and, thus, cannot be applied to dynamic conditions, e.g., inside a vehicle. In this work, we present our findings of a gap between building and in-vehicle scenarios regarding thermal comfort estimation. We provide evidence by comparing deep neural classifiers for thermal comfort estimation for indoor and in-vehicle conditions. Further, we introduce a temporal dataset for indoor predictions incorporating 31 input signals and self-labeled user ratings by 18 subjects in a self-built climatic chamber. For in-vehicle scenarios, we acquired a second dataset featuring human judgments from 20 subjects in a BMW 3 Series. Our experimental results indicate superior performance for estimations from time series data over single vector input. Leveraging modern machine learning architectures enables us to recognize human thermal comfort states and estimate future states automatically. We provide details on training a recurrent network-based classifier and perform an initial performance benchmark of the proposed dataset. Ultimately, we compare our collected dataset to publicly available thermal comfort datasets.

Heterogeneous Basal Thermal Conditions Underpinning the Adélie‐George V Coast, East Antarctica

AbstractAdélie‐George V Land in East Antarctica, encompassing the vast Wilkes Subglacial Basin, has a configuration that could be prone to ice sheet instability: the basin's retrograde bed slope could make its marine terminating glaciers vulnerable to warm seawater intrusion and irreversible retreat under predicted climate forcing. However, future projections are uncertain, due in part to limited subglacial observations near the grounding zone. Here, we develop a novel statistical approach to characterize subglacial conditions from radar sounding observations. Our method reveals intermixed frozen and thawed bed within 100 km of the grounding‐zone near the Wilkes Subglacial Basin outflow, and enables comparisons to ice sheet model‐inferred thermal states. The signs of intermixed or near thawed conditions raises the possibility that changes in basal thermal state could impact the stability of Adélie‐George V Land, adding to the region's potentially vulnerable topographic configuration and sensitivity to ocean forcing driven grounding line retreat.

Влияние длительного естественного старения теплоизоляционных минераловатных материалов на физико-химические и термические превращения

Purpose. The article studies physico-chemical and thermal transformations of mineral wool thermal insulation of natural ageing. The subject of the study is thermal insulation materials of natural ageing, and the object of the study is their physicochemical and thermal characteristics. The aim of the work is to establish physicochemical and thermal transformations of mineral thermal insulation of natural ageing. The research is aimed at identifying features of physico-chemical and thermal transformations of thermal insulation based on mineral fibers and organic binders in the ageing process. Methods. A set of precision physicochemical methods such as X-ray phase analysis (XRF), infrared spectroscopy and thermal analysis methods (TG, DTG, DSC) was used. Findings. The results of studying mineral thermal insulation (service life of 60 years) revealed characteristic changes in the structure of the material. The XRF method established that the ageing process of mineral wool materials is caused by occurring microdefects and disruption of material fibers structure organization. Changes in thermal insulation phase state have thermal fluctuation of kinetic nature of material mechanical destruction. The IR spectroscopy method identified changes in the areas of characteristic absorption bands: 2 800–2 200, 2 000–1 600 and 1 295–1 005 cm–1 caused by chemical destruction of organic binder in mineral thermal insulation. The nature of thermal transformations of the material was established, a tendency towards a decrease in the threshold temperatures for mass loss start due to destructing polymer binder was revealed. It is noted that natural ageing may result in loss of fire resistance of thermal insulation systems, as well as in intensificating smoldering combustion of thermal insulation. Research application field. The results are of interest to builders, designers, fire safety engineers and can be used in regulatory and technical as well as in reference literature on fire safety. Conclusions. During the ageing process irreversible physical and chemical changes occur in the structure of thermal insulation, leading to loss of thermal stability of the material and to a possible increase in the intensity of latent smoldering combustion. Technical obsolescence of the material leads to decreasing fire resistance limits of various thermal insulation systems due to loss of thermal insulation capacity and integrity.

Thermal Evolution of the Lithosphere‐Asthenosphere Boundary Beneath Arc and Its Geodynamic Implications: Depth Variation of Thermal Histories of Mantle Xenoliths From Ichinomegata, Northeast Japan

AbstractQuantitative reconstruction of thermal history recorded in mantle xenoliths is imperative for understanding the temporal change of thermal state and dynamics of the lithosphere‐asthenosphere boundary (LAB). We challenged this problem in the arc settings by examining nine spinel peridotite xenoliths from Ichinomegata maar in the back‐arc side of Northeast Japan Arc. Extensive mineral chemical analyses combined with the derivation depths of the xenoliths revealed a depth‐dependent variation of chemical zoning patterns in olivine and pyroxenes. The depth variation of thermal histories of the Ichinomegata xenoliths was decoded by applying diffusion‐controlled reaction modeling to reproduce the zoning patterns. The decoded thermal events in the order of occurrence are (a) ∼14 million years of cooling causing lithosphere thickening up to ∼55 km depth, (b) subsequent ∼12 thousand years of heating from the underlying asthenosphere resulting in lithosphere thinning up to the depths of ∼40 km, and (c) 1–68 days of heating during xenolith transportation by the host magma. The duration of the lithosphere thickening is consistently explained by the period of the Japan Sea opening. On the other hand, the timescale of the lithosphere thinning is too short to be explained by heat conduction through the ∼15 km thick LAB and requires a more effective heat transportation mechanism such as direct magma injection into the LAB or significant viscosity reduction of the mantle peridotite aided by the pervasive permeable flow of silicate melt.

Thermodynamic and dynamic effects of anomalous dragon boat water over South China in 2022

In 2022, persistent extreme precipitation events occurred during the Dragon Boat Water (DBW) period (May to June) over South China, with rainfall-breaking historical extremes at many stations. In this study, the relative importance of the thermodynamic and dynamic effects on this anomalous event was explored through budget equations of moisture and moist static energy (MSE). The moisture budget analysis suggests that the thermodynamic effect contributes to the precipitation anomaly by less than 10% through the advection of abnormal moisture by mean horizontal and vertical motion. However, the dynamic effect, associated with the mean moisture advection by anomalous vertical motion, makes the largest contribution. This seems to imply that the increase in water vapor due to global warming does not play a critical role in this extreme event. Nevertheless, further analysis of the MSE budget equation reveals that the anomalous vertical motion is governed by both the dynamical effect of atmospheric circulation changes and the thermodynamic effect of atmospheric thermal state changes. The thermodynamic effect, which accounts for 47.21% of the total effect (sum of the thermodynamic and dynamic effects), is caused by anomalous moist enthalpy (mainly dry enthalpy) advection due to the mean horizontal motion. In contrast, the dynamical effect is related to the warm and humid air advection caused by the anomalous southwest wind caused by the anomalous anticyclone over the northwest Pacific. Simultaneously, the anomalous northeast wind brings dry cold air, resulting in the convergence of cold and warm air over the Pearl River basin and persistent heavy rainfall events. The results of this study provide valuable insights into the direct and indirect physical mechanisms leading to anomalous DBW period over South China in 2022.

Effects of wall thermal state on shock wave/boundary layer interaction with foreign-gas supersonic film injection

Shock wave/boundary layer interaction (SWBLI) is considered to be one of the most complex physical phenomena in supersonic flowfield. The flow characteristics of SWBLI can be influenced by wall thermal state. However, in scramjet combustors, with supersonic film injected into the boundary layer, the effects of wall thermal state on SWBLI flow characteristics may have different characters. In this paper, the effects of wall thermal state on SWBLI with foreign-gas supersonic film injection are numerically investigated. During the numerical simulation, considering the actual application of scramjet engines, hydrogen and high-molecule gaseous hydrocarbon fueled supersonic film injections are taken into consideration. The results indicate that, either with or without supersonic film injection, wall thermal state changes both the wave structure and the flow characteristics. Furthermore, the interaction and separation length decrease with decreasing wall cooling heat flux. It is found that, the effects of wall thermal state on the interaction length are determined by its effects on the subsonic layer thickness. Moreover, decreased wall heat flux will cause momentum transport enhancement, which increases both near-wall momentum and wall shear stress, and consequently decreases the separation length. The interesting thing is that, foreign-gas injections lead to different relative variations of the interaction length and the separation length with wall thermal state. The effects of foreign-gas injections on the relative variations of the interaction length under different wall thermal states essentially depend on the foreign-gas specific heat capacity. Meanwhile, the relative variation of the separation length depends on the effects of foreign-gas injection on the relative density variation. It is worth mentioning that, due to the temperature range decrease caused by film injection, low-molecular hydrogen injection has significantly larger separation length relative variations compared with the situation without film injection and with hydrocarbon fuel injection. However, for high-molecular foreign-gas, the relative density variation depends on its own density change with temperature due to its high-density property.

Ice mass loss sensitivity to the Antarctic ice sheet basal thermal state

Sea-level rise projections rely on accurate predictions of ice mass loss from Antarctica. Climate change promotes greater mass loss by destabilizing ice shelves and accelerating the discharge of upstream grounded ice. Mass loss is further exacerbated by mechanisms such as the Marine Ice Sheet Instability and the Marine Ice Cliff Instability. However, the effect of basal thermal state changes of grounded ice remains largely unexplored. Here, we use numerical ice sheet modeling to investigate how warmer basal temperatures could affect the Antarctic ice sheet mass balance. We find increased mass loss in response to idealized basal thawing experiments run over 100 years. Most notably, frozen-bed patches could be tenuously sustaining the current ice configuration in parts of George V, Adélie, Enderby, and Kemp Land regions of East Antarctica. With less than 5 degrees of basal warming, these frozen patches may begin to thaw, producing new loci of mass loss.

A Data-Based Compact High-Order Volterra Model for Complex Blast Furnace System

In this article, a data-based compact Volterra model is constructed to carry out the silicon prediction task. The main motivations are to, on the one hand, make better use of the strong memory ability of the Volterra series, which is suitable for reflecting the large inertia of the blast furnace process, on the other hand, overcome the difficulty that high complexity of the original Volterra models may result in serious overfitting. Six kinds of models, including single-input and two-input linear, second-order and third-order compact Volterra models, are successively designed and verified through a real blast furnace case. The reasonable agreement between the predicted values and the observed values indicates the compact Volterra model, especially the single-input third-order Volterra model, are powerful and competitive for describing the complex blast furnace system. The experimental results can serve as a guide for the blast furnace operators to judge the in-furnace thermal state change in time and further provide an indication on how to control the blast furnace in advance.

A Statistical Approach to Satellite Time Series Analysis to Detect Changes in Thermal Activities: The Vulcano Island 2021 Crisis

Vulcano belongs to the seven volcanic islands forming the Aeolian archipelago (Italy) and has the privilege to define an eruptive style as “Vulcanian”. It has to be considered as an active volcano as its most recent activity demonstrated. Starting by late spring 2021, the thermal state of the Vulcano summit area changed and the gas emission increased. During the summer and, in particular, starting from September, geophysical and geochemical signals, precisely those linked to the activity of the hydrothermal system that feeds the fumaroles of the Fossa crater, varied. The temperature of the gases emitted by the fumaroles on the crater rim has increased and the composition of the gases has showed an increase in CO2 and SO2 (carbon dioxide and sulfur dioxide) concentration. For such reasons, the authors decided to follow this event by analyzing the remotely sensed available data suitable for detecting changes in thermal state. By processing the TIRS (Landsat 8) and ASTER time series, two long-term surface temperature logs were obtained and, therefore, by adopting a statistical approach, an analysis in both space and time domains has emphasized a thermal signature since mid-September 2021.

Mapping the Thermal State of Permafrost in Northeast China Based on the Surface Frost Number Model

Under the influence of climate change and human activities, the southern boundary of the permafrost region in Northeast China, which is located at the southern edge of the permafrost area of Eurasia, has moved north, the surface temperature has increased, and the thickness of the frozen layer has decreased. At present, there is a lack of classification standards or a map of the thermal state of permafrost that can reflect the dynamic change characteristics of permafrost in Northeast China. A vegetation impact factor consisting of normalized difference vegetation index and forest canopy closure was introduced into MODIS LST products, in order to improve the applicability of products in Northeast China. Based on the improved MODIS LST data, this study analyzed the distribution and change of the mean annual surface temperature and the surface frost number (SFnc) from 2003 to 2019. SFnc was used as the standard to classify the thermal state of permafrost, and a map of the thermal state distribution and changes of permafrost in Northeast China, with a spatial resolution of 1 km, was produced. Compared with the observation data of meteorological stations and field monitoring data, the reliability of classification results was nearly 95%. The map showed that there was no area of extremely stable permafrost (SFnc ≥ 0.667), the area of stable permafrost (0.55 ≤ SFnc< 0.667) changed from 14.9 × 104 km2 to 6.5 × 104 km2, the SFnc reduced from 0.564 to 0.557, the area of semi-stable permafrost (0.51 < SFnc < 0.55) changed from 17.68 × 104 km2 to 17.77 × 104 km2, the SFNc reduced from 0.529 to 0.528, and the area of transitional or unstable permafrost (0.49 ≤ SFnc ≤ 0.51) changed from 8.67 × 104 km2 to 9.56 × 104 km2. The thermal state of permafrost decreased and the distribution of stable permafrost shrank, due to continuous rising air temperature. The overall change characteristics of the thermal state distribution of permafrost were that the southern boundary of the permafrost region moved northward, the regional permafrost thermal state decreased, and there was an increased region of semi-stable, transitional or unstable permafrost from the frozen soil thawed at the edge of the permafrost region with higher stability. The permafrost region in Northeast China has lush vegetation, and the continuous degradation of permafrost will change the vegetation growth environment and affect the global carbon cycle process. This work will provide important data support for climate change feedback, natural disaster process research, and an early warning and prevention of terrestrial ecosystem response in the permafrost region of Eurasia.

Real-Time Construction of Thermal Model Based on Multimodal Scene Data

In commercial buildings, the total consumption of central air conditioning accounts for about 40%–50%. However, at present, the initial design value of building Heating Ventilation and Air Conditioning (HVAC) is usually far greater than the actual refrigeration value of refrigeration demand, which will lead to great energy consumption waste. Moreover, the operation of HVAC affects the thermal comfort of users, so it is necessary to establish a thermal model for the scene to control. The thermal model describes the temperature of the scene in different environments. So it is very important to design a thermal model to calculate the scene in real time. Because the flow of people, the opening of windows, the ventilation of the scene and other parameters influence the change of thermal state in the scene environment, these parameters are complicated to model. Human disturbance will lead to the instability of the state of the scene environment. The inconsistency of its thermal model will lead to energy allocation tracking strategies in different regions. To solve this problem, We propose a thermal model for building thermal comfort using a multimodal analysis framework. This paper analyzes multiple temperature and humidity sensors and area image by multimodal combination and processes the image and sensor data by combining CNN and LSTM. Our results show that when the thermal model analyzed by this method is deployed in a building in the south of China, the MSE accuracy of the local effect of temperature field prediction reaches 99%, and its AMAX reaches 94%, so the running stability of the model in the scene is high. In addition, the research shows that the thermal model analysis framework can make the Internet of Things (IoT) in buildings more intelligent, and it can be combined with this thermal model to improve human comfort, make it easier to deploy in each hot zone, and have a better overall energy-saving effect.

Thermal Imaging Study to Determine the Operational Condition of a Conveyor Belt Drive System Structure

The paper discusses the results of a study carried out to determine the thermal condition of a conveyor power unit using a thermal imaging camera. The tests covered conveyors in the main haulage system carrying coal from a longwall. The measurements were taken with a thermal imaging diagnostic method which measures infrared radiation emitted by an object. This technology provides a means of assessing the imminence and severity of a possible failure or damage. The method is a non-contact measuring technique and offers great advantages in an underground mine. The thermograms were analysed by comparing the temperature distribution. An analysis of the operating time of the conveyors was also carried out and the causes of the thermal condition were determined. The main purpose of the research was to detect changes in thermal state during the operation of a belt conveyor that could indicate failure and permit early maintenance and eliminate the chance of a fire. The article also discusses the construction and principle of operation of a thermal imaging camera. The findings obtained from the research analysis on determining the thermal condition of the conveyor drive unit are a valuable source of information for the mine’s maintenance service.

Hyperspectral Imagery for Assessing Laser-Induced Thermal State Change in Liver.

This work presents the potential of hyperspectral imaging (HSI) to monitor the thermal outcome of laser ablation therapy used for minimally invasive tumor removal. Our main goal is the establishment of indicators of the thermal damage of living tissues, which can be used to assess the effect of the procedure. These indicators rely on the spectral variation of temperature-dependent tissue chromophores, i.e., oxyhemoglobin, deoxyhemoglobin, methemoglobin, and water. Laser treatment was performed at specific temperature thresholds (from 60 to 110 °C) on in-vivo animal liver and was assessed with a hyperspectral camera (500–995 nm) during and after the treatment. The indicators were extracted from the hyperspectral images after the following processing steps: the breathing motion compensation and the spectral and spatial filtering, the selection of spectral bands corresponding to specific tissue chromophores, and the analysis of the areas under the curves for each spectral band. Results show that properly combining spectral information related to deoxyhemoglobin, methemoglobin, lipids, and water allows for the segmenting of different zones of the laser-induced thermal damage. This preliminary investigation provides indicators for describing the thermal state of the liver, which can be employed in the future as clinical endpoints of the procedure outcome.

Changing climate and the permafrost environment on the Qinghai–Tibet (Xizang) plateau

AbstractPermafrost on the Qinghai–Tibet Plateau (QTP) has undergone degradation as a result of recent climate change. This may alter the thermo‐hydrological processes and unlock soil organic carbon, and thereby affect local hydrological, ecological, and climatic systems. The relationships between permafrost and climate change have received extensive attention, and in this paper we review climate change for permafrost regions of the QTP over the past 30 years. We summarize the current state and changes in permafrost distribution and thickness, ground temperature, and ground ice conditions. We focus on changes in permafrost thermal state and in active‐layer thickness (ALT). Possible future changes in ground temperature and ALT are also discussed. Finally, we discuss the changes in hydrological processes and to ecosystems caused by permafrost degradation. Air temperature and ground temperature in the permafrost regions of the QTP have increased from 1980 to 2018, and the active layer has been thickening at a rate of 19.5 cm per decade. The response of permafrost to climate change is not as fast as in some reports, and permafrost degradation is slower than projected by models that do not account for conditions deep in permafrost.

Application of computer training systems for qualification perfection of technological personal of blast furnace shops

Effective control of thermal state of a blast furnace (BF), considerably depending on the qualification of the technological personal, is an important condition for smelting of hot metal of required composition. Application of computer training systems (CTS) in the process of education of technological personal of BF shops is one of the effective methods of professional knowledge and skill perfection. The CTS, implemented at PAO NLMK, based on a model of thermal state of BF, elaborated in Ural Federal University and supplemented with the models of existing disturbances. Adjusting of dynamic characteristics accomplished on the base of regularity of heat- and mass exchange. According to the tasks of BF heat operative control, during the training at the CTS transient processes are studied through channels of BF thermal state control, skill is mastered to identify the tendencies of BF thermal state change in case of non-controlled disturbances action. Most important stage of the training – implementation of adequate solutions to compensate declination of BF thermal state parameters from the set-up level. The CTS implemented at PAO NLMK is operating in the mode of training and testing. The main parameters of BF operation for every particular scenario are displayed at a mnemonic diagram, which completely corresponds to the mnemonic diagram of particular BF. Within the frame of transient processes dynamics studies, tasks are stipulated to modify a BF thermal state by application of control programs. When a scenario of BF thermal state control in case of non-controlled disturbances action is realized, the process parameters change is imitated at the mnemonic diagram. It will be done in case of one of the following parameters change: coke quality change, reducibility change, iron ore material grain size change, distribution of ore by radius change. The CTS includes a module of administration, which allows collecting the statistics of tasks fulfilment by pupils and estimating the results according to accepted algorithm. The application of CTS enabled to perfect the competence of technological personal, which was expressed by declining of off-grade hot metal share.

Activation of Cryogenic Processes in Central Yamal as a Result of Regional and Local Change in Climate and Thermal State of Permafrost

Various climatic parameters (average annual, winter, and summer air temperature, winter and summer total precipitation) and their temporal variability are analyzed to explain the activation of cryogenic processes in Central Yamal. The effect of fluctuations of these parameters on the thaw depth and ground temperature is analyzed. The regression analysis is carried out to reconstruct ground temperature during earlier periods of time in the years preceding the activation of thermal denudation and the formation of gas emission craters.

The effects of cylinder deactivation on the thermal behaviour and fuel economy of a three-cylinder direct injection spark ignition gasoline engine

The changes in thermal state, emissions and fuel economy of a 1.0-L, three-cylinder direct injection spark ignition engine when a cylinder is deactivated have been explored experimentally. Cylinder deactivation improved engine fuel economy by up to 15% at light engine loads by reducing pumping work, raising indicated thermal efficiency and raising combustion efficiency. Penalties included an increase in NOx emissions and small increases in rubbing friction and gas work losses of the deactivated cylinder. The cyclic pressure variation in the deactivated cylinder falls rapidly after deactivation through blow-by and heat transfer losses. After around seven cycles, the motoring loss is ~2 J/cycle. Engine structural temperatures settle within an 8- to 13-s interval after a switch between two- and three-cylinder operation. Engine heat rejection to coolant is reduced by ~13% by deactivating a cylinder, extending coolant warm-up time to thermostat-opening by 102 s.

Statistical Forecasting of Current and Future Circum‐Arctic Ground Temperatures and Active Layer Thickness

AbstractMean annual ground temperature (MAGT) and active layer thickness (ALT) are key to understanding the evolution of the ground thermal state across the Arctic under climate change. Here a statistical modeling approach is presented to forecast current and future circum‐Arctic MAGT and ALT in relation to climatic and local environmental factors, at spatial scales unreachable with contemporary transient modeling. After deploying an ensemble of multiple statistical techniques, distance‐blocked cross validation between observations and predictions suggested excellent and reasonable transferability of the MAGT and ALT models, respectively. The MAGT forecasts indicated currently suitable conditions for permafrost to prevail over an area of 15.1 ± 2.8 × 106 km2. This extent is likely to dramatically contract in the future, as the results showed consistent, but region‐specific, changes in ground thermal regime due to climate change. The forecasts provide new opportunities to assess future Arctic changes in ground thermal state and biogeochemical feedback.

Utilization of heat quantity to model thermal errors of machine tool spindle

Thermal error modeling of the spindle plays an important role in predicting thermal deformation and improving machining precision. Even though the modeling method using temperature as the input variable is widely applied, it is less effective due to severe loss of thermal information and pseudo-hysteresis between temperature and thermal deformation. This paper presents a novel modeling method considering heat quantity as the input variable with theoretical analysis and experimental validation. Firstly, the change of thermal state of a metal part being heated is discussed to reveal the essence of the relationship between heat, thermal deformation and temperature, and the theoretical basis of the modeling method proposed in this paper is elaborated. Subsequently, the relationship between thermal deformation and heat quantity is further studied through modeling the thermal deformations of stretching bar and bending beam using heat quantity as the independent variable, and the stretching model is verified based on finite element method. Then, the thermal error models of the spindle are developed with the heat elastic mechanics theory and the lumped heat capacity method. In succession, the parameter identification of thermal error models is carried out experimentally using the least square method. The average fitting accuracy of these models is up to 91.3%, which verifies the good accuracy and robustness of the models. In addition, these models are of good prediction capability. The proposed modeling method deepens the research of thermal errors and will help to promote the application of relevant research results in the actual production.