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• A dual-layer analytical modeling approach that simplifies complex machine tool structural components into equivalent cuboids was presented. • An analytical modeling method for the predicting thermal characteristic of machine tool structural components via dual-layer equivalent cuboids has been proposed. • The mapping relationship between temperature field variations and equivalent thermal loads of the equivalent cuboids is unveiled. • Sensitivity coefficient of thermal power to thermal error is introduced to reveal the impact mechanism of thermal error caused by heat source conditions. Precision machine tools are sensitive to thermal effects. Thermal deformation of machine tool structural components can lead to changes in the relative pose between the spindle tool and the workpiece, causing thermally induced machining errors. Gaining insight into the mechanistic correlation between critical thermal condition parameters of heat sources and thermal errors in machine tools is essential to elevate the design of machine tool thermal attributes. To address this issue, this paper proposes a dual-layer equivalent analytical modeling method for characterizing the thermal properties of structural components. The construction of the temperature field analytical model for the dual-layer equivalent structure is achieved by setting and handling different interlayer heat flows and temperature boundary conditions. The dual-layer equivalent approach simplifies complex structural components into top and bottom layers, providing a more flexible and accurate capability for characterizing the thermal properties of structural components. This modeling method enables rapid prediction and evaluation of machine tool thermal characteristics. Furthermore, based on this analytical approach, the calculation method of sensitivity coefficient of thermal power to thermal error is proposed to elucidate the mapping relationship between different thermal condition parameters and thermal errors. This method facilitates the fast and accurate prediction of six thermally induced errors under various thermal conditions. Experimental results demonstrate that the key point temperature deviation predicted using the dual-layer analytical modeling method is less than 0.8 °C, and the thermally induced axial linear error deviation is less than 1.8 μm. The dual-layer analytical modeling approach introduced in this study presents a versatile technique applicable to enhancing the design and control of machine tool thermal characteristics, holding significant potential for advancing the stability of machine tools thermal accuracy. [Display omitted] [ABSTRACT FROM AUTHOR]

Because of uneven temperature distributions, machine tools can generate thermal errors, which significantly contribute to machining errors. Previous research has shown that thermal volumetric errors can be directly measured using optical methods or indirectly calculated using error mapping methods. However, these methods are limited to or restricted by specific working conditions. Therefore, our study focused on developing a novel R-test measurement system for realising accurate thermal volumetric error measurements. The R-test measurement system consists of a three-dimensional (3D) ball array plate, R-test detecting head, temperature monitoring module, and data processing module. This system allows the measurement of deviation in the X, Y, and Z directions simultaneously at different fixed points in a 3D cube. Furthermore, considering the temperature and thermally induced volumetric accuracy, it was possible to derive the deformation tendency of the machine tool. An uncertainty analysis and systematic error corrections were conducted. The measurement uncertainty of this system is approximately 4 μm. The thermal volumetric errors were examined using the developed R-test measurement system and an interferometer under the same thermal conditions. The experimental results indicated that the R-test measurement system was able to accurately and rapidly detect thermal volumetric errors. This system provides a measurement technique with a low level of uncertainty, high accuracy, and low cost, which can be used to measure, compensate, and control the thermally induced volumetric accuracy of horizontal machine tools. [ABSTRACT FROM AUTHOR]

Conventional three-probe method of artifact roundness and spindle error measurements is subjected to the trouble of harmonic suppression, which is also mathematically complicated due to complex transformation processing. A novel three-probe method by solving system of multivariable equation (SSME) method is presented in this paper. The presented method simplifies the mathematical processing and has good robustness to the measurement angles which are difficult for conventional three-probe method. This paper gives mathematical models, detailed theoretical derivations, and numerical simulations. Selection criteria of the optimal measurement angle combinations can be determined in accordance with rank and condition number of the coefficient matrix. Then, to validate the feasibility and repeatability of the proposed method, experimental measurements are performed on a vertical machine tool spindle by using nanometer-resolution capacitive displacement sensors, high-precision indexing table, and professional data acquisition system. Artifact roundness error and spindle radial error are tested to validate separation accuracy by specialized instruments. The comparisons demonstrate that the proposed method has good feasibility and repeatability (the maximum deviations of spindle error and roundness error are 9.62 and 3.86%). SSME method, due to its simplicity in computation and the uniqueness of the solution provided, is more suitable to separate spindle radial error from the artifact roundness error. [ABSTRACT FROM AUTHOR]

Thermal error is one of the primary factors affecting the machining accuracy of precision machining tools. Therefore, it is important to study the transient thermal characteristics of machine tools and the thermal-error control strategies. Thus far, a transient analytical modelling method for characterising the thermal characteristics of machine tools was proposed and an active error control strategy was provided. First, temperature-field modelling was conducted using an analytical method based on the Fourier series method and partial differential equations of heat conduction. Second, using the derived temperature field, the thermal deformation field was calculated based on finite element theory. Subsequently, the continuous real-time effect of the thermal power per unit heat source on the temperature and deformation fields of precision machine tools was studied. The proposed analytical modelling method not only predicts the machine tool heat deformation based on the working conditions of the heat source, but also matches the thermal control source power with the demand of the machine tool heat deformation. The optimal real-time power of the thermal control source is dynamically iterated and matched, such that the thermal deformation caused by the heat and thermal control sources can be balanced in real time at the displacement control point. Finally, the volumetric thermal error was actively controlled by adjusting the temperature field of the machine tool. The simulated and experimental results indicate that the transient analytical model can accurately predict the real-time thermal characteristics of the machine tool and that the real-time active thermal control method can effectively reduce volumetric thermal errors. Using active thermal control, the squareness error in the YZ-plane was reduced by approximately 45%, the spindle thermal elongation was reduced from 23 μm to 7 μm, and the volumetric thermal error in the X, Y, and Z directions were reduced by approximately 16, 14, and 17 μm, respectively. [Display omitted] • Analytical modelling method for transient thermal characterizing of machine tool structural components and spindle is proposed. • The continuous real-time effect of the unit thermal power of the heat source on the temperature and deformation fields of precision machine tools is revealed using the analytical method. • Real-time thermal power matching strategy of thermal control sources to reduce volumetric thermal error is presented. [ABSTRACT FROM AUTHOR]

Modeling method investigation about spindle thermal errors is significant for spindle thermal optimization in design phase. To accurately analyze the thermal errors of motorized spindle unit, this paper assumes approximately that 1) spindle linear thermal error on axial direction is ascribed to shaft thermal elongation for its heat transfer from bearings, and 2) spindle linear thermal errors on radial directions and angular thermal errors are attributed to thermal variations of bearing relative ring displacements. Based on prerequisites, an analytical modeling method is developed to analyze these spindle thermal errors. Firstly, thermal-mechanical models of rotating ring geometry and interference assembled rotating ring geometries are established, for thermal variation modeling of relative ring displacements of short cylindrical roller bearing and angular contact ball bearing. Secondly, these thermal variation models are associated with heat-fluid-solid coupling FE (finite element) simulation technique, to model spindle linear thermal errors on radial/axial directions and angular thermal errors by the analytical simulation method. Consequently, verification experiments clarify that the presented method is accurate for spindle thermal errors modeling, and can be effectively applied into the design and development phases of motorized spindle units. [ABSTRACT FROM AUTHOR]

Temperature variations in the machine tool structural components may lead to relative pose variations between the tool tip and the workpiece. Different thermal layouts may lead to various temperature distributions and generate various thermal deformations. Thermal symmetric design is often used to complete thermal balancing of machine tools. Studies on theoretical methods to guide the layout design of the heat sources (HS) and cooling sources (CS) in machine tools are insufficient. To address this problem, a novel analytical approach for characterising the equivalent cuboid thermal response of machine tool structural components is presented in this paper. The proposed analytical modelling method can realise analytical temperature field modelling with Green's function, calculating the equivalent thermal moment with Reissner's theory, and matching the thermal power-deformation mapping coefficient (TPDMC) using the finite element method (FEM). The explicit and correlative formulation between the thermal power of the HSs and CSs and the guideway thermal deviations is deduced. Furthermore, the layout principles of the CSs are presented according to the maximum efficiency of the thermal moment and the characterisation matching of the TPDMC curves. Afterwards, power matching of the CS is obtained with the aid of the minimum deformation principles of the key positions. Simulated and experimental results illustrated that the proposed method can be used to rapidly and accurately analyse the temperature and thermal deformation responses of the machine tool, as well as to provide a thermal balancing strategy according to specific thermal conditions. The analytical approach proposed in this paper is a general method suitable for the thermal balancing design of machine tools, and it is of great value for improving the thermally induced accuracy stability of machine tools. [Display omitted] • Analytical modelling method for thermal characterizing of machine tool structural components is presented. • Effects of heat sources powers on temperature and deformation are theoretically investigated. • Layout principle of heat/cooling sources is summarised. • Thermal balancing strategy to reduce thermal deformation is developed. [ABSTRACT FROM AUTHOR]