[Abstract]: This paper introduces the selection method of temperature sensors, discusses the arrangement principle of temperature sensors, compares and analyzes several commonly used temperature sensor optimization arrangement methods at home and abroad, and makes an outlook on future research trends. [Keywords]: CNC machine tool; thermal error; temperature sensor; sensitive point CLC number: TP2 Document code: A With the development of precision and ultra-precision machining technology and the emergence of automation systems, people have put forward higher requirements for the machining accuracy of CNC machine tools. A large number of studies have shown that thermal error is the largest source of machine tool error, accounting for 40% to 70% of the total machine tool error[sup][1,2][/sup]. Simply relying on hardware improvement methods such as improving machine tool structure design, or directly controlling temperature to reduce machine tool thermal error, increases costs and the effect is not ideal. The method of establishing a CNC machine tool thermal error model and then realizing thermal error compensation has been proven to be the most economical and effective[sup][3][/sup]. In the research on thermal error measurement, modeling and compensation of CNC machine tools, the arrangement and selection of temperature measurement points is a difficult point. The selection of the number and location of sensors involves many aspects such as cost and efficiency. From an economic point of view, it is desirable to use as few sensors as possible, but too few sensors will inevitably reduce the recognition accuracy. Therefore, optimizing the temperature sensors and determining the optimal number and location of the sensors has important practical value, and its optimized arrangement strategy has become a key technology in the research of thermal error identification and modeling. 1 Selection of Temperature Sensors in Thermal Error Modeling of CNC Machine Tools Currently, scholars at home and abroad mostly establish mathematical models of the relationship between thermal error and machine tool temperature field through experiments. They measure the temperature field of the machine tool in real time during the processing and calculate the thermal deformation, and then feed it back to the CNC system for error compensation. How to select effective temperature measuring elements, build a temperature measuring system, and obtain the temperature change of the machine tool are important factors in realizing the modeling and compensation of machine tool thermal deformation. The development of temperature sensors used in CNC machine tools has roughly gone through the following three stages: traditional temperature sensors, analog integrated temperature sensors/controllers, and intelligent temperature sensors. Traditional temperature sensors are represented by resistance temperature detectors (RTDs), thermocouples, and thermistors. These sensors generally output analog signals and require subsequent signal processing and A/D conversion. The coordination of conversion circuits. Such sensors suffer from drawbacks such as poor linearity, small signal strength, and poor anti-interference capability. Analog integrated temperature sensors are manufactured using silicon semiconductor integrated technology; analog integrated temperature controllers mainly include temperature control switches and programmable temperature controllers, forming a self-contained system that operates independently of microprocessor control, and have a certain market share. Traditional temperature sensors and analog integrated temperature sensors/controllers are widely used, but due to the unparalleled advantages of new intelligent temperature sensors, they are gradually being replaced. Currently, internationally, new temperature sensors are developing from analog to digital, and from integrated to intelligent and networked. Intelligent temperature sensors (also known as digital temperature sensors) are the culmination of microelectronics, computer technology, and automatic testing technology (ATE). Internally, they include a temperature sensor, A/D converter, signal processor, memory (or register), and interface circuitry. Because digital temperature sensors have advantages over traditional temperature sensors, such as strong anti-interference capability, high resolution, good linearity, and low cost, digital temperature sensors are given priority when designing temperature measurement systems for CNC machine tools. 2. Temperature Sensor Arrangement Principles 2.1 Temperature Sensitive Points In CNC machine tool thermal error control and compensation technology, the reasonable selection of temperature measurement point locations is crucial. Since thermal error is a function of time, the temperature field characteristics of the machine tool must be recorded simultaneously with error measurement. Experiments show that the degree of influence of temperature rise on the surface and interior of the CNC machine tool on the machine tool's thermal error varies. There are always some points where temperature rise changes will cause significant changes in the machine tool's thermal error. In the thermal error compensation system, only by using these points as input to the model can the number of temperature measurement points be minimized while ensuring accuracy, resulting in fast calculation speed and optimal compensation effect during real-time compensation. These points are called sensitive points affecting the thermal error of CNC machine tools. 2.2 Temperature Sensor Arrangement Principles Temperature sensors should be able to quickly and accurately reflect changes in temperature information to improve the system's detection accuracy. Based on the theory of temperature sensitive points, temperature sensors should be arranged in places that are most sensitive to signal changes and least affected by interference from other measurement points, i.e., places most sensitive to temperature changes, to accurately reflect changes in temperature variable signals. To successfully achieve thermal modeling, The system must meet the conditions of controllability and observability. For the arrangement of temperature sensors, after meeting the observability condition, the following principles are generally followed: (1) The sensors should be arranged at the thermal excitation source or the location of the maximum thermal deformation as much as possible; (2) If uniform heating is required, the sensors should be arranged at the fixed end; (3) The sensors should not be too close to each other to reduce mutual interference and improve the sensitivity of the system detection. Taking a horizontal machining center as an example, as shown in Figure 1, a thermal deformation modeling test is conducted on it. A series of temperature sensitive points need to be selected and temperature sensors are arranged on them to measure the temperature rise of the machine tool. Figure 1 shows 14 temperature sensitive points selected. Temperature sensors T1 and T2 are used to measure the temperature of the X-axis lead screw and nut; T3 and T4 measure the temperature of the Y-axis lead screw and nut; T5 and T6 measure the temperature of the Z-axis lead screw and nut; T7 and T8 measure the spindle temperature; T9, T10, and T11 measure the temperature of the spindle. T12 measures the column temperature; T13 measures the X-axis bed temperature; T14 measures the Z-axis bed temperature. A non-contact displacement sensor is installed on the Z-axis bed to measure the spindle thermal deformation error. The data collected by these 14 temperature sensors and 1 displacement sensor can be used for subsequent CNC machine tool thermal error modeling and compensation. 3 Temperature Sensor Layout Optimization Generally speaking, the more temperature measurement points on the machine tool, the more accurate the established thermal error prediction model and the more accurate the estimation of thermal error. However, too many temperature measurement points will greatly increase the workload of data processing. Considering the cost of the temperature measurement system, it is necessary to optimize the calculation and processing of temperature measurement points. Temperature measurement point optimization refers to replacing numerous temperature measurement points with fewer temperature measurement points while ensuring the accuracy of the thermal error model, so as to simplify the thermal error modeling and compensation system. The following methods are currently used domestically and internationally for optimizing the placement of temperature sensor points: 3.1 Trial and Error Method In early thermal error compensation systems, The process of determining temperature sensors is, to some extent, a trial-and-error process based on experience. Typically, based on engineering judgment, a large number of sensors are installed at different locations, and then statistical or analytical methods are used to select a small number of temperature sensors for modeling error components. Trial and error is the most direct and intuitive method, but its drawback is that the accuracy of engineering judgment affects the prediction accuracy and robustness of the thermal error model. Establishing the correspondence between the comprehensive error and the temperature field requires a significant amount of time and sensors, and these sensors are no longer used in the final thermal error modeling after optimization. If the minimum number of temperature measurement points can be used while ensuring compensation accuracy, this will greatly facilitate the practical application of compensation technology and reduce usage costs. 3.2 Gaussian Integral Method Gaussian integral is a method for theoretically modeling the temperature field of machine tools. By constructing and solving the analytical equations of the machine tool temperature field and thermal deformation field, a machine tool thermal deformation model is obtained, and subsequent thermal error compensation can be performed based on this model. Debra A. Krulewich The temperature field of the entire machine tool is analyzed using the Gaussian integration method. Temperature sensor placement points are used as Gaussian integration points, distributed within a predetermined temperature field. Since the number and distribution of temperature measurement points can be predetermined, the extensive measurement time required to obtain the machine tool temperature field is avoided. Because the temperature measurement points are the input to the equations, the number of measurement points is only related to the dimension of the equations; that is, the number of measurement points required to satisfy the dimension of the equations allows for model construction. Compared to other methods, the number of measurement points required for the experiment is significantly reduced and can be obtained in advance. The thermal error compensation model established using this method can reduce spindle thermal deformation errors. The model obtained by the Gaussian integration method is a simple theoretical linear model, but the actual thermal deformation field of a CNC machine tool is a nonlinear system with multiple factors. There is a certain deviation between the theoretical model and the actual deformation process, thus the Gaussian integration method has significant limitations. 3.3 Thermal Modal Analysis Optimization Method Thermal modal theory introduces modal analysis methods into the thermal deformation problem of machine tools. Based on the similarity between thermal modes and vibration modes, ignoring the difference in dimensions, the thermal modal characteristics of the machine tool can be obtained. According to the thermal modal theory, the thermal modal analysis method is used to find the points with the highest thermal sensitivity as the optimal placement points for temperature sensors. The search strategy for thermally sensitive points is as follows: (1) Decompose the machine tool into several blocks according to the basic components; (2) For the basic components, such as the box-type components, search by surface; (3) When searching by surface, first excite the mesh nodes, compare their thermal sensitivity, and gradually shrink the area enclosed by the excitation points to determine the optimal point; (4) Compare the optimal points of each surface to determine the optimal point of the basic component, and further determine the optimal point of the whole machine. The optimization method of thermal modal analysis has been repeatedly verified in theory, but since the concept of thermal modes does not have an intuitive physical meaning, and thermal load is difficult to obtain by experimental methods, the implementation of the thermal modal analysis method is relatively difficult. 3.4 Clustering and Correlation Analysis Method Clustering and correlation analysis are the most frequently used methods for optimizing temperature points in CNC machine tool thermal error modeling in recent years. Chih-Hao Lo et al. [sup][10][/sup] improved upon the traditional method by using Mallow's G-statistical analysis to establish a model of multiple thermal error components. They grouped and searched temperature sensors, using correlation grouping, typical variable search, and group search to optimize the distribution of temperature measurement points. Initially, more than 80 temperature sensors were arranged on the machine tool, but after grouping and optimization, only 4 sensors were used for thermal drift of the origin of the spindle coordinate system in the x-axis direction. In practical applications, using this optimization method to collect temperature information and thermal deformation information for modeling compensation can reduce the thermal error from 20 μm to 2.2 μm. Yang Jianguo et al. of Shanghai Jiaotong University [sup][11,12][/sup] used a variable selection method based on the basic principle of cluster analysis. By analyzing the correlation between variables and using certain aggregation methods to cluster them, and then selecting certain variables based on the clustering results, stepwise regression is used to further eliminate unnecessary temperature variables from the regression model, thus establishing the optimal regression model. The combination of these two methods offsets the impact of differences in results caused by different aggregation methods in cluster analysis, and reduces the workload of stepwise regression in judging variables one by one. It is convenient to select the minimum number of temperature variables and establish a model that meets the accuracy requirements. For the variable selection process, the distance in cluster analysis is selected as the correlation coefficient, which can obtain the similarity matrix between variables. Clustering is performed according to the centroid method, and the variables with the closest distance are merged into one class according to the similarity coefficient. Then, the similarity relationship between the new class and the remaining classes is compared, and the two closest classes are selected to continue merging until all variables are aggregated into one class, thereby achieving the optimal selection of temperature variables. Fu Jianzhong et al. of Zhejiang University [sup][4][/sup] optimized 14 temperature measurement points on a CNC milling machine using the main factor strategy and the uncorrelated strategy, and finally selected 4 temperature measurement points for thermal error compensation modeling. Zhang Yiqun et al. from Tianjin University [sup][13][/sup] also used fuzzy clustering analysis to select temperature measurement points in machine tool thermal error modeling and applied it to a vertical three-axis machining center, effectively reducing the number of temperature measurement points. Clustering and correlation analysis methods have shown significant advantages in temperature measurement point optimization, but further exploration and improvement are still needed. If a linear or near-linear relationship can be found between thermal error and the selected temperature field measurement data, the compensation model can be greatly simplified, and the thermal characteristic identification time will be greatly reduced due to the good interpolation and extrapolation performance of the linear prediction model. 4 Development Trends In recent years, some new sensor position optimization methods have been rapidly developed, such as topology optimization, singular value decomposition, and genetic algorithms. These methods have been widely used in the fields of vibration actuator/controller, damper, and material detector optimization [sup][14,15][/sup], but few have been applied to sensor optimization in the field of machine tool thermal error identification modeling. Introducing these methods into the optimized arrangement of machine tool temperature sensors can be considered as a new exploration and attempt. 4.1 Genetic Algorithm Optimization The basic idea of ​​a genetic algorithm is that during the genetic computation process, the genes of individuals with higher fitness are inherited, while the genes of individuals with lower fitness gradually disappear. Selection, crossover, and mutation are the three main operators of a genetic algorithm, which constitute the so-called genetic operations, giving the genetic algorithm characteristics that other traditional methods do not have. A genetic algorithm includes the following five basic elements: parameter encoding, initial population setting, fitness function setting, genetic operation design, and control parameter setting. These five elements constitute the core content of a genetic algorithm. In the available literature, genetic algorithms have not been applied to sensor optimization problems in the field of machine tool thermal error identification and modeling. Theoretically, it has been proven that, as long as a suitable fitness function is selected, genetic algorithms can be introduced into the field of machine tool temperature sensor optimization to improve its optimization results, serving as a research direction for temperature sensor optimization problems in machine tool thermal error modeling. 4.2 Virtual Instruments Another research direction for temperature sensor optimization is the introduction of virtual instrument technology. Virtual instruments combine general-purpose computers with relevant instrument hardware through software, allowing users to operate them via a graphical interface (often called a virtual front panel). Utilizing the powerful capabilities of computer systems and corresponding instrument hardware, and employing a modular structure, they significantly overcome the limitations of traditional instruments in signal transmission, data processing, display, and storage, enabling users to easily define, maintain, expand, and upgrade them. Simultaneously, they achieve resource sharing, reduce costs, and thus demonstrate strong vitality, promoting the further integration of instrument technology and computer technology. The use of virtual instrument technology has opened up another avenue for sensor optimization in the field of machine tool thermal error identification and modeling. 5. Conclusion Improving machine tool accuracy through error compensation technology is receiving increasing attention; therefore, the optimized arrangement of temperature sensors in the process of machine tool thermal error identification is crucial. The key to sensor optimization research lies in determining the minimum number of temperature measurement points, based on which a model can simply and accurately reflect the thermal deformation of the machine tool. Research in this area is gradually moving beyond the stage of relying solely on empirical trial-and-error methods, which have low accuracy, or numerical calculations, which are complex processes. Statistical analysis methods are being used to make the determination of temperature-sensitive points more reasonable. Genetic optimization algorithm and virtual instrument technology, due to their excellent characteristics, provide two feasible directions for further research in the future. At present, there are still many problems to be solved in the optimization selection of temperature measurement points. 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