## 1 Introduction  
The steel drill pipe was widely used in traditional drillings. Owing to the high density of steel, the drilling depth was limited. With the increase of drilling depth, the weight of the steel drill pipe increased rapidly, resulting in a significant increase in the requirements for the capacity of drilling equipment. Therefore, for deep continental drilling and deep-water offshore drilling, it was very necessary to use light aluminum alloy drill pipe to improve drilling efficiency and reduce power consumption. Using an aluminum alloy drill pipe, more portable drilling equipment could be used at the same well depth, which greatly saved costs. For the aluminum alloy drill pipe, the connection between the steel joint and aluminum alloy pipe was not only the weak part, but also the main failure part of aluminum alloy drill pipes. Thus, the connection reliability would directly affect the reliability of the whole drill pipe. [PERSON] [1] carried out a correlational study on the fatigue analysis of aluminum alloy drill pipe thermal assembly. The fatigue strength of the connection was improved by optimizing the thread. [PERSON], [PERSON] [2; 3; 4] used a finite element program and inverse heat conduction model to identify the heat transfer coefficient during thermal assembly in line with the experimental data and then obtained the correlation curve between cooling water flow and the convective heat transfer coefficient. [PERSON] [5] studied the connection between ST 2024 aluminum alloy drill pipe and steel drill pipe in a curved hole trajectory. The research showed that the ST 2024 aluminum alloy drill pipe had a great influence on the critical load allowed for the combined load and stability loss of the drill string. ST 2024 aluminum alloy drill pipe had good wear resistance and corrosion resistance even at a high temperature. In recent years, as the precision of machinery equipment and measurement technology develop, the precision level of modern precision engineering has entered the micro-nano era. The effects of thermal deformation on machinery mechanical precision cannot be ignored. Therefore, more and more attention has been paid to the study of the thermal expansion mechanism, accurate calculation and the measurement of thermal deformation by domestic and foreign industries. It was of great significance to study the rule of metal thermal expansion for analyzing the mechanism of mechanical thermal deformation and for improving the practical application technology [6; 7; 8; 9]. The thermal elasticity theory found numerous applications for solving thermal deformation problems of various new materials and complicated mechanical parts. [PERSON] [10] studied n-order deformation theory based on the theory of thermodynamics. [PERSON] [11] studied the stress distribution of double-layer metal circular tube structures based on thermoelastic theory. In recent years, thermal deformation research methods have been introduced into high-end computer numerical control (CNC) machining equipment to research thermal errors [12; 13; 14]. Back propagation (BP) neural network is a kind of multilayer feedforward neural network trained by an error back propagation algorithm. It has become one of the most widely used neural network models. A BP neural network has a very strong nonlinear mapping capability; it could automatically sum up the functional relationship between input and output data through training without any prior formula, and thus it is widely used in modeling [15; 16; 17; 18; 19]. [PERSON] [20] predicted the heat load based on a BP neural network-Markov prediction model. The results showed that compared with other heat load forecasting methods, the BP neural network had obvious advantages in predicting accurately, and this model resulted in a good heat load forecasting effect. [PERSON] [21] introduced the BP neural network to establish a new effective thermal error model for machining centers. The validity of the method is validated by an experiment in a machining center.