## 1 Introduction  
The interference fit has the advantages of simple structure, good neutrality, strong load-carrying capacity, good impact resistance, and so on, so it has a wide application in mechanical engineering [1]. Many scholars have done a lot of research on the algorithm and influence of interference fit. [PERSON] [2] studied the influence of cylindricity and surface modification on the load-carrying capacity of interference fit components. [PERSON] et al. [3] analyzed the influence of different influence factors on the dynamic performance of oblique cone interference fit. Compared with the equal diameter cylindrical interference fit, the influence of interference magnitude on the local contact stress is obvious. [PERSON] et al. [4, 5] proposed a variety of algorithms for multi-layer interference fit based on thick-wall cylinder theory and analyzed the effects of many factors on the performance of multi-layer interference fit. [PERSON] [6] studied the phenomenon of torque increase during the loading cycle of the interference specimen. By establishing a cycle wear test, the reason for the torque increase is related to the friction coefficient between interference fit. The research provides a basis for the optimization of interference fit design. Based on the geometric defects and surface roughness of the interference specimen, [PERSON] et al. [7, 8] studied its influence on the strength of interference connection. [PERSON] et al. [9, 10] studied the effect of interference size on the fretting fatigue life of carbon fiber reinforced polymers and titanium alloy bolts. The interference components usually work at high speed and under a temperature field, various rotational speeds and temperatures have different effects on the performance of interference components. At present, some scholars have made some research in these fields. For example, [PERSON] [11] studied the dynamic characteristics and mechanical properties of ball bearings with or without centrifugal force. [PERSON] [12] established a displacement mathematical model based on centrifugal force and temperature in the bearing inner ring, coupled with the bearing dynamic model of bearing, and studied change rule of bearing interference fit and the influence on spindle system dynamics. The results show that the initial interference magnitude will increase with the combined influence factors of temperature increase and centrifugal force, and eventually lead to the increase of bearing stiffness. [PERSON] [13] analyzed the calculation method of the interference magnitude and stress between the rotor and the permanent magnet, establishing a finite element model for stress analysis, and the results were compared. [PERSON] [14] established a three-dimensional single-layer interference cylinder model and analyzed influence of centrifugal force on the interference fit. [PERSON] et al. [15] proposed an algorithm for calculating contact pressure and stress of multi-layer interference fit under multi contact and temperature. An engine crankshaft bearing case was established using finite element method to verify the correctness of its algorithm. However, the research on the influencing factors of interference fit is mainly concentrated in a single layer. Currently, multi-layer interference fit is widely used in engineering, for example low-speed coupling of wind turbine (Figure 1), which can be used as the typical application of multi-layer interference cylinder [16]. Here, the effects of centrifugal force and temperature gradient on the contact pressure of multi-layer interference cylinder are analyzed. The matrix model of contact pressure and interference magnitude of multi-layer interference cylinder under centrifugal force and temperature gradient is derived. Four kinds of interference cylinder models are built to respectively analyze the influence of centrifugal force and temperature gradient on the performance of multi-layer interference cylinder.