## 1 Introduction
Along with the ongoing research, as is known, the rotor-bearing system needs to regard the rotor as a complete system that includes the rotor shaft, bearings, support frame, etc. [PERSON] [17] established the finite element model of the rotor-bearing system, and studied the influence of the supporting stiffness and damping coefficients of the rubber O-ring on the stability of the system. [PERSON] [20] built a rotor-bearing system model using the finite element method, and investigated the effect of different types of support on the stability of the system. Some scholars [21; 22; 23] studied the dynamics of the rotor system based upon different views of the modeling method. The transient response of the bearing-rotor system during variable speed is one of the main research problems. [PERSON] et al. [24] studied the transient vibration of asymmetric rotor systems during acceleration based on the finite element model and [PERSON]'s method. [PERSON] et al. [25] proposed a transient response analysis technique of the rotor system, and used the generalized finite element modeling method of a rotor-bearing system. [PERSON] et al. [26] performed damage detection from non-stationary mechanical vibration signals collected during acceleration and deceleration. In addition to theoretical modeling, experimental testing is another important method to study the dynamic characteristics of the rotor system. It is difficult to obtain dynamic data of the rotor directly with contact measurement, because the rotor rotates at a high speed. Non-contact measurement technology does not interfere with the rotor rotation, and the sensor is easy to arrange. It is the first choice method for mechanical vibration measurement of the rotor system. [PERSON] et al. [27] measured the actual axial clearance of the scroll air compressor under a working condition by using an eddy current displacement sensor, and the results show that the eddy current sensor has high sensitivity and preferable static and dynamic performances. [PERSON] et al. [28] developed a novel eddy current speed sensor to measure the rotation speed of conductive objects. However, the eddy current displacement sensor has high requirements for the tested object, such as a metal conductor. Unfortunately, there are some paper tubes around the winding rotor, which hinder the application of the eddy current sensor in the winding rotor. Although these methods are not applied to measure the vibration of the winding rotor, these references could throw light upon the thoughts of vibration displacement amplitude measurement of the winding rotor. This paper aimed to investigate the dynamic characteristics of the winding rotor during its speeding up. Construction features of the winding rotor were analyzed in depth and the corresponding finite element model was established through a Timoshenko beam element and flexible support, considering the frequency-dependent supporting parameters of the rubber O-ring and the time-varying rotational speed. The dynamic equations considering the coupling effect between different nodes were derived by [PERSON]'s second law, and the dynamic responses were simulated under the different supporting stiffness and damping coefficients of the rubber O-rings, as well as the speed-up time by means of Newmark time integration. The non-contact measurement device was then developed, the mechanical vibration of the winding rotor was carried out under different speed-up times. The test results show that the test curves are in good agreement with the simulation curves. The method and the main findings presented in this study can be used for mechanical vibration analysis of other types of high-speed flexible rotors.