# Correlation Analysis and Its Application on an Asymmetry
## 1 Introduction  
Overhung rotors are found in many industrial applications. Many works on rotors with overhung design have been reported. For instance, electromagnetic motors [1; 2; 3; 4], spindle in ultra-precision machine [5], turbine generator [6; 7; 8; 9; 10; 11; 12; 13], compressor [14], and turbine power rotors [15] are rotor structures which must or may have overhung parts. Taking the turbine generator rotor as an example, the overhung parts always exist to implement the field winding. The mass and electromagnetic field of the overhung part would affect the dynamical behaviours of the rotor system conversely. Although rotors are carefully designed for fatigue loading and a high level of safety by using high-quality materials and precise manufacturing techniques, catastrophic failures occur in high-speed rotating machines, particularly for the overhung rotor which has considerable weight. Many researchers have modeled and studied the dynamical responses of overhung rotors using different approaches. [PERSON] et al. [16] studied the nonlinear dynamic behavior of the bladed overhang rotor system with squeeze film damper, using the lumped mass method and the Lagrange approach. [PERSON] et al. [17] presented an analytical method based on transfer relations for an axial flux permanent magnet machine, while taking the overhang length into account. [PERSON] et al. [18] investigated an overhang rotor with two discs supported by a couple of tilting-pad journal bearings. In [PERSON]'s work, active lubrication, based on injecting pressurized oil into the bearing gap through orifices machined in the bearing sliding surface, is utilized. [PERSON] et al. [19] considered the overhang effect according to the various rotor types of permanent magnet machine is analyzed by using 3D magneto-static finite element method. [PERSON] et al. [20] presented a novel outer rotor permanentmagnet vernier machine for in-wheel direct-drive application and introduced the overhang structures of the rotor and flux modulation pole. [PERSON] et al. [21] described the analysis and design of a spoke-type motor using ferrite permanent magnet. [PERSON] et al. [22] dealt with the characteristic analysis of the fan motor considering ferrite bonded magnet in an inner-rotor overhang type Brushless DC motor. [PERSON] et al. [23] used a downwind configuration with a coning angle prescribed to allow load alignment for critical conditions to achieve moment reduction by changing the sign of variables like the overhang. [PERSON] et al. [24] built an overhung rotor-support system to study the dynamic characteristics of rotor and support experimental systems under sudden unbalance excitation. [PERSON] et al. [25] proposed a permanent magnet vernier machine as a suitable alternative for direct-drive applications due to its high torque feature at a low operated speed and gave out the reasons. [PERSON] et al. [26] conducted an experimental comparison of response for a healthy and cracked overhung rotor system. [PERSON] et al. [27] investigated the primary resonances of a cantilever flexible shaft carrying a rigid disk at its free end (overhung rotor). [PERSON] et al. [28; 29] presented the response of the overhung rotor on isotropic support and an-isotropic support subject to unbalanced force. All these research works give beneficial results on overhung rotors. However, it is still difficult to conduct the balancing of rotors with a long overhang. In the field of engineering, to connect with the other parts of a whole system the rotor structures usually have overhang parts whose gravity will introduce moment to the supports. Meanwhile, the nonlinear factors of the rotor system will make this additional moment introduced vibration more complex, i.e., different lengths and position of the overhang will lead to different effects on the vibration of the rotor system. Thus, the motivation of this work is to tackle the problem by modeling, dynamical analysis, statistical analysis and experimentation.