Dynamic Analysis of Flexible Shaft and Elastic Disk Rotor System Based on the Effect of Alford Force

Abstract

Taken the flexible shaft and elastic disk rotor system as the research object, vibration differential equations are established by the modal synthesis method. Based on the Runge–Kutta method of direct integration, dynamic equations are solved successfully. Then, the effects of Alford force caused by the airflow excitation are researched on the stability and dynamic response. The results show modal vibration of the disk takes a great effect on the coupled natural frequency of shaft transverse vibration in the high rotational speed region. The effect of shaft-disk coupling makes rotor frequency to decrease, and different rotational speeds have little effect on rotor frequency. Eccentric distance is sensitive to the amplitude of rotor response, but it has little effect on rotor stability, motion law, and relative relationship of two response frequencies. The proportion of rotor responses caused by aerodynamic excitation force becomes larger with the increase of rotational speed and disk radius. However, the proportion decreases with the second support moving to the right, and it is helpful for the stable operation of the rotor system.

Nonlinear Responses of a Rotor‐Bearing‐Seal System with Pedestal Looseness

“…In recent years, there are an increasing number of scholars who pay attention to the nonlinear vibration of the seal-bearingrotor system because of its strong nonlinear characteristics, including oil-film instability and other coupling faults, such as the airflow-induced vibration [21][22][23][24][25][26][27][28][29][30][31][32]. For example, Wang et al [21] studied the effect of the real high-pressure methane gas properties on the nonlinear behavior of the seal-rotor system.…”

Stress Analysis of a Rectangular Shaft Carrying a Rotor System Due to Eccentricity

“…Using uniformly distributed load of 5 N, tensile stresses and deflections were obtained for all cases. Many types of stresses and deflections in all directions for this shaft are obtained and discussed as following: In figures (3,4,5,6) when the eccentricity (e = 0.1x10 -3 ) the value of Von Mises stress (σ von ) begins from (33) Mpa at (N= 1000 R.P.M) and reach to (36.5) Mpa at (N= 4400 R.P.M) but (under the same conditions) in the case of the eccentricity (e = 0.3x10 -3 ) will be (43) Mpa at (N= 1000 R.P.M) and reach to (161) Mpa at (N= 4400 R.P.M). In figures (7,8,9,01), when the eccentricity (e = 0.1x10 -3 ) the value of (σ 3 ) stress begin from (-39.4) Mpa at (N= 1000 R.P.M) and reach to (-41.7) Pa at (N= 4400 R.P.M) but (under the same conditions) in the case the eccentricity (e = 0.3x10 -3 ) will be (-51.1) Mpa at (N= 1000 R.P.M) and reach to (-203) Mpa at (N= 4400 R.P.M).…”

“…deflection was take place at the midpoint of the shaft while the stresses and deflection are concentrating at the bottom of the bearing due to concentrating forces on this area. Wenjun Yang et al [4] investigate the vibration differential equation of a shaft -disc rotor system by the model synthesis method. Runge-Kutta "s direct integration method has been used to extract the equation of system.…”

Analysis of Nonlinear Characteristics and the Factors Affecting the Operation of the Active Magnetic Bearings Rotor System Considering Alford Force

“…Taking the flexible shaft and elastic disk rotor system as the research object, Yang et al established the vibration differential equation with the modal synthesis method and solved the equation by using the Runge−Kutta method. The results showed that the increase of speed and disk radius will lead to the increase of rotor response, which can help to improve the stability of the system by adjusting the support position [6]. Li et al analyzed the impact of nonlinear coupling factor and blade-bending vibration to dynamic characteristics of rotor-bearing system and the results indicated that the Alford force caused by blade tip clearance makes the motion state of the system more complex [7].…”

“…will lead to the increase of rotor response, which can help to improve the stability of the system by adjusting the support position [6].Li et al analyzed the impact of nonlinear coupling factor and bladebending vibration to dynamic characteristics of rotorbearing system and the results indicated that the Alford force caused by blade tip clearance makes the motion state of the system more complex [7].…”