Vibration Generated on a Rotating Shaft by Passing Through its Critical Speed with some Angular Acceleration (2nd Report)

1948 ◽  
Vol 51 (360) ◽  
pp. 360-361
Author(s):  
Yoshinori SHIMOYAMA ◽  
Toshio YAMAMOTO
Keyword(s):  
Critical Speed ◽  
Angular Acceleration ◽  
Rotating Shaft

Nonstationary analysis of nonlinear rotating shafts passing through critical speed excited by a nonideal energy source

2016 ◽  
Vol 232 (4) ◽  
pp. 572-584 ◽  
Author(s):  
A Mahmoudi ◽  
SAA Hosseini ◽  
M Zamanian
Keyword(s):  
Energy Source ◽  
Critical Speed ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Continuous System ◽  
Multiple Scale ◽  
Sommerfeld Effect ◽  
Rotating Shaft ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion

In this paper, the effect of nonlinearity on vibration of a rotating shaft passing through critical speed excited by nonideal energy source is investigated. Here, the interaction between a nonlinear gyroscopic continuous system (i.e. rotating shaft) and the energy source is considered. In the shaft model, the rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The nonlinearity is due to large deflection of the shaft. Firstly, nonlinear equations of motion governing the flexural–flexural–extensional vibrations of the rotating shaft with nonconstant spin are derived by the Hamilton principle. Then, the equations are simplified using stretching assumption. To analyze the nonstationary vibration of the nonideal system, multiple-scale method is directly applied to the equations expressed in complex coordinates. Three analytical expressions that describe variation of amplitude, phase, and angular acceleration during passage through critical speed are derived. It is shown that Sommerfeld effect in specific range of driving torque occurs. Finally, effect of damping and nonlinearity on occurrence of Sommerfeld effect is investigated. It is shown that the linear model predicts the range of Sommerfeld effect occurrence inaccurately and, therefore, nonlinear analysis is necessary in the present problem.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

scholarly journals A Dynamic Analysis of the Rotary Cutting System of King Grass Shredder

2020 ◽  
Vol 145 ◽  
pp. 02080
Author(s):  
Zunxiang Li ◽  
Ou Zhongqing ◽  
Jiao jing ◽  
Huang xiaohong ◽  
Du jihua
Keyword(s):  
Finite Element ◽  
Critical Speed ◽  
Great Influence ◽  
Second Order ◽  
Belt Drive ◽  
Finite Element Models ◽  
Rotating Shaft ◽  
First Order ◽  
Rotary Cutting ◽  
Cutting System

With the rotary cutting system of king grass shredder as the research object, this paper established finite element models for rotating shaft, rotating shaft-belt pulley, rotating shaft-rotary cutting part and rotary cutting system and analyzed the influences of belt pulley and rotary cutting part on the dynamic characteristics of rotary cutting system. The results showed that the belt pulley and rotary cutting part had a great influence on the second order critical speed of rotary cutting system, and the rotary cutting part had a greater influence on the critical speed of first order forward precession than the belt pulley. Meanwhile, the critical speed of rotary cutting system that conformed to facts was calculated. There was a big difference between its first order and second order critical speeds, but the critical speed of first order backward precession was lower. Finally, it was found after analysis that the natural frequency of rotary cutting system was lower than the vibration frequency induced by belt drive, so the shredder can run safely.

Nonlinear Analysis Based on Experiments of the Rotation Shaft System of Mine Drainage Motor and Pump

2011 ◽  
Vol 341-342 ◽  
pp. 271-275
Author(s):  
Wu Zhao ◽  
Gui Yu
Keyword(s):  
Optimization Design ◽  
Critical Speed ◽  
Mine Drainage ◽  
Stable State ◽  
Dynamic Responses ◽  
Mechanical Seal ◽  
Rotating Shaft ◽  
Nonlinear Characteristics ◽  
Study Results ◽  
Multiple Frequencies

The experimental study results show that the system’s nonlinear characteristics, incluing the dynamic responses of the poincare mapping, the bifurcation plots, three-dimensional waterfalls diagrams etc. The effects factors of system experiment are studied and analyzed, including the misalignment and the rub-impact stiffness on system responses. So, the faults characteristics of the misalignment and the rub-impact of the rotation shaft-mechanical seal system on the drainge motor and drainge pump are also gained by the experiment. The dynamic performance of the system show nonlinear characteristics in different working conditions. The rotating shaft-mechanical seal system on the drainge motor and drainge pump can be optimization design and performance prediction based on the studied results of our work. The experiment’s results show that: the multiple frequencies are produced of the rotating shaft-mechanical seal system on drainge motor and drainge pump, and the frequencies of 1-time and 2-time are dominating components under the exciting force effects of misalignment and imbalance. At the fault state of misalignment coupling rub-impact, the multiple frequencies including 2-time, 3-time, 4-time and so on, will be induced under the critical speed. Over the value of the critical speed, will cause the phenomenon of frequency demultiplication and chaos. With rub-impact stiffness value increased, the phenomenon of frequency demultiplication and chaos are induced more frequently; with the degree of misalignment increased, the phenomena of chaos will decrease and the system will tend to be the stable state.

Sign in / Sign up

Export Citation Format

Share Document