scholarly journals Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shanle Li ◽  
Feng Liu ◽  
Hongyan Wang ◽  
Haijun Song ◽  
Kuilong Yu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Magnetic Force ◽  
Rotor System ◽  
Kutta Method ◽  
Rotor Vibration ◽  
Motion Equations ◽  
Runge Kutta Method ◽  
Static Eccentricity ◽  
New Formula

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.

Research on Lateral Nonlinear Vibration Behavior of Composite Shaft-Disk Rotor System

2018 ◽  
Vol 875 ◽  
pp. 149-161 ◽  
Author(s):  
Chun Jin Zhang ◽  
Yong Sheng Ren ◽  
Shu Juan Ji
Keyword(s):  
Nonlinear Vibration ◽  
Strain Energy ◽  
Nonlinear Deformation ◽  
Lagrange Equation ◽  
Rotor System ◽  
Kutta Method ◽  
Response Curves ◽  
Runge Kutta Method ◽  
Composite Shaft ◽  
Ihb Method

The characteristics of the lateral nonlinear vibration in composite shaft-disk rotor system with nonlinear deformation are studied. Firstly, the equations of the kinetic energy of the composite shaft, the disk and the eccentric mass as well as the equations of the strain energy of the composite shaft are derived. Based on these equations, the nonlinear vibration equations are deduced by using the Lagrange equation. Then, the frequency response curves and time response curves of the system are obtained by using the IHB method and verified by the fourth order Runge-Kutta method. Experimental results show that the external damping coefficient, the size of eccentric mass only influences the nonlinear amplitude. Moreover, the ply-angle, thickness to diameter(T/D) ratio, length to diameter (L/D) ratio, and the position of disk in the shaft not only produce an effect on the nonlinear amplitude, but also influence the nonlinear vibration frequency.

Coupled Bending-Torsional Vibration Analysis of Rotor System with Two Asymmetric Disks

2011 ◽  
Vol 130-134 ◽  
pp. 2335-2339
Author(s):  
Jun Hong Zhang ◽  
Zhen Peng He ◽  
Wen Peng Ma ◽  
Liang Ma ◽  
Gui Chang Zhang
Keyword(s):  
Phase Difference ◽  
Vibration Analysis ◽  
Initial Phase ◽  
Rotor System ◽  
Dynamic Equations ◽  
Force Model ◽  
Torsional Angle ◽  
Kutta Method ◽  
Internal Damping ◽  
Initial Phase Difference

The dynamic equations derived based on the actual rotor system with two asymmetric disks. In the analysis, the eccentric, rubbing fault characteristics and internal damping effects is considered, and all the analysis is established based on nonlinear oil film force model and coupled bending-torsional differential equations. The Rugge-Kutta method is used to solve numerical model, the torsional displacement response, torsion angle and Poincare map are obtained. The results show torsion amplitudes with initial phase difference π / 2 is larger than initial phase difference of π and 0. In order to eliminate the rigid rolling component the relative torsional angle must be considered.

Dynamic stability and nonlinear vibration analysis of a rotor system with flexible/rigid blades

2016 ◽  
Vol 105 ◽  
pp. 633-653 ◽  
Author(s):  
Saeed Bab ◽  
Siamak E. Khadem ◽  
Amirhassan Abbasi ◽  
Majid Shahgholi
Keyword(s):  
Nonlinear Vibration ◽  
Dynamic Stability ◽  
Vibration Analysis ◽  
Rotor System

scholarly journals Nonlinear vibration behaviors of marine rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion

2021 ◽  
Vol 13 (12) ◽  
pp. 168781402110673
Author(s):  
Xuan Xie ◽  
Ming Li ◽  
Junwei Wang
Keyword(s):  
Nonlinear Vibration ◽  
Rotor System ◽  
Rotating Speed ◽  
Floating Raft ◽  
Runge Kutta Method ◽  
Axis Orbit ◽  
Steady State Responses ◽  
Time Domain Response ◽  
Frequency Domain Response ◽  
State Responses

To study the nonlinear vibration behaviors of rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion, the dynamic model is established considering the effect of heaving motion, its steady-state responses are numerically obtained using Runge-Kutta method and the results are surveyed by tools such as the spectrum waterfall diagram, time-domain response, frequency-domain response, axis orbit, and Poincaré map. The effects of rotating speed, ship heaving amplitude, and its frequency on the nonlinear dynamic behavior of the system are mainly studied. The results show that the responses of the rotor and raft are of obvious nonlinear behaviors such as amplitude jumping, bifurcation, and chaos due to the effects of nonlinear oil film force and ship heaving motion. With the increase of rotating speed, the motion of rotor and raft presents quasi-periodic and chaotic vibrations. Ship heaving amplitude and its frequency all have great effect on the vibration of rotor and raft; as heaving amplitude or frequency increases, the motion state of rotor and raft changes, and the amplitude of raft increases significantly. The displacement restrictor can effectively limit the vibrating displacements of the raft when ship heaving amplitude or its frequency is large.

scholarly journals Nonlinear Parametric Resonance Behavior of Cables in a Long Cantilever Bridge for Sightseeing Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zengwei Guo ◽  
Pengfei Zi ◽  
Xuanbo He
Keyword(s):  
Differential Equation ◽  
Nonlinear Vibration ◽  
Damping Ratio ◽  
Element Model ◽  
Excitation Amplitude ◽  
Parametric Vibration ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Vibration Performance

In order to study the parametric vibration of stayed cables in a long cantilever bridge for a sightseeing platform, nonlinear parametric vibration equations of the stayed cables excited by the vibration of bridge deck and tower are derived. Then, a second-order differential equation is transformed into a first-order ordinary differential equation, which is solved by using the Runge–Kutta method. A finite element model of cables was also built to verify the solution of the Runge–Kutta method. Then, the inherent dynamic characteristics of the full structure and all the cables with different lengths were analyzed to discuss the potential risk of parametric vibration. The longest and shortest cables were taken as examples to explore their nonlinear vibration performance. The effects of damping ratio, excitation position, and amplitude on cables’ nonlinear vibration performance were investigated. The results show that it will be more efficient and convenient to use the Runge–Kutta method to calculate cables’ nonlinear vibration amplitude without loss of accuracy. In addition, short cables have more resonance zones compared to long cables. Especially, with the cable length shortening, the dominant frequencies of the dynamic response and its amplitude increase significantly, and the number of resonance zones also increases. However, excessive excitation amplitude will also cause multiple resonance zones in the cable. The parametric analysis results show that it is effective and efficient to mitigate the nonlinear vibration by adjusting the frequency relationship between the bridge and the cables, rather than by increasing the damping ratio.

Dynamic Response of SFD-Sliding Rigid Bearing Rotor -System

2013 ◽  
Vol 706-708 ◽  
pp. 1310-1313
Author(s):  
Ji Yan Wang
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Periodic Motion ◽  
Rotor System ◽  
Rigid Rotor ◽  
Kutta Method ◽  
Sliding Bearing ◽  
Runge Kutta Method ◽  
Stable Periodic ◽  
Runge Kutta

This paper establishes a linking dynamic model of SFD-sliding bearing rigid rotor system by employing Runge-Kutta method to solve dynamic question of the above systems. The study has shown: rigid rotor system can keep stable periodic motion in a certain scope with the following quasi-periodicity bifurcation.

Analyzing the Vibration of Warp Yarns in Lengthwise and Crosswise

2014 ◽  
Vol 541-542 ◽  
pp. 798-803
Author(s):  
Fei Chen ◽  
Yi Sheng Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Longitudinal Vibration ◽  
Lateral Vibration ◽  
Kutta Method ◽  
Warp Yarn ◽  
Runge Kutta Method ◽  
Galerkin Truncation

This article adopts nonlinear vibration method to analyze the fluctuation process of warp yarn. Selecting Kelvin model.A differential equation of the warp yarn vibration in lengthwise and crosswise is established by Newton law.And using Galerkin truncation method to separate the variables of time and space and to discrete partial differential equations into ordinary differential equations.The vertical and lateral vibration response of the warp are analyzed by 4-order Runge-Kutta method and matlab. Getting transverse and longitudinal vibration of warp yarns.

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