scholarly journals Dynamic Analysis of Integrally Geared Compressors with Varying Workloads

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Ming Zhang ◽  
Zhinong Jiang ◽  
Jinji Gao
Keyword(s):  
Critical Load ◽  
Axial Force ◽  
High Efficiency ◽  
Dynamic Responses ◽  
Dynamic Behaviors ◽  
Meshing Stiffness ◽  
Dynamic Coefficients ◽  
Coupling System ◽  
Rotor Bearing ◽  
Bearing System

Integrally geared compressors are characterized by compact and high efficiency machines, which are widely used in modern processing industries. As an important part of integrally geared compressors, a geared rotor-bearing system exhibits complicated dynamic behaviors. When running at rated speeds, a coupling system likely produces resonance with an adjusted workload, and a critical load phenomenon occurs. The dynamic coefficients of bearings, axial force and torque, and gear meshing stiffness vary with workload because of the interaction between rotors. In this study, a dynamic model of a geared rotor-bearing system influenced by the dynamic coefficients of bearings, axial force and torque, and gear meshing stiffness is developed. The dynamic responses of the coupling system are calculated and analyzed by using a typical five-shaft integrally geared compressor as an example. The effects of different parameters on the dynamic behaviors of the proposed system are also considered in the discussion. The geared rotor-bearing system is further investigated to examine the failure mechanism of the critical load.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

Nonlinear Vibration Signature Analysis of a High Speed Rotor Bearing System Due to Race Imperfection

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
High Speed ◽  
Nonlinear Differential Equations ◽  
Mathematical Formulation ◽  
Nonlinear Damping ◽  
Dynamic Responses ◽  
Fast Fourier Transformation ◽  
Surface Waviness ◽  
Contact Points ◽  
Rotor Bearing ◽  
Bearing System

In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

scholarly journals Nonlinear Dynamic Analysis of Rotor-Bearing System with Cubic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Guofang Nan ◽  
Yujie Zhu ◽  
Yang Zhang ◽  
Wei Guo
Keyword(s):  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Hertzian Contact ◽  
Stable Operation ◽  
Nonlinear Stiffness ◽  
Cubic Nonlinearity ◽  
Dynamic Behaviors ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Bearing System

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

Effects of gearbox housing flexibility on dynamic characteristics of gear transmission system

2020 ◽  
pp. 107754632095373
Author(s):  
Xiannian Kong ◽  
Jinyuan Tang ◽  
Chen Siyu ◽  
Zehua Hu
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Lightweight Design ◽  
Transmission System ◽  
Structure Design ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamic Behaviors ◽  
Gear Transmission System ◽  
Rotor Bearing

The lightweight design of the gear system is the current tendency. The gearbox housing is modeled as a rigid body and is neglected in the gear dynamic analysis. It is of great significance to introduce the gearbox housing flexibility into the dynamic analysis and analyze the influence of the gearbox housing flexibility on the dynamic behaviors of the gear transmission system, as this can provide important instructions for the lightweight structure design of the housing. The gear–rotor–bearing model and the gear–rotor–bearing–housing model are established by the finite element node method. A Timoshenko beam element is used to represent the shafts. To illustrate the housing effect, two kinds of housing model are established: one tends to be rigid and the other to be flexible and lighter. The housings are simplified as a super element obtained by the dynamic substructure method. Natural frequencies and dynamic responses are illustrated to indicate the effects of housing flexibility. Comparisons of numerical results show that the rigid housing can be neglected for its little effect on the dynamic analysis. The flexibility of the housing slightly reduces the natural frequencies of the gear transmission system, and the maximum reduction is 6.05%. Meanwhile, the amplitudes of the first two resonance peaks of the dynamic transmission error decrease by 9.5% and 5.05%. Besides, more response peaks emerge at higher speeds when the flexibility of housing increases. The complete phenomena of dynamic behaviors of the gear transmission system can be obtained by considering the housing flexibility.

Chaos and Nonlinear Dynamic Analysis of Porous Air Bearing System

2015 ◽  
Vol 764-765 ◽  
pp. 204-207
Author(s):  
Cheng Chi Wang ◽  
Jui Pin Hung
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Effective Means ◽  
Nonlinear Dynamic Analysis ◽  
Transformation Method ◽  
Dynamic Responses ◽  
Air Bearing ◽  
Dynamic Behaviors ◽  
Rotor Mass ◽  
Bearing System

The chaos and nonlinear dynamic behaviors of porous air bearing system are studied by a hybrid numerical method combining the finite difference method (FDM) and differential transformation method (DTM). The numerical results are verified by two different schemes including hybrid method and FDM and the current analytical results are found to be in good agreement. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass is increased. From the dynamic responses of the rotor center, they reveal complex dynamic behaviors including periodic, sub-harmonic motion and chaos. The results of this study provide an understanding of the nonlinear dynamic behavior of PAB systems characterized by different rotor masses. Specifically, the results have shown that system exists chaotic motion over the ranges of rotor mass 10.66≤Mr<13.7kg. The proposed method and results provide an effective means of gaining insights into the porous air bearing systems.

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