Study on the Nonlinear Characteristic of a Rotor-Bearing System between the Continuum Model and Discrete Model

2009 ◽  
Vol 16-19 ◽  
pp. 851-855
Author(s):  
Chao Feng Li ◽  
Wei Sun ◽  
Chen Yi Liu ◽  
Bang Chun Wen
Keyword(s):  
Nonlinear Dynamic ◽  
Discrete Model ◽  
Continuum Model ◽  
Three Dimensional ◽  
Element Model ◽  
Significant Difference ◽  
Rotor Bearing ◽  
Comparison Of The Results ◽  
Bearing System ◽  
The Continuum

The nonlinear dynamic behavior of a rotor-bearing system is analyzed with its finite element model based on the analysis of the discrete model, with considering some other important influencing factors such as, material damping, gyroscopic effect, inertia distribution, shear effect and so on, which make the description of the system more embodiment avoiding the casualness of selection with system parameters. With the comparison of the results on the bifurcation map and three-dimensional spectrum, significant difference is appeared with the addition of the considered factors. It is suggested that the substitution of continuum model for the discrete ones can get more accurate and abundant results. Furthermore, these results can provide more accurate verification and reference for the experiment and nonlinear dynamic design of the complex rotor system.

Nonlinear Dynamics Characteristic of Rotor-Bearing System by a Finite Element Model

2009 ◽  
Author(s):  
Chaofeng Li ◽  
Zhaohui Ren ◽  
Xiaopeng Li ◽  
Bangchun Wen
Keyword(s):  
Nonlinear Dynamic ◽  
Discrete Model ◽  
Element Model ◽  
Dynamic Responses ◽  
Runge Kutta Method ◽  
Significant Difference ◽  
Rotor Bearing ◽  
Comparison Of The Results ◽  
Bearing System ◽  
The Continuum

The nonlinear dynamic behavior of a rotor-bearing system is analyzed with its continuum model based on the analysis of the discrete model, with considering some other important influencing factors besides the nonlinear factors of the bearing, such as, the effect of inertia distribution and shear, transverse-torsion, structural geometric parameters of the system, which make the description of the system more embodiment and avoid the casualness of selection of system parameters. The dynamic responses of the continuum system and discrete system in the same unbalance condition are approached by the Runge-Kutta method and Newmark-β method. With the comparison of the results, significant difference about the dynamic characteristics is found with the addition of the considered factors. It is suggested that the substitution of discrete model by the continuum ones can get more accurate and abundant results. Furthermore, these results can provide more accurate verification and reference for the experiment and nonlinear dynamic design of the more complicated rotor system.

Nonlinear dynamic characteristics of a three-dimensional rod-fastening rotor bearing system

2014 ◽  
Vol 229 (5) ◽  
pp. 882-894 ◽  
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Xin Wang ◽  
Minqing Jing
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Three Dimensional ◽  
Dynamic Features ◽  
Stability Margins ◽  
Mass Eccentricity ◽  
Nonlinear Dynamic Characteristics ◽  
Rotor Bearing ◽  
Rod Fastening Rotor ◽  
Bearing System

The nonlinear dynamic characteristics of three-dimensional rod-fastening rotor bearing system are investigated in this paper. The rod-fastening rotor includes discontinuous shaft, rotating disks, circumferentially distributed rods, and macrointerfaces between disks. The first three parts are discretized by three dimensional elements, and the macrointerfaces are connected by some springs whose stiffness is determined by a proposed linear partition method. For comparison, the three-dimensional dynamic model of a corresponding complete rotor bearing system is also built. After the rod-fastening and complete rotor bearing system are reduced by a component mode synthesis, periodic motions and stability margins are calculated by using the shooting method and path-following technique, and the local stability of system is obtained by using the Floquet theory. Comparative results show the both systems have a resemblance in the bifurcation features when mass eccentricity and rotating speed are changed. The vibration response has the identical frequency components when typical bifurcations occur. The dynamic stress is obtained by regarding the displacements of all nodes as load. Moreover, the unbalanced and insufficient of the pre-tightening forces lead to obvious disadvantageous influence on the stability and vibration of the both systems. Generally, this paper considers the interfacial effect of the rod-fastening rotor bearing system and the relative nonlinear dynamic features are obtained.

scholarly journals Nonlinear Dynamic Behavior of Double-Disk Isotropic Rotor System with Axial Rub-Impact

2011 ◽  
Vol 2-3 ◽  
pp. 678-682
Author(s):  
Y. Zhang ◽  
W.M. Wang ◽  
J.F. Yao
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
High Speed ◽  
Element Model ◽  
Rotor System ◽  
Self Healing ◽  
Rotor Bearing ◽  
Nonlinear Dynamic Behavior ◽  
Operation Stability ◽  
Bearing System

In the case of considering the shear effect and gyroscopic effect, a finite element model is developed to study the nonlinear dynamic behavior of a double-disk isotropic rotor- bearing system with axial rub-impact in this paper. The influences of rotational speed and initial phase difference on the operation stability of the rotor-bearing system are discussed. It transpires that the response of the rotor system with axial rub- impact is mainly synchronous periodic motion. The vibration signals of axial rub-impact include such as the synchronous signal and the multiple frequencies, in which the synchronous signal is dominating signal. There is no weakening wave phenomenon in time wave plot. All the results are in reasonable good agreement with those observed in engineering. The results of this paper could provide certain reference for fault diagnosis and self-healing of large high-speed rotating machinery system, thus ensuring the safe operation of the system.

Effects of Typical Machining Errors on the Nonlinear Dynamic Characteristics of Rod-Fastened Rotor Bearing System

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Nanshan Wang
Keyword(s):  
Nonlinear Dynamic ◽  
Three Dimensional ◽  
Analysis Data ◽  
System Stability ◽  
Dynamic Features ◽  
Machining Precision ◽  
Machining Errors ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Bearing System

The effects of typical machining errors on the dynamic features of rod-fastened rotor bearing system (RBS) are studied in this paper. Three micron-sized machining errors are considered in a three-dimensional (3D) rod-fastened model. The static effects of machining errors are investigated by applying finite element method. Results demonstrate that machining errors not only bring about mass eccentricity but also cause obvious rotor bending due to large pretightening force. Then, nonlinear dynamic features such as stability and bifurcation are analyzed by using target-shooting technique, track-following method, and Floquet theory. Analysis data indicate that rotor bending originated from machining errors reduces the system stability evidently. It is also observed that the vibration value continues to go up after critical speed as rotating speed increases. It is a particular property compared with integral rotor. It explains the reason why the machining precision of rod-fastened rotor is much higher than that of the corresponding integral rotor to some extent. Moreover, differences between machining errors are compared and the results show that the machining precision of axial assembly interfaces should be paid more attention in the rod-fastened rotor design.

Numerical investigation on the nonlinear dynamics of a breathing cracked rotor supported by flexible bearings

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6815-6826 ◽  
Author(s):  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang ◽  
Fahui Zhu
Keyword(s):  
Crack Depth ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Element Model ◽  
Induced Response ◽  
Cracked Rotor ◽  
Tangent Stiffness Matrix ◽  
Rotor Bearing ◽  
Breathing Mechanism ◽  
Bearing System

The steady-state response and breathing mechanism of a cracked rotor supported by flexible bearings are investigated in this paper. The generalized and efficient method proposed in this paper can be used to study the dynamics of complicated cracked structures without much modification. First, a three-dimensional finite element model of the cracked rotor-bearing system is established in the rotating frame and a general contact model for modeling the breathing crack is proposed. A component mode synthesis is used to form a reduced-order model. Then, a procedure combining multi-harmonic balance method with arc-length method is used to search the response solution. To accelerate the calculation, the analytical formulations for calculating the tangent stiffness matrix are used. Finally, the gravity induced response and breathing mechanism of a cracked rotor-bearing system are obtained. Interesting result is that the rotational speed and the crack depth will influence the breathing mechanism even if the load remains unchanged.

Thermo-structural analysis of a honeycomb-type volumetric absorber for concentrated solar power applications

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Masoud Behzad ◽  
Benjamin Herrmann ◽  
Williams R. Calderón-Muñoz ◽  
José M. Cardemil ◽  
Rodrigo Barraza
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Steady State ◽  
Discrete Model ◽  
Continuum Model ◽  
Transient State ◽  
Operating Conditions ◽  
Steady State Condition ◽  
Content Type ◽  
The Continuum

Purpose Volumetric air receivers experience high thermal stress as a consequence of the intense radiation flux they are exposed to when used for heat and/or power generation. This study aims to propose a proper design that is required for the absorber and its holder to ensure efficient heat transfer between the fluid and solid phases and to avoid system failure due to thermal stress. Design/methodology/approach The design and modeling processes are applied to both the absorber and its holder. A multi-channel explicit geometry design and a discrete model is applied to the absorber to investigate the conjugate heat transfer and thermo-mechanical stress levels present in the steady-state condition. The discrete model is used to calibrate the initial state of the continuum model that is then used to investigate the transient operating states representing cloud-passing events. Findings The steady-state results constitute promising findings for operating the system at the desired airflow temperature of 700°C. In addition, we identified regions with high temperatures and high-stress values. Furthermore, the transient state model is capable of capturing the heat transfer and fluid dynamics phenomena, allowing the boundaries to be checked under normal operating conditions. Originality/value Thermal stress analysis of the absorber and the steady/transient-state thermal analysis of the absorber/holder were conducted. Steady-state heat transfer in the explicit model was used to calibrate the initial steady-state of the continuum model.

Nonlinear Dynamic Behavior of a Rotor Bearing System With Nonlinear Viscous Damping Suspension

2017 ◽  
Author(s):  
Shuai Yan ◽  
Bin Lin ◽  
Jixiong Fei ◽  
Pengfei Liu
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Vibration Isolation ◽  
Lubricating Oil ◽  
Viscous Damping ◽  
Oil Viscosity ◽  
Speed Range ◽  
Rotor Bearing ◽  
Nonlinear Dynamic Behavior ◽  
Bearing System

Nonlinear damping suspension has gained attention owing to its excellent vibration isolation performance. In this paper, a cubic nonlinear viscous damping suspension was introduced to a rotor bearing system for vibration isolation between the bearing and environment. The nonlinear dynamic response of the rotor bearing system was investigated thoroughly. First, the nonlinear oil film force was solved based short bearing approximation and half Sommerfeld boundary condition. Then the motion equations of the system was built considering the cubic nonlinear viscous damping. A computational method was used to solve the equations of motion, and the bifurcation diagrams were used to display the motions. The influences of rotor-bearing system parameters were discussed from the results of numerical calculation, including the eccentricity, mass, stiffness, damping and lubricating oil viscosity. The results showed that: (1) medium eccentricity shows a wider stable speed range; (2) rotor damping has little effect to the stability of the system; (3) lower mass ratio produces a stable response; (4) medium suspension/journal stiffness ratio contributes to a wider stable speed range; (5) a higher viscosity shows a wider stable speed range than lower viscosity. From the above results, the rotor bearing system shows complex nonlinear dynamic behavior with nonlinear viscous damping. These results will be helpful to carrying out the optimal design of the rotor bearing system.

scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

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