Three-Dimensional Solid Finite Element Contact Model for Rotordynamic Analysis: Experiment and Simulation

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Joseph Oh ◽  
Baik Jin Kim ◽  
Alan Palazzolo
Keyword(s):  
Surface Roughness ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Contact Model ◽  
Element Formulation ◽  
Interface Surface ◽  
Analysis Experiment ◽  
Rotor Bearing ◽  
Solid Finite Elements ◽  
Bearing System

Abstract Conventional rotordynamic analyses generally treat the rotor as a continuous body without considering effect of clamped joints. However, in modern rotating machines, rotors are often assembled with multiple complex-shaped parts and joints, which may significantly affect rotordynamic behavior. Several authors have proposed methods for implementing contact effects in rotordynamic analysis, but a more general modeling method for handling arbitrary contact geometries with various levels of surface roughness is needed. The present paper suggests a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.

Stability of Non-Axisymmetric Rotor and Bearing Systems Modeled With Three-Dimensional-Solid Finite Elements

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Joseph Oh ◽  
Alan Palazzolo ◽  
Lingnan Hu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Computational Efficiency ◽  
Degrees Of Freedom ◽  
Monodromy Matrix ◽  
Three Dimensional ◽  
Element Formulation ◽  
System Matrix ◽  
Rotor Bearing ◽  
Solid Finite Elements

Abstract Although rotors are simplified to be axisymmetric in rotordynamic models, many rotors in the industry are actually non-axisymmetric. Several authors have proposed methods using 3D finite element, rotordynamic models, but more efficient approaches for handling a large number of degrees-of-freedom (DOF) are needed. This task becomes particularly acute when considering parametric excitation that results from asymmetry in the rotating frame. This paper presents an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements. The 10-node quadratic tetrahedron element is used for the finite element formulation of the rotor. A rotor-bearing system, matrix differential equation is derived in the rotor-fixed coordinate system. The system matrices are reduced by using Guyan reduction. The current study utilizes the Floquet theory to determine the stability of solutions for parametrically excited rotor-bearing systems. Computational efficiency is improved by discretization and parallelization, taking advantage of the discretized monodromy matrix of Hsu's method. The method is verified by an analytical model with the Routh–Hurwitz stability criteria, and by direct time-transient, numerical integration for large order models. The proposed and Hill's methods are compared with respect to accuracy and computational efficiency, and the results indicate the limitations of Hill's method when applied to 3D solid rotor-bearing systems. A parametric investigation is performed for an asymmetric Root's blower type shaft, varying bearing asymmetry and bearing damping.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

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.

Analytical and Experimental Study of Dynamic Characteristics of Rod Fastened Rotor-Bearing System Under Preload Saturation

2013 ◽  
Author(s):  
Mingjian Lu ◽  
Haipeng Geng ◽  
Guohui Xu ◽  
Lie Yu ◽  
Weimin Wang
Keyword(s):  
Dynamic Characteristics ◽  
Critical Speed ◽  
Contact Stiffness ◽  
Element Model ◽  
Analysis And Design ◽  
Contact Effect ◽  
Rotor Bearing ◽  
Equivalent Bending Stiffness ◽  
Rod Fastening Rotor ◽  
Bearing System

This paper investigates the dynamic characteristics of a composite rotor fastened by rods. Contact stiffness and equivalent bending stiffness between discs with different rod preloads of the rotor are obtained respectively by using the elastic and elastic-plastic contact theory. The finite element model of rotor-bearing system is built with Timoshenko beam elements. Critical speeds are respectively calculated with and without the consideration of contact effect, including the changing bearing dynamic coefficients. A test rig of rod fastening rotor-bearing system has been constructed to verify the numerical model results. The results show that the critical speed increases with rod preload and it keeps almost constant when the rod preload reaches a certain value, called preload saturation. The experiments demonstrate that the rod fastening rotor under preload saturation has the similar dynamic characteristics as integral rotor, such as the critical speed and backward whirl with asymmetric support stiffnesses. This kind of rotors which are under preload saturation can be analyzed and designed as an integral one without considering the contact effect. The study gives referential recommendations for analysis and design of a class of composite rotors which contain discs and rods.

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.

scholarly journals Time-Varying Dynamic Analysis of a Helical-Geared Rotor-Bearing System with Three-Dimensional Motion Due to Shaft Deformation

2020 ◽  
Vol 10 (4) ◽  
pp. 1542
Author(s):  
Ying-Chung Chen
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Helix Angle ◽  
Dynamic Responses ◽  
Time Varying ◽  
Contact Ratio ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Shaft Deformation ◽  
Bearing System

The rotordynamics of a helical-geared rotor-bearing system were investigated. A new dynamic model for a helical-geared rotor-bearing system, which takes into account three-dimensional (3-D) motion due to rotating shaft deformation, was proposed. The proposed model considers the time-varying effect, which in other models, is considered constant. The system equations of motion were obtained by applying Lagrange’s equation, and the dynamic responses were computed by the fourth-order Runge–Kutta method. The time-varying dynamic responses of the helix angle, transverse pressure angle, gear pair center distance, and total contact ratio were investigated. The numerical results show that the time-varying effect is an important factor in gear vibration analysis and cannot be neglected when the helical geared rotor-bearing system has a lower stiffness.

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.

Application of Finite Element Method in Time Domain to a Rotor System With Nonlinear Supports

2001 ◽  
Author(s):  
Liguo Wang ◽  
Wenhu Huang ◽  
Chao Hu
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Nonlinear Differential Equations ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Periodic Response ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
The Time Domain ◽  
Bearing System

Abstract A new method for analyzing periodic response of rotor dynamic system with nonlinear supports is presented in this paper. Based on a finite element formulation in the time domain, this method transforms nonlinear differential equations governing the dynamic behavior of rotor-bearing system into a set of nonlinear algebraic equations that can be reduced and calculated by the characteristic set of Wu elimination method. The analytic solution of the nodal displacement has been obtained finally. According to this result the behavior of periodic response is analyzed. The feasibility and advantage of the proposed method are illustrated with an example of flexible Jeffcott rotor-bearing system with nonlinear supports.

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