scholarly journals Dynamics of a rotor system coupled with water-lubricated rubber bearings

2018 ◽  
Vol 232 (23) ◽  
pp. 4263-4277 ◽  
Author(s):  
YF Shi ◽  
M Li ◽  
GH Zhu ◽  
Y Yu
Keyword(s):  
Elastic Deformation ◽  
Dynamic Characteristics ◽  
Hydrodynamic Lubrication ◽  
Dynamic Performance ◽  
Elastohydrodynamic Lubrication ◽  
Rotor System ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Mass Unbalance ◽  
Rubber Bearings

Dynamic behaviour is significantly important in the design of large rotor systems supported on water-lubricated rubber bearings. In this study, the mathematical model of elastohydrodynamic lubrication of the bearing is established based on the theory of hydrodynamic lubrication after considering the elastic deformation of rubber, and the dynamic characteristics of water-lubricated rubber bearings are analysed under small perturbation conditions according to the load increment method and the finite difference method. Next, the differential equation of rotor systems coupled with the water-lubricated rubber bearing is deduced using Lagrange’s approach, and its critical speeds, stability, and unbalanced responses are analysed in detail. The numerical results show that several parameters, such as the eccentricity, length–diameter ratio, and clearance of bearing and the rotating speed of the rotor, have a great impact on the dynamic performance of water-lubricated rubber bearings, and this influence cannot be ignored, especially in the case of large eccentricity ratios. The dynamic characteristics of rotor systems guided by water-lubricated rubber bearings reveal that the critical speeds are much lower than the ones under the rigid supports because of the elastic deformation, and they also indicate that the rotor system supported on water-lubricated rubber bearings has a weaker stability. In addition, the steady-state responses of the rotor system are analysed when the mass unbalance of the propeller exists, and the effect of the thickness of the rubber liner is also considered.

Non-Linear Lubricant Behavior in Concentrated Contacts

2001 ◽  
Author(s):  
Andras Z. Szeri
Keyword(s):  
Elastic Deformation ◽  
Hydrodynamic Lubrication ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Contact ◽  
Material Behavior ◽  
Solid Surfaces ◽  
Hydrodynamic Theory ◽  
Shear Rates ◽  
Liquid Lubricant ◽  
Temperature And Pressure

Abstract Elastohydrodynamic lubrication (EHL) is the name given to hydrodynamic lubrication when it is applied to solid surfaces of low geometric conformity (counterformal contacts) that are capable of, and are subject to, elastic deformation. In bearings relying on EHL principles, the residence time of the fluid is less than 1 ms, the pressures are up to 4 GP, the film is thin, down to 0.1 μm, and shear rates are up to 108 s−1 — under such conditions lubricants exhibit material behavior that is distinctly different from their behavior in bulk at normal temperature and pressure. In fact, without taking into account the viscosity-pressure characteristics of the liquid lubricant and the elastic deformation of the bounding solids, hydrodynamic theory is unable to explain the existence of continuous lubricant films in highly loaded gears and rolling contact bearings.

Effect of flight/structural parameters and operating conditions on dynamic behavior of a squeeze-film damped rotor system during diving–climbing maneuver

2020 ◽  
pp. 095441002094261
Author(s):  
Xi Chen ◽  
Xiaohua Gan ◽  
Guangming Ren
Keyword(s):  
Dynamic Characteristics ◽  
Rotor System ◽  
Elastic Support ◽  
Outer Ring ◽  
Squeeze Film ◽  
Inertial Forces ◽  
Oil Film ◽  
Maneuvering Flight ◽  
Mass Unbalance ◽  
Static Eccentricity

During aircraft maneuvering flights, engine's rotor-bearing systems are subjected to parametric excitations and additional inertial forces, which may cause severe vibration and abnormal operation. Based on Lagrange's principle combined with finite element modeling, the differential equations of motion for a squeeze film damped rotor-bearing system mounted on an aircraft in maneuvering flight are derived. Using Newmark–Hilber–Hughes–Taylor integration method, dynamic characteristics of the nonlinear rotor system under maneuvering flight are investigated. The factors are considered, involving mass unbalance, oil–film force, gravity, parametric excitations and additional inertial forces, and instantaneous static eccentricity of journal induced by maneuvering loads. The effects of forward velocity, radius of curvature, rotating speed, mass unbalance, oil–film clearance, and elastic support stiffness on transient responses of rotor system are discussed during diving–climbing maneuver. The results indicate that when the aircraft performs a diving–climbing maneuver in the vertical plane, the journal deviates from the center of oil–film outer ring, and the excursion direction of whirl orbit is determined by centrifugal acceleration and additional gyroscopic moment. The journal whirls asynchronously around the instantaneous static eccentricity and its magnitude is related to the maneuvering loads and the supporting stiffness. Increasing forward velocity or decreasing pitching radius, the rotor vibration will enter earlier into or withdraw later from the relatively large eccentricity. Rotating near critical speeds or excessive mass unbalances should be prevented during maneuvering flights. For large maneuver, the oil–film radial clearance needs to be enlarged properly to avoid hard contact between journal and outer ring. In addition, the stiffness of elastic support needs to be appropriately determined for damping performance. Overall, it provides a flexible approach with good expandability to predict dynamic characteristics of on-board squeeze-film damped rotor system during maneuvering flights in the design process.

Vibration Analysis of Multi-Disk Multi-Profiled Shaft-Rotor Systems

2014 ◽  
Vol 612 ◽  
pp. 17-22 ◽  
Author(s):  
P.M.G. Bashir Asdaque ◽  
R.K. Behera ◽  
Jakeer Hussain Shaik
Keyword(s):  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Shear Force ◽  
Bending Moment ◽  
Rotor System ◽  
Step Response ◽  
Rotor Systems

Cantilevered shaft-rotor systems consisting of multi disks and multi profiled shafts are considered. In this paper the procedures for the determination of the deflection, slope, shear force and bending moment at the extremities of the shaft are employed. Critical speeds or whirling frequency conditions are computed using transfer matrix method (TMM). For particular shaft-lengths, rotating speeds and shaft-profiles, the response of the system is determined for the establishment of the dynamic characteristics. A built-in shaft-rotor system consisting of two disks and two different profiled shafts is investigated for illustration purposes. Step response of the multi profiled shaft-rotor system is also found out.

Transient Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions During Start-Up

2018 ◽  
Author(s):  
Xi Chen ◽  
Mingfu Liao
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Axial Rotation ◽  
Rotor System ◽  
Transient Characteristics ◽  
Rotor Systems ◽  
Rotating Speed ◽  
Mass Unbalance ◽  
Start Up ◽  
Lateral Rotation

Using Newmark-Hilber-Hughes-Taylor (Newmark-HHT) integration method, transient characteristics of the dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions during start-up are illustrated. Rotary inertia, gyroscopic moment, shear deformation, mass unbalance and deterministic base motions are considered. Due to variable angular velocities, additional stiffness matrices associated with rotating angular accelerations are also introduced in the equations of motion. The effects of base motion parameters on the dynamic characteristics of the dual-rotor system are discussed, including base axial rotation, lateral rotations, and harmonic translations. The results show that base axial rotation significantly changes the transient critical speeds and resonant amplitudes of the dual-rotor system. In the case of base lateral rotation, the center of the orbit is no longer on the bearing centerline, but with a dynamic offset. When increasing the rotating speeds, the dynamic offset becomes greater. Unlike base lateral rotation, base harmonic translation doesn’t result in dynamic offset, but it amplifies response amplitudes over the entire range of rotating speed. In conclusion, it provides a flexible approach with high efficiency and good expandability to predict transient responses of dual-rotor systems under base motions, and to prevent dual-rotor systems against potential excessive vibration in the design phase.

On the Coupling of Foil Bearing Supported Rotors: Part 1 — Analysis

2007 ◽  
Author(s):  
Hooshang Heshmat ◽  
James F. Walton ◽  
Crystal A. Heshmat
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Ball Bearing ◽  
Dynamic Performance ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Flexible Rotors ◽  
Coupling Dynamic ◽  
Bearing System

The expanded application of high-speed rotor systems operating on compliant foil bearings will be greatly enhanced with the ability to adequately couple multiple shaft systems with differing bearing systems and dynamic performance. In this paper the results of an analytical tradeoff study assessing coupling dynamic characteristics and their impact on coupled rotor-bearing system dynamics are presented. This analysis effort was completed in an effort to establish the form of characteristics needed to couple foil bearing supported rotors to ball bearing supported rotors, other foil bearing supported rotors as well as coupling rigid and flexible rotors both supported on foil bearings. The conclusions from this study indicate that with appropriate coupling design, a wide array of foil bearing supported rotor systems may be successfully coupled.

scholarly journals Reliability Sensitivity Analysis of Bearing-Rotor System Based on the Dynamic Coefficient

2011 ◽  
Vol 2-3 ◽  
pp. 1004-1007
Author(s):  
Qun Chao Zhao ◽  
Yi Min Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Hydrodynamic Lubrication ◽  
Dynamic Performance ◽  
Rotor System ◽  
Engineering Practice ◽  
Sliding Bearing ◽  
Overall Design ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Selection Of

According to components reliability sensitivity theory methods, looking upon the dynamic characteristics of hydrodynamic lubrication sliding bearing as the target for study, doing some reliability sensitivity analysis for the bearing-rotor system instability issues, numerical simulation results are given though analyzing. The outcome of the dynamic performance index is proposed based on the sliding bearing selection method for engineering practice to the selection of the radial journal bearing and provides a theoretical basis for overall design of shafting.

Constrained Optimization of a Rotor-Bearing System Based on an Evolutionary Algorithm

2012 ◽  
Author(s):  
Donghua Wang ◽  
Wanyou Li ◽  
Zhigang Liu ◽  
Zhansheng Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Optimal Solution ◽  
Population Based ◽  
Rotor System ◽  
System Configuration ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Elite Strategy ◽  
Practical Design ◽  
Bearing System

How to modify a rotor system configuration to adjust some critical speeds distribution for safety and achieve the least change of system configuration at the same time, is a focus in the rotordynamics field. An existing method is introduced and its disadvantages are analyzed. To overcome these difficulties smoothly, a more robust mathematical model for optimal design of critical speeds distribution is presented, with more constraints considered. And a Population-based Evolutionary Algorithm with Elite Strategy (PEAES) is developed to solve the proposed optimization model. The results of study on a rotor system in different cases show that the proposed method can find the optimal solution and may be applicable in the practical design process of rotor systems.

Squeeze and Entraining Motion in Nonconformal Line Contacts. Part I—Hydrodynamic Lubrication

1989 ◽  
Vol 111 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Rong-Tsong Lee ◽  
B. J. Hamrock
Keyword(s):  
Hydrodynamic Lubrication ◽  
Dynamic Performance ◽  
Elastohydrodynamic Lubrication ◽  
Constant Load ◽  
Initial Guess ◽  
Maximum Pressure ◽  
Performance Parameters ◽  
Velocity Parameter ◽  
Dimensionless Velocity ◽  
Line Contacts

An analytical solution to the problem of combined entraining and normal squeeze motion in nonconformal line contacts hydrodynamically lubricated with an isoviscous, incompressible lubricant has been obtained without any limitations on dimensionless load, dimensionless entraining velocity, and dimensionless velocity parameter. The dimensionless load and entraining velocity are fixed for a complete range of operating parameters for both normal approach and separation. Results show that the lubrication of the outlet boundary and the location of the maximum pressure move upstream into the inlet region as the central film thickness decreases or the dimensionless velocity parameter increases from negative (normal approach) to positive (normal separation). All the dynamic performance parameters relating to the steady-state bearing performance parameters have been found to be functions of only the dimensionless velocity parameter with constant load and entraining velocity. The dimensionless velocity parameter significantly influenced those dynamic performance parameters. The results of this study will be used as the initial guess for the elastohydrodynamic lubrication of nonconformal line contacts.

Stability and Damped Critical Speeds of Rotor-Bearing Systems

1975 ◽  
Vol 97 (4) ◽  
pp. 1325-1332 ◽  
Author(s):  
P. N. Bansal ◽  
R. G. Kirk
Keyword(s):  
Rotor System ◽  
System Stability ◽  
Mode Shapes ◽  
Computational Time ◽  
System Matrix ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Analytical Technique ◽  
Rotor Bearing ◽  
Response Amplification

This paper describes an analytical technique to calculate the damped critical speeds and the instability threshold speed of multimass rotor-bearing systems. Necessary equations are developed to study the effect of bearing as well as bearing support flexibility and damping on the system stability, thereby enhancing the current state of the art. Included in the analysis are the effects of linearized disk gyroscopic moments, shear deformation, and speed dependent bearing characteristics. The method of solution is based on the Transfer Matrix approach and uses complex variable notation to develop the overall system matrix. Mutter’s quadratic interpolation technique is employed to extract the complex eigenvalues of the rotor system and the corresponding mode shapes are found by back substitution. The analysis has been programmed for digital computer solution. Computational time is saved by eliminating from the polynomial the complex conjugates of the roots already found. Numerical overflow/underflow is controlled via scale factors. In addition to calculating the damped critical speeds, the computer program also provides information about the undamped frequencies, peak response frequencies, response amplification factors, and logarithmic decrements of the system. The accuracy of the predictions of the program has been verified and is shown to be acceptable for typical rotor systems. The results of an extensive investigation of an intershaft journal bearing instability in a dual rotor system are summarized. The stability map for this system is presented and clearly indicates the effect of rotor radial misalignment on system stability.

scholarly journals The Gyroscopic Effect on Dynamic Characteristics of Dual- Disk Rotor System

2011 ◽  
Vol 2-3 ◽  
pp. 942-947
Author(s):  
Mei Ling Wang ◽  
Qing Kai Han
Keyword(s):  
Dynamic Characteristics ◽  
Rotor System ◽  
Simplified Model ◽  
Gyroscopic Effect ◽  
Moments Of Inertia ◽  
Critical Speeds ◽  
Asymmetric Rotor ◽  
Gyroscopic Effects

Although the gyroscopic effect on rotor system has been noticed for decades, it is often underestimated and even ignored in the simplified model; moreover the comparing analyses of it on dynamics of rotor system with distributed masses are rarely performed. In this paper, a model of dual-disk rotor system with 8 degree-of-freedoms is developed to show the gyroscopic effects, especially on asymmetric rotor system, in which the polar and transversal moments of inertia of the disks are incorporated. The critical speeds and unbalance responses of such a rotor system are simulated numerically and compared respectively in 4 different asymmetric cases, including 2 cases of position asymmetry and another 2 cases of support stiffness asymmetry. The analysis results clearly show that the gyroscopic effect has obvious influence on the critical speeds and unbalance responses under different asymmetry conditions.

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