Dynamic analysis of water-lubricated motorized spindle considering tilting effect of thrust bearing

2016 ◽  
Vol 231 (20) ◽  
pp. 3780-3790 ◽  
Author(s):  
Huihui Feng ◽  
Shuyun Jiang
Keyword(s):  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Large Diameter ◽  
Machining Process ◽  
Motorized Spindle ◽  
Thrust Bearings ◽  
Dynamic Coefficients ◽  
Key Issues ◽  
Dynamic Performances

The dynamic modeling for the rotor with large diameter thrust bearings is one of the key issues in the design and operation of water-lubricated motorized spindle. In the machining process, the spindle not only translates along the x, y, z directions, but also tilts about the x and y axes under the cutting forces. As a result, the tilting effect of the thrust bearing on the dynamic performances of the motorized spindle should be considered. A five degree-of-freedom dynamic model for the spindle is established based on the Newton’s Laws and the principle of Angular Momentum. The translational and tilting dynamic coefficients for both the journal and thrust water-lubricated bearings were obtained by using Reynolds equation. The computed results show that the tilting effect of the thrust bearing on the dynamic performance of the motorized spindle should be considered when a large diameter thrust bearing is employed.

Dynamic Analysis of High-Speed Hybrid Thrust Bearings

2013 ◽  
Vol 365-366 ◽  
pp. 304-308
Author(s):  
Lei Wang
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Orifice Diameter ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Stiffness And Damping

An analysis is conducted and solutions are provided for the dynamic performance of high speed hybrid thrust bearing. By adopting bulk flow theory, the turbulent Reynolds equation is solved numerically with the different orifice diameter and supply pressure. The results show that increasing supply pressure can significantly improve the bearing stiffness and damping, while the orifice diameters make a different effect on the bearing stiffness and damping.

Dynamics of a motorized spindle supported on water-lubricated bearings

2016 ◽  
Vol 231 (3) ◽  
pp. 459-472 ◽  
Author(s):  
Huihui Feng ◽  
Shuyun Jiang
Keyword(s):  
Reynolds Equation ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Motorized Spindle ◽  
Dynamic Coefficients ◽  
Numerical Predictions ◽  
Tilting Angle ◽  
Dynamic Performances ◽  
Experimental Values ◽  
Rotor Dynamic

The purpose of this paper is to investigate the dynamic performances of a motorized spindle supported on water-lubricated bearings. A modified transfer matrix method considering both of the translational and tilting dynamic coefficients of the bearings is established. The turbulent Reynolds equation is adopted and numerically solved by the perturbation method and the finite difference method, and the dynamic characteristics of the water-lubricated journal bearings are obtained; the effects of the eccentricity ratio, tilting angle, and the rotational speed on the dynamic coefficients of the water-lubricated journal bearings are analyzed. The critical speed, the dynamic stiffness of spindle nose, and unbalance response of the motorized spindle are investigated. Finally, a comparative study of rotor dynamic behaviors between the 32- and the eight-coefficient bearing models is conducted. The numerical predictions obtained by the 32-coefficient bearing models correlate well with the experimental values available in the literature.

Effects of wedge curvature on performances of foil thrust bearing and the profile design in compressor system

2020 ◽  
pp. 135065012097552
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Lei Qi ◽  
Lu Gan
Keyword(s):  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Testing System ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Set Up ◽  
Foil Thrust Bearing ◽  
Excellent Stability

Foil thrust bearings have attracted considerable attention in small-sized turbo machines with its excellent stability, high compliance, temperature durability. Geometric structure play an important role on the performance of foil thrust bearings. However, the current research on the structure mainly focuses on the underlying foil type, such as bump foil, protuberant bump. In fact, the foil profile, especially in the convergent region has significant influence. In this paper, foil thrust bearings were classified into convex, slope and concave types according to the profile curvature. A numerical model of six pads foil thrust bearing was established by combining the shell model and Reynolds equation. The static and dynamic performance of thrust bearings with different curvature was calculated. The results showed that the convex convergent possessed higher capacity and was not sensitive to displacement disturbance. A stiffness testing system for thrust foil bearing was set up, and the results verified that the foil with convex wedge had higher stiffness. The experiment also indicated that all the thrust foil bearings had typical damping hysteresis. The axial force of a 10 kW on-board compressor was calculated. Based on the conclusion of this paper, the design scheme of curvature value β = 0.6 and gas thickness h2=15 µm was given in consideration of bearing capacity and machining robustness.

scholarly journals Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Reliable Prediction ◽  
Two Phase ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Run Up ◽  
The Impact

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

Analysis on Dynamic Performance of Hydrodynamic Tilting-Pad Gas Bearings Using Partial Derivative Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Analytical Method ◽  
Gas Turbines ◽  
High Speed ◽  
Dynamic Performance ◽  
Gas Bearings ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Dynamic Performances ◽  
Perturbation Frequency ◽  
San Andres

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020–1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings.

scholarly journals Dynamic Performance of Partially Orifice Porous Aerostatic Thrust Bearing

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 989
Author(s):  
Muhammad Punhal Sahto ◽  
Wei Wang ◽  
Ali Nawaz Sanjrani ◽  
Cheng Xu Xu Hao ◽  
Sadiq Ali Shah
Keyword(s):  
Thrust Bearing ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Research Work ◽  
Analysis Model ◽  
Thrust Bearings ◽  
Damping Characteristics ◽  
Fluent Software ◽  
Perturbation Frequency ◽  
The Impact

The aerostatic thrust bearing’s performance under vibration brings certain changes in stiffness and stability, especially in the range of 100 to 10,000 Hz, and it is accompanied by significant increase in fluctuations due to the changes in frequency, and the size of the gas film damping. In this research work, an analysis is carried out to evaluate the impact of throttling characteristics of small size orifice on stiffness and stability optimization of aerostatic thrust bearings. There are two types of thrust bearing orifices such as: partial porous multiple orifice and porous thrust bearings and their effects on variations in damping and dynamic stiffness are evaluated. A simulation based analysis is carried out with the help of the perturbation analysis model of an aerostatic thrust bearing simulation by using FLUENT software (CFD). Therefore, two models of aerostatic thrust bearings—one with the porous and other with partial porous orifice are developed—are simulated to evaluate the effects of perturbation frequencies on the damping and dynamic stiffness. The results reveal a decrease in the amplitude of dynamics capacity with an increase in its frequency, as well as a decrease in the damping of partial porous aerostatic thrust bearings with an increase in the number of orifices. It also reveals an increase in the radius of an orifice with an increment of damping of bearing at the same perturbation frequency and, with an increase in orifice height, a corresponding decrease in the damping characteristics of bearings and in the dynamic stiffness and coefficient of damping of bearing film in the frequency range less than 100 Hz.

A semianalytical method for studying the performances of aerostatic thrust bearing

2018 ◽  
Vol 233 (4) ◽  
pp. 628-637
Author(s):  
Jianbo Zhang ◽  
Chunxiao Jiao ◽  
Donglin Zou ◽  
Na Ta ◽  
Zhushi Rao
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Separation Of Variables ◽  
Orifice Diameter ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Semianalytical Method

The solution of Reynolds equation and computational fluid dynamics are widely employed for the lubrication performance analysis of aerostatic thrust bearing. However, the solution of Reynolds equation may be inaccurate and cannot present detailed performance near orifice, while computational fluid dynamics method has low computational efficiency with time consumption in mesh generation and solving Navier–Stokes equations. In order to overcome the drawbacks of Reynolds equation and computational fluid dynamics, based on the method of separation of variables, a semianalytical method is developed for describing the characteristics of aerostatic bearings available. The method of separation of variables considering the initial and viscous effect is more accurate than the Reynolds equation and can present detailed performance near orifice in the aerostatic thrust bearings, while method of separation of variables has great computational efficiency compared to computational fluid dynamics. Meanwhile, the pressure distribution calculated by method of separation of variables is compared to the published experimental data and the results obtained by computational fluid dynamics. The comparative results indicate validity of the method. Furthermore, the influences of flow and geometry parameters, such as supply pressure, orifice diameter, film thickness, and bearing radius, on the characteristics of aerostatic thrust bearings with single orifice are studied. The results show that there exists pressure depression phenomenon near orifice. The depression phenomenon is strengthened with increase of film thickness and supply pressure and decrease of orifice diameter and bearing radius, while the maximum speed increases with strengthening of pressure depression due to decrease of minimum local pressure near orifice. Moreover, the bearing capacity increases with increase of supply pressure, orifice diameter, and bearing radius and decreases with increase of film thickness, while mass flow rate increases with supply pressure, orifice diameter, and film thickness and it is not sensitive to bearing radius.

Dynamic Coefficients of the Coupled Journal and Thrust Bearings Considering Five Degrees of Freedom for a General Rotor-Bearing System

2007 ◽  
Author(s):  
G. H. Jang ◽  
S. H. Lee ◽  
H. W. Kim
Keyword(s):  
Degrees Of Freedom ◽  
Thrust Bearing ◽  
Numerical Differentiation ◽  
Reynolds Equations ◽  
Thrust Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Translational Displacement ◽  
Finite Displacements ◽  
Perturbation Equations

This paper proposes a method to calculate the stiffness and the damping coefficients of the coupled journal and thrust bearings considering tilting motion. The Reynolds equations and their perturbation equations are derived by linearization of bearing reaction with respect to the general five degrees of freedom, i.e. the tilting displacement and angular velocity as well as the translational displacement and velocity. Reynolds equations and their perturbation equations are transformed to the finite element equations by considering the continuity of pressure and flow at the interface between the journal and the thrust bearings. It also includes the Reynolds boundary condition in the numerical analysis to simulate the cavitation phenomena. The stiffness and the damping coefficients of the proposed method are compared with those of the numerical differentiation of the loads with respect to finite displacements and velocities of bearing center. It shows that the proposed method can calculate the dynamic coefficients of a coupled journal and thrust bearing more accurately and efficiently than the differentiation method.

Rotor-dynamic performance of porous hydrostatic thrust bearing operating under magnetic field

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Vivek Kumar ◽  
Vatsalkumar Ashokkumar Shah ◽  
Simran Jeet Singh ◽  
Kuldeep Narwat ◽  
Satish C. Sharma
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Steady State ◽  
Magnetic Fluid ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Performance Indices ◽  
Content Type ◽  
Rotor Dynamic

Purpose The porous bearings are commonly used in slider thrust bearings owing to their self-lubricating properties and cost effectiveness as compared to conventional hydrodynamic bearings. The purpose of this paper is to numerically investigate usefulness of porous layer in hydrostatic thrust bearing operating with magnetic fluid. The effect of magnetic field and permeability has been analysed on steady-state (film pressure, film reaction and lubricant flow rate) and rotor-dynamic (stiffness and damping) parameters of bearing. Design/methodology/approach Finite element approach is used to obtain numerical solution of flow governing equations (Magneto-hydrodynamics Reynolds equation, Darcy law and capillary equation) for computing abovementioned performance indices. Finite element method formulation converts elliptical Reynolds equation into set of algebraic equation that are solved using Gauss–Seidel method. Findings It has been reported that porosity has limited but adverse effects on performance parameters of bearing. The adverse effects of porosity can be minimized by using a circular pocket for achieving better steady-state response and an annular/elliptical pocket, for having better rotor-dynamic response. The use of magnetic fluid is found to be substantially enhancing the fluid film reaction (53%) and damping parameters (55%). Practical implications The present work recommends use of circular pocket for achieving better steady-state performance indices. However, annular and elliptical pockets should be preferred, when design criteria for the bearing are better rotor-dynamic performance. Originality/value This study deals with influence of magnetic fluid, porosity and pocket shape on rotor-dynamic performance of externally pressurized thrust bearing. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0289/

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