Tilting Pad Bearing Pivot Friction and Design Effects on Thermal Bow-Induced Rotor Vibration

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Dongil Shin ◽  
Alan B. Palazzolo
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Design Parameters ◽  
Flexible Beam ◽  
Thermally Induced ◽  
Tilting Pad ◽  
Speed Range ◽  
Transient Simulations ◽  
Nonlinear Transient ◽  
Tilting Pad Journal Bearing

Abstract The Morton effect (ME) is a thermally induced vibration problem observed in a rotor supported by hydrodynamic bearings. The journal’s synchronous orbiting induces nonuniform viscous heating on its circumference, and the ensuing thermal bow often causes unacceptable vibration levels in the rotor. This paper investigates the influence of the tilting pad journal bearing (TPJB)’s pivot design on the severity and instability speed range of ME vibration. Simulations are conducted with two different types of pivots: cylindrical (CYL) and spherical (SPH), which produce different pad degrees-of-freedom and nonlinear pivot stiffness due to their geometries. The friction between pad and pivot, which only exists with the spherical pivot, is modeled, and its impact on the ME is evaluated. The example rotor model, as obtained from the literature, is single overhung, with experimentally measured excessive vibration and large journal temperature differentials, near 8000 rpm. The bearing and journal are modeled with three-dimensional (3D) finite elements, and the shaft with flexible beam elements for ME simulation. Nonlinear transient simulations are carried out for a wide operating speed range with varying pivot design parameters. Simulation results indicate that the predicted ME instability is sensitive to the pivot shape, pivot flexibility, and pad-pivot friction.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

scholarly journals A computational fluid dynamics investigation of the segmented integral squeeze film damper

2019 ◽  
Vol 254 ◽  
pp. 08005 ◽  
Author(s):  
Petr Ferfecki ◽  
Jaroslav Zapoměl ◽  
Marek Gebauer ◽  
Václav Polreich ◽  
Jiří Křenek
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Three Dimensional ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Ansys Cfx ◽  
Squeeze Film Dampers ◽  
Tilting Pad ◽  
Vibration Attenuation ◽  
Tilting Pad Journal Bearing

Rotor vibration attenuation is achieved with damping devices which work on different, often mutually coupled, physical principles. Squeeze film dampers are damping devices that have been widely used in rotordynamic applications. A new concept of a 5-segmented integral squeeze film damper, in which a flexure pivot tilting pad journal bearing is integrated, was investigated. The damper is studied for the eccentric position between the outer and inner ring of the squeeze film land. The ANSYS CFX software was used for solving the pressure and velocity distribution. The development of the complex three-dimensional computational fluid dynamics model of the squeeze film damper, learning more about the effect of the forces in the damper, and the knowledge about the behaviour of the flow are the principal contributions of this article.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Zhiyong Yan ◽  
Yi Lu ◽  
Tiesheng Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Local Coordinate System ◽  
Dynamical Behavior ◽  
Complete Model ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Generalized Force ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part II: Dynamic Response

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Jongin Yang ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Dynamic Response ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Static Response ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Part II presents a novel approach for predicting dynamic coefficients for a tilting pad journal bearing (TPJB) using computational fluid dynamics (CFD) and finite element method (FEM), including fully coupled elastic deflection, heat transfer, and fluid dynamics. Part I presented a similarly novel, high fidelity approach for TPJB static response prediction which is a prerequisite for the dynamic characteristic determination. The static response establishes the equilibrium operating point values for eccentricity, attitude angle, deflections, temperatures, pressures, etc. The stiffness and damping coefficients are obtained by perturbing the pad and journal motions about this operating point to determine changes in forces and moments. The stiffness and damping coefficients are presented in “synchronously reduced form” as required by American Petroleum Institute (API) vibration standards. Similar to Part I, an advanced three-dimensional thermal—Reynolds equation code validates the CFD code for the special case when flow Between Pad (BP) regions is ignored, and the CFD and Reynolds pad boundary conditions are made identical. The results show excellent agreement for this validation case. Similar to the static response case, the dynamic characteristics from the Reynolds model show large discrepancies compared with the CFD results, depending on the Reynolds mixing coefficient (MC). The discrepancies are a concern given the key role that stiffness and damping coefficients serve instability and response predictions in rotordynamics software. The uncertainty of the MC and its significant influence on static and dynamic response predictions emphasizes a need to utilize the CFD approach for TPJB simulation in critical machines.

Multibody Analysis and Control of a Full-Wrist Exoskeleton for Tremor Alleviation

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Jiamin Wang ◽  
Oumar R. Barry
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Wrist Joint ◽  
Three Dimensional ◽  
Design Parameters ◽  
Light Power ◽  
Multibody Modeling ◽  
Flexion Extension ◽  
Reliable Performance ◽  
Rotational Joint

Abstract Uncontrollable shaking in the human wrist, caused by pathological tremor, can significantly undermine the power and accuracy in object manipulation. In this paper, the design of a tremor alleviating wrist exoskeleton (TAWE) is introduced. Unlike the works in the literature that only consider the flexion/extension (FE) motion, in this paper, we model the wrist joint as a constrained three-dimensional (3D) rotational joint accounting for the coupled FE and radial/ulnar deviation (RUD) motions. Hence TAWE, which features a six degrees-of-freedom (DOF) rigid linkage structure, aims to accurately monitor, suppress tremors, and provide light-power augmentation in both FE and RUD wrist motions. The presented study focuses on providing a fundamental understanding of the feasibility of TAWE through theoretical analyses. The analytical multibody modeling of the forearm–TAWE assembly provides insight into the necessary conditions for control, which indicates that reliable control conditions in the desired workspace can be acquired by tuning the design parameters. Nonlinear regressions are then implemented to identify the information that is crucial to the controller design from the unknown wrist kinematics. The proposed analytical model is validated numerically with V-REP and the result shows good agreement. Simulations also demonstrate the reliable performance of TAWE under controllers designed for tremor suppression and movement assistance.

Three-Dimensional Dynamic Model of TEHD Tilting-Pad Journal Bearing—Part I: Theoretical Modeling

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Junho Suh ◽  
Alan Palazzolo
Keyword(s):  
Heat Conduction ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Tilting Pad ◽  
Fluid Film Thickness ◽  
Three Dimensional Finite Element ◽  
Tilting Pad Journal Bearing

This paper is focused on a new modeling method of three-dimensional (3D) thermo-elasto-hydro-dynamic (TEHD) cylindrical pivot tilting-pad journal bearing (TPJB). Varying viscosity Reynolds equation and 3D energy equation are coupled via lubricant temperature and viscosity relationship. Three-dimensional finite element method (FEM) is adopted for the analysis of: (1) heat conduction in shaft and bearing pad, (2) thermal deformation of shaft and pad, (3) flexible bearing pad dynamic behavior, and (4) heat conduction, convection, and viscous shearing in thin lubricant film. For the computational efficiency, modal coordinate transformation is utilized in the flexible pad dynamic model, and pad dynamic behavior is represented only by means of modal coordinate. Fluid film thickness is calculated by a newly developed node based method, where pad arbitrary thermal and elastic deformation and journal thermal expansion are taken into account simultaneously. The main goal of this research is to provide more accurate numerical TPJB model than developed before so that the designers of rotating machinery are able to understand the bearing dynamic behavior and avoid unpredicted problem by selection of physical parameters.

Improvement and Analysis for a Gaseous Cavitation Model Applied in a Tilting-Pad Journal Bearing

2019 ◽  
Author(s):  
Aoshuang Ding ◽  
Xuesong Li ◽  
Yuhong Li
Keyword(s):  
Journal Bearing ◽  
Three Dimensional ◽  
Cavitation Model ◽  
Local Pressure ◽  
Cavitation Process ◽  
Air Volume ◽  
Tilting Pad ◽  
Sst Model ◽  
Tilting Pad Journal Bearing ◽  
Good Agreement

Abstract Considering the gaseous cavitation rate is influenced by local pressure, a transient gaseous cavitation model is developed from an equilibrium gaseous cavitation model in consideration of transient gaseous cavitation theories and the Bunsen solubility. With the shear stress transport (SST) model with low-Re correction and air backflow from the bearing outlets, the transient gaseous cavitation model is applied to the three-dimensional simulations of an entire tilting-pad journal bearing at 3000 rpm speed and under 180 kN load. The simulated bearing pressure and load are in good agreement with the experimental data, indicating that the transient gaseous cavitation model performs well in the bearing simulations. Based on the comparisons of the simulated air and dissolved air distributions between the transient and equilibrium gaseous cavitation models, the simulated cavitation process of the transient gaseous cavitation is proved to be not in equilibrium and mass transfer occur between the backflow air and oil. The purpose of building the transient gaseous cavitation model is thus met. Analyses of the air distributions indicate that high cavitation rates and low dissolution rates makes air volume a major part of the total air volume and close to the physical gaseous cavitation process.

Three-Dimensional Dynamic Model of TEHD Tilting-Pad Journal Bearing—Part II: Parametric Studies

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Junho Suh ◽  
Alan Palazzolo
Keyword(s):  
Dynamic Analysis ◽  
Numerical Integration ◽  
Equilibrium Condition ◽  
Journal Bearing ◽  
Fe Model ◽  
Time Step ◽  
Transient Dynamic ◽  
Tilting Pad ◽  
Nonlinear Transient ◽  
Tilting Pad Journal Bearing

This paper presents a new analysis method for a thermo-elasto-hydro-dynamic (TEHD) tilting pad journal bearing (TPJB) system to reach a static equilibrium condition adopting nonlinear transient dynamic solver, whereas earlier studies have used iteration schemes such as Newton–Raphson method. The theoretical TPJB model discussed in Part I of this research is combined into a newly developed algorithm to perform a bearing dynamic analysis and present dynamic coefficients. In the nonlinear transient dynamic solver, physical and modal coordinates coexist for computational efficiency, and transformation between modal and physical coordinate is performed at each numerical integration time step. Variable time step Runge–Kutta numerical integration scheme is adopted for a reliable and fast calculation. Nonlinear time transient dynamic analysis and steady thermal analysis are combined to find the static equilibrium condition of the TPJB system, where the singular matrix issue of flexible pad finite element (FE) model is resolved. The flexible pad TPJB model was verified by comparison with other numerical results. Simulation results corresponding with the theoretical model explained in Part I are presented and discussed. It explains how the TPJB dynamic behavior is influenced by a number of eigenvector of flexible pad FE model and pad thickness. Preload change under fluid and thermal load is examined.

Mechanical and Thermal Deformation Analysis of a Large Polymer Lined Tilting Pad Journal Bearing

2021 ◽  
Author(s):  
Michael Stottrop ◽  
Beate Bender
Keyword(s):  
Deformation Analysis ◽  
Maximum Pressure ◽  
Deformation Characteristics ◽  
Thermally Induced ◽  
Tilting Pad ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings ◽  
Insulating Properties

Abstract An increase of specific load in large tilting pad journal bearings (TPJB) leads to major mechanically and thermally induced deformation of the pads and limits the load carrying capacity. In this paper, we present a theoretical approach to determine deformation of a TPJB with PEEK (Polyetheretherketone) polymer lined pads by means of a thermo-elasto-hydrodynamic model. The objective of this investigation is a quantitative analysis of the deformation characteristics of a five-pad TPJB with a nominal diameter of 500 mm. Mechanical and thermal deformations are simulated for both the steel backing and the polymer lining. The deformation characteristics calculated with the numerical model are compared to simulation results of an experimentally validated model with a white-metal lining. The results indicate an improvement in bearing characteristics with the PEEK lining, as maximum pressure decreases and minimum film thickness increases. Due to the insulating properties of the PEEK layer, thermally induced pad deformation is reduced significantly.

Tilting Pad Journal Bearings—A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in.) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency-dependent stiffness and damping. Measured hot-bearing clearances are approximately 30% smaller than measured cold-bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

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