Unbalance Response of Rotors Considering the Distributed Bearing Stiffness and Damping

1994 ◽  
Author(s):  
A. S. Sekhar ◽  
B. S. Prabhu
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Journal Bearings ◽  
Principle Of Virtual Work ◽  
Unbalance Response ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Element Technique ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Usually while modelling rotor-bearing systems the bearings are treated as point supports. In the present paper, using the finite element technique, the unbalance response of rotors is studied by considering distributed bearing stiffness and damping. The bearing stiffness and damping terms are derived by the principle of virtual work. Unbalance responses of rotors with bearing distributed effects are compared with the model using point supports and for different supports Viz., cylindrical journal bearings, tilting pad journal bearings, offset and three lobe journal bearings.

Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects due to Pivot Flexibility

2006 ◽  
Vol 129 (3) ◽  
pp. 865-869 ◽  
Author(s):  
Waldemar Dmochowski
Keyword(s):  
High Speed ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Properties ◽  
Frequency Effects ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Tilting-pad journal bearings (TPJBs) dominate as rotor supports in high-speed rotating machinery. The paper analyzes frequency effects on the TPJB’s stiffness and damping characteristics based on experimental and theoretical investigations. The experimental investigation has been carried out on a five pad tilting-pad journal bearing of 98mm in diameter. Time domain and multifrequency excitation has been used to evaluate the dynamic coefficients. The calculated results have been obtained from a three-dimensional computer model of TPJB, which accounts for thermal effects, turbulent oil flow, and elastic effects, including that of pad flexibility. The analyzes of the TPJB’s stiffness and damping properties showed that the frequency effects on the bearing dynamic properties depend on the operating conditions and bearing design. It has been concluded that the pad inertia and pivot flexibility are behind the variations of the stiffness and damping properties with frequency of excitation.

Dynamic Identification of 280mm Diameter Tilting Pad Journal Bearings: Test Results and Measurement Uncertainties Assessment of Different Designs

2020 ◽  
Author(s):  
Riccardo Ferraro ◽  
Alice Innocenti ◽  
Mirko Libraschi ◽  
Michele Barsanti ◽  
Enrico Ciulli ◽  
...  
Keyword(s):  
High Performance ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Dynamic Identification ◽  
Damping Characteristics ◽  
Flexible Rotors ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Abstract Tilting pad journal bearings (TPJBs) are crucial elements in turbomachinery applications providing stiffness and damping characteristics that determine rotor system dynamic behavior. Hence, a correct design and an accurate dynamic properties prediction is fundamental for the successful industrial operation of rotating machinery. Current design trends in turbomachinery aiming at higher efficiency and power through weight optimization and higher operating speeds determine the development of large flexible rotors that are particularly important from the rotordynamic standpoint. The dynamic feasibility of this type of machine relies on bearing stiffness and damping characteristics that must be predicted with a certain level of confidence in order to increase the accuracy of the expected rotordynamic behaviour and avoid unpredicted vibration issues when rotors are operated. Furthermore, large centrifugal compressors commonly used in Liquified Natural Gas (LNG) applications make the bearings operate at very high peripheral speed where the transition from laminar to turbulent regime occurs, increasing the necessity of predictions accuracy. In this paper a test campaign on different large TPJB solutions operating in turbulent lubrication regime has been performed on a dedicated test rig designed for investigations on large size high-performance oil bearings. In the present work both static performance and dynamic identification of the tested TPJB solutions are presented and compared to numerical model predictions. The results of an uncertainty quantification, performed to validate the experimental results, are also shown.

Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects Due to Pivot Flexibility

2006 ◽  
Author(s):  
Waldemar Dmochowski
Keyword(s):  
High Speed ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Properties ◽  
Frequency Effects ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Tilting-pad journal bearings (TPJB) dominate as rotor supports in high speed rotating machinery. The paper analyzes frequency effects on the TPJB’s stiffness and damping characteristics based on experimental and theoretical investigations. The experimental investigation has been carried out on a five pad tilting-pad journal bearing of 98 mm in diameter. Time domain and multifrequency excitation has been used to evaluate the dynamic coefficients. The calculated results have been obtained from a three-dimensional computer model of TPJB, which accounts for thermal effects, turbulent oil flow, and elastic effects, including that of pad flexibility. The analyzes of the TPJB’s stiffness and damping properties showed that the frequency effects on the bearing dynamic properties depend on the operating conditions and bearing design. It has been concluded that the pad inertia and pivot flexibility are behind the variations of the stiffness and damping properties with frequency of excitation.

On the Frequency Dependency of Tilting-Pad Journal Bearings

2019 ◽  
Author(s):  
Laurence F. Wagner
Keyword(s):  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Investigations ◽  
Single Degree Of Freedom ◽  
Frequency Dependency ◽  
Exciting Frequency ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Rotational Damping ◽  
Tilting Pad Journal Bearings

Abstract Controversy regarding the dynamic modeling of tilting-pad journal bearings (TPJB) has existed for years, with the question of the effective stiffness and damping properties, and the requirement for consideration of frequency dependency, being of great concern. There is a partial disconnect between the results of theoretical and many experimental investigations. This paper attempts to examine this issue in more of a macro sense; broadening the scope of the geometric and operating domains, and in turn expanding an understanding of related frequency effects. The investigation hinges on a single-pad, single degree-of-freedom (DOF) model that represents various geometries and operating conditions for a full bearing. The results clearly show that the dynamic coefficients must be dependent upon the “exciting” frequency, and that the dependency is primarily associated with the pad rotational damping.

The Subsynchronous Dynamic Behavior of Tilting-Pad Journal Bearings

1992 ◽  
Vol 114 (1) ◽  
pp. 167-173 ◽  
Author(s):  
M. F. White ◽  
S. H. Chan
Keyword(s):  
High Speed ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Frequency Effect ◽  
Tilting Pad ◽  
Dimensional Finite Element ◽  
The Stability ◽  
Element Technique ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

Tilting-pad journal bearings are being increasingly used to avoid bearing instability problems. This paper describes the theory and results from a design program which has been developed for tilting-pad journal bearing calculations. The present approach is based on the numerical solution of the Reynolds equation using a one-dimensional finite element technique which considers temperature and viscosity changes and can also take into account the effect of turbulent flow. Computed results of dynamic stiffness and damping coefficients show very good agreement with data from the literature. The effects of various factors which may influence the bearing dynamic characteristics are discussed. For bearings with small preloads and operating at high Sommerfeld numbers, the effective damping at subsynchronous frequencies is considerably lower than that predicted for synchronous vibration. The stiffness is also affected by frequency. This frequency effect is attenuated by increased bearing preloads and offsets. Such factors have important consequences on the stability of high speed turbomachinery supported by tilting-pad journal bearings.

Modeling of Flexible Tilting Pad Journal Bearings With Radial Oil Injection

2008 ◽  
Author(s):  
Asger M. Haugaard ◽  
Ilmar F. Santos
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
System Of Equations ◽  
Servo Valve ◽  
Tilting Pad ◽  
Dimensional Finite Element ◽  
Oil Injection ◽  
Tilting Pad Journal Bearings

The static and dynamic properties of tilting-pad journal bearings with controllable radial oil injection are investigated. The tilting pads are modelled as flexible structures and their dynamics are described using a three dimensional finite element framework and linear elasticity. The oil film pressure and flow are considered to follow the modified Reynolds equation, which includes the contribution from controllable radial oil injection. The Reynolds equation is solved using a two dimensional finite element mesh. The rotor is considered to be rigid. The servo-valve flow is governed by a second order ordinary differential equation, where the right hand side is controlled by an electronic input signal. The constitutive flow pressure relationship of the injection nozzles is that of a fully developed laminar velocity profile and the servo-valve is introduced into the system of equations by a volume conservation consideration. The Reynolds equation is linearized with respect to displacements and velocities of the nodal degrees of freedom. When all nodal points satisfy the static equilibrium condition, the system of equations is dynamically perturbed and subsequently condensed to a 2 by 2 system, keeping only the lateral motion of the rotor. As expected, rotor stability is heavily influenced by the control parameters.

Elastohydrodynamics Applied to Active Tilting-Pad Journal Bearings

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Asger M. Haugaard ◽  
Ilmar F. Santos
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Flexible Structures ◽  
Journal Bearings ◽  
System Of Equations ◽  
Tilting Pad ◽  
Dimensional Finite Element ◽  
Oil Injection ◽  
Tilting Pad Journal Bearings

The static and dynamic properties of tilting-pad journal bearings with controllable radial oil injection are investigated theoretically. The tilting pads are modeled as flexible structures and their behavior is described using a three-dimensional finite element framework and linear elasticity. The oil film pressure and flow are considered to follow the modified Reynolds equation, which includes the contribution from controllable radial oil injection. The Reynolds equation is solved using a two-dimensional finite element mesh. The rotor is considered to be rigid in terms of shape and size, but lateral movement is permitted. The servovalve flow is governed by a second order ordinary differential equation, where the right hand side is controlled by an electronic input signal. The constitutive flow-pressure relationship of the injection orifices is that of a fully developed laminar velocity profile and the servovalve is introduced into the system of equations by a mass conservation consideration. The Reynolds equation is linearized with respect to displacements and velocities of the nodal degrees of freedom. When all nodal points satisfy static equilibrium, the system of equations is dynamically perturbed and subsequently condensed to a 2×2 system, keeping only the lateral motion of the rotor. As expected, bearing dynamic coefficients are heavily influenced by the control parameters and pad compliance.

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