Prediction of nonlinear dynamic coefficients of tilting-pad journal bearings with pad perturbation

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number, eccentricity ratio, and length to diameter ratio. Similar to the case of linear dynamic coefficients of TPJB, it is observed that the eccentricity ratio effects on nonlinear dynamic coefficients are more notable when the eccentricity ratio is higher than 0.8 or less than 0.2.

Experimental Characterization of Large Turbomachinery Tilting Pad Journal Bearings

The paper deals with the experimental characterization of different 280 mm diameter tilting pad journal bearings for turbomachines using a dedicated test rig. The test articles were a 5-pad Direct Lube Rocker Pivot bearing, a 5-pad Flooded Rocker Pivot bearing, and a 4-pad Flooded Ball and Socket Pivot bearing. The three bearings were tested in their specific design range of operating conditions. Their static and dynamic behavior was investigated as a function of different operating parameters. In particular, the assumed journal center eccentricity and pads temperature were measured, and the power loss determined as a function of angular speed for different static loads. Dynamic stiffness and damping coefficients were determined as a function of excitation frequency for different speeds and loads. The experimental results were compared showing the influence of the operating parameters, configuration, and oil supply.

Numerical and experimental study on dynamic characteristics of tilting-pad journal bearings considering pivot stiffness in a vertical rotor system

Purpose The purpose of this paper is to study the influence of pivot stiffness on the dynamic characteristics of tilting-pad journal bearings (TPJBs) and the stability of the bearing-rotor system. Design/methodology/approach A theoretical numerical model is established, and the influences of pivot stiffness on TPJBs and a bearing-rotor system are analyzed. Then, two kinds of pivot structures with different stiffness are designed and the vibration characteristics are tested on the vertical rotor bearing test bench. Findings The pivot stiffness has an obvious effect on the dynamic characteristics of the TPJBs and the stability of the bearing-rotor system. As a result of appropriate pivot stiffness, the critical speed and the vibration amplification factor can be reduced, the logarithmic decay rate and the stability of the rotor system can be effectively increased. While the journal whirl orbit is smoother and the rubbing is obviously reduced when the bearings have flexible pivots. Originality/value The influence of pivot stiffness on TPJBs and a vertical rotor-bearing system is studied by theoretical and experimental methods.

Measurements to Quantify the Effect of a Reduced Flow Rate On the Performance of a Tilting Pad Journal Bearing (LBP) with Flooded Ends

Operation of tilting pad journal bearings (TPJBs) with a reduced flow improves system energy efficiency by reducing drag power losses, albeit the temperature rise in both the bearing pads and the lubricating oil become a concern. This paper presents measurements of the static and dynamic load performance of a flooded ends TPJB with flowrates ranging from 150% to ~5% of a nominal supply condition. The test bearing is a four-pad, 102 mm diameter, center pivot, with single orifice feeds, and configured with end seals. Experiments include operation at two shaft speeds = 6 krpm and 12 krpm and under three specific loads = 0.345 MPa, 1.03 MPa and 2.07 MPa applied in between pads (LBP). The measurements show the bearing drag power loss decreases by nearly 20% when flow rate drops to 50% of nominal. However, halving the flow produces a raise in pad subsurface temperatures, ~7 °C for operation at 12 krpm. Flow reduction below 50% results in substantial power savings; however, it also produces too hot pad temperatures that approach a known limit for Babbitt material safe operation. Damping coefficients decrease by ~30% as the flow rate decreases from 150% to just a few % of nominal flow. The experimental results are first to quantify operation of a TPJB supplied with minute amounts of lubricant flow. A test with a very low flow rate at ~2% of nominal and under a light load produced the emergence of a broadband subsynchronous vibration frequency, albeit with very small amplitude.

Impact Dynamics in Four-Segment Tilting Pad Journal Bearings Subjected to Pad Fluttering

This paper presents a transient analysis of the motion of unloaded upper pads in a tilting pad journal bearing. It is known that such pads can exhibit self-excited vibration called pad fluttering, which can initiate fatigue damage due to elastic contacts between the fluttering pad and the journal. Unlike previous studies, this work attempts to evaluate forces in the contact. This evaluation is done using a robust nonlinear model, which considers hydrodynamic lubrication, out-of-balance forces and Hertzian contacts. Furthermore, qualitative changes of the bearing’s components motions are analysed in a wide range of journal speeds using bifurcation diagrams, phase portraits and estimates of the largest Lyapunov coefficients. The analysis reveals the intriguing nature of the system, which bifurcates between the periodic motion, period-doubling and chaos.

Numerical and experimental study on the dynamic bearing properties of a four-pad and eight-pad tilting pad journal bearings in a vertical rotor

In this paper, the dynamics of tilting pad journal bearings with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier-Stokes equation. A nonlinear bearing model is developed and used in the steady state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16 % and 38 %, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excite the system at the third and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed.

A method for the experimental estimation of direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators

This article presents a method to experimentally estimate the direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators and other similar rotating machinery for damage detection purposes. Based on a simplified second-order model of a journal bearing in the state-space, the method employs only the usually monitored vibrations, the shaft radial relative, and the bearing radial absolute vibrations originated by the hydro-generator residual unbalance or by hydraulic excitations in the turbine rotor. This article shows that the method was successfully tested using the shaft and bearing vibration signals synthesized by a mathematical model of a 700 MW hydro-generator, even when these signals are contaminated with random noise. This article also shows the method’s performance when applied to real vibration signals acquired from the modeled hydro-generator. Finally, it discusses the possible measures to improve the method’s efficiency.