Lund’s Tilting Pad Journal Bearing Pad Assembly Method

Abstract

This paper summarizes the development during the last 50 years of tilting pad journal bearing analysis and design. The major impetus of this development was a landmark paper published by Jørgen Lund in 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing.” His paper contained the first widely published dynamic coefficients for tilting pad bearings along with his pad assembly method equations. In the 38 years since Lund’s publication, many other authors have written tilting pad journal bearing codes, the first of which were based on Lund’s assembly method. These assembly method codes were utilized for many years to analyze and design tilting pad bearings for improved rotordynamic performance. During this time, some key design tools were developed utilizing Lund’s method. Other authors have written newer codes which solve the energy and elasticity equations iteratively with the pressure equation, including pad degrees of freedom. With the simple addition of a turbulence correction and heat balance, many designers continue to utilize Lund’s method, shunning the more modern codes.

Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations

“…There are three pitch stabilizers on each axial face of the test bearing housing serving the following functions: (1) to react against the torque developed from the test bearing, (2) to align the center axis of the test bearing with the central axis of the test rotor, (3) to provide radial compliance to the system ensuring translational movement of the test bearing with respect to the test rotor, and (4) to axially restrain the test bearing. The forced excitation into the system was delivered through the bearing housing using two orthogonally mounted electrohydraulic shakers (exciters), which enabled the precise control of the excitation frequency and amplitude.…”

“…In 1964, Lund [1] presented in a landmark paper the first formal analysis for predicting dynamic force coefficients of tilting pad bearings [2]. In this analysis, eight synchronously reduced bearing dynamic coefficients were calculated from individual contributions of each pad.…”

A Review of Tilting Pad Bearing Theory

“…Nicholas et al used the synchronously reduced bearing coefficients to estimate the compressor stability margin. During the discussion of the paper, Lund told the presenter that the use of synchronously reduced coefficients for stability margin was mathematically incorrect and that reduction at the rotor natural frequency was correct [24]. This comment spurred much research into the development of nonsynchronous bearing dynamic models.…”

“…Including pad preload was also claimed to improve dynamic characteristics. It was shown later [23,24] that low preload leads to more stable systems.…”

Analytical model of a tilting pad bearing including turbulence and fluid inertia effects

“…This load was used to calculate the stiness and damping of each pad, then these coecients were summed up to establish the stiness and damping of the bearing. One of the important conclusions of his study, highlighted by Nicholas [2], was to infer that cross coupling terms of stiness and damping vanish when pad inertia is zero. Some eects cannot be neglected in higher rotation speed such as turbulence and uid inertia.…”