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The effect of residual shaft bow on the unbalance response of a single mass rotor on rigid supports has been examined with a theoretical analysis. The analysis determined the amplitude, phase angle, and peak rotor response speed for various combinations of residual bow and unbalance. For most combinations the phase angle corresponding to the peak rotor response speed was significantly different from the 90 degrees observed in the conventional unbowed rotor. If the residual bow and unbalance were exactly out of phase, the rotor amplitude was zero for a rotor speed equal to the square root of the ratio of residual bow amplitude to unbalance eccentricity. The results of the study suggested a simple method for determining the relative amplitudes of residual bow and unbalance eccentricity based upon the motion of a timing mark on an oscilliscope screen. If the residual bow was less than the unbalance eccentricity, the timing mark moved first in the direction of rotor rotation as the speed is increased and then moved in the opposite direction at a speed less than the critical speed. In the reverse situation, the timing mark moved opposite to the direction of rotation as the speed is increased. At some speed above the critical, it reversed direction. Part II of this paper presents theoretical and experimental results for balancing of a single mass rotor with a residual bow.

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.

No abstract

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.