Pad Temperature In High Speed, Lightly Loaded Tilting Pad Journal Bearings.

LecturePg. 73-84The principal results from an extensive experimental investigation of the steady state characteristics of tilting pad journal bearings are presented. The conditions examined were primarily concerned with operation at high speed (>200ft/sec) and light load (<50 psi specific pressure). The stimulus for this work was the observation of significantly higher than predicted pad temperatures in several steam turbine service applications. The bearings involved were of the conventional pressurized supply (flooded), centrally pivoted, self-aligning type, loaded between pad. High temperatures occurred on both four and five inch diameter bearings designed to operate at shaft speeds up to 14,000 rpm. To investigate this, four and five inch diameter bearings of almost identical design to the service bearings were tested in a laboratory steam turbine at shaft speeds up to 16,000 rpm. The test data acquired show the relationships that exist between the steady state characteristics of pad temperature and power loss, and the parameters of speed, bearing geometry, oil flowrate, and pad material. These results are compared with predicted values from the same tilting pad journal bearing computer program used to evaluate the service bearings. Of primary interest in the data gathered is the observation of an apparent laminar to turbulent transition region. The results verify the actual behavior of the service bearings and identify limitations of the theoretical model used for predicting steady state performance. It is anticipated that the results presented will be of use to bearing designers, and of general interest to manufacturers of rotating machinery

Retrofitting A Large Steam Turbine With A Mechanically Centered Squeeze Film Damper.

LecturePg. 29-40Reviewed is the application of a squeeze film damper to a large steam turbine that addresses high vibration passing through the first critical speed. The turbine was the fifth near identical machine purchased over the course of several expansion projects at a large LNG plant. The original machine was designed in the early 1970s, and had a highly responsive first critical speed with an amplification factor in the upper teens. With a rotor this sensitive to unbalance, heavy rubs and operational difficulties were often encountered during start up and shut down transients. For the fifth machine, it was inquired how the rotor's response sensitivity could be improved without compromising rotor interchangeability with the sister units. A squeeze film damper bearing, being the only practical solution, was proposed and implemented. The design and analysis methodology used in the development of the squeeze film damper bearing is discussed. To maintain rotor interchangeability, the design covers how the damper bearing was optimized to fit the available limited envelope. The systematic analytical approach demonstrates the importance of including support stiffness effects beyond the damper bearing. Test results are presented that illustrate the accuracy of the analysis, and the reduction in synchronous rotor response at the first critical speed

Profiled Leading Edge Groove Tilting Pad Journal Bearing For Light Load Operation.

LecturePg. 1-16Optimization of a leading edge groove tilting pad journal bearing for application in a small, high speed, multistage steam turbine is described. Rotordynamics constraints to meet a design objective maximum operating speed of 1 8000 rpm resulted in a rotor with a 51.0 in bearing span and 5.0 in diameter tilting pad journal bearings. This configuration yielded a design with projected bearing loads of less than 25 psi, and journal surface speeds that could approach 400 ft/sec. Under these conditions, the applicable limits of conventional style tilting pad journal bearings are stretched, since operation is well into the turbulent flow regime. This can result in significantly higher than predicted operating pad temperatures and increased frictional losses. Furthermore, at very light pad loads, bearing dynamic performance and influence on rotor behavior often does not correlate well with theory. For this application, high efficiency leading edge groove bearings (journal and thrust) were used, due to their preferred steady state operating characteristics at high speed. However, as is often observed with lightly loaded conventional style journal bearings, dynamic performance did not precisely match that predicted by theory. This was investigated by profiling the exit side of the leading edge groove with both a tapered and pocket geometry. Two case histories are presented demonstrating their effect on rotor-bearing stability and unbalance response. The modified bearings yielded greater system stability at high speeds, reduced overall vibration amplitudes, and greatly improved effective damping on passing through the rotor's first peak response speed

Subtracting Residual Unbalance For Improved Test Stand Vibration Correlation.

LecturePg. 7-18The importance of correlating rotordynamic analytical results to actual test data has become extremely important in recent years. Many user specifications require the verification of vendor generated analytical results in conjunction with shop unbalance testing. This correlation generally includes critical speed, amplification factor, and vibration magnitude. Several problems arise during shop unbalance testing. First, it is not always feasible to place an unbalance test weight in a location where it will logically excite the mode in question. This can lead to test runs where, despite a large unbalance weight, the residual unbalance is more influential than the test weight. Thus, the resulting rotor vibration is controlled by the residual unbalance and not the test unbalance. Consequently, any type of analytical correlation for this situation is extremely difficult. Another problem with test stand data is that it usually comes from four different vibration probe locations. This results in four vibration plots and, in many cases, four different critical speeds, amplification factors, and vibration magnitudes. Again, the analytical correlation for this situation is extremely difficult, since determining the actual values for these parameters is somewhat nebulous. These problems are addressed herein and a solution is offered. Several examples of analytical and test stand results are presented for steam turbines and centrifugal compressors. These examples highlight and discuss the problem areas identified. A method is presented for subtracting the vibration due to residual unbalance from that of the verification test. The resulting vibration with residual subtraction isolates the effect of the unbalance weight, and leads to improved correlation with analytical predictio

On averting the tragedy of the commons

One of the enduring facts of the human condition is that the earth's resources are finite and its environment fragile. It is also evident that human behavior is rarely based on an appreciation of these facts. While the outlook may be bleak, so are some of the proposed solutions. Reasonable people have suggested that, to survive, an environmentally enlightened authoritarian government must be adopted. This article suggests that such a solution is unworkable, in part because it fails to consider critical aspects of human nature. A framework is proposed for developing solutions compatible with human capabilities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48163/1/267_2005_Article_BF01867519.pd

Optimized Short Bearing Theory for Squeeze Film Dampers

ABSTRACT It is well established that classical short bearing theory can be applied to assess squeeze film dampers whirling in circular centered orbits. This theory yields accurate values for the stiffness and damping coefficients for designs with small length-to-diameter (L/D) ratios (typically less than 0.5) whirling at amplitudes of less than half the damper radial clearance. For L/D ratio designs above 0.5 and/or whirling amplitudes approaching the damper radial clearance, the short bearing theory increasingly overestimates the stiffness and damping coefficients that stretch its applicability for some designs. There are two limitations with the classical theory that compromise the solution at high L/D ratios and large whirling amplitudes. The first is that as the L/D ratio increases, the unrestricted end flow assumption that forms the basis of the short bearing theory introduces increasingly larger errors. The second is that as the whirling amplitude approaches the damper radial clearance, the stiffness and damping coefficients approach infinity much more rapidly than those from a full solution of the governing lubrication equation. The ideal method for determining more exact values is to numerically solve the full lubrication equation, although not everyone has access to such a code. An alternative approach is to use the expressions presented in this paper that are derived from an optimized solution of the short bearing theory that appreciably reduces the errors introduced at high L/D ratios and whirling amplitudes approaching the damper radial clearance. The optimized solution yields a simple closed form correction factor based on Galerkin&apos;s method that minimizes these errors over the positive pressure region of the oil film. This analytic correction factor increases the accuracy of the short bearing theory for all whirling amplitudes and extends the applicability of the closed form solution to larger L/D ratio damper designs. The simple closed form expressions presented herein apply to a damper whirling in a circular centered orbit for both a partial pi-film cavitated model and a full-film uncaviated model. Examples are given that demonstrate the optimized solution yields stiffness and damping values that are significantly closer to the numerical solution for L/D ratio designs up to 1.0 and/or whirling amplitudes approaching the damper radial clearance. INTRODUCTION Squeeze film dampers are used in modern turbomachinery as a means of adding external damping to highly flexible rotorbearing systems. They are widely applied in aircraft jet engines as a means of controlling rotor critical speed peak response amplitudes by augmenting the almost nonexistent damping in the rolling element bearing designs used to support the rotors, but also can be found in a variety of land based machinery that often employ oil film bearings. In the latter case, squeeze film dampers are more frequently applied in high pressure centrifugal compressors to eliminate rotordynamic instability due to the destabilizing forces associated with impellers and seals, Memmott [1]; although they have been applied in other types of machinery with highly flexible rotors, Edney and Nicholas [2]. An overview of the history and application of squeeze film dampers along with a discussion on theoretical models and design considerations can be found in Zeidan, et al [3] and Della Pietra and Adiletta [4]. Included in these papers is a general review of the influence of end seals, pressure effects introduced by circumferential feed grooves, cavitation in the squeeze film, and the relevance of fluid inertia. Simple closed form analytical solutions for estimating the stiffness and damping coefficients of squeeze film dampers were originally derived by Gunter, et al [5] over thirty years ago. These approximate solutions for a damper whirling in a circular centered orbit and for pure radial squeeze were derived from the 2D Reynolds equation with simplifyin

Designing High Performance Steam Turbines With Rotordynamics As A Prime Consideration.

Tutorialpg. 205-224Steam turbines first produced useful work well over a century ago. Their reliability, efficiency, and versatility are possibly the three man attributes that have contributed to their widespread utilization in a wide range of applications. Steam turbines can be found driving equipment ranging from generators, compressors, pumps, fans, and mills to the main propulsion units of marine vessels. They are employed in a variety of industries from utility, petrochemical, and mining to pulp and paper. Of the steam turbines employed in these industries, the most sophisticated and consequently challenging design is that which drives a synthesis-gas compressor of the type used in ammonia and methanol plants. Steam turbines that drive synthesis-gas compressors are required to operate at high speeds with high throttle flows and elevated inlet steam conditions. These turbines have condensing exhausts and often contain a controlled extraction that adds to bearing span and hence rotor flexibility. These features present unique challenges to the rotor and bearing design that must be carefully addressed to assure sound and reliable operation. For example, partial admission steam forces from the inlet and extraction sections can be large enough to affect bearing loading and, therefore, rotor response. Furthermore, the destabilizing forces from steam swirl in the high-pressure labyrinth seals and blade tip clearance leakage can be large enough to drive the rotor unstable. These issues are discussed along with other factors that must be considered in the design of a rotor for a high performance steam turbine. In the case study presented, the dynamic performance of the rotor was a prime consideration in establishing the main parameters of the design. Rotor geometries, such as bearing span, shaft diameter, wheel and overhung weight, along with the bearing and support structure properties, are parameters that can be varied to tune critical speeds in relation to the operating range and reduce response sensitivity to steam forces. The objective is to produce a design that not only complies with the requirements of any applicable specifications, but also one that has minimal dynamic sensitivity to external operational influences. Although the rotating component of a high performance steam turbine is reviewed, the analysis methodology presented can be used in the rotordynamics evaluation of all steam turbines. Furthermore, some of the features discussed can be incorporated into other steam turbine designs, as well as other types of turbomachinery

Eliminating A Rub-Induced Startup Vibration Problem In An Ethylene Drive Steam Turbine.

LecturePg. 65-78A 16 megawatt ethylene drive steam turbine built in 1973 experienced rub related startup vibration problems for many years. The turbine would lock into a rub as it accelerated through the rotor’s first critical speed causing high vibration and often damage to components. Many possible causes of the rub were identified including casing distortion from bound keys, a steam leak at the horizontal joint flange, and a deteriorated foundations after many years of operation subjected to high vibration. Finally, the sensitivity of the rotor’s first critical speed was a concern. This paper describes how these problems were attacked in a concerted effort to eliminate the rub-induced vibration. The horizontal joint seal face was redesigned to address the steam leak; all sliding keys were removed, cleaned, and lubricated; the foundation repaired and regrouted; the original labyrinth seals replaced with retractable packing; and a squeeze film damper added to reduce the critical speed response sensitivity