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The objective of the following work was to determine frequency-dependent rotordynamic force coefficients for a new annular gas damper seal design. Both rotating and nonrotating experimental tests are presented for inlet pressures at 1000psig(69bar), a frequency excitation range of 20-300Hz, and rotor speeds up to 15,200rpm. Two different testing methods were used for determining coefficients: (1) dynamic pressure response method and (2) mechanical impedance method. The dynamic pressure method required the measurement of internal seal cavity pressure modulations in combination with the vibratory motion, whereas the mechanical impedance method used the measurement of external shaker forces, accelerations, and motion of the mechanical system. In addition to the new fully partitioned damper seal (FPDS) tests, the same experiments were conducted for a conventional pocket damper seal (PDS) design. Results of the frequency-dependent force coefficients and the internal seal dynamics for the two different gas damper seals are compared. The conclusions of the tests show that the FPDS design possesses significantly more positive direct damping and direct stiffness compared to the conventional PDS. The experiments also show the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for both seals, which indicate that the seals do not produce a destabilizing influence on rotor-bearing systems.

This paper presents measured frequency dependent stiffness and damping coefficients for 12-bladed and 8-bladed pocket damper seals (PDS) subdivided into four different seal configurations. Rotating experimental tests are presented for inlet pressures at 69 bar (1000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the eight-bladed PDS. Results of the frequency dependent force coefficients for the four PDS designs are compared. The conclusions of the tests show that the eight-bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12-bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a destabilizing influence on rotor-bearing systems.

Metal mesh is a commercially available material used in many applications including seals, heat shields, filters, gaskets, aircraft engine mounts, and vibration absorbers. This material has been tested by the authors as a bearing damper in a rotordynamic test rig. The test facility was originally used to support the design of a turboprop engine, developing squirrel cages and squeeze film dampers for both the gas generator and power turbine rotors. To design the metal mesh damper, static stiffness and dynamic rap test measurements were first made on metal mesh samples in a specially designed nonrotating test fixture. These property tests were performed on samples of various densities and press fits. One sample was also tested in an Instron machine as an ancillary and redundant way to determine the stiffness. Using the stiffness test results and equations derived by a previous investigator, a spreadsheet program was written and used to size metal mesh donuts that have the radial stiffness value required to replace the squirrel cage in the power turbine. The squirrel cage and squeeze film bearing damper developed for the power turbine rotor was then replaced by a metal mesh donut sized by the computer code. Coast down tests were conducted through the first critical speed of the power turbine. The results of the metal mesh tests are compared with those obtained from previous testing with the squeeze film damper and Show that the metal mesh damper has the same damping as the squeeze film at room temperature but does not lose its damping at elevated temperatures up to 103 °C. Experiments were run under several different conditions, including balanced rotor, unbalanced rotor, heated metal mesh, and wet (with oil) metal mesh. The creep, or sag, of the metal mesh supporting the rotor weight was also measured over a period of several weeks and found to be very small. Based on these tests, metal mesh dampers appear to be a viable and attractive substitute for squeeze film dampers in gas turbine engines. The advantages shown by these tests include less variation of damping with temperature, ability to handle large rotor unbalance, and the ability (if required) to operate effectively in an oil free environment. Additional testing is required to determine the endurance properties, the effect of high impact or maneuver loads, and the ability to sustain blade loss loads (which squeeze films cannot handle).

Pocket damper seals perform a dual function: both sealing the pressurized gas around a rotating shaft and providing large amounts of vibration damping. The annular cavity between the labyrinth seal teeth is subdivided into separate annular cavities around the circumference of the rotor by partitioning walls. Also, the upstream and downstream teeth have different radial clearances to the rotor. These seals have been shown to provide a remarkable amount of direct damping to attenuate vibration in turbomachinery, but they generally leak more than conventional labyrinth seals if both seals have the same minimum clearance. Conversely, brush seals allow less than half the leakage of labyrinth seals, but published test results show no significant amount of damping. They are considered to be a primary choice for the seals in new aircraft engine designs because of their low leakage. This paper will describe a recently invented hybrid brush/pocket damper seal that combines high damping with low leakage. Previous brush seal results were studied and calculations were made to select a brush seal to combine with the pocket damper design. The result is a hybrid seal with high damping and low leakage. A special design feature can also allow active vibration control as a bonus benefit. A computer code written for the original pocket damper seal was modified to include the brush element at the exit blade. Results from the computer code indicate that the hybrid seal can have less leakage than a six bladed (or 6 knives) labyrinth seal along with orders of magnitude more damping. Experimental evaluations of the damping and leakage performance of the hybrid seal are being conducted by the authors. The experimental work reported here tested the damping capability of the new hybrid brush seal by exciting the seal journal through an impedance head. A conventional six-bladed labyrinth seal of the same working dimensions was also tested. The brush hybrid pocket damper seal is found to leak less than the labyrinth seal while producing two to three times more damping than the original pocket damper seal, (orders of magnitude more than the conventional labyrinth).

Selection criteria and design evaluations of several types of bearing dampers with active control for application to aircraft engines were described in a companion paper (Vance, Ying, and Nikolajsen, 1999). A disk type electrorheological (ER) damper was chosen for further study and testing. The results of the tests and the final conclusions of the study are described in this paper. Experimental results including stiffness and damping coefficients are presented for the ER bearing damper with two types of ER fluid, 350 CS and 10 CS (centistokes) viscosity. The vibration attenuation performance of the ER damper was measured on a rotordynamic test rig in the form of free vibration decay, rotor orbits, and runup unbalance responses. The results show that the ER fluid with lower viscosity has the better characteristics for rotordynamic applications. It was found that ER fluids produce both Coulomb and viscous damping. If only the damping is considered, the Coulomb type is less desirable, but with active control it can also achieve control of rotor stiffness as analyzed in Vance and San Andres (1999). A feedback control system was developed and applied to the ER damper with the objective of improving the overall rotordynamic performance of the rotor bearing system, considering both vibration amplitudes and dynamic bearing forces. A “bang-bang” (on and off) simple control logic was found to work better in practice than more sophisticated schemes. The measured runup responses of the rotor-bearing system with this control approximated the desired vibration response curves fairly well. The tests highlighted some of the practical considerations that would be important for aircraft engine applications, such as the ER fluid limitations, the electrical power supply requirements, the electrical insulation requirements, the nonlinear relationship between the voltage and the damping, and the relative benefits of active control. It is concluded that active control of bearing damping is probably not a practical improvement over the passive squeeze film dampers currently used in most aircraft gas turbine engines.

A gas-operated bearing damper for turbomachinery has been designed, analyzed, and experimentally investigated in the laboratory. The damper utilizes air bled off from the compressor to power an actuator through orifices with area modulated by the vibratory displacement at the bearing support. The design objective for this passive device is to make the actuating dynamic gas pressure phase lead the vibratory displacement by 90 deg. Several variations of the basic concept have been tested. An analysis was performed to guide the experiments. All of the designs tested to date can produce positive damping, and one particular design has produced a damping coefficient of 8756 N-s/m (50 lb-sec/in.) with a power penalty of 5.2 kW (7 hp) at 310 KPa (45 psi). This design was installed on a laboratory rotor with flexibly supported ball bearings, and significant damping of the critical speed response was demonstrated. The experimental results to date suggest that further research can produce significant improvements in performance, and the device appears to be especially adaptable to high-temperature applications for aircraft engines.

This paper presents a theoretical model for analytical study of internal friction-induced whirl instability due to shrink fit and interference fit joints in rotating machines. It is the theoretical continuation of an experimental study on the effects of internal friction published in a companion paper. The theoretical study shows that the follower force internal friction model proposed by Gunter in 1965 is a physically incorrect model due to its inconsistency with Newton’s Third Law of Motion. The internal moments model proposed by Lund in 1976 to explain unstable sub-synchronous vibrations due to micro-slip in interference and shrink fit joints is physically consistent with the basic principles of mechanics and can explain rotordynamic instability due to internal friction in rotating machines. Rotordynamic simulations of the experimental single-disk and two-disk rotor based on an internal moments model are carried out using finite element based rotordynamics software. Rotordynamic simulations of the unstable experimental rotors using the linear viscous form of the internal moments model, with selected moment stiffness and damping parameters at the interface, result in correct prediction of the instabilities (negative real part of the damped eigenvalues).

This paper presents an experimental study of internal friction effects on two different test rotors with shrink fit and interference fit joints. One of the setups was a single-disk rotor with an interference fit joint to the main shaft through a mechanically adjustable tapered sleeve; the other setup was a two-disk rotor with a variable cross-section shaft, having the two disks shrunk fit into an aluminum sleeve at the ends. The slippage in these types of joints is known to be a potential source of sub-synchronous rotordynamic instability in rotating machines. The experimental results from the rotor setups show the presence of strong unstable sub-synchronous rotor vibrations initiated at operating speeds above the first critical speeds of the rotor-bearing systems. The experiments with the two-disk rotor demonstrated that different distributions of shrink fit at two locations (loose fit at one end; tight fit at the other end) were necessary to produce rotordynamic instability. The instability in that case caused complete wreckage of the test rig, showing that the sub-synchronous vibrations caused by slippage at interference fit joints are potentially dangerous to the safe operation of rotating machines. Furthermore, a critical radial interference (shrink fit) of 1 mils (25.4 μm) at speed was identified to cause an onset of instability in several of the experiments.Copyright © 2008 by ASME

Rotordynamic instability, commonly observed as subsynchronous vibration, is a serious problem that can cause heavy damage to a turbomachine or make it incapable of operation due to high vibration levels. However, all subsynchronous vibrations are not necessarily unstable. A way to quickly diagnose them would be helpful. In an earlier paper, the authors presented data from experiments that simulated various causes of sub-synchronous vibrations, some causes being genuine rotordynamic instabilities and some others being benign (stable), and identified ways to diagnose and classify the subsynchronous motions. In a continuation of the same study, subsynchronous vibrations due to coupled lateral-torsional effects are experimentally simulated, the objective being to signal-analyze these vibrations to find unique signatures that identify this cause and also be able to recognize if they are a true rotordynamic instability or not. To this end, a test rig was built with parallel shafts coupled by gears, driven by a DC motor at one end and loaded at the other end, to closely simulate a real-world machine. A torsional mathematical model for the test rig is also presented to predict its torsional natural frequencies. Experiments were conducted wherein the first torsional natural frequency was externally excited, with the shaft spinning at a higher speed. The result was a false sub-synchronous “instability” signal in the lateral measurements. A method to distinguish these vibrations from a genuine lateral non-synchronous instability is presented. Also, a new diagnostic method to classify the subsynchronous vibration as benign is elucidated.Copyright © 2008 by ASME

Rotordynamic instability can be disastrous for the operation of high speed turbomachines in the industry. Most ‘instabilities’ are due to de-stabilizing cross coupled forces from variable fluid dynamic pressure around a rotor component, acting in the direction of forward whirl and causing subsynchronous orbiting of the rotor. However, all subsynchronous whirling are not unstable and methods to diagnose the potentially unstable kind from the benign are critical to the health of the rotor-bearing system. In this study, methods to demarcate between the two are detailed. Orbit shape, “frequency tracking” and agreement of subsynchronous frequencies with known eigenvalues are used as diagnostic tools. It is shown that a change in synchronous phase angle produced by de-stabilizing cross coupled forces can be used as a definitive indicator of incipient instability. Typical signatures of subharmonic vibrations induced from non-linear stiffness of the rotor- bearing system are examined analytically and through experiments.Copyright © 2007 by ASME

Rotordynamic instability, commonly observed as subsynchronous vibration, is a serious problem that can cause heavy damage to a turbomachine or make it incapable of operation due to high vibration levels. However, all subsynchronous vibrations are not necessarily unstable. If the amplitude of the subsynchronous vibration is large, it can cause damage to seals, bearings, or process wheels. If it is small, the question arises as to whether it has the potential to grow larger (“instability”) or whether it is benign and harmless. A way to know would be helpful. The objective of this study is to signal-analyze subsynchronous vibration in turbomachinery and distinguish benign subsynchronous vibration from true rotordynamic instability. Effort is also made to identify unique signatures to a cause, thereby aiding in faster diagnosis. A computer simulation study is conducted on four rotors, including two gas-reinjection compressors that went unstable, to examine the possibility of using the change in synchronous phase angle as a possible indicator of impending instability. Two other rotors in laboratory test rigs were also studied, both experimentally and with computer simulations of the phase angle response. The computer simulations and experimental results agree very closely on the test rigs. Measured signals from another rotor, with bearings having a dead-band clearance are studied as an example of a benign cause that can result in subsynchronous vibration. The effect is studied with the rotor in both horizontal and vertical positions and clear indicators are discovered that confirm the subsynchronous vibration to be benign in nature. Signatures from another rotor with internal friction are also presented. The experimental data clearly shows indicators that distinguish it as a genuine instability. Dry friction whip is also experimentally produced on a test rig. The measurements show that dry friction whip defies all general rules of thumb for diagnosing a true instability and at the same time is a very violent one as well.Copyright © 2007 by ASME

In a previous ASME paper the second author reported experiments on wire mesh bearing dampers (WMD) incorporated in a power turbine rotor-bearing system in order to enable a direct comparison between WMD and squeeze film dampers (SFD). The results showed that both WMD and SFD perform equally well for reducing the rotordynamic amplitudes of vibration. Moreover the WMD were found to have significant advantages over SFD. The damping provided by the wire mesh is independent of temperature changes and presence of turbine oil. Experiments by another investigator showed that WMD are capable of sustaining more than twice the unbalance as compared to SFD, which promises possible application to withstand blade loss loads. This paper presents empirically developed non-dimensional design equations for WMD, capable of predicting stiffness and damping for a wire mesh ‘donut’ subject to changes in various design, installation, and operational parameters.Copyright © 2005 by ASME

A model of impact of a tennis ball with a flat surface is developed based on a planar, two-mass, linear, four degree of freedom vibration system idealization. The impact is assumed to be incident on a flat surface with friction. The incident parameters of the ball include the centre of mass translational velocity, angle of impact with the surface and the incident angular spin of the ball. The linear, piecemeal vibration model predicts the corresponding rebound parameters of the tennis ball. The model also predicts the duration of contact of the tennis ball with the flat surface, the transition of motion of the tennis ball during contact with the ground from sliding to rolling contact, and the resulting contact forces developed between the tennis ball and the flat surface. The model is computationally efficient because the governing differential equations of motion are linear and their standard solutions can be easily implemented on a personal computer. Predictions of the rebound parameters from the model are compared with experimental findings on tennis balls which are incident on a flat surface with various angles, velocities and angular spins (zero spin, topspin and backspin). For selected parameters of the two-mass model, the comparisons show excellent agreement between the model and the measurements.

Pocket damper seals (PDSs) have been shown to offer an improved rotordynamic performance compared to conventional labyrinth seals, providing large amounts of direct damping and small cross-coupled coefficients. To this date, the rotordynamic characteristics of the PDSs have been determined using linearized models, with validity limited to small displacements of the rotor. The present investigation determines the effect of the nonlinear forces arising from the pocket damper seal on the response and stability of a PDS-rotor system when subjected to large dynamic excitations. It is determined that the nonlinear forces maintain bounded amplitudes of vibration (“limit cycles”) after the rotor passes the threshold speed of instability predicted by the linear theory. It is also found that the critical speed of the PDS-rotor system is well predicted by using both linear and nonlinear models of the seal forces, as both predictions compare well with the experimental measurements.Copyright © 2003 by ASME

Pocket damper seals can produce large amounts of damping in turbomachines where the working fluid is compressible. Even with non-optimum design configurations, they have solved rotordynamic instability problems in high-pressure compressors. They do not rely on viscous effects, so they are ideal for oil-free applications. It is shown here that proper sizing of the seal pockets can maximize the damping. Significant parameters and variables have been identified, both experimentally and theoretically, that reflect the fundamental effects of the pocket damper seal to produce rotordynamic damping. Dimensionless analysis was performed, resulting in significant Pi groups involving damping, stiffness and leakage parameters. Of particular interest is a Helmholtz Pi group that shows 1) the benefit from optimizing the volume of the pockets around the seal, and 2) the frequency dependence of the seal. Dimensionless prediction equations are shown graphically. The graphs were generated by a computer code that uses a single control volume model. The code has been verified experimentally on several different seal test rigs with data taken at different vibration frequencies spaced an octave apart.Copyright © 2002 by ASME

In a previous ASME paper experiments were reported on metal mesh bearing dampers (MMD) that were tested in a power turbine rotor at speeds up to 12,000 rpm. They were made of 0.229 mm stainless steel 304 wire mesh, compressed to 57% density, which is close to the maximum density that was economically available. After balancing, a level of vibration was achieved similar to that previously observed with squeeze film dampers. These experiments showed that the MMD could suppress vibration amplitudes of the 22.7 kg rotor at critical speeds of 4,000 rpm and 9,300 rpm. Much of the testing showed the rotor having little or no response to unbalance on coastdown through the critical speeds. The donut-shaped MMD in those tests were the only bearing supports; no squirrel cages were used. A question was raised about the feasibility of using MMD in parallel with a squirrel cage bearing support so that the stiffness can be controlled independently of the damping. This paper presents experimental results for metal mesh dampers with a squirrel cage as a parallel bearing support. Experiments with copper mesh as seal elements (on another project) had indicated that copper mesh has higher damping than stainless steel, so copper was chosen for these experiments. Both a linear viscous damping model and a hysteretic damping model were investigated. Some hysteretic damping models predict that damping depends on stiffness. A different hysteretic model turned out to be useful and promising as a prediction model for two reasons: a) it fits the measured data, and b) it predicts that the damping is not lost if the MMD is put in parallel with a steel structure such as a squirrel cage bearing support. The measurements reported here support the validity of that prediction.Copyright © 2001 by ASME

This paper describes some of the requirements for bearing dampers to be used in an aircraft engine and briefly discusses the pros and cons of various types of dampers that were considered as candidates for active control in aircraft engines. A disk type of electrorheological (ER) damper was chosen for further study and testing. The paper explains how and why the choice was made. For evaluating potential applications to aircraft engines, an experimental development engine (XTE-45) was used as an example for this study. Like most real aircraft engines, the XTE-45 ran through more than one critical speed in its operating speed range. There are some speeds where damping is desirable and other speeds where it is not. Thus, the concept of a damper with controllable forces appears attractive. The desired equivalent viscous damping at the critical speeds along with the available size envelope were two of the major criteria used for comparing the dampers. Most previous investigators have considered the ER damper to produce a purely Coulomb type of damping force and this was the assumption used by the present authors in this study. It is shown in a companion paper (Vance and San Andres, 1999), however, that a purely Coulomb type of friction cannot restrain the peak vibration amplitudes at rotordynamic critical speeds and that the equivalent viscous damping for rotordynamics is different from the value derived by previous investigators for planar vibration. Control laws for Coulomb damping are derived in Vance and San Andres, (1999) to achieve minimum rotor vibration amplitudes in a test rig while avoiding large bearing forces over a speed range that includes a critical speed. The type of control scheme required and its effectiveness was another criterion used for comparing the dampers in this paper.

Attempts have been made in the past to use Coulomb damping for vibration suppression in rotating machinery. Typically, a dry friction damper is designed to operate on a flexible bearing support. These designs have usually been unsuccessful in practice, partly because the Coulomb coefficient changes with temperature, with ingress of dirt or lubricant, and with the surface wear conditions. It is known that purely Coulomb damping forces cannot restrain the peak rotor whirl amplitudes at a critical speed. The invention of a disk type of electroviscous damper, utilizing a fluid with electrorheological (ER) properties, has recently revived the interest in Coulomb type dampers. Several investigations have suggested that a Coulomb friction model was the best representation for an ER damper with voltage applied. This model was used to study the feasibility of developing actively controlled bearing dampers for aircraft engines. This paper analyzes the imbalance response of two different rotordynamic models with Coulomb friction damping and shows the benefit of adding active control. Control laws are derived to achieve minimum rotor vibration amplitudes while avoiding large bearing forces over a speed range that includes a critical speed. The control laws are derived for purely Coulomb type of damping and assuming a combination of Coulomb and viscous damping effects. It is shown that the most important feature of Coulomb damping for minimal rotordynamic amplitude response is the control of rotor support stiffness, i.e. leading to the relocation of critical speeds, rather than control of a damping coefficient.Copyright © 1999 by ASME

A new type of labyrinth gas seal for damping vibration and whirl, called the TAMSEAL, has been evaluated in both non-rotating and rotating tests at Texas A&M University. Test results of the prototype, along with comparison tests of a conventional labyrinth seal, show up to one hundred times more direct damping than the conventional bladed seal. The new design also has a feature that blocks swirl of the working fluid, which is known to be rotordynamically destabilizing in machines with conventional seals. Coastdown tests of the new seal were conducted at various pressures on a rotordynamic test apparatus with a critical speed at 4000 rpm and compared with identical testing of a conventional labyrinth seal. Rap tests of both seals were also conducted to measure the logarithmic decrement of free vibration, and the leakage of both seals was measured. Test results show large reductions in peak vibration at the critical speed in all cases, with the critical speed being completely eliminated by the TAMSEAL at some pressure drop conditions. The leakage rate of the tested TAMSEAL is higher than the conventional seal at the same clearance, but the large reductions in vibration and whirl amplitudes suggest that the TAMSEAL could be operated with smaller clearances than conventional labyrinth seals.Copyright © 1995 by ASME

Experimental measurements have been made to evaluate the rotordynamic performance of straight-through labyrinth seals under conditions that are realistic for many turbomachines. Both teeth-on-rotor and teeth-on-stator gas seals were tested, each with twelve blades, 173 mm (6.8″) blade diameter, and 102 mm (4″) total length. The nominal blade tip clearance was 0.5 mm (20 mils). The teeth-on-stator seal was tested with the blade tip clearances diverging (in the direction of the flow), uniform, and converging. The teeth-on-rotor seal was tested with uniform clearances. The inlet air pressure to the seals was varied from 1.7 bar to 14.6 bar (25 psi to 200 psig) with the last blade exhausting to the atmosphere. Coastdown tests of all the seals were performed on a rotordynamic test rig to show their effect on synchronous response to imbalance when passing through a 3700 rpm critical speed. For the teeth-on-rotor seal, rap tests at 4500 rpm were also conducted to measure the effective damping coefficient for subsynchronous vibration. The synchronous response to imbalance was generally increased by all the seals at inlet pressures up to about 11.2 bar (150 psig). The worst case was for the teeth-on-rotor seal at about 2.7 bar (35–45 psi) inlet pressure where the rotor whirl amplitude was increased from .1 mm (3.75 mils, peak to peak) to over .13 mm (5 mils). In most cases the rotor whirl amplitude was slightly decreased at inlet pressures above 13 bar (176 psig). The teeth-on-rotor seal provided a small amount of damping to attenuate the 61 Hz subsynchronous vibration with the rotor running at 4500 rpm. A computer model which includes both the rotor and housing dynamics was developed to evaluate the possible range of values of the rotordynamic seal coefficients. Simulations show that the effective subsynchronous damping coefficient of the teeth-on-rotor seal ranges from 175 N-s/m at 5.1 bar inlet pressure (1 lb-s/in at 75 psi) to 876 N-s/m at 10.2 bar (5 lb-s/in at 150 psi). This corresponds to a range of 0.3% to 1.4% of critical damping added by the seal for subsynchronous vibration, even though the seal increased the synchronous response at the critical speed. It is shown that the orbit conditions for the synchronous and subsynchronous tests were radically different, as they likely will be in most turbomachines.

A new type of labyrinth seal for damping vibration and whirl in turbomachinery has been invented and tested at Texas A&M University (TAMU). Test results of the prototype, along with a conventional labyrinth seal, show that the new design has fifteen times more direct damping than the conventional bladed seal. The design also has a feature that blocks swirl of the working fluid, which is known to be destabilizing in machines with conventional seals. This paper shows how the new design is different from conventional bladed seals and honeycomb seals, describes the test apparatus and results, describes a theory which explains the test results, and explains how the seal can be much more effective than a bearing damper for reducing vibration in turbomachines with a compressible working fluid.

The effect of fluid inertia on the synchronous steady-state operation of a centrally preloaded single mass flexible rotor supported in squeeze film bearing dampers is examined theoretically. For a model representative of some aircraft engine applications, frequency response curves are presented exhibiting the effect of fluid inertia on rotor excursion amplitudes and imbalance transmissibilities for both pressurized and unpressurized short open-ended squeeze film damper supports. It is shown that a significant reduction in amplitude response and transmitted force is possible for dampers operating at moderately large squeeze film Reynolds numbers. Furthermore, for unpressurized dampers the possibilities of bistable operation and jump phenomena are shown to be reduced and virtually disappear at sufficiently large operating Reynolds numbers.

This is the first part (Part I) of two papers describing results of a research program directed at verifying computer programs used to calculate critical speeds of turbomachinery. This research program was undertaken since questions existed about the accuracy of calculations for the second and higher critical speeds. Part I describes improvements in computer programs and data modeling that resulted from comparing measured and calculated “free-free” natural frequencies of several shafts and rotors. Program modifications to improve accuracy include consideration of the effect of disk/shaft attachment stiffness, revised treatment of the end masses, and an improved convergence. Modifications resulting from the study are applicable to many other damped and undamped critical speed computer programs.

An extensive study was made to determine current needs for research in rotor dynamics to solve problems encountered in small high-speed turboshaft engines for helicopter and aircraft propulsion. The purpose of this paper is to report the state-of-the-art for this area as completely and concisely as possible. The present and past philosophy of rotor-bearing system design including the impact of the demand for front drives, is discussed. Methods for critical speed prediction and high-speed balancing are reviewed. The trend to higher speeds is seen to require consideration of new approaches to balancing through flexural modes. The major parameters available for control by the designer are shown to be the bearing support properties, and recommendations are made for improving the accuracy of prediction of these properties. Nonsynchronous excitation is categorized according to the mechanisms producing the forces, and a need is shown for better methods to identify the resulting whirling and vibration, since several of these motions are potentially unstable. Finally, reasons are given for the predominant use of rolling-element bearings in these engines, and the potential for special applications of oil-film and gas bearings is discussed.

Abstract Shock subs have been in use for several years in oilwell drill strings to reduce longitudinal and torsional vibrations. In this paper a mathematical investigation is made into the longitudinal vibrations of a drill string, with and without a shock sub. The Laplace transformation method of solution is used, with the inverse transformation being accomplished by the theory of residues and facilitated by the use of a digital computer. The solution curves are mathematically exact at each computed point, and confirm favorable field reports on the use of the sub. Introduction Several years ago a device known as a shock sub was introduced to the oiltool field. Its purpose is the reduction of drill string vibrations, both longitudinal and torsional. Reports from the field indicate that the shock sub successfully performs this function, at least to a degree and under some conditions. A mathematical analysis of the longitudinal vibrations of an idealized drill string, with and without a shock sub, makes possible a determination of the precise mechanism of the action of the sub so that its effect can be quantified and best conditions established for optimum performance. Several authors have mathematically performance. Several authors have mathematically analyzed drill string vibrations due to various sources, but have not considered the effect of a shock sub. The shock sub is effectively a spring with internal damping and is located as a segment of the drill string directly above the bit and below the drill collars. Garrett published a paper giving experimental observations at the top of the drill string, both with and without the shock sub installed. He noted that the predominant observed frequencies of longitudinal vibration are three times the rotational frequency of the drill string. Photographs are included showing bottom-hole Photographs are included showing bottom-hole patterns with a three-lobe shape around the area patterns with a three-lobe shape around the area swept by the bit. This lobe pattern was formed by a tricone roller bit. It is believed by some investigators that the number of cones on the bit determines the number of lobes formed on the bottom of the hole and, consequently, the frequency of the driving force generating the longitudinal vibration in the drill string. The buildup of a bottom-hole lobe pattern is most apparent when drilling hard rock with a roller bit and may not occur at all under other conditions of drilling. In this investigation the bottom-hole lobes are assumed to be the primary cause of longitudinal vibration of the drill string; hence the driving force for longitudinal vibration is assumed to be a sinusoidal displacement function at the drill bit with a frequency of N times the rotational frequency of the drill string, where N is the number of cones on the bit. THE MATHEMATICAL MODEL A schematic of the entire system to be described by the mathematical model is shown in Fig. 1. The system is considered to be linear throughout. The internal damping of the shock sub element is neglected in the analysis, although viscous damping of the drill string is included. Bradbury has shown the effect of the tool joints on the undamped vibrations of the drill string to be negligible for the frequency range encountered here, although their effect on the damping coefficient could be considerable. The longitudinal motion along the doll pipe and drill colors is described by the solution to the classical wave equation, linearly damped, subject to the boundary conditions at the top and bottom of the drill string and at the point of junction of the pipe and collars. The wave equations and associated pipe and collars. The wave equations and associated boundary conditions which must be satisfied along the drill string are shown in Fig. 2. SPEJ P. 349

A study of problems related to vibration and dynamic loads in helicopter propulsion systems was made. It was found that engine vibration, shaft whirling, and dynamic instabilities seriously limit helicopter performance and reliability. It is recommended that studies be made to justify an intelligent standardization of engine vibration limit specifications for helicopters, that impedance-mobility methods be developed for optimizing engine/ airframe interface design, that research and development of helicopter power transmission shafts and couplings be carried out to solve whirling problems, and that new methods and hardware be developed to eliminate torsional instabilities in helicopter drive systems with automatic fuel control.

Experiments and field applications have demonstrated that multiple-pocket gas damper seals effectively eliminate subsynchronous vibration and attenuate imbalance response at the critical speeds in turbomachinery. A one-control volume, turbulent bulk-flow model for the prediction of the seal leakage and rotordynamic force coefficients of centered multiple-pocket damper seals is hereby detailed. Comparisons of numerical predictions with experimental force coefficients for a four-pocket damper seal are presented. The bulk-flow model and experiments indicate the seal direct stiffness and damping force coefficients are insensitive to journal speed while the cross-coupled stiffnesses increase slightly. However, the current model overpredicts the direct damping coefficient and underpredicts the direct stiffness coefficient for increasing test pressure ratios. Computed results show that the force coefficients of multiple-pocket gas damper seals are also functions of the rotor excitation frequency.