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Technical Papers Authored or Co-authored By Dr.  Robert  H.  Badgley

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Order: #1

1.  Badgley, R. H. and Booker, J. F. , "Turborotor Instability – Effect of Initial Transients on Plane Motion, " ASME Paper No. 68-Lub-7, presented at the ASME-ASLE Lubrication Conference, Atlantic City, N. J. , October 8-10, 1968, and published in Trans. ASME, Journal of Lubrication Technology, Vol. 91, Series F, No. 4, October 1969, p. 625-633.

The rigid-body dynamics of rotors supported in plain, cylindrical, cavitated, fluid-film journal bearings are investigated numerically by Runge-Kutta extrapolation techniques. Expressions for journal force due to the fluid-film are developed for the short-bearing (Ocvirk), long-bearing (Sommerfeld), and finite-length-bearing (Warner) approximate solutions to the Reynolds equation. Stability of Plane motion is investigated for each solution under the assumption of light initial impact. The long-bearing solution appears to be most conservative (that is, it predicts the onset of instability at lower angular velocity ratios than the other solutions) for static eccentricity ratios between a and 0. 5, while the finite-bearing solution, with bearing length-to-diameter ratio L/D equal to 1, appears most conservative at higher static eccentricity ratios. Variations in L/D between 0. 5 and 2. 0 appear not to affect journal path shapes appreciably. Variations in initial journal center velocity are found to be important, at least with the short-bearing solution: large initial velocities are observed to produce instability for certain parameter combinations which are stable under small initial position or velocity disturbances. In all cases investigated, instability is not observed above static eccentricity ratios of 0. 83.
Order: #2

2.  Badgley, R. H. And Booker, J. F. , "Rigid-Body Rotor Dynamics: Dynamic Unbalance and Lubricant Temperature Changes, " ASME Paper No. 69-Lub-14, presented at the ASME-ASLE Lubrication Conference, Houston, Texas, October 14-16, 1969, and published in Trans. ASME, Journal of Lubrication Technology, Vol. 92, Series F, No. 3, July 1970, p. 415-424.

The case of a symmetric rotor supported on two identical, rigidly mounted, self-aligning, finite-length (L/D =1) fluid-film journal bearings is considered. Rotor position is described by two translation coordinates in a plane perpendicular to the bearing line of centers, and by three Euler angles. Introduction of various amounts of dynamic unbalance via the inertia tensor off-diagonal terms (products of inertia) allows determination of angular velocity and static eccentricity ratio combinations leading to bearing "failure" defined for arbitrary maximum allowable eccentricity ratios. Instability hysteresis, defined here as the persistence, during rotor deceleration, of instability to speeds below which it first appeared, is considered by means of the above model. Equations and methods developed for the unbalance investigation are adapted to a variable-speed analysis. With both constant and variable mean bearing temperatures, variable-speed simulations terminating at constant speed are observed to be stable when the terminating point is below the instability threshold curve on the angular velocity-static eccentricity ratio parameter plane and unstable when above. The slope of the threshold curve and the shape of the equilibrium-condition path on the parameter plane (single-line path for constant temperature, closed curve for variable temperature) apparently combine to produce hysteresis in the variable temperature case and none at constant temperature.
Order: #3

3.  Badgley, R. H. , "Mechanical Aspects of Gear-Induced Noise in Complete Power Train Systems, " ASME Paper No. 70-WA/DGP-1, presented at the ASME Winter Annual Meeting, November 29 – December 3, 1970, New York, N. Y.

The author presents an in-depth systems approach to the problem of interior helicopter noise, showing that step-by-step consideration of the flow of vibration energy within the drive train yields both qualitative understanding of the problem and technology required to alleviate it. Since precise methods for computing interior noise from design and operating data, are more economical than cut and try techniques for evaluating proposed noise-reduction design changes, the development of precise methods is stressed in the study. In-flight vibration and noise measurements, gathered to form a data bank, are used to assist in understanding the vibration energy flow and assessing adequacy and accuracy of the analytical procedures (comparison of calculated and measured noise spectra). The author uses laboratory experiments on parts of the system to study the behavior of critical components. The overall study, directed specifically at UH-1D and CH-47 helicopters, is coordinated and controlled by a comprehensive plan and schedule designed to ensure inclusion of all aspects of the problem.
Order: #4

4.  Tessarzik, J. M. , Badgley, R. H. And Anderson, W. J. , "Flexible Rotor Balancing by the Exact Point-Speed Influence Coefficient Method, " ASME Paper No. 71-Vibr-91, presented at the ASME Vibrations Conference, Toronto, Canada, September 8-10, 1971, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 94, Series B, No. 1, February 1972, p. 148-158.

A test program was conducted to confirm experimentally the validity of the exact point-speed influence coefficient method for balancing rotating machinery, and to assess the practical aspects of applying the method to flexible rotors. Testing was performed with a machine having a 41-in, long, 126-lb rotor. The rotor was operated over a speed range encompassing three rotor-bearing system critical speeds: two" rigid-body" criticals and one flexural critical. Rotor damping at the flexural critical was very low due to the journal bearings being located at the nodal points of the shaft. The balancing method was evaluated for three different conditions of initial rotor unbalance. The method was found to be effective and practical. Safe passage through all the critical speeds was obtained after a reasonable number of balancing runs. Success of the balancing method was, in large part, due to the accuracy of the instrumentation system used to obtain phase-angle measurements during the balancing procedure.
Order: #5

5.  Badgley, R. H. , "Gearbox Dynamics – The Key to Understanding and Reducing Acoustic-Frequency Energy in Geared Power Trains, " presented at the Meeting of the Aerospace Gearing Committee of the American Gear Manufacturers Association, Cleveland, Ohio, January 17-18, 1972.

The problem of interior noise in large helicopters is most effectively attacked by a systematic, step-by-step study of the flow of high-frequency vibration energy within the rotor drive train. Such a study, which begins with an examination of the mechanism by which high-frequency disturbances are generated at the gear meshes, includes in due course a study of the responses to these disturbances (both torsional and lateral) of the drive train shafts and shaft support elements. Comparison of predicted vibration amplitudes and dynamic stresses with carefully-measured values can be expected to yield both a qualitative understanding of the noise problem and also solution techniques which can be applied to other designs. Such a comparison is in fact underway for the Boeing-Vertol CH-47 helicopter forward rotor gearbox. This paper presents the results of calculations of the vibration response of the CH-47 forward rotor gearbox spiral-bevel gear shafts to spiral-bevel mesh-induced disturbances. These calculations have shown logical reasons why noise is generated by the gearbox at the spiral-bevel mesh frequency.
Order: #6

6.  Badgley, R. H. , "Reduction of Noise and Acoustic-Frequency Vibrations in Aircraft Transmissions, " AHS Paper No. 661, presented at the 28th Annual National Forum of the American Helicopter Society, Washington, D. C. , May 1972.

The most objectionable components of helicopter interior noise are usually generated by either the accessory systems or the rotor drive-train gear boxes. In small and medium-size helicopters, the accessories are often as important as the rotor- drive components with regard to noise, whereas in large helicopters the latter sources are generally more important. The problem of rotor drive-train gearbox noise is most amenable to solutions which involve a systematic, step-by-step study of the flow of high-frequency vibration energy within the drive train. Such studies, which begin with an examination of the mechanism by which mesh-frequency disturbances are generated, must include in due course a ·study of the response (both torsional and lateral)of the drive-train shafts and shaft sup- port elements; This paper presents the results of calculations of the vibration response to spiral- bevel mesh-induced disturbances for the spiral- bevel gearshafts in the Boeing-Vertol CH-47 forward rotor gearbox and the Bell UH-lD main rotor-drive gearbox. The calculations indicate both logical reasons why noise is generated by these gearboxes at the bevel mesh frequencies and also the effects of typical shaft-bearing system design changes which may be useful for noise reduction at those frequencies. Comparison of predicted vibration amplitudes with measured values can be expected to yield both a qualitative understanding of the noise problem and also verified solution techniques which can be applied to other designs.

During the past several years the problem of helicopter internal noise has become of increasing concern to the U. S. Army as the effects of noise on both health and mission performance became better understood. Active support for efforts to under- stand the sources of. noise and to reduce noise levels in operating helicopter aircraft has been provided by the Eustis Directorate of the U. S. Army Air Mobility Research and Development Laboratory (formerly U. S. Army Aviation Materiel Laboratories). These efforts have been directed at the reduction of noise generated by rotor-drive gearboxes, which are major sources of noise in helicopter aircraft. The primary thrust of these efforts has been at the development and verification of analytical proce- dures for dealing directly with the major causes of gearbox noise at their sources:(1)the deviations from uniform gear rotation (referred to herein as "excitations") which are present in even the high- est quality gears under ncrrmal operating conditions, and (2) the amplification of these deviations by the dynamic properties (torsional and lateral)of the drive train components, resulting in loud- speaker-type behavior of the gearbox casing or even the airframe. A considerable measure of success has been achieved to date in obtaining realistic predictions of the levels of gear mesh excitation and the resulting dynamic behavior of the gearbox components.
Order: #7

7. Rieger, N. F. and Badgley, R. H. , "Flexible Rotor Balancing of a High-Speed Gas Turbine Engine, " SAE Paper No. 720741, presented at the Society of Automotive Engineers National Combined Farm Construction & Industrial Machinery and Powerplant Meetings, Milwaukee, Wisconsin, September, 11-14, 1972.

ABSTRACT: The need for balancing a high-speed rotor in a manner that accounts for its speed-dependent deformations is discussed. The influence coefficient method of flexible rotor balancing is described with reference to the balancing of an advanced gas turbine engine rotor. This engine rotor-bearing system is then studied in detail as an application of flexible rotor bal-ancing, using the influence coefficient method. The relative effectiveness of various combinations of balance speeds and numbers of balance planes is compared...

Order:

8. Gu, A. L. , Pan, C. H. T. and Badgley, R. H. , "Dynamic Stability of Gimbaled Spiral-Grooved Thrust Bearing, " ASME Paper No. 72-Lub-13, presented at the ASME-ASLE International Lubrication Conference, New York, N. Y. , October 9-12, 1972, and published in Trans. ASME, Journal of Lubrication Technology,   Vol. 95, Series F, No. 2, April 1973, p. 222-235.

A general, easily implemented technique is developed by which stability maps may be determined for gimbaled, gas-lubricated, spiral-grooved thrust bearings. This technique is based upon the spectral analysis (frequency domain) method in which the neutrally stable states of the stator-gimbal system are determined through solution of the system's characteristic equations. The method has proven effective for conducting low-cost investigations of the sensitivity of system instability thresholds to changes in various system design parameters. Containing data valid for a wide range of gimbal inertias, stability maps are presented for a range of bearing compressibility numbers, for several bearing geometries, and for several values of mechanical damping in order to illustrate both the power of the technique and also its effectiveness. Limited experimental information which is presently available verified the essential features of the corresponding stability maps. The technique has been reduced to a form usable in the design of gas bearings for use in gas turbine engines.
Order:

9. Chiang, T. and Badgley, R. H. , "Reduction of Vibration and Noise Generated by Planetary Ring Gears in Helicopter Aircraft Transmissions, " ASME Paper No. 72-PTG-11, presented at the Mechanisms Conference and International Symposium on Gearing and Transmissions, San Francisco, CA, October 8-12, 1972, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 95, Series B, November 1973, p. 1149-1158.

Rotor-drive gearboxes are major noise sources in helicopter aircraft. Narrow band examination of this noise often indicates the presence of several or more very high, narrow noise peaks, which are located at gearbox mesh frequencies or their multiples. Important exceptions are sideband noise components, located so near the main signal component as to be indistinguishable except by very narrow band reduction. Noise of this type is most effectively treated through a systematic study of the flow of high-frequency vibration energy in the drive train. Such studies should examine the mechanism by which gear meshes generate vibrations, and the vibration response of the gearbox components which support the gears. Results of such calculations are presented for the planetary reduction ring-gear casing elements in the Boeing-Vertol CH-47forward rotor drive gearbox and the Bell UH-lD main rotor-drive gearbox. The calculations indicate logical reasons why noise is generated. Typical ring-gear casing design changes are examined for noise reduction.
Order: #10

10.  Badgley, R. H. and Rieger, N. F. , "The Effects of Multiplane Balancing on Flexible Rotor Whirl Amplitudes, " SAE Paper No. 730102, presented at the Society of Automotive Engineers International Automotive Engineering Congress and Exposition, Detroit. Michigan, January 8-12, 1973.

ABSTRACT: Influence coefficient balancing of an advanced gas turbine rotor in fluid-film bearings with nonsymmetrical properties has been examined. The effect of the number of balancing planes in use of the quality of balance has been studied with particular attention being paid to the reasons why an increase from three planes to four planes gives no apparent improvement. Effects examined include the influence of nonsymmetrical bearing properties, the effect of having a bending critical speed close to either side of the intended operating speed, and the effect of correction weight errors on balance quality. Reasons why the addition of a fifth balancing plane resulted in a significant improvemen t in balance quality are given.

Order: #11

11.  Badgley, R. H. and Hartman, R. M. , "Gearbox Noise Reduction: Prediction and Measurement of Mesh-Frequency Vibrations Within an Operating Helicopter Rotor-Drive Gearbox, " ASME Paper No. 73-DET-31, presented at the ASME Design Engineering Technical Conference, Cincinnati, Ohio, September 9-12, 1973, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 96, Series B, No. 2, May 1974, p. 567-577.

This paper presents correlations between analysis and test results for a complex mechanical system. While the paper is specificially concerned with a helicopter rotor-drive gearbox, the results and methods employed are general enough to be broadly applicable to gearboxes of all kinds. The development of gearbox noise reduction technology has been the objecti!Ie of an extensive U. S. Army-supported program over the past five years. The gearbox noise problem has been recast as a mechanical vibrations problem, and detailed analytical methods have been developed to treat it. Gear excitation analyses, drive-train response analyses, and empirically-based acoustic spectrum predictiol1 methods have been developed and published in considerable detail. Rolling-element bearing stiffness prediction methods and thin-shell vibration response prediction techniques have been shown to be essential elements in the procedure"!In order to verify the analytical methods, a detailed and comprehensive test prof!. ram was undertaken on a complete CH -47 forward-rotor-drive gearbox, operating under normal torque conditions in a test-cell en- vironment. At the same time, predictions were made of quantities to be measured using the previously publishe{J, analytical methods. Comparisons between predicted and measured quantities show reasonably good correlation, indicating that the analytical procedures are suitable for careful use in gearbox design or redesign efforts directed at vibration and noise reduction. A reas in which the analytical methods can be improved were also identified.
Order: #12

12.  Tessarzik, J. M. and Badgley, R. H. , "Experimental Evaluation of the Exact Point-Speed and Least-Squares Procedures for Flexible Rotor Balancing by the Influence Coefficient Method, " ASME Paper No. 73-DET-115, presented at the ASME Design Engineering Technical Conference, Cincinnati, Ohio, September 9-12, 1973, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 96, Series B, No. 2, May 1974, p. 633-643.

An experimental test program was conducted to extend the verified operating region of the Influence Coefficient Method's Exact Point-Speed procedure for balancing of flexible rotating machinery. Also, the Least-Squares procedure (of which the Exact Point-Speed procedure is a particular case) was applied to several test cases which were identical to those investigated by the Exact Point-Speed procedure. A comparison of the effectiveness of both balancing procedures under identical test conditions was thus obtained. The practical aspects of balancing real, flexible rotors were investigated through inclusion of rotor out-of-roundness data at the measurement probe locations. The computer program was demonstrated to be fully capable of handling out-of-roundness data in the investigation. Testing was performed predominantly with a machine having a 41-in. (104 cm) long, 126-lb (57 kg) rotor. This rotor was operated over a speed range encompassing three rotor-bearing system critical speeds. Both balancing procedures were evaluated for several different conditions of initial rotor unbalance. Safe (and slow) passage through all the critical speeds was obtained after two or three balancing runs in most cases. The Least-Squares procedure was found to be generally equivalent in capability to the Exact Point-Speed procedure for the configurations studied.

Order: #13

13.  Tessarzik, J. M. , Chiang, T. and Badgley, R. H. , "The Response of Rotating Machinery to External Random Vibration, " ASME Paper No. 73-DET-110, presented at the ASME Design Engineering Technical Conference, Cincinnati, Ohio, September 9-12, 1973, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 96, Series B, No. 2, May 1974, p. 477-489.

A high-speed turbogenerator employing gas-lubricated hydrodynamic journal and thrust bearings was subjected to external random vibrations for the purpose of assessing bearing performance in a dynamic environment. The pivoted-pad type journal bearings and the step-sector thrust bearing supported a turbine-driven rotor weighing approximately twenty-one pounds at a nominal operating speed of 36, 000 rpm. The response amplitudes of both the rigid-supported and flexible-supported bearing pads, the gimballed thrust bearing, and the rotor relative to the machine casing were measured with capacitance type disPlacement probes. Random vibrations were applied by means of a large electrodynamic shaker at input levels ranging between 0. 5 g (rms) and 1. 5 g (rms). Vibrations were aPPlied both along and perpendicular to the rotor axis. Response measurements 1eJere analyzed for amplitude distribution and power spectral density. Experimental results compare well with calculations of amplitude power spectral density made for the case where the vibrations were applied along the rotor axis. In this case, the rotor-bearing system was treated as a linear, three-mass model.

Order: #14

14.  Badgley, R. H. , "The Potential Impact of Multiplane-Multispeed Balancing on Gas Turbine Production and Overhaul Costs, " ASME Paper No. 74-GT-94, presented at the ASME Gas Turbine Conference, Zurich, Switzerland, March 31 – April 4, 1974.

This paper describes recent advances in the development of a practical, cost-effective method for balancing, in a single step, a final shaft-bearing assembly simultaneously in a number of planes and at a number of speeds. This method is capable of overcoming assembly-introduced unbalance, and will permit rotor operation through critical speeds in which component elastic axis bending occurs. Detailed results of test efforts are presented in order to illustrate the effectiveness of the method. The procedure by which method may be applied to gas turbine engine shafts, and the potential cost advantages expected to accure therefrom, are described and discussed.

Order: #15

15.  Badgley, R. H. and Tessarzik, J. M. , "Balancing of High-Speed Interconnect Shafting for Operation Above Multiple Bending Critical Speeds, " AHS Paper No. 873, presented at the 30th Annual National Forum of the American Helicopter Society, Washington, D. C. , May 1974.

ABSTRACT: Supercritical shafting has long been considered for use in transmitting power from one point to an-other in aircraft applications. Vibration energy management problems, however, have prevented wide application of this concept. Inability to achieve precise balance levels in a cost-effective manner, coupled with difficulties in extracting residual vibration energy through the use of practical dampers, has led shaft designers to shaft system configurationa which are insensitive to unbalance. Presently operating shafts thus employ many bearings, are larger in diameter than they must be based on torque considerations, and turn at speeds well below those at which they might operate. Desires for cost and weight economies, together with the ever-present need for simple, reliable designs, are forcing drive train designers to seek new methods for achieving order-of-magnitude improvements in shaft balance in order to overcome these difficulties. A method with such capabilities has recently become available as a result of NASA-sponsored vibration reduction technology efforts. This paper describes this proven multiplane balancing method, and illustrates the results of its analytical application to a practical size high-speed drive shaft. The shaft thus treated is predicted to be able to operate at reasonable vibration amplitudes over a speed range encompassing five bending critical speeds with conservatively low values of analytically-specified damping.

 

Order: #16

16.  Badgley, R. H. , "Recent Developments in Multiplane-Multispeed Balancing of Flexible Rotors in the United States, " presented at the Symposium on Dynamics of Rotors, IUTAM, Lyngby, Denmark, August 12-16, 1974.

ABSTRACT: This paper describes current developments in the evolution of a computer-implemented balancing procedure which permits flexible rotors to be precisely balanced in a cost-effective manner. Corrections in virtually any reasonable number of planes, computed by the procedure using signals from vibration sensors at critical locations, permit rotor operation over any design speed range. Steady-state operation at un-damped critical speeds has been demonstrated. Results of recent test efforts indicate that the procedure can be applied with equal effectiveness to rotors of any size. Manufacturing and overhaul cost reductions are expected to flow from its adoption, together with performance advantages from operation in hitherto restricted dynamic regimes.

Order: #17

17. Cundiff, R. A. , Badgley, R. H. and Reddecliff, J. , "Design, Manufacture and Operation of a Dynamic Simulator for Testing Advanced Small Gas Turbine Engine Components, " presented at the Symposium on Propulsion System Structural Integration and Engine Integrity, Monterey, CA, September 6, 1974.

A rotor-bearing system has been designed and manufactured to be dynamically representative of an entire class of gas turbine engines: the two-spool front-drive, power-turbine engine, which is widely used in helicopter applications. The test rig configuration, with the addition of low-pressure compressor and fan simulator disks. would be dynamically representative of the turbojet and turbofan classes of engines, respectively. The simulator has been designed to permit developmental testing and evaluation of a number of advanced components and procedures. Among these are advanced intershaft bearings, rolling-element bearing dampers, and advanced balancing procedures. The apparatus has been utilized to date for initial evaluation of air-lubricated intershaft foil bearings, and for demonstration of an advanced balancing procedure. For these tests, the shaft was operated on elastically-mounted ball bearings without support damping over "a speed range encompassing two bending critical speeds. Rotor balancing via the recently-developed multiplane-multispeed balancing procedure was used to suppress both the first bending critical speed and a pedestal resonance, and to leave a'distinct vibration peak at 'the second bending critical speed. An air-lubricated inte"rshaft foil bearing of the hydrodynamic, resiliently-supported type proved to be capable of raising the second critical speed above the normal operating speed range of the power turbine shaft.

Order: #18

18.  Badgley, R. H. , "Implications of Multiplane-Multispeed Balancing for Future Turbine Engine Design and Cost, " SAE Paper No. 740865, presented at the Society of Automotive Engineers National Aerospace Engineering and Manufacturing Meeting, San Diego, California, October, 1-3, 1974.

ABSTRACT: This paper describes several alternative approaches, provided by multiplane-multispeed balancing, to traditional gas turbine engine manufacture and assembly procedures. These alternatives, which range from addition of trim-balancing at the end of the traditional assembly process to modular design of the rotating system for assembly and balancing external to the engine, require attention by the engine designer as an integral part of the design process. Since multiplane-multispeed balancing may be incorporated at one or more of several points during manufacture-assembly, its deliberate use is expected to provide significant cost and performance (reduced vibration) benefits. Moreover, its availability provides the designer with a firm base from which he may advance, with reasonable assurance of success, into the flexible rotor dynamic regime.

Order: #19 Currently Unavailable

19. Gu, A. L. , Badgley, R. H. and Chiang, T. , "Planet-Pass-Induced Vibration in Planetary Reduction Gears, " ASME Paper No. 74-DET-93, presented at the ASME Design Engineering Technical Conference, New York, NY, October 5-9, 1974.

Order: #20

20. Gu, A. L. and Badgley, R. H. , "Prediction of Vibration Sidebands in Gear Meshes, " ASME Paper No. 74-DET-95, presented at the ASME Design Engineering Technical Conference, New York, NY, October 5-9, 1974.

A computer-implemented analysis has been established for predicting vibratron sidebands produced by variations in gear parameters, such as centerline distance, tooth transmitted force, and tooth support discontinuities for single gear mesh systems The sidebands are normally found at mesh frequency harmonics plus and minus inteqer multiples of the frequency of variation of the gear parameter. The sideband amplitudes depend on the magnitude of variation of the gear parameters. The vibration sideband spectra produced by spiral bevel gear shaft runout, externally imposed tooth mesh force variation, and a decrease in support stiffness over a number of consecutive ring gear teeth have been obtained for gear meshes in the CH-47 helicopter forward rotor drive transmission. This sideband analysis is useful both for designing low-vibration gear systems by properly controlling important gear pararneters and for identifving the existence of several types of gear problems, such as gear runout, drive train resonances, and tooth cracks.

Order: #21 Currently Unavailable

21.  Darlow, M. S. and Badgley, R. H. , "Early Detection of Defects in Rolling Element Bearings, " presented at the Society of Automotive Engineers Automotive Engineering Congress and Exposition, Detroit, Michigan, February 26, 1975.

Order: #22

22.  Badgley, R. H. , "Implications of Multiplane-Multispeed Balancing for Future Turbine Engine Design and Cost, " SAE Paper No. 740865, presented at the Society of Automotive Engineers Automotive Engineering Congress and Exposition, Detroit, Michigan, February 26, 1975 (Re-presentation of paper No. 18 above at SAE request).

Order: #23

23.  Weinert, E. P. and Badgley, R. H. , "Down With Vibration.   Lateral Vibration in Gas Turbines: Let’s Lower It Now, " Gas Turbine International, Vol. 16, No. 1, January-February 1975, p. 58.

Lateral vibration in gas turbines is too high -It's responsible for excessive downtime, forced outages and high corrective maintenance costs. Let's lower it now.

Gas turbine engines are widely used throughout the world. On land, at sea, and in the air they deliver promised performance without fanfare. In some applications they have no peer: in remote locations, severe environments where high horsepower is needed, and for aircraft propulsion, they have no equal.

As gas turbine engine experience grows, the user sees that high availability could be made higher and corrective maintenance cost lower by reducing frequency and severity of interruptions caused or aggravated by lateral vibration. No user nor type of engine design is immune. !, 2 No matter where it occurs - §enerating electric power, 3 performing in process industries, propelling ships, s pumping petroleum crude, natural gas, and refined products, dredging pipe trenches and driving aircraft6 - vibration related shutdown is always unwelcome and failure, costly.

Until a user is able to reflect on enough experience of his own, or that of others having similar engines performing the same function, he has very limited perspective. But experience is available to most if they seek it. It points out, in many ways, that vibration is higher than necessary and the percentage of problems, so caused or aggravated, is too large! Remedial measures with existing engines can lower corrective maintenance downtime and cost.

 

Order: #24

24.  Darlow, M. S. and Badgley, R. H. , "Applications for Early Detection of Rolling-Element Bearing Failures using the High-Frequency Resonance Technique, " presented at the ASME Vibrations Conference, Washington, DC, September 1975.

The High-Frequency Resonance Technique (HFRT) has been demonstrated to be a highly sensitive, accurate procedure for the early identification of impending rolling-element bearing failures. This paper presents the theory behind the HFRT, and describes its application to rolling-element bearing defect analysis. Some HFRT tests results are presented and described in order to illustrate both the procedure and the nature of the HFRT data. The HFRT lends itself to both continuous and periodic testing procedures, and thus can be used in a wide range of rolling-element bearing defect identification situations. Several of these situations are discussed herein, but they by no means exhaust the field of possible applications of the HFRT. In addition, it is noted that the HFRT can be usM not only for identification of defects in rolling-element bearings, but also to identify defects in other dynamic machinery elements, such as gears. The HFRT is felt to be an extremely valuable tool with a potential which is only now beginning to be exploited.

Order: #25

25. Tessarzik, J.M., Badgley, R.H., and Fleming, D.P., "Experimental Evaluation of Multiplane-Multispeed Rotor Balancing Through Multiple Critical Speeds," ASME Paper No. 75-DET-73, presented at the ASME Vibrations Conference, Washington, D.C., September 1975, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 98, Series B, No. 3, August 1976, p.988-998.

Experimental tests have been conducted to further demonstrate the ability of the Influence Coefficient Method to achieve precise balance of flexible rotors of virtually any de-sign for operation through virtually any speed range. Four distinct practical aspects of flexible-rotor balancing were investigated in the present work: (1) Balancing for operation through multiple bending critical speeds; (2) balancing of rotors mounted in both rigid and flexible bearing supports, the latter having significantly different stiffnesses in the horizontal and vertical directions so as to cause severe ellipticity in the vibration orbits; (3) balancing of rotors with various amounts of measured vibration response information (e. g. , numbers of vibration data sets, and numbers and types of vibration sen. sors), and with different number of correction planes; (4) balancing of rotors with different (though arbitrary) initial unbalance configurations. Tests were made on a laboratory quality machine having a 122-cm (48-in. ) long rotor weighing 50 kg (110 Ib) and covering a speed range up to 18, 000 rpm. The balancing method was found in every instance to be effective, practical, and economical, permitting safe rotor operation over the full speed range covering four rotor bending critical speeds...

Order: #26

26.  Badgley, R. H. , Smalley, A. J. and Fleming, D. P. , "Drive Train Dynamics Technology: State-of-the-Art and Design of a Test Facility for Advanced Development, " ASME Paper No. 75-DET-74, presented at the ASME Vibrations Conference, Washington, DC, September 1975.

Mechanical power transfer systems (drive trains) are widely used because of high transfer efficiency, and low cost and weight. Since it is frequently necessary to change the rotational speed and/or the path of the transmitted power, transmissions are a common and critical component of mechanical drive trains. Considerable engineering effort has been expended on gearbox design, often to the relative neglect of the other aspects of drive train design and operation. In particular, except for torsional vibration considerations, little attention has been given to the fact that the drive train, comprising gears, couplings, shafts, bearings, dampers, and clutches, is also rotor-dynamics system which is dynamically coupled with the driving and driven machinery. The result is that drive train for advanced applications increasingly encounter a regime of operation wherein undesirable design compromises or operating deficiencies must be accepted because of an inadequate understanding of drive train dynamics technology. This paper treats briefly the background of flexible dynamic drive-train systems, discusses the present state-of-the-art in several important areas, and finally describes the design characteristics and capabilities of a drive train test facility which is being constructed for advanced development of drive train dynamics technology and components.

Order: #27

27. Tessarzik, J.M., Chiang, T., and Badgley, R.H., "Suppression of Rotor Bearing System Vibrations Through Flexible Bearing Support Damping," ASME Paper No. 75-DET-117, presented at the ASME Vibrations Conference, Washington, D.C., September 1975, and published in Trans. ASME, Journal of Engineering for Industry, Vol. 98, Series B, No. 3, August 1976, p.1053-1061.

A bearing damper, operating on the support flexure of a pivoted pad in a tilting-pad type gas-lubricated journal bearing, has been designed, built, and tested under externally applied random vibrations. A 36, 000 rpm, 10 Kwe turbogenerator had previously been subjected to external random vibrations, and vibration response data had been recorded and analyzed for amplitude distribution and frequency content at a number of locations in the machine. Based upon data from that evaluation, a piston-type damper was designed and developed for each of the two flexibly-supported journal bearing pads (one in each of the two three-pad bearings). A modified turbogenerator, with dampers installed, has been retested under random vibration conditions. Root-mean-square vibration amplitudes were determined from the test data, and displacement power spectral density analyses have been performed. Results of these data reduction efforts have been compared with vibration tolerance limits and previously reported response characteristics of the unmodified machine. Results of the tests indicate significant reductions in vibration levels in the bearing gas-lubricant films, particularly in the rigidly mounted pads. The utility of the gas-lubricated damper for limiting rotor-bearing system vibrations in highspeed turbomachinery has thus been demonstrated.

Order: #28

28. Tessarzik, J.M., Smalley, T.J., and Badgley, R.H., "Testing for Material Dynamic Properties," presented at the ASME Vibration Testing - Instrumentation and Data Analysis Symposium, Washington, D.C., September 17-19, 1975, and published in ASME Symposium Volume AMD-Volume 12, 1975, p.117-141.

Many methods have been developed and applied to study the dynamic behavior of materials in which vibration energy is dissipated. A number of the important methods are reviewed and compared in terms of their applicability to different conditions of amplitude and frequency and the nature of the instrumentation required to implement them. A recently developed base excitatio~ resonant mass test method for elastomer materials is described for the purpose of illustrating various sensors and methods of data acquisition. Since the objective of determining dynamic material properties differs in important respects from the objective of determining performance data for specific components, the nature of typical ·material behavior is also reviewed and the additional constraints which must be imposed on tests designed to provide universally applicable material properties are identified.

Order: #29

29.  Badgley, R. H. and Reddecliff, J. , "Evaluation of a Gas-Lubricated Foil Bearing for Control of Gas Turbine Engine Rotor Critical Speeds, " SAE Paper 751072, presented at the Society of Automotive Engineers National Aerospace Engineering and Manufacturing Meeting, Los Angeles, CA, November 1975.

Order: #30

30.  Badgley, R. H. and Fleming, D. P. , "Rotor Balancing Aids New Gas Turbine Design, " Mechanical Engineering, p. 71, December 1975.

Recent trends in high-speed machinery - of which the gas turbine is a prime example - are toward higher power densities. This means even higher speeds and also higher temperatures, and smaller sizes. In these designs, rotor speeds often penetrate hitherto "forbidden" critical speed regimes, where high vibration is expected. To avoid vibration at these speeds, undesirable design compromises are made, and ultra-precise manufacturing tolerances are specified. In spite of these costly measures, high-speed machinery all too often exhibits high vibration when placed in service. As many as one third of industrial gas turbine outages or unscheduled shutdowns are directly related to vibration. Possibly another third are due to causes aggravated by vibration...

Order: #31

31.  Badgley, R. H. , "Modern Influence Coefficient Techniques for Multiplane Rotor Balancing in the Factory, Test Cell and Field, " Conference Proceedings, Vibrations in Rotating Machinery, I. Mech. E. Conference Publication 1976-9, p. 201, Institution of Mechanical Engineers, London.

SYNOPSIS: Several modern techniques have been developed for performing multiplane-multispeed balancing by the influence coefficient procedure. These techniques include the use of digital minicomputers to control the performance of multiple low-cost spin-up stands in'high-production factory environments, as well as the use of remotely accessed time-sharing computer systems for field balancing and occasional user appli-cations. Significant improvements in balance quality are now achievable, together with manufacturing cost reductions. New machinery is now being designed to take advantage of this new capability.

Order: #32

32.  Badgley, R. H. , "Advanced Rotor Balancing Techniques: A User’s Guide for Factory, Test Cell and Field Applications, " presented at the 5th Turbomachinery Symposium, Texas A&M University, College Station, Texas, October 1976.

SUMMARY: During the past ten years several new methods of performing rotor balancing have corne on the scene. The initial reason for the development of the earliest of these methods, known as ''Modal Balancing", was the need of the steam turbine-generator industry, which produces rotor-bearing systems that are acknowledged to be supercritical. That is, their rotor speeds lie above one or more bending critical speeds eering demand. Precision balancing of truely flexible rotors was the engin-Modal Balancing was the response to this rotor balancing need at a time when neither the existing analytical methods nor the available experimental measure-ment sensors and instruments were sufficiently advanced to perform the job separately. Thus, Modal Balancing combined the then-available techniques for calculating response amplitudes for the various rotor vibrational modes, with then-available instruments for measuring actual installed vibration levels. Particularly difficult was the separation of different modes using the filters-then on the market. Since all vibration data was handled manually, only limited quantities of data could be managed. During the late 1960's and early 1970's, several key advances occurred which made newer balancing methods both desireable and possible. First, other types of rotor-bearing systems began to be designed for supercritical operation. The need for better rotordynamic tools was spotlighted to support these designs, so that today a number of extremely powerful response and stability computer programs are commercially available. These tools can, and are now being used to optimize rotor design from the balancing standpoint...

Order: #33

33.  Smalley, A. J. , Tessarzik, J. M. and Badgley, R. H. , "The Stability of an Asymmetric Rotor in Damped Supports, " ASME Paper No. 78-GT-172, presented at the ASME Gas Turbine Conference, London, England, April 1978.

A general-purpose method of evaluating the stability of an asymmetric flexible rotor, mounted in symmetric damped bearings, is defined. This method evaluates the complex eigenvalues of the rotor system by solving the equations of motion in a rotating coordinate frame. The application of this method to a rotor mounted in tilting-pad bearings is demonstrated. The observed behavior of a number of different rotor configurations is compared with corresponding predictions of stability. For the configurations predicted to be unstable, a distinct and unnegotiable threshold of instability is encountered. The sharpness of this threshold is emphasized by careful balancing at speeds fractionally below the threshold. In a final configuration predicted to be marginally stable, lightly damped resonant behavior, negotiable by balancing, is encountered in the region of the first critical speed.

Order: #34

34.  Badgley, R. H. and Gilbert, J. S. , "Computerized Assessment of Machinery Performance and Health, " presented at the ASME Winter Annual Meeting, San Francisco, CA, December 1978, and published in ASME Symposium Volume BR. H00130, "Diagnosing Machinery Health, " 1978.

ABSTRACT: A number of very important advances have occurred in the last several years in the area of minicomputer hardware and software. Off the shelf computer hardware which can operate in the plant environment now costs no more than the newer analog signal processor instruments, and software now available permits the computer to do virtually automatically all of the data gathering and manipulating steps previously done by hand. Decision-making (diagnosis) software is also now being introduced. As a result, the machinery operator about to update his condition monitoring scheme should investigate the use of the small, on-site computer. This option could very well provide the same data processing power at lower cost than some of the more traditional methods" or for a fixed investment, could provide dramatic improvement in machinery understanding through on-line data analysis and increased flexibility. The low-cost in-plant minicomputer is an engineering tool whose time has come.

Order: #35

35.  Parkinson, A. G. , Darlow, M. S. , Smalley, A. J. and Badgley, R. H. , "An Introduction to a Unified Approach to Flexible Rotor Balancing, " ASME Paper No. 79-GT-161, presented at the ASME Gas Turbine Conference, San Diego, CA, March 1979.

Several successful methods for balancing flexible rotating shafts have been developed In recent years. The methods can apparently be subdivided into a group which is based on modal characteristics and another set which employs influence coefficients. The relative merits of these two approaches have been the subject of much discussion and argument -most of it inconclusive and rather fruitless. The authors consider that, in practice, many of the differences are more apparent than real and that they seem to occur because the various techniques are normally presented in relatively simple and ideal, theoretical terms. This paper represents the start of a Joint project which hopes to resolve the apparent differences and, eventually, develop a unified approach to such balancing. A discussion of the theoretical basis for this unified approach is presented along with a description of a test program conducted to explore the possibilities of such an approach.

Order: #36

36.  Badgley, R. H. , "A Knowledge-Based System Approach to Improved Marine Diesel Engine Condition Assessment, " presented at the Society of Automotive Engineers Government/Industry Meeting & Exposition, Washington, DC, May 1985, and published in Marine Engine Development, SP-625, p. 95-104, Society of Automotive Engineers, Inc. , 400 Commonwealth Drive, Warrendale, PA 15096, May 1985.

Order: #37

37.  Thompson, B. D. and Badgley, R. H. , "Development of an Advanced Hybrid Rotordynamics Model for Vibration Analysis of the Entire Structure of a Marine Gas Turbine Engine, " presented at the Second International Symposium on Transport Phenomena, Dynamics, and Design of Rotating Machinery, and published in Preprints Volume 2: Dynamics, April 1988, p. 212-225.

Order: #38

38.  Thompson, B. D. and Badgley, R. H. , "Application of an Advanced Hybrid Rotordynamics Model to the Complete Structure of a Marine Gas Turbine Engine, " published in Trans. ASME, Journal of Engineering for Gas Turbines and Power, Vol. 110, October 1988, p. 578-584.

Order: #39

39.  Thompson, B. D. , Badgley, R. H. and Raczkowski, R. , "Methods and Procedures for Trim Balancing the LM2500 Marine Gas Turbine in the Test Cell and Aboard Ship, " ASME Paper No. 89-GT-318, presented at the ASME Gas Turbine and Aeroengine Congress and Exposition, Toronto, Canada, June 1989.

ABSTRACT: Extensive fleet experience with LM2500 marine gas turbines shows that engines with higher than normal vibration are more likely to show early wear. Gas generator rotor unbalance has been identified as the main cause of high vibration. Rotor rebalancing reduces vibration to acceptable levels, at the same time reducing or eliminating many wear out modes. Initially, the only rebalance option was to remove the gas generator from the ship and send it to the depot. The high cost of this option led to a search for alternatives, and the successful development of a procedure for rebalancing the gas generator rotor aboard ship. The method adopted was the well known influence coefficient procedure, developed by the National Aeronautics and Space Administration (NASA) in the late 1960's. This method is well suited for implementation on portable computers, and fits readily into a practical procedure for use by trained technicians. The NASA program originally included a procedure to minimize peak residual vibration. Navy engineers added an improved optimizing procedure and a method to account for engine nonlinearities. Rebalancing involves mounting four external accelerometers on the engine, along with a tachometer to give a one-per-rev signal for phase angle measurement. Baseline vibration measurements, together with stored influence coefficients for the LM2500 engine series, permit first shot multi-plane, multi-speed trim correction weights to be calculated. The compressor case is readily opened and the weights installed without disturbing the engine. Application of this procedure has been highly successful: vibration levels of less than 0. 001 inch peak-to-peak over the entire speed range have been achieved. The avoided cost of removal, replacement and repair of an LM2500 is estimated to be about $500, 000.

Order: #40

40.  Badgley, R. H. and Shade, W. A. , "Vibration Analysis for Immediate Assessment of Battle Damaged Gas Turbine Engines, " ASME Paper No. 89-GT-96, presented at the ASME Gas Turbine and Aeroengine Congress and Exposition, Toronto, Canada, June 1989.

Order: #41

41.  Thompson, B. D. , Badgley, R. H. and Hartranft, J. J. , "Experience from Expansion of On-Board Maintenance for Marine Gas Turbines, " ASME Paper No. 89-GT-232, presented at the ASME Gas Turbine and Aeroengine Congress and Exposition, Toronto, Canada, June 1989.

Order: #42

42.  Badgley, R. H. , "A Knowledge-Based Approach to Plant Machinery Condition Based Maintenance, " presented at the First International Conference on Improving Reliability in Petroleum Refineries and Chemical and Natural Gas Plants, Houston, Texas, November 1992.

Machinery system availability strongly affects overall plant availability in the petroleum, chemical, and natural gas industries. Unscheduled or unnecessarily scheduled maintenance actions can result in large lost-production costs. Once failure has occurred, machinery repair costs also can quickly become excessive. However, there are few if any machinery systems in service today or being purchased that cannot be made cost-effectively free of operating failures. This objective may be achieved through the use of new Condition Based Maintenance techniques which are based upon application of an expert system with a comprehensive knowledge base.These tools can diagnose simultaneously all failure modes which can be described in engineering terms.

The ratio of benefits to cost savings achievable by this method is conservatively estimated to be at least six-to-one, and in one case has exceeded more than 100-to-1. Experience now shows that machines with low levels of vibration at all frequencies of interest usually have adequate mechanical integrity -that is they experience little or no mechanical degradation during operation.This is important because vibration is not only a symptom, but is also the root cause of many, if not most,mechanical failures. After excessive mechanical vibrations have been identified and eliminated by a Multi-Frequency Analysis, most failure modes no longer occur. After satisfactory mechanical integrity has been established, then Condition Based Maintenance monitoring can be used to provide early warning of distress in specific internal components. Inplace repairs then are possible, and often are most cost effective, because they allow the machine to be returned to service at the earliest time. New or revised maintenance procedures often result from the improved knowledge of machinery systems condition, further improving the picture.

Order: #43

43.  Badgley, R. H. , "A Knowledge-Base Approach to Safe, High Quality Aircraft Engines and Helicopter Gearboxes, " published in the Institution of Engineers Singapore (IES) Journal, Vol. 35, No. 2, March 1995, p. 54-59, Institution of Engineers, Singapore.

ABSTRACT Engine and gearbox quality, as measured by vibration and other key parameters, strongly affects flight safety and cost of ownership. Unscheduled or unnecessarily scheduled maintenance actions can result in large financial losses due to lack of service availability for commercial aircraft engines, and excessive maintenance-caused downtime for military aircraft. Once failure has occurred, repair costs also can quickly become high because increasing numbers of internal parts are damaged as the failure progresses.

With today's technology, however, there are few if any engines and gearboxes now in service or being purchased that cannot be made virtually free of operating failures in a cost-effective manner. The key is the use of new Condition Based Maintenance techniques, based upon application of an expert system with a comprehensive knowledge base. With such a tool, technicians can diagnose precisely the presence of almost all failure mode precursors.The ratio of benefits to cost savings achievable through this approach is conservatively estimated to be at least six-to-one,and in one case has exceeded 100-to-1. Experience now shows that machines with low levels of vibration at all frequencies of interest usually have adequate mechanical integrity - that is they experience little or no mechanical degradation during operation. This is important because vibration is not only a symptom, but is also the root cause of many, if not most, mechanical failures.

After excessive mechanical vibrations have been identified by a Multi-Frequency Analysis, and eliminated through good engineering practice, most failure modes will no longer occur. After satisfactory mechanical integrity has thus been established, then Condition Based Maintenance monitoring can be used to provide early warning of distress in machinery internal components. In place repairs, where possible, may be most cost effective, because they allow the equipment to be returned to service at the earliest time. New or revised maintenance procedures may also evolve from the improved knowledge of machinery condition, further improving the picture.

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