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

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Order: #9

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.

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