0
TECHNICAL PAPERS

Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

[+] Author and Article Information
Rafiq Maliha, Can U. Doǧruer

Mechanical Engineering Department, Middle East Technical University, Ankara 06531, Turkey

H. Nevzat Özgüven

Mechanical Engineering Department, Middle East Technical University, Ankara 06531, Turkeye-mail: ozguven@metu.edu.tr

J. Mech. Des 126(3), 534-541 (Sep 01, 2003) (8 pages) doi:10.1115/1.1711819 History: Received February 01, 2003; Revised September 01, 2003
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Özgüven,  H. N., and Houser,  D. R., 1988, “Mathematical Models Used in Gear Dynamics—A Review,” J. Sound Vib., 123, pp. 383–411.
Blankenship, G. W., and Singh, R., 1992, “A Comparative Study of Selected Gear Mesh Interface Dynamic Models,” ASME Proceedings of the 6th International Power Transmission and Gearing Conference, Phoenix, pp. 137–146.
Velex, P., 1993, “Modélisation du Comportement Dynamiques des Transmissions par Engrenages,” Comportement Dynamique et Acoustique des Transmissions par Engrenages, Chapter 2, CETIM, pp. 39–35.
Seireg, A., 1966, “Whirling of Shafts in Geared System,” American Society of Mechanical Engineers Paper 66-WA/MD-6.
Johnson,  D. C., 1962, “Modes and Frequencies of Shafts Coupled by Straight Spur Gears,” J. Mech. Eng. Sci., 4, pp. 241–250.
Iiada,  H., Tamura,  A., Kikuch,  K., and Agata,  H., 1980, “Coupled Torsional-Flexural Vibration of a Shaft in a Geared System of Rotors (1st Report),” Bull. JSME, 23, pp. 211–2117.
Iiada, H., and Tamura, A., 1984, “Coupled Torsional-Flexural Vibration of a Shaft in a Geared System,” Proceedings of the Conference on Vibration in Rotating Machinery, Institution of Mechanical Engineers, pp. 67–72.
Iiada,  H., Tamura,  A., and Oonishi,  M., 1985, “Coupled Dynamic Characteristics of a Counter Shaft in a Geared Train System,” Bull. JSME, 28, pp. 2694–2698.
Iiada,  H., Tamura,  A., and Yamamoto,  H., 1986, “Dynamic Characteristics of Gear Train System with Softly Supported Shafts,” Bull. JSME, 29, pp. 1811–1816.
Iwatsubo,  T., Arii,  S., and Kawai,  R., 1984, “Coupled Lateral-Torsional Vibration of Rotor System Trained by Gear (1st Analysis by Transfer Matrix Method),” Bull. JSME, 27, pp. 271–277.
Neriya, S. V., Bhat, R. B., and Sankar, T. S., 1985, “Vibration of a Geared Train of Rotors with Torsional-Flexural Coupling,” American Society of Mechanical Engineers, 85-DET-124.
Neriya,  S. V., Bhat,  R. B., and Sankar,  T. S., 1985, “Coupled Torsional-Flexural Vibration of a Geared Shaft System by Using finite Element Analysis,” Shock Vib. Bulletin, 55, pp. 13–25.
Özgüven,  H. N., and Özkan,  Z. L., 1984, “Whirl Speeds and Unbalance Response of Multibearing Rotors Using Finite Elements,” ASME J. Vibr. Acoust. Stress, Reliab. Des., 106, pp. 72–79.
Kahraman,  A., Özgüven,  H. N., Houser,  D. R., and Zakrajsek,  J. J., 1992, “Dynamic Analysis of Geared Rotors by Finite Elements,” ASME J. Mech. Des., 114, pp. 507–514.
Velex,  P., and Mataar,  M., 1996, “A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behavior,” J. Sound Vib., 191, pp. 629–660.
Lin,  H. H., Towsend,  D. P., and Oswald,  F. B., 1993, “Prediction of Gear Dynamics Using Fast Fourier Transform of Static Transmission Error,” Mech. Struct. Mach., 21(2), pp. 237–260.
Lin,  H. H., Towsend,  F. B., and Towsend,  D. P., 1994, “Dynamic Loading of Spur Gears with Linear or Parabolic Tooth Profile Modifications,” Mech. Mach. Theory, 29(8), pp. 1115–1129.
Blankenship,  G. W., and Singh,  R., 1995, “A New Gear Mesh Interface Dynamic Model to Predict Multi-Dimensional Force Coupling and Excitation,” Mech. Mach. Theory, 30(1), pp. 43–57.
Blankenship,  G. W., and Singh,  R., 1995, “Dynamic Force Transmissibility in Helical Gear Pairs,” Mech. Mach. Theory, 30(3), pp. 323–339.
Vinayak,  H., Singh,  R., and Padmanabhan,  C., 1995, “Linear Dynamic Analysis of Multi-Mesh Transmissions Containing External Rigid Gears,” J. Sound Vib., 185(1), pp. 1–32.
Vinayak,  H., and Singh,  R., 1998, “Multi-Body Dynamics and Modal Analysis of Compliant Gear Bodies,” J. Sound Vib., 210(2), pp. 171–214.
Kahraman,  A., 1994, “Dynamic Analysis of a Multi-Mesh Helical Gear Train,” ASME J. Mech. Des., 116, pp. 706–712.
Vinayak, H., and Singh, R., 1996, “Linear Dynamic Analysis of Multi-Mesh Transmissions Containing External, Compliant Gears,” ASME Proceedings of the 7th International Power Transmission and Gearing Conference, San Diego, pp. 535–541.
Lim, T. C., and Houser, D. R., 1997, “Dynamic Analysis of Layshaft Gears in Automotive Transmission,” Proceedings of SAE Noise and Vibration Conference, pp. 739–749.
Lim,  T. C., and Li,  J., 1999, “Dynamic Analysis of Multi-Mesh Counter-Shaft Transmission,” J. Sound Vib., 219(5), pp. 905–919.
Raclot,  J. P., and Velex,  P., 1999, “Simulation of the Dynamic Behavior of Single and Multi-stage Geared System with Shape Deviations and Mounting Errors by Using Spectral Method,” J. Sound Vib., 220(5), pp. 861–903.
Munro, R. G., 1962, “Dynamic Behavior of Spur Gears,” Ph.D. Dissertation, Cambridge University.
Kubo,  A., Yamada,  K., Aida,  T., and Sato,  S., 1972, “Research on Ultra High Speed Gear Devices (Reports 1–3),” Trans. Jpn. Soc. Mech. Eng., 38, pp. 2692–2715.
Baud,  S., and Velex,  P., 2002, “Static and Dynamic Tooth Loading in Spur and Helical Geared Systems—Experiments and Model Validation,” ASME J. Mech. Des., 124, pp. 834–846.
Kahraman,  A., and Blankenship,  G. W., 1997, “Experiments on Nonlinear Dynamic Behavior of an Oscillator with Clearance and Periodically Time-Varying Parameters,” ASME J. Appl. Mech., 64, pp. 217–226.
Kahraman,  A., and Singh,  R., 1990, “Nonlinear Dynamics of a Spur Gear Pair,” J. Sound Vib., 142(1), pp. 49–75.
Kahraman,  A., and Singh,  R., 1991, “Nonlinear Dynamics of a Geared Rotor-Bearing System with Multiple Clearances,” J. Sound Vib., 144(3), pp. 469–506.
Kahraman,  A., and Singh,  R., 1991, “Interactions Between Time-Varying Mesh Stiffness and Clearance Nonlinearities in a Geared System,” J. Sound Vib., 146(1), pp. 135–156.
Özgüven,  H. N., and Houser,  D. R., 1988, “Dynamic Analysis of High Speed Gears by Using Loaded Static Transmission Error,” J. Sound Vib., 125(1), pp. 71–83.
Özgüven,  H. N., 1991, “A Nonlinear Mathematical Model for the Dynamic Analysis of Spur Gears Including Shaft and Bearing Dynamics,” J. Sound Vib., 145(2), pp. 239–260.
Blankenship,  G. W., and Kahraman,  A., 1994, “Steady State Force Response of a Mechanical Oscillator with Combined Parametric Excitation and Clearance Type Nonlinearity,” J. Sound Vib., 185, pp. 734–765.
Kahraman,  A., and Blankenship,  G. W., 1996, “Interactions Between Commensurate Parametric and Forcing Excitations in a System with Clearance,” J. Sound Vib., 194, pp. 317–335.
Budak, E., and Özgüven, H. N., 1990, “A Method for Harmonic Reponses of Structures with Symmetrical Nonlinearities,” Proceedings of the 15th International Seminar on Modal Analysis and Structural Dynamics, Leuven, Belgium, Vol. 2, pp. 901–915.
Budak,  E., and Özgüven,  H. N., 1993, “Iterative Receptance Method for Determining Harmonic Response of Structures with Symmetrical Nonlinearities,” Mech. Syst. Signal Process., 7(1), pp. 75–87.
Tanrikulu,  Ö., Kuran,  B., Özgüven,  H. N., and İmregün,  M., 1993, “Forced Harmonic Response Analysis of Nonlinear Structures Using Describing Functions,” American Institute of Aeronautics and Astronautics, 31(7), pp. 1313–1320.
Houser, D. R., 1990, “Gear Noise Sources and Their Prediction by Using Mathematical Models,” SAE Gear Design, Manufacturing and Inspection Manual, Chap. 16, pp. 213–283.
Maliha, R., 1994, “Nonlinear Dynamic Analysis of Geared Rotors to Internal Excitation by Using Describing Functions and Finite Elements Methods,” Ph.D. Dissertation, Middle East Technical University, Ankara, Turkey.
Royston,  T. J., and Singh,  R., 1996, “Periodic Response of Mechanical Systems with Local Nolinearities Using an Enhanced Galerkin Technique,” J. Sound Vib., 194(2), pp. 243–263.
Cipra,  R. J., and Uicker,  J. J., 1981, “On the Dynamic Simulation of Large Non-linear Systems, Part 1: An Overview of the Simulation Technique Substructuring and Frequency Domain Considerations,” ASME J. Mech. Des., 103, pp. 849–856.
Cipra,  R. J., and Uicker,  J. J., 1981, “On the Dynamic Simulation of Large Non-linear Systems, Part 2: The Time Integration and Time Response Loop,” ASME J. Mech. Des., 103, pp. 857–865.
Ren,  Y., and Beards,  C. F., 1994, “A New Receptance Based Perturbative Multi-Harmonic Balance Method for the Calculation of the Steady State Response of Nonlinear Systems,” J. Sound Vib., 172(5), pp. 593–604.
Özgüven,  H. N., 1987, “A New Method for Harmonic Response of Nonproportionally Damped Systems Using Undamped Modal Data,” J. Sound Vib., 117, pp. 313–338.

Figures

Grahic Jump Location
Generic model of experimental gear system used in Case Study 2
Grahic Jump Location
A typical geared rotor system
Grahic Jump Location
Dynamic model of a spur gear mesh interface
Grahic Jump Location
Generic model of Kubo’s experimental gear system used in Case Study 1
Grahic Jump Location
Loaded static transmission error used in Case Study 1
Grahic Jump Location
Comparison of the computational results obtained by NLGRD with Kubo’s experimental results. Upper and lower bounds of Kubo’s experimental results –, NLGRD —— .
Grahic Jump Location
Comparison of the computational results obtained by NLGRD with those obtained by DYTE for Kubo’s experimental system. DYTE –, NLGRD —— .
Grahic Jump Location
Comparison of the computational results obtained by NLGRD with the experimental results of Kahraman and Blankenship. Experimental results ▵, NLGRD – .

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In