Abstract
This study models a 3-dimensional planetary gear system using the transfer matrix method. The local transfer matrices between each component of the planetary gear set were derived with consideration of the tooth width, and the transfer matrix of a planetary gear system corresponding to the inertial transfer matrix was determined. The eigenvalue analysis of the transfer matrix suggested an analysis method in the form of a lambda matrix, instead of the direct search method through a characteristic polynomial. The boundary conditions at the first and the last stations of the entire transfer matrix were partitioned into known and unknown values to generate a concentrated transfer matrix and a latent equation, and the eigenvalue problem in the lambda matrix was solved. The characteristics of the responses according to the phase state of the harmonic component of the transmission error were reviewed through the steady-state response and mode shape type.
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References
D. H. Hibner, Dynamic response of viscous damped multi shaft jet engine, Journal of Aircaft, l12 (4) (1975) 305–312.
A. Kahraman, Load sharing characteristics of planetary transmissions, Mechanisms and Machine Theory, 29 (8) (1994) 1151–1165.
A. Kahraman, Planetary gear train dynamics, Journal of Mechanical Design, 116 (3) (1994) 713–720.
J. Lin and R. G. Parker, Planetary gear parametric instability caused by stiffness variation, Journal of Sound and Vibration, 249 (1) (2002) 129–145.
M. Botman, Epicyclic gear vibration, Journal of Manufacturing science and Engineering, 98 (3) (1976) 811–815.
A. Saada and P. Velex, An extended model for the analysis of the dynamic behavior of planetary trains, Journal of Mechanical Design, 117 (2A) (1995) 241–247.
P. Sondkar and M. Tech, Dynamic modeling of double-helical planetary gear sets, The Ohio State University (2012).
C. G. Cooley and R. G. Parker, Unusual gyroscopic system eigenvalue behavior in high-speed planetary gears, Journal of Sound and Vibration, 332 (2013) 1820–1828.
Y. Zhang, Q. Wang, H. Ma, J. Hung and C. Zhao, Dynamic analysis of three-dimensional helical geared rotor system with geometric eccentricity, Journal of Mechanical Science and Techology, 27 (11) (2013) 3231–3242.
J. W. Daws, An analytical investigation of three-dimensional vibration in gear-coupled rotor system, Virginia Polytechnic Institute and State University (1979).
N. G Park, An analytical investigation of geared system dynamics containing spur and helical gears, North Carolina State University (1987).
S. T Choi and S. Y. Mau, Dynamic analysis of geared rotorbearing systems by the transfer matrix method, Transactions of the ASME, 123 (4) (2001) 562–568.
T. R. Griffin, Computer-aided design software for torsional analysis, Virginia Polytechnic Institute and State University (1998).
T. Yamamoto and Y. Ishida, Linear and nonlinear rotordynamics, Wiley (2001).
K. Umezawa, T. Suzuki and H. Houjoh, Estimate of vibration of power transmission helical gear by means of performance diagrams on vibration, JSME International Journal Series III, 31 (3) (1988) 598–605.
R. Parker and J. Lin, Mesh phasing relationships in planetary and epicyclic gears, Journal of Mechanical Design, 126 (2) (2004) 365–370.
J. S. Rao, Rotor dynamics, New York, Wiley (1983).
D. Kim and J. W. David, An improved method for stability and damped critical speeds of rotor-bearing systems, Journal of Vibration and Acoustics, 112 (1) (1990) 112–118.
P. Lancaster, A fundamental theorem on lambda matrix with applications ordinary differential equations with constant coefficients, Linear Algebra and its Applications, 18 (3) (1977) 189–211.
C. W. Lee, Vibration analysis of rotors, Kluwer Academic Publishers (1993).
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Recommended by Associate Editor Cheolung Cheong
Jeong Su Kim was born in Korea on August 25, 1987. He is under Ph.D. degree course of Department of Mechanical Design Engineering, Pusan National University. He received his master degree in Department of Mechanical Design Engineering, Pusan National University. He is interested in geared system design and dynamic characteristic.
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Kim, J.S., Park, N. & Lee, H. Vibration analysis of a planetary gear system based on the transfer matrix method. J Mech Sci Technol 30, 611–621 (2016). https://doi.org/10.1007/s12206-016-0115-8
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DOI: https://doi.org/10.1007/s12206-016-0115-8