Effect of Coupled Torsional and Transverse Vibrations of the Marine Propulsion Shaft System

Abstract

In this study, the coupled torsional–transverse vibration of a propeller shaft system owing to the misalignment caused by the shaft rotation was investigated. The proposed numerical model is based on the modified version of the Jeffcott rotor model. The equation of motion describing the harmonic vibrations of the system was obtained using the Euler–Lagrange equations for the associated energy functional. Experiments considering different rotation speeds and axial loads acting on the propulsion shaft system were performed to verify the numerical model. The effects of system parameters such as shaft length and diameter, stiffness and damping coefficients, and cross-section eccentricity were also studied. The cross-section eccentricity increased the displacement response, yet coupled vibrations were not initially observed. With the increase in the eccentricity, the interaction between two vibration modes became apparent, and the agreement between numerical predictions and experimental measurements improved. Given the results, the modified version of the Jeffcott rotor model can represent the coupled torsional–transverse vibration of propulsion shaft systems.

Keywords

Coupled torsional–transverse vibrations / Forced vibrations / Marine propulsion shaft system / Cross-section eccentricity / Jeffcott rotor / Coupled vibration in rotor system

References

[1] Al-Bedoor BO. Modeling the coupled torsional and lateral vibrations of unbalanced rotors. Comput Methods Appl Mech Eng, 2001, 190(45): 5999-6008

[2] Chahr-Eddine K, Yassine A. Forced axial and torsional vibrations of a shaft line using the transfer matrix method related to solution coefficients. J Mar Sci Appl, 2014, 13: 200-205

[3] Das AS, Dutt JK, Ray K. Active control of coupled flexural-torsional vibration in a flexible rotor–bearing system using electromagnetic actuator. Int J Non-Linear Mech, 2011, 46(9): 1093-1109

[4] Friswell M, Penny J, Garvey S, Lees A. Dynamics of rotating machines, 2010, Cambridge: Cambridge University Press

[5] Gayen D, Chakraborty D, Tiwari R. Whirl frequencies and critical speeds of a rotor-bearing system with a cracked functionally graded shaft–Finite element analysis. Eur J Mech A Solids, 2017, 61: 47-58

[6] Gayen D, Chakraborty D, Tiwari R. Free vibration analysis of functionally graded shaft system with a surface crack. J Vib Eng Technol, 2018, 6: 483-494

[7] Gayen D, Tiwari R, Chakraborty D. Static and dynamic analyses of cracked functionally graded structural components: a review. Compos B Eng, 2019, 173: 106982

[8] Han H, Lee K. Experimental verification for lateral-torsional coupled vibration of the propulsion shaft system in a ship. Eng Fail Anal, 2019, 104: 758-771

[9] Han H, Lee K, Jeon SH, Park S. Lateral-torsional coupled vibration of a propulsion shaft with a diesel engine supported by a resilient mount. J Mech Sci Technol, 2017, 31(8): 3727-3735

[10] Hashemi SM, Richard MJ. A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams. Aerospace Sci Technol, 2000, 4(1): 41-55

[11] He X, Shi J, He W, Sun C. Boundary vibration control of variable length crane systems in two-dimensional space with output constraints. IEEE/ASME Trans Mechatron, 2017, 22(5): 1952-1962

[12] He W, Wang T, He X, Yang LJ, Kaynak O. Dynamical modeling and boundary vibration control of a rigid-flexible wing system. IEEE/ASME Trans Mechatron, 2020, 25(6): 2711-2721

[13] Hong J, Yu P, Ma Y, Zhang D. Investigation on nonlinear lateral-torsional coupled vibration of a rotor system with substantial unbalance. Chin J Aeronaut, 2020, 33(6): 1642-1660

[14] Hua C, Cao G, Rao Z, Ta N, Zhu Z. Coupled bending and torsional vibration of a rotor system with nonlinear friction. J Mech Sci Technol, 2017, 31(6): 2679-2689

[15] Huang Q, Yan X, Wang Y, Zhang C, Wang Z. Numerical modeling and experimental analysis on coupled torsional-longitudinal vibrations of a ship's propeller shaft. Ocean Eng, 2017, 136: 272-282

[16] Huang Q, Yan X, Zhang C, Zhu H. Coupled transverse and torsional vibrations of the marine propeller shaft with multiple impact factors. Ocean Eng, 2019, 178: 48-58

[17] Mohiuddin MA, Khulief YA. Coupled bending torsional vibration of rotors using finite element. J Sound Vib, 1999, 223(2): 297-316

[18] Murawski L. Axial vibrations of a propulsion system taking into account the couplings and boundary conditions. J Mar Sci Technol, 2004, 9: 171-181

[19] Murawski L. Shaft line alignment analysis taking ship construction flexibility and deformations into consideration. Marine Structure, 2005, 18(1): 62-84

[20] Papadopoulos CA. The strain energy release approach for modeling cracks in rotors: a state of the art review. Mech Syst Signal Process, 2008, 22(4): 763-789

[21] Qu Y, Su J, Hua H, Meng G. Structural vibration and acoustic radiation of coupled propeller-shafting and submarine hull system due to propeller forces. J Sound Vib, 2017, 401: 76-93

[22] Rao MA, Srinivas J, Rama Raju VBV, Kumar KVSS. Coupled torsional-lateral vibration analysis of geared shaft systems using mode synthesis. J Sound Vib, 2003, 261(2): 359-364

[23] Shi L, Xue D, Song X. Research on shafting alignment considering ship hull deformations. Mar Struct, 2010, 23(1): 103-114

[24] Tiwari R. Rotor systems: analysis and identification, 2017, Boca Raton: CRC Press

[25] Yang Y, Che C, Tang W. Shafting coupled vibration research based on wave approach. J Shanghai Jiao Tong Univ (Science), 2014, 19(3): 325-336

[26] Yuan Z, Chu F, Lin Y. External and internal coupling effects of rotor's bending and torsional vibrations under unbalances. J Sound Vib, 2007, 299(1–2): 339-347

[27] Zhang Z, Zhang Z, Huang X, Hua H. Stability and transient dynamics of a propeller-shaft system as induced by nonlinear friction acting on bearing-shaft contact interface. J Sound Vib, 2014, 333(12): 2608-2630