Calculation of Free and Forced Lateral Vibrations of a Shaft Line Using Solution Coefficient Vectors

ABSTRACT: In this paper, the free and forced lateral vibrations of a marine propulsion shafting system on anisotropic supports are computed using the vectors of solution coefficients method. The transverse vibrations are considered in two orthogonal planes. The effect of the oil film in the bearings is taken into account. The stern tube bearing is considered as an elastic support of Winkler’s type. The whirling mode shapes for free vibrations of the system were calculated using the algebraic complements according to I.P. Natanson. The results show a decrease in vertical static deformation due to the distributed weight of the shaft line during the operation of the propelling system. This straightening of the propeller shaft explains the increase in the thickness of the oil film in the stern bearing, as observed by naval engineers.

KEYWORDS: Propulsion Shafting Lateral Vibrations, Whirling Mode Shapes, Solution Coefficient Vectors Method, Anisotropic Bearing Supports, Oil Film Stiffness Coefficients, Forced Vibration Response, Natural Frequency Separation Margin, Static Deflection of Shaft Line

REFERENCES

Batrak, Y., Batrak R., Berin D. 2015. Mikhno A., Propulsion shafting whirling vibration: case studies and perspectives. SNAME 14th Propeller and Shafting Symposium, Norfolk, Virginia, USA, September 2015. Paper Number: SNAME-PSS-2015-002. - doi:10.5957/PSS-2015-002

Volcy, G. C. 1978. Interaction and Compatibility Between Machinery and Hull from a Static and Vibratory Point of View. The Society of Naval Architects and Marine Engineers, Ship Vibration Synposium, Arlington, Va., October 16-17,1978.

Bureau Veritas. 2025. BV rules for the classification of steel ships, part C, machinery, electricity, automation and fire protection. Chap. 1, Sec. 9. BureauVeritas, Neuilly-sur-Seine, France, 156.

LIoyd Register of Shipping. 2025. Guidance notes (LR) rules and regulations for the classification of ships. Lloyd’s Register, London, UK.

DetNorskVeritas DNV. 2021. Ship Vibration and Noise.Rules for the Ship Classification.

Zou, D., Rao, Z., TA, N. 2016. Coupled longitudinal-transverse dynamics of a marine propulsion shafting under superharmonic resonances. Journal of sound and vibration. 372, 299-316. - doi:10.1016/j.jsv.2016.03.001

Busquier, S., Martinez, S., Legaz, M.J. 2018. Marine propulsion shafting: A study of whirling vibrations. Progress in Maritime Technology and Engineering, 1st Edition, 2018. - doi:10.1201/9780429505294-28

Kim, YG., Kim, UK. 2020. Design and analysis of the propulsion shafting system in a ship with single stern tube bearing. J Mar Sci Technol 25, 536–548 (2020). ). - doi:10.1007/s00773-019-00659-8

Huang, Q., Zhang, C., Jin, Y., Yuan C., Yan, X. 2015. Vibration analysis of marine propulsion shafting by the coupled finite element method. Journal of Vibroengineering, Vol. 17, Issue 7, 2015, p. 3392-3403.

Zhang, Y., Xu, W., Li Z., He, J. and Yin, L. 2019. Dynamic Characteristics Analysis of Marine Propulsion Shafting Using Multi-DOF Vibration Coupling Model, Shock and Vibration, Volume 2019 |Article ID 5169156 | - doi:10.1155/2019/5169156

Qin, H., Zheng, H., Wenyuan, Q. and Zhang Z. 2019. Lateral vibration control of a shafting-hull coupled system with electromagnetic bearings journal of Low Frequency Noise, Vibration and Active Control 2019, Vol. 38(1) 154–167. - doi:10.1177/1461348418811516

Murawski, L. 2005. Shaft line alignment analysis taking ship construction flexibility and deformations into consideration. Marine Structures 18 (2005) 62–84. - doi:10.1016/j.marstruc.2005.05.002

Murawski, L. 2005. Shaft Line Whirling Vibrations: Effects of Numerical Assumptions on Analysis Results. Marine Technology, Vol. 42, No. 2, April 2005, pp. 53-60. - doi:10.5957/mt1.2005.42.2.53

Myklestad, N. O. 1944. A New Method of Calculating Natural Modes of Vibration of Airplane Wings and Other Types of Beams, J. Aeronaut. Sei., 11, pp. 153-162. - doi:10.2514/8.11116

Kandouci, Ch. and Adjal, Y. 2014. Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients. Journal of Marine Science and Application, (2014) 13: 200-205. - doi:10.1007/s11804-014-1251-0

Hamdi Cherif, Z., Kandouci, Ch. 2020. Dynamic Characteristics of Multi-disk shaft System Using the Vectors of Solution Coefficients, Journal of Mechanical Engineering. Universiti Teknologi MARA (UiTM), Malaysia, 17(3), 2020, 95-115. - doi:10.24191/jmeche.v17i3.15315

Kandouci, C. 2022. Whirling Analysis of Stepped Timoshenko Shaft Carrying Several Rigid Disks. Journal of Mechanical Engineering. Universiti Teknologi MARA (UiTM), Malaysia,19( 2): 97–124. - doi:10.24191/jmeche.v19i2.19767

Kandouci, C, Adjal Y, HamdiCherif, Z, Tayeb, R. 2023. Whirling Analysis of Unbalanced Rotor Using the Vectors of Solution Coefficients. Journal of Vibration and Control. 2024;30(15-16):3659- 3676. doi:10.1177/10775463231198897. - doi:10.1177/10775463231198897

Carlton, J. S. Marine Propellers and Propulsion, 4th Edi.; Butterworth-Heinemann, Elsevier Ltd. Oxford, United Kingdom, 2019; pp. 285-288.

Natanson I., P. Chap. VII. Determinnts. In Short Course in Higher Mathematics; Publishing house Lan, St. Petersburg, 1999; pp: 399-401. (in Russian).

Citation note:

Hamiani A., Boumediene K., Kandouci C.: Calculation of Free and Forced Lateral Vibrations of a Shaft Line Using Solution Coefficient Vectors. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 19, No. 3, doi:10.12716/1001.19.03.39, pp. 1041-1051, 2025

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Authors in other databases:

Ahmed Hamiani: ORCID iD icon

orcid.org/0009-0005-0349-0193

Kadda Boumediene: ORCID iD icon

orcid.org/0000-0002-5569-3022 Scopus icon

57210442613 Scholar icon

5T8DVZ8AAAAJ

Chahreddine Kandouci: ORCID iD icon

orcid.org/0000-0002-7383-8459

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