Full-film hydrodynamic lubrication of marine propulsion shafting journal bearings in running condition is discussed. Considerable computational difficulties in non-linear determining the quasi-static equilibrium of the shafting are highlighted. To overcome this problem the approach using two optimization methods (the particle swarm method and the interior point method) in combination with the specially developed relaxation technique is proposed. The developed algorithm allows to calculate marine propulsion shafting bending with taking into account lubrication in all journal bearings and exact form of journal inside bearings, compared to results of most of the publications which consider lubrication only in the aft most stern tube bearing and assume rest of bearings to be represented by points. The calculation results of typical shafting design with four bearings are provided. The significance of taking into account lubrication in all bearings is shown, specifically more exact values of bearings’ reactions, shafting deflections, minimum film thickness and maximum hydrodynamic pressure in the stern tube bearing in case of considering lubrication in all bearings.
1. Andreau C. Ferdi F. Ville R. et al.: A method for determination of elastohydrodynamic behavior of line shafting bearings in their environment. In Proceedings of ASME/STLE International Joint Tribology Conference San Diego 2007. DOI:10.1115/IJTC2007-44056.
2. Batrak Y.: New CAE package for propulsion train calculations. International conference on computer applications in shipbuilding 3 Vol. 2. (2009). pp. 187–192.
3. Batrak Y. A. Shestopal V. P. Batrak R. Y.: Propeller hydrodynamic loads in relation to propulsion shaft alignment and vibration calculations. Proceedings of the Propellers/Shafting Symposium. 2012.
4. Byrd R. H. Hribar M.E. Nocedal J.: An interior point algorithm for large-scale nonlinear programming. SIAM J Optimization 9(4) (1999) pp. 877–900. DOI:10.1137/S1052623497325107.
5. de Kraker A. Ostayena R. A. J. and Rixen D. J.: Calculation of Stribeck curves for (water) lubricated journal bearings. Tribology International 40 (2007) pp. 459–469. DOI:10.1016/j.triboint.2006.04.012.
6. Gurr C. Rulfs H.: Influence of transient operating conditions on propeller shaft bearings. Journal of Marine Engineering and Technology 7(2) (2008) pp. 3–11. DOI:10.1080/20464177.2008.11020209.
7. Hirani H. Rao T. V. Athre K. et al.: Rapid performance evaluation of journal bearings. Tribology International 30 (11) (1997) pp. 825–834. DOI:10.1016/S0301-679X(97)00066-2
8. Hutchinson J. R.: Shear coefficients for Timoshenko beam theory. Journal of Applied Mechanics 68(1) (2001) pp. 87-92. coefficientsfortimoshenkobeamtheory.
9. Kennedy J. Eberhart R.: Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks Vol 4 (1995) pp. 1942–1948. DOI:10.1109/ICNN.1995.488968.
10. Litwin W.: Water-lubricated bearings of ship propeller shafts - Problems experimental tests and theoretical investigations. Polish Maritime Research 4(62) Vol 16 (2009) pp. 42–50.
11. Litwin W.: Influence of main design parameters of ship propeller shaft water-lubricated bearings on their properties. Polish Maritime Research 4(67) Vol 17 (2010) pp. 39–45.
12. Mourelatos Z.P. Parsons M. G.: Finite-element analysis of elastohydrodynamic stern bearings. SNAME Transactions 93(11) (1985) pp. 225–259.
13. Poli R.: Analysis of the publications on the applications of particle swarm optimisation. Journal of Artificial Evolution and Applications 2008. DOI:10.1155/2008/685175.
14. Przemieniecki J. S.: Theory of matrix structural analysis Dover Publications Inc. New York 1968.
15. Segerlind L. J. (1976). Applied Finite Element Analysis 1 ed. John Wiley and Sons Inc. New York/London/Sydney/Toronto.
16. ShaftDesigner – the shaft calculation software (2018). Retrieved from http://www.shaftdesigner.com/.
17. ShaftDesigner – the shaft calculation software by IMT (2018). Retrieved from http://shaftsoftware.com/.
18. Shi Y. Eberhart R. A.: Modified particle swarm optimizer. 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360) 1998 pp. 69–73. DOI:10.1109/ICEC.1998.699146.
19. Stachowiak G. W. Batchelor A. W.: Engineering tribology Butterworth Heinemann. 2001.
20. Vulic N.: Advanced shafting alignment: Behaviour of shafting in operation. Brodogradnja 52 (2004) pp. 203–212.
21. Waltz R. Morales J. Nocedal J. et al.: An interior algorithm for nonlinear optimization that combines line search and trust region steps. Mathematical Programming 107(3) (2006) pp. 391–408. DOI:10.1007/s10107-004-0560-5.
22. Wright M. H.: The interior-point revolution in optimization: history recent developments and lasting consequences. Bulletin of the American Mathematical Society 42 (2005) pp. 39–56.
23. Xie Z. Rao Z. Ta N. et al.: Investigations on transitions of lubrication states for water lubricated bearing. Part I: determination of friction coefficients and film thickness ratios. 68(3) (2016) pp. 404–415. DOI: 10.1108/ILT-10-2015-0146
24. Xie Z. Rao Z. Ta N. et al.: Investigations on transitions of lubrication states for water lubricated bearing. Part II: further insight into the film thickness ratio lambda. Industrial Lubrication and Tribology 68(3) (2016) pp. 416–429. DOI: 10.1108/ILT-10-2015-0147
25. Xing H. Wu Q. Wu Z. et al.: Elastohydrodynamic lubrication analysis of marine sterntube bearing based on multi-body dynamics. In 2012 International Conference on Future Energy Environment and Materials 2012 pp. 1046–1051. DOI:10.1016/j.egypro.2012.01.167.