Study On Gyroscopic Vibration Of Propulsion Shafting And Vibration Characteristics Of The Supporting Structures

The propulsion shafting is one of the most important components of a ship’s powerdevice, and the noise and vibration prediction and control of the shafting and its coupledstructure with cylindrical shell is a very important research project in ship engineering. Forthe gyroscopic moment because of the rotation cantilever propeller and the effectivesupported stiffness and location of the stern bearing, developing the precise dynamic models,and studying the influence to the shafting and the coupled structure will be of great theoreticalsignificance and applied value. Surrounding the gyroscopic effect of the propulsion shafting,the dynamic characteristics of the stern bearing, and the influence of the cantilever propellerto the shafting, the coupled vibration problem of the shafting and cylindrical shell, thedetailed research work has been carried out in this thesis as follows:The dynamic analysis model of the shafting’s gyroscopic vibration is established usingthe Fourier Series Expanded Method based on the Euler-Bernoulli beam theory. Thecorrectness of the application of the method is validated by comparing with the resultsobtained by published papers and FEA model. Through the introduction of Dirac deltafunction, considering the propeller as a lumped mass and analyzing its gyroscopic moment,the governing differential equation of the shafting with lumped mass and gyroscopic effect isobtained and a standard matrix eigenvalue problem for gyroscopic vibration can be developedusing the orthogonal of trigonometric functions. The gyroscopic dynamic response in timedomain under harmonic or arbitrary load is obtained using the Newmark numericalstep-by-step integration method. The accurate and efficient of the method is validated bycomparing with the results obtained by published papers, National Standard and FEA model.The method which is based on theory of continuous system can solve natural characteristicsand forced responses of gyroscopic vibration of shafting with elastic-surpport boundaryconditions, various section areas and multi-span.Based on the Reynolds equation, the calculating approach of eight dynamic parametersabout stiffness and damp of infinite long and short bearing is deduced through the impedancerelationship using the oil film thickness of misaligned journal bearing. Combining theimpedance relationships of the infinite long and short bearing, the calculating formulas ofstiffness and damp of finite long bearing are derived using an experiential impedancerelationship for the finite long bearing. And the effective supported stiffness and location areobtained. The correctness of the method is validated by comparing with the results ofmaximal oil film pressure obtained by published papers with difference misalignments. Andthe influences of the misalignment to the lubricating characteristics, the effective supported stiffness and location of the journal bearing and to the gyroscopic vibration of shafting areanalyzed.The in-plane free vibration model of multi-span curved beam system with elasticllysupported and connected boundary condition is established using the two-dimentional FourierSeries Expanded Method. According to the enegy principle, the in-plane vibrationdisplacements along radial and tangent directions are both expressed as the superposition of adouble Fourier cosine series and four supplementary functions in the form of the product of apolynomial fuction. The use of these supplementary functions is to overcome thediscontinuity problems of the elastic boundary conditions. And a standard matrix eigenvalueproblem about the unknow displacement amplitude coefficients is derived through solving theHamilton’s equation using the Rayleigh-Ritz Method and the natural frequencies and modeshapes of multi-span curved beams can be solved. At the same time, the contribution of otherdistributed and lumped parameters to the whole mass and stiffness matrix is considered. Theresults of two-span curved beams with free, simple supported, clamped and elasticllysupported boundary conditions are obtained and compared with the results got from the FEMmodel to validate the correctness of the present method. And the effect of curvature andconnecting stiffnesses between two-span curved beams on the vibration frequencies isdescribed.The vibration of cylindrical shell with elasticlly supported boundary conditions is solvedthrough introducing the wave propagation method. The method is applied to the cylindricalshell with traditional boundary conditions. And the wave number along the axial direction issolved using the governing equation directly rather than solved from beam structures havingthe same boundary conditions with the shell used by the most papers. Applying to the elasticboundary conditions, the accurate of the method is validated by comparing with the resultsobtained by published papers and FEA model through considering the classical homogeneousboundary conditions as the special cases when the stiffness for each set of springs is equal toeither infinity or zero. The influence of the elasticlly supported along various directions to thevibration of the cylindrical shell is studied.The vibration characteristic of coupled structure of the beam and its supportedcylindrical shell is worked out using the Mechanical Impedance Synthesis Method. The basicconcept the mechanical impedance are introduced firstly, and the methods used formulti-coordinate, coupled substructures under harmonic load are analyzed. The impedanceexpressions in frequency domain of the multi-span beam system with elastic boundaryconditions and the cylindrical shell with shear diaphragm-shear diaphragm (SD-SD) boundary conditions under harmonic load are obtained, and the results of the harmonic responses arevalidated accurate compared with the results calculated from FEA models. The approach isfirst used to determine the modal properties of a double-deck beam system consisting of twobeams coupled in parallel, which serves to both validate the substructure synthesis techniqueand demonstrate the versatility of the beam substructure in contrasting to its seeminglylimited face value. The vibrational responses of a coupled beam-cylindrical shell system arethen used to validate the current solution technique and to study the effects of modifying somemodel parameters.Finally, an experimental system is designed to quantitative analyze the influence ofelastic deformation to gyroscopic vibration of the shafting. Through mass ratio of thepropeller to the whole shafting design, inertia ratio of the equivalent radius of propeller to themaster radius of shafting design and length-radius ratio of length to master radius of shaftingdesign, and the dynamic design setting the location of the bearing, the system could make ananalogy to the shafting. Various experimental measurement works are performed throughresizing the vertical location of the stern bearing in order to describe the influence of elasticdeformation to gyroscopic vibration of the shafting.