Study On Several Dynamic Problems Of Shafting System

As important parts of ship power plants,Shafting system is the main source of vibration and noise.With requirements of international Maritime Organization to the noise level of ships turned severer,the purpose of dynamic analysis of shafting is extended from strength check to low level vibration design.In real engineering,according to complexities of the shafting and its supporting system,techanical status of modal test for shafting system,there still exist difficulties for analysing dynamic characteristics of shafting structure.For better understanding and optimization of the dynamic characteristics of the shafting system,development of betternumerical methods and testing procedures are still needed.Surrounding theoretical modelling methods,moving load problems during maching process,model updating and testing methods based on receptance,the following research work has been carried out in this thesis:Based on energy principle,the Fourier Spectral Method(FSM)is employed for vibration analysis of shafting considering the gyroscopic effect.The FSM is an analytical approach with excellent convergence and accuracy.As a kind of analytical method,connecting stiffnesses are intrduced here to analyse shafting system with multi-span.Mass matrix,stiffness matrix and gyroscopic matrix of all corresponding parts including shaft segments,supporting stiffness and lumped masses are derived.Several numerical examples are also presented.By comparing results with those from literatures and calculated using Finite Element Method(FEM),the correctness and convergence of the proposed method are checked.As a kind of analytical method,FSM can hardly be applied to problems with arbitrary shaped strucutres which limited the application range of the proposed method.However,for FEM,such difficulties do not exist.In this thesis,a hybrid FEM-FSM modelling method forvibration analysis of structures with elastic boundaryconditions is proposed.The key point of this method is todivide the whole structure into FEM and FSM zones,andthenfictitiousspringsareintroducedtocoupletwozonesat their interface within the framework of energy principle.Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that thepresent method has good accuracy and efficiency.Further,one irregular-shaped plate also demonstrates the capability of the present method applied to irregular structures.Turning is considered as moving load problem in which the work piece is always established as a beam with conventional boundary conditions such as simply-support and clamped.Such boundary conditions are not accurate enough to study the dynamic characteristics of the work piece under moving turning forces.In this thesis,one rotating workpiece is simplified as a rotating Rayleigh beam with elastic boundary conditions.Beforethis,modal test are conducted on the work piece installed on turning lathe.Modal assurance criterion(MAC)is used to compare the measured mode shapes and the analytical mode shapes numerically.By comparing both the frequencies and mode shapes,the numerical model of the work piece is updated especially the boundary conditions based on 2-norm optimization algorithm.Then,with the upated model,the dynamic characteristics of the rotating work piece under moving load are simulated.The effects of bending moment resulted from the translation of the axial force,speed of the moving load,rotatingspeed of the work piece,initial conditions and gyroscopic effect are analysed.Based on receptance method,one indirect method for measuring the torsional receptance of the shafting system are presented with additional structure attached to one end of the shafting structure.The relationship between translational receptance of the combined structure and the torsional receptance of the shafting system are derived.In order to check the derivation,numerical model of shafting,aditional structure and combined structure are established.Random noise is added to both the nominal parameters of the additional structure and translational receptance during the process of estimating the torsional receptance of the sahfting with Monte-Carlo procedure.From the simulation results,in consequence of the random noise added,bending frequencies appeared in the torsional receptance which is abnormal.Such special phenomen are analysed both theoretically and numerically.Then,procedures to identify such special peaks are also given.Finally,one experiment rig with two disks and two bearings including additional structure are designed and manufactured.With one hamer and several acceleration sensors,translational receptance of the combined structure are obtained.After this,with the proposed indirect torsional receptance measurement method,the torsional vibration receptance of the shafting are estimated.It can be seen from the experimental results that the proposed method can be used to estimate the torsional receptance with enough accuracy,which can be used to update models,conduct structural identification and diagnosis,make structural modifications or carry out vibration control of real rotating machineries.