Study On Dynamical Behaviour Of Complex Rotor Systems

Study on Dynamic Behaviour of Complex Rotor SystemsLarge assembled centrifugal compressor units are comprised of multi-parallel rotor bearing system, which are dynamic coupled by gear box and coupling. With the development of compressor units towards to high speed, maximization and complication, it's necessary to research the rotor-bearing system dynamic behavior for improving the system stability, security and reliability.On the background of rotor dynamic modeling and solution of large assembled centrifugal compressor units, this thesis studies on several aspects, such as, the model and algorithm of turbulent nonlinear oil-film forces and their Jacobian matrices, the model of tilting pad journal bearing, the model and nonlinear solution of complicated rotor bearing systems. Some achievements are acquired by current research from theory and practice, and conclusions that are reached are beneficial to study on the behavior of rotor-bearing system and engineering applications.In detail, there are the following achievements and contents in current research.(1) Based on the variational inequality of general quasilinear elliptic partial differential equation in free boundary condition, a kind of model with an efficient algorithm is presented to get the nonlinear oil-film force and its Jacobian matrices by solving turbulent Reynolds equation. Considering the condition of bearing side-pressure not equal to zero, the proper oil-film pressure function is chosen in the form of multiplier of weight function and linear interpolation function, and one-dimensional discrete variational inequality of turbulent Reynolds equation is built up. An amendatory direct-method is proposed to solve the oil-film force and its Jacobian matrices. During the process, the operations are restricted within the positive pressure region, and no iteration is involved.(2) Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model as well as mathematical method which contains 2n+2 degrees of freedom is presented for calculating the dynamical characteristics of tilting pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement and generalized force vector are chosen. The concise transformation of generalized displacement, generalized force and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using Newton-Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration.(3) The dynamic model of gear-coupled multi parallel rotor is presented using the finite element method. A method of quadratic normal reduction is presented for complex dynamic system with local nonlinearities. The degrees of freedom are reduced and the equivalent system is obtained by quadratic normal reduction and the effects of local nonlinear forces in the modal transformation are considered. Meanwhile the supporting shooting method is proposed to solve the periodic responses and the stability is determined by the Floquet theory. When the response is unstable, the long-term response is obtained by direct numerical integration method.(4) The relevant program of current algorithm is developed. The linear and nonlinear dynamic behaviors are calculated for the industrial rotor system supported by tilting-pad journal bearing and one industrial assembled PTA centrifugal compressor train. The efficiency and reliability of the model and algorithm in this thesis is proven.