Nonlinear Dynamical Behaviors Of The Coupling Blade-Rotor-Bearing System

Nowadays, in the practical design, rotating systems become lighter and more flexible with higher operating speed, and the flexibilities of the blade and rotor are close to each other in some situations. The working rotating speed of the rotor is often above the critical speed, and many rotating components, which may be assumed to be rigid at the low speed, should to be considered to be elastic components which may couple to the rotor vibration as the rotating speed is getting higher. Actually, an effective modeling strategy that addresses the interaction between the rotor and the blade is crucial in estimating system performance.On the other hand, improving the parameters of the rotating machinery, the effect of the nonlinear factor on the behavior of the rotor is more significantly. The journal bearing is one of the necessary components of the rotating machine, and the nonlinear oil film force of the journal bearing is one of the nonlinear factors in the rotor system and can cause the occurrence of the oil whirl and oil whip which may cause the failure of the machine. Therefore, the precise nonlinear model should be developed to describe the interaction between the rotor, blade and bearing, and to be used to analyze the nonlinear behaviors such as the bifurcation and chaos by the theory of the nonlinear dynamics.In the design and manufacture of large-scale rotating machinery such as aircraft engines and steam turbines, the coupling dynamics of rotor-bearing systems with blades is a crucial problem. In this dissertation, a coupling nonlinear dynamical model of the blade-rotor- bearing system is developed to analyze the interaction between the rotor, blade and bearing. Research achievements on the coupling dynamics of blade-rotor-baering model are obtained, and this may be beneficial to the engineering applications. The main contents and achievements are listed here.The nonlinear coupling model of the blade-rotor-bearing system is established by the Lagrange approach. The lumped mass method is used to discrete the rotor, and the blades are modeled as pendulums to emphasize the inertia coupling between blades and rotor. To reduce the coupling model, first, orthogonal transformations are employed to decouple the one nodal diameter equations of motion, which are coupled with the equations of motion of the rotor, from k-nodal diameter ( k≠1) equations of motion for an array of elastic blades. The coupling equations with 8 + 2n( n≥3)-degree-of-freedom are divided into two parts: one is the coupling nonlinear model with 12-degree-of- freedom which describe the interaction between the motion of the rotor and the 1-nodal diameter motion of blades, the others are the independent linear system with (2n-4)-degree-of-freedom which describe the k-nodal diameter ( k≠1) motion of blades. Then, the coupling equations of the blade-rotor-bearing system are transferred to a time-invariant model in terms of periodic transformations. After the two sets of transformations, the coupling nonlinear model is reduced to a lower dimensional system which can be easily solved numericaly in comparison with the solving of the original coupling system.With the assumption of a rigid rotor, the degree-of-freedom of the blade-rigid rotor-bearing system is reduced to 4. The nonlinear oil film force model based on the short bearing theory is adopted here. The system is numericaly solved and the dynamical responses of the system are used to analyze the nonlinear dynamical behaviors of the coupling model. The bifurcation diagrams for the corresponding rigid rotor-bearing model, in which the effect of the vibration of blade is neglected, are given as a comparison of the results obtained from the blade-rigid rotor-bearing model.To analyze the interaction between the elastic blade, flexible rotor and journal bearing, the model of blade-rotor-bearing systems with both single and double disks are proposed respectively based on the assumption of the symmetrical rotor, in which the deflection motions of the rotor and the out-of-plane motion of blades are neglected. After decoupling, the degree-of-freedom of these two models are reduced to 8 and 12, respectively. Then the coupling interaction between the elastic blade and rotor-bearing system is investigated.With the assumption of the asymmetrical rotor, the model of the blade-rotor-bearing system with the gyroscopic moment is developed. Obtaining the numerical solutions of the coupling model with the 12-degree-of-freedom, the nonlinear dynamical behavior of the coupling system is investegated. And the effect of the different stiffnesses and lengths of the blade on the behavior of the rotor is discussed. By analyzing the responses of the in-plane and out-of-plane motion of blades, the nonlinear characteristic of the vibration of blades is shown.For the overhung rotor, the model of the blade-cantilever rotor- squeeze film bearing model is established. In the model, there are two disks on the rotor, one is fixed between two bearing, and the other is fixed at the end of the overhung rotor. The many elastic blades are fixed to each disk. The oil film force of the squeeze film damper based on the theory of short bearing with the Raynolds boundary is adopted. After decoupling, there exist 24 equations in the coupling nonlinear system. Using the numerical solutions of the coupling system, the effect of the vibration of blades on the nonlinear dynamical behavior of the overhung rotor is shown.