转子动力学中文讲稿解决方案.ppt

转子动力学;1.转子动力学基础;转子在300MW汽轮机中的位置;汽轮机低压转子;转子在航空涡扇发动机中的位置;转子在大型燃气轮机中的位置;1.2 旋转机械中存在的转子动力力学问题及主要内容;1.3 THEJEFFCOTT MODEL:CRITICAL SPEEDS AND SYNCHRONOUS IMBALANCE RESPONSE the Jeffcott flexible motor model is illustrated in Figure 1.1,and consists of a flat disk supported by a uniform, massless, flexible shaft, which is supported at its ends by rigid frictionless bearings.;The X,Y,Z coordinate system is inertial, with Z the nominal axis of rotor rotation. The x,y,z system is fixed to the disk, and its origin is defined by the vector R relative to the X,Y,Z system. The mass center of the disk does not lie on the elastic axis of the shaft, and its position relative to the origin of the x,y,z system is defined by the vector a. The rotation of the x,y,z system relative to the X,Y,Z system is defined by the angle φ. The equations of motion for the system illustrated in Figure 1.1 can be stated from Newton’s laws of motion as;Further, k is the shaft-stiffness coefficient, m is the rotor (disk) mass, and Jz is its moment of inertia about the z axis. The components of the external force vector are denoted by fX,fY, and the component of the external moment vector along the z axis is MZ. An inspection of Eqs.(1.1) shows that transverse motion of the rotor can be readily excited by the components of the external force vector fX,fY. Typically, however, the dominant source of rotor excitation is the vector a, the rotor imbalance vector. We are initially concerned with the response of the .. . rotor R to the imbalance vector a for constant running speed; i.e., φ=0. φ=ω, φ=ωt. The dimensionality of the governing equations (1.1) can be reduced by introducing the following complex variables:;The steady-state solution for ω≠λ is:;Forω much greater then λ, the two vectors are 1800 out of phase. Forω=λ, the amplitude of R grows linearly with time, and its phase is 90