tailieunhanh - Rotating Machinery Vibration 2011 Part 4

Tham khảo tài liệu 'rotating machinery vibration 2011 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 54 Chapter 2 . Addition of Nonstructural Mass and Inertia to Rotor Element Nonstructural mass is added mass and inertia lumped at mass stations that does not contribute to element flexibility. The rotor element in Fig. 8 shows a concentrated disk at each end. A concentrated disk Mtd 7pd and Ít may be added at any rotor mass station. For a purely concentrated nonstructuralpoint mass 7pd Ít 0. Because construction of the complete matrices for the rotor alone next topic overlays the element matrices at their connection stations nonstructural mass and inertia are added to the left mass station of each element prior to that overlay of element matrices as reflected in the following equations. The exception is the far right rotor station where nonstructural mass is added to the right station. Complete element mass matrix M i M or M d or M 0 0 0 0 0 0 o 0 Aficft 0 0 0 0 0 0 0 0 r d 1 0 0 0 0 0 -ị- 0 0 0 r d 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0. 53 Complete element gyroscopic matrix G 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -I- 0 0 ojl fr 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .0 0 0 0 0 0 0 0. 54 . Matrices for Complete Free-Free Rotor The M C and if matrices for the complete free-free rotor . free of connections to ground and free of external forces are assembled by linking all the corresponding individual rotor-element matrices. The right mass station of each rotor element is overlaid on the left mass station of its immediate right neighbor. Lateral Rotor Vibration Analysis Models 55 Thus the total number of rotor mass stations 7VST is equal to the total number of rotor elements 7VEL plus one. The total number of rotor DOFs is four times i VST. Vst V . 1 A rdof 4 Vsr 55 Accordingly the rotor matrices are expressible as follows. 56 C r 57 58 56 Chapter 2 Note that the free-free rotor damping matrix contains only the shaft gyroscopic terms. As further explained in Sec. 4 .