Evaluation of impact dynamics and contact forces in a hydropower rotor due to variations in damping and lateral fluid forces

Nonlinear vibrations of a misaligned bladed Jeffcott rotor

“…with a rotating speed lower than the frequency of the fundamental mode of vibration. It is typically the case of hydropower rotors which have a low operating speed [17,18]. Despite the differences between the numerical and experimental case, the sudden jump from periodic to chaotic motion at 1/3 and 2/3 of the natural frequency was observable in both cases.…”

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets

“…Nomenclature c 1 damping coefficients of the generator rotor c 2 damping coefficients of the turbine runner D the damping coefficient e 1 mass eccentricity of the generator rotor e 2 mass eccentricity of the turbine runner E f output of excitation controller E q ' internal transient voltage F x1 , F y1 the x-and y-direction additional forces acting on the generator rotor F x2 , F y2 the x-and y-direction additional forces acting on the hydro turbine runner H the Hamiltonian function J the rotary inertia of the HTGS J 1 rotary inertia of the generator rotor J 2 rotary inertia of the turbine runner k 1 stiffness of the up guide bearing k 2 stiffness of the lower guide bearing k 3 stiffness of the hydro turbine bearing L the Lagrange function m 1 mass of the generator rotor m 2 mass of the hydro turbine runner M gB the generator rated torque M g the generator magnetic torque. M t the hydro turbine torque p i the generalized momentums Q x1 , Q y1 the external forces acting on the generator rotor Q x2 , Q y2 the external forces acting on the hydro turbine runner R 1 radius of the generator rotor R 2 radius of the hydro turbine runner r 1 radial displacement of the generator rotor r 2 radial displacement of the turbine runner r 3 radial displacement of the up guide bearing r 4 radial displacement of lower guide bearing r 5 radial displacement of turbine bearing S gB the generator rated power T total kinetic energy of the HTGS T j inertia time constant of the generator T j1 inertia time constant of the generator rotor T j2 inertia time constant of the turbine runner T d0 ' the time constant U elastic potential energy of the HTGS U s the infinite bus voltage x 1 , y 1 central coordinates of the generator rotor x 10 , y 10 mass coordinates of the generator rotor x 2 , y 2 central coordinates of the turbine runner x 20 , y 20 mass coordinates of the turbine runner X ad the d-axis armature reaction reactance X d the d-axis synchronous reactance X d ' the d-axis transient reactance X f the excitation winding reactance X L the transmission line reactance X q the q-axis synchronous reactance X T reactance of transformer δ rotor angle φ rotation angle of the generator rotor ω angular speed of the HTGS ω B basic value of electrical angular speed ω e electric angular speed ω mB basic value of mechanical angular speed…”

“…One of the purposes defining the generalized momentum is that the substitution of the differential items in the Hamiltonian function and equation can reduce the order of the equation. In this paper, the motion equation of the variables 1  and 1  will be substituted with the generator model while connecting the shafting model. Therefore, the speed item of the four axis variables will be substituted while the angular speed item will remain the same.…”

“…From the generator model (39), the equation of the rotor angle δ is similar to the equation of the shafting angle 1  . So the order of the system can be reduced by directly calculating 1  from δ.…”

“…the shafting computational model [1,2]), the simulation computation [3,4], the faulty diagnosis [5,6], and the active control [7,8] have been developed to investigate the rotor dynamics. Though some achievements have been made using these approaches, it is still difficult to directly analyze the shafting transient state generated arising coming from control and regulation of the HTGS [9].…”