Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Experimental artefacts in 2D-MAS exchange experiments: non-uniform mixing time within a single 2D run

The practical realization of rotor-synchronized mixing-times in 2D-MAS exchange experiments without the need for a special hardware is reviewed; its consequence for the ‘true mixing time' of the experiment is discussed. We demonstrate influences on experimental rate constants derived from such experiments as well as on the appearance of the 2D-MAS spectra, taken at short mixing times.     

A nondestructive method for estimation of the fracture toughness of CrMoV rotor steels based on ultrasonic nonlinearity

The objective of this paper is to develop a nondestructive method for estimating the fracture toughness (K(IC)) of CrMoV steels used as the rotor material of steam turbines in power plants. To achieve this objective, a number of CrMoV steel samples were heat-treated, and the fracture appearance transition temperature (FATT) was determined as a function of aging time. Nonlinear ultrasonics was employed as the theoretical basis to explain the harmonic generation in a damaged material, and the nonlinearity parameter of the second harmonic wave was the experimental measure used to be correlated to the fracture toughness of the rotor steel. The nondestructive procedure for estimating the K(IC) consists of two steps. First, the correlations between the nonlinearity parameter and the FATT are sought. The FATT values are then used to estimate K(IC) using the K(IC) versus excess temperature (i.e., T-FATT) correlation that is available in the literature for CrMoV rotor steel.     

Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision

This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Balance Method (HBM). As the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these oscillation are also clarified.     

转镜式光谱仪光程差和非线性的研究

对转镜式高速干涉光谱仪的基本原理进行了介绍,给出了无晃动和有晃动两种情况下,轴上和轴外光线的光程差公式,并对结果进行了初步分析,发现晃动将使光程差大小发生变化,但不改变轴上光线零光程差的位置.光程差的非线性是转镜式干涉仪的天生缺陷,它和转镜的折射率、工作角等参量有关,使非线性最小可得出最佳折射率为2.9左右,从光程差误差的容限可以计算出对工作角的要求,折射率为最佳时,工作角可达13.3°,根据对非线性的分析结果,给出了转镜主要参量选择的原则.     

Some studies on rotors with polynomial type non-linear external and internal damping

Non-linear internal damping in rotating cylindrical shafts leads to isotropic non-linear circulatory and dissipative force fields. Orbital instability in such class of systems arises when the regenerative work due to circulatory forces exceeds the dissipative work done over an orbit. In this paper, stability condition for rotor shafts with polynomial type non-linear internal damping is derived and also it is shown that distortion of the critical orbit, which results in larger change in orbital path as compared to the change in enclosed area, may lead to stable orbit at normally unstable operating conditions. This principle is applied to stabilize a simple rotor with discontinuous stiffness characteristics, which come into effect on exceeding some threshold displacement of the rotor itself.     

Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions

The effect of non-linear magnetic forces on the non-linear response of the shaft is examined for the case of superharmonic resonance in this paper. It is shown that the steady-state superharmonic periodic solutions lose their stability by either saddle-node or Hopf bifurcations. The system exhibits many typical characteristics of the behavior of non-linear dynamical systems such as multiple coexisting solutions, jump phenomenon, and sensitive dependence on initial conditions. The effects of the feedback gains and imbalance eccentricity on the non-linear response of the system are studied. Finally, numerical simulations are performed to verify the analytical predictions.     

Effects of multiple blade interaction on the containment of blade fragments during a rotor failure

A finite element analysis is used to study the impact and the containment aspects of rotor blade fragments that are produced during a aircraft jet engine rotor failure. The impact and containment studies are performed on a ring-type containment structure and various fragment types are considered in this study. For each type of fragment, the ring thickness is varied incrementally and the ring response, residual kinetic energy level of the fragments, magnitude of impact forces and the overall containment or failure are determined. First, only a single fragment is considered and the rotor is assumed to contain no other blades. Next, the remaining blades are introduced and the effects of multiple collisions with the other blades on the containment are analyzed. The explicit, nonlinear finite element code Dyna3d is used for the numerical computations in this study and the results are compared with the experimental results performed on a T58 rotor at the spin facility of the Naval Air Propulsion Test Center.     

A general mathematical model for continuous generating machining of screw rotors with worm-shaped tools

Screw rotors play a crucial role in the performance of compressors. For the large-batch production of small- or medium-sized rotors, continuously rotor hobbing or grinding may be more efficient than form machining. In this study, a general mathematical model was developed for the generating machining of screw rotors with a worm-shaped tool. A two-parameter enveloping theory was applied to simulate the cutting process as the tool conducts polynomial feed motion considering its cutting edge. The normal errors of the generated cutting lines were computed and presented on the rotor tooth surface topologies to show the correctness and practicability of the proposed model.