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Modeling and Analysis
Published in Arthur W. Lees, Vibration Problems in Machines, 2020
Following the philosophy for nonrotating structures, the first step here is to consider natural frequencies, but with the added complication that these natural frequencies will be a function of rotational speed. A plot of the natural frequencies as a function of shaft speed is the Campbell diagram, an example of which is shown in Figure 3.4. The curved lines emanating near the origin arise from modes controlled by the fluid bearings which have speed-dependent properties. The modes at 9, 27, and 58 Hz all have two components corresponding to forward and backward modes. In this instance, the splitting is only slight, but there is more discussion of this phenomenon in Chapter 4.
Instability of Flexible Rotors Mounted on Flexible Bearings
Published in Rajiv Tiwari, Rotor Systems: Analysis and Identification, 2017
In a previous chapter, we studied the instability in a single mass rotor emanating from various kinds of sources—for example, fluid-film bearings, seals, asymmetrical shafts, hysteretic or material damping of the shaft, and steam whirl. We also studied instability in an asymmetrical rotor with distributed mass and stiffness properties by the continuous approach by including higher effects like the gyroscopic effect and rotary inertia. Predictions of the instability regions due to fluid-film bearings for practical rotors are a great challenge. The disadvantage of the Routh–Hurwitz stability criteria is that it is difficult to apply to multi-degree-of-freedom (DOF) rotor-bearing systems. In Chapters 9 and 10, the multi-DOF rotor system was analyzed using the finite-element method (FEM) without considering the dynamic characteristics of flexible supports. The main complexities in only rotors were considered—for example, the rotary inertia, shear deformation, and gyroscopic couples. In the present chapter, the multi-DOF rotor-bearing system will be analyzed for obtaining natural whirl frequencies, critical speeds, logarithmic decrements, and forced responses. The main tool for such analyses will be finite-element methods; in previous chapters (Chapters 7, 9 and 10) we have already seen the versatility of finite-element methods in rotors for difficult boundary conditions such as multiple rigid supports. In Chapter 4, it was demonstrated that even for a single mass rotor and mounted on two bearings, the analysis using the conventional method becomes very complex. For modeling of fluid-film bearings, the short bearing approximation (refer to Chapter 3) is taken. The stiffness and damping coefficients of fluid-film bearings are speed-dependent and lead to the natural whirl frequency being speed-dependent. To obtain critical speeds, the Campbell diagram is very useful; moreover, in the Campbell diagram apart from the natural whirl frequencies, logarithmic decrements are also provided, which predicts the instability behavior of the rotor at different speeds.
Whirling analysis of shaft line with a new compact flexible coupling
Published in C. Guedes Soares, Y. Garbatov, Progress in the Analysis and Design of Marine Structures, 2017
A Campbell diagram is a very useful tool for understanding the interaction between the vibration sources with the natural modes (Genta 2008). In this case study, the firing order of the engine are considered.
Field test and analysis of the abnormal vibration of the medium-speed maglev train with mid-mounted linear motors
Published in Vehicle System Dynamics, 2021
Yaozong Liu, Shaoyi Wang, Shengquan Zhao, Hongping Xu, Minglei Xu
In order to analyse the frequency characteristics of the longitudinal and vertical vibrations of the linear motor, the Campbell diagrams of the longitudinal and vertical vibrations of the motor are drawn, as shown in Figure 5. Campbell diagram is mainly used to represent the relationship between vibration frequency, amplitude and rotational speed of rotating machinery. For the maglev train with linear motor, the speed is equivalent to the rotation speed of the motor. Therefore, the frequency spectrum of the longitudinal and vertical acceleration data of the motor at different speeds are analysed, and the amplitude and frequency of each spectrum peak are obtained. With the speed as the abscissa, the frequency of the spectrum peak as ordinate and the amplitude as the radius, the Campbell diagrams of the longitudinal and vertical acceleration of the motor are drawn in Figure 6.
Variable frequency drive harmonics and interharmonics exciting axle torsional vibration resulting in railway wheel polygonisation
Published in Vehicle System Dynamics, 2020
The interaction of the harmonics and interharmonics with mechanical torsional resonant frequencies of drive trains is often studied by means of interference or Campbell diagrams. The Campbell diagram is used to show the change in frequencies of the harmonics and interharmonics as a function of the operating speeds. The torsional natural frequencies are included as constant frequency lines and areas of interference are marked as operating speeds where torsional excitation could occur. The interference diagram and the prediction of pulsating torque frequencies from the VFD supply were discussed and applied by Song-Manguelle et al. [28,29].
Hybrid composite shaft of High-Speed Rotor-Bearing System - A rotor dynamics preview
Published in Mechanics Based Design of Structures and Machines, 2021
Thimothy Harold Gonsalves, Mohan Kumar Garje Channabasappa, Ramesh Motagondanahalli Rangarasaiah
The critical speed evaluation is carried out using the Campbell diagram which graphically represents the whirling speeds of the rotor-bearing system. In a general form applied to any rotating system or a component, Campbell diagram represents the natural frequencies plotted versus the rotational speed. Critical speeds are identified where the excitation lines intersect the natural frequency lines. Identifying the critical speeds of the rotor-bearing system using the Campbell diagram is an important step in the present work as hybrid composite shaft is being envisaged to eliminate the supercritical operation.