Intermittent behaviour of a Cracked Rotor in the resonance region

Vibrations of the Jeffcott rotor are modelled by a three degree of freedom system including coupling between lateral and torsional modes. The crack in a rotating shaft of the rotor is introduced via time dependent stiffness with off diagonal couplings. Applying the external torque to the system allows to observe the effect of crack "breathing" and gain insight into the system. It is manifested in the complex dynamic behaviour of the rotor in the region of internal resonance, showing a quasi--periodic motion or even non-periodic behaviour. In the present paper report, we show the system response to the external torque excitation using nonlinear analysis tools such as bifurcation diagram, phase portraits, Poincare maps and wavelet power spectrum. In the region of resonance we study intermittent motions based on laminar phases interrupted by a series nonlinear beats.Comment: 12 pages, 6 figure

Review of Rotordynamics

Book Review of Rotordynamics, by Agnieszka (Agnes) Muszynska. CRC Press, Taylor & Francis Group, Boca Raton, FL, 2005, 1128 pp., ISBN: 0-8247-2399-

Review of Rotordynamics

Book Review of Rotordynamics, by Agnieszka (Agnes) Muszynska. CRC Press, Taylor & Francis Group, Boca Raton, FL, 2005, 1128 pp., ISBN: 0-8247-2399-

Comparison of Mobility Method and Mass Conservation Method in a Study of Dynamically Loaded Journal Bearings

The inverse problem of dynamically loaded journal bearings was solved using generalized Reynolds equation coupled with a complete mass conservative cavitation boundary conditions, as outlined by the Jacobsson-Floberg and Olsson (JFO) cavitation theory. In the course of solution, the modified Thomas algorithms was employed, instead of standard Gauss±Jordan reduction method, which fully utilizes the sparse character of the system matrix, and thus greatly reduces computational time. The developed model was tested against the well-known mobility method for the case of journal bearings in a commercial reciprocating air compressor. It was found that the mobility method overestimates minimum film thickness and underestimates such parameters as lubricant flow rate and bearing power loss. In general, the level of error is acceptable for most industrial applications. However, for the journal bearing where the feed pressure is time dependent and starvation effects are predominant, the mobility method may produce large not acceptable errors

Nonlinear Vibrations of Fractionally Damped Systems

This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing\u27s equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior

Modal Uncoupling of Damped Gyroscopic Systems

A new approach for uncoupling the equations of motion typical for rotordynamical systems is presented. The method does not neglect the speed-dependent e!ects, such as gyroscopic e!ects, and can be particularly valuable in the controller design of actively controlled rotors. In the presence of hysteretic type of damping, the resulting uncoupled gyroscopic systems come with an equivalent viscous damping, equivalent in a sense of yielding the same natural frequency and decay rate. The approach is illustrated through three examples of technical interest: a Je!cott rotor with hysteretic damping, a Stodola}Green rotor, and a rotor of a small gas turbine. The generated results demonstrate that the developed approach is correct and straightforward

Balanced Dissipative Controllers for Flexible Structures

A balanced approach to shaping the closed-loop properties of the dissipative controllers for flexible structures is presented. In the balanced representation the properties of flexible structures are introduced, and a simple method of designing of the dissipative controllers is obtained. It relates the controller gains with the closed-loop pole locations. The examples illustrate the accuracy of the design method

Modal Uncoupling of Damped Gyroscopic Systems

A new approach for uncoupling the equations of motion typical for rotordynamical systems is presented. The method does not neglect the speed-dependent e!ects, such as gyroscopic e!ects, and can be particularly valuable in the controller design of actively controlled rotors. In the presence of hysteretic type of damping, the resulting uncoupled gyroscopic systems come with an equivalent viscous damping, equivalent in a sense of yielding the same natural frequency and decay rate. The approach is illustrated through three examples of technical interest: a Je!cott rotor with hysteretic damping, a Stodola}Green rotor, and a rotor of a small gas turbine. The generated results demonstrate that the developed approach is correct and straightforward

Controlled Deflection Approach for Rotor Crack Detection

Atransverse shaft crack is a serious malfunction that can occurdue to cyclic loading, creep, stress corrosion, and other mechanismsto which rotating machines are subjected. Though studied for manyyears, the problems of early crack detection and warning arestill in the limelight of many researchers. This is dueto the fact that the crack has subtle influence onthe dynamic response of the machine and still there areno widely accepted, reliable methods of its early detection. Thispaper presents a new approach to these problems. The methodutilizes the coupling mechanism between the bending and torsional vibrationsof the cracked, nonrotating shaft. By applying an external lateralforce of constant amplitude, a small shaft deflection is induced.Simultaneously, a harmonic torque is applied to the shaft inducingits torsional vibrations. By changing the angular position of thelateral force application, the position of the deflection also changesopening or closing of the crack. This changes the waythe bending and torsional vibrations are being coupled. By studyingthe coupled lateral vibration response for each angular position ofthe lateral force one can assess the possible presence ofthe crack. The approach is demonstrated with a numerical modelof a rotor. The model is based on the rigidfinite element method (RFE), which has previously been successfully appliedfor the dynamic analysis of many complicated, mechanical structures. TheRFE method is extended and adopted for the modeling ofthe cracked shafts. An original concept of crack modeling utilizingthe RFE method is presented. The crack is modeled asa set of spring-damping elements (SDEs) of variable stiffness connectingtwo sections of the shaft. By calculating the axial deformationsof the SDEs, the opening/closing mechanism of the crack isintroduced. The results of numerical analysis demonstrate the potential ofthe suggested approach for effective shaft crack detection