Nonlinear dynamic analysis of a rub-impact rotor supported by oil film bearings

A general model of a rub-impact rotor system is set up and supported by oil film journal bearings. The Jacobian matrix of the system response is used to calculate the Floquet multipliers, and the stability of periodic response is determined via the Floquet theory. The nonlinear dynamic characteristics of the system are investigated when the rotating speed and damping ratio is used as control parameter. The analysis methods are inclusive of bifurcation diagrams, Poincaré maps, phase plane portraits, power spectrums, and vibration responses of the rotor center and bearing center. The analysis reveals a complex dynamic behavior comprising periodic, multi-periodic, chaotic, and quasi-periodic response. The modeling results thus obtained by using the proposed method will contribute to understanding and controlling of the nonlinear dynamic behaviors of the rotor-bearing system.     

Nonlinear dynamic behaviors of a bolted joint rotor system supported by ball bearings

Archive of Applied Mechanics - A dynamic model of the rotor-bearing system with bolted joint structure is set up based on the Lagrange’s equations, which considers the bearing clearance, the...     

Nonlinear oscillations of rotor active magnetic bearings system

In this paper, an analytical approximate solution is constructed for a rotor-AMB system that is subjected to primary resonance excitations at the presence of 1:1 internal resonance. We obtain an approximate solution applying the method of multiple scales, and then we conducted the system bifurcation analyses. The stability of the system is investigated applying Lyapunov’s first method. The effects of the different parameters on the system behavior are investigated. The analytical results showed that the rotor-AMB system exhibits a variety of nonlinear phenomena such as bifurcations, coexistence of multiple solutions, jump phenomenon, and sensitivity to initial conditions. Finally, the numerical simulations are performed to demonstrate and validate the accuracy of the approximate solutions. We found that all predictions from analytical solutions are in excellent agreement with the numerical integrations.     

Bifurcation and nonlinear dynamic analysis of a rigid rotor supported by two-lobe noncircular gas-lubricated journal bearing system

This paper presents the study of the dynamic analysis of a rigid rotor supported by a two-lobe non-circular gas-lubricated journal bearing. A finite element method has been employed to solve the Reynolds equation in static and dynamical states and the dynamical equations have been solved using Runge–Kutta method. To analyze the behavior of the rotor center in horizontal and vertical directions under the different operating conditions, the dynamic trajectory, the power spectra, the Poincare maps, and the bifurcation diagrams are used. Results of this study indicates that by considering bearing number and rotor mass as the parameters of the system, complex dynamic behavior comprising periodic, KT-periodic, and quasi-periodic responses of the rotor center has occurred.     

Nonlinear dynamic responses of a rigid rotor supported by active bump-type foil bearings

Nonlinear Dynamics - Active bump-type foil bearings (ABFBs) enhance the rotordynamic characteristics of rotor–bearing systems with the advantage of controllable mechanical preloads. However,...     

Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings

The dynamic force transmissibility (DFT) of aerospace flywheel rotor system (FRS) supported by angular contact ball bearings (ACBBs) is examined in this paper. The influence of combined loads and contact angle variation is considered in the Sjovall formula to accurately solve the load distribution and nonlinear stiffness of ACBB. Subsequently, the lateral vibration model of FRS is established by considering the nonlinear stiffness characteristics of ACBB. The DFT of the system is solved via harmonic balance method and arc length continuation, and the stability of the results is determined. Numerical integration and dynamic tests are utilized to verify the accuracy of harmonic balance results. Based on the proposed model, the effects of rotor unbalance excitation, axial preload, and rotor damping on the DFT of the system are discussed. The soft-stiff transition phenomenon is observed in terms of the varying supporting stiffness of ACBB wherein deformation is measured under axial preload. The value of rotor unbalanced mass determines the nonlinear characteristics of FRS. The results provide an important reference for dynamic performance evaluation and vibration isolation device design of aerospace FRS.

     

Bifurcation analysis for nonlinear multi-degree-of-freedom rotor system with liquid-film lubricated bearings

The oil-film oscillation in a large rotating machinery is a complex high-dimensional nonlinear problem. In this paper, a high pressure rotor of an aero engine with a pair of liquid-film lubricated bearings is modeled as a twenty-two-degree-of-freedom nonlinear system by the Lagrange method. This high-dimensional nonlinear system can be reduced to a two-degree-of-freedom system preserving the oil-film oscillation property by introducing the modified proper orthogonal decomposition (POD) method. The efficiency of the method is shown by numerical simulations for both the original and reduced systems. The Chen-Longford (C-L) method is introduced to get the dynamical behaviors of the reduced system that reflect the natural property of the oil-film oscillation.     

Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.     

Nonlinear analysis of a cracked rotor with whirling

ＩｎｔｒｏｄｕｃｔｉｏｎＤｙｎａｍｉｃｓａｎａｌｙｓｉｓｏｆｃｒａｃｋｅｄｒｏｔｏｒｗｈｅｎｉｇｎｏｒｉｎｇｎｏｎｌｉｎｅａｒｗｈｉｒｌｉｎｇｃｏｕｌｄｂｅｆｏｕｎｄｉｎｍａｎｙＲｅｆｅｒｅｎｃｅｓ [1 -3 ] .Ｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｏｆｃｒａｃｋｅｄｒｏｔｏｒｗｉｔｈｗｈｉｒｌｉｎｇｈａｖｅｂｅｅｎｓｔｕｄｉｅｄｂａｓｅｄｏｎｆｏｒｍｅｒｓｃｈｏｌａｒ’ｓｗｏｒｋ[4 ]ａｎｄｔｈｅｗｈｉｒｌｉｎｇｅｑｕａｔｉｏｎｓｏｆａｃｒａｃｋｅｄｓｈａｆｔｈａｖｅｂｅｅｎｅｓｔａｂｌｉｓｈｅｄ .Ｔｈ…     

Static and dynamic behaviour of a rigid rotor on journal bearings

This experimental investigation concerns the static and dynamic behaviour of a rigid balanced rotor on journal bearings. Running conditions were chosen in order to obtain relatively high eccentricity ratios near the instability threshold speeds.The results, compared also with the theoretical predictions of some authors, have substantially shown the importance of examining the static behaviour near the instability threshold speed to allow a correct interpretation of some aspects of the dynamic behaviour.In order to clarify the discrepancies between the observed and the theoretically predicted dynamic behaviour, some further tests have been carried out.

---

Sommario E' stato esaminato sperimentalmente sia il comportamento statico che quello dinamico di un rotore rigido e bilanciato sostenuto da cuscinetti cilindrici lubrificati.Le condizioni di funzionamento sono state scelte in modo tale che, in prossimità della soglia di instabilità, il valore del rapporto di eccentricità risultasse relativamente grande.I risultati, confrontati anche con le indicazioni teoriche di altri autori, hanno sostanzialmente evidenziato l'importanza dell'esame del comportamento statico in prossimità della soglia di instabilità al fine di interpretare correttamente alcuni aspetti del fenomeno dell'instabilità.Sono state inoltre effettuate una serie di ulteriori indagini con lo scopo di chiarire le discordanze fra il comportamento dinamico osservato e quello previsto dalla teoria.

     

Preload effect on nonlinear dynamic behavior of a rigid rotor supported by noncircular gas-lubricated journal bearing systems

This paper presents the effect of preload, as one of the design parameters, on nonlinear dynamic behavior of a rigid rotor supported by gas-lubricated noncircular journal bearings. A finite element method has been employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using the Runge–Kutta method. To analyze the behavior of the rotor center in horizontal and vertical directions under different operating conditions, dynamic trajectory, power spectra, Poincare maps, and bifurcation diagrams are used. Results of this study reveal how the complex dynamic behavior of two types of noncircular bearing systems comprising periodic, KT-periodic, and quasi-periodic responses of the rotor center varies with changes in preload value.     

Dynamic analysis of the variable stiffness support rotor system with elastic rings

Nonlinear Dynamics - Elastic rings are common rotor supporting structure, which have been widely used in aeroengine rotor support system. However, large inertia force and gyroscopic moment may...     

Modelling and dynamic analysis of spline-connected multi-span rotor system

Meccanica - Self-excited oscillation induced by the internal frictions of spline joints is a major cause of rotor system instability. In this study, the dynamic equations of spline-connected...     

Nonlinear dynamic analysis of a structure with a friction-based seismic base isolation system

Many dynamical systems are subject to some form of non-smooth or discontinuous nonlinearity. One eminent example of such a nonlinearity is friction. This is caused by the fact that friction always opposes the direction of movement, thus changing sign when the sliding velocity changes sign. In this paper, a structure with friction-based seismic base isolation is regarded. Seismic base isolation can be employed to decouple a superstructure from the potentially hazardous surrounding ground motion. As a result, the seismic resistance of the superstructure can be improved. In this case study, the base isolation system is composed of linear laminated rubber bearings and viscous dampers and nonlinear friction elements. The nonlinear dynamic modelling of the base-isolated structure with the aid of constraint equations, is elaborated. Furthermore, the influence of the dynamic characteristics of the superstructure and the nonlinear modelling of the isolation system, on the total system’s dynamic response, is examined. Hereto, the effects of various modelling approaches are considered. Furthermore, the dynamic performance of the system is studied in both nonlinear transient and steady-state analyses. It is shown that, next to (and in correlation with) transient analyses, steady-state analyses can provide valuable insight in the discontinuous dynamic behaviour of the system. This case study illustrates the importance and development of nonlinear modelling and nonlinear analysis tools for non-smooth dynamical systems.     

Nonlinear dynamic analysis of a quarter vehicle system with external periodic excitation

In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system.     

Nonlinear stochastic dynamics of a rub-impact rotor system with probabilistic uncertainties

Nonlinear Dynamics - This paper presents a stochastic model for performing the uncertainty and sensitivity analysis of a Jeffcott rotor system with fixed-point rub-impact and multiple uncertain...     

Nonlinear dynamics of one disk asymmetrical rotor supported by two journal bearings

Asymmetrical one disk rotor interacting with fluid films of short journal bearings is considered. Gyroscopic moments acting on a disk are taken into account. The forces of the journal bearing fluid film are derived analytically. The system of four nonlinear ordinary differential equations is obtained to study the rotor vibrations. The origination of self-sustained vibrations of rotor is studied by means of Shaw–Pierre nonlinear modes. The harmonic balance method is applied to study the self-sustained vibrations with large amplitudes.     

Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

In this paper, the nonlinear vibration characteristics of geared rotor bearing system and the interactions among gears, shafts, and plain journal bearings were studied. First, with the consideration of backlash, transmission error, time-varying mesh stiffness, and layout parameters, the dynamic model of geared rotor bearing system featuring confluence transmission was proposed. The nonlinear oil-film forces were computed with the Reynolds equation for finite-length journal bearings. Second, the responses of meshing vibration and bearing vibration were discussed. The numerical results revealed that the system exhibited a diverse range of periodic, sub-harmonic, and chaotic behaviors. Under different ranges of rolling frequency, the system got into chaos state through different roads. Moreover, in lower frequency, meshing vibration showed coexist of different periodic motions. Lastly, couplings of nonlinear oil-film force and nonlinear gear mesh force were discussed through a range of rolling frequencies. Gear-bearing dynamic interactions were demonstrated through the analysis of dynamic gear loads and dynamic bearing loads, and the coupling effect behaved different when rolling frequency changed.