Search Results (20)

Elastic rings are extensively utilized in aero-engine rotor systems owing to their compact size and ease of assembly, where they play a critical role in vibration suppression during engine operation. The dynamic behavior of elastic rings is governed by their structural parameters, with stiffness being a pivotal factor influencing the rotor system’s performance. This study employs finite element methods to investigate the effects of elastic ring structural parameters, particularly the geometric features of bosses and internal/external assembly clearances, on stiffness nonlinearity, with a focus on its mechanisms and contributing factors. The results reveal that stiffness nonlinearity emerges when the whirling radius exceeds a critical threshold. Specifically, increasing the boss width, reducing the boss height, or augmenting the number of bosses all attenuate stiffness nonlinearity under identical whirling radii. Furthermore, external clearances exhibit a stronger capability to suppress stiffness nonlinearity compared to internal clearances. Engineering insights suggest that maintaining a small clearance fit during assembly effectively mitigates stiffness nonlinearity, thereby enhancing the rotor’s dynamic performance. This study elucidates the stiffness nonlinearity behavior of elastic rings in practical applications and provides actionable guidance for their design and operational optimization in rotor systems. Full article

Previous studies on rub-impact faults have mainly focused on the rub-impact between rotors and stators, with less research on inter-rotor rub impact. The impact of inter-rotor rub impact on rotor nonlinear vibration is particularly significant. This study investigates the effects of inter-shaft rub impact on the vibration characteristics and whirl behavior of dual-rotor systems. Initially, a dual-rotor model with inter-shaft bearings is established using the finite element method, and inter-shaft rub-impact forces are derived based on contact mechanics. Next, the system response is solved using the Newmark method. Vibration characteristics are analyzed through Campbell diagrams, 3D waterfall plots, time-frequency domain plots, and steady-state rub-impact force plots. Finally, the influence of inter-shaft rub impact on the whirl behavior of the dual-rotor system is studied based on the theory of full-spectrum analysis. The study concludes that inter-shaft rub-impact faults shift the system’s resonance points backward, increase harmonic and combination frequency components, and significantly affect the system response under dual-rotor co-rotation. Excessive friction can lead to self-excited vibrations and sudden amplitude increases, particularly in the LP rotor frequency. Additionally, inter-shaft rub impact primarily affects the whirl behavior of the LP-compressor disk1, showing multiple cycles of forward and backward whirl alternation during acceleration due to combined unbalanced and rub-impact excitations. Full article

Whirl flutter is a phenomenon caused by an aeroelastic instability, causing oscillations to propagate in manned or unmanned rotor-nacelle type aircraft. Under the conditions where multi-segmented freeplay are present, complex behaviors can dominate these oscillations and can lead to disastrous consequences. This study investigates a rotor-nacelle system with multi-segmented stiffnesses with a freeplay gap to encompass the real-world influences of aircraft. The mathematical aerodynamics model considers a quasi-steady application of strip theory along each blade to outline the external forces being applied. A free-body diagram is then used to incorporate the structural stiffness and damping terms with multi-segmented freeplay considered in the structural stiffness matrix. Multiple structural responses of the defined system are investigated and characterized to determine the influence of varying symmetric and asymmetric multi-segmented stiffnesses with varying gap parameters, including a route to impact investigation. The findings are characterized using phase portraits, Poincaré maps, time histories, and basins of attraction. It is found that under these conditions, the structural influences can lead to aperiodic oscillations with the existence of grazing bifurcations. Furthermore, these results unveil that under certain conditions and high freestream velocities, the sticking phenomenon becomes apparent which is strongly dependent on the strength of the multi-segmented representation, its gap sizes, and its symmetry. Lastly, a route to impact study shows the strong coupled influence between pitch and yaw when asymmetric conditions are applied and the possible presence of grazing-sliding bifurcations. The numerical simulations performed in this study can form a basis for drone designers to create reliable rotor-nacelle systems resistant to whirl flutter caused by freeplay effects. Full article

Part 2 of this work presents a numerical methodology, validated using the experimental results presented in Part 1, to calculate the added modal coefficients of a submerged cylinder in water both when it oscillates and when it rotates with a whirling motion. The numerical methodology is based on computational fluid dynamic simulations that obtain the added modal forces on the cylinder when it is forced to vibrate with mode shapes calculated using acoustic-structural modal analysis. Then, these forces are processed with a curve-fitting algorithm to extract all the coefficients. Most numerical coefficients presented a close agreement with the corresponding experimental ones, although the added modal damping was overestimated. In general, the added modal mass was found to be independent of both the rotating speed and the whirling frequency except for low whirling frequencies when it increased. The added modal damping was found to depend on both parameters, and the rest of the coefficients were independent of the whirling frequency and only depended on the rotating speed. As a conclusion, this numerical approach has permitted the study of particular conditions that could not be experimentally tested and thus broadened the knowledge of the behavior of the added modal coefficients of rotating submerged cylinders. Full article

The operation of submerged rotating machines, such as marine current or tidal turbines, can present deleterious fluid phenomena that may provoke extreme structural vibrations. To predict their dynamic responses, it is necessary to know the added modal coefficients of their runners under a whirling motion. For that purpose, a bespoke test rig was designed to investigate the added modal coefficients of a submerged cylinder, which could rotate at different speeds both in air and completely submerged in water inside a cylindrical tank. First, the modes of vibration were experimentally measured by exciting the cylinder with a push-release method during steady tests or with ramps in rotating speed during transient tests. The calculated natural frequencies and damping ratios were then used in a mathematical model of the dynamic system to calculate the added modal coefficients. During steady tests, the natural frequencies and damping ratios of the whirling modes changed significantly as a function of the rotating speed. Additionally, a whirling mode was observed to change its direction at a given rotating speed. During transient tests, rotating speed ramps with high accelerations were found to present lower lock-in amplitude and frequencies. Moreover, fast downward ramps presented lock-in amplitudes four times higher than fast upward ramps. Consequently, the added modal coefficients changed accordingly as a function of the rotating speed, ramp acceleration, and ramp direction. For these reasons, it was confirmed that the modal responses of submerged rotating bodies must be calculated for each operational rotating speed, even at low velocities, and for each transient event in order to precisely predict their vibration behaviors. Full article

A fire whirl, a unique fire behavior, occurs when a vertical vortex of flames skyrockets due to specific surrounding temperatures and thermal gradient conditions during a fire. Compared with conventional fire plumes, fire whirls exhibit a higher air entrainment rate, tangential velocity, and axial velocity, thus presenting greater risks and destructive capabilities. Thus, studying the combustion characteristics of fire whirls becomes necessary. This experiment employed a small-scale, fixed-frame fire whirl generator. We investigated how varying air-inlet widths and fuel pan diameters influence the fire whirl’s combustion characteristics. Experimental images indicated a negative correlation between the fire whirl’s flame height and the air-inlet width, and a positive correlation with the fuel pan diameter. Our findings showed that the burning rate of the fire whirl during the quasi-steady-state combustion phase initially increased and then decreased as the air-inlet width expanded, peaking at a width of 7 cm. The data demonstrated a corresponding power-law relationship between the fire whirl’s dimensionless flame height and excess temperature. Ultimately, our results indicated a positive correlation between the 2/5 power of the fire whirl’s dimensionless heat release rate and the dimensionless flame height. The ratios of maximum to mean flame height and mean to continuous flame height are 1.35 and 1.5, respectively. Significantly, these ratios remain unaffected by the air-inlet width, fuel pan diameter, environmental temperature, and heat release rate. Full article

Turbulence and transport phenomena play a crucial role in the confinement and stability of tokamak plasmas. Turbulent fluctuations in certain physical quantities, such as density or temperature fluctuations, can have a wide range of spatial scales, and understanding their correlation length is important for predicting and controlling the behavior of the plasma. The correlation length in the radial direction is identified as the critical length in real space. The dynamics in real space are of significant interest because transport in configuration space is primarily focused on them. When investigating transport caused by the $\mathbf{E}\times \mathbf{B}$ drift, the correlation length in real space represents the size of $\mathbf{E}\times \mathbf{B}$ whirls. It was numerically discovered that in drift wave turbulence, this length is inversely proportional to the normalized mode number of the fastest growing mode relative to the drift frequency. Considerable time was required before a proper analytical derivation of this condition was accomplished. Therefore, a connection has been established between phenomena occurring in real space and those occurring in k-space. Although accompanied by a turbulent spectrum in k-space with a substantial width, transport in real space is uniquely determined by the correlation length, allowing for accurate transport calculations through the dynamics of a single mode. Naturally, the dynamics are subject to nonlinear effects, with resonance broadening in frequency being the most significant nonlinear effect. Thus, mode number space is once again involved. Resonance broadening leads to the detuning of waves from particles, permitting a fluid treatment. It should be emphasized that the consideration here involves the total electric field, including the induction part, which becomes particularly important at higher beta plasmas. Full article

Fire whirls are reported to occur frequently in the wilderness and in urban areas due to the influence of ambient winds. Fire whirls that occur on sloped fuel surfaces are common in the wilderness and have received less attention despite their potential to significantly alter fire behavior. Particularly in terms of frequency and height, previous studies have been performed on flatlands but less so on slopes. This paper presents an experimental study of fire whirls in sidewind line fires, focusing on the frequency of occurrence and the height of fire whirls. Regarding the effect of a side wind, it is shown that a side wind increases the frequency of occurrence, while the velocity component parallel or perpendicular to the line fire has a competing effect. In contrast, an increase in the slope reduces the height of the fire whirl; this phenomenon has been justified on the basis of experimental data from our work and the literature and explained in terms of the mechanism of vortex generation and movement. Full article

Diagnosis of faults in a rotor system operating in a fluid is a complex task in the field of rotating machinery. In an ideal scenario, a forced shutdown due to rotor-stator contact failure would necessitate the replacement of the rotor or stator. However, factors such as time constraints, economic considerations, and the aging of infrastructure make it imprudent to abruptly shut down machinery that can still be safe to operate. The purpose of this paper is to present an experimental study that validates the theoretical results of the dynamic behavior and friction detection using the wavelet synchrosqueezing transformation (WSST) method for recurrent rotor-stator contacts in a fluid environment, as presented in a previous study. The investigation focused on the analysis of whirl orbits, shaft deflection, and fluctuation frequency during passage through critical speeds. The WSST method was used to decompose the dynamic responses of the rotor in the supercritical speed zone into several supercomponents. The variation of the high-frequency component was studied based on the fluctuation of the instantaneous frequency (IF) technique. Additionally, the fast Fourier transform (FFT) method, in conjunction with the WSST technique, was used to calculate the variation in the amplitude of high-order frequencies in the vibration signal spectrum. The experimental study revealed that the split in resonance caused by rubbing effects is reduced when the rotor and stator interact with an inviscid fluid. However, despite the effects of elasticity and fluid boundaries generating self-excitation at low frequencies and uneven motion due to stator clearance, the experimental results were consistent with the theoretical analysis, demonstrating the effectiveness of the contact detection method based on WSST. Full article

It is of practical interest to investigate the mechanical behaviors of a sidetracking tool system and to describe the sidetracking tool’s vibration mechanical response, as this can provide an important basis for evaluating and optimizing the tool structure and effectively controlling the profile of the sidetracking window. In this article, three nonlinear dynamic models with ten, six, and two degrees of freedom, respectively, are established using the Lagrange method to characterize the behavior of the sidetracking tool. It should be noted that in these models, the axial, lateral, and torsional vibration of the tool system are fully coupled. The process of the sidetracking tool mills in the casing-pipe wall is divide into three typical stages, i.e., the window mill, pilot mill, and watermelon mill grinding the casing, respectively. The dynamic response of the three stages is studied to more effectively analyze the influence of the sidetracking tool vibration deformation on the window width. The Runge–Kutta method, which is easy to implement, is applied to solve the supposed nonlinear dynamic model, and some useful findings are as follows. The effects of sidetracking tool vibrations at different stages on window widening size are illustrated quantitatively. The vibration trajectory pattern of the sidetracking tool is different from that of the conventional drilling tool due to the influence of the whipstock, which changes from the general whirling motion pattern to the X reciprocating pattern, and the vibration amplitude decreases. Due to the influence of the tool’s lateral amplitude, the window profile is widened. The widened window size of the window mill and the pilot mill are 3.30 mm and 2.74 mm, respectively, and the extended window size of the watermelon mill is 0.07 mm, while the maximum window width formed by the sidetracking tool is 374.34 mm. This work proposes, for the first time, the coupled vibration model of the sidetracking tool system, which is helpful to better understand the nonlinear dynamic effects of the sidetracking tool, laying the foundation for the optimization of the sidetracking parameters. Full article

Gas bearings have been widely applied to high-speed rotating machines due to their low friction and high rotational speed advantages. Nevertheless, gas lubrication is low viscosity and compressible. It causes the gas bearing-rotor system easy to produce self-excited vibration, which leads to instability of the rotor system and hinders the increase of rotor system speed. It is necessary to study the nonlinear behaviors of the aerostatic bearing-rotor system and the nonlinear vibration of the gas bearing-rotor system, especially considering the distribution mass and flexible and gyroscopic effects of the real rotor. In this paper, the nonlinear behavior of the gas bearing-rotor system is investigated from the viewpoint of nonlinear dynamics. Firstly, the dynamics model of a gas bearing rotor is established by combining the transient Reynolds equation and rotor dynamic equation obtained by finite element method (FEM). The transient Reynolds equation is solved using a hybrid method combining the differential transform method (DTM) and finite difference method (FDM). Then the transient gas force is substituted into the FEM rotor dynamic equation. In the end, based on the bifurcation diagram, the orbit of the rotor center, the frequency spectrum diagram and Poincaré map, the rotor system’s nonlinear behaviors are studied using a solution for the rotor dynamic equation with the Newmark method. Results show that there exists a limited cycle motion in the autonomous rotor system and half-speed whirl in the nonautonomous rotor system. Full article

This paper focuses on the development and demonstration of a novel blade morphing system within a whirl tower facility. The scope is to investigate the behavior of the proposed architecture under representative loads, demonstrating its capability to alter the blade original shape in operation under centrifugal, aerodynamic, and internal forces. The morphing concept was developed inside the European project “Shape Adaptive Blades for Rotorcraft Efficiency”, SABRE, and consists of a shape memory alloy system able to change the original twist law and, in this way, enhance rotor performance at certain specific regimes, such as hover and vertical flight. These phases, indeed, are generally penalized with respect to other more extended flight regimes (cruise). The work starts with an overview of the research in the field of morphing, with specific reference to the researches envisaging rotary wing demonstrations. Then, an overview of the morphing twist concept is provided, with particular attention paid to those features particularly suited for the whirl tower representative test environment. The laboratory characterization and commissioning operations are illustrated. Then, the task of the installation of the prototype on the whirl tower facility is described together with the testing modality adopted. Finally, the results of the test campaign are illustrated and critically discussed, providing the reader with insights and possible future steps to be taken in further research. The impact on the morphing capability of the following different parameters was investigated: the number of the prototype segments switched on, the speed and thus the centrifugal actions, and the angles of attack. The stiffening effect due to centrifugal actions was quantified through the measurement of the actual twist and the internal deformation. The link between speed, angle of attack at root, and twist and flap angles was also tracked, building a database useful for the comprehension of the phenomenon, and for the assessment of numerical predictive models. The achieved results highlighted the capability of the system to produce a twist angle matching the target of 8° per blade radius; this figure is related to a potential power saving of 10% in hover and vertical flight and an improvement of about 1% on the over-all efficiency of the rotorcraft. Full article

This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young’s modulus, Poisson’s ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange’s equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail. Full article

Rotor systems installed in a transportation system or under seismic excitations are considered to have a moving base. Although extensive research has been conducted on the dynamic behavior of the single-rotor system under base motions, few studies have dealt with the dynamics of dual-rotor systems, especially the counter-rotating dual-rotor systems used in airplane engines. Moreover, mass unbalance and gravity are unavoidable excitations for most rotor systems. Therefore, the vibration properties of a counter-rotating dual-rotor system with the coupled effects of base motions, mass unbalance and gravity are investigated in this paper for the first time. Using the Lagrange principle associated with the finite element method, a general model for dual-rotor systems under base motions was established by using Timoshenko beam elements, leading to a detailed analysis of the natural properties and harmonic responses of the system. The results revealed that different whirling modes (backward, forward or both) may be mutually excited. This research can be helpful for the design and vibration analysis of dual-rotor systems concerned with base motion. Full article

Aerial drones have improved significantly over the recent decades with stronger and smaller motors, more powerful propellers, and overall optimization of systems. These improvements have consequently increased top speeds and improved a variety of performance aspects, along with introducing new structural challenges, such as whirl flutter. Whirl flutter is an aeroelastic instability that can be affected by structural or aerodynamic nonlinearities. This instability may affect the prediction of potentially dangerous behaviors. In this work, a nonlinear reduced-order model for a nacelle-rotor system, considering quasi-steady aerodynamics, is implemented. First, a parametric study for the linear system is performed to determine the main aerodynamic and structural characteristics that affect the onset of instability. Multiple polynomial nonlinearities in the two degrees of freedom nacelle-rotor model are tested to simulate possible structural nonlinear effects including symmetric cubic hardening nonlinearities for the pitch and yaw degrees of freedom; purely yaw nonlinearity; purely pitch nonlinearity; and a combination of quadratic, cubic, and fifth-order nonlinearities for both degrees of freedom. Results show that the presence of hardening structural nonlinearities introduces limit cycle oscillations to the system in the post-flutter regime. Moreover, it is demonstrated that the inclusion of quadratic nonlinearity introduces asymmetric oscillations and subcritical behavior, where large and potentially dangerous deformations can be reached before the predicted linear flutter speed. Full article