High-Frequency Vibration Analysis and Optimization of Irregular Wear of Pantograph Carbon Strips

The irregular wear of carbon current collector pantograph strips increases the railway maintenance costs and introduces safety hazards in the railway operation. This paper presents a method for analyzing the irregular wear of carbon strips with numerical dynamic analyses and modal tests. The carbon strips were studied in laboratory tests, and an equivalent numerical model for the investigation of their irregular wear and performance improvement was established. The results from the computational simulations were evaluated based on the laboratory results, and the correlation between the high-frequency vibration and irregular wear of the carbon strips was studied. The irregular wear contour of the carbon strips coincides with the high-frequency mode shape according to the experimental and numerical results. Moreover, the dynamic design for carbon strips was optimized with the validated computational model. The results suggest that the optimized schemes effectively mitigate the irregular wear of carbon strips.

Investigation of Flow Around a Slender Body at High Angles of Attack

A numerical investigation of flow around a slender body at high angles of attack is presented. Large eddy simulation of the flow around an ogive-cylinder body at high angles of attack is carried out. Asymmetric vortex flow was observed at angles of attack of α = 55◦ and 65◦ . The results showed that the phenomenon is present in the absence of artificial geometrical or flow perturbation. Contrary to the accepted notion that flow asymmetry is due to a convective instability, the development of vortex asymmetry in the absence of perturbations indicates the existence of absolute instability. An investigation of the unsteady flow field was carried out using dynamic mode decomposition. The analysis identified two distinct unsteady modes; high-frequency mode and low-frequency mode. At angle of attack 45◦ the high-frequency mode is dominant in the frontal part of the body and the low-frequency mode is dominant at the rear part. At α = 55◦ , the highfrequency mode is dominant downstream of vortex breakdown. At α = 65◦ , the spectrum shows a wide range of modes. Reconstruction of the dynamical modes shows that the low-frequency mode is associated with the unsteady wake and the high-frequency mode is associated with unsteady shear layer.

Inertial regimes in a curved electromagnetically forced flow

We investigated experimentally the flow driven by a Lorentz force induced by an axial magnetic field $\boldsymbol{B}$ and a radial electric current $I$ applied between two fixed concentric copper cylinders. The gap geometry corresponds to a rectangular section with an aspect ratio of $\unicode[STIX]{x1D702}=4$ and we probe the azimuthal and axial velocity profiles of the flow along the vertical axis by using ultrasonic Doppler velocimetry. We have performed several runs at moderate magnetic field strengths, corresponding to moderate Hartmann numbers $M\leqslant 300$. At these forcing parameters and because of the geometry of our experimental device, we show that the inertial terms are not negligible and an azimuthal velocity that depends on both $I$ and $B$ is induced. From measurements of the vertical velocity we focus on the characteristics of the secondary flow: the time-averaged velocity profiles are compatible with a secondary flow presenting two pairs of stable vortices, as pointed out by previous numerical studies. The flow exhibited a transition between two dynamical modes, a high- and a low-frequency one. The high-frequency mode, which emerges at low magnetic field forcing, corresponds to the propagation in the radial $r$-direction of tilted vortices. This mode is consistent with our previous experiments and with the instability described in Zhao et al. (Phys. Fluids, vol. 23 (8), 2011, 084103) taking place in an elongated duct geometry. The low-frequency mode, observed for high magnetic field forcing, consists of large excursions of the vortices. The dynamics of these modes matches the first axisymmetric instability described in Zhao & Zikanov (J. Fluid Mech., vol. 692, 2012, pp. 288–316) taking place in an square duct geometry. We demonstrated that this transition is controlled by the inertial magnetic thickness $H^{\prime }$ which is the characteristic length we introduce as a balance between the advection and the Lorentz force. The key point here is that when the inertial magnetic thickness $H^{\prime }$ is comparable to one geometric characteristic length ($H/2$ in the vertical or $\unicode[STIX]{x0394}r$ in the radial direction) the corresponding mode is favoured. Therefore, when $H^{\prime }/(H/2)\approx 1$ we observe the high-frequency mode taking place in an elongated duct geometry, and when $H^{\prime }/\unicode[STIX]{x0394}r\approx 1$ we observe the low-frequency mode taking place in square duct geometry and high magnetic field.

Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers

This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

A Loading Correction Scheme for a Structure-Dependent Integration Method

A structure-dependent integration method may experience an unusual overshooting behavior in the steady-state response of a high frequency mode. In order to explore this unusual overshooting behavior, a local truncation error is established from a forced vibration response rather than a free vibration response. As a result, this local truncation error can reveal the root cause of the inaccurate integration of the steady-state response of a high frequency mode. In addition, it generates a loading correction scheme to overcome this unusual overshooting behavior by means of the adjustment the difference equation for displacement. Apparently, these analytical results are applicable to a general structure-dependent integration method.

Nonlinearity of Finite-Amplitude Waves in Rectangular Containers

This paper investigates the two-dimensional nonlinear finite-amplitude sloshing dynamics of an irrotational, incompressible fluid in a rectangular container. In specific, the paper addresses the influence of surface tension represented by a coefficient, β, and the ratio between the fluid height and the container’s width, represented by h/L, on the nonlinear normal sloshing modes. To achieve this objective, we first study the influence of, β, and, h/L, on the modal frequencies and generate a map in the (h/L, β) parameters’ space to highlight regions of possible nonlinear internal resonances up to the fifth mode. The map is used to characterize the regions where a single uncoupled nonlinear mode is sufficient to capture the response of surface waves. For these regions, we study the influence of surface tension on the effective nonlinearity of the first four modes and illustrate its considerable influence on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, we investigate the response of the sloshing waves near internal resonance of the two-to-one type. We show that, in the vicinity of these internal resonances, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the higher frequency mode (un-coupled high-frequency mode response). We show that the regions where the coupled-mode uniquely exists has a clear dependence on the surface tension.

Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control

We use direct numerical simulation (DNS) of the Navier–Stokes equations in the low-Mach-number limit to investigate the hydrodynamic instability of a lifted jet diffusion flame. We obtain steady solutions for flames using a finite rate reaction chemistry, and perform a linear global stability analysis around these steady flames. We calculate the direct and adjoint global modes and use these to identify the regions of the flow that are responsible for causing oscillations in lifted jet diffusion flames, and to identify how passive control strategies might be used to control these oscillations. We also apply a local stability analysis to identify the instability mechanisms that are active. We find that two axisymmetric modes are responsible for the oscillations. The first is a high-frequency mode with wavemaker in the jet shear layer in the premixing zone. The second is a low-frequency mode with wavemaker in the outer part of the shear layer in the flame. We find that both of these modes are most sensitive to feedback involving perturbations to the density and axial momentum. Using the local stability analysis, we find that the high-frequency mode is caused by a resonant mode in the premixing region, and that the low-frequency mode is caused by a region of local absolute instability in the flame, not by the interaction between resonant modes, as proposed in Nichols et al. (Phys. Fluids, vol. 21, 2009, article 015110). Our linear analysis shows that passive control of the low-frequency mode may be feasible because regions up to three diameters away from the fuel jet are moderately sensitive to steady control forces.

Planetary Gear Modal Vibration Properties Torque Sensitivity

The effect of preload torque on planetary gear behavior is investigated with experiments and mathematical models. Natural frequencies, mode shapes, and damping are influenced by mean torque levels. Natural frequencies increase with greater torque. Damping increases in some modes and decreases in others. The mode shapes undergo various changes as torque increases as demonstrated in the trajectory of a planet gear in a high frequency mode. A finite element bearing model is used to obtain the load dependent stiffness of the planet bearings, and these values greatly increase the accuracy of a lumped parameter model in predicting the natural frequencies measured in experiments.