This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Kármán vortex street regime that sets in for supercritical Reynolds numbers Re > 46. Barkley (Europhys. Lett. vol.75, 2006, p. 750) has recently studied the linear properties of the associated mean flow, i.e. the flow which is obtained by a time average of this unsteady periodic flow. He observed, thanks to a global mode analysis, that the mean flow is marginally stable and that the eigenfrequencies associated with the global modes of the mean flow fit the Strouhal to Reynolds experimental function well in the range 46 < Re < 180. The aim of this article is to give a theoretical proof of this result near the bifurcation. For this, we do a global weakly nonlinear analysis valid in the vicinity of the critical Reynolds number Rec based on the small parameter ε = Rec−1 − Re−1 ≪ 1. We compute numerically the complex constants λ and μ′ which appear in the Stuart-Landau amplitude equation: dA/dt = ε λA − εμ′ A|A|2. Here A is the scalar complex amplitude of the critical global mode. By analysing carefully the nonlinear interactions yielding the term μ′, we show for the cylinder flow that the mean flow is approximately marginally stable and that the linear dynamics of the mean flow yields the frequency of the saturated Stuart-Landau limit cycle. We will finally show that these results are not general, by studying the case of the bifurcation of an open cavity flow. In particular, we show that the mean flow in this case remains strongly unstable and that the frequencies associated with the eigenmodes do not exactly match those of the nonlinear unsteady periodic cavity flow. It will be demonstrated that two precise conditions must hold for a linear stability analysis of a mean flow to be relevant and useful.

The impact of the accuracy class of bearings, rotational speed, load, clearances, and fits on the vibration levels of electric motor bearing units is investigated. The ways to reduce the vibrations of mechanical origin are offered. The boundary vibration levels of asynchronous motors limited by vibration levels of 40 dB at a frequency of 5 Hz and 80 dB at a frequency of 10,000 Hz are determined. The effect of increasing the rotational speed and load on the vibration levels of bearing units has been determined, and reserves for reducing vibration while ensuring the optimum bearing preload on the shaft journal have been identified. It is established that the clearance between the cap and the bearing when it is fixed in the housing (primer) does not ensure the unambiguity of the bearing unit assembly, which results in a large variation in vibration levels compared with rigid and elastic fixation. The results of this research can be applied to all types of traction electric motors.

The heterodyne technique has a number of advantages over the homodyne technique when an accurate characterization of particle-size distribution (PSD) of heterogeneous systems is required. However, there are problems related to acoustic vibrations that make it difficult to take advantage of the heterodyne technique. An instrument developed for quasi-elastic light scattering (QELS) that uses the optical heterodyning principle is described. Vibration-related problems are considerably reduced because of the incorporation of all optical elements into one solid optical block. A real-time correlation analysis of the photocurrent fluctuations is performed by a PC-embedded analog-to-digital converter card with a digital signal processor. Investigation of the PSD in biological fluids for medical diagnostics is presented as a typical application. A diagnostic analysis of the PSD requires a simultaneous processing of a huge number of QELS data. An original statistical algorithm to accomplish this analysis has been developed. Technical specifications of instrumentation for heterodyne QELS measurement are discussed.

No abstract

No abstract