This paper investigates the nonlinear characteristics of varying compliance contact resonance in a rotor–bearing system and takes into consideration the Hertzian contact deformation and internal radial clearance. We created an experimental rig of a rigid rotor supported by rolling element bearings. In the course of the rotational speed run up and down, the frequency–amplitude curves of the varying compliance vibrations were observed during experiments using different radial loads and compared with the results of our numerical simulations. The experimental and numerical results indicate that the varying compliance contact resonance in the vertical direction presents the soft spring characteristic, while the soft and hard spring characteristics coexist for the horizontal resonance.

The varying compliance (VC) vibration directly reflects the oscillation intensity of a rolling bearing, and it can be fully revealed in the VC resonance. Moreover, we define the bearing vibration intensity as the bearing vibration information in this paper. Besides the rolling element number of the bearing, the rotor eccentricity is also an inevitable influencing factor for the VC vibration. This paper focuses on the VC resonance characteristics in a ball bearing rotor system. An analytical model is established, and the vibration responses of the system are calculated in a large speed range with the consideration of different ball numbers and different rotor eccentricities. The theoretical results show that the VC vibration is clearer in low-speed range where the VC resonance exist, while it is suppressed in high-speed range. In general, the intensity of the VC resonance decreases with the increase of ball numbers and is not sensible to the rotor eccentricities in low-speed range. Finally, a ball bearing rotor experiment system is setup, the VC resonance is clearly detected, and the high-quality bearing vibration information is obtained. The experimental results qualitatively agree with the theoretical results.

Molecular complexes formed in the organic phase during solvent extraction may self-assemble as reverse micelles, and therefore induce a supramolecular organization of this phase. In most of the cases, water molecules play an essential role in the organization of this non polar medium. The aim of this work is to investigate the speciation of the aggregates formed in the organic phase during solvent extraction, and especially to assess their stability as a function of the number of water molecules included in their polar core. We have focused on malonamide extractants that have already been investigated experimentally. Different stoichiometries of reverse micelles in the organic phase have been studied by means of classical molecular dynamics simulations. Furthermore, umbrella-sampling molecular dynamics simulations have been used to calculate the equilibrium constant (K°) representing the association/dissociation pathways of water molecules in the aggregates and the corresponding reaction free energies (Δ_rG°).