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Vibration analysis of ball bearing considering waviness under high speed and an axial load

Hou P. P., Wang L. Q., Peng Q. Y.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

Vol. 68, nr 3

517--527

Based on the rolling bearing vibration measurement principle in ISO standard, a nonlinear dynamic model of ball bearing is built and motion equations of the inner ring, outer ring, and rolling elements are derived by using Lagrange’s equation. The ball bearing model includes the influence of waviness, rotational speed, external load, arbor supporting stiffness and arbor eccentricity. Ball bearing high-speed vibration tests are performed and used to verify the theoretical results. Simulated results showed that specific waviness orders produced the principal frequencies that were proportional to rotational speed. Rotational speed mainly affected the value of the natural frequency of the bearing system, and RMS (Root Mean Square) of the full band had a great fluctuation with the increase of rotational speed. In the experiment, spectrum and RMS of 2 ƒs-30 kHz (ƒs : the rotational frequency of inner ring/arbor) under high speed could include not only the influence of rotational speed but also principal frequencies produced by waviness, which could cover the part of requirements of the standard bearing vibration measurement.

Two Supramolecular Complexes with Hydrogen-bonds of N-H ··· O and C-H ··· O between Dicarboxylic Acids and Bis-imidazoles

Jin S. W., Wang D. Q., Jin Z. J., Wang L. Q.

Polish Journal of Chemistry

2009

Vol. 83, nr 11

1937-1944

Two imidazole derived supra molecular complexes (N,N'-butylenebis(imidazole) : (tere - phthalic acid)2 (1), and N,N'-butylenebis(imidazole) : sebacic acid (2)) were synthesized and structurally characterized by X-ray crystallography. Compounds 1 and 2 both crystallize in the triclinic P-1 space group. In compound 1, one-dimensional grid structure is formed through imidazolium moieties hydrogen bonded to mono-ion carboxylate groups of two par al lel terephthalate chains. Ad ja cent grids packed along the b axis through C-H ··· O hydrogen bonds form 3D network. For compound 2, with strong O-H ···N hydrogen bonds, the bis(imidazole) and the sebacic acid are arranged alternatively to form 1D in finite chain, which is further stacked into a 3D net work structure through additional C-H ··· O hydrogen bonds.