Progress in Rolling Bearing Vibration Research and Control

Tallian, T. E.; Gustafsson, Olof

doi:10.1080/05698196508972094

Cited by 85 publications

(28 citation statements)

References 9 publications

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“…The application of such a correction has been shown to be meaningful with these particular initial conditions. 6 Since the assumed distribution of instantaneous line sources on the bottom of the diffusion vessel is unknown it is impossible to calculate the complete concentration distribution at a particular moment. If we make the simplifying assumption that the mean con-centration (c) can be described by the simple plane source solution, we get c=co(7rDt)-1/2 exp( -x2/4Dt).…”

Section: Di=xs/ln[(x+s)/ (X-s)]mentioning

confidence: 99%

“…The zeroth order vibronic states are eigensolutions of the "crude" adiabatic approximation. 6 We consider the following set of states: 4Js, the lowest vibrational state of SI; (4JTl, a small set of vibronic levels of Tz (i.e., the lowest and first few vibrational states of Tz); the dense manifold of vibrationally excited states of T 1 , (4Jd, which are equally spaced in energy with spacing f. (The density of states PI is thus f-1 .) The residual interaction between these states consists of spin-orbit interaction (between CPs and (4JT 1 and between 4Js and (4JIJ) and vibronic interaction (between (4Jd and [4Jzl) .3,6 For the cases we will consider, the manifold {4Jzl has two disjoint subsets: one of which interacts with 4Js through spin-orbital coupling and one of which interacts with [4Jd via vibronic coupling.…”

Section: Modelmentioning

confidence: 99%

“…In our included in the mathematical description provided the work we have chosen the second alternative because diffusing substance is supplied at the bottom of the of what we believe a greater flexibility in the choice of diffusion vessel. 6 Because of this circumstance we have recording instruments. In order to eliminate the used the very simple technique of dropping a solid temperature gradients and the convection currents in crystal of the diffusing substance to the bottom of a the air of the light passages through the thermostat properly formed container and then we have studied walls, the construction was such that the pressure the diffusion of the solute into the solvent.…”

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confidence: 99%

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Interdiffusion Measurements in Fused Alkali Nitrates by Wave-Front-Shearing Interferometry

Arvidsson

Afsenius

Gustafsson

1970

The Journal of Chemical Physics

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Interdiffusion coefficients in molten alkali nitrate systems have been measured by recording the phase variations introduced on an initially plane wave front when passing through a diffusion vessel. The recording of the path differences is performed with a wave-front-shearing interferometer giving a high degree of accuracy. Two different methods have been used to initiate bottom layer diffusion experiments, one of which has been developed in the course of this work. The interdiffusion studied here has been that of rubidium and cesium ions and in some cases that of sodium and potassium ions diffusing into the pure melts of lithium nitrate, sodium nitrate, and potassium nitrate. The diffusion coefficients have been measured over a temperature range of some 100°C above the melting point.The marked decrease in fluorescent quantum yield of anthracene in going from crystal to solution is discussed theoretically. The relative importance of direct and indirect radiationless transitions from the excited singlet to the triplet manifold is calculated using a simple model.

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Section: Di=xs/ln[(x+s)/ (X-s)]mentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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Interdiffusion Measurements in Fused Alkali Nitrates by Wave-Front-Shearing Interferometry

Arvidsson

Afsenius

Gustafsson

1970

The Journal of Chemical Physics

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“…The defects in rolling element bearings can be categorized as 'local' or 'distributed'. The distributed defects in rolling element bearings include surface roughness, waviness, misaligned races, and off-size rolling elements [1,2]. The surface features are considered in terms of wavelength compared to Hertzian contact width of the rolling element raceway contacts.…”

Section: Introductionmentioning

confidence: 99%

Non-linear vibration signature analysis of a high-speed rotating shaft due to ball size variations and varying number of balls

Upadhyay

Jain

Harsha

2009

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this article, a mathematical model has been developed to predict the non-linear dynamic behaviour of a high-speed unbalanced rotating shaft due to ball size variations and varying number of balls. In the mathematical formulation, the contact between balls and inner/outer races is considered as a non-linear spring, whose stiffness is obtained using Hertzian elastic deformation theory. A detailed contact-damping model reflecting the influences of the surface profiles and the speeds of both contacting elements is developed and applied in the rolling element bearing formulation. This formulation also accounts for sources of non-linearity such as Hertzian contact force, varying number of balls, and off-sized balls resulting transition from noncontact to contact state between balls and races. The equations of motion of a rolling element bearing are formulated using Lagrange's equation considering the vibration characteristics of individual constituents such as inner race, outer race, rolling elements, and shaft. To overcome the strong non-linearity of the governing equations of motion, a modified Newmark-β time integration technique has been used to solve the equations of motion numerically. All results have been presented in the form of fast Fourier transformations and Poincaré maps. The highest radial vibrations due to ball size variation are at a speed of the number of balls times the cage speed (ω = kω cage Hz). The other vibrations due to ball size variation also occurr at (X ± kω cage ), where k is a constant. When the number of balls is increased, the centre of oscillations approaches zero, implying a stiffer system. From this it can be predicted that increasing the number of balls will reduce the effect of the BPF. Hence it is implied from the analysis that the number of balls and the size variation of balls are important parameters and should be considered at the design stage.

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“…After the image of the slot became clear (~ 3 hr), a small crystal of solute was dropped into the cell from a height of about 1 m. The crystals were prepared by melting the solute material in a nitrogen atmosphere and allowing it to cool. The initial condition of the bottom layer in this method has already been discussed [7]. After the image of the shear became clearly detectable, the interferograms were recorded with appropriate intervals.…”

Section: Methodsmentioning

confidence: 99%

High-Dilution Diffusion of K + , Rb + , Cs + , and Tl + in the Molten System (Li-K)NOs Studied by Wave-Front-Shearing Interferometry

Odawara

Okada

Kawamura

1979

Zeitschrift Für Naturforschung A

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The high-dilution diffusion coefficients of K+, Rb + , Cs+, and T1+ in molten LiN03-KN03 mixtures are measured over a wide range of temperatures and concentrations by means of wavefront-shearing interferometry. A slightly positive deviation from linearity is found for the concentration dependence of the diffusion coefficient of K + , Rb + , and T1+, while no deviation is found for Cs + within the experimental error. This is qualitatively discussed from the viewpoint of the ionic radii, the free space in the solvent, and the interaction between the diffusing and the surrounding ions.

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Progress in Rolling Bearing Vibration Research and Control

Cited by 85 publications

References 9 publications

Interdiffusion Measurements in Fused Alkali Nitrates by Wave-Front-Shearing Interferometry

Interdiffusion Measurements in Fused Alkali Nitrates by Wave-Front-Shearing Interferometry

Non-linear vibration signature analysis of a high-speed rotating shaft due to ball size variations and varying number of balls

High-Dilution Diffusion of K + , Rb + , Cs + , and Tl + in the Molten System (Li-K)NOs Studied by Wave-Front-Shearing Interferometry

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