Volume 17, Issue 3, 01 March 1946
Index of content:
Film‐Lubrication between Spherical Surfaces: with an Application to the Theory of the Four‐Ball Lubricant Testing Instrument17(1946); http://dx.doi.org/10.1063/1.1707699View Description Hide Description
The paper is concerned mainly with the flow of viscous liquid between the outer surfaces of two equal spheres placed in an infinite body of the liquid so that the ``minimum separation'' of the surfaces (the distance apart at the points of closest approach) is small compared with the radius; one sphere is held at rest, the other rotates at constant speed about an axis which does not pass through the center of the fixed sphere. The assumption is made that the surfaces are separated by a continuous film of liquid to which the classical theory of hydrodynamical lubrication can be applied—that is, ``boundary lubrication'' and actual contact between the surfaces are excluded; the partial differential equation (the Reynolds equation) for the pressure distribution in this film is set up, and it is shown that with a suitable choice of boundary conditions a solution can be found in very simple form. From this solution are deduced the total force exerted by the liquid on the moving sphere and the torque, about the axis of rotation, of the forces acting on the fixed sphere. The results are applied to the particular case of the four‐ball lubricant testing instrument, in which a sphere is made to rotate about a vertical axis, under axial load, in the central space formed by a set of three equal spheres held stationary so as to touch one another with their centers in a horizontal plane; the whole set of spheres is immersed in the lubricant to be tested. The relations finally obtained express the load on the moving sphere and the torque on the set of fixed spheres in terms of the radius of the spheres, the velocity of rotation, and the viscosity of the liquid; they involve as a parameter the minimum separation of the moving sphere from the fixed spheres, and elimination of this gives the relation between the measurable quantities, load, and torque, which could provide a basis for the use of the instrument as a viscometer. It is found that the torque is a very slowly varying function of the load, being approximately proportional to the logarithm of the load. Further, if it is assumed that the hydrodynamical theory of lubrication is valid only for films whose thickness is greater than some agreed minimum, then the expression for the load on the moving sphere, into which the minimum separation enters, provides a criterion for the range of conditions (of which the load is much the most important) within which the theory does in fact apply to the instrument. Numerical examples are considered, and it is shown that, with allowance for wide departures from the standard size and speed of operation of the instrument, the maximum load which can be supported by the moving sphere in the hydrodynamical regime cannot be expected to exceed a few hundred grams weight; for loads of greater order the standard continuous‐film theory cannot hold, and the forces on the spheres are no longer determined by the viscosity of the liquid.
The Analysis of Multicomponent Mixtures of Hydrocarbons in the Liquid Phase by Means of Infra‐Red Absorption Spectroscopy17(1946); http://dx.doi.org/10.1063/1.1707700View Description Hide Description
This is a general method of applying infra‐red absorption spectroscopy to the analysis of multicomponent hydrocarbon mixtures in the liquid phase. The procedure is calibrated by measuring optical densities of synthetic standard samples. A constant thickness cell is used for both standard and unknown samples. Two procedures for converting optical densities to concentrations are described. Examples are given for four‐ and five‐component mixtures. Data are presented to show the reproducibility of repeated measurements of optical density on the same sample, and results are given to show the agreement between the infra‐red analyses and the known composition of synthetic mixtures.
17(1946); http://dx.doi.org/10.1063/1.1707701View Description Hide Description
By adapting an electro‐dynamic loudspeaker, an apparatus was assembled to test the strength of glass rods in flexure. This apparatus will apply the stress in 2 to 3 milliseconds and permit static loading for times as short as 0.01 second. Using an additional long time loading apparatus, which simultaneously tested eighteen rods, it was possible to run static fatigue tests on glass rods from 1000 seconds to 86,400 seconds. The method of testing and errors due to the apparatus are discussed.
17(1946); http://dx.doi.org/10.1063/1.1707702View Description Hide Description
Static loading tests were run on glass and porcelain rods inch in diameter for times ranging in duration from 0.01 second to 24 hours, by using specially designed apparatus. It was found that glass can support for 0.01 second about 3 times the stress that would break it in 24 hours. The effects are generally the same for all glassy materials. Porcelain showed the effect somewhat less than glass. It appeared that adsorbed moisture and gases reduced the strength.
17(1946); http://dx.doi.org/10.1063/1.1707703View Description Hide Description
The strength of glass was measured in various surrounding media. It was found that glass is 20 percent stronger when dry than when wet, and two to two and a half times as strong when baked in vacuum than when tested wet (on tests of ten seconds duration). Apparently, the chief cause of the loss of strength, as compared with that in vacuum, is moisture, but gases, especially CO2, seem to have some effect. It was found that fatigue of glass disappears when the glass is tested in a vacuum.
Autoclaving tests showed that glass is rapidly etched by water at higher temperatures, and that even silica glass is considerably attacked. It appears that the attack of water on glassy surfaces produces gels, and this attack goes on inside the flaws, thus considerably complicating the problem of the strength of glass.
17(1946); http://dx.doi.org/10.1063/1.1707704View Description Hide Description
The decline in the breaking strength of glass with an increase in the length of time it is under stress has been noted by various experimenters. Based on the experimental results of T. C. Baker, an empirical relationship is obtained which indicates that the reciprocal of the breaking stress is a linear function of the logarithm of the duration of the stress. Certain implications of this relationship are discussed.
17(1946); http://dx.doi.org/10.1063/1.1707705View Description Hide Description
This paper deals with the heat input to hollow cylindrical metal cores subjected to induction heating. The rigorous expression for the heat input, valid for the whole frequency range, is developed and is presented by Eq. (27) of this paper. It is shown in an example how the equation is used for numerical computations. Existing approximate formulas for the low frequency and the high frequency range are checked by means of the rigorous equation; the maximum deviation between the rigorous and approximate equations is about 10 percent.
17(1946); http://dx.doi.org/10.1063/1.1707706View Description Hide Description