Part 32
[Illustration: FIG. 7.]
_Thrust Block Bearing._--In cases where a bearing is required to resist a longitudinal movement of the shaft through it, as for example in the case of the propeller shaft of a marine engine or a vertical shaft supporting a heavy load not carried on a footstep, the shaft is provided with one or more collars which are grooved with corresponding recesses in the brasses of the bearing. A general sketch of a thrust block for a propeller shaft is shown in fig. 7. There are seven collars turned on the shaft and into the circumferential grooves between them fit corresponding circumferential projections on the brasses, these projections being formed in the case illustrated by means of half rings which are fitted into grooves turned in the brasses. This method of construction allows an individual ring to be replaced or adjusted if it should get hot. The total area of the rubbing surfaces should be proportioned so that the average load is not more than from 50 to 70 lb. per sq. in. Arrangements are usually made for cooling a thrust block with water in case of heating. The spindles of drilling machines, boring machine spindles, turbine shafts may be cited as examples of vertical shafts supported on one collar. Experiments on the friction of a collar bearing have been made by the Research Committee of the Institution of Mechanical Engineers (_Proc. Inst. Mech. Eng._, 1888).
_Roller and Ball Bearings._--If rollers are placed between two surfaces having relative tangential motion the frictional resistance to be overcome is the small resistance to rolling. The rollers move along with a velocity equal to one half the relative velocity of the surfaces. This way of reducing frictional resistance has been applied to all kinds of mechanical contrivances, including bearings for shafts, railway axle boxes, and axle boxes for tramcars. An example of a roller bearing for a line shaft is illustrated in figs. 8 and 9. The main casting, A, and cap, C, bolted together, form a spherical seating for the part of the bearing E corresponding to the brasses in a bearing of the usual type. Between the inside of the casting E and the journal are placed rollers held in position relatively to one another by a "squirrel cage" casting, the section of the bars of which are clearly shown in the half sectional elevation, fig. 9. This squirrel cage ensures that the several axes of the rollers keep parallel to the axis of the journal during the rolling motion. The rollers are made of hard tool steel, and the surfaces of the journal and bearing between which they roll are hardened.
[Illustration: FIG. 8.]
[Illustration: FIG. 9.]
Two rings of balls may be used instead of a single ring of rollers, and the kind of ball bearing thus obtained is in general use principally in connexion with bicycles and motor cars (see BICYCLE). In ball bearings the load is concentrated at a few points, the points where the balls touch the race, and in the roller bearing at a few lines, the lines of contact between the rollers and the surfaces of the journal and bearing; consequently the load which bearings of this kind carry must not be great enough to cause any indentation at the points or lines of contact. Both rollers and balls, and the paths on which they roll, therefore, are made of hard material; further, balls and rollers must all be exactly the same size in an individual bearing in order to distribute the load between the points or lines of contact as uniformly as possible. The finest workmanship is required therefore to make good roller or good ball bearings.
_Bearings for High Speeds and Forced Lubrication._--When the shaft turns the metallic surfaces of the brass and the journal are prevented from actual contact by a film of oil which is formed and maintained by the motion of the shaft and which sustains the pressure between the journal and the brass provided the surfaces are accurately formed and the supply of oil is unlimited. This film changes what would otherwise be the friction between metallic surfaces into a viscous resistance within the film itself. When through a limited supply of oil or imperfect lubrication this film is imperfect or fails altogether and allows the journal to make metallic contact with the brass, the friction increases; and it may increase so much that the bearing rapidly becomes hot and may ultimately seize, that is to say the rubbing surfaces may become stuck together. With the object of reducing the friction at the points of metallic contact and of confining the damage of a hot bearing to the easily renewable brass, the latter is partially, sometimes wholly, lined with a soft fusible metal, technically known as white metal, which melts away before actual seizure takes place, and thus saves the journal which is more expensive because it is generally formed on a large and expensive shaft. However perfectly the film fulfils its function, the work required to overcome the viscous resistance of the film during the continuous rotation of the shaft appears as heat, and in consequence the temperature of the bearing gradually rises until the rate at which heat is produced is equal to the rate at which it is radiated from the bearing. Hence in order that a journal may revolve with a minimum resistance and without undue heating two precautions must be taken: (1) means must be taken to ensure that the film of oil is complete and never fails; and (2) arrangements must be made for controlling the temperature should it rise too high. The various lubricating devices already explained supply sufficient oil to form a partial film, since experiments have shown that the friction of bearings lubricated in this way is akin to solid friction, thus indicating at least partial metallic contact. In order to supply enough oil to form and maintain a film with certainty the journal should be run in an oil bath, or oil should be supplied to the bearing under pressure sufficient to force it in between the surfaces against the load. A bearing to which forced lubrication and water cooling are applied is illustrated in fig. 10, which represents one of the bearings of a Westinghouse turbo-alternator installed at the power station of the Underground Electric Railways Company of London at Lots Road, Chelsea. Oil flows under pressure from a tank on the top of a tower along a supply pipe to the oil inlet O, and after passing through the bearing and performing its duty as a film it falls away from each end of the journal into the bottom of the main casting, from which a pipe, E, conveys the oil back to the base of the tank tower where it is cooled and finally pumped back into the tank. There is thus a continuous circulation of oil through the bearing. The space C is for cooling water; in fact the bearing is water jacketed and the jacket is connected to a supply pipe and a drain pipe so that a continuous circulation may be maintained if desired. This bearing is 12 in. in diameter and 48 in. long, and it carries a load of about 12.8 tons. The rise in temperature of the bearing under normal conditions of working without water circulating in the jacket is approximately 38 deg. F. The speed of rotation is such that the surface velocity is about 50 ft. per second.
[Illustration: FIG. 10.]
Forced lubrication in connexion with the bearings of high-speed engines was introduced in 1890 by Messrs Belliss & Morcom, Ltd., under patents taken out in the name of A.C. Pain. It should be understood that providing the film of oil in the bearing of an engine can be properly maintained a double-acting engine can be driven at a high speed without any knocking, and without perceptible wear of the rubbing surfaces. Fig. 11 shows that the general arrangement of the bearings of a Belliss & Morcom engine arranged for forced lubrication. A small force-pump F, driven from the eccentric strap X, delivers oil into the pipe P, along which it passes to A, the centre of the right-hand main bearing. There is a groove turned on the inside of the brass from which a slanting hole leads to B. The oil when it arrives at A thus has two paths open to it, one to the right and left of the groove through the bearing, the other along the slanting hole to B. At B it divides again into two streams, one stream going upwards to the eccentric sheave, and a part continuing up the pipe Q to the eccentric pin. The second stream from B follows the slanting hole in the crank shaft to C, where it is led to the big end journal through the pipe R to the crosshead pin, and through the slanting hole to D, where it finds its way into the left main bearing. The oil forced through each bearing falls away to the right and to the left of the journal and drops into the bottom of the engine framing, whence it is again fed to the pump through a strainer. The parts of an engine lubricated in this way must be entirely enclosed.
[Illustration: FIG. 11.]
_Load on bearings._--The distribution of pressure over the film of lubricant separating the rubbing surfaces of a bearing is variable, being greatest at a point near but not at the crown of the brass, and falling away to zero in all directions towards the boundaries of the film. It is usual in practice to ignore this variation of pressure through the film, and to indicate the severity with which the bearing is loaded by stating the load per square inch of the rubbing surfaces projected on to the diametral plane of the journal. Thus the projected area of the surfaces of a journal 6 in. in diameter and 8 in. long is 48 sq. in., and if the total load carried by the bearing is 20,000 pounds, the bearing would be said to carry a load of 417 pounds per square inch. When a shaft rotates in a bearing continuously in one direction the load per square inch with which it is safe to load the bearing in order to avoid undue heating is much less than if the motion is intermittent. A table of a few values of the bearing loads used in practice is given in the article LUBRICANTS.
_Bearing Friction._--If W is the total load on a bearing, and if [mu] is the coefficient of friction between the rubbing surfaces, the tangential resistance to turning is expressed by the product [mu]W. If v is the relative velocity of the rubbing surfaces, the work done per second against friction is [mu]Wv foot pounds. This quantity of work is converted into heat, and the heat produced per second is therefore [mu]Wv/778 British Thermal Units. The coefficient [mu] is a variable quantity, and bearing in mind that a properly lubricated journal is separated from its supporting brass by a film of lubricant it might be expected that [mu] would have values characteristic of the coefficient of friction between two metallic surfaces, merging into the characteristics properly belonging to fluid friction, according as the oil film varied from an imperfect to a perfect condition, that is, according as the lubrication is partial or complete, completeness being attained by the use of an oil bath or by some method of forced lubrication. This expectation is entirely borne out by experimental researches. Beauchamp Tower ("Report on Friction Experiments," _Proc. Inst. Mech. Eng._, November 1883) found that when oil was supplied to a bearing by means of a pad the coefficient of friction was approximately constant with the value of 1/100, thus following the law of solid friction; but when the journal was lubricated by means of an oil bath the coefficient of friction varied nearly inversely as the load on the bearing, thus making [mu]W = constant. The tangential resistance in this case is characteristic of fluid friction since it is independent of the pressure. Tower's experiments were carried out at a nearly constant temperature. The later experiments of O. Lasche (_Zeitsch. Verein deutsche Ingenieure_, 1902, 46, pp. 1881 et seq.) show how [mu] depends upon the temperature. Lasche's main results with regard to the variation of [mu] are briefly:--[mu]W is a constant quantity, thus confirming Tower's earlier experiments; [mu] is practically independent of the relative velocity of the rubbing surfaces within the limits of 3 to 50 ft. per second; and the product [mu]t is constant, t being the temperature of the bearing. Writing p for the load per unit of projected area of the bearing, Lasche found that the result of the experiments could be expressed by the simple formula p[mu]t = constant = 2, where p = the pressure in kilograms per square centimetre, and t = the temperature in degrees centigrade. If p is changed to pounds per square inch the constant in the expression is approximately 30. The expression is valid between limits of pressure 14 to 213 pounds per square inch, limits of temperature 30 deg. to 100 deg. C., and between limits of velocity 3 to 50 ft. per second.
[Illustration: FIG. 12.]
_Theory of Lubrication._--After the publication of Tower's experiments on journal friction Professor Osborne Reynolds showed (_Phil. Trans._, 1886, p. 157) that the facts observed in connexion with a journal lubricated by means of an oil bath could be explained by a theory based upon the general principles of the motion of a viscous fluid. It is first established as an essential part of the theory that the radius of the brass must be slightly greater than the radius of the journal as indicated in fig. 12, where J is the centre of the journal and I the centre of the brass. Given this difference of curvature and a sufficient supply of oil, the rotation of the journal produces and maintains an oil film between the rubbing surfaces, the circumferential extent of which depends upon the rate of the oil supply and the external load. With an unlimited supply of oil, that is with oil-bath lubrication, the film extends continuously to the extremities of the brass, unless such extension would lead to negative pressures and therefore to a discontinuity, in which case the film ends where the pressures in the film become negative. The minimum distance between the journal and the brass occurs at the point H (fig. 12), on the off side of the point O where the line of action of the load cuts the surface of the journal. To the right and left of H the thickness of the film gradually increases, this being the condition that the oil-flow to and from the film may be automatically maintained. With an unlimited supply of oil the point H moves farther from O as the load increases until it reaches a maximum distance, and then it moves back again towards O as the load is further increased until a limiting load is reached at which the pressure in the film becomes negative at the boundaries of the film, when the boundaries recede from the edges of the brass as though the supply of oil were limited.
In the mathematical development of the theory it is first necessary to define the coefficient of viscosity. This is done as follows:--If two parallel surfaces AB, CD are separated by a viscous film, and if whilst CD is fixed AB moves in a tangential direction with velocity U, the surface of the film in contact with CD clings to it and remains at rest, whilst the lower surface of the film clings to and moves with the surface AB. At intermediate points in the film the tangential motion of the fluid will vary uniformly from zero to U, and the tangential resistance will be F = [mu]U/h, where [mu] is the coefficient of viscosity and h is the thickness of the film. With this definition of viscosity and from the general equations representing the stress in a viscous fluid, the following equation is established, giving the relations between p, the pressure at any point in the film, h the thickness of the film at a point x measured round the circumference of the journal in the direction of relative motion, and U the relative tangential velocity of the surfaces,
d / dp\ dh -- ( h^3-- ) = 6[mu]U -- (1) dx \ dx/ dx
In this equation all the quantities are independent of the co-ordinate parallel to the axis of the journal, and U is constant. The thickness of the film h is some function of x, and for a journal Professor Reynolds takes the form,
h = a {1 + c sin([theta] - [phi]0)}
in which the various quantities have the significance indicated in fig. 12. Reducing and integrating equation (1) with this value of h it becomes
dp 6R_[mu]U_c {sin([theta] - [phi]0) - sin([phi]1 - [phi]0)} -------- = --------------------------------------------------------- (2) d[theta] a^2{1 + c sin([theta] - [phi]0)}^3
[phi]1 being the value of [theta] for which the pressure is a maximum. In order to integrate this the right-hand side is expanded into a trigonometrical series, the values of the coefficients are computed, and the integration is effected term by term. If, as suggested by Professor J. Perry, the value of h is taken to be h = h0 + ax^2, where h0 is the minimum thickness of the film, the equation reduces to the form
dp 6[mu]U C - -- = ------------- + ------------- (3) dx (h0 + ax^2)^2 (h0 + ax^2)^3
and this can be integrated. The process of reduction from the form (1) to the form (3) with the latter value of h, is shown in full in _The Calculus for Engineers_ by Professor Perry (p. 331), and also the final solution of equation (3), giving the pressure in terms of x.
Professor Reynolds, applying the results of his investigation to one of Tower's experiments, plotted the pressures through the film both circumferentially and longitudinally, and the agreement with the observed pressure of the experiment was exceedingly close. The whole investigation of Professor Reynolds is a remarkable one, and is in fact the first real explanation of the fact that oil is able to insinuate itself between the journal and the brass of a bearing carrying a heavy load. (See also LUBRICATION.) (W. E. D.)
BEAR-LEADER, formerly a man who led bears about the country. In the middle ages and Tudor times these animals were chiefly used in the brutal sport of bear-baiting and were led from village to village. Performing bears were also common, and are even still sometimes seen perambulating the country with their keepers, generally Frenchmen or Italians. The phrase "bear-leader" has now come colloquially to mean a tutor or guardian, who escorts any lad of rank or wealth on his travels.
BEARN, formerly a small frontier province in the south of France, now included within the department of Basses-Pyrenees. It was bounded on the W. by Soule and Lower Navarre, on the N. by Chalosse, Tursan and Astarac, E. by Bigorre and S. by the Pyrenees. Its name can be traced back to the town of Beneharnum (Lescar). The _civitas Beneharnensium_ was included in the _Novempopulania_. It was conquered by the Vascones in the 6th century, and in 819 became a viscounty dependent on the dukes of Aquitaine--a feudal link which was broken in the 11th century, when the viscounts ceased to acknowledge any suzerain. They then reigned over the two dioceses of Lescar and Oloron; but their capital was Morlaas, where they had a mint which was famous throughout the middle ages. In the 13th century Gaston VII., of the Catalonian house of Moncade, made Orthez his seat of government. His long reign (1229-1290) was a perpetual struggle with the kings of France and England, each anxious to assert his suzerainty over Bearn. As Gaston left only daughters, the viscounty passed at his death to the family of Foix, from whom it was transmitted through the houses of Grailly and Albret to the Bourbons, and they, in the person of Henry IV., king of Navarre, made it an apanage of the crown of France. It was not formally incorporated in the royal domains, however, until 1620. None of these political changes weakened the independent spirit of the Bearnais. From the 11th century onward, they were governed by their own special customs or _fors_. These were drawn up in the language of the country, a Romance dialect (1288 being the date of the most ancient written code), and are remarkable for the manner in which they define the rights of the sovereign, determining the reciprocal obligations of the viscount and his subjects or vassals. Moreover, from the 12th century Bearn enjoyed a kind of representative government, with _cours plenieres_ composed of deputies from the three estates. From 1220 onward, the judiciary powers of these assemblies were exercised by a _cour majour_ of twelve barons _jurats_ charged with the duty of maintaining the integrity of the _fors_. When Gaston-Phoebus wished to establish a regular annual hearth-tax (_fouage_) in the viscounty, he convoked the deputies of the three estates in assemblies called _etats_. These soon acquired extensive political and financial powers, which continued in operation till 1789. Although, when Bearn was annexed to the domains of the crown, it was granted a _conseil d'etat_ and a parlement, which sat at Pau, the province also retained its _fors_ until the Revolution.
See also Olhagaray, _Histoire de Foix, Bearn et Navarre_ (1609); Pierre de Marca, _Histoire de Bearn_ (1640). This work does not go beyond the end of the 13th century; it contains a large number of documents. Faget de Baure, _Essais historiques sur le Bearn_ (1818); _Les Fors de Bearn_, by Mazure and Hatoulet (1839), completed by J. Brissaud and P. Roge in _Textes additionnels aux anciens Fors de Bearn_ (1905); Leon Cadier, _Les Etats de Bearn depuis leur origine jusqu'au commencement du XVI^e siecle_ (1888). (C. B.*)
BEAS or BIAS, a river of India. The Beas, which was the Hyphasis of the Greeks, is one of the Five Rivers of the Punjab. It issues in the snowy mountains of Kulu at an altitude of 13,326 ft. above sea-level, flows through the Kangra valley and the plains of the Punjab, and finally joins the Sutlej after a course of 290 m. It is crossed by a railway bridge near Jullundur.
BEAT (a word common in various forms to the Teutonic languages; it is connected with the similar Romanic words derived from the Late Lat. _battere_), a blow or stroke; from the many applications of the verb "to beat" come various meanings of the substantive, in some of which the primary sense has become obscure. It is applied to the throbbing of the pulse or heart, to the beating of a drum, either for retreat, or charge, or to quarters; in music to the alternating sound produced by the striking together of two notes not exactly of the same pitch (see SOUND), and also to the movement of the baton by which a conductor of an orchestra or chorus indicates the time, and to the divisions of a bar. As a nautical term, a "beat" is the zigzag course taken by a ship in sailing against the wind. The application of the word to a policeman's or sentry's round comes either from beating a covert for game and hence the term means an exhaustive search of a district, or from the repeated strokes of the foot in constantly walking up and down. In this sense the word is used in America, particularly in Alabama and Mississippi, of a voting precinct.