BEARINGS, the name given to the supports of a rotating shaft. The shaft imposes a load on each of the bearings support ing it, and it is turned against the frictional resistances caused by this loading.
The main shaft seen in a workshop carries pulleys from which belts transmit power to the machinery. Such a shaft loads its bearings not only with its own weight and the weights of the pulleys, clutches, and couplings keyed to it, but with the ten sions from the driving belts on the pulleys and with the dynamical forces caused by the mere rotation of unbalanced masses. The dynamical forces increase as the square of the speed. The dynam ical force, f, acting on the shaft at a point where a mass weigh ing W lb. is unbalanced in the sense that its centre of mass is r feet from the axis of rotation, may be calculated from In this expression n is the speed of the shaft in revolutions per second, r is in feet, and f is in pounds. If, for example, a large pulley on the shaft is out of balance to the extent of i olb. at i ft. radius, then when the shaft turns 30o times per minute the force f is 3oolb. This force always acts along the radius of the un balanced mass. If the speed be doubled to 600 turns per minute, the force f is quadrupled to i,2oolb. This force not only increases the friction at the bearings but sets up vibration because it is con tinually changing in direction. All parts attached to the shaft and rotating with it should therefore be carefully balanced to prevent undue loading of the bearings and to avoid setting up vibration. The rotation of the shaft against the frictional resistances in the bearings caused by the loading, absorbs energy from the prime mover, and this energy is converted into heat. Shafts and bear ings assume the temperature of their surroundings when not at work, but immediately the shaft is set in motion, heat is produced at the rubbing surfaces of shaft and bearing and the temperature of the bearing rises, and continues to rise until the heat pro duced by friction per second is exactly balanced by the heat escaping from the bearing per second by conduction, convection, and radiation to the cooler surroundings. When the balance is struck the temperature of the bearing remains constant. Thus a bearing at work must always be hotter than its surroundings in order to establish a heat flow sufficient to dissipate the heat produced.
The dominating principle of design is therefore so to propor tion the parts to the loads and the lubrication to the speed that the heat necessarily produced by the rotation of the shaft is dis sipated without undue rise of temperature. If by any chance the frictional resistance is abnormally increased by failure of the lubrication, by dirt getting between the rubbing surfaces, or by unexpected increases of load or speed, the temperature of the bearing rises dangerously until ultimately the rubbing surfaces may seize together, causing perhaps a broken shaft and other troubles.
A Plummer Block.—The mechanical details of a bearing in common use for general millwrighting purposes are shown in fig. z.
The brasses are made of gun metal or brass and are often lined with antifriction metal. The metal is usually an alloy of tin, antimony and lead (the proportions vary), and from its col our is called generally white metal. An antifriction metal must be soft enough to yield to slight inequalities in the shaft but hard enough to resist abrasion on the surface.
The condition of speed cannot be stated precisely because the viscosity of the oils used for lubrication vary with the kind of oil, the pressure in the film, and the temperature. The plummer block illustrated in fig. i is an example in which the conditions are not fulfilled because the supply of oil is not copious enough from the wick lubricator to allow the film to form even when a sufficient relative velocity is reached. The axle box is an example in which viscous lubrication is approached. The bottom of the journal is always kept greased by the pad ; oil is carried round and a film will form if there is enough oil carried. Beauchamp Tower found that with pad lubrication oil was not carried to the brass in sufficient quantity to form a true film. After the experiments of Beauchamp Tower had been published and the fact had been established that, in suitable conditions, an oil film forms, Prof. Osborne Reynolds showed that its formation could be predicted from the principles of the flow of viscous fluids, and he deduced an expression relating the pressure at any given point in the film to the dimensions of the bearing and the variables of the lubricant. This work was published in the Phil. Trans. of 1886. A brief account of this outstanding investigation is given below.
Before the existence of a film was suspected and the advantages of forced lubrication were understood, it was the practice to con struct high speed engines single acting only, to avoid the reversal of thrust at the bearings when the connecting rods change their action from push to pull. Since the bearings are always a little larger than the journal, a reversal of thrust in the absence of an oil film causes a knock and high speeds are impossible.
The Michell principle of pad lubrication has been extended to journals supporting vertical loads. An ordinary high speed bear ing may be regarded as a single pad bearing, the conditions for the formation of the oil wedge being realized by slight automatic movement of the journal into an eccentric position in relation to the brass. When a number of pads are incorporated in a bearing, then as many oil wedges form as there are pads, and the size of a bearing for a given load is considerably reduced. The twin-screw steamship "Gouverneur-General Chanzy," built by Cammell Laird and Co. Ltd., is stated to be the first ship in which the whole of the main and thrust bearings of the propelling machinery have been constructed on the Michell principle. The details may be studied in Engineering, July 28, 1922.
Ball and Roller Bearings.— Ball bearings enable the resist ance to rolling to be substituted for sliding resistance and are es pecially useful for high-speed bearings r e q u i r e d to carry moderate loads. The ball ele ments - - of a bearing are manufactured as standard units and these units are incorporated in the complete design of a bearing. A typical ball bearing unit with a single row of balls is shown in fig. 7. The inner and the outer race, representing two diameters, enclose completely the ring of balls. A cage is added to prevent adjacent balls from touching be cause, when rolling in their races, adjacent surfaces are moving in opposite directions. The cage is seen clearly in the perspective sketch to the left of the figure.
Units are made with double rows of balls. A single plate thrust bearing is shown in fig. 8. It con sists of two flat rings with races formed on their faces for the single ring of balls seen. A cage is added to separate the balls.
Balls are made of high grade steel hardened and finished to exact dimensions. The ball races and rings are also made of high grade steel hardened and finished by grinding. Rolling resistance is not easily analysed into all the factors involved in the total resistance, but the minute elastic dis tortions of the hardened balls and races and the slight relative slipping, probably contribute the major part of the resistance when the bearing is properly housed and set up. (See Reynolds, Scien tific Papers Vol. I. for theory of rolling friction.) The manufac turers supply a wide range of sizes in each type together with corn plete particulars regarding loads and speeds, so that a suitable unit may be selected for the particular problem in hand. The units have then to be incorporated in a suitably designed housing.
A Skefko design of a lathe head incorporating two double row self-aligning bearings and a double row thrust bearing is shown in fig. 9. This illustrates a fundamental principle of design in the use of ball bearing units, namely that the shaft must be located by one unit only. The outer races of the other bearing must be free to take up longitudinal position determined by the balls. The lathe spindle is located by the middle plate of the double thrust bearing. This plate is clamped to the spindle by the bushes of which one is a nut. The outer plates then abut against faces in the housing, but the outer rings of the double thrust bearing supporting the spindle are free to slide longi tudinally in the housing. The inner races are however clamped securely to the spindle in the way shown in the sketch.
A Timken design for a front axle bearing for a motor-car is shown in fig. 1o. This illustrates the use of a taper roller bearing. Adjustment can be made for any slight wear that may occur.
Ball and roller bearings are used in motor vehicles, and the quietness and smoothness of the motion of a well-made car are due to the frictionless qualities of the ball bearings in which the moving parts are mounted. Experiments on ball and roller bear ings are recorded in "Roller and Ball Bearings" by Prof. Goodman, Proc. Inst. Civil Eng., Vol. 189. Much technical information will be found in A. W. Macaulay's Handbook on Ball and Roller Bear ings (1924).
Bearing Friction.—If W is the total load on a bearing, and if /2 is the co-efficient of friction between the rubbing sur faces, the tangential resistance to turning is expressed by the product µW. If v is the relative velocity of the rubbing surfaces, the work done per second against friction is µ Wv foot pounds. The co-efficient s is a variable quantity. It varies between val ues characteristic of solid friction for imperfectly lubricated sur faces and values characteristic of fluid friction for surfaces sepa rated by an oil film. Beauchamp Tower ("Report on Friction Experiments," Proc. Inst. Mech. Eng., Nov. 1883' found that when oil was supplied to a bearing by means of a pad the co-effi cient of friction was approximately constant with the value I/Ioo, thus following the characteristics of solid friction; but when the journal was lubricated by means of an oil-bath the co-efficient of friction varied nearly inversely as the load, thus making Wµ a constant, a characteristic of fluid friction. Tower's experiments were carried out at nearly constant temperature. 0. Lasche (Zeit. Verein deutsche Ingenieure 1902, 46, pp. 1881 et seq.) found that the formula pµt = 2 expressed the results of his experiments. In this expression p is the load per unit of projected area of the bearing in kilograms per sq. cm., t is the temperature of the bear ing in degrees C. If p is changed to lb. per sq. in., the constant 2 is changed to 3o approximately. The expression is valid be tween the limits of pressure 14 and 213 lb. per sq. in., between limits of temperature 3o°C and ioo°C and between limits of relative velocity between the rubbing surfaces of 3 and soft. per sec. Experiments bearing on the value of µ are recorded in O. Lasche's Materials and Design in Turbo-Generator Plant, trans. by A. L. Mellanby (1927).
With the exception of the work of Michell, nothing of funda mental importance has been done since the researches of Beau parative result it was found that the co-efficient of viscosity for castor oil at 40°C is about six times as great at a pressure of six tons per sq. in. as at one atmosphere, whilst an animal oil called trotter oil shows a viscosity only 1•16 times as great for the same range of pressure, and yet the tests show that the fric tional resistance in the bearing of both oils is about the same. The inference is that the frictional resistance of an oil film does not depend only upon the viscosity of the lubricant. The report contains much experimental work relating to the properties of lubricating oil of value to the engineer. A new committee, The Lubrication Research Committee, was appointed in 1925 to con tinue research in the subject but it has not yet issued a report.
Theory of the publication of Tower's experiments on journal friction Osborne Reynolds showed (Phil. Trans., i886, p. 157) that the facts observed in connection with a journal lubricated by means of an oil-bath could be explained champ Tower carried out for the Institution of Mechanical Engi neers (1883-91) and the brilliant work of Osborne Reynolds based upon the results. The Report of the Lubricants and Lubri cation Enquiry Committee appointed by the Department of Sci entific and Industrial Research in 1917 was published in 1920. The Committee reviewed the knowledge existing at the time of their report Aid compiled an exhaustive bibliography of the sub ject. This bibliography is not separately published but may be consulted at the office of the Department, 16, Old Queen street, London. Included in the report are many data derived from experiments initiated by the Committee. The report gives the following approximate values of A.
Unlubricated surfaces o•i to 0.4 Imperfectly lubricated surfaces called greasy surfaces o-oi to o-t Completely lubricated surfaces with formation of oil film giving what is called viscous friction o-ooi to o.oi Included in the report are the results of experiments made to find how tc varied with high pressures. Quoting only one com 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. I t, 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, i.e., 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. I I), on the off side of the point 0 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 0 as the load increases until it reaches a maximum distance, and then it moves back again towards 0 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 bound aries 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 neces sary to define the co-efficient 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 = µ U/h, where ,u is the co-efficient 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, a = (1) In this equation all the quantities are independent of the co-ordi nate 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 Reynolds takes the form, h = a t i-f-c sin(e-4e) 1 in which the various quantities have the significance indicated in fig. I 1. Reducing and integrating equation (I) with this value of h it becomes 0 being the value of 0 for which the pressure is a maximum. In order to integrate this the right-hand side is expanded into a trig onometrical series, the values of the co-efficients are computed, and the integration is effected term by term. If, as suggested by Prof. J. Perry, the value of h is taken to be where is the minimum thickness of the film, the equation reduces to the form dfi = C (3) dx and this can be integrated. The process of reduction from the form (I) to the form (3) with the latter value of h, is shewn in full in The Calculus for Engineers by Prof. Perry (p. 331), and also the final solution of equation (3), giving the pressure in terms of x.
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 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. Reynolds assumed the bearing to be of infinite width. In the actual bearing of finite width the oil leaks away from the film at the sides and is not all discharged from the front edge of the brass. Michell developed the theory and solved the problem of a bearing of finite width (see Zeit. fur Math. and Physik, Vol. pp. 1904; and two articles in Engineering, "The Theory of the Michell Thrust Bearing," Feb. 20, 1920, p. 233, and "The Michell Thrust Bearing" by Robert Oliphant Boswell, Aug. 7, 1925). Reference may be made to the report of the Lubricants and Lubrication Enquiry Committee, mentioned above, for impor tant references to papers and experimental results, and also to Lubrication and Lubricants, by Archbutt and Deeley (1927).
(See also LUBRICATION.) Bearings signify the stationary support which carries a moving element of a machine. The commonest form is the support of a revolving shaft. The quality usually required in a bearing is that it shall allow the supported member perfect freedom for one form of motion, such as rotation, at the same time preventing it from performing any other form of motion. The contacting sur faces between the moving and stationary elements offer more or less resistance to motion, depending on the material used and the smoothness of the surfaces. In nearly all cases the surfaces are separated either by a film of oil or by steel balls or rollers. Bear ings may be classified into two distinct types ; sliding, and rolling.
There is no possibility of the endwise movement of rolls such as that existing in a straight roller bearing. The angle of the tapered roller bearing can be proportioned to obtain endwise thrust capac ity of any desired ratio to its radical capacity. Perfect alignment of the rolls is thus obtained, resulting in a rolling contact along the entire length of the roll. The Timken tapered roller bearing is provided with a one-piece cage which acts as a roll spacer and as a retainer when the bearing is stored or handled. In the mounting of a roller bearing of this type two or more bearings are mounted on the shaft, with the tapers in opposite direction for holding the adjusted running clearance, and for taking thrust load in either direction. The tapered roller bearing is adjustable for proper running clearance with liberal tolerances for dimensions of the finished parts surrounding the bearings. This feature is particu larly valuable where tight fits must be used for securing the inner race of the bearing to the shaft. The inner race or cone is expanded because of the tight fit, which would cause pinching of the rolls in bearings of the non adjustable type. Close adjust ment without pinching or cramp ing is desirable, because if a roller bearing has a large running clear ance, the entire load may come on one roll. This applies also to ball bearings. Fig. 14 shows a phantom view of Timken tapered roller bearings as used on a large number of American railway passenger cars (see W. C. San ders, Journal of the American So ciety of Mechanical Engineers, Dec. 1927).
A modified form of roller bear ing employing a barrel shaped roll is being made by the S. K. F. Industries, Inc. The pur pose of this form of roll is to permit a spherical surface in the outer race, a self-aligning feature. The cross-section of the inner race has a contour conforming to the shape of the roll, pro ducing a slight slippage near the ends. Tangent lines drawn through the rolling contact points of the roll converge at a common point on the centreline of the shaft, similarly to the tapered roller bearing. This causes the roll to bear firmly against a rib on the inner race. The area of contact on this rib is also spheri cal and serves to prevent the roll from skewing out of line. A one piece cage serves to space the rolls. Two sets of rolls opposing each other make up a self-contained bearing unit, each having a separate cage riding on the inner race. The running clearance between the rolls and races is large enough to allow for the expansion of the inner race when properly fitted on a shaft. The bearing is non-adjustable due to the use of one-piece races in a double-row bearing. Another modified form of roller is used in the Shafer roller bearing as shown in fig. 15. The inner race has a spherical form in order to produce a self-aligning effect. The roll makes contact with the inner race over a portion of the roll length. The roll therefore has a smaller diameter at its middle than toward the ends, thus producing considerable slippage. The rolls are held in alignment by means of a one-piece cage. The outer raceway has a convex curvature of cross-section to conform nearly with the shape of the roll.
Two sets of rolls opposing each other on the same inner race produce an adjustable self-con tained bearing, each set of rolls having a separate cage and sep arate outer race.
Ball Bearings, when subjected to a load between two surfaces, are deformed from their original shape—as is also the surface in contact with the balls—which produces an area of contact stead of point contact. This causes slippage on a portion of the surfaces as the ball rolls along. The nearest approach to a pure rolling motion of a ball is obtained in the single row bearing under radial load. Lines drawn tangent to the ball at the two contacts are parallel with the shaft. The capacity for carrying a load becomes maximum when the cross-sectional curvature of the way is made slightly larger in radius than that of the ball. The reason for this is that the area of contact increases as the curvature of ball and race are made more nearly coincident. Each ball in a bearing of this construction can be loaded only at two points diametrically opposed to each other. When under radial load, the tangent lines through these points are parallel to the shaft, the ball is theoretically free from any spinning effect. This is the condition of minimum slippage. Centrifugal force has the effect of increasing the radial load on the balls and outer race and therefore does not introduce a disturbing force to cause spinning of the ball. When a deep groove ball bearing is subjected to thrust load parallel to the axis of the shaft, the tangent lines through the ball contacts are parallel to each other, but are not parallel to the shaft. The axis of ball rotation is therefore con stantly changing position, causing a pivoting or spinning effect about the contact points. This ac counts for the reduced capacity or durability of a ball when used in a thrust bearing. In fact, this is the principle used in the manufacture of a steel ball for grind ing the finished surface. The ball is ground between two ro tating discs, one of which has an abrasive surface. At high speeds, centrifugal force in a thrust bearing has the effect of moving the contact points off the diametric line. The spinning effect is there fore greatly increased. Some designers have attempted to over come the spinning effect of a ball in. a thrust bearing by providing double contact grooves as shown in fig. 16 and fig. 17. Lines drawn through the contact points intersect at a point on the bearing. A commercial bearing based on this principle is made by the Auburn Ball Bearing pany. The areas at the tacts of the balls are however at a considerable angle with the axis of ball rotation, therefore, producing a pivoting effect in addition to the rolling motion. The Gurney type of single roll ball bearing permits the full circle to be filled with balls by omitting most of the rib on one side of the outer race. The outer race is sprung into position after heating it in oil. Thrust can be applied only in one direction.
Double Row ball bearing, in which each row of balls is equally loaded by an external radial load, is shown in fig. 19. The bearing is not adjustable. A large number of balls can be used because the outer race swings out of the way during assembly. A one-piece retainer cage is used to hold both rows of balls. Ball bearings of types shown in fig. 18 A, C and D can be given a maximum number of balls without the use of a filling slot. In fig. 18, A shows a double row rigid type without filling slot. The outer race is of two piece construction and held together by an enclosing shell. It is of the cup and cone principle, being partially adjustable. Each row of balls can receive thrust in one direction. In case of design fig. 18 B, thrust is taken in either direction by both sets of balls, but requires great accuracy in its manufacture. The balls in this bearing are inserted either through a slot which is later closed, or by the eccentric race method.
Ball and roller bearings need a small amount of lubrication in spite of the practical absence of friction. The pure rolling motion, as well as the contacts between the balls or rollers and their cages are benefited by the presence of lubricant. The inherent char acteristics of a properly designed and produced ball or roller bearing are—durability, long life and continuity of service; simplicity in construction and operating principle ; low frictional resistance and absence of any internal condition in the bearing or surrounding parts which is liable to produce rapid wear; and positiveness and cheapness of lubrication. (W. C. S.) formerly a man who led bears about the country. In the middle ages and Tudor times these animals were used in the brutal sport of bear-baiting and were led from village to village; performing bears were also common. 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.