COEFFICIENT OF FKICTION.] 



APPLIED MECHANICS. 



901 



In dynamometers of this kind the friction-strap i 

 plentifully supplied with oil, and it is found better t 

 face the interior of the friction-strap with blocks of wooc 

 bearing on the surface of the pulley ; because the friction 

 of wood on iron is of a more constant character than 

 that of iron on iron. When iron rubs on iron withou 

 the presence of oil or grease, great heat is produced, am 

 the metal surfaces cut into each other and become 

 roughened. But when wood bears on iron, if the sur 

 faces are not oiled, the heat produced by the friction wil 

 only char the wood without damaging the iron, and wil 

 not effect any great variation in the amount of friction. 

 BREAKS. Friction is also employed as a means o: 

 arresting motion in the case of carriages on declivities 

 and railway trains. By the use of wheels to carriages 

 the friction is transferred from the surface of the road or 

 rail to that of the axle. As the radius of the wheel is 

 the length of lever at which any obstacle opposed to its 

 progress acts, while the very much smaller radius of the 

 axle is the lever at which its friction acts to oppose the 

 rotation of the wheel, the larger the wheel and the 

 smaller the axle, the less is tho resistance from friction. 

 If we were to suppose the axle extended to almost the 

 whole dimensions of the wheel that, in fact, the wheel 

 were only the thin iron tyre revolving round a solid 

 central part, the resistance to the motion of the carriage 

 would be almost as great as if it were dragged along like 

 a sledge. So if the wheel be prevented from revolving, 

 it has to be dragged along the road, and the opposition 

 which the friction thereby created presents, acts as a 

 great retarding force. In ordinary carriages the wheel 

 is generally prevented from revolving by placing under 

 it a skid or plate of iron attached to the carriage by a 

 chain, which baa to be dragged along like a sledge. In 

 railway carriages, the rotation of the wheels is arrested 

 by means of blocks of wood pressed against their cir- 

 cumferences. These blocks are connected by levers and 

 rods with screws conveniently situated, so that the engine- 

 driver and guards can force them against the wheels, or 

 remove the pressure at pleasure. 



RESISTANCE OP FRICTION. Except in these 

 few instances, and that of pulleys and straps, in which 



Tig. 268. 



I 



friction is employed as a means of communicating power 



or arresting motion, it acts as a resistance in all me- 

 chanical arrangements. Although this resistance cannot 

 be totally overcome, yet by carefully designing the ar- 

 rangements of machinery with regard to the simplicity 

 and proper formation of its parts, by good execution of 

 the work, by the selection of suitable materials, and due 

 provision of lubricating materials wherever surfaces move 

 in contact with each other, it may be diminished to a 

 very great extent. 



In order that we may form a clear estimate of friction 

 as a retarding force, we may suppose A (Fig. 268) to be 

 a piece of material, such as iron, wood, brass, or the 

 like, having a smooth lower surface in contact with a 

 smooth table B of the same or any other material. If 

 A be pressed down by a perpendicular force C, it will be 

 found, that in order to move it laterally along the table, 

 some force D will have to be impressed upon it, and 

 this force will be greater the greater the perpendi- 

 cular pressure C. There is, therefore, under these cir- 

 cumstances, a force acting in the direction of the arrow 

 E, not tending to put A in motion, but resisting its 

 motion in obedience to the force D. The resisting force 

 E is the friction of the surfaces A and B. In order to 

 measure the amount of this resistance, let us suppose a 

 force F A acting obliquely at such an angle as just to 

 cause A to slide along the table ; then, on completing 

 the parallelogram F G A H, while F H or G A measures 

 the amount of force acting perpendicularly to the table, 

 FG or HA measures the force acting parallel to the 

 table, and causing A to slide along it. 



Now it is found, practically, that whatever be the abso- 

 lute force F A, and whatever be the extent of A's sur- 

 face in contact with B, the obliquity of F A, or the angle 

 FAG, which it makes with the perpendicular, when 

 it just oauses A to slide, is very nearly constant for any 

 given material. 



The ratio which A H bears to A G, or the fraction ex- 

 pressing the division of A H by A G, is called the co- 

 efficient of friction, and the angle F A G is called the 

 limiting angle of resistance. Some very careful experi- 

 ments have been made to determine the values of these 

 for different materials ; their results are embodied in the 

 accompanying table. The coefficient of friction is the 

 tangent of the limiting angle of resistance ; and if we 

 know the one, we can easily find the other from a trigo- 

 nometrical table. We have, however, given an approxi- 

 mate value of both, to save the trouble of reference. As 

 an example of the practical application of these numbers, 

 we may take the case of brass and iron, for which the co- 

 efficient of friction is '142, and the limiting angle 8. If, 

 then, a piece of smooth iron weighing 1 cwt. rested on a 

 brass plate, it would require a lateral force of 16 Ibs. to 

 cause it to slide, for 112 Ibs. (the vertical pressure) 

 X "143= 16 Ibs. Or, if the brass plate were inclined 8 

 the horizon, the iron would slide along it from its own 

 weight. Or, again, if we suppose a smooth round shaft 

 of iron, weighing 1 ton, revolving in a brass bearing, the 

 *orce necessary to be applied at the circumference of the 

 ihaft to overcome its friction, would be 2240 X 143 = 320 Ibs. 

 Assuming the shaft to be 6 inches diameter, or to have a 

 radius of 3 inches at the bearing, the length of the radius, 

 J inches, is the leverage at which the friction acts to resist 

 ts rotation, and the resistance, 320 Ibs., at this leverage 



12 in. 

 is equivalent to 320 x ~3~{ n ~~ = 80 Ibs. at a radius of 1 



oot. By a similar method of calculation, the resistance 

 lue to the sliding friction either of plane or of cylindrical 

 urfaces of these or other materials may be readily 

 stimated. 



Tbe numbers in the following table apply in the case 

 if smooth surfaces, such as are employed in well-con- 

 tructed machinery. When the surfaces are rough, the 

 esistance may be increased indefinitely, and there can be 

 10 means of calculating its amount. When the surfaces 

 ire oiled, the friction is considerably reduced ; but as, in 

 ill machinery, tho rubbing surfaces are liable to become 

 .ry, or roughened by wes-r or the presence of grit, we 

 hink that in estimating the loss by friction, the numbers 



