TABLE 19 con.-WEIGHT AND HORSEPOWER OF CAST-IRON SPUR-Wheels.

PITCH 3 IN., FACE11 IN. WIDE. PITCH 3 IN., FACE 12 IN. WIDE. Pitch 4 IN., FACE 14 IN. WIDE.

-WEIGHT AND HORSEPOWER OF CAST-IRON SPUR-WHEELS

PITCH 3IN., FACE II IN. WIDE. PITCH 31 IN., FACE 12 IN. WIDE. Pitch 4 IN., FACE 14 IN. WIDE.

FRICTION OF SHAFTS.

Friction of Shafts.-Friction is governed by pressure, and is inde pendent of surface, and the friction of a revolving body is nearly indepen dent of its velocity. Shafting should be made as light as possible consistent with strength and stiffness, because the friction of shafts on their bearings is directly proportional to their weight. The friction of any two surfaces when no lubricant is interposed, is directly proportional to the force with which they are pressed together, and is entirely independent of the extent of surfaces in contact; so that the power absorbed by friction does not increase with the length of bearing. But when the surfaces in contact are lubricated, then the amount of friction depends upon the adhesive nature of the lubricant, and the effect will be in proportion to the extent of the surfaces between which it is interposed. Therefore, to diminish the power absorbed by friction as much as possible, and to secure easy working, it is important to use the best quality of oil.

Machinery Oils.-The best lubricant for high-speed machinery under light pressure is sperm oil; for heavy machinery at low speeds, rape oil; for general machinery, olive oil; for general light machinery, equal parts of sperm oil and good mineral oil; for heated machinery and pistons, neatsfoot oil mixed with tallow and plumbago.

Resistance due to Friction.-The amount of friction between two surfaces, is found by multiplying the weight or force in lbs. with which they are pressed together by the co-efficient of friction in the following table. The co-efficient of friction, means the resistance from friction, between two surfaces, due to a pressure of 1 lb.

The power absorbed by Friction, is found by multiplying the resistance due to friction, found by the above rule, by the space in feet passed through by one surface upon the other.

The power absorbed by friction in footpounds, on round shafts in one revolution, is found thus: Multiply the diameter of the shaft in inches by 26, and by the product of the weight of the shaft by the co-efficient of friction; which will give the power absorbed for one revolution in foot-lbs.

The weight of pulleys and the load due to the pull of belts must be added to the weight of the shafting in calculating the power absorbed by friction. Shafting 24 inches diameter, making 100 revolutions per minute with the ordinary proportional number of pulleys upon it, but without belts. on, requires about 1 horse-power to drive it alone, for every 120 feet in length. Horse-power absorbed by Friction on a revolving shaft with parallel necks is found thus: Multiply the power absorbed in one revolution, found by the last rule, by the number of revolutions per minute, and divide the product by 33,000.

The co-efficients of Friction for ordinary shafts and shafting, under ordinary conditions, deduced from the experiments on friction, by the Institution of Mechanical Engineers, are given in the following Table.

Table 20.-FRICTION OF SHAFTING AND SHAFTS IN MOTION UPON WELL-FITTED AND EFFICIENTLY LUBRICATED BEARINGS.

These data apply to Horizontal Shafting with Parallel Necks.
of Upright Shafting is 20 per cent. less.

The Friction

The above co-efficients x the Nominal Load Nominal Friction Resistance per square inch of Bearing. The Nominal Load per square inch, is the total load on the Bearing divided by the product of the diameter in inches, and the length in inches of the Bearing.

SHAFTING.

Strain on Shafting.-Shafting is subject to two forces-twisting and bending. The twisting force is due to the power transmitted, and increases in proportion to the power; but decreases in proportion to the velocity. The bending force is due to the weight of the shaft, also to the strain of belts upon it, and the weights of pulleys and gearing. When the weight is distributed along the length of a shaft, it only causes one-half the quantity of deflection that it would if placed on the middle of the shaft.

Torsional Strength of Shafts.-The strength of round shafts to resist being twisted asunder is in proportion to the cubes of their diameters. and is independent of the length. A bar of wrought-iron of average quality, I inch diameter, is twisted asunder by a weight of 800 lbs. at the end of a lever 12 inches long, or at the pitch-line of a wheel 24 inches diameter; and a cast-iron shaft is twisted asunder by a weight of 450 lbs. applied in the same way. From these data, any other diameter can be calculated, the strength increasing as the cube of the diameter. power of a bar to resist load is in inverse proportion to the length of lever; thus a lever 24 inches long, only requires one-half the weight to break a bar, that would be required with a lever 12 inches long.

Safe Torsional Strength of Shafts.-To find the safe working strain in lbs. that may be put on to the circumference of wheels and pulleys fixed to shafts, Mr. Fairbairn's rule is: multiply the cube of the diameter of the shaft in inches, by 1765 for wrought iron, or by 980 for cast iron, and divide the pro luct by the radius of the wheel or pulley in inches li a lever or crank is employed, use the length of the lever or crank as a divisor in the above rule. For steel shafts, use a multiplier of 2500.

Hollow Shafts.-To find the relative value for transmitting power of a hollow shaft, from the cube of the outside diameter deduct the cube of the inside diameter; the result will be the relative value of that shaft.

The Diameter of Hollow-Shafting of Whitworth's CompressedSteel may be found by this rule.-Multiply the indicated horse-power the shaft is required to transmit by 90, divide the product by the number of revolutions per minute, and the cube root of the quotient will be the external diameter of the shaft in inches; the internal diameter of the shaft to be = the external diameter of the shaft multiplied by '56.

Torsional Stiffness of Shafting.--Stiffness in shafting is more important than strength; when the length of a line of shafting does not exceed 100 feet, the tendency is greater to bend than to twist; but a long line of shafting of from 140 to 200 feet long is very elastic, and when driving machinery at the extreme end, it has a great tendency to twist, so much so, that the driving end may make nearly a revolution before the extreme end begins to turn. A shaft that bends or yields to the strain, will take more power to keep it in motion, than would be required by a heavier shaft, stiff enough to resist the same strain. Consequently, when long lines of shafting are employed, sufficient stiffness should be given to them to withstand the torsion at the extreme end, by making the lengths of shafting increase in diameter towards the driving end, each length being made stiff in proportion to the anticipated stress. A shaft may be strong enough to resist the twisting strain, but may not be stiff enough to drive steadily without vibration. The torsional stiffness of shafting varies as the fourth power of the diameter divided by the length. Shafting of 5 inches diameter and upwards, which is strong enough to resist the torsional strain, will be stiff enough to work properly; but, below that size. a larger shaft should be used than is necessary to resist the torsional strain, in order to ensure proper stiffness and steady driving power.

RELATIVE STRENGTH OF METALS TO RESIST TOrsion, that of Wrought

Size of Crankshafts.-The size of a crankshaft should be determined by the maximum strain it has to resist, which may be found as follows:1. Find the maximum of pressure on the crank exclusive of friction, thus : multiply the area of the piston in square inches, by the pressure of steam in lbs. per square inch.