Useful Charts and Tables.—No. 5.
Page 19
If you've noticed an error in this article please click here to report it so we can fix it.
By George Watson, A.M.I.Mech.E.
Centrifugal Tension, or Stress, in Fly-wheel Rims.
When watching the revolving fly-wheel of a high-speed petrol engine, the question often arises to one's mind : "What would be the result should the fly-wheel burst?" Such cases are not absolutely unknown with motor engines and, as the consequences might be disastrous to the vehicle, and, even, fatal to the driver, passengers or pedestrians, it is a matter of vital importance that the linear velocity of the fly-wheel should never exceed the safe limit for the material of which it is made. Whilst it is possible, in some cases, to make a fly-wheel of stamped mild steel, they are, more often, made of cast steel, malleable iron, or cast iron, on account of their shape, or for reasons of design. In addition to the possibilities of flaws in the casting, there is, always, a great initial stress set up in the cooling of the casting, so that the usually-accepted, safe limit of stress might prove extremely dangerous, if applied to a cast fly-wheel. The elastic strength of cast-iron is about io,000lb. per square inch, and, if we take a factor of safety of five on this value, we shall have an allowable stress per square inch of 2,000lb. Malleable iron is about one and a half times as strong, so we may take 3,000lb. per square inch as the value for that material. Cast steel is about eight times as strong but, if we take it as four times, we shall be within safe limits; thus, for cast steel, we have 8,cxiolb. per square inch.
In calculating the centrifugal tension, or stress, in the rim of a fly-wheel, it is best to assume that it receives absolutely no assistance from the arms, web, or vanes connecting it to the hub, and to treat it, simply, as a whirling hoop, the formula for which is :
12 W. \,2 48 W. T2. i1l.//'22'
Centrifugal stress in lb. per sq. in. = Where S=Centrifugal stress in the rim in lb. per sqr. inch. w=Weight of one cubic inch of the material, in lb. r=.-Mean radius of rim in feet.
n=Number of revs. per second.
=3'1416
g=32.2.
V=Linear velocity of rim in feet per second_
By " Mean radius" is meant the distance from the centre of rotation, or the centre of the fly-wheel, to the centre of gravity of the section of the rim. Taking a simple flywheel to illustrate the meaning of this, say, 2I inches external diameter with a rim a inches thick by 4 inches width of face. The mean radius, in this case, would be the distance from the centre of the fly-wheel to the centre of the rim (the centre of the rim being the centre of gravity) and would be 91 inches, or the mean diameter would be 191 inches.
In constructing the chart given on the following page, the writer has given the mean diameter in inches, and the number per minute, instead of per second, as these will be found to be much more useful than feet and seconds in using the chart. The two curves in the chart represent
constants derived from —g. The upper one represents cast iron, or malleable iron, and the lower one, cast steel or mild steel, the weights per cubic inch being, practically, the same for cast and malleable iron and for cast and mild steel. The necessity for accuracy in all calculations relating to fly-wheels is very great, and some means of checking calculations, or of eliminating them altogether, is always acceptable to the designer.
The chart is constructed from the formula given above, and from it may be obtained'S, the linear velocity of the rim, in feet per second; velocity squared; the centrifugal tension, or stress, in the rim, in lb. per square inch; the safe number of revolutions per minute; or the diameter of the flywheel for a given speed or stress.
Taking examples in each case we have : Example 1. What is the linear velocity, in feet per second, of a fly-wheel whose rim has a mean diameter of 23 inches, and which is running at a speed of 700 revs. per minute?
Commencing.at 23 inches and reading up to the diagonal for 700r.p.m., read across to the left and find the answer = 70 feet per second, or V2 = 4,90n, which may be read at the right of the chart, on the same horizontal as for speed.
Example 2. What will be the centrifugal stress, in lb. per square inch, in the rim of a fly-wheel 23 inches mean diameter, running at i,600r.p.m., the material being cast iron?
Commence at 23 inches and read up to the diagonal for 1,600r.p.m. : now, read across, until the curve for cast iron is cut; then, read up to the top,and, find answer = 2 ,5001b. per square inch.
Example 3. What will be the safe speed, in r.p.m., of a cast-iron fly-wheel, 23 inches in diameter, if the stress is not to exceed 2,500lle per square inch? Start at 2,300lb. per square inch and read down the chart until the curve for cast iron is cut; now, trace across the chart, until directly over 23 inches on the base line. The diagonal passing through this point
will give the speed in r.p.na. 1,boo.
Example 4. What diameter of fly-wheel will produce a stress of 2,300lb. per square inch, when running at 1,600r.p.m., the material being cast iron? Commence at 2,soolb. per square inch, and read down until the curve for cast-iron is cut ; now, cross the chart to the point of intersection with the diagonal for 7,600r.p.m.; then, the figure, vertically below this, will give the mean diameter of the fly-wheel, viz., 23 inches. The above examples will give a clear idea of the uses to which the chart may be put.