Example: What is the circumference of a 48-in. fly wheel? C=3.1416×4=12.5664 ft., Answer. This is much shorter than it would be to multiply 3.1416 by 48 and then divide the product by 12. 52. Circumferential Speeds.-When a fly wheel or emery wheel or any circular object makes one complete revolution, each point on the circumference travels once around the circumference and returns to its starting-point. When the wheel turns ten times, the point will have travelled a distance of ten times. the circumference. In one minute, it will travel a distance equal to the product of the circumference times the number of revolutions per minute. The distance, in feet per minute, travelled by a point on the circumference of a wheel is called its Circumferential Speed, Rim Speed, or Surface Speed. It is also sometimes called Peripheral Speed, because the circumference is sometimes given the name of periphery. It is the surface speed by which we determine how to run our fly wheels, belts, emery wheels, and grindstones, and what speeds to use in cutting materials in a machine. Written as a formula: S=CXN where: S is the surface speed C is the circumference N is the number of revolutions per minute (R. P. M.). Expressed in words this formula states that the surface speed of any wheel is equal to the circumference of the wheel multiplied by the number of revolutions per minute. Example: What would be the rim speed of a 7 ft. fly wheel when running at 210 revolutions per minute? C = π XD 22 C= X7=22 ft. 7 = S=CXN S=22×210=4620 4620 ft. per min., Answer. Explanation: First we find the circumference of the wheel, by multiplying the diameter by л. Here is a case where it is much easier to use 22 for than to use the decimal 3.1416, and the result is sufficiently accurate for our purposes. We get 22 ft. for the circumference. We can now get the rim speed, which is equal to the product of the circumference times the number of revolutions per minute; or S-C×N. C being 22 ft. and N being 210 revolutions per minute, we find that S is 4620 ft. per min. Hence, the rim of this fly wheel travels at a speed of 4620 ft. per minute. If we have given a certain speed which is wanted and have the circumference of the wheel, then the R. P. M. (revolutions per minute) will be obtained by dividing the desired speed by the circumference. In the example just worked, if we want to give the fly wheel a rim speed of 5280 ft. per minute, it requires no argument to show that the wheel will have to run at 5280÷22=240 revolutions per minute. In such a case, we would use our formula in the form N=S This formula expresses the same relation as S=NXC, but now it is rearranged to enable us to find the R. P. M. when the rim speed and the circumference are given. Sometimes, especially with emery wheels, we know the proper surface speed and we have an arbor belted to run a certain number of R. P. M. The problem then is to find the proper size of stone to order. The desired speed divided by the number of R. P. M. will give the circumference, and from this we can figure the diameter of the stone. S Here again we have merely rearranged the formula S=CX N so as to be in more suitable form for finding the circumference when the surface speed and the R. P. M. are given. 53. Grindstones and Emery Wheels.-Makers of emery wheels and grindstones usually give the proper speed for the stones in feet per minute. This refers to the distance that a point on the circumference of the stone should travel in 1 minute and is called the "surface speed" or the "grinding speed." The proper speed at which to run grindstones depends on the kind of grinding to be done and the strength of the stones. For heavy grinding they can be run quite fast. For grinding edge tools they must be run much slower to get smooth surfaces and to prevent heating the fine edges of the tools. The following surface speeds may be taken as representing good practice: Grindstones: For machinists' tools, 800 to 1000 ft. per minute. Grindstones for very rapid grinding: Coarse Ohio stones, 2500 ft. per minute. Fine Huron stones, 3000 to 3400 ft. per minute. Sometimes the rule is given for grindstones as follows: "Run at such a speed that the water just begins to fly." This is a speed of about 800 ft. per minute and would be a good average speed for sharpening all kinds of tools. Examples: 1. A 36-in. grindstone, used for sharpening carpenters' and patternmakers' tools, is run at 60 R. P. M. Is this speed correct? We must first find the circumference and then the surface speed to see if it falls between the allowable limits. 36 in.÷12=3 ft., the diameter C=3.1416X3=9.4248 ft. S=CXN S=9.4248X60=565.488 Explanation: First we find the circumference, which comes out 9.4248 ft. Using this and the R. P. M., we find S to be 565 F. P. M. (feet per minute). As this lies between the allowed limits (550 to 600 F. P. M.) the speed of the stone is correct. 2. At what R. P. M. should a 50-in. Huron stone be run if it is to be used for rough grinding? Emery wheels are usually run at a speed of about 5500 ft. per minute. A good, ready rule, easy to remember, is a speed of a mile a minute. Most emery wheel arbors are fitted with two pulleys of different diameters. When the wheel is new, the larger pulley on the arbor should be used and, when the wheel becomes worn down sufficiently, the belt should be shifted to the smaller pulley. Never shift the belt on an emery wheel, however, without first calculating the effect on the surface speed of the wheel. Many serious accidents have been caused by emery wheels bursting as a result of being driven at too great a speed. Before cutting a new wheel on an arbor the resultant surface speed should be calculated, to see if the R. P. M. is suitable for the size of the wheel. Example: What size wheel should be ordered to go on a spindle running 1700 R. P. M.? Note.-A wheel of exactly 12 in. diameter would, at 1700 R. P. M., have a surface speed of 5340 F. P. M. (1700×π=5340). 54. Cutting Speeds.-Cutting speeds on lathe and boring mill work may be calculated in the same way that grinding speeds are calculated. The life of a lathe tool depends on the rate at which it cuts the metal. This cutting speed is the speed with which the work revolves past the tool and is, therefore, obtained by multiplying the circumference of the work by the revolutions per minute. The same formulas are used as in the calculations for emery wheels and grindstones but, of course, the allowable speeds are much different. Tables of proper cutting speeds are given in many handbooks in feet per minute. To find the necessary R. P. M., divide the cutting speed by the circumference of the work. The cutting speeds used in shops have increased considerably with the advent of the high speed steels. No exact figures can be given for the best speeds at which to cut different metals. The proper speed depends on the nature of the cut, whether finishing or roughing, on the size of the work and its ability to stand heavy cuts, the rigidity and power of the lathe, the nature of the metal being cut, and the kind of tool used. If the work is not very rigid it is, of course, best to take a light cut and run at rather high speed. On the other hand, it is generally agreed that more metal can be removed in the same time if a moderate speed is used and a heavy cut taken. As nearly as any general rules can be given, the following table gives about the average cutting speeds. A casting is 30 in. in diameter. Find the number of R. P. M. necessary for a cutting speed of 40 ft. per minute. The same principles apply to milling and drilling, except that in these cases the tool is turning instead of the work. Consequently, the cutting speeds are obtained from the product of the circumference of the tool times its R. P. M. In calculating the cutting speed of a drill, take the speed of the outer end of the lip or, in other words, the speed of the drill circumference. Example: A-in. drill is making 300 revolutions per minute; what is the cutting speed? .131×300=39.3 ft. per minute, cutting speed. 55. Pulleys and Belts.—If the rim of a pulley is run at too great a speed, the pulley may burst. The rim speeds of pulleys are calculated in the same manner as are grinding and cutting speeds. A general rule for cast iron pulleys is that they should not have a rim speed of over a mile a minute (5280 ft. per minute). |