ference 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 by the surface speed that we determine how fast to run our flywheels, belts, emery wheels, and grindstones, and what speeds to use in cutting materials in a machine. Written as a formula: S = C XN 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: 210 r.p.m.? C = = π X D 22 What would be the rim speed of a 7-ft. flywheel when running at C= X 7 7 S = CX N S = = 22 ft. 22 X 210 = 4620 4620 ft. per min., Answer. Explanation: First we find the circumference of the wheel, by multiplying the diameter by π. 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 CX N. C being 22 ft. and N being 210 r.p.m., we find that S is 4620 ft. per min. Hence, the rim of this flywheel travels at a speed of 4620 ft. per minute. = If we have given the rim speed or surface speed of a flywheel or pulley, and we know the circumference, we can find the r.p.m. by using the method of "working backwards," as explained in Art. 54. Since r.p.m. X Circumference Surface Speed, it is also true that Speed Circumference = r.p.m. This is just a matter of reversing the first operation. In the example just worked, if we want to give the flywheel 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 r.p.m. In this case, we have the relation, = Surface Speed Circumference S C This formula expresses the same relation as S = CX N, but it is now rearranged to enable us to find the r.p.m. when the rim speed and the circumference are given. Again, we frequently know the proper surface speed and the number of r.p.m. which a wheel is to run, but the question is to determine the diameter which will satisfy these conditions. This sometimes happens in the case of emery wheels. In the example above we divided the rim speed by the circumference to get the r.p.m., and in a similar manner we can divide the rim speed by the r.p.m. to get the circumference. After finding the circumference, we can find the diameter by dividing by 3.1416. 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 r.p.m. are given. Examples: = 1. A 12-in. grindstone has a surface speed of 2200 ft. per minute. 2. A pulley is to be run at 3500 r.p.m., and its surface speed should be about 5500 ft. per minute. What diameter pulley should be used? First we find the circumference: 56. Grindstones and Emery Wheels.-Makers of grindstones and emery wheels 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 min. and is called the "surface speed" or the "grinding speed." The proper speed at which to run grindstones depends upon 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 more slowly 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 = TX D C = 3 ft., the diameter 3.1416 X 3 S = CX N S= 9.4248 X 60 = 565.488 f.p.m. 9.4248 ft. = 565.488 Explanation: First we find the circumference, which is 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. How many r.p.m. should a 50-in. Huron stone be run if it is to be used for rough grinding? Explanation: First we find the 157.08 in. circumference of the stone in feet, 13.09 ft. = 246.+r.p.m. which is a little over 13 ft. The proper speed is given as 3000 to 3400 f.p.m. Trying 3200 we find that N is 246 r.p.m. The stone should, therefore, be belted to run about 240 or 250 r.p.m. Emery wheels are usually run at a speed of about 5500 f.p.m. 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. The belt on an emery wheel should not be shifted, 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 putting a new wheel on an arbor the resultant surface speed should be calculated to see if the speed in r.p.m. is suitable for the size of the wheel. Example: What size emery 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). 57. 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 upon 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 r.p.m. 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 f.p.m. To find the necessary r.p.m., divide the cutting speed by the circumference of the work measured in feet. 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 upon 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. CUTTING SPEEDS IN FEET PER MINUTE An iron casting is 30 in. in diameter. Find the number of r.p.m. necessary for a cutting speed of 40 f.p.m. 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, figure 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 r.p.m.; what is the cutting speed? |