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? 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). This speed may be exceeded somewhat if care is taken that the pulley is well balanced and is sound and of good design. The proper speeds for belts is taken up fully in a later chapter under the general subject of belting. It is well, however, to point out now that the speed at which any belt is travelling through the air is practically the same as that of the rim of either of the pulleys over which the belt runs; and, if we neglect the small amount of slipping which usually occurs between a belt and its pulleys, we can say that the speed of a belt is the same as the rim speed of the pulleys. It will be seen from this that if two pulleys are connected by a belt, their rim speeds are practically the same. PROBLEMS 101. A stack is measured with a tape line and its circumference found to be 88 in. What is the diameter of the stack? 102. An emery wheel 16 in. in diameter runs 1300 R. P. M. Find the surface speed. 103. The Bridgeport Safety Emery Wheel Co., Bridgeport, Conn., build an emery wheel 36 in. in diameter and recommend a speed of 425-450 revolutions. Calculate the surface speeds at 425 and at 450 revolutions. 104. An emery wheel runs 1000 R. P. M. to give a surface speed of 5500 ft.? What should be its diameter 105. A grindstone 3 ft. in diameter is to be used for grinding carpenters' tools; how many R. P. M. should it run? 106. Calculate the belt speed on a high-speed automatic engine carrying a 48 in. pulley and running at 250 R. P. M. 107. How many revolutions will a locomotive driving wheel, 72 in. in diameter, make in going 1 mile? 108. What would be the rim speed in feet per minute of a fly wheel 14 ft. in diameter running 80 R. P. M.? 109. At how many R. P. M. should an 8 in. shaft be driven in a lathe to give a cutting speed of 60 ft. per minute? 110. At what R. P. M. should a 1 in. high speed drill be run to give a cutting speed of 80 ft. per minute? If the drill is fed .01 in. per revolution, how long will it take to drill through 2 in. of metal? CHAPTER VIII RATIO AND PROPORTION 56. Ratios.-In comparing the relative sizes of two quantities, we refer to one as being a multiple or a fraction of the other. If one casting weighs 600 lb., and another weighs 200 lb., we say that the first one is three times as heavy as the second, or that the second is one-third as heavy as the first. This relation between two quantities of the same kind is called a Ratio. In comparing the speeds of two pulleys, one of which runs 40 revolutions per minute and the other one 160 revolutions per minute, we say that their speeds are "as 40 is to 160," or "as 1 is to 4." In this sentence, "40 is to 160" is a ratio, and so also is "1 is to 4" a ratio. Ratios may be written in three ways. For example, the ratio of (or relation between) the diameters of two pulleys which are 12 in. and 16 in. in diameter can be written as a fraction, 18; or, since a fraction means division, it can be written 12÷16; or, again, the line in the division sign is sometimes left out and it becomes 12:16. The last method, 12:16, is the one most used and will be followed here. It is read "twelve is to sixteen." A ratio may be reduced to lower terms the same as a fraction, without changing the value of the ratio. If one bin in the stock room contains 1000 washers, while another bin contains 3000, then the ratio of the contents of the first bin to the contents of the second is as 1000 is to 3000." The relation of 1000 to 3000 can be reduced by dividing both by 1000. This leaves the ratio 1 to 3. 66 1000÷1000 1 30001000 3 Hence, the ratio between the contents of the bins is also as 1 is to 3. Likewise, the ratio 24:60 can be reduced to 2:5 by dividing both terms by 12. If we write it as a fraction we can easily see that The ratio of the 1000 washers to the 3000 washers is 1000:3000 or 1:3. The ratio of 8 in. to 12 in. is 8:12 or 2:3. The ratio of $1 to $1.50 is 1:1 or 2:3. The ratio of 30 castings to 24 castings is 30:24 or 5:4. 57. Proportion.-When two ratios are equal, the four terms are said to be in proportion. The two ratios 2:4 and 8:16 are clearly equal, because we can reduce 8:16 to 2:4 and we can therefore write 2:4-8:16. When written thus, these four numbers form a Proportion. Likewise, we can say that the numbers 6, 8, 15, and 20 form a proportion because the ratio 6:8 is equal to the ratio of 15:20. 6:8=15:20 Now, it will be noticed that, if the first and fourth terms of this proportion be multiplied together, their product will be equal to the product of the second and third terms: This is true of any proportion and forms the basis for an easy way of working practical examples, where we do not know one term of the proportion, but know the other three. The first and fourth terms are called the Extremes, and the second and third are called the Means. Then we have the rule: "The product of the means is equal to the product of the extremes." This relation can be very nicely and simply expressed as a formula. Let a, b, c, and d represent the four terms of any proportion so that Let us now see of what practical use this is. We will take this example: If it requires 137 lb. of metal to make 19 castings, how many pounds will it take to make 13 castings from the same pattern? Now very clearly the ratio between the number of castings 19:13 is the same as the ratio of the weights, but one of the weights we do not know. Writing the proportion out and putting the word "answer" for the number which we are to find, we have 19:13=137:Answer |