CONSTANTS FOR DETERMINING CHORDAL PITCH AND RADIUS OF SPUR GEARS Radius of pitch circle EXAMPLES: 1. What is radius of pitch circle of a gear having 45 teeth, 1 inch pitch? Follow 40 in table to column 5 (making 45 teeth), and find 7.163. Multiply by pitch, 1 inch, and get 12.53 inches radius or 25.06 pitch diameter. 2. What is the chordal pitch of a gear 32 inches pitch diameter, 67 teeth? Follow 60 in table to column 7 and find 10.665. Divide radius (of 32 = 16 inches) by constant. 16 ÷ 10.665 pitch. = 1.5 inch 3. What number of teeth has a gear of 1.5 inch chordal pitch and pitch diameter 32 inches? Divide by 2 to get radius. Divide this by chordal pitch which will give constant. 16 ÷ 1.5 in table for this constant which will be found to represent 67 teeth. TABLE OF CONSTANTS = 10.665. Look о 60 70 80 90 110 2.229 1.273 1.432 2.706 2.865 3.024 4.138 4 297 5.889 6.048 6.208 0.000 0.159 0.318 0.477 0.636 0.795 0.955 1.114 10 1.591 1.750 1.910 2.069 2.387 2.546 20 3.183 3-342 3.501 3.661 3.820 3.979 30 4-775 4.934 5.093 5.252 5.412 40 6.367 6.526 6.685 6.844 7.003 7.163 7.322 7.481 7.640 7.799 50 7-959 8.118 8.277 8.436 8.595 8.754 8.914 9.073 9.232 9.391 9.550 9.709 9.869 10.028 10.187 10.346 10.505 10.665 10.824 10.983 11.142 11.301 11.460 11.620 11.779 12.938 12.097 12.256 12.416 12.575 12.734 12.893 13.052 13.211 13.371 13.530 13.689 13.848 14.007 14.167 14.326 14.485 14.644 14.803 14.962 15.122 15.281 15.440 15.599 15.758 100 15.918 16.077 16.236 16.395 16.554 16.713 16.873 17.032 17.191 17.350 17.509 17.668 17.828 17.987 18.146 18.305 18.464 18.624 18.783 18.942 120 19.101 19.260 19.419 19.579 19.738 19.897 20.056 20.215 20.375 20.534 130 20.693 20.852 21.011 21.170 21.330 21.489 21.648 21.807 21.966 22.126 140 22.285 22.444 22.603 22.762 22.921 23.081 23.240 23.399 23.558 23.717 150 23.877 24.036 24.195 24.354 24.513 24.672 24.832 24.991 25.150 25.309 25.468 25.627 25.787 25.946 26.105 26.264 26.423 26.583 26.742 26.901 170 27.060 27.219 27.378 27.538 27.697 27.856 28.015 28.174 28.334 28.493 180 28.652 28.811 28.970 29.129 29.289 29.448 29.607 29.766 29.925 30.085 30.242 30.403 30.562 30.721 30.880 31.040 31.199 31.358 31.517 31.676 200 31.830 31.989 32.148 32.307 32.446 32.625 32.785 32.944 33.103 33.262 33-427 33.586 33.746 33.905 34.064 34.223 34.382 34.542 34.701 34.860 220 35.019 35.178 35-337 35.497 35.656 35.815 35.974 36.133 36.293 36.452 36.611 36.770 36.929 37.088 37.248 37.407 37.566 37.725 37.884 38.044 240 38.203 38.362 38.521 38.680 38.839 38.999 39.158 39.317 39.476 39.635 250 39.795 160 190 210 230 To obtain the size of any part of a diametral pitch not given in the table, divide the corresponding part of 1 diametral pitch by the pitch required. As it is natural to think of gear pitches as the distance between teeth the same as threads, it is well to fix in the mind the approximate center distances of the pitches most in use. Or it is easy to remember that if the diametral pitch be divided by 34 we have the teeth per inch on the pitch line. By this method we easily see that in a 10 diametral pitch gear there are approximately 3 teeth per inch while in a 22 diametral pitch there will be just 7 teeth to the inch. Whole Depth of To obtain the size of any part of a diametral pitch not given in the table, divide the corresponding part of 1 diametral pitch by the pitch required. As it is natural to think of gear pitches as the distance between teeth the same as threads, it is well to fix in the mind the approximate center distances of the pitches most in use. Or it is easy to remember that if the diametral pitch be divided by 34 we have the teeth per inch on the pitch line. By this method we easily see that in a 10 diametral pitch gear there are approximately 3 teeth per inch while in a 22 diametral pitch there will be just 7 teeth to the inch. Whole Depth of Tooth I 2111 1.5708 1.0000 .6366 1.2732 .7366 15 1.6755 .9375 .5968 1.1937 .6906 1.7952 .8750 .5570 1.1141 .6445 13 1.9333 .8125 .5173 2.0944.7500 .4775 12.1855 .7187 .4576 2.2848.6875 .4377 2.3562.6666 .4244 2.3936 .6562 .4178 2.5133.6250 .3979 2.6456 .5937 .3780 2.7925 .5625 .3581 12.9568 .5312 .3382 3.1416 5000 .3183 1.0345 .5985 9549 5525 .9151.5294 .8754 .5064 .8488 .4910 .8356 .4834 .7560 .4374 .7958 .4604.8583 .3875 -4188 .8156 .3681 .3978 .7162 .4143 7724 .3488 .3769 .6764 .3913 7295 3294 3559 .6366 .3683 181 3.3510 .4687 .2984 .6866 .3100 .3350 .5968 .3453 .6437 .2906 .3141 3.5904 4375.2785 13.8666 .4062 .2586 .4775 2762 To obtain the size of any part of a circular pitch not given in the table, multiply the corresponding part of 1" pitch by the pitch required. As an example take a gear having 21 diametral pitch to find the various tooth parts. Take 1 diametral pitch and divide 3.1416 by 21 to find the corresponding circular pitch, which is tooth thickness is 1.5708÷ 21 04761; the working depth is 2.÷ 21. = 5570 3223 .6007 .2713 .2931 .5092 .2946 5492 .2480.2680 .5150 .2325 .2513 .4720.2131.2303 .4577 .2066 .2233 .4291.1938 .2094 .4120 .1860.2010 A 2 24 ΙΟ 16 20 20 P S D" s+f D"+f P'X.31 P'X.335 6.2832 .2500.1592.3183 .1842 3433 .1550 .1675 .0443.0479 .0414.0446 To obtain the size of any part of a circular pitch not given in the table, multiply the corresponding part of 1" pitch by the pitch required. pitch line in 1.1571÷ 21 = .0551 and the whole depth is 2.1571÷ 21.1027 inches. These could also have been obtained by splitting the difference between the figures for 20 and 22 pitch. The same can be done for circular pitch except that we multiply instead of divide. |