The steps of the cone should be so proportioned that the belt will shift from one to the other, and have the same degree of tension, while at the same time they should give a uniform graduation or variation of speed throughout, whether the lathe runs in single gear or with the back gear in. This is not usually quite the case although the graduation is sufficiently accurate for practical purposes. The variation in the diameter of the steps of a lathe cone varies from an inch for lathes of about 12-inch swing, up to 2 inches for lathes of about 30-inch swing, and 3 inches for lathes of 5 or more feet of swing.
To enable the graduation of speed of the cone to be uniform throughout, while the tension of the belt is maintained the same on whatever step the cone may be, the graduation of the steps may be varied, and this graduation may be so proportioned as to answer all practical purposes if the overhead or countershaft cone and that on the lathe are alike.
The following on this subject is from the pen of Professor D. E. Klein, of Yale College.
“The numbers given in the following tables are the differences between the diameters of the adjacent steps on either cone pulley, and are accurate within half a hundredth of an inch, which is a degree of accuracy sufficient for practical purposes.
By simply omitting a step at each end of the cone, the two tables given will be found equally well adapted for determining the diameters of cones having four and three steps respectively.
The following are examples in the use of the tables. Suppose the centres of a pair of pulley shafts to be 60 inches apart, and that the difference of diameter between the adjacent steps is to be as near to 21⁄2 inches as can be, to obtain a uniformity of speed graduation and belt tension, also that each cone is to have six steps, the smallest of which is to be of five inches diameter.
I.—TABLE FOR FINDING CONE PULLEY DIAMETERS WHEN THE TWO PULLEYS ARE CONNECTED BY AN OPEN BELT, AND ARE EXACTLY ALIKE.
| The numbers given in table are the differences between the diameters of theadjacent steps on either cone pulley, and can beemployed when there are either six or four steps on a cone. When there are six steps, the largest is the first, and the smallestthe sixth step of the table. When there are four steps, the largest is the second, and the smallest the fifth step of the table. | |||||||||||||||
| Average difference between the adjacent steps. | Adjacent steps, whose difference is given in table. | Distance between the Centres of Cone Pulleys. | |||||||||||||
| 10 inches. | 20 inches. | 30 inches. | 40 inches. | 50 inches. | 60 inches. | 70 inches. | 80 inches. | 90 inches. | 100 inches. | 120 inches. | 240 inches. | ||||
| 1 inch | 1st | and | 2nd | 0.87 | 0.94 | 0.96 | 0.97 | 0.98 | 0.98 | 0.98 | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 |
| 2nd | „ | 3rd | 0.94 | 0.97 | 0.98 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 1.00 | 1.00 | |
| 3rd | „ | 4th | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
| 4th | „ | 5th | 1.06 | 1.03 | 1.02 | 1.02 | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 | 1.00 | 1.00 | |
| 5th | „ | 6th | 1.13 | 1.06 | 1.04 | 1.03 | 1.02 | 1.02 | 1.02 | 1.02 | 1.01 | 1.01 | 1.01 | 1.00 | |
| 11⁄2 inch | 1st | and | 2nd | 1.21 | 1.36 | 1.40 | 1.43 | 1.44 | 1.45 | 1.46 | 1.46 | 1.47 | 1.47 | 1.48 | 1.49 |
| 2nd | „ | 3rd | 1.36 | 1.43 | 1.45 | 1.46 | 1.47 | 1.48 | 1.48 | 1.48 | 1.49 | 1.49 | 1.49 | 1.49 | |
| 3rd | „ | 4th | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | |
| 4th | „ | 5th | 1.64 | 1.57 | 1.55 | 1.54 | 1.53 | 1.52 | 1.52 | 1.52 | 1.51 | 1.51 | 1.51 | 1.51 | |
| 5th | „ | 6th | 1.79 | 1.64 | 1.60 | 1.57 | 1.56 | 1.55 | 1.54 | 1.54 | 1.53 | 1.53 | 1.52 | 1.51 | |
| 2 inches | 1st | and | 2nd | 1.47 | 1.74 | 1.83 | 1.87 | 1.90 | 1.92 | 1.93 | 1.93 | 1.94 | 1.95 | 1.96 | 1.98 |
| 2nd | „ | 3rd | 1.74 | 1.87 | 1.92 | 1.93 | 1.95 | 1.96 | 1.96 | 1.97 | 1.97 | 1.97 | 1.98 | 1.99 | |
| 3rd | „ | 4th | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | |
| 4th | „ | 5th | 2.26 | 2.13 | 2.08 | 2.07 | 2.05 | 2.04 | 2.04 | 2.03 | 2.03 | 2.03 | 2.02 | 2.01 | |
| 5th | „ | 6th | 2.53 | 2.26 | 2.17 | 2.13 | 2.10 | 2.08 | 2.07 | 2.07 | 2.06 | 2.05 | 2.04 | 2.02 | |
| 21⁄2 inches | 1st | and | 2nd | 1.66 | 2.10 | 2.23 | 2.30 | 2.34 | 2.37 | 2.39 | 2.40 | 2.41 | 2.42 | 2.43 | 2.47 |
| 2nd | „ | 3rd | 2.10 | 2.30 | 2.37 | 2.40 | 2.42 | 2.43 | 2.44 | 2.45 | 2.46 | 2.46 | 2.47 | 2.49 | |
| 3rd | „ | 4th | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | |
| 4th | „ | 5th | 2.90 | 2.70 | 2.63 | 2.60 | 2.58 | 2.57 | 2.56 | 2.55 | 2.54 | 2.54 | 2.53 | 2.51 | |
| 5th | „ | 6th | 3.34 | 2.90 | 2.77 | 2.70 | 2.66 | 2.63 | 2.61 | 2.60 | 2.59 | 2.58 | 2.57 | 2.53 | |
| 3 inches | 1st | and | 2nd | 1.76 | 2.42 | 2.62 | 2.71 | 2.77 | 2.81 | 2.84 | 2.86 | 2.87 | 2.88 | 2.90 | 2.95 |
| 2nd | „ | 3rd | 2.42 | 2.71 | 2.81 | 2.86 | 2.88 | 2.90 | 2.92 | 2.93 | 2.94 | 2.94 | 2.95 | 2.98 | |
| 3rd | „ | 4th | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | |
| 4th | „ | 5th | 3.58 | 3.29 | 3.19 | 3.14 | 3.12 | 3.10 | 3.08 | 3.07 | 3.06 | 2.06 | 3.05 | 3.02 | |
| 5th | „ | 6th | 4.24 | 3.58 | 3.38 | 3.29 | 3.23 | 3.19 | 3.16 | 3.14 | 3.13 | 3.12 | 3.10 | 3.05 | |
| 4 inches | 1st | and | 2nd | 3.95 | 3.31 | 3.49 | 3.59 | 3.66 | 3.71 | 3.75 | 3.78 | 3.80 | 3.83 | 3.91 | |
| 2nd | „ | 3rd | 2.94 | 3.49 | 3.66 | 3.75 | 3.80 | 3.83 | 3.85 | 3.87 | 3.88 | 3.89 | 3.91 | 3.96 | |
| 3rd | „ | 4th | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | |
| 4th | „ | 5th | 5.06 | 4.51 | 4.34 | 4.25 | 4.20 | 4.17 | 4.15 | 4.13 | 4.12 | 4.11 | 4.09 | 4.04 | |
| 5th | „ | 6th | 5.05 | 4.69 | 4.51 | 4.41 | 4.34 | 4.29 | 4.25 | 4.22 | 4.20 | 4.17 | 4.09 | ||
| 5 inches | 1st | and | 2nd | 3.33 | 3.92 | 4.20 | 4.36 | 4.47 | 4.55 | 4.60 | 4.64 | 4.68 | 4.74 | 4.87 | |
| 2nd | „ | 3rd | 3.31 | 4.19 | 4.47 | 4.60 | 4.68 | 4.74 | 4.77 | 4.80 | 4.82 | 4.84 | 4.86 | 4.93 | |
| 3rd | „ | 4th | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | |
| 4th | „ | 5th | 6.69 | 5.81 | 5.53 | 5.40 | 5.32 | 5.26 | 5.23 | 5.20 | 5.18 | 5.16 | 5.14 | 5.07 | |
| 5th | „ | 6th | 6.67 | 6.09 | 5.80 | 5.64 | 5.53 | 5.45 | 5.40 | 5.36 | 5.32 | 5.26 | 5.13 | ||
| 6 inches | 1st | and | 2nd | 3.52 | 4.42 | 4.83 | 5.08 | 5.23 | 5.34 | 5.42 | 5.49 | 5.55 | 5.62 | 5.80 | |
| 2nd | „ | 3rd | 4.83 | 5.23 | 5.42 | 5.54 | 5.62 | 5.67 | 5.71 | 5.75 | 5.77 | 5.81 | 5.90 | ||
| 3rd | „ | 4th | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | ||
| 4th | „ | 5th | 7.17 | 6.77 | 6.58 | 6.46 | 6.38 | 6.33 | 6.29 | 6.25 | 6.23 | 6.19 | 6.10 | ||
| 5th | „ | 6th | 8.48 | 7.58 | 7.17 | 6.92 | 6.77 | 6.66 | 6.58 | 6.51 | 6.45 | 6.38 | 6.20 | ||
To find the diameters for the remaining steps, we look in [Table I.] (corresponding to cone pulleys with six steps), under 60 in. and opposite 21⁄2 in. and obtain the differences,
| 2.37 | 2.43 | 2.50 | 2.57 | 2.63 |