When gearing the attachment for relieving a tap or hob having spiral flutes, the gears are not selected for the actual number of flutes around the circumference but for a somewhat larger number which depends upon the lead of the hob thread and the lead of the spiral flutes. Let us assume that a hob has 6 spiral flutes and that the attachment is geared for that number. The result would be that as the tool advanced along the thread, it would not keep “in step” with the teeth because the faces of the teeth lie along a spiral (or helix which is the correct name for this curve); in other words, the tool would soon be moving in too late to begin cutting at the proper time, and to compensate for this, the attachment is geared so that the tool will make a greater number of strokes per revolution of the work than the actual number of flutes around the circumference.
With this attachment, the two gears listed on the index plate for the actual number of flutes are selected, and then two compensating gears are added, thus forming a compound train of gearing. The ratio R of these compensating gears is determined as follows:
| r + 1 | ||
| R | = | ——— |
| r |
in which
| r | = | L ÷ l; |
| L | = | lead of spiral; |
| l | = | lead of hob thread. |
For example, if a hob has a pitch circumference of 3.25, a single thread of 0.75 inch lead, and 6 spiral flutes, what compensating gears would be required?
The lead L of the spiral flutes is first determined by dividing the square of the circumference C of the hob at the pitch line by the lead l of the hob thread. Thus lead L = C2 ÷ l, or, in this case, L = 3.252 ÷ 0.75 = 14 inches, approximately. Then r = 14 ÷ 0.75 = 182/3. Inserting these values in the formula for ratio R,
| 182/3 + 1 | 192/3 | 192/3 × 3 | 59 | |||||
| R | = | ———— | = | ——— | = | ———— | = | —— |
| 182/3 | 182/3 | 182/3 × 3 | 56 |
Hence, the compensating gears will have 56 and 59 teeth, respectively, the latter being the driver. As the gears for 6 flutes listed on the regular index plate are, stud-gear 60 teeth, cam-shaft gear 40 teeth, the entire train of gears would be as follows: Gear on stud, 60; driven intermediate gear, 56; driving intermediate gear, 59; cam-shaft gear, 40. It will be understood that the position of the driving gears or the driven gears can be transposed without affecting the ratio.