Formula Differential Indexing 69 Teeth With Examples

of a revolution

As the worm-spindle ratio is 40 to 1,

39 39

= 0fareV0luti0n

Negative Compounding

Note that in negative compounding, the movements are in opposite directions (Figure 14-5). Move the index crank one hole in the 19-hole circle. Disengage the stop pin and rotate the index plate one hole in the opposite direction in the 20-hole circle. The resultant rotation of the worm is as follows:



Diagram The Index Plate
Figure 14-5 Basic diagram of an index plate, showing negative compounding.

The worm-spindle ratio is 40 to 1; the spindle movement, therefore, is

380 15,200

To index work that requires divisions such as a 69-hole circle, for example, the crank should be turned:

1 40

69 69

If the index plate contained a 69-hole circle, it would only be necessary to move the crank 40 holes to obtain one spindle revolution. However, in the absence of a 69-hole plate, the same result can be obtained by compounding, using an index plate with both 23-hole and 33-hole circles.

In compound indexing with these index circles, first move the crank counterclockwise 21 holes in the 23-hole circle. Then, withdraw the stop pin and move the index plate clockwise 11 holes in the 33-hole circle. The resulting movement of the crank from its original position is

21 _ 11 _ 693 - 253 _ 440 40 23 33 ~ 759 ~ 759 ~ 69

As the ratio between the crank and spindle is 40 to 1,

—- X — = — revolution of the spindle 69 40 69 r

Determining Which Index Circles to Use

The procedure for determining the index circles that can be used can be illustrated for the previous example (Vfo revolution of the spindle; 40 to 1 ratio), as follows:

1. Resolve into factors the number of divisions required. 69 = (23 X 3)

2. For trial and error, choose an index plate. Arbitrarily select two index circles (for example, a 23- and a 33-hole circle).

3. Subtract the number of holes in the smaller index circle from the number of holes in the larger index circle.

5. Place the two factors (from 1 and 4) above a horizontal line. (23 X 3)(2 X 5)

6. Factor the number of turns of the crank required for one revolution of the spindle.

7. Factor the number of holes for each of the trial index circles. 23 = (23 X 1)

8. Place these three sets of factors (from 6 and 7) below the horizontal line.

9. Cancel the equal factors both above and below the horizontal line.


If all factors above the line cancel, the two selected trial index circles can be used. If all factors above the line do not cancel, two other index circles must be selected for trial and error, and the procedure must be repeated.

10. To obtain crank movement in a forward direction and plate movement in a reverse direction, multiply the uncanceled factors below the horizontal line. 2X2X1X11=44

11. Thus, the indexing number is 44. This means that to move the spindle V<S9 revolution, the index crank must be turned forward 44 holes in the 23-hole circle, and the index plate must be turned 44 holes in the reverse direction in the 3 3-hole circle (step 3). The same result can be obtained by making the forward movement in the 3 3-hole circle and the reverse movement in the 23-hole circle.

This example illustrates negative compounding. Plus ( + ) and minus (-) symbols are used to indicate the forward and reverse directions of movement in the indexing tables.

In compound indexing, the choice of correct index circles (step 2) usually cannot be solved on the first attempt, as in the example. Normally, two or more selections are necessary before all the factors above the horizontal line can be canceled (step 9).

Compound indexing should not be used when the required divisions can be obtained by simple indexing, because there is a greater possibility for making an error. For this reason, compound indexing has been replaced to a large extent by the differential method. However, knowledge of compound indexing can be valuable for the machinist.

Sometimes the plain and compound indexing systems can be combined to advantage in an operation such as gear cutting. Every other tooth can be cut by plain indexing, and then the spindle can be positioned to locate the cutter in the center of spaces already cut. Then, the remaining spaces are cut by plain indexing as before.

Differential Indexing

In this method of indexing, the spindle is turned through a desired division by manipulating the index crank. The index plate is rotated, in turn, by proper gearing that connects it to the spindle. As the crank is rotated, the index plate also rotates a definite amount, depending on the gears that are used. The result is a differential action of the index plate, which can be either in the same direction or in the opposite direction in relation to the direction of crank movement, depending on the gear setup. As motion is a relative matter, the actual motion of the crank at each indexing is either greater or less than its motion relative to the index plate.

In compound indexing, the index plate is rotated manually, with a possibility of error in counting the holes. This is avoided in differential indexing; therefore, chances for error are greatly reduced.

Usually, determination of the gears between the index plate and the spindle can be accomplished by means of an index table that accompanies the machine. The table provides data for both plain and differential gearing. Thus, it can be determined quickly whether the latter method can be used.

In the differential indexing operation, the index crank is moved relative to the index plate in the same circular row of holes in a manner that is similar to plain indexing. Since the spindle and index plate are connected by interposed gearing, the index plate stop pin on the rear of the plate must be disengaged before the plate can be rotated.

In the gearing hookup, the number of idlers determines whether the plate movement is positive (in the direction of crank movement) or negative (opposite the direction of crank movement). The gear arrangements are as follows:

• Simple—The use of one idler provides positive motion, or the use of two idlers provides negative motion to the index plates.

• Compound—The use of one idler provides negative movements, or the use of two idlers provides positive movement.

In general, the spindle rotates by means of the worm and worm wheel gearing, as the crank is turned. The index plate is rotated by the gearing between the spindle and the plate. The direction of rotation is either positive or negative, depending on the gear hookup. The total motion or movement of the crank in indexing is equal to its total movement in relation to the index plate—that is, the sum of its positive motion and its negative motion.

In simple differential indexing (Figure 14-6), the gear on the worm shaft is the driver, and the gear on the spindle is the driven gear. The ratio between the number of teeth in each gear determines the spacing between the divisions. The number of teeth in the idler is not important, because the idler is used only to connect the other two gears and to cause the gear on the spindle to rotate in the desired direction. Two idlers are often used.

In compound differential indexing (Figure 14-7), the idler is also used to cause the gear on the spindle to rotate in the desired direction. Again, the number of teeth in the idler is not important, but the other gears must have the correct number of teeth for the desired spacing. The gear on the worm shaft and the second gear on the stud are driver gears, and the first gear on the stud and the gear on the spindle are driven gears.

To select the correct change gears, it is necessary to find the required gear ratio between the spindle and the index plate. The correct gears can then be determined. The following formulas can be used to determine these gears, in which

N is the number of divisions required,

H is the number of holes in the index plate, n is the number of holes taken at each indexing,

V is the ratio of gearing between the index crank and the spindle,





Figure 14-6 Gearing diagram for simple differential indexing.





Compound Indexing

Figure 14-7 Gearing diagram for compound differential indexing.

X is the ratio of the train of gearing between the spindle and the index plate,

S is the gear on the spindle (driven), Gj is the first gear on the stud (driven), G2 is the second gear on the stud (driver), and W is the gear on the worm shaft (driver).

If HV is larger than Nn, then


For simple gearing, S

For compound gearing, SGj

Angular Indexing

The operation of rotating the spindle through a definite angle (in degrees) by turning the crank is called angular indexing. Sometimes, instead of specifying the number of divisions or sides required for the work to be milled, a given angle, such as 20° or 45°, may be specified for indexing.

The number of turns of the index crank required to rotate the spindle 1° must first be established to provide a basis for rotating the spindle through a given angle. Usually, 40 turns of the index crank are required to rotate the spindle one complete revolution (360°). Thus, one turn of the crank equals 360 + 40 = 9 degrees, or xh turn of the crank rotates the spindle 1°. Accordingly, to index one degree, the crank must be moved as follows:

As an example, on an 18-hole index plate, calculate the crank movement needed to index 35°.

Since one turn of the crank equals 9°, 35 ^ 9 = 3% turns of the crank for 35°. On an 18-hole plate, Vs> turn equals 18-^9, or 2 holes, and % turn equals 2 X 8, or 16 holes. Therefore, to index 35° on an 18-hole plate, three turns of the crank plus 16 holes on the plate are required. It should be noted that

• One hole in the 18-hole circle equals V20.

• One hole in the 27-hole circle equals V30.

Say you want to calculate the indexing for 15 minutes (15'). The calculation procedure is as follows:

Compound Angular Indexing

When the index crank is moved one hole in the 27-hole circle, the spindle rotates 20 minutes (20'); when the crank is moved one hole in the 18-hole circle, the spindle rotates 30 minutes (30'). The compound method can be used to index angles accurately to 1 minute (1'), as follows:

1. Place a 27-hole plate outside a 20-hole plate so that any two holes register, and fasten them together in position.

2. Turn the plates clockwise three holes in the 20-hole circle. Then, turn the crank counterclockwise four holes in the 27-hole circle. Thus, the total of these movements is a resultant spindle movement of exactly 1 minute (1') in a clockwise direction.

Block Indexing

This is sometimes called multiple indexing and is adapted to gear cutting. In this operation, the gear teeth are cut in groups separated by spaces. The work is rotated several revolutions by the spindle while the gear teeth are being cut.

For example, when cutting a gear that has 25 teeth, the indexing mechanism is geared to index four teeth at the same time. During the first revolution, six widely separated spaces are cut. During the second revolution, the cutter is placed one tooth behind the previously milled spaces. On the third indexing, the cutter drops behind still another tooth. In this example, the work is revolved four times to complete the gear.

The chief advantage of block indexing is that the heat generated by the cutter (especially when cutting cast iron gears with coarse pitch) is distributed more evenly around the rim of the gear. Thus, distortion caused by local heating is avoided, and higher speeds and feeds can be used.

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