Dividing Head

Objectives: At the end of this unit, the student/trainee should

be able to:

1. Familiarize with the function of a dividing head.

2. Calculate for the use of dividing head using direct indexing.
3. Calculate for the use of dividing head using indirect
indexing.
4 Calculate for the use of dividing head using indexing by
degrees of angle.
5 Calculate for the use of dividing head using differential /
universal indexing.
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 Dividing Head

Indexing

Indexing is usually done with a mechanism called a dividing

head, which is also called an indexing head.

Circular tables also called rotary tables or circular milling

attachments are also used to perform the indexing operations
when they are equipped with an index plate.

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 Dividing Head

Indexing

Indexing operations are most frequently performed on a

milling because of its great versatility.

Therefore, it is usually associated with milling-machine work.

There are no restrictions to the use of dividing head other
than the ability of the machine tool to support it and the ability
of the dividing head to support the workpiece.
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 Dividing Head

Indexing

Indexing is used to divide the circumference or the periphery

of a job into specified distance or angular separations.
Indexing operations are carried out with a dividing head or
indexing head.

In its basic construction, a dividing head consist of a worm

drive.
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 Dividing Head

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 Dividing Head

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 Dividing Head

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 Dividing Head

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 Dividing Head

Figure 1: Worm Drive

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Figure 2: Section through a dividing head,
showing the spindle and index plate.

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 Dividing Head

Direct Indexing

Direct indexing also known as rapid indexing, is the simplest

form of indexing.

It is performed by disengaging the worm shaft from the worm

wheel by means of an eccentric device in the dividing head.

The index plate contains holes or slots, and a plunger pin (fig.
3) is used to engage in the proper hole.
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Figure 3: Adjusting the plunger pin to fit into
the proper hole circle or slot.

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 Figure 4: The plunger pin and the direct
indexing plate.

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 Figure 5: Direct Indexing Plate

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 Dividing Head

Direct Indexing

Direct indexing is used for quick indexing of the workpiece

when cutting flutes, hexagon, square, and other shapes.

The work is rotated the required amount and held in place by

a pin which engages into a hole in the direct indexing plate
mounted on the end of the dividing head spindle.

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 Dividing Head

Direct Indexing

The direct indexing plate usually contains 24 hole circle.

The number of divisions it is possible to index is limited to

numbers which are factors of 24.

The common divisions that can be obtained by direct indexing

are 2, 3, 4, 6, 8, 12, and 24.

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 Dividing Head

Example 1:

What direct indexing is necessary to mill eight flutes on a reamer

blank?

24 Note:
nh =
N Never count the hole or slot in
which the plunger pin is
24 engaged.
= = 3 holes
8

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 Dividing Head

Simple Indexing

i = transmission ratio / speed ratio (usually 40 : 1)

N = number of division required or

T = spacing step, indexing number

 = pitch angle of the workpiece

nc = crank rotation per spacing step

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 Dividing Head

Simple Indexing

A. Number of divisions required divides evenly into 40, i.e.,

the speed ratio (gear ratio)

speed ratio
no. of crank rotation =
no. of division required

40
nc =
N
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 Dividing Head

Simple Indexing

B. Number of divisions required does not divide evenly into

40.

In this case the index crank must be moved into fractional

parts of a turn.

This is done with index plate.

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 Dividing Head

The dividing head generally is

furnished with three index plates.
Each plate has six circles of
holes.

Brown and Sharpe:

Plate 1: 15 – 16 – 17 – 18 – 19 – 20

Plate 2: 21 – 23 – 27 – 29 – 31 – 33

Plate 3: 37 – 39 – 41 – 43 – 47 – 49
Figure 6: Index Plate
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 Dividing Head

Cincinnati Standard Plate

Plate 1:

24 – 25 – 28 – 30 – 34

37 – 38 – 39 – 41 – 42 – 43

Plate 2:
46 – 47 – 49 – 51 – 53

54 – 57 – 58 – 59 – 62 – 66
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 Dividing Head

Example 2: Index a job with 18 divisions.

Solution:
Note:
40
nc = The whole number indicates the
N compete turns of the index crank,

40 the denominator represents the

= index circle,
18
and the numerator gives the
4 number of holes to use on that
= 2 turns
18 hole circle.
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 Dividing Head

Example 2: Index a job with 18 divisions.

Solution:
Note:
40
nc = Therefore,
N

40 nc = 2 full turns of the index

=
18 crank and 4 holes on a 18-hole
4 circle.
= 2 turns
18
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 Dividing Head

Example 3: Index a job of seven divisions.

Solution:
Note:
40
nc = When the denominator of the
N indexing fraction does not match
with any of the available index
40 circle,
=
7
change it to a number
5 represented in one of the hole
= 5 turns circles.
7
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 Dividing Head

Example 3: Index a job of seven divisions.

Solution:
Note:
40
nc = Do this by multiplying or dividing
N the numerator by the same
number.
40
=
7 5 × 3 15
=
7 × 3 21
5
= 5
7
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 Dividing Head

Example 3: Index a job of seven divisions.

Solution:
Therefore,
40
nc =
N nc = 5 full turns of the index
crank and 15 holes on a 21-hole
40
= circle.
7

5 15
= 5 = 5 turns
7 21
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 Dividing Head

Angular Indexing 360° rot. of workpiece ≙ to 40

rot. of dividing crank

 rot. of workpiece ≙ to 40 /
360°

Conclusion:


nc =
9°
Figure 7
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 Dividing Head

Example 4: Calculate the indexing for 45°.

Solution:


nc =
9°

45°
=
9°

= 5 complete turns

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 Dividing Head

Example 5: Calculate the indexing for 60°.

Solution: Therefore, nc = 6 full turns of

 the index crank and 12 holes on
nc =
9° a 18-hole circle.

60° 2 × 6 12
= =
9° 3 × 6 18

2 12
= 6 = 6 turns
3 18
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 Dividing Head

If the dimensions are given in degrees and minutes, it will be

necessary to convert the degrees into minutes (number of
degrees × 60') and add this product to the minutes required.

The indexing in minutes is calculated as follows:

no. of minutes required

no. of crank rotation =
540'
min
nc =
540'
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 Dividing Head

Example 6: Calculate the indexing for 20'.

Solution:

min
nc =
540'

20'
=
540'
Therefore, nc = 1 hole on a 27-
1
= turn hole circle.
27
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 Dividing Head

Example 7: Calculate the indexing for 24° 30'.

Solution: First convert 24° 30' into minutes:

60'
24° × = 1440'
1°

1440' + 30' = 1470'

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 Dividing Head

Example 7: Calculate the indexing for 24° 30'.

Solution:

min
nc =
540'
Therefore, nc = 2 full turns of
1470' the index crank and 13 holes on
=
540' a 18-hole circle.
13
= 2 turns
18
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 Dividing Head

Differential Indexing / Universal Indexing

When it is impossible to calculate the required indexing by the

simple/indirect indexing method, that is, when the fraction
40/N cannot be reduced to a factor of one of the available
hole circles, it is necessary to use differential indexing.

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 Dividing Head

Differential Indexing / Universal Indexing

With this method of indexing, the index plate must be

revolved either forward or backward a part of a turn while the
index crank is turned to attain the proper spacing of indexing.

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 Dividing Head

Differential Indexing / Universal Indexing

In differential indexing, as in simple indexing, the index crank

rotates the dividing head spindle. The rotation of the plate
may be either in same direction (positive) or in opposite
direction (negative) of the index crank. This change of
rotation is effected by an idler gear or gears in the gear train.

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 Dividing Head

Differential Indexing / Universal Indexing

When it is necessary to calculate the indexing for a required

number of divisions by the differential method, a number is
chosen close to the required divisions which can be index by
simple indexing.

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 Dividing Head

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 Dividing Head

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Dividing head geared for differential indexing.

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 Dividing Head

Differential Indexing / Universal Indexing

The method of calculating the number crank rotation and the

change gears required are as follows:

no. of crank rotation

40
nc =
A

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 Dividing Head

Change gear ratio:

driving gear (spindle) Zt 40

= = ( A – N ) ×
driven gear (worm) Zg A

A = approximate no. of divisions or

T′ = auxiliary indexing no.

N = required no. of divisions or T = indexing no.

Z = gear wheels (1 and 3 are driving gears)

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 Dividing Head

Gear Wheels: There is always an indirect ratio between

gear wheels and rotational speed:

Z driving n driven
=
Z driven n driving

Customary set of change gears:

24, 24, 28, 32, 36, 40, 44, 48, 56, 64, 72,
86, & 100
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 Dividing Head

Example 8: Calculate the indexing and change gears required

for 57 divisions.

1. Indexing

40 40
nc = =
A 57

Since there is no 57-hole circle and since it is impossible to

reduce this fraction to suit any hole circle, it is necessary to
select an approximate number close to 57, for which simple
indexing may be calculated.

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 Dividing Head

2. Let the approximate number of divisions equal 56.

3. Indexing 56 divisions

40 40 5 3 15
nc = = = × =
A 56 7 3 21

Therefore, nc = 15 holes on the 21-hole circle.

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 Dividing Head

4. Gear Ratio

Zt 40
= ( A – N ) × or ( A – N ) × nc
Zg A

5
= ( 56 – 57 ) ×
7

5 8 40 spindle gear
= – × =
7 8 56 worm gear
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 Dividing Head

Example 9: A sprocket with 53 teeth is to be cut using a

universal index-head (40:1). Calculate the
number of crank revolutions and the gear wheels
required for the 15 hole circle chosen. The
auxiliary indexing number is to be 60.

Given: N = 53 T

A = 60

Lk = 15

Find: nc & gear wheels

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 Dividing Head

Solution:

1. Indexing 60 teeth

40 40 2 5 10
nc = = = × =
A 60 3 5 15

Therefore, nc = 10 holes on the 15-hole circle.

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 Dividing Head

2. Gear Ratio

Zt 2 × 7
= ( A – N ) × nc =
Zg 1 × 3

2 2 × 32
= ( 60 – 53 ) ×
3 1 × 32

2 64
= 7 × =
3 32
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 Dividing Head

2. Gear Ratio

2 × 7 64 × 56 driving gear (spindle)

=
1 × 3 32 × 24 driven gear (worm)

7 × 8
3 × 8 Z1 = 64 Z3 = 56

Z2 = 32 Z4 = 24
56
=
24
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