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Krar • Gill • Smid

Technology of Machine Tools6th Edition

Gear Cutting

Unit 70

70-2

Objectives

• Select the proper cutter for any gear to be

cut

• Calculate gear-tooth dimensions for inch

gears

• Calculate gear-tooth dimensions for

metric gears

• Set up and cut a spur gear

70-3

Gear Cutting

• Usually cut to repair or replace gear broken

or lost or no longer carried in inventory

• Industry mass-produces gears on special

machines designed for this purpose

– Gear-shaping machines

– Gear-hobbing machines

70-4

Involute Gear Cutters

• Sharpened on face

• Ensures exact duplication of shape of teeth

– Regardless of how far back face of tooth has

been ground

• Available in many sizes

– Range from 1 to 48 diametral pitch (DP)

– Special cutters for teeth smaller than 48 DP

70-5

Comparative Gear-Tooth Sizes: 4 to 16 DP

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Permission required for reproduction or display.

70-6

Gear Cutting

• Cutter must be chosen to suit both DP and number

of teeth (N)

– Tooth space for small pinion cannot be same shape as

tooth space for large mating gear

– Teeth on smaller gears must be more curved to prevent

binding of meshing gear teeth

• Sets of gear cutters

– Made in series of slightly different shapes to permit

cutting of any desired number of teeth with assurance

that teeth will mesh with another gear(same DP)

70-7

Cutters

• Generally made in sets of eight

– Numbered from 1 to 8 (also in half sizes)

• Gradual change in shape (sides)

– #1 cutter with straight to #8 with curved sides

• Number of teeth

– #1 will cut teeth in gear 135 teeth to a rack

– #8 will cut only 12 and 13 teeth

• Cutter number permits a more accurate meshing of

teeth (for gears to mesh must have same DP)

70-8

Cutter

Number Range

1 135 teeth to a rack

11⁄2 80 to 134 teeth

2 55 to 134 teeth

21⁄2 42 to 54 teeth

3 35 to 54 teeth

31⁄2 30 to 34 teeth

4 26 to 34 teeth

41⁄2 23 to 25 teeth

Cutter

Number Range

5 21 to 25 teeth

51⁄2 19 and 20 teeth

6 17 to 20 teeth

61⁄2 15 and 16 teeth

7 14 to 16 teeth

71⁄2 13 teeth

8 12 and 13 teeth

Involute Gear Cutters

70-9

Example: Selecting a Cutter

A 10-DP gear and a pinion in mesh have 100 teeth

and 24 teeth, respectively. What cutters should be

used to cut these gears?

Cutter Selection

Since the gears are in mesh, both must be cut with a

10-DP cutter.

A #2 cutter should be used to cut the teeth on

the gear, since it will cut from 55 to 134 teeth.

A #5 cutter should be used to cut the pinion,

since it will cut from 21 to 25 teeth.

70-10

Procedure For Machining a Spur Gear

Example: A 52-tooth gear with an 8 DP is required

1. Calculate all necessary gear data (See previous table)

in. 750.68

54

8

2522 Ndiameter Outside a. ==

+=

+=

DP

in. 2697.8

157.2157.2 tooth ofdepth Wholeb. ===

DP

Cutter number = 3 (35 to 54 teeth)

Continue …

70-11

d. Indexing (using Cincinnati standard plate)

circle hole 39on holes 30 3

3 x

13

10

52

4040====

N

2. Turn gear blank to proper outside diameter

(6.750 in.)

3. Press gear blank firmly onto mandrel

4. Mount index head and footstock, and check the

alignment of the index centers

5. Set dividing head so index pin fits into hole on

39-hole circle and sector arms set for 30 holes

70-12

6. Mount mandrel (and workpiece), with

large end toward indexing head, between

index centers

7. Move table close to column to keep setup

as rigid as possible

8. Mount an 8 DP#3 cutter on milling

machine arbor over approximate center of

the gear

• Be sure to have cutter rotating in direction of

indexing head

70-13

9. Center gear blank with cutter by either of the following methods:

• Place square against outside diameter of gear

• With pair of inside calipers or rule, check distance between square and side of cutter

• Adjust table until distances from both sides of gear blank to sides of cutter are the same

• More accurate method of centralizing cutter is to use gage blocks instead of inside calipers

10. LOCK THE CROSS-SLIDE

11. Start milling cutter and run work under cutter

70-14

12. Raise table until cutter just touches work

13. Set graduated feed collar on the vertical

feed to zero

14. Move work clear of cutter by means of

the longitudinal feed handle

• Raise table to 2/3 depth of tooth (.180 in.)

• Lock knee clamp

15. Slightly notch all gear teeth on end of

work to check for correct indexing

70-15

16. Rough-out first tooth and set automatic

feed trip dog after cutter is clear of work

17. Return table to starting position

• Clear end of work with cutter

18. Cut remaining teeth and return table to

starting position

19. Loosen knee clamp, raise table to full

depth of .270 in., and lock knee clamp

20. Finish-cut all teeth

70-16

Metric Gears

• Countries using metric system usually use

module system of gearing

– Module (M) of a gear equal pitch diameter (PD)

divided by number of teeth (N)

– M is actual dimension

N

PDM =

Table 70.2 in text gives

necessary rules and

formulas for metric

spur gears

70-17

Metric Module Gear Cutters

• Most common available in modules

ranging from 0.5 to 10 mm

• Available in set of eight cutters numbered

from #1 to #8

– Range of each cutter reverse of DP cutter

• Table on next slide shows cutters available

and rang of each cutter in set

70-18

Milling Cutter Numbers

ModuleSize (mm) Cutter No. For Cutting

0.5 3.5

0.75 3.75 1 12 to 13 teeth

1 4 2 14 to 16 teeth

1.25 4.5 3 17 to 20 teeth

1.5 5 4 21 to 25 teeth

1.75 5.5 5 26 to 34 teeth

2 6 6 35 to 54 teeth

2.25 6.5 7 55 to 134 teeth

2.5 7 8 135 teeth to rack

2.75 8

3 9

3.25 10

Metric

Module

Gear

Cutters

70-19

Metric Example:

A spur gear has a PD of 60 mm and 20 teeth. Calculate:

1. Module

2. Circular pitch

3. Addendum

4. Outside diameter

5. Dedendum

6. Whole depth

7. Cutter number

70-20

Solution:

mm320

60

N

PDM .1 ===

mm 9.425 3.1416 x 3 x M CP .2 === π

mm 3.498 1.166 x 3 1.166 x M D .5 ===

mm 66 3 x 22 M x 2) (N OD .4 ==+=

mm 3 M A .3 ==

mm 6.498 2.166 x 3 2.166 x M WD.6 ===

3 table)previous (seenumber utter .7 =C

70-21

Another Metric Example:

Two identical gears in mesh have a CCD of 120 mm. Each gear has 24 teeth. Calculate:

1. Pitch diameter

2. Module

3. Outside diameter

4. Whole depth

5. Circular pitch

6. Chordal thickness

70-22

Solution:

mm 1202

240

2

120 x 2

2

CD x 2 PD 1. ====

524

120

N

PD M 2. ===

mm 130 5 x 26 M x 2) (N OD 3. ==+=

mm 10.83 2.166 x 5 2.166 x M WD4. ===

mm 15.708 3.1416 x 5 x M CP 5. === π

mm 85.72

3.1416 x 5

2

x M CT 6. ===

π

70-23

Gear-Tooth Measurement

• Measure with gear tooth vernier caliper

– Set to corrected addendum

• May also be checked by measuring over wires or pins of a specific diameter placed in two diametrically opposite tooth spaces of the gear

– Tables in most handbooks give measurement over wires having given number of teeth and specific pressure angle

70-24

Gear-Tooth Measurement

• Accurate measurement of inch gears need diametral pitch and number of teeth of gear

– For metric gears, the module must be known

• Wire or pin size to use determined by

1. For external inch spur gears, wire or pin size equal to 1.728 divided by DP of gear

2. For internal inch spur gears, wire size equal to 1.44 divided by DP of gear

3. Metric module gears measured using wire size equal to 1.728 multiplied by module of gear

70-25

Example (Inch):

Determine wire size and measurement over the

wires for a 10-DP external gear having 28 teeth

and a 14.50º pressure angle.

in. 1728.10

1.728 size Wire ==

In handbook tables, size over wires for gear having

28 teeth and 14.50º pressure angle should be

30.4374 in. divided by DP.

in. 0437.310

30.4374 ==