1. Helical Milling
Unit 71

2. Objectives Calculate the lead and helix angle of a helical gear
Set up a milling machine to machine a helix
Make the calculations and setup for milling a helical gear

3. Helical Milling Process of milling helical grooves
Flutes in drill, teeth in helical gears, or worm thread of shaft
Performed on universal milling machine by gearing dividing head through worm shaft to lead screw of milling machine

4. Helix
Theoretical line or path generated on a cylindrical surface by a cutting tool fed lengthwise at a uniform rate, while cylinder also rotated at same uniform rate
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5. Spiral
Path generated by point moving at fixed rate of advance along surface of a rotating cone or plane
Example conical spiral
Threads on wood screw
Example plane
Watch springs
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6. Cutting an Inch (Metric) Helix
Must know two of the following:
Lead of helix
Longitudinal distance helix advances axially in one complete revolution of work
Angle of helix
Formed by intersection of helix with axis of work
Diameter (and circumference) of workpiece

7. Lead of a Helix Varies with:
Diameter of work
Angle of helix
If surface of cylinder unwound to produce flat surface, helix would form hypotenuse of right-angle triangle, with circumference forming side opposite and lead side adjacent
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8. Steps to Cut a Helix on a Cylinder
Swing table in proper direction to angle of helix
Ensures that groove of same contour as cutter produced
Work must rotate one turn while table travels lengthwise the distance equal to lead
Achieved by installing proper change gears between worm shaft on dividing head and milling machine lead screw

9. Determining the Helix Angle
To ensure groove of same contour as cutter is produced, the table must be swung to angle of helix
Tangent of helix
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10. Example: Inch Measure
To what angle must the milling machine table be swiveled to cut a helix having a lead of in. on piece of work 2 in. in diameter?

11. Example: Metric Measure
To what angle must the milling machine table be swiveled to cut a helix having a lead of 250 mm on piece of work 40 mm in diameter?

12. Determining Direction to Swing Table
After helix angle calculated necessary to determine direction to swivel table
Hold cylinder on which helix is cut in horizontal plane with axis running in right-left direction
Right-hand helix: helix slopes down and to right
Counterclockwise direction
Left-hand helix: helix slopes down and to left
Clockwise direction

13. Calculating Change Gears to Produce the Required Lead
To cut helix, work must rotate and move lengthwise at same time
Lead: amount work travels lengthwise with one revolution
Rotation caused by gearing worm shaft of dividing head to lead screw of machine
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14. Inch Calculations
Dividing head ration is 40:1 and standard milling machine lead screw has 4 threads per inch (tpi)
Lead screw revolves one turn, dividing head spindle 1/40th revolution
For dividing head spindle to revolve one turn, lead screw must revolve 40 times
Table would travel 40 x ¼, or 10 in. while work revolves one turn
Lead of milling machine is 10 in. when lead screw (4 tpi) connected to dividing head (40:1) with equal gears

15. Calculation of Change Gears
Ratio of gears required to produce lead on milling machine having lead screw with 4 tpi always equal to fraction having lead of helix for numerator and 10 for denominator

16. Example: Inch Solution:
Calculate change gears required to produce helix having lead of 25 in. on piece of work. The available change gears have the following number of teeth: 24, 24, 28, 32, 36, 40, 44, 48, 56, 64, 72, 86, 100
Solution:
Since 10- and 25-tooth gears not supplied with standard dividing heads, necessary to multiply 25:10 ration by any number that will suit change gears available.

17. Example: Inch Solution:
Calculate change gears required to produce helix having lead of 25 in. on piece of work. The available change gears have the following number of teeth: 24, 24, 28, 32, 36, 40, 44, 48, 56, 64, 72, 86, 100
Solution:
Since 10- and 25-tooth gears not supplied with standard dividing heads, necessary to multiply 25:10 ration by any number that will suit change gears available.

18. Metric Calculations Pitch of lead screw stated in millimeters
Lead screws have 5-mm pitch
Dividing head has ratio of 40:1
Therefore, lead of machine would be 40 times pitch of lead screw

19. Example: Inch
Calculate the change gears required to cut a helix having a lead of 500 mm on a workpiece using a standard set of gears. The milling machine lead screw has a pitch of 5 mm.
The normal change gears in set are: 24, 24, 28, 32, 36, 40, 44, 48, 56, 64, 72, 86, 100

20. Direction of Spindle Rotation
To cut left-hand helix, the gear on lead screw and worm gear revolve in same direction
To cut right-hand helix, spindle must revolve in opposite direction
Another idler must be inserted but acts merely as means of change direction or rotation of dividing head spindle
Direction of spindle rotation for simple gearing opposite to that for compound gearing

21. Cutting Short Lead Helices
Disengage dividing head worm and wormwheel
Connect change gears directly from table lead screw to dividing head spindle
Permits machining leads to one-fortieth of leads shown in handbook tables

22. Example:
A plain helical milling cutter to the following specifications is required
Diameter: 4 in.
Number of teeth: 9
Helix: right-hand
Helix angle: 25º
Rake angle: 10º positive radial rake
Angle of flute: 55º
Depth of flute: ½ in.
Length: 4 in.
Material: tool steel

23. Procedure For Cutting Short Lead Helices
Dimensions of helical milling center
Turn blank to sizes indicated
Apply layout die to end of blank and lay out
Lay out a line on periphery to indicate direction of the right-hand helix
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24. Press cutter blank firmly on mandrel Mount dividing head and footstock
If threaded mandrel used, tighten nut securely
Mount dividing head and footstock
Calculate indexing for nine divisions
Set sector arms to 8 holes on 18-hole circle (do not count hole where pin engaged)

25. Disengage index plate locking device
Calculate lead of helix

26. Consult any handbook for change gears to cut lead closest to 26.949 in. (27)
If handbook not available, change gears can be calculated for closest lead – 27 in.
Change gears for 27 in lead calculated:

27. Mount change gears, allowing slight clearance between mating teeth
Mount work between centers, with large end of mandrel against dividing head
Swivel table 25º counterclockwise
Adjust crossfeed handwheel until table about 1 in. from face of column
Swing table back to zero
Mount 55º double-angle cutter so it revolves toward dividing head and center it over flute layout

28. Rotate blank until flute layout is aligned with cutter edge
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29. With work clear of cutter, set depth to .500 in.
Rotate table 25º (counterclockwise), and lock securely (right end in toward column)
Carefully cut first tooth space, checking accuracy of location and depth
Index for and cut remaining flutes
Remove fluting cutter and mount plain helical milling cutter

30. Rotate work (using index crank) until line at 30º to side of flute parallel to table
May be checked by means of surface gage
Blank may be rotated by indexing an amount equal to

31. Adjust workpiece under cutter
With cutter rotating, raise table until width of land on workpiece is about in. wide
Cut secondary clearance (30º angle) on all teeth of workpiece