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# Helical Milling Unit 71.

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Helical Milling Unit 71

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

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

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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?

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?

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

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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

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

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.

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.

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

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

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

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

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

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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)

Disengage index plate locking device
Calculate lead of helix

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:

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

Rotate blank until flute layout is aligned with cutter edge
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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

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

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

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