2 Objectives Calculate the lead and helix angle of a helical gear Set up a milling machine to machine a helixMake 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 shaftPerformed on universal milling machine by gearing dividing head through worm shaft to lead screw of milling machine
6 Cutting an Inch (Metric) Helix Must know two of the following:Lead of helixLongitudinal distance helix advances axially in one complete revolution of workAngle of helixFormed by intersection of helix with axis of workDiameter (and circumference) of workpiece
8 Steps to Cut a Helix on a Cylinder Swing table in proper direction to angle of helixEnsures that groove of same contour as cutter producedWork must rotate one turn while table travels lengthwise the distance equal to leadAchieved by installing proper change gears between worm shaft on dividing head and milling machine lead screw
10 Example: Inch MeasureTo 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 tableHold cylinder on which helix is cut in horizontal plane with axis running in right-left directionRight-hand helix: helix slopes down and to rightCounterclockwise directionLeft-hand helix: helix slopes down and to leftClockwise direction
14 Inch CalculationsDividing 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 revolutionFor dividing head spindle to revolve one turn, lead screw must revolve 40 timesTable would travel 40 x ¼, or 10 in. while work revolves one turnLead 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, 100Solution: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, 100Solution: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 pitchDividing head has ratio of 40:1Therefore, lead of machine would be 40 times pitch of lead screw
19 Example: InchCalculate 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 directionTo cut right-hand helix, spindle must revolve in opposite directionAnother idler must be inserted but acts merely as means of change direction or rotation of dividing head spindleDirection of spindle rotation for simple gearing opposite to that for compound gearing
21 Cutting Short Lead Helices Disengage dividing head worm and wormwheelConnect change gears directly from table lead screw to dividing head spindlePermits machining leads to one-fortieth of leads shown in handbook tables
22 Example:A plain helical milling cutter to the following specifications is requiredDiameter: 4 in.Number of teeth: 9Helix: right-handHelix angle: 25ºRake angle: 10º positive radial rakeAngle of flute: 55ºDepth of flute: ½ in.Length: 4 in.Material: tool steel
24 Press cutter blank firmly on mandrel Mount dividing head and footstock If threaded mandrel used, tighten nut securelyMount dividing head and footstockCalculate indexing for nine divisionsSet 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 headSwivel table 25º counterclockwiseAdjust crossfeed handwheel until table about 1 in. from face of columnSwing table back to zeroMount 55º double-angle cutter so it revolves toward dividing head and center it over flute layout
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 depthIndex for and cut remaining flutesRemove 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 gageBlank 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. wideCut secondary clearance (30º angle) on all teeth of workpiece