Posted by BillS on April 24, 2012 at 17:23:55:
In Reply to: Re: first helical gear posted by josh on April 24, 2012 at 15:10:32:
Hi Josh,
The involute form is geometrically "drawn" by a string that unwinds from
the Base Circle, whose diameter is calculated by as:
Pitch Diameter x cos PA
If Pitch Dia and Pressure Angle (PA) are given for a nominal gear, the involute curve unwinds starting from the tooth root and stops at its top (OD). The base circle still has "string" wound at the root, since base circle is smaller than root circle, again for a nominal gear. You know all this, but I wanted to bring others along for whom gear design is a mystery.
Shifting the profile simply means moving the OD and the Root Dia as joined together by depth of cut, all other things being equal.
I.e. as profile shifts (+) , the OD increases and the root dia increases, to keep the same tooth depth.
Pitch diameter doesn't change. However, for a (+) profile shift, the pitch circle is closer to the root diameter, but it is because the root diameter has changed.
If the mating part has the same profile shift but (-), then its pitch circle is closer to the OD. Again, its pitch diameter doesn't change, just the OD of the gear is smaller. As you can see, if pitch diameters don't change, they still intersect at the same point as if they were nominal gears.
If the members don't both shift - Say we profile shift the pinion (+), its OD gets larger, but we don't profile shift the gear. Where do the pitch circles intersect? Same place as before. As long as we don't make the pinion shift too large, the gear root won't interfere. It is normal practice to shift both profiles to extend the gear dedendum to accommodate the larger pinion addendum.
Involute gears that mesh correctly have a common point of contact, or Pitch Point on their
pitch circles. At least, that is the intent of a good design.
Shifting the pinion profile (+) results in longer pinion addendum, which usually requires
the gear to shift profile (-). This reduces gear root diameter and, can cause root diameter to
be at or below base circle diameter. This has its own consequences with tip interference,
but the pitch point doesn't change.
Said another way, if the pitch circles fail to intersect, I would not know what to expect. All this is true for involute gears only, which can be generated from a rack form cutter by hobbing.
Shaper cut gears are different from involute gears in that they can approximate involute geometry, but the approximation breaks down if the cutter is not designed to cut a small number of teeth and you are applying it to a small number of teeth. Shaper cutters exhibit involute seeming shapes, which are "more" involute in profile when ground for cutting larger numbers of teeth. Cutter design changes as they are designed for smaller tooth number pinions, and are thus designed for tooth ranges (eg. 6 to 10). Of course, shaper cutter design also depends on the cutter's number of teeth and pitch diameter.
The shaper cutter is an engineering marvel, IMHO.