Tooth gap relieved enveloping worm
A worm comprises enveloping worm teeth having relieved ends. The worm is machined in three steps comprising machining a threaded section, machining a first end section, and machining a second end section. The threaded section is machined utilizing a rack-form tool having a rack-form thickness. The first end section and the second end section are machined utilizing a larger rack-form thickness, thereby, providing relieved ends. The teeth of the worm having such relieved ends mesh with the teeth of a mating gear at full depth throughout preventing partial teeth engagement.
1. A worm made from a worm blank, said worm blank comprising a length thereby defining a center point, an axial axis along the length and through the center point, and a positive direction and a negative direction along the axial axis and about the center point, said worm comprising:
(a) a threaded section made by machining the worm blank into a conjugate worm comprising a conjugate-thread length along the axial axis thereby defining a conjugate-thread center point that coincides with the center point, a positive half-conjugate length in the positive direction, and a negative half-conjugate length in the negative direction, via a rack-form tool utilizing a first rack-form thickness;
(b) a first end section made by machining the conjugate worm starting at the positive half-conjugate length for a first predetermined length in the positive direction, via the rack-form tool utilizing a second rack-form thickness;
(c) a second end section made by machining the conjugate worm starting at the negative half-conjugate length for a second predetermined length in the negative direction, via the rack-form tool utilizing the second rack-form thickness; and
wherein the worm blank is machined into the conjugate worm according to equations:
Ratio= N G ÷N W ;
R =Module× N G ÷cos H÷ 2;
P= 2 R×π÷N G ; and
A T =tan −1 (tan A N ÷ cos H ); and
wherein,
N G =number of teeth in a gear;
N W =number of enveloping worm teeth in the worm;
A N =normal pressure angle;
A T =transverse pressure angle;
R=operating pitch radius;
P=transverse circular pitch;
H=helix angle;
A R =rack form addendum; and
T=rack-form thickness.
2. The worm of claim 1 , wherein the conjugate-thread length is equal to 24 inches.
3. The worm of claim 1 , wherein the positive half-conjugate length is equal to the negative half-conjugate length which is equal to ½ the conjugate-thread length.
4. The worm of claim 1 , wherein the first predetermined length is equal to the second predetermined length Which is equal to 3 inches.
5. The worm of claim 1 , wherein the first rack-form thickness is equal to 0.25 inches.
6. The worm of claim 1 , wherein the second rack-form thickness is equal to 0.35 inches.
7. The worm of claim 1 , wherein the worm blank is machined into the conjugate worm via a CNC turning lathe.
8. The worm of claim 1 , wherein the conjugate worm comprises enveloping worm teeth.