This is a special case of crossed helical gears, where the worm is a helical gear with  one to six teeth, and the worm gear has a high number of teeth (e.g., above 30).  The pitch elements of a crossed helical worm and worm gear are cylinders (Fig. 2).  Both members—worm and worm gear—are manufactured like helical gears, with  standard hobs, for example. The profile of both members is involute. The hobbing  tool in Case A is not identical to the worm. The two members have line contact,  which appear instead as point or small contacting zones.


Case B. Cylindrical worm gear drives (single-throat worm gear drives)

image

A typical worm gear drive; here the worm also has one to six teeth (starts), and the  worm gear has a high number of teeth (e.g., 30 to 300). The profile is not a  generated involute but a straight line. The geometry of a cylindrical worm  therefore is similar to an ACME screw. The worm gear is manufactured with a hob  and the hob’s enveloping surface is identical to the mating worm. This enveloping  surface generates the same involute profile on the worm teeth as seen in Case A.  However, the tooth thickness of the hob is thicker by the desired backlash amount.  The difference in the gear in Case A is the shape of the pitch element, which in  Case B has a hyperbolic form known as “throat.” The throat is formed merely by  plunging the hob cutter at the center of the face width. The two members have  line contact that appears on the worm gear member like slim ellipses with a major  ori- entation (if projected in an axial plane) parallel to the worm gear axis.


Case C. Double-enveloping worm gear drives (double-throated worm gear drives)

image

These are special types of worm gear drives with a very high con- tact ratio and  high torque transmission abilities. Again, here the worm has one to six teeth  (starts) and the worm gear has a high number of teeth (e.g. 30 to 300). The worm  is manufactured on a lathe, where the cutting blade profile rotates around a  center point while it moves along the face width. The distance between the cutting  blade pitch point and the center of blade rotation is identical to the pitch radius of  the worm gear. The profile is not a generated involute, but in a straight line. The  worm gear is manufactured with a hob that has the pitch diameter of the worm at  the center of the throat and the same number of starts, unlike the number of  worm teeth. Also, here the worm gear is cut (as in Case B) by plunging with the  hob cutter at the cen- ter of the worm gear’s face width. The two members have  line contact that appears even under light load, as with large elliptical zones—even  in single angular positions.


It should be mentioned that in Case B, where the worm gear tool resem- bles the  mating member within the flank surfaces, there remain several differences. The  tool face is extended in order to machine sufficient top- root clearance, and the  top-land corners to the flanks are rounded with the desired root fillet radius. The dedendum depth of the tool is equal to the addendum of the worm, plus an excess  amount to prevent any cutting action at the worm gear top-lands. Cylindrical worm gear drives “B” are the most common form. Their tooth profiles  of the worms depend on the manufacturing method.  Different profile forms according to DIN 3975 are: ZH: Disk cutter with convex cutting edges, causing hollow flank profiles in axial  section on worm teeth. ZI: Tooth profile in face section is an involute; manufactured, for example, by  hobbing, like a cylindrical pinion. The hob for the worm gear manufacturing is a  “duplicate” of the worm (however serrated and considering clearance and  backlash). ZA: Profile is a trapezoid in an axial section; manufactured, for example, by  turning. ZN: Profile is a trapezoid in a normal section; manufactured, for example, by  turning with cutting blade tilted to lead angle of worm. ZK: Profile with crowning. Tool is disk cutter with trapezoidal profile, which is tilted  to lead angle of worm. Profile crown generated depending on disk cutter  diameter.

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