<Dd> η m a x = 1 − sin ⁡ φ 1 + sin ⁡ φ (\ displaystyle \ eta _ (max) = (\ frac (1 - \ sin (\ phi)) (1 + \ sin (\ phi)))) </Dd> <P> Where α (\ displaystyle \ alpha \,) is the helix angle, φ (\ displaystyle \ phi \,) is the friction angle, and η m a x (\ displaystyle \ eta _ (max)) is the maximum efficiency . The friction value is dependent on the materials of the screw and interacting nut, but ultimately the efficiency is controlled by the helix angle . The efficiency can be plotted versus the helix angle for a constant friction, as shown in the adjacent diagram . The maximum efficiency is a helix angle between 40 and 45 degrees, however a reasonable efficiency is achieved above 15 ° . Due to difficulties in forming the thread, helix angle greater than 30 ° are rarely used . Moreover, above 30 ° the friction angle becomes smaller than the helix angle and the nut is no longer self - locking and the mechanical advantage disappears . </P> <P> In helical and worm gears, the helix angle denotes the standard pitch circle unless otherwise specified . Application of the helix angle typically employs a magnitude ranging from 15 ° to 30 ° for helical gears, with 45 ° capping the safe operation limit . The angle itself may be cut with either a right - hand or left - hand orientation . In its typical parallel arrangement, meshing helical gears requires that the helix angles are of the same magnitude and cut oppositely . </P> <P> Worm gears resemble helical gear seats, the difference being that the shafts of a worm train are aligned perpendicularly . In this case, the helix angle of the worm meshes with the lead angle of the worm gear . </P>

For helical gear the helix angle generally ranges from