Helix angle

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In mechanical engineering, a helix angle is the angle between any helix and an axial line on its right, circular cylinder or cone.^[1] Denoted in engineering textbooks as either an α, λ, or ψ, the helix angle plays a critical role in engineering applications where mechanical transfers of power are involved. The more common applications of helix angles, which include screws, helical gears, and worm gears, are discussed below.

The helix angle references the axis of the cylinder, distinguishing it from the lead angle, which references a line perpendicular to the axis. Naturally, the helix angle is the geometric complement of the lead angle. Calculations of helix angle usually employs the degree unit (°), as opposed to radians, to facilitate visualization.

Contents 1 Concept 2 Engineering Applications 2.1 Screw 2.2 Helical Gear 2.3 Worm Gear 3 References

[edit] Concept

In terms specific to screws, the helix angle can be found by unraveling the helix from the screw, representing the section as a right triangle, and calculating the angle that is formed. Note that while the terminology directly refers to screws, these concepts are analogous to most mechanical applications of the helix angle.

The diagram below shows how one can obtain a helix angle value from a representation triangle:

The helix angle can be expressed as:

where

c is the circumference of the screw at the pitch diameter.

p is the pitch of the of the screw, which is the axial distance from a point on a thread to a corresponding point on an adjacent thread, and

[edit] Engineering Applications

The helix angle is crucial in mechanical engineering applications that involve power transfer and motion conversion. Some examples are outlined below, though its use is much more widely spread.

[edit] Screw

Cutting a single helical groove into a screw-stock cylinder yields what is called single-thread screw. Similarly, one may construct a double-thread screw provided that the helix angle is steeper, and a second thread is cut in the space between the grooves of the first. For certain applications, triple and quadruple threads are in use.^[2] The helix may be cut either right hand or left hand. In screws especially, the helix angle is essential for calculating torque in power screw applications.

[edit] Helical Gear

In helical and worm gears, the helix angle denotes the standard pitch circle unless otherwise specified.^[3] 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.^[4] In its typical parallel arrangement, meshing helical gears requires that the helix angles are of the same magnitude and cut oppositely.

[edit] Worm Gear

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.^[5]

[edit] References

1. ^ ANSI/AGMA. ANSI/AGMA Standards 1012-G05 Gear Nomenclature, Definitions of Terms with Symbols. American Gear Manufacturers Association, 2005.
2. ^ Norton, Robert L. Machine Design: An Integrated Approach. 3rd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
3. ^ ANSI/AGMA. ANSI/AGMA Standards 1012-G05 Gear Nomenclature, Definitions of Terms with Symbols. American Gear Manufacturers Association, 2005.
4. ^ Shigley, Joseph E., and Larry D. Mitchell. Mechanical Engineering Design. 4th ed. New York: McGraw-Hill, Inc, 1983.
5. ^ Spotts, M F., and T E. Shoup. Design of Machine Elements. 7th ed. Upper Saddle River, NJ: Prentice Hall, 1998.