Precession (mechanical)

Precession, also called epicyclic fretting precession,[1] (or more accurately hypocyclic fretting precession since "epicyclic" applies to a round part spinning outside a circle and "hypocyclic" applies to a round part spinning inside a circle)[2] is the process of a round part in a round hole rotating with respect to that hole because of clearance between them and a radial force on the part that changes direction. The direction of rotation of the inner part is opposite to the direction of rotation of the radial force.[3] Fretting between the part and the hole is often a result of this motion. "In machinery, fretting is the micro-motion of tightly fitting parts that superficially appear immobile with respect to each other."[3]

Mechanical precession is the process of a round part (in blue) in a round hole (in red) rolling in the direction opposite to the rotational direction of the applied radial force. (The applied radial force is depicted by the green arrow. The arrow's counterclockwise rotation depicts the direction of precession, while the direction of rotation is shown by the clockwise rotation of the blue square. The center of the blue square is traversing counterclockwise along a small circle, the orbit, of diameter equal to the difference of the diameters of the red circle and the blue circle, even though the blue square rotates clockwise). If the blue circle has a diameter d  and the red circle a diameter d + δ.  The instant the green arrow is pointing downwards, the blue circle is pressed against the red circle at the bottom (point A on the blue circle). The force rotating counterclockwise causes the blue circle to roll around the red circle clockwise. When it has rolled a distance πd, the circumference of the blue circle, point A again touches the red circle. Since the circumference of the red circle is π(d + δ), point A touches the red circle a distance πδ  clockwise from the bottom.

"For a pedal, a rotating load arises from downward pedaling force on a spindle rotating with its crank making the predominantly downward force effectively rotate about the pedal spindle. What may be less evident is that even tightly fitting parts have relative clearance due to their elasticity, metals not being rigid materials as is evident from steel springs. Under load, micro deformations, enough to cause motion, occur in such joints. This can be seen from wear marks where pedal spindles seat on crank faces."[3]

This precession is a process purely due to contact forces and does not depend on inertia and is not inversely proportional to spin rate. It is completely unrelated to torque-free and torque-induced precession.

Examples

Precession caused by fretting can cause fastenings under large torque loads to unscrew themselves.

Automobile lug nuts

Automobiles have also used left-threaded lug nuts on left-side wheels, but now commonly use tapered lug nuts, which do not precess.

Bicycle pedals

Bicycle pedals are left-threaded on the left-hand crank so that precession tightens the pedal rather than loosening it. This may seem counter-intuitive, but the torque exerted due to the precession is several orders of magnitude greater than that caused by a jammed pedal bearing.

Shimano SPD axle units, which can be unscrewed from the pedal body for servicing, have a left-hand thread where the axle unit screws into the right-hand pedal; the opposite case to the pedal-crank interface. Otherwise precession of the pedal body around the axle would tend to unscrew one from the other.

Bicycle bottom brackets

English threaded bicycle bottom brackets are left-threaded on the right-hand (usually drive) side into the bottom bracket shell. This is the opposite of pedals into cranks because the sense of the relative motion between the parts is opposite. (Italian and French threaded bottom brackets have right-hand threading on both sides.)

Bicycle sprockets

Splined sprockets precess against any lockring which is screwed into the freehub. Shimano uses a lockring with detents to hold cassette sprockets in place, and this resists precession. Sturmey-Archer once used 12-splined sprockets for 2- and 3-speed racing hubs, and these were secured with a left-threaded lockring for the same reason. (Fixed gear bicycles also use a left-threaded lockring but this is not because of precession; it is merely to ensure that the lockring tends to tighten, should the sprocket begin to unscrew.)

Bearings in manual transmissions

A bearing supported gear in a manual transmission rotates synchronously with its shaft due to the dog-gear engagement. In this case, the small diametrical clearance in the bearing will induce precession of the roller group relative to the gear mitigating any fretting that occurs if the same bearing rollers always push against the same spot on the gear. Typically the 4th and 5th gears will have precession inducing features, while 1st through 3rd gears might not since cars spend less time in those gears. Transmission failure due to lack of precession is possible in gear boxes when low gears are engaged for long periods of time.

See also

References
  1. Bob Booty (June 11, 2012). "1936 Bugatti Atlantic Replica Project Knock-Off Hubs Discussion". Archived from the original on October 10, 2011. Retrieved 2013-05-18.
  2. A.C. (Aarnout) Brombacher (Winter 1997). "Cycloids, Hypocycloids, Epicycloids - Hypotrochoids and Epitrochoids (an investigation in movement using GSP)". Retrieved 2014-02-12.
  3. Brandt, Jobst (2004). "Left Hand Threads". Retrieved 2014-08-21.
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