An expanding pulley uses two opposed conical flanges on one shaft. Moving one flange axially changes the V-groove width, so a fixed-width V-belt moves to a different pitch radius while remaining in contact with both cone faces.
Expanding Pulley Interactive Calculator
Watch one flange close and see the belt rise along the two conical faces. Calculate the ideal pitch-diameter change.
Equation Used
- Opposed straight conical faces with entered included angle.
- Fixed belt cross-section remains in two-face contact.
- Axial closure is relative flange motion.
- No belt elasticity, friction, slip, clamping force, speed or power rating.
Single-pulley, rigid-belt cross-section geometry. Axial closure is relative motion between the cone faces. A complete drive also requires a second pulley, belt-length compatibility, tension, force, slip and power-capacity analysis.
Opposed conical flanges
Two frusto-conical flange faces form a V-shaped belt groove on a common shaft. At least one flange slides axially. Moving it toward the fixed flange narrows the groove and forces the fixed-width belt outward to a larger pitch radius.
Both belt sides contact the cone faces in this ideal cross-section.
Variable-pitch belt drives
Adjustable pulleys can provide a continuously variable effective diameter. A full transmission uses a cooperating pulley and a method of maintaining belt engagement and compatible belt length.
V-groove geometry
For included groove angle alpha and relative axial closure x, each belt contact rises radially by x/[2 tan(alpha/2)]. Pitch diameter therefore increases by x/tan(alpha/2), giving D=Dmin+x/tan(alpha/2).
Interpreting the result
The displayed ratio D/Dmin describes only this pulley's pitch-diameter change. It is not the speed ratio of a complete drive unless the effective diameter of the mating pulley is also known.
Scope and limitations
The model omits belt thickness conventions, elastic deformation, centrifugal effects, sidewall friction, slip, clamping force, bearing load, fatigue and allowable speed or power.
Questions
Why does the belt move outward?
The narrowing V can accommodate the same belt width only at a larger radius.
Do both belt sides stay in contact?
Yes, in the ideal symmetric geometry shown.
Is D/Dmin the transmission ratio?
No. It is this one pulley's diameter ratio.
Mechanism references
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