An equalizer sheave allows rope length to transfer between two sides of a reeving system. With an ideal freely rotating sheave and parallel vertical legs, equal tension means each leg carries half their total. This calculator compares that ideal tension with sheave size, groove size and an explicitly defined breakaway difference.
Equalizing Pulley Interactive Calculator
Compare local rope tensions and sheave proportions. Enter the total pull of the two legs, pitch diameter, rope diameter, groove cross section and measured breakaway tension difference.
Equation Used
- Parallel vertical rope legs at the sheave.
- D is rope-centreline pitch diameter.
- Circular groove cross section for the size comparison.
- No-slip inextensible rope in the illustrative motion.
- No certified working-load or groove-tolerance recommendation.
Fixed axle and two vertical rope legs. Ideal kinematic motion and resistance-threshold comparison are separate.
One continuous rope transfers length
The rope passes over the top half of a fixed sheave. When one leg lengthens, the other shortens by the same amount. The animated rope markers and wheel use the same no-slip movement.
The two rope ends shown are cut boundaries leading to the rest of the reeving. Their illustrative motion is not a complete crane lifting cycle. The fixed-axle reaction balances the total vertical pull of those two legs.
The manufacturer reference shows an equalizer sheave within a wire-rope hoist. This drawing isolates that component to make its length exchange and forces visible; it does not reproduce that entire hoist.
Interpret the five measurements
W is the sum of the two vertical leg tensions at this sheave. It is not automatically the hook load in a system with additional supporting rope parts. D is measured to the rope centreline around the sheave. The rope diameter is d.
The groove input g is the circular cross-section diameter of the groove, not the overall sheave diameter. The enlarged section uses g and d directly and marks interference when the groove is smaller than the rope.
Fb is defined as the difference between leg tensions at incipient sheave rotation. Use a measured or otherwise established value under the relevant conditions; the calculator does not infer it from a generic bearing type.
Tension, proportions and breakaway
Ideal equal tension is T 0=W/2. The sheave-to-rope ratio is D/d. Groove oversize is 100(g/d−1) percent; negative oversize indicates that the entered groove is smaller than the rope.
The displayed breakaway percentage is 100 Fb/T 0. If the axle resists rotation, the threshold condition is |T 1−T 2|=Fb with T 1+T 2=W. The threshold pair is therefore (W−Fb)/2 and (W+Fb)/2. The corresponding resisting axle moment is FbD/2000 N·m when D is in millimetres.
The two straight-leg lengths are L+q and L−q. Their sum plus the half-circle wrap, 2 L+πD/2, remains constant. Wheel angle is tied to q through the pitch radius, so the rope does not slide through a stationary wheel.
10,000 N total pull on a 450 mm sheave
The ideal leg tension is 5000 N. A 10 mm rope gives D/d=45. A 10.3 mm groove is 3% larger in diameter than that rope.
With Fb=80 N, the breakaway comparison is 1.6% of ideal leg tension. The threshold tensions are 4960 N and 5040 N, corresponding to 18 N·m axle resistance.
These numbers are comparisons, not an approval of a particular rope, groove or hoist. The ideal motion loop remains separate from the breakaway threshold calculation.
Geometric comparisons are not ratings
No universal minimum D/d, groove tolerance, rope construction, inspection interval or safety classification is assigned by this calculator. Those requirements depend on the specified equipment and rope.
A groove that is larger than the rope is not automatically suitable. Groove contour, support angle, surface condition and the rope manufacturer’s requirements still matter. Negative oversize is displayed rather than hidden.
The model omits rope elasticity, mass, bending loss, fleet angle, acceleration and the remainder of the hoist reeving. If Fb reaches W, the lower threshold tension is zero and the assumed pair of taut legs is at its limit.
Equalizer-sheave questions
Is W the hook load?
Only if your force diagram establishes that equivalence. Here it means the total of the two local vertical leg tensions.
Does breakaway make the ideal tension output change?
No. W/2 remains the ideal comparison. The diagram separately shows the unequal threshold pair implied by the entered resistance.
Why is the groove red?
The entered circular groove diameter is smaller than the rope diameter.
Is the motion a friction simulation?
No. It demonstrates conserved rope length and no-slip wheel rotation at an inspection speed.
Reference
- Yale EWR Electric Wire Rope Hoists — operating and maintenance manual — page 15, equalizer-sheave re-reeving description and diagrams. The calculator isolates a generic fixed equalizer sheave; it does not supply Yale equipment ratings.
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