Is the two-position decomposition approximate?

With equal correction radii and exact continuous masses, the two adjacent vectors reproduce the requested vector exactly. Practical error comes from mass increments, placement radius, angle and installation tolerances.

Why is the scalar mass sum larger?

Scalar mass is not vector unbalance. The two oblique vectors can require a scalar mass sum greater than the single ideal mass while their vector sum remains exact.

What angle convention is used?

Position 1 is 0 degrees and positive angles advance in the user-defined positive direction. The same datum, viewing side, rotation direction and add/remove convention must be used as the balancing instrument.

Does ISO 21940 prescribe this formula?

This sine decomposition follows ordinary planar vector equilibrium. ISO 21940-11:2016 plus Amendment 1:2022 provides rigid-rotor balancing procedure and tolerance context; this page does not claim the formula is an ISO formula.

Can mass be welded or removed anywhere on a blade?

No. Correction locations and attachment or removal methods require rotor-manufacturer and structural approval, including stress, fatigue, containment and aerodynamic considerations.

Strumento di ingegneria gratuito — #012

Fixed-Position Correction Vector Calculator

Resolve a same-radius correction vector between adjacent equally spaced positions and quantify the residual after available mass increments.

Exact Vector EquilibriumMass-Step OptimizationSame Radius Only

Correction Distribution

Continuous exact masses

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Posizione A

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Posizione B

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Best available-step masses

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Achieved correction vector

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Residual vector error

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Equal-radius vector decomposition

m_A = m sin(θ_B−θ) / sin(θ_B−θ_A)

m_B = m sin(θ−θ_A) / sin(θ_B−θ_A)

These equations follow from resolving the two mass vectors into Cartesian components. Because all three radii are equal, radius cancels from the mass equations. The vector check uses U=mR, not the scalar sum of the two masses.

Practical mass increments

The calculator searches nearby non-negative multiples of the entered mass increment and selects the pair with the smallest Cartesian residual against the requested unbalance vector. It reports the achieved vector and residual in g·mm.

Standard context

ISO 21940-11:2016 più Amendment 1:2022 is current rigid-rotor procedure/tolerance context and replaced ISO 1940-1:2003. The sine equations above are general vector mechanics, not claimed as formulas copied from ISO.

Limitazioni: equal radius, one correction plane, equally spaced positions, positive added masses and a rigid vector model. Different radii require moment decomposition in mass×radius units. Final residual must be verified by a balancing run.