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.

免費工程工具 — #012

固定位置校正向量計算器

將同半徑校正向量分解至相鄰等間隔位置，並量化可用質量增量後的殘餘量。

精確向量平衡質量步進最佳化僅限同半徑

校正分配

連續精確質量

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位置 A

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位置 B

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最佳可用步進質量

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達成校正向量

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殘餘向量誤差

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等半徑向量分解

m_A = m sin(θ_B−θ) / sin(θ_B−θ_A)

m_B = m sin(θ−θ_A) / sin(θ_B−θ_A)

這些方程式源自將兩個質量向量分解為笛卡爾座標分量。由於三個半徑均相等，半徑在質量方程式中相互抵消。向量檢查使用 U=mR，而非兩個質量的標量總和。

實用質量增量

計算器會搜尋輸入質量增量附近的非負倍數，並選取與要求不平衡向量相比殘餘笛卡爾分量最小的一對。它會報告達成的向量及以 g·mm 為單位的殘餘量。

標準背景

ISO 21940-11:2016 加修正案 1:2022 為目前剛性轉子程序/公差背景，並取代 ISO 1940-1:2003。上述正弦方程式為一般向量力學，非宣稱抄自 ISO 之公式。

限制： 等半徑、單一校正平面、等間隔位置、正添加質量與剛性向量模型。不同半徑需以質量×半徑單位進行力矩分解。最終殘餘不平衡必須透過動平衡運轉驗證。