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.

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固定位置校正向量计算器

在相邻等间距位置之间分解同半径校正向量，并量化可用质量增量后的残余量。

精确向量平衡质量步长优化仅限同半径

校正分配

连续精确质量

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A位置

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B位置

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最佳可用步长质量

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实际校正向量

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残余向量误差

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等半径向量分解

m_A = m sin(θ_B−θ) / sin(θ_B−θ_A)

m_B = m sin(θ−θ_A) / sin(θ_B−θ_A)

这些方程源于将两个质量向量分解为笛卡尔分量。由于三个半径相等，半径在质量方程中相互抵消。向量校验使用 U=mR，而非两个质量的标量和。

实际质量增量

计算器搜索输入质量增量附近的非负倍数，并选择相对于请求的不平衡向量具有最小笛卡尔残余的一对质量。它以 g·mm 为单位报告实际校正向量和残余量。

标准背景

ISO 21940-11:2016 加第 1 号修正案：2022 是当前刚性转子程序/公差背景，并取代了 ISO 1940-1:2003。上述正弦方程属于通用向量力学，并非声称复制自 ISO 的公式。

限制： 等半径、单一校正平面、等间距位置、正添加质量及刚性向量模型。不同半径需在质量×半径单位下进行力矩分解。最终残余量必须通过动平衡运行进行验证。