What is a Campbell diagram?

A Campbell diagram (also called interference diagram) plots excitation frequencies (harmonics of running speed) against natural frequencies. Where harmonic lines cross natural frequency lines, a potential resonance or critical speed exists.

What are harmonic orders?

Harmonic orders represent multiples of the rotational speed. 1× is the fundamental (1 per revolution), 2× is twice per revolution (common for misalignment), and higher orders relate to blade pass, gear mesh, etc.

How do I find critical speeds from the diagram?

Critical speeds occur where harmonic order lines intersect natural frequency lines. The crossing RPM = fn × 60 / order, where fn is the natural frequency in Hz and order is the harmonic number.

Why are critical speeds dangerous?

At critical speeds, a harmonic excitation coincides with a natural frequency, causing resonance. This leads to amplified vibration, potential structural damage, and accelerated bearing/component wear.

How do I avoid critical speeds?

Ensure operating speed is at least 20% away from any critical speed. Options include changing natural frequencies (stiffening/mass changes), adding damping, or adjusting operating speed range.

免費工程工具 — #015

坎貝爾圖計算器

繪製諧波激振階次與自然頻率之間的干擾。識別旋轉機械的臨界轉速交叉點。

最多 5 個自然頻率諧波 1×–10× 臨界轉速

臨界轉速交叉點

轉速範圍內的總交叉點數

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轉速範圍

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自然頻率

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坎貝爾圖

坎貝爾圖原理

坎貝爾圖繪製激振頻率與轉速的關係。對於每個諧波階次 k，在轉速 n 時的激振頻率為：

當諧波激振與自然頻率匹配時，會發生交叉（臨界轉速）：

常見諧波階次

階次	來源
1×	不平衡、轉子彎曲、偏心
2×	不對心、橢圓軸承、鬆動
3×	不對心（嚴重）、聯軸器缺陷
k×（葉片通過頻率）	葉片數 × RPM
k×（齒輪嚙合頻率）	齒數 × RPM

實務範例

範例 — 離心泵

已知： f_n1 = 25 Hz, f_n2 = 48 Hz, 諧波：1×, 2×, 3×

1× 在 f 處的交叉點_n1：RPM = 25 × 60 / 1 = 1500 RPM

2× 交叉點於 f_n1：RPM = 25 × 60 / 2 = 750 RPM

1× 在 f 處的交叉點_n2：RPM = 48 × 60 / 1 = 2880 RPM

⚠️ 注意： 運轉速度應至少與任何臨界速度保持 20% 的距離。若升速過程中必須通過臨界速度，請快速加速通過共振區。