What is critical speed?

Critical speed is the rotational speed at which a shaft's rotational frequency equals one of its natural bending frequencies, causing resonance. At critical speed, even small unbalance produces large vibrations that can damage bearings, seals, and the shaft itself.

Why avoid operating near critical speed?

Operating near critical speed amplifies vibrations exponentially due to resonance. The standard practice is to operate at least 20–30% below or above the critical speed. The region within ±20% of critical speed is called the critical speed band and should be avoided.

How to raise critical speed?

Critical speed can be raised by increasing shaft diameter (raises stiffness by d⁴), using a stiffer material (higher E modulus), reducing shaft length, reducing rotor mass, or changing support conditions from simply supported to fixed-fixed.

What is the difference between rigid and flexible rotor?

A rigid rotor operates well below its first critical speed (typically below 70% of Ncr). A flexible rotor operates above its first critical speed and must pass through resonance during run-up and coast-down. Flexible rotors require more careful balancing.

What safety margin is recommended?

API 610 and API 617 recommend that the first critical speed be at least 20% above the maximum continuous operating speed (for rigid rotors) or that operating speed be at least 15–20% above the critical speed (for flexible rotors passing through resonance).

免費工程工具 — #009

轉子臨界轉速計算器

使用瑞利法計算具有集中質量或分佈質量軸的第一臨界轉速（自然頻率）。與運轉 RPM 比較以確保安全裕度。

集中質量瑞利法 3 種支撐類型

軸長 L (mm)

軸徑 d (mm)

轉子質量 m (kg)

材料（楊氏模量 E）

支撐類型

運轉速度（轉速，選填）

快速預設

結果

臨界轉速（集中質量）

—

自然頻率

—

角頻率 ω_n

—

慣性矩 I

—

軸剛性 k

—

運轉轉速裕度

—

截面二次矩

集中質量 — 簡支

對於具有集中質量的軸 m 位於跨中且兩端簡支：

支撐條件係數

剛性係數 k 隨支撐類型變化：

支撐	剛性 k	相對於簡支的係數
簡支（中心載荷）	48EI / L³	1.00
固支-固支（中心載荷）	192EI / L³	4.00
懸臂（端部載荷）	3EI / L³	0.0625

實務範例

範例 — 泵軸

已知： L = 800 mm, d = 50 mm, m = 30 kg, 鋼 E = 210 GPa, 簡支

I = π × 50⁴ / 64 = 306,796 mm⁴

k = 48 × 210,000 × 306,796 / 800³ = 6,040 N/mm

ω_n = √(6,040,000 / 30) = 448.7 rad/s

N_cr = 448.7 × 60 / (2π) = 4,285 RPM

⚠️ 注意： 此簡化模型假設軸為無質量且僅具單一集中質量。對於重型軸，若需更精確的結果，請考慮採用瑞利（Rayleigh）或登克萊（Dunkerley）方法，以納入軸的分布質量。