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。
結果
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
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。
Critical speed is the rotational speed at which a shaft's rotational frequency matches one of its natural bending frequencies, causing resonance. At critical speed, even tiny unbalance forces are amplified dramatically, leading to dangerous vibration levels.
Every rotating shaft has one or more critical speeds. The first (lowest) critical speed is the most important for design purposes.
Operating near critical speed causes:
- Exponential amplification of vibration from unbalance
- Excessive bearing loads and premature failure
- Shaft deflection beyond elastic limits
- Seal damage and oil leakage
- Risk of catastrophic shaft failure
The industry standard is to maintain at least a 20% margin between operating speed and any critical speed.
Critical speed can be increased by:
- Increasing shaft diameter — stiffness scales with d⁴, very effective
- Reducing shaft length — stiffness scales with 1/L³
- Using stiffer material — higher E modulus
- Reducing rotor mass — lighter rotor = higher frequency
- Changing supports — fixed-fixed is 4× stiffer than simply supported
A rigid rotor operates well below its first critical speed (N_op < 0.7 × N_cr). It can be balanced at low speed in a balancing machine.
A flexible rotor operates above its first critical speed and must pass through resonance during startup. It requires high-speed balancing and may need modal balancing at multiple speeds.
Common standards recommend:
- API 610/617: First critical speed ≥ 120% of max continuous speed (rigid rotors)
- API 612: Operating speed ≥ 115% above first critical (flexible rotors)
- General practice: Stay at least 20–30% away from any critical speed
The ±20% band around a critical speed is considered the danger zone and should be avoided during continuous operation.
本頁所述的操作流程由 Vibromera 團隊使用 Balanset-1A（一款用於現場轉子平衡的便攜式雙通道動平衡儀及振動分析儀）開發並經過實地測試。
專業現場動平衡儀器與軟體。測量振動、找出臨界轉速，並在現場對轉子進行動平衡。已在 50 多個國家使用。
Nikolai Shelkovenko
Nikolai Shelkovenko是一名振動分析工程師，也是Vibromera的創辦人兼執行長。 15年多來，他一直在現場——而非在試驗台上——為旋轉設備進行動平衡校正：粉碎機、工業風機、破碎機、離心機、軸與主軸。正是這些實際工作催生了Balanset系列儀器——它們被設計為一種專業人員可以隨身攜帶到機器旁、在現場獨立使用的工具，而非實驗室設備。 Vibromera成立於2017年，自2023年起總部設於葡萄牙波爾圖。Balanset系列產品的研發、組裝與支援均在此完成。旗艦產品是Balanset-1A，一款用於單平面及雙平面動平衡校正與振動診斷的可攜式分析儀。 Nikolai親自參與客戶支援工作，處理各種棘手的動平衡校正案例，並參與軟體開發。他以任何語言為全球客戶提供服務。
