免费工程工具 — #009
转子临界转速计算器
利用瑞利法计算具有中心质量或分布质量的轴的第一临界转速（固有频率）。并与运行转速进行比较，以获得安全裕度。
成果
面积二次矩
中心质量——简支
对于具有集中质量的轴 m 跨中和简支端：
支持条件因素
刚度系数 k 随支撑类型而变化：
| 支持 | 刚度 k | 因子与SS |
|---|---|---|
| 简支梁（中心荷载） | 48EI / L³ | 1.00 |
| 固定-固定（中央负载） | 192EI / L³ | 4.00 |
| 悬臂梁（端部受力） | 3EI / L³ | 0.0625 |
实例
已知： L = 800 mm，d = 50 mm，m = 30 kg，钢材弹性模量 E = 210 GPa，简支梁
I = π × 50⁴ / 64 = 306,796 毫米⁴
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： 这种简化的模型假设轴的质量可以忽略不计，只有一个集中质量。对于重型轴，为了获得更精确的结果，请考虑采用考虑分布质量的瑞利法或邓克利法。
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.
本页所述的操作流程由 Vibromera 团队使用 Balanset-1A（一款用于现场转子平衡的便携式双通道动平衡仪及振动分析仪）开发并经过实地测试。
专业现场动平衡仪器和软件。可测量振动、确定临界转速并现场平衡转子。产品已在全球50多个国家/地区使用。
Nikolai Shelkovenko
Nikolai Shelkovenko是一名振动分析工程师，也是Vibromera的创始人兼首席执行官。 15年多来，他一直在现场——而非在试验台上——为旋转设备进行平衡：粉碎机、工业风机、破碎机、离心机、轴和主轴。正是这些实际工作催生了Balanset系列仪器——它们被设计为一种专业人员可以随身携带到机器旁、在现场独立使用的工具，而非实验室设备。 Vibromera成立于2017年，自2023年起总部设于葡萄牙波尔图。Balanset系列产品的研发、组装与支持均在此完成。旗舰产品是Balanset-1A，一款用于单平面及双平面平衡和振动诊断的便携式分析仪。 Nikolai亲自参与客户支持工作，处理各种棘手的平衡案例，并参与软件开发。他以任何语言为全球客户提供服务。
