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固有频率计算器
计算质量-弹簧系统的固有频率。输入质量和弹簧刚度，即可得到频率（单位：赫兹）、角频率、周期、等效转速和静态挠度。
成果
质量-弹簧系统的固有频率
无阻尼单自由度质量-弹簧系统的固有频率：
- k — 弹簧刚度（N/m）。如果单位为N/mm，则乘以1000。
- m — 质量（公斤）
角频率
周期和静态挠度
其中： g = 9.81 m/s²，k 的单位为 N/mm，挠度结果的单位为 mm。
实例
已知： 机器质量 = 150 kg，总弹簧刚度 k = 300 N/mm
k 的单位为牛顿/米 = 300 × 1000 = 300,000 牛顿/米
f_n = (1/2π) × √(300,000/150) = (1/6.2832) × 44.72 = 7.12 赫兹
ω_n = 2π × 7.12 = 44.7 弧度/秒
T = 1/7.12 = 0.140秒
等效转速 = 7.12 × 60 = 427 转/分
δ_static = 150 × 9.81 / 300,000 × 1000 = 4.9毫米
⚠️ 注意： 确保运行速度与固有频率至少相差 20–30%，以避免共振。如果接近共振频率运行，则需增加阻尼或调整刚度/质量。
Natural frequency is the frequency at which a system oscillates freely after being displaced from its equilibrium position and released. For a mass-spring system, it depends only on the mass and the spring stiffness.
Every mechanical structure has one or more natural frequencies, and they are fundamental properties used in vibration analysis, structural design, and machine diagnostics.
Knowing the natural frequency of a machine or its components is critical because if the operating speed (excitation frequency) coincides with the natural frequency, resonance occurs.
Resonance causes dramatically amplified vibrations that can lead to excessive wear, fatigue failure, bearing damage, and even catastrophic structural collapse. Engineers design machines so that operating speeds are well separated from natural frequencies.
Spring stiffness (rate) can be measured by applying a known force to the spring and measuring the resulting deflection. Stiffness k = Force / Deflection.
For example, if a 100 N force compresses a spring by 2 mm, the stiffness is 100/2 = 50 N/mm. You can also use a compression testing machine for accurate results, or consult the manufacturer's datasheet for the spring rate specification.
When the operating speed (excitation frequency) matches the natural frequency of the system, resonance occurs. At resonance, vibration amplitudes increase dramatically — theoretically to infinity in an undamped system, and to very high levels in real (lightly damped) systems.
This can cause rapid fatigue failure, excessive noise, bearing damage, and structural collapse. This is why vibration analysis always checks for proximity to resonance.
There are several strategies to avoid resonance:
- Change the operating speed so it is at least 20–30% away from any natural frequency
- Modify the stiffness by adding braces, stiffeners, or changing spring rates
- Change the mass of the vibrating component
- Add damping using vibration dampers, rubber isolators, or tuned mass dampers
- Use variable-speed drives to avoid dwelling at critical speeds during startup or shutdown
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。
专业便携式平衡机、振动分析仪和状态监测系统已在50多个国家使用。可现场识别共振问题并平衡转子。
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。
