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自然頻率計算器
計算質量-彈簧系統的自然頻率。輸入質量與彈簧剛性，即可獲得以 Hz 為單位的頻率、角頻率、週期、等效 RPM 以及靜態撓度。
結果
質量-彈簧系統的自然頻率
無阻尼單自由度質量-彈簧系統的自然頻率：
- k — 彈簧剛性 (N/m)。若給定單位為 N/mm，請乘以 1000。
- m — 質量 (kg)
角頻率
週期與靜態撓度
其中 g = 9.81 m/s² 且 k 的單位為 N/mm，撓度結果單位為 mm。
實務範例
已知： 機器質量 = 150 kg，總彈簧剛性 k = 300 N/mm
k 的單位為 N/m = 300 × 1000 = 300,000 N/m
f_n = (1/2π) × √(300,000/150) = (1/6.2832) × 44.72 = 7.12 Hz
ω_n = 2π × 7.12 = 44.7 rad/s
T = 1/7.12 = 0.140 s
等效 RPM = 7.12 × 60 = 427 RPM
δ_static = 150 × 9.81 / 300,000 × 1000 = 4.9 mm
⚠️ 注意： 確保運轉速度至少遠離自然頻率 20–30%，以避免共振。若在共振附近運轉，請增加阻尼或調整剛性/質量。
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。
專業便攜式平衡機、振動分析儀與狀態監測系統，應用於 50 多個國家。識別共振問題並進行現場轉子動平衡校正。
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。
