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依目標頻率選定彈簧
計算指定質量與目標自然頻率所需的彈簧剛性。透過確定所需的彈簧係數來設計振動隔離系統。
結果
所需彈簧剛性
給定質量與期望的自然頻率，所需的彈簧剛性可由解出 k 的自然頻率方程式得出：
- m — 支撐機組的質量 (kg)
- f — 目標自然頻率 (Hz)
- k — 所需總彈簧剛性 (N/m)；除以 1000 可換算為 N/mm
RPM 轉 Hz 換算
靜態撓度 & 每根彈簧剛性
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： 機組質量 = 300 kg，目標頻率 = 4 Hz，4 根彈簧
ω = 2π × 4 = 25.13 rad/s
k = 300 × (25.13)² = 300 × 631.7 = 189,510 N/m = 189.5 N/mm
δ_static = 300 × 9.81 / 189,510 × 1000 = 15.5 mm
每根彈簧 k = 189.5 / 4 = 47.4 N/mm
等效 RPM = 4 × 60 = 240 RPM
ℹ️ 設計原則： 為有效隔離振動，自然頻率應不超過最低運轉頻率的 1/3。這可確保至少 87.5% 的隔離效果。
To select springs for vibration isolation, first determine the mass of the machine and the desired natural frequency of the isolation system. The natural frequency should be well below the operating frequency — typically less than 1/3 of the lowest excitation frequency.
Use the formula k = m × (2πf)² to calculate the required total spring stiffness, then divide by the number of springs to get the stiffness per spring. Verify that the static deflection is acceptable and that the springs can support the load.
For effective vibration isolation, the natural frequency should be at most 1/3 of the lowest operating frequency. For example, if a machine runs at 1500 RPM (25 Hz), the isolation system should have a natural frequency below about 8 Hz.
Lower natural frequencies provide better isolation but require softer springs and larger static deflections. Typical isolation systems target 2–8 Hz depending on the application.
The transmissibility of a vibration isolation system depends on the ratio of operating frequency to natural frequency. Isolation only begins when this ratio exceeds √2 ≈ 1.41.
At a ratio of 3 (natural frequency = 1/3 of operating), transmissibility drops to about 12.5%, meaning 87.5% of vibration is isolated. Below √2, the system actually amplifies vibrations, with the worst case at resonance (ratio = 1).
The number of springs depends on the machine size, weight distribution, and mounting configuration:
- 4 springs — most common, one at each corner for rectangular machines
- 3 springs — triangular layouts
- 6+ springs — large machines requiring distributed support
The total required stiffness is divided equally among all springs. Ensure all springs have equal stiffness to prevent tilting.
Static deflection is the amount a spring compresses under the weight of the supported mass due to gravity (δ = mg/k). It matters because:
- It determines how much the machine sinks on the springs
- It is directly related to natural frequency — larger deflection = lower frequency = better isolation
- The spring must have enough travel for static deflection plus dynamic motion
- Excessive deflection can cause stability issues
Typical isolation springs have 5–25 mm of static deflection.
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，已應用於 50 多個國家。設計最佳隔離系統並現場驗證效能。
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。
