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等效彈簧剛性計算器
計算串聯或並聯彈簧的等效剛性。輸入最多 5 個個別彈簧剛度，並可選計算自然頻率。
結果
並聯連接
彈簧共享相同撓度；受力相加：
串聯連接
彈簧共享相同受力；撓度相加：
相同彈簧簡化
用於 n 剛性相同的彈簧 k:
自然頻率
在彈簧系統上安裝已知質量時：
其中 keq 單位為 N/m（將 N/mm 乘以 1000），且 m 單位為 kg。
實務範例
已知： 質量 m = 200 kg，4 個相同彈簧並聯，每個 k = 45 N/mm。
keq = 4 × 45 = 180 N/mm = 180,000 N/m
ωn = √(180,000 / 200) = √900 = 30 rad/s
fn = 30 / (2π) = 4.77 Hz
💡 提示： 並聯彈簧會增加剛性（系統更硬，自然頻率更高）。串聯彈簧會降低剛性（系統更軟，自然頻率更低）。
Use parallel springs when you need to increase the overall stiffness — for example, mounting multiple springs side by side under a machine. The equivalent stiffness is the sum of all individual stiffnesses.
Use series springs when you need to decrease the overall stiffness or increase flexibility — for example, stacking springs end-to-end. The equivalent stiffness is always less than the weakest individual spring.
In a parallel arrangement, all springs share the same deflection but each carries a portion of the load. The total force is the sum of the forces in each spring, so the effective stiffness is keq = k₁ + k₂ + … + kₙ.
For n identical springs of stiffness k, the equivalent stiffness is simply n × k.
Series spring configurations appear in many engineering systems:
- Multi-stage shock absorbers with stacked springs
- Automotive valve springs in some configurations
- Rubber isolation pads stacked vertically
- Multi-layer leaf spring systems
- Drill string assemblies
Yes. Natural frequency depends on both mass and stiffness: f = (1/2π)√(k/m). Adding springs in parallel increases keq, raising the natural frequency. Adding springs in series decreases keq, lowering it.
Doubling identical parallel springs doubles keq and increases frequency by √2 ≈ 1.41.
Spring stiffness can be measured several ways:
- Static test: Apply a known force and measure deflection. k = F/δ.
- Compression testing machine: Record the full force-deflection curve.
- Dynamic test: Mount a known mass, measure free vibration frequency. k = m × (2πf)².
- Manufacturer datasheet: Most commercial springs have a rated spring rate.
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。優化彈簧選型並現場驗證隔振性能。已應用於 50 多個國家。
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。
