How is the spring rate calculated?

The spring rate k for a helical compression spring is k = Gd⁴/(8D³n), where G is the shear modulus, d is wire diameter, D is mean coil diameter, and n is the number of active coils. This formula assumes round wire and negligible pitch angle.

What is the Wahl correction factor?

The Wahl factor Kw accounts for curvature and direct shear effects in helical springs. Kw = (4C-1)/(4C-4) + 0.615/C, where C = D/d is the spring index. It increases the calculated shear stress, especially for small spring indices (tight coils).

What spring index C should I target?

A spring index C = D/d between 4 and 12 is typical. C 12 can lead to tangling and buckling. C = 6–10 is optimal for most applications.

What is solid height and why does it matter?

Solid height is the length of the spring when fully compressed so all coils touch. It equals (total coils) × wire diameter. The spring must never be compressed to solid height in service, or permanent set (plastic deformation) will occur.

Which shear modulus G should I use?

Common values: Music wire (ASTM A228) G ≈ 79.3 GPa, Stainless 302 G ≈ 69 GPa, Chrome-vanadium G ≈ 77.2 GPa, Phosphor bronze G ≈ 41.4 GPa. G varies slightly with temperature and wire diameter.

免費工程工具 #064

螺旋壓縮彈簧設計計算器

設計螺旋壓縮彈簧。輸入線徑、彈簧中徑、自由長度、有效圈數與剪力模數，以計算彈簧常數、最大負荷、剪應力與壓實高度。

彈簧常數 k 沃爾因子自動計算

線徑 d (mm)

彈簧中徑 D (mm)

自由長度 L₀ (mm)

有效圈數 n

材質 (剪力模數 G)

端部型式

快速預設

結果

彈簧常數 k

—

壓實時最大負荷 (F_solid)

—

最大剪應力 τ (含 Kw)

—

壓實高度

—

彈簧指數 C

—

沃爾因子 K_w

—

彈簧剖面

彈簧常數

經沃爾修正之剪應力

沃爾因子

其中 C = D/d 為彈簧指數。

壓實高度

材料	G (GPa)	典型用途
琴鋼線 (A228)	79.3	通用型，高疲勞壽命
鉻釩鋼	77.2	高應力，衝擊負荷
302 不鏽鋼	69.0	耐腐蝕性
磷青銅	41.4	電氣應用，無磁性
鈹銅	44.8	無火花，導電

範例 — 琴鋼線彈簧

已知： d = 4 mm, D = 30 mm, L₀ = 80 mm, n = 10, G = 79300 MPa

C = 30/4 = 7.5

k = 79300 × 4⁴ / (8 × 30³ × 10) = 79300 × 256 / 2,160,000 = 9.39 N/mm

壓實高度 = (10+2) × 4 = 48 mm → 行程 = 80 − 48 = 32 mm

F_solid = 9.39 × 32 = 300.5 N

⚠️ 注意： 在運行中切勿將彈簧壓縮至壓實高度。設計工作行程應 ≤ 可用撓度的 80%。若自由長度/平均直徑 > 4，請檢查是否會發生挫曲。