Compression Spring Calculator & Designer

The calculation follows the close-coiled spring methods of Shigley, chapter 10, with separate static, fatigue, stability and dynamic screens.

With mean diameter $D$, wire diameter $d$ and active turns $N_a$, torsional compliance gives $k=Gd^4/(8D^3N_a)$ and $\delta=F/k$. Both end options have $N_t=N_a+2$; estimated solid height is $N_t d$ for ground ends and $(N_t+1)d$ without grinding. These are conventional geometric estimates, not guaranteed manufacturing limits.

Peak shear uses $C=D/d$, $K_W=(4C-1)/(4C-4)+0.615/C$ and $\tau=K_W8FD/(\pi d^3)$. Curvature and direct shear are already included; no second correction is applied. See Chiu et al., attached pp.4–6, Eqs.(10), (24) and (26).

The proportional-load Goodman factor is $n_f=[\tau_a/S_{se}+\tau_m/S_{su}]^{-1}$, with $\tau_a=(\tau_{\max}-\tau_{\min})/2$ and $\tau_m=(\tau_{\max}+\tau_{\min})/2$. The static factor is $n_y=S_{sy}/\tau_{\max}$. $S_{se}$ must be the zero-mean, fully reversed shear intercept after relevant corrections. The Goodman boundary at required factor is $\tau_a=S_{se}(1/n_{\rm req}-\tau_m/S_{su})$.

For buckling, $\lambda=\alpha L_0/D$, $C_1=E/[2(E-G)]$ and $C_2=2\pi^2(E-G)/(2G+E)$. When $C_2/\lambda^2<1$, $\delta_b=L_0C_1[1-\sqrt{1-C_2/\lambda^2}]$. Otherwise the model predicts no buckling; the unavailable critical deflection is intentionally blank. Ideal restraint factors are 0.5, $\sqrt{0.5}$, 1 and 2. Chiu et al., attached pp.4–5, Eq.(13), reproduces this Shigley model. Its printed Eq.(14) has a reversed inequality: the prose specifies $C_2/\lambda^2>1$ for absolute stability, consistent with Eq.(15); that is the criterion implemented here.

For surge, the active-wire mass is $m_a=\rho\pi^2d^2DN_a/4$. The uniform distributed-spring wave equation gives $f_1=\frac12\sqrt{k/m_a}$ between fixed/driven plates and $\frac14\sqrt{k/m_a}$ with one end free. Here $k$ is in N/m. This wave-equation reduction is derived here, consistent with Shigley’s longitudinal-mode treatment; it differs from the lumped spring–mass frequency $1/(2\pi)\sqrt{k/M}$. The screen uses $f_1/f_{\rm drive}\ge20$.

Reference checks retain published rounding. IGNOU’s uncorrected stress is compared only with the nominal-torsion step. Jönköping’s Bergsträsser stress is not substituted for Wahl stress.

Centered compressive force; cylindrical, constant-pitch active body; circular wire; small helix angle; homogeneous isotropic linear elasticity with $0\le\nu<0.499$. Closed ends contribute two inactive turns. No beneficial presetting or residual-stress credit is applied. Strength inputs are user-supplied design data; defaults are an illustrative spring-steel-like scenario, not a material certificate. Use shear properties, not tensile values.

Fatigue assumes repeated loading between the two specified forces, an endurance-limit model and proportional scaling of both loads for the reported factor. It does not calculate cycle life or failure probability. The animation is quasistatic and slowed down independently of the entered operating frequency. Its uniform active-wire color represents the local peak shear at each ideal active section, not stress over the wire cross-section. The wire stroke is exaggerated for legibility; coil centerline geometry follows the selected dimensions.

Use for preliminary sizing of ordinary round-wire compression springs with closed ends. A spring index of 4–12 and helix angle at or below 12° are practical screening recommendations, not hard manufacturing boundaries. Working compression must remain below estimated solid travel. Solid-load and solid-stress results are elastic extrapolations to first full contact, not post-contact predictions; discard the extrapolation beyond yield.

Buckling assumes ideal unguided end restraints, not a guide rod or bore. Initial crookedness, misalignment and friction can cause earlier lateral motion. No post-buckling result is provided. Surge excludes supported masses, damping, contact, end-seat flexibility and variable pitch; the 20:1 screen is not a complete resonance assessment. Static loading can be assessed through the yield result; a nonzero steady mean stress still gives a formal Goodman intercept factor even with zero amplitude.

Supply endurance data corrected for the actual wire size, surface treatment, reliability, temperature and environment. A fatigue factor above the requested value does not certify service life. The tool does not apply EN 13906 fatigue tables, manufacturing tolerances, set-removal rules, thermal relaxation or corrosion allowances.