Spring Testing Machine Experiment: Procedure, Stiffness Calculation, and Wahl Correction Factor

Aim: To determine the stiffness (spring constant k) of a helical coil spring under compressive or tensile loading, and to calculate the modulus of rigidity (G) of the spring wire material.

Apparatus Required

• Spring Testing Machine (Straining frame with loading platform and dial gauge)
• Helical close-coiled springs (compression and extension type)
• Vernier caliper (to measure wire diameter d and mean coil diameter D)
• Known weights / calibrated loading plates
• Scale for measuring deflection (or dial gauge, 0.01 mm resolution)

Theory

For a close-coiled helical spring under axial load W, the deflection δ is: δ = 8WD³n / Gd⁴, where D = mean coil diameter, d = wire diameter, n = number of active coils, G = modulus of rigidity of wire material.

Spring stiffness: k = W/δ = Gd⁴ / 8D³n (N/mm)
Modulus of rigidity: G = 8WD³n / δd⁴ (GPa). For steel spring wire, G ≈ 80 GPa.

Stiffness of springs in series: 1/k_total = 1/k₁ + 1/k₂
Stiffness of springs in parallel: k_total = k₁ + k₂

Procedure

1. Measure wire diameter (d), mean coil diameter (D), and count active coils (n) using vernier caliper.
2. Mount the spring in the testing frame. Set the dial gauge to zero (no load).
3. Apply loads incrementally (e.g., 5 N, 10 N, 15 N, 20 N, 25 N). Record the deflection at each load.
4. Unload in the same increments. Record the deflection during unloading to check for hysteresis.
5. Plot Load (W) vs Deflection (δ), slope = spring stiffness k (N/mm).
6. Calculate G from the slope and measured spring geometry.
7. Repeat for springs in series and parallel configurations.

Frequently Asked Questions

What is the spring stiffness formula?
Spring stiffness k = W/δ = Gd⁴/8D³n, where G is the modulus of rigidity (shear modulus) of the wire material, d is wire diameter, D is mean coil diameter, and n is the number of active coils. Stiffness increases with larger wire diameter and decreases with more coils or larger coil diameter.

What is the modulus of rigidity and how is it calculated from the spring test?
Modulus of rigidity (G) is the shear modulus, the ratio of shear stress to shear strain. From the spring test: G = 8WD³n / δd⁴. For steel spring wire G ≈ 80 GPa; for copper alloy wire G ≈ 40 GPa. Calculating G from the spring test and comparing to the standard value verifies the material and test accuracy.

How do springs in series and parallel differ?
Springs in series share the same load but deflections add, total stiffness 1/k = 1/k₁ + 1/k₂ (softer combined stiffness). Springs in parallel share the same deflection but loads add, total stiffness k = k₁ + k₂ (stiffer combined). Series springs are used where more deflection is needed; parallel springs where higher load capacity with less deflection is required.