Cylindrical Coil Spring

This test lets you check the rigidity of a cylindrical coil spring clamped at an extremity and submitted to a longitudinal force. You will use 1D and 3D models.

Reference:

Analytical solution

Specifications

Geometry Specifications

Spring height: h = 40 mm

Coiling diameter: D = 40 mm

Wire diameter: d = 0.9 mm

Number of turns: i = 8

Analysis Specifications

Young Modulus (material):
E = 70 GPa

Poisson's Ratio (material):
ν = 0.346

Mesh Specifications:

  • 1D mesh: beam element of 1 mm

  • 3D mesh: Linear hexahedron elements (HE8): sweep 3D from linear quadrangle elements (QD4) of 0.1 mm.

Restraints:
Clamp on B

Loads:
Distributed force in compression at point A Fz = -10 mN
 

Results

Analytical solution

For an acute angle of inclination of turns ( < 8° ) the spring stiffness is:

Where:
G: shear modulus

For = 7.13°

Computed results

You may get the same stiffness as previously using the formula:

: spring displacement

The table below presents the analysis results:

Models

Maximum displacement on z [mm]

Experimental k [N/m]

Normalized results

1D

2.399

4.168404

1.001058

3D

2.52412

3.961777

0.951435

To Perform the Test:

The spring_1d.CATAnalysis document presents a complete analysis of this case.

The spring_3d.CATAnalysis document presents a complete analysis of this case.

To compute the case, proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the case in the Generative Structural Analysis workbench.

  3. Create a global sensor (Maximum displacement) and a local sensor (Displacement vector).