Shear Stress on Compression Spring

It is very important to always validate your FEA results with analytical calculation. 


Finite Element Analysis

Some modifications need to be done, before the cylindrical helical spring was simulated. Since the coils will be in contact with each other when subjected to the loads, a solution need to be thought, so that the contact between these coils can be defined. In order to do this, the cross-section of the spring is divided into two. The spring wire also needs to be cut into two, so that it will be possible to select the surface and specify the contact pairs.

The contacts between the coil surfaces were designated to be frictionless and Augmented Lagrange was used to formulate the contact behavior. For these frictionless contacts, the interface treatment was set to adjust to touch. This setting is beneficial to ensure the initial contact takes place even when there is gap between the corresponding contacts (as long as the gap is within the defined pinball region). The normal stiffness factor FKN=1 was selected because the contact is not the focus of this study and by using smaller value it will help convergence behavior. As the contact stress at contact interface between the plate surface and the spring end surface is not important, the linear bonded contact type was used.


The advantage of cutting the spring coil into two is, some of the spring coils can be swept with the brick elements. As the large deflection is expected in this analysis, the large deformation option in the solver control setting was activated. By using the step control setting, the load was distributed into 10 load steps. The reason for this, as the solving of an analysis with nonlinearity will require a convergence of iterative solution routine, a maximum of 100 substeps were defined. This convergence of the solution procedure will ensure the load to be gradually applied using the intermediate load values at intermediate solution points also known as substep.

Analytical Calculation


The calculated maximum shear stress using analytical method with consideration of the curvature effect on the inner region of the wire is 275 MPa and the maximum shear stress extracted from FEA is 303 MPa. The difference of results between the two methods  is below 10%. This is considered O.K.

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