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Strength analysis of pneumatic clamps - linear buckling analysis

Strength analysis of pneumatic clamps - linear buckling analysis

Request: Customer needs to validate that the pneumatic clamps are well designed and there is no plastic deformation at working surfaces.

Solution:

  • Obtain a 3D CAD model
  • Simplify model to save time and costs
  • Load validation
  • Proposed new design

The pneumatic clamps have to be analyzed in three separate studies.

The first study is a linear static analysis. Aim of the linear static analysis is to identify stresses which should not exceed allowable values of each component. It is the yield strength of a material in this case.
The second study is a linear buckling analysis. This analysis validates that clamps are rigid enough, that buckling does not occur under the maximal force exerted by a pneumatic cylinder.
The third study is a non-linear static analysis. As clamps are designed to plastically deform metal pin, analysis is performed to verify, that no plastic deformation occurs on clamps working surfaces.

This post describes the procedure of the second study – linear buckling analysis.

The clamps CAD model is shown in Figure 1 and supplied by a customer. The peripherals are removed as they have no impact on results. The pneumatic cylinder is also removed and it is replaced by the force acting to the clamp arms. As the model is symmetric it is convenient to only consider half of the model to save costs and time. Figure 2 shows the half-symmetry model suitable for analysis.

Fig. 1 – Customer CAD model

Fig. 2 – Half-symmetry CAD model
The Finite Element Method is suitable to analyse complex shapes of prototypes and products. The regular mesh of elements is created by meshing the half-symmetry CAD model. The linear Tetra elements (4 nodes) should not be used as they are too stiff. Complicated model shapes are usually easier meshed by tetra elements than by hex elements. Quadratic Tetra elements with 10 nodes and quadratic Hexa elements with 20 nodes are used in this case.

Fig. 3 – Meshed half-symmetry CAD model

Fig. 4 – Mesh element type, HEX8, HEX20, TETRA4, TETRA10

Boundary conditions are shown in Figure 5: Lower flange of basement profile is fixed in all 6 degrees of freedom (C). The symmetry plane is constrained by frictionless support (A). The clamp working face is also constrained by frictionless support (B). The maximum force (produced by the operating pressure of the pneumatic valve) acts to the lower part of the arm shown in Figure 6. The surfaces between components are in No Separation contact.

Fig. 5 – Boundary conditions application – constraints
Fig. 6 – Boundary conditions application – force
The material properties are defined and assigned to the parts. The first study shows that no plastic deformation occurs on the components. However, it is necessary to evaluate if the buckling behaviour does not occur when force is exerted. The buckling eigenvalue result represents the load multiplier. If load multiplier is smaller than 1, it means that linear buckling occurs before the maximal load is exerted. Therefore the eigenvalue has to be greater than 1 to be on the safe side of design. Figure 7 shows the buckling mode with the eigenvalue greater than 15. It means that the acting force from pneumatic cylinder has to the 15 times greater to buckling behaviour occur.
Fig. 7 – Linear buckling eigenvalue multiplier

Conclusion: Analysis has shown that buckling behaviour does not occur. The buckling occurs at load which have to 15 times greater than actual load. The first study deals with the plasticity of components. It is clear that plasticity would occur much earlier than buckling behaviour. Therefore the buckling behaviour is not managing.

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