3.2.3 Summary
This section has developed an idealised representation for the geometry of the industrial context closure assembly. Consideration was given to the observed stiffness increase to represent the industry component on a smaller, controlled scale. An analytical representation was investigated to develop an understanding of the mechanics of the structure during torsion. The complete design was developed using a finite element model with a number of constraints; these constraints were based on the physical limitations of creating the structure and executing the experiments in the laboratory. The final structure formed a square with an outside edge length of 500 mm.
3.3
Assembly process finite element model
To study the mechanics involved in the assembly of sheet metal, specifically joining process sequencing, a finite element model was developed that incorporates sufficient complexity to represent the problem. As highlighted in Chapter 2, Section 2.4, establishing the model requires capturing a number of non-linearities; namely, geometric non-linearity and contact non-linearity. For the purposes of this work, material non-linearity was not considered because the assembly operation should not be inducing plastic effects. However, it is noted that this may occur in some practical situations.
The simulations were performed using ABAQUS/Standard static implicit solver. A multi-step approach was used, incorporating contact interactions. Both the weld tips and clamps were represented by analytical rigid surfaces. The analytical rigid surfaces were fixed in five degrees of freedom with the sixth, in the direction of operation, connected via a weak spring and damper to ground. The non-linear geometry flag, NLGEOM, was also activated.
conditions between the sheet metal component and the analytical rigid bodies. The combination of the analytical rigid surface and the surface defined from the structure’s elements provides an improved contact representation that allows a larger mesh size to be acceptable, consequently allowing for an improved computation performance. Where possible, Small-Sliding was activated to minimise computational expense and to increase simulation robustness.
The sheet metal component was modelled using a four node, stress/displacement shell element with reduced integration, S4R, and a 10 mm mesh size. This element has six degrees of freedom per node and will appropriately capture the shear effects leading to warping described in Section 3.2.1. Reduced integration was selected to avoid sheer locking that can occur with full integration elements. Given the expected deformations, it was deemed unlikely that the zero stiffness hour glass mode would occur; however, the potential still exists close to the contact interaction points. Additionally, although continuum elements would provide a greater level of robustness to the simulation due to their improved performance when handling contact interactions, the increase in the necessary degrees of freedom of the simulation would be too detrimental to processing time and as such, they were not used.
The component was located in space according to the fixture design. The fixture pin and slot were represented by restricting the appropriate degrees of freedom of the nodes at the appropriate locations. To achieve convergence of the implicit solver, the main assembly was also grounded via very weak springs and dampers. In total there were 24 welds and four clamping locations, as illustrated in Figure 3.5.
§3.3 Assembly process finite element model 55
Figure 3.5: Complete finite element model representing the structure along with analytical rigid surfaces representing the fixture clamps and weld tips (illustrated at the centre of the assembly).
The Resistive Spot Weld tip control method used in these simulations is the positional style. The lower weld tip is moved into position and then the upper weld tip is forced downward. An element, representing the spot weld nugget, is added to tie together the position and orientation of the two closest nodes at that location. The simulation steps were performed as follows:
1. Apply all clamps 2. Perform weld:
(a) Move weld tips to position
(b) Move lower weld tip to the component
(c) Squeeze the upper weld tip down with sufficient force to completely close the gap
(d) Add element representing spot weld nugget (e) Release weld tips
3. Repeat step 2 for each weld in the sequence 4. Release clamps
Thermal effects were not incorporated into this study because the focus is on the interaction between the assembly components. For the purposes of this work only a linear material response was incorporated into the simulation, not material plasticity. In practice, components should not be subject to conditions where non- linear material properties are observed, apart from those that occur local to the weld zone. However, it should be noted that the upper limit of the gap input variation specified in this work would, in practice, likely lead to stresses great enough for plastic deformation to occur during the joining operations.
The development of this model allows the study of different weld sequences, clamp sequences and a variety of different input variations to be simulated. In the next section, an experimental design is presented that will allow for validation of the presented modelling formulation.