Building the finite element model

In order to integrate this elastic foot in the rigid bodies‟ dynamic numerical model with its elastic properties, an elastic model of the foot must be built and introduced into the model. For this purpose the FEM program ANSYS was selected. This program is also compatible with the multibody simulation program SIMPACK already used in building the rigid bodies dynamic gait model.

The C-Walk foot consists of two elastic elements: the C-spring and the base spring. All other elements are much stiffer and can be considered as rigid bodies.

In order to build a FE model of the C-spring with properties consistent with the real foot, the deformation of the spring is measured experimentally. In the experimental measurements the spring is loaded with vertical loads since the vertical loads are the largest and most dominant in the human gait. The deformation shows a linear relation with the applied vertical force. This curve is used in selecting a modulus of elasticity for the FE model of the spring that will lead to a deformation matching the real case. According to these experimental results the modulus of elasticity (Young‟s modulus) of the equivalent spring is found to be 57 GPa. The C-spring deflection is studied without the titan ring, which in reality influences the deformation of the C-spring since this ring is to be modelled in the multibody model later. The FE model of the spring is constructed with two c-shaped shell elements to match the real shape as much as possible. The load deflection relations for both the measured and the numerically calculated values are plotted in Figure 5.12.

The FE model of the spring is shown in Figure 5.13. The holes represent the position of the bolts in the spring. The loading points are at the top and bottom of it. At the top is the pylon mounting point and at the bottom is the base spring mounting point.

Since this elastic model of the C-spring is to be used in the multibody model, it will be very difficult and time consuming to integrate it using all its finite but very large number of elements.

A limited number of nodes are to be selected that are the most important and have the most influence on the deformations of the whole system, and the rest of the model should be reduced through the condensation process already explained in the theoretical background. Accordingly, the most important nodes are the mounting nodes, which make contact with the other elements in the system. Two points are selected: one at the top in the centre of the upper hole and the second at the bottom in the middle of the spring‟s lower surface (at the global coordinate reference system lines in Figure 5.13). These points are called the master degrees of freedom.

Also here it is considered that the deflection of one point can be misleading when all the forces are applied at just one point instead to be distributed all over the mounting area also when this point is at the centre of the force application area. This problem is solved through defining the force application points – which are master degree of freedom points - as a pilot point connected to many neighbouring elements in the FE model. This distributes the acting forces on the whole area and the deflection of these pilot points is combined with the deflection of all neighbouring elements connected to them with the same amount. Now that the FE model of the C-spring is completed and it can be further condensed and reduced into a single element that contains the dynamic characteristic of the original system and can be integrated after that in the dynamic multibody model.

Figure 5.12: The deflection of the C-spring for the real and the numerical model

0 200 400 600 800 1000 1200 1400 1600 1800

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

applied force [N]

deflection [m]

measured numerical

Figure 5.13: The C-spring

As in the case of the C-spring also the foot base spring is to be modelled in FEM with properties consistent with that of the real base spring. The deformation of the spring is measured experimentally. The spring is loaded with vertical loads since the vertical loads are the largest and most dominant in the foot of the human during normal gait. The deformation shows a linear relation with the applied vertical force. This curve is used in selecting a modulus of elasticity for the FE model of the base spring that will lead to a deformation matching the real case.

According to these experimental results the modulus of elasticity (Young‟s modulus) of the equivalent spring is found to be 28.5 GPa. The deformation was measured at a point located 128 mm from the mounting edge. The FE model of the spring is built of one shell element but the form of this element was not built like the real one but rather in a symmetric form as it is shown in Figure 5.15. The load deflection relations for both the measured and the numerically calculated values are plotted in Figure 5.14. Both are measured at a distance 128 mm from the edge and at the middle line of the foot.

Like in the C-spring this elastic model is to be used in the multibody model and should be reduced. Since the base spring is the part that makes contact with the ground a larger number of master degrees of freedom should be selected to make the contact with ground smooth and closer to reality. Accordingly, eight nodes are selected (some are shown in Figure 5.15), one node is selected as a mounting point for the system with the rest of the multibody model. This point is at the middle of the edge and also defined as a pilot point with contact to many neighbouring points. The other seven points are selected along the axis of the foot also in the middle of the sole. To reduce the effect of local deformation of just one point on the results (since in real system the contact is done at all the surface and not just specific points), the master degrees of freedom are also modelled as pilot points and connected to many neighbouring nodes.

Now, the base spring can be condensed and reduced to a single element that still contains the dynamic characteristic required for the dynamic analysis.

Figure 5.14: The deflection of the base spring for the real and the numerical model

Figure 5.15: The base spring

The spring models built in FEM are three dimensional, and the MBS model is two dimensional.

The possible problem of extra torques that may appear when the GRFs act on the whole foot is solved through selecting the contact points with the ground along the middle of the foot such that the torques developed due to these forces are working perpendicularly to the working surface.