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Applications - Tyres

It is now possible to predict handling and ride characteristics of tyres by computer simulation using LS-DYNA. These techniques can be used by tyre manufacturers to reduce the time and cost to market for new tyre products, by short-circuiting the traditional prototype-and-test development cycle.

Until recently, it was too difficult to simulate the tests as they are carried out in practice: the tyres roll on a moving surface. The challenges of tyre modelling include the complexity of the tyre structure, the large deformations in the tyre, the constantly changing contact conditions, and the sheer volume of calculations needed to track the behaviour of the tyre as it performs several revolutions over the test surface. Now, advanced features in LS-DYNA and the power of modern computers have come together to offer the possibility to simulate the tests realistically.

The models can be used to assess the effect of different layups, section shapes and bias angles on ride and handling characteristics. Forces and stresses can be calculated as the tyre rolls over an obstacle, leading to prediction and resolution of tyre durability problems and also providing an input to vehicle refinement calculations.

Model Construction

Figure 1 shows a model of a truck tyre, containing 13000 elements. The construction of the model (Figure 2) is brick elements representing the tread and sidewall, and shell elements representing the carcass. Each shell element is built up from a series of 10 to 15 layers that represent the liner, plies, ply topping, breakers, chafer, etc. Stiffness properties and bias angles are defined for each layer. The "layered shell" modelling method has the advantage of reducing the number of elements (and hence computing times); however, it does introduce the assumption of strains being distributed linearly with depth through the section.

Some researchers are creating more detailed models, in which each stiff layer (ply, breaker, etc) is modelled individually with shell elements, with the rubber layers between being represented with brick elements. It is also becoming common to model the tread pattern; with these enhancements, a tyre model can contain up to 100000 elements. Each step of added realism increases the accuracy of the results, but at the price of longer computing times to solve the models.

The road surface is modelled using rigid planes. In the examples shown, friction has been represented using a simple Coulomb factor.

Figure 1. Model of truck tyre

Figure 2. Construction of tyre model

Loads and Boundary Conditions

Loads and boundary conditions are applied in sequence:

• Start with the tyre oriented vertically (no camber or slip), with a small gap to the road surface
• Apply internal pressure and downforce, achieve a steady state
• Apply forward motion, accelerating from zero to the desired speed
• Apply slip angle, camber angle or include an obstacle in the road surface.

This process is illustrated in Figures 3 and 4 for the truck tyre mounting a 25mm step placed at 30 degrees to the rolling direction.

A further example is shown in Figure 5. A motorcycle tyre is rolled with constant slip angle, and gradually increasing camber angle.

Figure 3a. Application of Internal Pressure and Downforce

Figure 3b. Application of Internal Pressure and Downforce

Figure 4. Tyre model rolling over angled step

Figure 5. Motorcycle tyre with increasing camber angle

Sample of Results

The response of the truck tyre to an angled step was shown in Figure 4 above. Cornering studies have also been undertaken with the truck tyre model. Figure 6 shows lateral shear stress at the contact patch for a slip angle of 2 degrees. As expected from classical tyre theory, the stresses are concentrated behind the centre of the contact patch, leading to self-aligning torque.

For the motorcycle tyre, cornering force was predicted by the model for a range of slip and camber angles and compared with test results (Figure 7). Forces have been non-dimensionalised to protect confidentiality. The graphs show the cornering force versus camber angle for zero slip (yellow lines), one degree slip (blue lines) and two degrees slip (green lines). The major steering mechanism for motorcycle tyres is camber steer, and it can be seen that the overall trend in camber steer stiffness (the slope of the lines) is well predicted. It is thought that the level of correlation could be improved by increasing the level of detail in the tyre model and by better representation of friction at the road/tyre interface.

Figure 6. Lateral shear stress at the contact patch

Figure 7. Cornering force correlation

Acknowledgement

The rolling tyre simulations shown on this web page were performed on behalf of and with the assistance of Dunlop Tyres Ltd.