Resumen de Measurement of tyre-road contact forces through the strains measured in the rim and harmonic elimination techniques
María Dolores Gutiérrez López
Knowledge of the tyre-road contact forces is essential for improving car safety, handling characteristics and comfort. For this reason, test vehicles, used to design new systems, and prototypes of new models are frequently equipped with dynamometric wheels. However, these wheels are often found to be very expensive, there being cases where just one such wheel could cost more than the vehicle itself. Furthermore, the dynamometric wheels replace the original wheels of the vehicle, thus modifying its dynamic behaviour and therefore altering the measured values from the true desired contact forces and moments.
Moreover, if accurate real time measurements of the tyre-road contact forces could be obtained in production vehicles, the capabilities of the active safety systems of these vehicles could be markedly improved. However, since the dynamometric wheels used for R&D are too complex and expensive to be used in a production vehicle, the development of new low cost measurement devices is of high interest.
In this Thesis, a method has been developed that allows a conventional wheel that meets certain general conditions to be converted into a dynamometric wheel. Therefore, the original wheels of the vehicle can be used, reducing the cost significantly and also preventing the dynamic behaviour of the vehicle from being significantly altered. To do this, the method proposed is based on bonding strain gauges to the rim and on using harmonic elimination techniques. The strain gauges are arranged in concentric circumferences and in angularly equidistant radial lines. This configuration is suitable for most commercial wheels. The number of radial lines generally depends on the geometric shape of the rim. The strain signals measured in each circumference are linearly combined to produce new signals where the continuous component and as many harmonics as possible (except for the first or second harmonics) are eliminated from the original strain signals. By eliminating the continuous component of the strain signals, the influence of variables with axial symmetry, such as temperature, tyre pressure or centrifugal forces is cancelled. The combinations required to obtain these new signals are very simple; constant coefficients that depend only on the number of radial lines used are considered.
The influence of the wheel rotation angle in the signals that contain the first or second harmonic is eliminated afterwards in order to obtain other signals that are linearly dependent on the forces applied in the tyre-road contact area. The non-eliminated higher-order harmonics are also present in these new signals and introduce a ripple that may or may not be negligible. The amplitude of this ripple depends on the fulfilment of some symmetry conditions, on the number of strain signals available per circumference, on the radii thereof and in general, on the type of rim used. When the ripple due to the non-eliminated harmonics is not negligible, it is still possible to eliminate it completely by means of more complex linear combinations, whose coefficients depend both on the radii of the circumferences and on the geometry of the rim itself. They must be obtained therefore, by calibration.
Thanks to the harmonic elimination techniques used, the present method allows practically continuous-time measurements of the tyre-road contact forces and moments to be obtained, with no limitations other than those coming from the AD converters used and the capacity of the onboard microcontroller to process and transmit the resultant signals.
The aforesaid method is described in detail in this Thesis by means of an optimization process and through complex analysis. All the work presented is justified with the results of the FEM analysis of different types of wheels, some of which meet certain conditions of symmetry while others do not. Along with the theoretical FEM verifications, a prototype dynamometric wheel, based on a BRAID ten-spoke rim, has been built. This wheel has been calibrated according to two different possible configurations, each with a different number of circumferences and radial lines. Both the test workbench and the appropriate experimental tests needed for this calibration process are described in detail. Once the calibration is completed and the suitable parameters of the wheel are determined, a new set of tests is carried out to check the accuracy of the method. For example, with the configuration that uses the minimum number of sensors (10 sensors), the mean error in the estimation of FY, FZ and MX has been 0.72%, 1.11% and 4.05% respectively. With a configuration that uses more sensors than are strictly required (30 sensors), these errors are 0.72%, 0.83% and 3.78% respectively. Finally, the conclusions of this Thesis and the potential future work, which is particularly promising in this case, are presented.
