Chapter 24 Estimation of Wheel Center Forces of a Car, Without Neither Load Sensor Nor Strain Gauge Measurements When Crossing a Groove on the Road Alexandre Débarbouillé, Zoran Dimitrijevic, Franck Renaud, Denis Chojnacki, Laurent Rota, and Jean-Luc Dion Abstrac t To design a vehicle suspension the knowledge of wheel loads is required. These loads are due to road unevenness and can be identified thanks the acquisition of measurements during vehicle rolling on roads or tracks. Some offline methods are used to identify them; most of these methods are based on transfer functions between points of measurements and consider the hypothesis of linear dynamic behavior of the vehicle. This hypothesis leads to misestimation of the exceptional load. We propose an approach based on a nonlinear multi-body model of the half-vehicle and an extended Kalman filter augmented and constrained for the data fusion with measurements from accelerometers, gyrometer, tachometer, and GPS. This half vehicle model lies in a 2D plane. The Kalman state vector is composed of positions and velocities of each solid, the road/track loads are unknown but estimated by the filter, and the state prediction is constrained by kinematic links between bodies . Keyword s Extended Kalman filter · Numeric twin · Nonlinear 2D model · Load estimation · Constrained method 24.1 Introduction Designing elements of vehicle suspension needs the knowledge of loads due to road unevenness. To estimate loads we can use measurements done in vehicle rolling on roads or tracks. Most methods use some transfer functions between points of measurements. However, the description of end tail distribution of the loads is misestimated with such linear approaches. We propose a method based on a twin numerical model of the car (multi-body model of car body and bodies of the ground connection) and a specific Kalman filter [1]. In this approach the nonlinear behavior of the suspension is implemented in our model and the Kalman filter; the data fusion uses measurements from accelerometers, gyrometer, tachometer, and GPS. One can find in [2] a virtual sensing approach for estimating wheel center forces. A simplified multi-body suspension system taking into account only few solids was used to estimate loads at wheel center in the three directions. They propose to improve their approach by the implementation of nonlinearities [3]. In our study a complete multi-body vehicle dynamic system is developed with fully nonlinear geometric behavior. We present here the methodology to estimate the longitudinal and vertical wheel center forces of the 2D multi-body model with a few sensors and an extended Kalman filter [4] to correct the predictions. The Kalman filter is used in several domains like the estimation of attitude. In aerospace domain [5] a Kalman filter is implemented with differential equation for the state model based on the relation between gyrometer and quaternion for the attitude representation. Some works in heavy vehicle domain use the Kalman filter to predict vehicle attitude to improve the techniques of fuel savings [6]. A new branch of study makes investigation on health monitoring [7]. In general, the attitude estimation is done by the measurement of one accelerometer and a magnetometer in the measurement model and A. Débarbouillé ( ) Équipe Vibroacoustique, Structures et Formes Mécaniques, Laboratoire Quartz - EA 7393, ISAE, Supméca, Paris, France Stellantis, Technical center of Vélizy, Vélizy, France e-mail: alexandre.debarbouille@isae-supmeca.fr Z. Dimitrijevic · D. Chojnacki · L. Rota Stellantis, Technical center of Vélizy, Vélizy, France e-mail: zoran.dimitrijevic@stellantis.com; denis.chojnacki@mpsa.com; laurent.rota@stellantis.com F. Renaud · J.-L. Dion Équipe Vibroacoustique, Structures et Formes Mécaniques, Laboratoire Quartz - EA 7393, ISAE, Supméca, Paris, France e-mail: franck.renaud@supmeca.fr; jean-luc.dion@supmeca.fr © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_24 189
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