PSI - Issue 77

Francisco Castro et al. / Procedia Structural Integrity 77 (2026) 611–630 Francisco Castro/ Structural Integrity Procedia 00 (2026) 000 – 000

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2.1. CoG height measurement in motion

2.1.1. CoG height estimation by braking maneuver A dynamic approach to estimate a vehicle’s center of gravity (CoG) height based on its response during a longitudinal braking motion is introduced. Considering that the vehicle’s CoG height changes during braking or on a nonzero road grade, i.e., occurs during load transfer to the frontal axle caused by the suspension spring deformation, by selecting a suitable longitudinal dynamics model and capturing vehicle motion through readily available sensors, it becomes possible to estimate unknown parameters, such as the CoG height, through the integration of model predictions and sensor measurements. This method relies on a simplified vehicle longitudinal dynamics model that represents the behavior of the vehicle during straight-line deceleration (Figure 1), in which Accel is the vehicle acceleration in function of time; is the vehicle’s CoG height position; and are the horizontal forces due to tire adhesion against track surface at front and rear axles, respectively; and are the normal reaction of the ground force to the front and rear wheels, respectively. is the angular displacement – pitch angle – when braking; is the longitudinal CoG position in relation to the rear axle and is the vehicle’s wheel base (it is assumed that these parameters are known and constant); and are the suspension stiffnesses of front and rear, respectively; P is the vehicle’s total weight. A few assumptions were established in order to remove complexities related to the vehicle model and its movement, • The vehicle mass ℎ and respective dynamic inertial properties are assumed as centered on the vehicle’s center of mass. Moreover, the mass considered for the vehicle is totally sprung. • The vehicle is symmetrical with the four wheels simplified into front and rear axles. • The vehicle runs in a straight line, which means lateral and roll motions won’t be consider on this analysis. • The air resistance force ( = 1 2 × × × × 2 ) was not considered. • The tire stiffness should be associated in series to the suspension spring. However, as tire stiffness is much higher than the stiffness of the suspension, the tire stiffness will be ignored in this series association. This approach and simplification were already assumed in other studies, such as in (Yue et al., 2015), that can be justified due to small changes of tire radius with the increasing of vertical force (Wang et al., 2021). • The pitch angle is sufficiently small, that it can be approximated to sin = and cos =1 . This approximation error is smaller than 1 degree for angles below 14 degrees, considering that the vehicle runs under normal driving conditions. • The road grade and bank angle were not considered. The main advantage of this approach, compared to a roll dynamics-based model estimation method, is that it only requires longitudinal maneuvers, namely acceleration or deceleration, avoiding the need for cornering tests. As such, it significantly reduces the risk of rollover during testing and offers a safer alternative for experimental implementation.