PSI - Issue 77

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

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Francisco Castro/ Structural Integrity Procedia 00 (2026) 000 – 000 = × , = × × Finally, substituting the previous equations into equation (3) , the following equation is obtained, ℎ × × = [ ×( − ) 2 + × 2 ]× Thus, the expression that allows to estimate the CoG height position is presented, = [ ×( − ) 2 + × 2 ]× ℎ × 2.1.2. CoG height estimation by cornering maneuver A dynamic method for estimating the vehicle’s center of gravity (CoG) height at real -time based on a roll dynamics model during cornering maneuvers (Figure 2) is presented. According to the D'Alembert principle, every accelerated movement can be equivalent to a D'Alembert inertia force or moment. Therefore, a dynamic problem can be transformed into a pseudo-static one. The centripetal force ( = ℎ × ) is applied in the vehicle’s CoG, which causes the roll dynamics of the vehicle. 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 effect of side wind wasn’t considered. • The vehicle is symmetrical with the four wheels simplified into front and rear axles. Additionally, the front and rear wheels on the same side of the vehicle are subjected to the same force when cornering. • 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. • The roll angle of the unsprung mass isn’t considered, and the roll 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. Once this method may lead to rollovers, to apply this method without compromising safety, cornering maneuvers at moderate speeds are required in order to induce sufficient roll response. Comparing it to the longitudinal method presented in the previous chapter, the roll dynamics model permits direct exploitation of the physical relationship between lateral forces and roll moment, providing a complementary perspective for CoG estimation under real driving conditions. Moreover, once the CoG position remains constant for long periods, it is feasible to wait for an appropriate maneuver to perform the estimation. (9) (10) (11)