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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2.2.2. Static setup The static measurement method intends to estimate the real value of the vehicle’s CoG position, in order to validate the results that will be obtained through the dynamics methods developed. Static CoG method formulation To obtain the real vehicle’s CoG position in the three directions ( , , ) , which can be obtained through simple equations of static equilibrium, the following expressions were applied in order to obtain the reference position for each direction. To evaluate the CoG height position, the lifting method was applied (Yue et al., 2015). The method consists of positioning the vehicle’s axles on load cells. After, the front or rear axle are lifted to a known angle position , which corresponds to a known height. = × + = 2 × × (18) = ( _ ℎ + _ ℎ )× × (19) For the estimation the static CoG height with the front axle lifted, = × cos + ℎ × × ×cos sin (20) Where: is vehicle mass (kg); is gravitational acceleration ( / 2 ) ; is the vehicle’s track; is the vehicle’s wheelbase; _ ; _ ℎ ; _ and _ ℎ are the vehicle wheel reactions on ground; and : centre of mass position to vehicle axis. It’s important to note that, since this is a static procedure, there isn’t any influence on the results due to the spring suspension. However, the same doesn’t apply for a dynamic procedure for assessing the coordinates of a vehicle center of gravity. Static CoG experimental setup A laboratory setup (Figure 5) was developed to measure the weight of each vehicle wheel individually, using the mathematical formulation previously presented. For that, the measurements were performed using 4 load cells (5 kg load cell with amplifier board: JOY-IT SEN-HX711-05) and the signals were obtained using a National Instruments (NI) DAQ (Data Acquisition system) and corresponding software.

Figure 5 – Laboratory static setup developed. To obtain the position of the vehicle’s CoG, equation (18) and equation (19) are going to be used to estimate the x-y CoG coordinates and equation (20) is going to be used to estimate the CoG height .