###### Abstract  
Considering the importance of increasing driving safety, the study of safety is a popular and critical topic of research in the vehicle industry. Vehicle roll behavior with sudden steering input is a main source of untripped rollover. However, previous research has seldom considered road excitation and its coupled effect on vehicle lateral response when focusing on lateral and vertical dynamics. To address this issue, a novel method was used to evaluate effects of varying road level and steering wheel input on vehicle roll behavior. Then, a 9 degree of freedom (9-DOF) full-car roll nonlinear model including vertical and lateral dynamics was developed to study vehicle roll dynamics with or without of road excitation. Based on a 6-DOF half-car roll model and 9-DOF full-car nonlinear model, relationship between three-dimensional (3-D) road excitation and various steering wheel inputs on vehicle roll performance was studied. Finally, an \(E\)-Class (SUV) level car model in CARSIM(r) was used, as a benchmark, with and without road input conditions. Both half-car and full-car models were analyzed under steering wheel inputs of 5\({}^{\circ}\), 10\({}^{\circ}\) and 15\({}^{\circ}\). Simulation results showed that the half-car model considering road input was found to have a maximum accuracy of 65%. Whereas, the full-car model had a minimum accuracy of 85%, which was significantly higher compared to the half-car model under the same scenario. dynamics modeling; 3-D road excitation; vehicle roll; CARSIM(r) simulation 2017 7 570 [; ;  
4-DOF half-car suspension model to obtain vehicle roll angle and roll rate while driving. In addition, a rollover index was used to indicate rollover danger, which was computed using measured lateral acceleration and yaw rate estimated roll angle and roll rate. [PERSON] et al. (2014, 2015) proposed a sensor fusion algorithm based on a 3-DOF vehicle roll model to estimate roll angle and center of gravity (C.G.) height. Experimental data was used to confirm performance reliability of developed algorithms in different maneuvers such as constant steering, ramp steering, double lane change and sine with dwell steering tests. [PERSON] et al. (2016) proposed an anti-rollover control algorithm based on a 3-DOF vehicle roll model to calculate Time-To-Rollover (TTR) in real-time. [PERSON] et al. (2017) developed a new predictive lateral load transfer ratio (PLTR) based a 4-DOF vehicle roll model, which utilized the driver's steering input and several other sensor signals available from the vehicle's electronic stability control system. This new PLTR index provided a time-advanced measurement of rollover propensity, thereby, offering significant benefits for closed-loop rollover prevention. [PERSON] et al. (2018) proposed an approach based on a 5-DOF vehicle roll model to estimate vertical forces affecting a vehicle using high-order sliding-mode (HOSM) observes. Employing previously estimated vertical forces; lateral rollover indicating rollover status was determined. [PERSON] et al. (2019) proposed possibility of using slow active suspension control to reduce body roll and thus reducing rollover propensity. From the previous work reported in literature, it can be showed that an accurate model is required to approximate actual behavior. From the discussion above, it can be seen that a majority of the vehicle roll dynamics models were established without considering road excitation and its coupling effects between vertical and lateral dynamics, i.e., no road input. This is in fact an important factor, as real roads are complex and in practice vehicle movements should be considered as variants. To solve the above-mentioned problems, following two contributions are taken into account in this paper:  
* Influence of three-dimensional (3-D) road profile excitation on vehicle lateral and vertical coupling model is studied using half-car and full-car roll models.