Velocity & acceleration-dependent damping characteristic modeling for adjustable shock absorbers based on hydraulic impedance physics

To address the failure of conventional solely velocity-dependent adjustable shock absorber damping models to express the strong “cloud-like” hysteresis, a velocity & acceleration-dependent damping model is proposed which forsake the classical “one-to-one” mapping between stiffness-displacement, damping-velocity, inertia-acceleration. The hydraulic impedance dynamics of the shock absorber is analyzed in detail and the shock absorber damping is expressed by the coupled hydraulic resistance and hydraulic reactance components. Thus a velocity & acceleration-dependent damping model (VADM) is established. By adding the acceleration as another governing state variable, the full-order hydraulic impedance model could better represent the “cloud-like” force-velocity (F-v) characteristic under random road inputs. To further describe nonlinear force saturation, a nonlinear VADM (NVADM) is developed by substituting linear damping elements with nonlinear fractional-power one. Validation results demonstrate excellent generalization capability across the entire working range, with the coefficient of determination (R2) consistently maintained between 0.89 and 0.96. Comparison in simulation and Hardware-in-the-Loop (HiL) testing confirms that the proposed model significantly minimizes the discrepancy between the simulation and the physical system. This work effectively bridges the gap between the idealized resistance and actual impedance characteristics, providing a paradigm for the high-fidelity impedance modeling of such kind of mechanical and electric systems. Fa Su, Jiaqi Zhao and colleagues develop velocity & acceleration-dependent damping models that couple hydraulic resistance and reactance in adjustable shock absorbers. The models bridge the gap between idealized resistance and actual impedance behaviour, capturing cloud-like hysteresis across currents (R2 = 0.89 − 0.96) and improving simulation and Hardware-in-the-Loop agreement.