Inertial delay-based performance model for regenerative vehicle dampers

This study presents a comprehensive mathematical model of a regenerative dual-clutch rack and pinion (DCRP) damper for automotive applications, emphasizing the impact of system delay on energy recovery. Unlike conventional hydraulic dampers, the DCRP system offers energy regeneration capabilities, which are inherently limited by inertial system delay. The model identifies a trade-off between ride comfort and regeneration, where high-frequency excitation can lead to instability and discomfort due to the sixth-order unstable nature of the system. Simulation results demonstrate that an increase in delay angle by 10° reduces the regeneration bandwidth by 3 mHz, and the critical frequency beyond which the damper behaves like a traditional hydraulic damper drops by 2.95 mHz. Additionally, with every 1 Ω rise in external resistance, the damping sensitivity decreases linearly by 16.90 N/rad/Hz. The fraction of energy recovered primarily depends on the inertial delay parameter (α), which is material-dependent, and the external load resistance (R e ), which can be tuned electronically for adaptive control. Validation against experimental energy fraction data confirms the model's reliability despite minor mechanical losses and gear backlash. This work highlights the importance of optimizing delay and resistance parameters in DCRP damper design to balance energy harvesting and vehicle stability. The findings serve as a foundation for developing advanced regenerative suspension systems, especially in electric vehicles where energy efficiency is a paramount.