• Optimal desulfurization of low-rank high-sulfur lignite achieved at vibration intensity C=5.80, inlet airflow velocity 2.55 m/s, amplitude 2.4–2.5 mm, and frequency 23–24 Hz.
• Particle collision behavior transitions from disordered to directional to cataclastic with increasing vibration intensity and airflow, influencing separation efficiency.
• The compound dry cascade separation bed establishes three functional axes: OX for transverse diffusion, OY for longitudinal transport, and OZ for vertical density stratification.
• Under optimal conditions, clean coal yield reaches 72.02% with sulfur content reduced to 0.98%, demonstrating effective desulfurization and ash reduction.