1) The document analyzes the dynamic behavior of a direct spring-operated pressure relief valve and the influence of the poppet's radial clearance on that behavior.
2) A mathematical model is developed and represented in MATLAB/Simulink. Simulation results show that smaller radial clearances lead to longer opening times and greater pressure overshoots, while larger clearances result in shorter opening times and smaller overshoots.
3) An optimal poppet radial clearance is estimated that provides a settling time of 0.02 seconds and minimizes pressure overshoot. The model can predict valve behavior and help select optimal settings.