In shock absorbers damper-rod force not only depends on damper-rod velocity, but also on position and acceleration. Since hydraulic losses are responsible for velocity-dependent forces, other phenomena are responsible for the dependence of force on position and acceleration, they are: compliances of the chambers and of the seals, compressibility of oil and gas and inertia of oil. The presence of position and/or acceleration-dependent terms in the force causes a hysteresis loop in the force-velocity diagram and a delay between force and velocity in the force-time diagram, which affect the performance of the shock absorber. Usually test benches measure only the damper-rod force, hence, it is difficult to recognize the physical phenomena that generate the hysteresis loop. This paper deals with a research program in which a high performance motorcycle shock absorber was tested by means of a specific test bench which includes the measurement of pressures inside the cambers during harmonic tests (frequency range 1–7 Hz). The experimental results with proper mathematical models made it possible to analyze the hysteresis loops of the pressures in the various chambers and the generation of the hysteresis loop and time delay of damper-rod force. First some experimental results dealing with pressures inside compression, rebound and compensation chambers are shown. Then a simplified mathematical model is presented, it is able to capture the most relevant physical phenomena that generate the hysteresis loop of the total force. Finally a complete model of the shock absorber is described, it takes into account details of oil motion inside the valves and it is able to predict the behavior of the shock absorber for a wide range of working conditions. Some numerical results obtained with the complete model are presented and compared with experimental results.

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