Cold Judder in Tractor Drivelines: An Essential Model for Stability Analysis

Current scientific literature classifies the well-known clutch judder phenomenon in friction judder and pressure-induced judder, based on the mechanisms that generate it. Friction judder is associated to a negative gradient of the friction coefficient and to stick-slip phenomena, while pressure-induced judder is mainly caused by geometric disturbances. The peculiarities of the torsional oscillations experimentally observed in dual-clutch transmissions of tractors, incompatible with the explanations found in the current literature, led to consider parametric excitation as a possible cause of instability. Consequently, the clutch was modelled by means of a system of three coupled linear differential equations with time-periodic coefficients. Stability analysis, performed by adopting Floquet theory, allowed to draw stability maps as functions of the two excitation parameters, i.e. the frequency and the amplitude of the dither signal in the clutch actuation pressure. Stability maps proved to be particularly promising to explain the experimentally observed phenomenon. In addition, it was possible to show that clutch judder can also arise for positive gradients of the friction coefficient.