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In a dipole or in a quadrupole accelerator magnet, the displacement of the coil turns induced by the electromagnetic forces can cause quenches limiting the magnet performance. For this reason, an azimuthal preload is applied to avoid azimuthal movements of the coil up to the required operational current. However, several tests showed that accelerator magnets can operate with a partial preload, i.e. that coil unloading during the ramp does not prevent reaching higher currents. This issue is particularly relevant for Nb3Sn magnets, where the loads applied to the Nb3Sn filaments can reach the degradation limits of critical current. In order to investigate the impact of coil preload on the quench performance, the MQXFS6 short model quadrupole for the High Luminosity Upgrade was tested under an azimuthal preload at 80% of the short sample current, reaching 93% of short sample current at 1.9 K. The preload was then released to 60%, still showing ability to operate in the range of 80-85% of short sample current as required by HL-LHC project. With this lower preload, the ability of going above 90% of short sample was lost, and a significant training appeared above 85%. When the preload was restored to the original 80% value, the magnet reached with few quenches 95% of short sample (13.4 T peak field). Magnetic measurements confirm the larger movement of the coil in the case with lower preload, and agree with finite element simulations.