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Vibration and acoustic noise can be particularly severe in the switched reluctance machine (SRM). The results of an analytical study for calculating the radial force and predicting the acoustic noise are described. Building on an airgap permeance model, analytical developments take into account the slotting effects to determine the flux density harmonics and then the pressure components using a Maxwell formula. Mechanical aspects are also developed with natural frequencies determined using extended Jordan laws. A series of step-by-step experimentations allow validation of the analytical theory. Theoretical inductance, flux in the airgap, vibration and noise spectra are successively compared to experimental ones. A new noise cancellation technique is then presented, based on current harmonic injection in auxiliary windings. The new reduction technique concerns an SRM with two short pitch windings, such as the structure of brushless doubly fed reluctance machine. Using this new method, experimental results show that the vibration and acoustic noise produced by the SRM can be reduced dramatically. It allows the reduction of any mode 2 component of the acoustic spectrum without significant consequences on the other ones and without affecting the performance of the drive. An experimental example of marked reduction is given.