A method for relieving residual stresses in a part includes increasing the rotation speed, which includes measuring, at a first given instant, values representative of the rotation speed and the radial enlargement; measuring, at a second given instant after the first instant, values representative of the rotation speed and the radial enlargement; determining a leading coefficient of a first affine function from the preceding values; determining a target radial enlargement value as a function of a value representative of the rotation speed, in the form of a second affine function, the origin of which is the value of a desired final residual enlargement and the leading coefficient of which is the leading coefficient of the first affine function; stopping the increase in rotation speed of the part from the moment that the actual enlargement of the rotating part corresponds to the target relative radial enlargement value that has been determined.