An engine starter (10) comprises a hollow armature rotary shaft (16) having a plurality of cam surfaces (16a) of an over-running clutch mechanism (56) and having at one end a reduced-diameter portion (16b) on which a sleeve member (55) is press-fit and at the other end a stopper (16c). The sleeve member (55) has a rolled portion on its outer circumference on which an armature core (17) is secured by press-fit so that the armature core (17) is firmly held by the sleeve member (55) and the stopper (16c) on the armature rotary shaft (16). The armature rotary shaft may have a polygonal cross-sectional outer configuration so that the armature core can be firmly press-fit onto polygonal armature rotary shaft. A method for concurrently brazing and magnetically annealing the armature core comprises heating the armature assembly between 780 DEG C and 850 DEG C.
