hereinbelow , preferred embodiments of the invention will be described with reference to the embodiments illustrated in the appended drawings . fig1 to 4 illustrate a self - locking nut 1 according to one embodiment of the invention . in a plan view of the self - locking nut 1 ( hereinafter , also referred to as “ the nut ”), a portion extending from an entrance end portion 2 , from which a bolt will enter to engage threadedly with the nut , to a middle portion 4 has a hexagonal shape . on the other hand , an exit end portion 6 has an appearance in the shape of a frustum of a cone , and forms a tapered outer circumferential surface 7 . in the center of the nut 1 , an internal thread portion 8 is formed so as to extend therethrough from the entrance end portion 2 to the exit end portion 6 . the internal thread portion 8 comprises a main internal thread portion 10 extending from the entrance end portion 2 to the middle portion 4 and having a uniform minor diameter , and a contracted internal thread portion 12 extending continuously from and concentrically with the main internal thread portion 10 and contracted in the exit end portion 6 . the contracted internal thread portion 12 is taperingly contracted over the entire circumference thereof so that the minor diameters of the portion 12 are smaller than the minor diameter of the main internal thread portion 10 . the contracted internal thread portion 12 thus has a conical section . imaginary lines assumed ( not shown in the drawing ) linking the crests ( or the root ) of the main internal thread portion 10 form straight lines parallel to the thread axis . by contrast , imaginary lines linking the crests or the root of the contracted internal thread portion 12 form straight or curved lines which are inclined slightly so as to be the closer to the thread axis , the closer to the exit end portion 6 . that is , the closer to the exit end portion 6 , the higher the degree of the contraction is . in the relevant drawings herein , the degree of the contraction may be exaggerated for the sake of clarity , and the geometries of the embodiments may not be represented exactly . the contracted internal thread portion 12 comprises a little less than three threads . as shown in fig3 and 4 , on ridges in the portion 12 is formed corrugation 20 , which comprises projections and depressions alternating continuously along the circumference of the portion . the corrugation 20 is continuously formed throughout the ridges and , with respect to adjoining ridges , projections 22 and depressions 24 of the corrugation 20 are formed at locations corresponding to one another on straight lines traversing the ridges , i . e ., in vertical planes including the thread axis . in one thread of the contracted internal thread portion 12 are provided , for example , twelve pairs of the projections 22 and the depressions 24 of the corrugation 20 . the corrugation 20 starts from the end surface of the exit end portion 6 and terminates in a surface which lies adjacent to the border between the contracted internal thread portion 12 and the main internal thread portion 10 and which is parallel to the end surface ( i . e ., perpendicular to the thread axis ). the ridges forming a spiral , however , do not allow the corrugation 20 adjacent the starting point and the terminal point to cut off a ridge across the entire thickness thereof . in this respect , the complete corrugation 20 is formed on a little less than two threads , although the contracted internal thread portion 12 has a little less than three threads . in the corrugation 20 , the projections 22 project toward the center of the contracted internal thread portion 12 , and the depressions 24 are depressed away from the center of the portion 12 . the extremities of the projections 22 generally correspond to the extremities of the ridges of the above - mentioned contracted internal thread portion 12 , while the roots of the depressions 24 generally correspond to the roots of the contracted internal thread portion 12 . the contraction of the contracted internal thread portion 12 involves the contraction of the corrugation 20 . as a result , the diameter d 1 of an inscribed circle 26 which links the extremities of a plurality of projections 22 ranging continuously and circumferentially is made smaller than the root diameter of a bolt which is to be engaged threadedly . on the other hand , the diameter of an inscribed circle touching the root of a plurality of depressions 24 is larger than or generally equal to the root diameter of the bolt . adequate number and pitch of the projections and depressions in the corrugation 20 ( in other words , those of the projections 22 ) provided in the contracted internal thread portion 12 in consideration of the balance between the effect of preventing looseness and the tightening torque as well as the life of the die cannot be determined unconditionally , because those values may be varied depending on the average minor diameter d of the contracted internal thread portion 12 and the thread pitch of the contracted internal thread portion . the sizes and number of the projections and depressions of the corrugation 20 , however , are preferably determined so that , for example , the pitch s of the projections and depressions of the corrugation 20 is in the range of 0 . 1 d to 0 . 5 d with respect to the average minor diameter d of the contracted internal thread portion shown in fig5 . [ 0047 ] fig6 illustrates the function of the self - locking nut 1 , having such a structure , and a bolt b which are being engaged threadedly with each other . as the self - locking nut 1 is threadedly engaged with the bolt b ( or the bolt b is threadedly engaged with the self - locking nut 1 ) with the main internal thread portion 10 in the entrance end portion 2 engaged initially , the tip of the bolt b reaches the contracted internal thread portion 12 in the latter part of or nearly at the end of the threaded engagement of the bolt b and the nut 1 , as shown in the drawing in the middle of fig6 . with subsequent progress of the threaded engagement of the nut 1 and the bolt b , as shown in fig7 a plurality of projections 22 in the contracted internal thread portion 12 of the nut 1 are brought into contact with root 34 ( or flanks ) of the bolt b at a large number of locations on the circumference thereof , because the diameters d 1 ( in fig3 ) of the inscribed circles 26 on a large number of projections 22 in the contracted internal thread portion 12 is smaller than the root diameter of the bolt b . in this manner , the projections 22 and the root 34 ( or the flanks ) exert pressing forces on each other , and the projections 22 are elastically compressed . conceptually , however , compressed bodies of the projections 22 readily escape toward their both sides , because the depressions 24 exist on the both sides of the projections 22 . that is , the compressive force acting on the projection 22 in an outward direction along the diameter readily diffuses into the depressions 24 on both sides . accordingly , an excessive increase in torque in the threaded engagement can be prevented , in contrast to the configuration having no corrugation 20 . additionally , after the completion of the threaded engagement , the press - contact between the plurality of projections 22 and the root 34 ( or the flanks ) provides a sufficient effect of preventing looseness . such a state is illustrated in the lowest drawing in fig6 . as the contracted internal thread portion 12 of the nut 1 and the bolt b threadedly engage with each other while exerting pressing forces between the projections 22 and the root 34 ( or the flanks ), the minor diameters of the contracted internal thread portion 12 are typically increased to a certain extent in an elastic manner . in such a case , the cone angle of the minor diameters of the contracted internal thread portion 12 may be decreased from α2 to α3 in fig6 by a given amount . in this state , tension acts on the contracted internal thread portion 12 in the circumferential direction thereof , and further acts as pressing force on the root 34 ( or the flanks ) of the bolt , via a large number of projections 22 . as a result , a sufficient effect of preventing looseness can be obtained without causing an excessive increase in torque and a seizure . hereinbelow , a method of producing such a self - locking nut 1 will be described . for example , as shown in fig8 a material for the nut is set in a forging die and publicly known forging operation is performed to form the outside surface of the nut and to simultaneously form , inside the nut , a main hole 40 for the formation of the main internal thread portion 10 and an exit - side hole 42 provided with the corrugation 20 ( in fig4 ). at this time , the extremities of the projections 22 in the corrugation 20 are generally aligned with the crests of the internal thread which is to be formed , i . e ., with the inner surface of the main hole 40 . the bottom of the depressions are formed so as to generally coincide with the root of the internal thread which is to be formed . an internal thread 44 is then cut continuously on both the main hole 40 and the exit - side hole 42 of this intermediate product n 1 by a publicly known method using a tap or the like . thus the corrugation 20 ( in fig4 ) which coincides with ridges of the thread are formed on the entire circumference of the threaded portion in the exit end portion 6 . the threaded intermediate product n 2 is then pressed with a press die 52 , for example , as shown in fig1 , so that the exit end portion 6 is contracted . the cone angle θ1 of a tapered outer circumferential surface 7 ′ on the exit end portion 6 of the nut 1 which has not yet been contracted is formed so as to be smaller than the cone angle θ2 of the self - locking nut 1 , shown in the lower drawing of fig1 , which has been contracted . when the tapered outer circumferential surface 7 ′ of the intermediate product n 2 is crimped by a press surface 53 formed in conformity with the cone angle θ2 , the tapered outer circumferential surface 7 of the nut 1 as an end product undergoes plastic deformation so as to have the cone angle θ2 . as a result , the exit end portion 6 is contracted inwardly . as shown in fig1 and 13 , the pressing force acting on the tapered outer circumferential surface 7 ′ resolves into a compressive force in the direction x of the diameter of the intermediate nut n 2 and into a compressive force in the direction y of the axis . as shown in fig1 , the compressive force in the direction x of the diameter contracts the diameter d 1 of the exit end portion of the nut 1 as a finished product , thus providing the corrugation 20 with the function of preventing rotation , as mentioned above . on the other hand , the compressive force in the direction y of the axis acts so as to collapse the exit end portion of the nut 1 to a certain extent , so that a thread pitch pi in the exit end portion is necessarily reduced . in this manner , screwing a bolt into the nut forces thread ridges of the bolt to be threaded between the narrowed thread ridges of the nut 1 in the relevant part . as a result , frictional forces larger than usual act between the thread ridges of the bolt and of the nut 1 , and thus the frictional forces also contribute to the function of preventing rotation . in another method of producing the selflocking nut 1 , as shown in fig9 the exit - side hole 42 provided with the corrugation 20 ( fig4 ) may be formed by forging in advance , and then the main hole 40 may be stamped out by a press , and the processes of thread cutting and contracting may follow . alternatively , as shown in fig1 , those production processes may be performed in the following sequence : after the main hole 40 is formed by forging so as to extend therethrough axially , the exit - side hole 42 having the corrugation 20 is formed by a press . subsequently , the process of thread cutting on both the holes 40 and 42 and then the process of contracting are performed . the contracted internal thread portion may be provided with trapezoidal corrugation 62 , as shown in fig1 ( wherein , strictly , the top surface of the trapezoidal projection is in the shape of an arc - like depression and wherein the one - round total of an area si of a discrete thread ridge is , for example , between one - third and one - quarter or less of the one - round area of continuous thread ridge ), or may be provided with triangular corrugation 64 , as shown in fig1 . the invention is not limited to a nut , but may be generally applied to a member having an internal thread structure . for example , as shown in fig1 , in a plurality of projection - like internal thread portions 68 provided on a frame member 66 and having the function of preventing looseness , the same effect as the self - locking nut 1 can be obtained by contracting the exit end portions thereof and by providing corrugation on ridges of the internal threads inside the portions . the invention may be similarly applied to a pipe - like internal - thread member 72 , as shown in fig1 . a portion a in the drawing corresponds to the structure of the self - locking nut 1 above - mentioned .