[ 0014 ] fig1 schematically illustrates in cross - section a so called insert bearing 1 attached to a shaft 2 by way of a sleeve device 3 . the bearing unit arrangement shown in fig1 is similar to the bearing unit described in swedish patentskrift no . 512 651 and includes an inner bearing ring , an outer bearing ring and roller elements arranged between the inner and outer bearing rings as shown in fig1 . the sleeve device 3 includes a sleeve 4 and a radially outwardly extending annular flange 5 . in the illustrated embodiment , the sleeve 4 has a tapering outer peripheral or envelope surface which in the illustrated embodiment is defined by a number of consecutively arranged saw - tooth - shaped tapering surface portions . the tapering surface of the sleeve 4 cooperates with a complementary tapering inner bore surface of the inner bearing ring forming a part of the machine member . in the illustrated embodiment , the complementary tapering inner bore surface of the machine part is also defined by saw - tooth - shaped tapering surface portions . although not specifically shown in fig1 the sleeve 4 is split , preferably with an axially extending slot . one axial end of the sleeve 4 is axially engaged with or connected to the annular flange 5 which has a larger radial size ( e . g ., diameter ) than the sleeve 4 . the flange 5 has several threaded through - holes for receiving tightening devices 6 . in the illustrated embodiment , the tightening devices are in the form of set - screws and the through - holes are inclined inwardly relative to the axial direction as illustrated in fig1 . the tightening devices 6 are arranged to extend through the through - holes and , upon tightening , press against the machine member that is to be attached to the shaft 2 , i . e . the inner bearing ring of the insert bearing 1 . this causes an axial displacement between the inner bearing ring and the sleeve 4 , which results in an increased grip between the shaft 2 , the sleeve 4 and the inner bearing ring due to the mutual motion of the cooperating tapering surfaces . the cooperating tapering surfaces need not necessarily have a saw - tooth - shape , but each surface can form a single tapering portion . in addition , although the tightening devices 6 are shown as set screws extending through bores or through - holes that are inclined to the axial direction , it is of course possible that the tightening devices can be screws arranged in axially extending bores or other arrangements . [ 0018 ] fig2 is a perspective view of the sleeve device 3 and illustrates the longitudinally or axially extending slot 7 in the sleeve 4 that forms the split sleeve configuration . fig2 also illustrates the series of consecutively arranged saw - tooth - shaped surface portions 8 on the outer surface of the sleeve 4 . in addition , in the illustrated embodiment , the annular flange 5 has three tightening devices or screws 6 arranged at evenly space circumferential intervals . as better illustrated in the fig3 detailed view of a portion of the sleeve device 3 , the inner edge of the annular flange 5 has a flat nib , tab or projection 9 . this flat nib 9 projects inwardly and is positioned in the slot 7 , thereby limiting the possibility that the sleeve 4 and the flange 5 will move in the circumferential direction relative to each other . in this embodiment , the flat nib 9 is positioned diametrically opposite to one of the tightening devices 6 . this positioning of the flat nib 9 helps ensure that one of the three tightening devices 6 will not be situated at the position of the slot 7 . [ 0020 ] fig4 is a detailed view of a portion of the sleeve device 3 according to an alternative embodiment . in this embodiment , the sleeve 4 and the flange 5 are prevented from experiencing more than very small mutual movements in the circumferential direction by virtue of a flat nib , tab or projection 10 projecting radially outwardly from the surface of the sleeve 4 . this radially outwardly projecting flat nib 10 is positioned in a recess 11 in the inner edge of the annular flange 5 . as can be seen , the recess 11 is positioned adjacent or in circumferential alignment with one of the tightening devices 6 . although both illustrated embodiments of the sleeve device are equipped with interacting mechanisms for preventing free angular movement of the sleeve and the flange relative to each other , it is not necessary that such mechanisms be provided , although the provision of a nib entering into the slot of the sleeve or into a recess in the flange helps facilitates the handling of the sleeve device during mounting operations . fig5 - 8 schematically illustrate four consecutive steps associated with the mounting operation . fig5 shows the initial position , with the shaft 2 in cross - section , and the sleeve 4 arranged about the shaft so that the slot 7 in the sleeve 4 faces upwards . it is to be understood that the other features and details illustrated in fig1 such as the machine member are not illustrated in fig5 - 8 for purposes of simplifying the illustration and description . for example , it is recognized that the sleeve device 3 is positioned around the shaft 2 so that the sleeve 4 is between the outer surface of the shaft and the tapering inner bore of the machine element . [ 0023 ] fig6 illustrates the first step of the mounting operation . here , the first tightening device 6 is applied at a position diametrically opposite to the slot 7 . the tightening device 6 is illustrated as an arrow marked with a reversed 2 , although this mode of illustration is chosen only for purposes of simplification , it being understood that the tightening device 6 is , in the disclosed embodiment , preferably a set screw as illustrated in fig1 - 4 and has a longitudinal direction substantially in the axial direction of the shaft 2 . [ 0024 ] fig7 illustrates the next step in the mounting operation in which a second tightening device 6 , marked as arrow 1 , is applied . similar to the illustration in fig6 the arrow shown in fig7 represents a set - screw or other appropriate tightening device which is positioned in the same manner as shown for example in fig2 . in the last step shown in fig8 a third tightening device 6 , represented by the arrow 3 , is applied in the same manner , and the mounting is then completed . it has been found , quite surprisingly , that the relatively severe and problematic vibrations earlier experienced with a mounting of this kind , when the machine member after mounting was subjected to rotation , has been appreciably reduced when the mounting sequence has been performed in accordance with the steps illustrated in fig5 - 8 . this substantially improved effect is also clearly perceptible at high rotational speeds . it has also been found that one of the more important steps in the mounting method is that the first tightening device 6 is applied at a position which is diametrically opposed to the slot 7 in the split sleeve 4 . of course , diametrically opposite is also understood to include positions which may not be precisely diametrically opposite the slot , but are slightly spaced from such position . the order in which the other tightening devices 6 ( e . g . the other two tightening devices ) are applied is not necessarily critical , and no significant provable differences have been found if either of the tightening devices 6 marked by arrow 1 or arrow 3 is mounted after the one tightening device 6 ( i . e ., the tightening device 6 indicated by the arrow with a reversed 2 ) is provided diametrically opposite to the slot 7 . as described above , the sleeve 4 and the flange 5 have cooperating features or elements for preventing their mutual angular movement relative to each other except for a very short movement amount permitted by the play between the cooperating features . by virtue of this limited mutual mobility in the circumferential direction , it is possible to ascertain that the position of the first tightening device 6 is not mistakenly angularly displaced by from its desired position opposite to the slot in the sleeve by more than a few degrees . the principles , preferred embodiments and modes of operation of the present invention have been described in the foregoing specification . however , the invention which is intended to be protected is not to be construed as limited to the particular embodiments disclosed . further , the embodiments described herein are to be regarded as illustrative rather than restrictive . variations and changes may be made by others , and equivalents employed , without departing from the spirit of the present invention . accordingly , it is expressly intended that all such variations , changes and equivalents which fall within the spirit and scope of the present invention as defined in the claims , be embraced thereby .