one physical arrangement for a sharpener that has proved effective for sharpening with ultra fine abrasives is shown by way of example in fig4 in cut - away form . two sharpening disks 1 with abrasive coated surfaces 2 are mounted on shaft 3 driven by an electrical motor 4 . the disks 1 made of a metal stamping formed to present a uniform surface of rotation to the edge facet 7 of a knife 5 being shaped by contact with the abrasive surface 2 are mounted on hubs 6 which are driven by shaft 3 . the hubs 6 each have a central cylindrical bore hole that is sufficiently larger than the diameter of the shaft 3 to allow the mounted disk 1 to be physically displaced when the knife edge facet 7 contacts the abrasive surface 2 of the disk . a compression spring 8 mounted between the disks 1 forces the disks to return to a rest position that is precisely established by drive pins 9 that are secured to rotate with shaft 3 and of a diameter that fits with clearance in the slot 10 of hubs 6 . the terminus of the slots 10 in the hubs establish precisely the rest position of the hubs 6 when the force of spring 8 presses the hubs 6 into physical contact with the drive pins 9 . when the facet 7 of a knife edge is pressed with force against the abrasive surface 2 , the disk and its hub are displaced from the rest position by that force , equal to the spring force . in that manner the magnitude of the sharpening force can be controlled and limited by the spring force but that force will be equal to the spring force only if there is no friction between the cylindrical bore hole thru the hub 6 and the circumference of the shaft 3 on which it is driven . any friction between the sliding hub and the shaft will increase the force on the edge facet as it is being sharpened . this mounting and drive mechanism as described above and shown in fig4 operates stabily with spring forces on the order of 0 . 2 lb . or greater . however , sharpening forces of this level create excessively large burrs even with ultra fine abrasive grits . repeated attempts to reduce the burr by using springs of lower force initiated mechanical vibrations of the abrasive surface sufficient in magnitude to cause the sharpening disk to bounce into intermittent contact with the knife edge and the resulting impact of the abrasive surface with the edge facet damaged the ultra fine knife edge sufficiently that further reductions in spring tension becomes counter productive . it proved exceedingly difficult to establish the cause of these destructive vibrations with spring forces below 0 . 2 pound . these were found to be due to a number of factors and subtle interaction of these same variables . the sharpener of fig4 is shown again in fig3 but with a protective cover 11 in place over the supporting base 12 and with electrical switch 17 . the knife 5 is shown in alignment with guide surface 13 and its facet 7 in contact with the rotating abrasive coated surface 2 . a plastic support post 14 serves to support flexible plastic spring 15 of fig2 which has arms 16 that extend down and beside guide surface 13 . the plastic spring arms 16 contact and press the knife 5 as it is inserted against the knife guide surface 13 . thus the knife 5 is held at the correct angle and position so that its edge facet will be pressed into optimal contact with the rotating abrasive surface 2 : as shown in fig2 thru 4 there is only one pair of disks , however , more disks and sharpening stages can be added as in fig5 on a single shaft . this arrangement has the distinct advantage that a heavier spring can be used in the first stage ( stage 1 ) and an ultra light spring used in the second stage ( stage 2 ). normally one sharpens a first edge facet in the first slot of the first stage of fig5 and then the knife is moved to the second slot to sharpen the second knife facet . the first stage ( stage 1 ) is added to obtain far more aggressive presharpening to be followed by a final sharpening and edge finishing stage ( stage 2 ) with the ultra final grit and with ultra low spring force as described herein . [ 0021 ] fig6 , 8 and 9 show different views and in greater detail the construction of the rotating disk 1 , its hub 6 , the drive pin 9 , and the slot 10 in the supporting hub 6 . referring to fig4 the hub 6 made for example from plastic , is caused to rotate with shaft 3 by virtue of the drive pin 9 preferably cylindrical in shape which is attached thru the shaft 3 and sized to fit within slot 10 molded into the plastic hub . as the disk 2 is displaced from its rest position by a blade being sharpened , the disk on its hub moves slidingly and parallel to the axis of the motor shaft away from the blade and the drive pin slides within the elongated hub slot 10 while remaining constrained in that slot . the diameter of drive pin 9 must be less than the width of the hub slot 10 in order that it not restrain the displacement of the hub and its supporting disk . it is important that the force to displace the disk be substantially only the ultra low force of the restraining spring action provided by spring 8 . while the drive pin must be free to move within slot 10 it was discovered that objectionable vibrations of the hub and disk surface will occur if the width of the hub slot w is much greater than the diameter d of the drive pin 9 , of fig8 . these vibrations initiate when low force springs are used as the knife is withdrawn and can be sufficiently severe that the disk will not return to its rest position ; instead it will continue to resonate as the drive pin 9 impacts alternate sides of the hub slot 10 . because the disk does not properly return to its rest position , the sharpening action is severely compromised . it was found that the vibration and adverse resonance of the hub and disk could be eliminated by limiting width w ( fig8 ) of the slot to not more than 0 . 055 inch greater than the diameter d of the drive pin . this eliminates the opportunity for the pin to gain excessive angular velocity as it is accelerated by minor variations in motor speed and its force of impact on the wall of the hub slot was found to be insufficient to create a significant resonance of the hub . to reduce this resonance further it proved helpful to taper the walls of the drive slot as shown in fig9 so that the width of the slot at its bottom ( adjacent shaft ) is smaller than at the top of that slot . in this way the drive pin would strike the slot wall of the hub 6 only at the bottom of the slot , immediately adjacent to the shaft 3 where resonances could be damped promptly . it proved important to insure that the impact point of the drive pin 9 against the wall of the slot was as close as possible to the bottom of the slot wall — adjacent to the shaft 3 . because of the exceedingly light force spring used to restore the hub and disk to their rest position there is a tendency of the drive pin as it returns to its rest position to also impact the bottom of the slot with sufficient momentum to set up a resonance in the direction of the axis of the shaft and causes the hub / disk combination to vibrate in and out of the rest position — again interfering with the sharpening action . it was discovered that the magnitude of these vibrations could be reduced by placing filets in the inside corners of the slot curved to match the radius of the drive pin as shown in fig8 . this caused the pin to make random contact with a matching contour rather than at a single point along its circumference which helped to break up the tendency to resonate . some of the mechanical resonances that gave rise to the bouncing effect of the disks described above have their origin in the non - uniform angular speed of drive motors and the small but excessive instantaneous changes in the torque and speed of the motor as the magnetic poles of the motor armature cross the fixed poles of the motor . this is particularly a problem with inexpensive two pole shaded pole motors widely used in sharpening devices . these resonances occur also in part because of eccentricities of sharpening disks coupled with any looseness of the displaceable disks on the drive shaft . the disks must be free to move ( slide ) along the shaft in response when the edge of the knife contacts the abrasive surface of the sharpening disk . the sharpening disk or disks are held in a rest position on the shaft by the force of the restraining spring which pushes the disk to its rest position . the relationship of the locations of the stop - pin on the shaft , the abrasive surface on the disk and the knife guide must be extremely precise in order that when the blade to be sharpened is placed on the knife guide and slid into contact with an appropriate area on the abrasive surface of the disk the rotating disk will be displaced along the motor shaft during the actual sharpening process . this insures that the disk is always displaced somewhat during the sharpening process and the sharpening force on the facet of the blade edge can be controlled primarily by the force of the compression spring . because the disk assembly ( the disk held by its plastic hub ) must slide ( be displaced ) freely on the motor shaft against the spring force when contacted by the knife edge , there must be sufficient clearance between the cylindrical bore of the hub and the shaft surface to avoid frictional effects that are much greater than the restoring force of the spring . excessive friction will cause the hub to bend or freeze on the shaft and create excessive forces on the edge of the knife being sharpened and as a result gauge the knife edge , thus destroying the sharp edge being created . when a low force spring , below 0 . 2 pound , is used in order that the knife edge be abraded very gently , the frictional forces between the hub and shaft must be exceedingly small . however , if the bore size of the hub is increased sufficiently in order to reduce friction to that level that the frictional effects do not interfere with the spring action , mechanical resonances can be created that vibrate the abrading surface and lightly “ hammer ” the edge being sharpened . the quality and fineness of the edge is adversely deteriorated by the physical resonances that can occur . the optimum clearance between a shaft 3 of 0 . 2496 inch diameter and the cylindrical bore of the hub 6 was found to be about 0 . 0009 inch . the hammering effect that can occur due to these resonances is further exacerbated by the disk runout — namely any imperfections in the symmetry of the disk &# 39 ; s abrasive surface relative to its axis of rotation . if the runout is excessive the resonance will be enhanced and the hammering effect can be sufficient to prevent the creation of exceedingly sharp knife edges by the disk sharpening system . a convenient design for the abrasive disk is a thin adhered layer of abrasive particles , preferably diamonds , on a rigid shaped substrate such as a symmetrical metal disk for example in the shape of a truncated cone . with this design runout of the abrasive surface of the disks can be diminished by “ wearing in ” the surface abrasive the abrasive surface when the size of the abrasive grit or thickness of abrasive layer is significantly larger than the runout of the metal substrate . in effect initial wear of the abrasive on a disk surface with runout is largely at high spots on the disk surface and by “ wearing in ” any high spots are lowered which in turn improves the apparent runout of the disk . with a single layer of fine grit sized less than the magnitude of run - out , the amount of “ wearing in ” of the surface is limited . hence when using ultra fine grits there is a greater requirement that the initial runout of the disk be exceedingly small . efforts to create stable — non - resonating abrasive disk systems with grit sizes less than 0 . 002 inch diameter with spring forces less than 0 . 2 pound and as low as 0 . 01 pound ( 0 . 16 ounce ) restoring the disk to its rest positions , driven by conventional low cost motors at about 3000 to 3600 rpm were ineffective if the shaft of the driving motor or the shaft on which the sharpening disks were mounted had an eccentric motion , that is had a wobble or lateral motion of its axis greater than ±± 0 . 006 inch . such eccentric motion aggravated the resonance especially if the clearance between the drive shaft ( 0 . 2496 inch diameter ) and the hole in the plastic hub of the disk assembly exceeded 0 . 0009 inch . the resonance became unacceptable with clearances greater than 0 . 002 inch if one wished to create exceedingly sharp knives . it was possible in spite of the interaction of such small mechanical imperfections and the difficulty of isolating the cause of damaging resonances to establish the acceptable limits for each type of imperfection as described above .