Patent Publication Number: US-6210259-B1

Title: Method and apparatus for lapping of workpieces

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to lapping apparatus, and more particularly to an improved method and apparatus for lapping a group of flat-parallel or cylindrical workpieces. 
     BACKGROUND OF THE INVENTION 
     Lapping machines are used to treat the surfaces of workpieces using an abrasive assembly. Typically, lapping machines include upper and lower lapping discs which are made of a strong material and have precisely flat working surfaces which are loaded with an abrasive compound. Workpieces are carried within a cassette that is positioned between the upper and lower lapping discs and which effect treatment of the workpieces. Typically, the axes of the lapping discs are vertical and coaxial and treatment is accomplished by rotating one or both discs relative to the cassette such that the appropriate surfaces of the individual workpieces are abrased by the working surfaces of the lapping discs. 
     During the treatment of workpieces, it is desirable to ensure minimal differences in thickness (or diameter if the workpieces are cylindrical) between individual workpieces and that the top and bottom sides of each workpiece are essentially parallel to eachother and flat. Care must be taken to avoid lapping constantly over the same areas of the lapping disc so that the surface of lapping disc is evenly utilized. If the working surfaces of the lapping discs are unevenly worn, the surfaces of the workpieces cannot be lapped to a high finish and to an accurate flatness. Since the speed of each particle on the abrasive surface of the lapping discs is proportional to the distance between the centre of rotation and the particle, it is necessary to provide workpieces with an appropriate trajectory of movement between the lapping discs in order to minimize radial deformation of the working surfaces of the lapping discs and to optimize the accuracy of finishing of the workpieces. 
     In order to ensure even wear of the working surfaces of lapping discs, prior art lapping machines utilize cassettes that have sockets formed within for holding individual workpieces and which allow the cassette to be rotated independently from the lapping discs. Accordingly, the workpieces are provided with radial movement having a changing vector of velocity relative to the vertical axis of the lapping discs and move along a spiral trajectory relatively to the lapping disks. 
     One type of assembly which effects such movement of workpieces is a planetary lapping machine as in U.S. Pat. No. 3,662,498 to Caspers and U.S. Pat. No. 4,157,637 to Orlov et al. A planetary lapping machine utilizes a number of circular cages, each cage having individual workpiece sockets. Each cage is driven by a sun gear and a ring gear of a sun-and-planet gear which are rotated on vertical shafts coaxial with annular upper and lower lapping discs. This construction ensures that the center of workpieces being machined are moved along spiral trajectories over the working surface of the lower and upper lapping discs. Planetary movement is composed of the joint motion of the circular motion of each individual workpiece socket rotating within a circular cage around the individual cage axis and the larger circular orbiting movement of each socket around the axis of the lapping discs. 
     Another type of lapping assembly is disclosed in U.S. Pat. No. 3,541,734 to Clar, which describes a dual-disc lapping machine. A dual-disc machine is generally used for lapping cylinders and includes a cassette which is driven by an eccentric crank pin so that the cassette rotates in an eccentric manner and at a different speed than the upper and lower discs. 
     Both types of lapping assembly suffer from substantial and well known disadvantages. Lapping discs are unevenly worn during the course of treatment of workpieces. Also, the required spacing of individual workpieces inside the cassettes results in a relatively low yield of treated workpieces from the lapping machines. Finally, since each workpiece must be individually housed within cassette sockets, labour intensive loading and unloading of workpieces from the cassette is required. 
     These disadvantages can be overcome as described in USSR Patent No. 181,516-66 to Malkin, by vibrating one or both of the lapping discs using a vibration generator to provide translational circular motion therein. Further, the lapping discs can be provided with additional motion so that the axis of the lapping discs circumscribe a cone. This techniques improves the precision and productivity of the workpiece finishing process by allowing loosely packed workpieces to move between the upper and lower lapping discs in an orderly manner. 
     Further, as described in USSR Patent No. 227,127-67 to Malkin, one of the lapping discs can be suspended on a shock-absorber and fixedly secured to an unbalanced-mass vibration generator. The lapping discs are connected to each other by elastic elements such as, for example, radial helical coil springs, whose total rigidity exceeds the total rigidity of the shock-absorber. This apparatus provides simultaneous finishing of both surfaces of the workpieces and allows the user to adjust the amount of material to be removed from the workpieces. 
     One disadvantage of these approaches is that particles on the surface of the lapping disks move in a vertical direction at a linear acceleration that is proportional to the radial distance of the particle from the center of the lapping discs. This causes the surfaces of the lapping discs to be worn into a conjugate spherical shape. This defect is especially apparent when large workpieces are treated and accordingly, such an approach is most appropriate for small workpieces. Also, prior art machines do not effectively move individual workpieces in relation to particles on the surface of the lapping discs, especially when the pressure applied to the surfaces of the workpieces is substantial. Finally, it is difficult to apply the same level of treatment to both sides of a workpiece, since the intensity of oscillations applied to one lapping disk connected to vibrator is higher than that of the other disk (especially when the working pressure is high) and since oscillations are imperfectly transferred through elastic couplings. This results in workpieces being treated primarily on one side. 
     Accordingly, there is a need for an improved lapping assembly which provides even treatment to both surfaces of a group of workpieces, which effects even wear to the surfaces of lapping discs, which is easy to load and unload, which allows for treatment of a large number of workpieces, which comprises relatively few parts, and which is durable and relatively inexpensive to manufacture. 
     BRIEF SUMMARY OF THE INVENTION 
     It is therefore an object of the present invention to provide a lapping assembly for lapping a group of workpieces at a predetermined cutting speed, said lapping assembly comprising: 
     (a) first and second lapping discs, said lapping discs arranged next to one another, each said lapping disc having a working surface with abrasive particles for lapping the surfaces of the workpieces; 
     (b) a cassette positioned between said lapping discs for holding the group of workpieces, said cassette having a curvilinear opening formed within and dimensioned to receive the group of workpieces, said opening being defined by an inner wall; 
     (c) an oscillating assembly coupled to said lapping discs for providing two-component translational oscillations to said lapping discs in directions which are parallel to said working surfaces of said lapping discs, said translational oscillations being provided at the cutting speed of the group of workpieces; and 
     (d) a rotational assembly coupled to at least one of said cassette and said lapping discs, such that a point on the periphery of said cassette rotates in relation to an adjacent point on at least one of said lapping disks at a linear speed which is less than said cutting speed, such that the workpieces are caused to circulate within said opening of said cassette. 
     In another aspect the invention provides a lapping assembly for lapping a group of workpieces at a predetermined cutting speed, said lapping assembly comprising: 
     (a) first and second lapping discs, said lapping discs arranged next to one another, each said lapping disc having a working surface with abrasive particles for lapping the surfaces of the workpieces; 
     (b) a cassette positioned between said lapping discs for holding the group of workpieces, said cassette having an opening formed within and dimensioned to receive the group of workpieces, said opening being defined by an inner wall; 
     (c) an oscillating assembly comprising a first motor and first and second eccentric crank pins, said first eccentric crank pin being coupled to said first lapping disc and said second eccentric crank pin being coupled to said second lapping disc, said oscillating assembly providing two-component translational oscillations to said lapping discs in directions which are parallel to said working surfaces of said lapping discs, said translational oscillations being provided at the cutting speed of the group of workpieces. 
     In another aspect the invention provides a method of lapping a group of workpieces at a predetermined cutting speed, the workpieces being housed within a cassette having a curvilinear opening formed therein, said cassette being positioned between first and second lapping discs, said first and second discs each having a working surface having abrasive particles for lapping a surface of the workpieces, said method comprising the steps of: 
     (a) allowing said workpieces to move freely inside the opening of the cassette, said curvilinear shape serving to maintain the surfaces of the workpieces in contact with the working surfaces of the lapping discs; 
     (b) providing translational oscillations to the lapping discs in a plane parallel to the working surfaces of the lapping discs at the cutting speed; and 
     (c) rotating said cassette in relation to at least one of the lapping discs, such that a point on the periphery of said cassette rotates in relation to an adjacent point on at least one of said lapping disks at a linear speed which is less than said cutting speed. 
     Further objects and advantages of the invention will appear from the following description, taken together with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
     FIG. 1 is a side cross-sectional view of the lapping assembly according to a preferred embodiment of the present invention; 
     FIG. 2 is a sectional view of the lapping assembly taken along the line A—A′ of FIG. 1; 
     FIG. 3 is top plan view of an alternative embodiment of the cassette of FIG. 1; 
     FIG. 4 is side cross-sectional view of the lapping assembly containing an alternative embodiment of the cassette of FIG. 1; 
     FIG. 5 is a sectional view of the lapping assembly taken along the line B—B′ of FIG. 4; 
     FIG. 6 is a side cross-sectional view of an alternative embodiment of the lapping assembly of FIG. 1 which includes a sensing device for controlling the thickness of the finished workpieces; 
     FIG. 7 is a cross-sectional view of a one-spindle lapping machine which may be used in association with the lapping assembly of FIG. 1; 
     FIG. 8 is a cross-sectional view of a one-spindle lapping machine which may be used in association with the lapping assembly of FIG. 1; 
     FIG. 9 is a cross-sectional view of a two-spindle machine which may be used in association with the lapping assembly of FIG. 1; and 
     FIG. 10 is a diagrammatic view of the lapping assembly of FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Reference is first made to FIGS. 1 and 2, which show a lapping assembly  10  made in accordance with a preferred embodiment of the invention. Lapping assembly  10  includes a cassette  12  for holding a group of workpieces  14 , first and second lapping discs  16 ,  18  for lapping a group of workpieces  14 , elastic members  20   a  and  20   b  for preventing rotational movement of first and second lapping discs  16 ,  18 , and crank pins  21  and  22  for effecting oscillation of first and second lapping discs  16 ,  18 . 
     Cassette  12  is a generally round disc with an opening  24  (FIG. 2) dimensioned such that a substantial number of workpieces  14  may be located within opening  24  while still being able to freely circulate within opening  24 . Cassette  12  is typically made out of a hard metal (e.g. steel alloy). It is contemplated that cassette  12  is preferably formed with a diameter in the range of between 150 and 2000 millimeters. 
     In a preferred embodiment, opening  24  is defined by wall  25  having a scalloped curvilinear shape (e.g. the three intersecting circular shapes as shown). Accordingly, a number of protrusions  26  are present along wall  25  of opening  24  which assist with the circulation of workpieces  14  within opening  24  when lapping assembly  10  is in operation, as will be described. It has been determined that the required angle of the sides of the protrusion  26  can be reduced as the flatness of first and second lapping discs  16 ,  18  is increased. Cassette  12  is mounted on several rollers  28  rotatably coupled to the body  15  of a lapping machine so that cassette  12  may rotate around a stationary axis. Rotation of cassette  12  may be effected through conventional means such as a gear rim  30  coupled to a cassette-drive motor M1. It should be understood that cassette  12  could be caused to rotate using alternate types of conventionally known mechanisms. 
     First and second lapping discs  16  and  18  are well known abrasive lapping discs, made of a strong material (e.g. cast iron). First and second lapping discs  16 ,  18  have precisely flat working surfaces  17 ,  19  which are loaded with an abrasive compound (e.g. diamond, silicon carbide, fused alumina). Lapping (or “cutting”) of workpieces  14  is accomplished by rubbing the abrasive-loaded working surfaces  17 ,  19  of first and second lapping discs  16 ,  18  against the surfaces of workpieces  14  at an appropriate pressure. As a general rule, it is desired to provide first and second lapping discs  16 ,  18  with translational two-component oscillations in the plane of their working surfaces  17 ,  19  (i.e. they experience oscillations in the horizontal plane defined by the X-axis and the Y-axis, as shown). 
     One method of doing so is to simultaneously drive first and second lapping discs  16 ,  18  with a disc-drive motor (not shown) through eccentric crank pins  21 ,  22 , respectively (FIG. 1) while restraining them from rotating by elastic members  20   a ,  20   b , respectively. First and second crank pins  21  and  22  are conventional eccentric crank pins and have eccentricity e 1  and e 2 , respectively. Elastic members  20   a  and  20   b  are coupled to first and second lapping discs  16 ,  18 , respectively, as well as to body  15  of lapping machine (FIG. 1) to prevent first and second lapping discs  16 ,  18  from rotating. It should by understood that other conventionally known restraining members could be used in place of elastic members  20   a  and  20   b . Accordingly, first lapping disc  16  is provided with translational movement in the X 1  and Y 1  directions and second lapping disc  18  is provided with translational movement in the X 2  and Y 2  directions, as shown. 
     It should be understood that many other mechanical driving mechanisms could be used to provide first and second lapping discs  16 ,  18  with the desired two-component translational movement. Also, while first and second lapping discs  16 ,  18  are shown in a horizontal orientation in FIGS. 1 and 2, it should be understood that first and second lapping discs  16 ,  18  could be orientated in any other plane. 
     Preferably, first lapping disc  16  is provided with antiphase harmonic oscillation such that the X 1  and Y 1  components are equal in frequency (but 90 degrees out of phase) and have an amplitude of e 1  and second lapping disc  18  is provided with antiphase harmonic oscillation such that the X 2  and Y 2  components are equal in frequency (but 90 degrees out of phase) and have an amplitude of e 2 . Further, it is preferred to provide harmonic oscillation to first and second lapping discs  16 ,  18  such that the X 1 , Y 1  and X 2 , Y 2  components are antiphase (i.e. the oscillations of first lapping disc  16  are 180 degrees out of phase with those of second lapping disc  18 ). 
     Accordingly, particles on the working surfaces  17 ,  19  of first and second lapping discs  16 ,  18  will have circle trajectories of radius corresponding to e 1  and e 2 , respectively. It should be understood that first and second lapping discs  16 ,  18  may be provided with different amounts of translational movement (e.g. arbitrary frequencies and amplitudes of oscillation). However, in any case, in order for first and second lapping discs  16 ,  18  to provide effective treatment of workpieces  14 , first and second lapping discs  16 ,  18  must be oscillating at an appropriate cutting speed for treating the group of workpieces  14 . 
     When first and second lapping discs  16 ,  18  are provided with an oscillation of equal frequency and amplitude in antiphase, the forces of friction which act on the surfaces of workpieces  14  will cancel each other out and workpieces  14  will essentially remain motionless between first and second lapping discs  16 ,  18 . Even where there is some small difference in the force of friction being applied to the surfaces of an individual workpiece  14  which results in it being “captured” (i.e. caught and moved) by the lapping disc which exerts the stronger force, collisions with other workpieces, collision with the walls of the socket, and general forces of inertia will quickly bring workpiece  14  to a stop and prevent it from oscillating within opening  24 . It is noted that the stabilizing effect of the general inertia will increase as acceleration of oscillations of first and second lapping discs  16 ,  18  increases. 
     Cassette  12  must be rotated at a high enough speed such that individual workpieces  14  are circulated within opening  24 . If a workpiece  14  remains within a particular area, the sludge which is produced during abrasive treatment, will quickly slow down treatment, almost to a stop. However, cassette  12  must also be rotated at a low enough speed so that the speed of movement of workpieces  14  within opening  24  is slow enough so as not to affect the effectiveness of cutting. Specifically, it has been determined that cassette  12  must be rotated such that points on the outside edge of cassette  12  have a linear speed which is less than the cutting speed appropriate for a particular group of workpieces  14 . 
     When cassette  12  rotates with angular velocity Ω (FIG. 2) and first and second lapping discs  16 ,  18  provide oscillating force as previously described, freely placed workpieces  14  will circulate in a pseudo-random manner within opening  24 . Specifically, workpieces  14  are involved in two main movements as shown by arrow A (indicating relative motion of workpiece  14  to cassette  12 ) and arrow B (indicating the translational speed of workpiece  14  carried by cassette  12 ) on FIG.  2 . 
     Specifically, as cassette  12  rotates, wall  25  of opening  24  generally urges workpieces  14  to move in the same general direction as cassette  12 . As is conventionally understood, workpieces  14  positioned at a farther distance R from the center of opening  24  will have a greater linear speed than workpieces  14  positioned at a closer distance R&#39; from the center of opening  24 . Accordingly, working surfaces  17 ,  19  of first and second lapping discs  16 ,  18  will exert greater forces of friction on those workpieces  14  positioned further away from the center of opening  24  than on those workpieces  14  positioned closer to the center of opening  24 . Thus, workpieces  14  positioned further from the center of opening  24  will experience more of a retarding force against forward motion than workpieces  14  positioned closer to the center of opening  24 . 
     Further, the presence of protrusions  26  as well as the oscillating forces provided by first and second lapping discs  16 ,  18  assist in urging workpieces  14  to circulate within opening  24 . If first and second lapping discs  16 ,  18  were motionless (i.e. not undergoing oscillation), workpieces  14  would move within cassette  12  around the axis of cassette  12 . Due to the combination of oscillations of the first and second lapping discs  16 ,  18  and the rotation of cassette  12 , it has been observed that workpieces  14  move within opening  24  as if workpieces  14  were being pushed by cassette  12  under conditions of pseudo-viscous friction. This “force of friction” has been observed to increase as the speed of workpieces  14  increases. 
     The combination of all of these forces will result in workpieces  14  having relative motion in a direction along curved wall  25  that is opposite to the rotational motion of cassette  12  (arrow A in FIG.  2 ). Simultaneously, workpieces  14  will have translational motion together with cassette  12  (arrow B in FIG.  2 ). The overall movement of workpieces  14  will then be the combination of motion represented by arrow A and arrow B. The result is that workpieces  14  will circulate in a pseudo-random fashion within opening  24  of cassette  12 . 
     Correspondingly, working surfaces  17 ,  19  of first and second lapping discs  16 ,  18 , will be more evenly worn than is possibly using conventional lapping machines and lapping assembly  10  will provide even treatment to workpieces  14  on both sides. Since opening  24  is large enough to hold large quantities of workpieces  14  and cassette  12  does not require every workpiece  14  to be put in a separate socket, a higher number of workpieces  14  may be processed than is possible using conventional lapping machines and loading and unloading of workpieces  14  can be accomplished at a much faster rate. Also, when loading workpieces  14  into opening  24 , it is not necessary to position each workpiece  14  flat on second lapping disc  16 . Workpieces  14  are arranged on top of each other will quickly array themselves into one layer on the surface of second disc  16  once circular oscillation is provided to cassette  12 . Finally, when cassette  12  is filled with workpieces  14 , it is possible to “correct” (i.e. re-establish a flat profile of) working surface  17 ,  19  of first and second lapping discs  16 ,  18 , preferably using cylinders. 
     It should be understood that opening  24  of cassette  12  can be of any general shape, as long as at least two points on wall  25  of opening  24  are spaced apart from the center of rotation of either cassette  12  and/or first and second lapping discs  16 ,  18  at varying distances. That is, opening  24  can be of any general shape which allows workpieces  14  positioned against wall  25  to be able to easily move to another position along wall  25  which is at a different distance away from the center of rotation discussed above. As discussed above, since the linear speed of workpiece  14  varies with the distance it is from the center of rotation, workpieces  14  will circulate within opening  24  as long as it is possible for workpieces  14  to experience different degrees of linear speed (and thus different degrees of friction from first and second lapping discs  16  and  18 ) as workpieces  14  traverse within opening  24 . It should be understood however, that when shapes which contain corners (e.g. square or triangle shapes), workpieces  14  tend to get caught within the corners and movement of workpieces  14  within opening  24  is appreciably limited. 
     FIG. 3 shows an alternative embodiment of lapping assembly  10  wherein a socket-type cassette  42  is utilized. Cassette  42  contains a number of apertures  34 , each of which are sized to receive a satellite disc  36 . Each satellite disc  36  has a diameter which is slightly smaller than that of the corresponding aperture  34  and contains individual sockets  38  adapted to receive individual workpieces  14 . Where there is are insufficient number of workpieces  14  to fill the space of opening  24 , a smaller number of workpieces  14  can still be treated by inserting individual workpieces  14  into cassette  42 . 
     Workpieces  14  located within sockets  38  of satellite discs  36  move in relation to first and second lapping discs  16 ,  18  along epicycloid trajectories, similar to those in prior art planetary lapping machines. However, working surfaces  17 ,  19  of first and second lapping discs  16 ,  18  are worn more evenly than would be so in the case of prior art planetary lapping machines, due to translational motion of cutting first and second lapping discs  16 ,  18 . The oscillatory motion of first and second lapping discs  16 ,  18  assists satellite discs  36  in circulating freely within apertures  34 . Although cassette  12  of FIG. 2 achieves more even wear of first and second lapping discs  16 ,  18  than cassette  42  of FIG. 3, cassette  42  is still beneficial where a small quantity of workpieces  14  are to be treated. 
     FIGS. 4 and 5 show an alternative embodiment of lapping assembly  10  wherein an extended cassette  52  is used to further facilitate automatic loading and unloading of workpieces  14 . Cassette  52  includes a plurality of identical openings  54 , each opening  54  having an outside edge  56  with a curvilinear shape (similar to opening  24  of FIGS.  1  and  2 ). As a result, protrusions  58  are present along each outside edge  56  and extend into each opening  54 . Cassette  52  is rotatably supported by shaft  60  so that while workpieces  14  within one opening  54  are receiving treatment, workpieces  14  from the other openings  54  can be appropriately loaded and unloaded. 
     In this embodiment, cassette  52  is motionless during treatment and first and second lapping discs  16 ,  18  are oscillated using eccentric crank pins  21  and  22  (FIG.  5 ), as previously described in relation to FIGS. 1 and 2. In contrast to the embodiment of lapping assembly  10  shown in FIGS. 1 and 2, elastic members are not employed to restrain the rotational movement of first and second lapping discs  16 ,  18 . First and second lapping discs  16 ,  18  are preferably provided with low angular velocity Ω 1 , and Ω 2  (e.g. and preferably so that Ω 1 =Ω 2 ). It should be understood that it would also be possible to provide different angular velocities to first and second lapping discs  16 ,  18 , or alternatively, to provide rotation to only one of first and second lapping discs  16 ,  18 . 
     A conventional cogwheel drive mechanism having cogwheels  62  and  64  is seated on first and second lapping discs  16 ,  18 , and used to drive eccentric crank pins  21  and  22  as shown. Gear wheels  66  and  68  are coupled to cogwheels  62  and  64 , respectively as well as to body  15  of the lapping machine. It should be understood that any conventionally known drive mechanism may be used to rotate one or both of first and second lapping discs  16 ,  18 , as appropriate. 
     As specifically shown in FIG. 5, when cassette  12  is fixed and first and second lapping discs  16 ,  18 , are oscillated in the eccentric manner described, workpieces  14  generally experience a combination of oscillatory forces from first and second lapping discs  16 ,  18  in combination with rotational forces around the axis of first and second lapping discs  16 ,  18  (i.e. workpieces are “dragged” behind first and second lapping discs  16 ,  18 ). The overall trajectory of workpieces  14  is the combination of motion represented by arrow A&#39; and arrow B&#39;. 
     It should be understood that the cassette of this embodiment could equally be of the form of cassette  12 , previously described in relation to FIGS. 1 and 2. In such an arrangement instead of rotating cassette  12 , first and second lapping discs  16 ,  18  are rotated, such that the same relative speed between cassette  12  and first and second lapping discs  16 ,  18  is provided. 
     FIG. 6 shows an alternative embodiment of lapping assembly  10  wherein the height to which workpieces  14  are treated can be controlled. Specifically, second lapping disc  18  is coupled to a marking element  70  through rigid support  72 . First lapping disc  16  is coupled to a sensor  74  through rigid support  76 . It is possible to control the height of the finished workpiece  14  by setting the calibration instrumentation of sensor  74  to indicate when marking element  70  is a certain distance D away from sensor  74 . Once sensor  74  detects and indicates (e.g. using an indicator LED) that marking element  70  is a distance D away, lapping assembly  10  could be prevented from continuing treatment of workpieces  14  either manually, or automatically using a microcontroller, as is conventionally known. 
     FIG. 7 shows an alternative embodiment of the present invention as a one-spindle lapping machine  100  which may be used to oscillate first and second lapping discs  16 ,  18  and to rotate cassette  12  of lapping assembly  10 , as previously discussed. Lapping machine  100  also provides a mechanism for balancing the oscillating first and second lapping discs  16 ,  18  so that when first and second lapping discs  16 ,  18  are oscillated at optimum speed, minimal oscillations are transferred to body  15  of lapping machine  100 . Lapping machine  100  includes a rigid frame  102 , a second disc spindle assembly  104 , an first disc spindle assembly  106 , a bottom spindle assembly  108 , and a pressurizing assembly  110 . 
     Second lapping disc  18  is coupled to a tank  112  and is seated on nave  114  which is equipped with a radially supporting rolling bearing, as is conventionally known. Second crank pin  22  is coupled to a driving shaft  116  which rotates inside nave  114 . Elastic members  20   b  are coupled to second lapping disc  18  and to body  15  of lapping machine  100  to prevent second lapping disc  18  from rotating about its axis. The resulting motion is a two-component translational oscillation, as previously described. 
     First lapping disc  16  receives circular oscillations from first disc spindle assembly  106  through rigid frame  102  and two dog columns  118 , which enter openings  120  of plate  122 , rigidly connected to first lapping disc  16 . In order to effect noiseless breaking of dog columns  118 , rolling bearings could be installed in openings  120 . First crank pin  21  rotates inside nave  119  and is rigidly connected to a drive shaft  124 , which rotates inside bottom nave  125  of motionless spindle assembly  108  by means of disc-drive motor M2. Elastic members  20   a  are coupled to first lapping disc  16  and to body  15  of lapping machine  100  to prevent first lapping disc  16  from rotating about its axis. The resulting motion is a two-component translational oscillation, as previously described. 
     Balancing of lapping assembly  100  is achieved by driving first and second lapping discs  16 ,  18  in an antiphase manner through rigidly fixed together crank pins  21  and  22 , respectively. Crank pins  21  and  22 , together with drive shaft  124  form a unified spindle. Specifically, eccentricities e 1  and e 2  of crank pins  21  and  22 , respectively must be chosen such that the static moment of first lapping disc  16  (i.e. G 1  e 1  where G 1  is the combined weight of first lapping disc  16  and associated parts rigidly connected) is equal to that of second lapping disc  18  (i.e. G 2 e 2  where G 2  is the combined weight of second lapping disc  18  disc  16  and associated parts rigidly connected). In preferred operation, where first and second lapping discs  16 ,  18  are oscillated in antiphase, the cutting speed of lapping assembly  10  will be proportional to the sum of the eccentricities e 1  and e 1  (i.e. the sum of the eccentricity of the first crank pin  21  and that of the second crank pin  22 ). 
     Also, as is conventionally known, first and second lapping discs  16 ,  18  must be pressed together with an appropriate force G as is effected by pressurizing assembly  110 . Traverse member  126 , moveable on columns  127  and driven by motor M3 through conventionally known spring and hinge assembly  111 , can be used to provide a specific amount of force G to first lapping disc  16  which is movably coupled to a set of dog columns  118 , as shown. Alternatively, traverse member  126  could be lowered with the held of pneumatic or hydraulic cylinders. When first lapping disc  16  is positioned relatively high within lapping machine  100 , plate  122  (rigidly coupled to first lapping disc  16 ) is elevated over dog columns  118  and is held by swivel-supporting bolts  128 . Unavoidable unbalancing forces can be dampened by providing lapping machine  100  with a heavy body  15  and through the use of conventional shock absorbers  130 . In this way, force G is provided to first lapping disc  16  through transverse member  126 , swivel-supporting bolts  128 , and flexibly adjusting bolts  128   a  such that first lapping disc  16  will self-set itself into a horizonal operational position. It should be understood that a spherical hinge, elastic element, etc. may be used instead of bolts  128   a.    
     FIG. 8 shows another embodiment of the present invention as a one-spindle lapping machine  200  which differs from lapping machine  100  in that it does not use driving shaft  124  and motionless spindle assembly  108  of FIG.  7 . Like lapping machine  100 , lapping machine  200  is used to rotate cassette  12  and to provide oscillations to first and second lapping discs  16 ,  18 . 
     Second lapping disc  18  oscillates on swivel-supported bolts  132 , although rubber-metallic supports, elastic bolts or planar rolling or sliding supports could be used. First lapping disc  16  is supported on swivel-supporting bolts  128  as discussed in respect of lapping machine  100 . The combination of these two support structures provides lapping machine  200  with a self-balancing mechanism. That is, even if the mass of first and/or second lapping discs  16 ,  18  change, balancing and correlation of the real dynamic eccentricities will be adaptively achieved during the course of operation of lapping machine  200  as a result of the relative masses of weights of first and second lapping discs  16 ,  18  (i.e. G 1  and G 2 ) and the sum of eccentricities e 1  and e 2 . Accordingly, there is no need to make adjustments to the individual parts of lapping machine  200 . 
     One disadvantage of lapping machines  100  and  200  is that as the height (or diameter) of workpieces  14  receiving treatment increases, there is a commensurate rise of oscillations transferred to body  15  of the lapping machines. This is a direct result of the rigid coupling of cranks pins  21  and  22 . 
     FIG. 9 shows another embodiment of the present invention as a two-spindle lapping machine  300 . Lapping machine  300  is used to rotate cassette  12  and to provide oscillations to first and second lapping discs  16 ,  18 . Lapping machine  300  uses separate eccentric crank pins  21  and  22  which independently rotate in their own naves  136  and  138 , respectively. Crank pins  21  and  22  are fixed on diving shafts  140 ,  142  held in first and second naves  144  and  146 . Second nave  146  is fixed on body  15  of lapping machine  300 , and first nave  144  is fixed on traverse member  126 . 
     In this configuration, separate motors with independent angular velocity can drive shafts  140 ,  142  of crank pins  21 ,  22  of first and second lapping discs  16 ,  18 . Unless it is desired to obtain different qualities of top and bottom planes of workpieces  14 , the rotation of crank pins  21  and  22  should be synchronized. A toothed belt gear with belts  148  and  150  is utilized to provide such rotation synchronization for crank pins  21  and  22 . Rotation of shafts of first disc spindle assembly  144  and second disc spindle assembly  146  with identical angular velocities is provided by motor of disc-drive motor M2 via shaft  152 . Simultaneously, first and second lapping discs  16 ,  18  are supplied with oscillations having eccentricities e 1  and e 2 , in antiphase. Further, spindle assembly  144  is coupled to first lapping disc  16  through a spherical hinge  254 . The combination of these supporting structures have the effect of reducing the amount of oscillation which is transferred to body  15  of lapping machine  300 , which is especially important in the case of larger workpieces  14 . 
     In order to provide lapping machine  300  with the ability to accommodate various-sized workpieces  14  (i.e. various distances between first and second lapping discs  16  and  18 ) without an commensurate increase of oscillations of the body  15  of lapping machine  300 , unbalanced weights  154  and  156  can be coupled to lapping machine  300 , as shown. Unbalanced weights  154  and  156  are selected in such a way so as to compensate for the centrifugal moments and forces. 
     Finally, as shown, sensor  74  and marking element  70  are installed within lapping machine  300 . Accordingly, it is possible to control the height of the finished workpiece  14  by setting the calibration instrumentation of sensor  74  to indicate when marking element  70  is a certain distance D away from sensor  74 , as previously described. 
     FIG. 10 shows lapping assembly  10  in use within a typically lapping machine. Specifically, a user loads a sufficient number of workpieces  14  into opening  24  of cassette  12  to approximately fill opening  24  but leaving sufficient unoccupied space so that workpieces  14  may freely circulate within opening  24 . Once workpieces  14  are positioned within opening  24 , first lapping disc  16  may be lowered and locked into position with second lapping disc  18 . In this position, the working surfaces  17 ,  19  of first and second lapping discs  16 ,  18  are brought into physical contact with the both surfaces of workpieces  14 . Cassette  12  is then rotated in relation to first and second discs  16 ,  18  and first and second lapping discs  16 ,  18  are provided with oscillatory motion. As previously discussed, the resulting motion causes workpieces  14  to circulate within opening  24 , such that working surfaces  17 ,  19  of first and second lapping discs  16 ,  18 , will be more evenly worn than is possibly using conventional lapping machines and lapping assembly  10  will provide even treatment to workpieces  14  on both sides. Once lapping is finished, first lapping disc  16  can be lifted and finished workpieces  14  removed from lapping assembly  10 . 
     Accordingly, lapping assembly  10  provides even treatment to both surfaces of a group of workpieces and effects even wear to the surfaces of lapping discs,  16  and  18 . Lapping assembly  10  allows a large number of workpieces  14  to be easily loaded and unloaded from opening  24  which results in a higher yield of treated workpieces  14 . In fact, it has been observed that lapping assembly  10  with first and second lapping discs  16 ,  18  and cassette  12  of diameter of approximately 300 millimeters can provide the same yield of treated workpieces  14  as a conventional socket-type planetary lapping machine with a diameter of 1500 millimeters. 
     Also, while conventional lapping machines only achieve optimally flat treatment for workpieces  14  when workpieces  14  are located at the outer extremes of cassette  12 , lapping assembly  10  provides even treatment of all workpieces  14  positioned within an opening  24 , due to the even circulation of workpieces  14  within cassette  12 . Finally, since lapping assembly  10  does not use tooth-like elements, the typical wear and tear on conventional planetary lapping machines which utilize gears having teeth does not effect the lifetime of lapping assembly  10 . 
     As will be apparent to persons skilled in the art, various modifications and adaptations of the structure described above are possible without departure from the present invention, the scope of which is defined in the appended claims.