Patent Publication Number: US-2010119321-A1

Title: Method and apparatus for controlled-fracture machining

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. §120 and is a continuation-in-part of U.S. application Ser. No. 12/520,785, filed Jun. 22, 2009, entitled “METHOD AND APPARATUS FOR NON-ROTARY MACHINING,” which claims priority to PCT Application Serial No. PCT/US2006/0602572, filed Dec. 22, 2006, now WIPO Publication No. W02008/079151A1, all commonly assigned to Tennine Corporation and which are herein incorporated by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     This invention relates generally to methods, machines, and tools for machining parts and, more particularly, to those performing profiling operations. 
     BACKGROUND 
     There are two basic machining operations that are well known in the art. These might be broadly categorized as “profiling” where material is removed from a workpiece to produce a specified shape and surface finish and “holemaking” where material is removed from a workpiece to produce a drilled, tapped, or counterbored hole. With regard to profiling, in order to profile a workpiece, there are three basic processes for removing material from a workpiece viz. deformation, electrolysis and ablation. Deformation is a process where a cutting tool removes material from a workpiece by direct contact. This process is the least restricted in the shapes and materials that can be cut by the cutting tool. The “turning” and “milling” processes are the most common examples of deformation. Electrolysis is a process where a cathode electrochemically dissolves material from an anodized workpiece. This process is restricted to electrically conductive materials. Electrochemical and electrical discharge machining are examples of electrolysis. Finally, ablation is a process where a beam of energy vaporizes or erodes material from a workpiece. The ablation process is limited to flat work that lacks the requirement for three-dimensional features. Laser and water-jet cutting are examples of the ablation process. 
     In order to remove material by deformation, or sometimes called “contact machining”, there are two basic mechanisms. The first is rotary motion in which either the cutting tool or the workpiece is fixtured to a spindle and rotated to provide sufficient force to remove material. In turning, the workpiece rotates as the cutting tool moves through it. Similarly in a milling process, the cutting tool rotates as it moves through the workpiece. The second is non-rotary motion in which neither the cutting tool nor the workpiece rotates and the force of the linear motion of the tool relative to the workpiece is sufficient to remove material. Shaping, planning, and broaching are examples of non-rotary machining techniques using deformation. 
     A problem associated with these types of prior art processes is that they do not include techniques for precisely and rapidly machining complex and/or extreme shapes out of ductile and brittle materials in mass production, mass customization, and make-to-order manufacturing environments. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying figures where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the present invention. 
         FIG. 1  is a block diagram illustrating a basic apparatus as used in an embodiment of the present invention. 
         FIG. 2  is a flowchart diagram illustrating the basic method of the present invention&#39;s operation. 
         FIGS. 3A and 3B  are diagrams of the linear and rotary motions of the cutting tool and table according to an embodiment of the invention. 
         FIGS. 4A ,  4 B,  4 C and  4 D are illustrations showing side and front views of axially asymmetrical cutting tools used according to an embodiment of the invention. 
         FIGS. 5A ,  5 B and  5 C are chart diagrams illustrating elastic, plastic, and controlled-fracture phases respectively of deformation. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Before describing in detail embodiments that are in accordance with the present invention, it should be observed that the embodiments reside primarily in combinations of method steps and apparatus components related to controlled-fracture machining. Accordingly, the apparatus components and method steps have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein. 
     In this document, relational terms such as first and second, top and bottom, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “comprises . . . a” does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. 
     The present invention defines a unique combination of rotary and non-rotary machining apparatus and processes. The effect of a combination of rotary and non-rotary mechanisms enables the present invention to remove material by controlled fracturing, which is the ideal level of deformation for the purpose of profiling. The process and apparatus as defined herein are not achieved by any other method of machining known in the prior art. 
     The invention, as defined herein, is unrelated to a process sometimes called “controlled fracturing”, in which a flat piece of material is scored by a laser to facilitate its later breakage into uniform pieces. The controlled fracturing process of the invention occurs when a material&#39;s yield strength and breaking strength are exceeded simultaneously. In other words, strain is instantaneous so there is no plastic deformation of the material being machined. Additionally, this also avoids attendant phenomena, like expansive heating and strain-hardening, which can chaotically complicate the machining process. Because prior art methods of contact machining are restricted to plastic deformation for removing material from a workpiece, complications are inherent in their operation and work to severely restrict performance in terms of productivity, precision, and applicability. 
     In order to avoid these shortcomings, the present invention&#39;s removal of material by controlled fracturing is useful for a number of reasons: 1) the present invention can remove material from a workpiece at a much higher rate by at least one or two orders of magnitude than prior art machining techniques; 2) the present invention mitigates and sometimes eliminates the chaotic effects of expansive heating and strain-hardening inherent in current methods of contact machining and so is more precise in the fit and finish it imparts to a part; 3) for the same reason, the invention can also produce shapes that are complex (e.g., highly curved airfoiling) and extreme (e.g., very thin cross-sections) that cannot be done using prior art machining methods; and 4) the invention is usable with materials, such as carbon fiber composites, which are typically too brittle for plastic deformation, i.e. their yield strength is identical to their breaking strength and so are difficult or impractical to machine by other prior art methods. Thus, a purpose of the present invention is to profile parts by means of contact machining more rapidly and precisely than existing art, including parts of shapes and materials that are impractical or impossible to profile with using machining techniques presently available in the art. 
       FIG. 1  is an illustration of a controlled fracturing apparatus incorporating elements of the present invention. The controlled fracture machining apparatus  100 , as seen in  FIG. 1 , works to profile parts by means of contact machining This type of machine has greater precision and operates more rapidly to machine products having shapes and using materials that are impractical or impossible to profile with machines existing in the prior art. 
     More specifically, the controlled-fracture machining apparatus  100  includes one or more non-rotating cutting tools  101  fixtured at or near the outer circumference of a turret  102 . The tool may be attached to the turret by tool holders used with CNC lathes and the like. The rotation of the turret  103  operates to provide sufficient cutting force to achieve deformation by controlled fracturing as defined herein. In operation, one or more tables  104  are placed on an upper surface of a base  111 . Although the table  104  is shown in a substantially rectangular configuration, it will be evident to those skilled in the art that other shapes and sizes of table are also possible. At the top surface of the table  104 , a workpiece  105  is fixtured so that when the table  104  moves under the turret  102 , the circumferential movement of the cutting tool(s)  101  can engage the workpiece(s)  105  to remove material. As will be evident to those skilled in the art, each cutting tool  101  and each table  104  can move independently along separate sets of linear and/or rotary axes  106 , 107  within a three-dimensional work envelope. Those skilled in the art will recognize that mechanisms (not shown) are embedded in the turret  102  and in the base for moving the turret and table along the axes shown in  FIGS. 3A and 3B  as described herein. This has an advantage of allowing the cutting tool  101  and workpiece  105  to be offset from the arc of the turret&#39;s rotation  103 . The cutting tool  101  then works to remove material by cutting the workpiece  105  into any desired shape. 
     Additionally, a programmable controller  108  is used to produce the tool paths required for specific movements while a support mechanism  109  operates to synchronize the rotation  103  of the turret  102  with the movements along the rotary axis  106 , 107  of each cutting tool  101  and each table  104 . Although motors for the turret that provide driving motion as will as servos or linear drives used to provide positioning motions of the tool and the table are not shown, these devices are controlled by the programmable controller  108  and will be evident to those skilled in the art. Moreover, one or more microprocessors are used in combination with the programmable controller  108  along with software and other computer readable code to control tool path movement. The apparatus  100  is advantageous in that it uses no rotary motion that would impose axial symmetry upon the contour of either the cutting tool  101  or the workpiece  105 . Finally, these elements are configured so that the present invention is superior to all other methods and apparatuses of contact machining in productivity, precision, and applicability. 
       FIG. 2  is a flowchart diagram illustrating the basic method of the present invention&#39;s operation. The method of operation  200  of the invention includes the steps where the process begins with the apparatus at rest  201 . The workpiece is fixtured to the table  202  while the cutting tool is fixtured to a turret  203 . The turret rotates to provide the cutting tool with sufficient force to remove material from the workpiece, preferably at a magnitude that achieves controlled fracturing  204 . The table and the cutting tool both can move to a position for engagement of the cutting edge  110  of cutting tool with the workpiece  205 . The cutting tool and the table move simultaneously and continuously along their own sets of linear and/or rotary axes as needed to offset the cutting edge of the tool from the arc of the turret&#39;s rotation to machine the workpiece to the specified interim shape  206 . This is repeated as needed until the specified final shape to be produced by the cutting tool is achieved  207 . The table and the cutting tool (if necessary) retract to disengage the cutting tool from the workpiece  208 . If further machining is required, steps  203  through  208  are repeated with different cutting tools until machining is completed  209 . The turret stops  210  and the workpiece is removed from the table  211 . The process ends with the apparatus at rest  212 . 
     In that the turret  202  can act as a fixture for multiple cutting tools  203  and multiple workpieces can be placed on tables around the turret  202 , variations upon the operation  200  of the controlled-fracture machining apparatus are also possible. For example, one variation is using both identical cutting tools and identical workpieces so that each rotation of the turret  202  completes not just one cut on one workpiece but as many cuts on each workpiece as the number of cutting tools fixtured to the turret  202 . Therefore, if twelve cutting tools are engaged with twelve workpieces  205 , then each rotation of the turret  202  cuts at a rate twelve times faster for each of the twelve workpieces  206 . The result is that productivity of each rotation is increased, compared to a single tool cutting a single workpiece, by a multiple of the number of cutting tools times the number of tables. This facilitates mass production of a part. 
     Another variation is that all of the workpieces are identical, but the cutting tools differ to perform different operations on the workpieces  206 . For instance, the turret is fixtured with both tools for roughing and finishing the workpieces  203 , so that in the same rotation they are “roughed in” and then finished to the final shape  207 . The productivity gain would be similar to that above. As described herein, this type of operation greatly facilitates mass production of a part. 
     A third variation is that the workpieces differ and are set up on the tables as a family of parts that can be machined with the same set up of cutting tools  203 . Because the offsetting movements of each cutting tool and each table are independent of the others, the path of each cutting tool through each workpiece  206  can be altered as needed to produce a finished shape  207  unique to that part. This facilitates mass customization and make-to-order production of parts with the productivity of mass production. 
     Thus, the present invention employs two types of motion. The first is motion to drive the cutting tool through the workpiece with sufficient force to cause material deformation. This is a circumferential driving motion  103  and described with regard to  FIG. 2 . The second is motion to position the cutting tool and the workpiece relative to each other and to the path of the driving motion. This directs the deformation of the workpiece into the shape and finish specified for the completed part. This is the positioning motion as described with regard to  FIG. 2 . 
     The driving motion is produced by the rotation of the turret to which the cutting tool is attached. The cutting tool is static relative to the driving motion—i.e., its cutting edge does not rotate about an axis as does a milling tool. Therefore, the cutting tool removes material from the workpiece at step  206  in a manner superior to that of a milling tool in terms of productivity, precision, and applicability as disclosed in the Tingley invention. The present invention is distinguished from the Tingley invention in that it embodies a rotary driving motion to deliver sufficient cutting force to a static tool at step  204 . By means of this relationship between a rotary driving motion and a static cutting tool, axial symmetry is not imposed upon either the cutting tool or the workpiece and so allows for a nearly unrestricted range of shapes and materials to be machined as described in  FIG. 2 . This relationship for contact machining is unique to the present invention and not known in prior art. 
     By its nature, a rotary driving motion imposes a circular or arced tool path upon the cutting tool. Without further modification, the cutting tool could only machine into the workpiece a curve of a fixed radius. The positioning motions of the present invention offset the cutting tool and the workpiece from the arc of the driving motion so that any combination of segments and curves in three-dimensional space can be machined into the workpiece Furthermore, these positioning motions also change the orientation of the tool&#39;s cutting edge  110  relative to the surface to be cut into the workpiece for optimizing the performance of the cutting tool  101 . These positioning motions are produced, at a minimum, by moving the cutting tool along a set of linear and rotary axes  106 . This can be improved, in terms of speed and range of possible tool paths, by also moving the table, to which the workpiece is attached, along its own set of linear and rotary axes  107 . By this means a static cutting tool can profile a three-dimensional part as disclosed in the U.S. application Ser. No. 12/520,785 and not otherwise known in prior art. Again, the present invention is distinguished from the prior art in that the present invention embodies a turret utilizing a rotary driving motion  103 , from which the cutting tool and workpiece must be offset by the positioning motions via independent sets of axes  106 ,  107 . 
       FIGS. 3A and 3B  are diagrams illustrating both the linear and rotary motions of the tool and table respectively according to the embodiments of the present invention. As seen in  FIG. 3A , the present invention&#39;s axes of motion  300  determines the tool path that the cutting tool will take through the workpiece. Accordingly, there are eleven linear axes  301 ,  302 ,  303 ,  307 ,  308 ,  309  and rotary axes  304 ,  305 ,  306 ,  310 ,  311  of motion that are possible for the present invention. The conventions and mechanisms of the linear and rotary axes  106 ,  107  for positioning the cutting tool as seen in  FIG. 3A  and the table as seen in  FIG. 3B  will be evident to those skilled in the art. A primary feature of the invention involves using the rotary driving motion as a linear tool path axis which is neither shown nor suggested in the prior art.  FIG. 3A  illustrates the X-axis  301  of the cutting tool while the linear axis radial to the X-axis  301  is the Y-axis  302  of the cutting tool. The turret&#39;s rotation  103  provides motion along X-axis  301  while the rotary axis  106  provides motion along Y-axis  302  though rotary axis  306 . The linear axis perpendicular to the plane is defined by the X- and Y-axes  301 ,  302  is the Z-axis  303  of the cutting tool. The rotary sweep of the cutting tool around the X-axis  301  is the A-axis  304 . By a similar convention, the sweep around the Y-axis  302  is the B-axis  305 , and around the Z-axis  303  is the C-axis  306 . 
     Those skilled in the art will recognize that a control mechanism (not shown), located within the turret  102 , positions the cutting tool relative to the workpiece by motion along the Y-, Z-, A-, B-, and C-axes to produce the specified shape and finish of a part. The parallel linear axes of the table are illustrated as the U-, V-, and W-axes  307 ,  308 ,  309  respectively. Because the A-axis  304  motion of the cutting tool is sufficient for positioning in all cases, the table  104  does not necessarily require a parallel positioning axis. Therefore, the parallel rotary axes of the table  104  are illustrated as the E- and F-axes  310 ,  311 . Further, a control mechanism (not shown) located inside the base  111 , positions the table  104  relative to the cutting tool  101  by motion along the U-, V-, W-, E-, and F-axes to produce the specified shape and finish of a part. The rotary axis  107  provides motion along W-axis  307  though F-axis  311 . The “plus” and “minus” directions of all these axes  300  accord to the conventions known to skilled artisans familiar with machining apparatus and processes. 
       FIGS. 4A ,  4 B,  4 C and  4 D are illustrations of the side and front views respectively of axially asymmetrical cutting tools as used with the invention. The present invention&#39;s configuration of driving motion and positioning motions as described in step  206  of  FIG. 2 , avoid the need to rotate either the cutting tool or the workpiece about an axis. This eliminates the imposition of axial symmetry upon either cutting tool or workpiece. The practical effect of this is that the present invention can employ a cutting tool  101 , as detailed by the examples in  FIGS. 4A ,  4 B,  4 C, and  4 D. In these illustrations, tool  400  and tool  410  are cutting tools having a body  401 ,  411  and an extension  403 ,  412  that are axially asymmetrical, i.e. they do not have the same shape on opposite sides of the tools. The cutting tools include a cutting edge  402 A,  402 B, for the purpose of removing material from the workpiece as described with regard to  FIG. 2 , which may be either integral to the extension  403 ,  412  or inserted therein. Both tools  400 A,  400 B and  400 C,  400 D include tapered, recessed, or angled reliefs along the body allowing the tool to remain clear of features previously cut into a workpiece while retaining the tool&#39;s rigidity. These reliefs  413 ,  414  allow the tool to create an undercut for three-dimensional or other complex features that are either impractical or impossible in other methods of contact machining. 
       FIGS. 5A ,  5 B and  5 C are charts illustrating the nature of the elastic, plastic, and controlled-fracture phases of deformation. As seen in these charts, depending upon the cutting force of the driving motion  103 , the present invention removes material from the workpiece by either plastic deformation  504  or controlled fracturing  523 . In both cases, it does so at volumetric rates of material removal one or two orders of magnitude greater than that of existing art. However, controlled fracturing  523  is the superior process, because it mitigates or eliminates the expansive heating and strain-hardening that characterize plastic deformation  504 . These effects cause difficulties in the machining process by degrading speed and precision; limiting the range of shapes and materials that can be machined; shortening machine and tool life; and destabilizing production with unpredictable factors. To the extent that the cutting force that the present invention applies to the material of a workpiece approaches instantaneous strain  521 , and achieves controlled fracturing  523 , the period of plastic deformation  504  is reduced and so are its adverse effects. 
     As described herein, controlled fracturing  523  offers the ideal level of deformation in a profiling operation, and is the process of contact machining that works to achieve certain predefined goals. As seen in each of  FIGS. 5A and 5C , deformation of a ductile material occurs at three levels  503 ,  504 , and  523 . The first level is elastic deformation  503 , in which the material will return to its original shape once it is relieved of stress. If the stress exceeds the material&#39;s yield strength  501 , then the second level, plastic deformation  504 , is reached and the material is permanently deformed. The continued application of stress to a plastically deformed material will cause strain to accumulate  505  until it exceeds the material&#39;s breaking strength  502  allowing it to rupture  506 . For the methods of contact machining in existing art, this level of deformation is the best that can be achieved and is observed as the cutting tool operating to separate irregularly chipped material from a workpiece. 
     Generally, the longer it takes strain to accumulate  505 , the greater are the effects of expansive heating and strain-hardening, and the more severe is the resulting chaos in the material removal process. Therefore, reducing or even eliminating the time it takes the accumulation of strain  505  to rupture  506  a material is desirable. Thus, the ideal is instantaneous strain  521 , in which a material&#39;s yield strength  501  and breaking strength  502  are exceeded at the same time. This, in effect, makes a ductile material  500  behave like one that is brittle  510 , in which no plastic deformation  504  occurs as a cutting tool removes material from a workpiece, as seen in  FIG. 5B . Instead of pulling a material apart by rupturing it  506 , the force of the cutting tool cracks  522  the workpiece along lines of fracture to separate pieces of material, as seen in  FIG. 5C . This process is termed “controlled fracturing”  523 , which is the third level of deformation. The shape, orientation, and direction of the tool&#39;s cutting edge  110  determine how the material will fracture  522  by concentrating the heat generated from the cutting tool&#39;s  101  contact with the workpiece into adiabatic bands emanating from the perimeter of the cutting edge in the direction of the cutting tool&#39;s motion. The heating within these bands causes micro-cracks to form which then connect under the continued stress of the cutting force and fractures material loose from the workpiece along a line conforming to the perimeter of the cutting edge. The present invention controls these cutting tool factors to produce the desired shape and finish without the adverse effects of plastic deformation  504  that limit the performance of all other methods of contact machining in existing art. 
     In use, there are many possible configurations of the essential elements of the apparatus  100  and the motions  300  it can produce to execute the basic method  200  of the present invention and its variations. These include vertical and horizontal layouts of the turret; axial and radial orientations of the cutting tool and table to the turret; multiple cutting tools and multiple tables; partial to full sets of linear and rotary axes for positioning the cutting tool and the table; a double- or multiple-turret layout moving cutting tools along a belt- or chain-driven rail system that translates the rotary driving motion of the turrets into long linear drives for machining very large workpieces or very large numbers of workpieces; workstations integrated into the apparatus to perform non-profiling operations such as holemaking; incorporation of automation technologies with the apparatus such as probes, tool changers, and pallet systems; among other things. In one embodiment of the invention, the stylized illustration of the apparatus  100  shown in  FIG. 1  will include features where 1) the axis of the turret  102  is vertical to the base  111 ; 2) each cutting tool  101  is fixtured axially to the circumference of the turret  102 ; 3) the work surface of each table  104  is perpendicular to the axis of the turret  102 ; 4) twelve cutting tools  101  and twelve tables  104  may be uniformly located around the circumference of the turret  102 ; 5) each cutting tool  101  has a separate mechanism (not shown) for positioning on the Y-, Z-, A-, B-, and C-axes  302 ,  303 ,  304 ,  305 ,  306 ; 6) each table  104  has a separate mechanism for positioning on the U-, V-, W-, E-, and F-axes  307 ,  308 ,  309 ,  310 ,  311 ; and 7) probes, a tool changer, and a pallet system, known in prior art, are incorporated into the apparatus  100  to automate production. 
     Thus, the present invention as described herein employs a rotary driving motion  103 , positioning motions via axes  300 , and axially asymmetrical tooling  400 ,  410  used in a manner, not known to prior art. The invention makes possible a controlled fracturing process used on various materials used to profile parts. Consequently, the present invention is superior to the existing art for profiling machining operations in terms of: 
     1) Volumetric material removal rate: As described in U.S. Application Serial No. 12/520,785, the effective feed rate of the cutting tool through the workpiece is its surface footage for a given material. When restricted to plastic deformation, this can produce a volumetric material removal rate of approximately 40 times greater than milling in a profiling operation. Because the present invention uses a rotary driving motion to achieve controlled fracturing for removing material and so reduces or eliminates expansive heating, strain hardening, and friction, the feed rate of the cutting tool can exceed its generally accepted surface footage. Therefore, the volumetric material removal rate of the present invention in the controlled fracturing mode can be two orders of magnitude greater than milling; 
     2) Productivity: The present invention significantly increases the rate of production, compared to existing art, commensurate with its increased volumetric material removal rate. This is further enhanced with the preferred embodiment of the invention, which includes multiple cutting tools and multiple tables. As previously stated, these multiple workstations increase productivity by a multiple of the number of cutting tools times the number of tables. For example, with twelve of each, productivity is increased by as much as 144 times over a setup of a single cutting tool and single table. Combined with the present invention high volumetric removal rate of at least forty times greater than milling, such an embodiment of the present invention would have a productivity that is as much as 5,760 times greater than a milling machining center making the same part; 
     3) Precision: Because the process of material removal for contact machining in the existing art is plastic deformation, the accumulation of strain generates expansive heat and strain-hardening in the cutting tool and the workpiece. This increases the chaotic elements in a profiling operation, which reduces the dimensional precision of the shape being produced. It is the primary cause of process failure, usually by tool breakage. The present invention mitigates these adverse effects by significantly reducing the accumulation of strain, ideally to the point of instantaneous strain to achieve controlled fracturing. Precision is further enhanced because neither the cutting tool nor the workpiece is rotating on axis, as in the case of milling and turning respectively. The absence of this extra motion eliminates the imprecision caused by imperfections in the mechanism and operation of a spindle necessary to provide that rotation; 
     4) Finish: For the same reasons stated above, the surface finish that the present invention imparts to the part is improved. Furthermore, the present invention uses axially asymmetrical static cutting tools. Because they are axially asymmetrical, such tools can feature cutting edges that match the geometry of the specified shape. Because they are static, they can keep that edge continuously in cut in the workpiece. The result is a far more stable removal of material, compared to the discontinuous chipping of material by the rotating flutes of an end mill Thus, the present invention produces a smoother and cleaner surface finish on the part; 
     5) Range of machinable materials: The present invention can machine all materials that the existing art can. Furthermore, it can readily machine materials that are extremely difficult or impossible to machine by the existing art. In one category of such materials are heat-resistant alloys, nickel alloys, and titanium alloys. The heat that current methods of contact machining generate in these materials by plastic deformation becomes uncontrollable and leads to process failure unless the volumetric rate of material removal is kept very low. In another category are brittle materials, such as carbon-fiber composites, which tend to shatter  512  instead of rupture  506  when the cutting force applied by current methods of contact machining exceeds its breaking strength. This leads to uncontrolled fracturing  513  of the material in the form of splitting, cracking, and delamination beyond the area of the cut. The present invention overcomes these limitations in the existing art by achieving controlled fracturing in both categories of materials; and 
     6) Range of machinable shapes: For the same reasons stated above, the present invention can machine a greater range of shapes than the existing art. The elimination of excessive heating and uncontrolled fracturing makes it possible for the present invention to machine very thin cross-sections and other delicate features. Furthermore, the present invention&#39;s use of axially asymmetrical tools within a three-dimensional work envelope allow it to machine undercut features of nearly unrestricted geometry that are impossible with the existing art. 
     In the foregoing specification, specific embodiments of the present invention have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present invention as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of the present invention. The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims. The invention is defined solely by the appended claims, including any amendments made during the pendency of this application and all equivalents of those claims as issued.