Abstract:
Generating cutting processes for producing bevel gears and employing a single rotary disc cutter ( 36 ) wherein a portion of the generating cutting process effectively includes a reduction ( 38 ) of the workpiece roll angle ( 40 ) during generating thereby reducing or eliminating cutting action on the clearance side ( 42 ) of the rotary disc cutter.

Description:
This application claims the benefit of U.S. Provisional Patent Application No. 61/766,144 filed Feb. 19, 2013, the entire disclosure of which is hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The invention is directed to the production of gears and in particular to the generation of straight bevel gears utilizing rotary disc cutters. 
     BACKGROUND OF THE INVENTION 
     It is known to produce straight bevel gears, as well as skew bevel gears, face couplings and splined parts, by providing a pair of inclined rotary cutting tools whose rotating cutting blades effectively interlock to simultaneously cut the same tooth space on a workpiece. Examples of this type of machining can be seen, for example, in U.S. Pat. No. 2,586,451 to Wildhaber; U.S. Pat. Nos. 2,567,273 and 2,775,921 to Carlsen; U.S. Pat. No. 2,947,062 to Spear or in the company brochure “Number 102 Straight Bevel Coniflex® Generator” published by The Gleason Works. 
     Straight bevel gears may be formed by a non-generating process where the inclined tools are plunged into the workpiece to form a tooth slot with the profile surface of the tooth being of the same form as that of the blade cutting edge. Alternatively, tooth surfaces may be generated wherein the inclined tools are carried on a machine cradle which rolls the tools together with the workpiece via a generating roll motion to form a generated profile surface on the workpiece. In either instance, the tools may also include cutting edges that are disposed at a slight angle (e.g. 3°) to the plane of cutter rotation. Such an angled cutting edge, in conjunction with the inclination of the tools, removes more material at the ends of a tooth slot thereby resulting in lengthwise curvature of the tooth surface (i.e. lengthwise ease-off) for tooth bearing localization. 
     Bevel and hypoid gears can be cut in a single indexing process (face milling) or in a continuous indexing process (face hobbing). A basic cutting setup in the generating or cradle plane will put the center of the cutter head in a position which is away from the generating gear center (cradle axis) by the amount known as the radial distance. The silhouette of the cutter blades represents one tooth of the generating gear while the cutter rotates. Common face cutters for bevel gear cutting have several blade groups with each group having between one and four blades. Most common are alternating (completing) cutters with one outside and one inside blade. Peripheral cutter heads for the manufacture of straight bevel gears according to the above-described interlocking cutters method use only one kind of blades (e.g. outside blades) which have been used on conventional mechanical machines in the past. 
     On modern CNC machines, such as those machines known as 6-axis or free-form machines and disclosed by, among others, U.S. Pat. No. 6,715,566 the disclosure of which is hereby incorporated by reference, only one cutter from the above-discussed interlocking pair of cutters is used to cut a first tooth flank in a lower cutting position and, with the same cutter, also cut a second tooth flank in an upper cutting position in a single indexing process as disclosed in, for example, U.S. Pat. No. 7,364,391 the disclosure of which is hereby incorporated by reference. The cutting of the first flank faces the problem that material has to be removed not only on the cutting edge but also on the clearance edge of the blade. The result is high part temperature, poor cutting performance and low tool life. In a combined process, of vector feed and rolling, the clearance side of the blades during the first slot cutting can be moved away from the material which protects the clearance side of the cutting edge. However, a vector feed in straight bevel gear cutting has to use a very steep angle (only few degrees away from the blades center line) which makes the blade tip subject of severe chip removing loads. This leads to early failure of the blade tips and therefore results in low tool life. 
     Similar conditions occur if in a face cutting process only one kind of blades is used (e.g. inside blades only or full profile blades). The cutting blades will only be optimal on one side for high amounts of chip removal, which increases part temperature and reduces tool life. 
     SUMMARY OF THE INVENTION 
     The invention is directed to generating cutting processes for producing bevel gears and employing a single rotary disc cutter wherein a portion of the generating cutting process effectively includes a reduction of the workpiece roll angle during generating thereby reducing or eliminating cutting action on the clearance side of the rotary disc cutter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a conventional interlocking cutter arrangement. The upper cutter has cutting edges exposed on the top and the cutter axes are inclined such that the cutting edges represent the pressure angle of a generating rack profile. 
         FIG. 2  shows four views onto the cross-section in the middle of the face width of a straight bevel pinion with a peripheral cutter engaged. Only the lower cutter of  FIG. 1  is shown which has a horizontal orientation of the cutter axis. 
         FIG. 3  shows four views onto the cross-section in the middle of the face width of a straight bevel pinion with a peripheral cutter engaged. Only the upper cutter of  FIG. 1  is shown which has a horizontal orientation of the cutter axis. 
         FIG. 4  shows three views onto the cross-section in the middle of the face width of a straight bevel pinion with a peripheral cutter starting to engage in position  1 , the cutter being 50% engaged in position  2  and the cutter being fully engaged in position  3 . In spite of the rolling process, shown in  FIGS. 2 and 3 , the cutter is fed into the material along a linear path under a predetermined vector direction. 
         FIG. 5  shows four views onto the cross-section in the middle of the face width of a straight bevel pinion with a peripheral cutter engaged in a lower position as in  FIG. 2 . The work roll angle from the start work roll (position  1 ) to the position  3  has been reduced, the amount of reduction being proportional to the amount of work roll from the start. 
         FIG. 6  shows four graphics which accomplish in a reverse rolling mode (second pass of a double roll) the generation of the correct involute profile. After the sequence in  FIG. 5 , the flank profile is not the desired correct involute, which is caused by the work roll reduction. 
         FIG. 7  shows a cross section of the virtual cylindrical gear, which represents the straight bevel gear in its mean section. The cutter blade represents one side of the generating rack which follows the path marked with s Pitch  (or s 1 ) during the generation of the involute profile. 
         FIG. 8  shows the work and the cutter from  FIG. 7  rotated in clockwise direction by an angle α in order to receive a horizontal cutter axis.  FIG. 8  shows a number of radii and angles which are used in a set of proposed formulas to calculate the clearance side interference. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The terms “invention,” “the invention,” and “the present invention” used in this specification are intended to refer broadly to all of the subject matter of this specification and any patent claims below. Statements containing these terms should not be understood to limit the subject matter described herein or to limit the meaning or scope of any patent claims below. Furthermore, this specification does not seek to describe or limit the subject matter covered by any claims in any particular part, paragraph, statement or drawing of the application. The subject matter should be understood by reference to the entire specification, all drawings and any claim below. The invention is capable of other constructions and of being practiced or being carried out in various ways. Also, it is understood that the phraseology and terminology used herein is for the purposes of description and should not be regarded as limiting. 
     The details of the invention will now be discussed with reference to the accompanying drawings which illustrate the invention by way of example only. In the drawings, similar features or components will be referred to by like reference numbers. 
     The use of “including”, “having” and “comprising” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The use of letters to identify elements of a method or process is simply for identification and is not meant to indicate that the elements should be performed in a particular order. Although references may be made below to directions such as upper, lower, upward, downward, rearward, bottom, top, front, rear, etc., in describing the drawings, there references are made relative to the drawings (as normally viewed) for convenience. These directions are not intended to be taken literally or limit the present invention in any form. In addition, terms such as “first”, “second”, “third”, etc., are used to herein for purposes of description and are not intended to indicate or imply importance or significance. 
       FIG. 1  illustrates a conventional arrangement of a pair of inclined rotary disc cutters  2 ,  4  (commonly referred to as upper and lower cutters, respectively) having cutting blades  6  for cutting a tooth slot in a workpiece  8 . Upper cutter  2  is rotatable about axis  12  and lower cutter  4  is rotatable about axis  10 . In a generating process on a conventional mechanical cradle-style machine, the inclined cutters  2 ,  4  are usually fed into the workpiece to a predetermined depth and a generating roll of the machine cradle (not shown) is commenced in a synchronized manner with rotation of the workpiece  8  to generate tooth profile surfaces  14 ,  16 . 
     The cutters of  FIG. 1  comprise an interlocking cutter arrangement of rotary disc cutters. The upper cutter  2  has cutting edges  7  exposed on the top. The cutter axis  12  is inclined such that the cutting edges  7  represent the pressure angle of a generating rack profile. The blade edges  9  on the lower side of the upper cutter  2  are clearance edges, which are not sharp with respect to chip removal and therefore are not suited for participating in the cutting process. The lower cutter  4  has cutting edges  11  exposed to the bottom. The cutter axis  10  is also inclined by the same angle than the upper cutter  2  but in the negative direction. The blade edges  13  on the upper side of the lower cutter  4  are clearance edges, which are not sharp with respect to chip removal and therefore are not suited for participating in the cutting process. Since both cutters  2 ,  4  are oriented so as to provide an interlocking arrangement, every blade of the upper cutter  2  (with a cutting edge  7  on top) is followed by a blade from the lower cutter  4  (with a cutting edge  11  on the bottom). This type of blade interaction makes provides a completing process, with alternating blades which together cut both sides  14 ,  16  of one tooth slot in the workpiece  8 . During the generating rolling process, the two cutters  2 ,  4  are kept in their orientation to each other, while they swing around the generating gear axis which is the same as the cradle axis of an older cradle style mechanical machine. It should be understood that for the present invention, the center of roll position is the position where the cutters are symmetrically located within the tooth slot such as shown in  FIG. 1 . 
     The inventors have developed of a process that reduces or eliminates the clearance side cutting action on rotary disc cutters such as those shown at  2  or  4  in  FIG. 1  if single rotary disc cutters are used such as in the previously mentioned U.S. Pat. No. 7,364,391 for example. In the case of interlocking cutters as in  FIG. 1 , two separate cutters, one with cutting edges on the bottom side, the second with cutting edges on the top side are working simultaneously to remove chips from a tooth slot similar to alternating cutters. 
     However, If only one cutter is used in order to rough out a tooth slot and finish roll (i.e. generate) a first tooth flank, then a clearance side cutting action like that shown in  FIG. 2 , or a severe tip cutting action as shown in  FIG. 4 , occurs during the roughing portion of the cycle. 
       FIG. 2  shows four two dimensional views onto the cross section in the middle of the face width of a straight bevel pinion  20  with a peripheral cutter  22  engaged. Only one cutter (e.g. same as the lower cutter  4  of the two cutters in  FIG. 1 ) is shown having a now horizontal orientation of the cutter axis. This is the orientation in a free form machine (e.g. previously discussed U.S. Pat. No. 6,712,566 and U.S. Pat. No. 7,364,391) with horizontal cutter axis and horizontal work axis, which presents the axes configuration required to achieve a rolling process between tool and work with the same relative orientation between tool and work as it is in the mechanical machine with interlocking cutters. A free form machine with a single cutter spindle does not possess the ability to work with a pair of interlocking cutters. The problem therefore is the fact that one single cutter with only sharp cutting edges on one side  24  (i.e. the right side in  FIG. 2 ) has to rough out a tooth slot (cutting on both sides of the blades) and to finish cut (e.g. via a generating roll) a first tooth flank. This requires a form cutting action on the clearance side  26  of the blades.  FIG. 2  shows how the left side of the blades after the start work roll position (position  1 ) to the end work roll position (position  4 ) is continuously participating on the chip removing process. The cutting edges on the right side of the blades are formed sharp by a side rake angle of, for example, 4° to 12°. The left side of the blades is therefore dull due to a −4° to −12° side rake angle. The left sides of the blades are not well suited for chip removal which leads to poor cutting performance with high part temperature and low tool life. The original (i.e. theoretical) work roll rotation angle is equal the generating gear rotation angle times the ratio of roll (number of teeth on the generating gear/number of teeth on the workpiece). 
       FIG. 3  shows four two dimensional views onto the cross section in the middle of the face width of a straight bevel pinion  20  with a peripheral cutter  28  engaged (e.g. same as the upper cutter  2  of the two cutters in  FIG. 1 ) is shown but now with a horizontal orientation of the cutter axis. This can be the same cutter (i.e. cutter  22 ) that was used to cut in the lower position in  FIG. 2 , which can be repositioned by a free form machine in order to also cut and form the second flank. The problem of cutting action on the clearance side of cutting blades as noted in the lower cutting position does not occur in the upper position shown in  FIG. 3 . Since the slot roughing has already been performed in the lower cutting position, the process in the upper position is limited to finish rolling of the second flank. It is understood that the upper and lower positions could be exchanged. In such a case the lower position would be limited to finish rolling. 
       FIG. 4  shows three two dimensional views onto the cross section in the middle of the face width of a straight bevel pinion  30  with a peripheral disc cutter  32  starting to engage in the position  1 , the cutter being 50% engaged in position  2  and the cutter being fully engaged in position  3 . In spite of the rolling process, shown in  FIGS. 2 and 3 , the cutter is fed into the material along a linear path under a predetermined vector direction. The vector direction is chosen to take chip load away from the dull clearance side blade edge and move this chip load to the sharp cutting edge. The plunging process shown in  FIG. 4  is only suitable for the slot roughing. After plunging, a rolling and flank forming with the same cutter occurs in both the lower and the upper position. The vector feed plunging can move some chip load away from the clearance edge, however, it also directs a higher amount of chip load to the blade tips. Vector plunge roughing compared to a “roll only” process leads to a high blade tip wear and still is not capable of eliminating all cutting action on the clearance side blade edge. 
     The inventors discovered that in case of a “roll only” process (no rough plunging but slot roughing by rolling) the clearance side cutting action can be eliminated by reducing the amount of the work roll (rotation) angle. The work roll angle reduction is preferably achieved by reducing the rate of workpiece rotation (reduced with respect to an original theoretical amount) from the start roll position to and end roll position preferably not beyond the center roll position. A work roll reduction past the center roll position will cause an undercutting of the involute flank function, which makes it difficult in a second roll pass (double roll) to clean up the involute flank surface with a moderate set over. Optimal results can be achieved by utilizing a reduced work rotation rate (i.e. reduced with respect to an original theoretical work rotation rate) from the start roll position to the center roll position, preferably a position Δφi before the center roll position. The reduced work rotation rate is preferably constant from start roll to center roll positions, but may be varied in this interval. After the work roll reduction end position, the original, not reduced, rate of work rotation is preferably used. Most preferably, Δφi is a number between 0° and (end roll position—center roll position)/2. 
     The reduced work roll rate results in a form cut clearance side as shown in  FIG. 5  which provides enough clearance to prevent any clearance side cutting action. The amount of work roll rate reduction is preferably calculated such that enough material on the form cut clearance side is still present in order to form the second flank with a correct slot width in a second (upper) cutting step as shown in  FIG. 3 . 
       FIG. 5  shows four two dimensional views onto the cross section in the middle of the face width of a straight bevel pinion  34  with a peripheral cutter  36  engaged in a lower position such as in  FIG. 2 . The difference between  FIG. 5  and  FIG. 2  is a reduction  38  of the work roll angle  40  from the start work roll (position  1 ) to position  3 , the amount of reduction preferably being proportional to the amount of work roll from the start although disproportional amounts of work roll reduction are likewise contemplated. For example, in  FIG. 5 , a work roll reduction rate of −0.25 degrees per 15 degrees of roll motion is shown although the invention is not limited thereto. Thus, at position  3 , a work roll reduction angle of −0.75 degree has been achieved for a work roll angle of 45 degrees. At position  3  (which is near to the center roll position) the work roll reduction ends, which means that between position  3  and position  4  the change in work roll is exactly the value calculated (i.e. the original or theoretical amount) from the generating gear (cradle) rotation times the ratio of roll. 
     Rolling beyond the center roll position (from position  3  to position  4 ) while continuing with a reduced rate of work rotation will likely lead to an undercut of the root area and thus should be avoided. The work roll reduction between position  1  and position  4  rotates the left side  41  of the tooth slot away from the clearance side  42  of the blade  36 , such that the clearance side has no cutting contact during the entire roll of the first flank. The work roll reduction angle  38  has to be large enough to prevent cutting on the clearance side  42  of the blade  36 . However, a work roll reduction angle  38  that is too large will open the slot beyond the possibility to form a correct involute and achieve the proper slot width (no clean up in the following step). 
     After the rough rolling (where the blades have reached the root of the first flank) a set-over of the cutter versus the flank is performed in order to provide stock for a finish roll from root to top, as shown in  FIG. 6 . 
       FIG. 6  shows four two dimensional graphics which accomplish in a reverse rolling mode (second pass of a double roll) the generation of the correct involute profile. After the sequence in  FIG. 5 , the flank profile resulting from the work roll reduction  38  is not the desired correct involute. A set-over (which is a small clockwise work rotation Δε) towards the generated flank occurs which is followed by the reverse rolling (position  5  to position  8 ) which forms the correct profile from the bottom to the top. The set-over amount is between zero and a small amount (e.g. about 10% of the entire work roll reduction angle) to assure surface cleanup. Alternatively, the set-over amount may be a fixed amount (i.e. thickness) of stock material additionally removed from the tooth surface, such as, for example, 0.1 mm. 
     It should be understood that the “positions” shown in the Figures are for illustrative and explanatory purposes and the invention is not be limited to the number or location of the positions shown. 
       FIG. 7  shows a cross section of a virtual cylindrical gear  50  which represents a straight bevel gear in its mean section. The cutter disc  52  represents one side of the generating rack  54  (shown in the center of roll position) which follows the path marked with S Pitch  (or S 1 ) during the generation of the involute profile. In the example of  FIG. 7 , the cutter disc  52  has cutting edges  56  which are perpendicular to the axis of cutter rotation. Since the angle of the generating rack flanks is α, and the generating rack is horizontal, the cutter axis has to be inclined by α in order to simulate one flank of the generating rack. The distances S 1  and S Pitch  in  FIG. 7  are preferably identical. 
       FIG. 8  shows the work and the cutter from  FIG. 7  rotated in clockwise direction by an angle α in order to receive a horizontal cutter axis.  FIG. 8  shows a number of radii and angles which are used in a set of preferred equations to calculate the clearance side interference. The angle φ Int  indicates the angle of interference between the work material on the clearance side (as cut correctly by the tip of the blade). φ Int  is calculated from the work roll rotation (of the first cut point cut with the clearance side tip) and the location of the blades clearance point at the outside diameter in the center roll position. The interference angle is used for a work roll reduction between the left blade position and the right blade position in  FIG. 8 . 
       FIG. 8  shows one possibility for calculating the interference angle φ Int . The interference angle is the angular amount of material on top of the clearance side of the tooth slot which leads to interference with the clearance side of the blade.  FIG. 7  and  FIG. 8  represent the virtual cylindrical gear of a straight bevel pinion or gear which is calculated from the critical cross section (along the face width). The critical cross section is in mid face or at the heel. The shown calculation is based on the cross section in mid face. The virtual cylindrical gear approximates the profile relationships of the real straight bevel gear and it allows an observation of the profiles in a two-dimensional plane. This calculation is accepted as precise for profile observations and is known such as from, E. Buckingham,  Analytical Mechanics of Gears , McGraw-Hill Book Company Inc., 1949, pp. 324-328. Referring to the angles marked in  FIG. 8 , the following formulae can be applied: 
     Given:
     d 0  . . . mean pitch diameter   γ . . . pitch angle   h K  . . . addendum of real bevel gear   h F  . . . dedendum of real bevel gear   R Pitch  . . . pitch radius at mid face   R Top  . . . Outside radius at midface   R Root  . . . Root radius at midface   α . . . pressure angle of straight bevel gear   Δq . . . generating roll from start roll to center roll   RA . . . Ratio of roll between generating gear and work gear
 
 R   Pitch   =d   0 /(2 cos γ)  (1)
 
 R   Top   =R   Pitch   +h   K   (2)
 
 R   Root   =R   Pitch   −h   F   (3)
   

     from the relationship in  FIG. 8 :
 
 R   Top ·cos(φ 2 −α)= R   Root ·cos(φ 1 −α)  (4)
 
φ 1   =α+P   W /(2 R   Root )[rad]  (5)
 
Equation (5) into (4) delivers:
 
φ 2 =arccos( R   Root  cos(φ 1 −α)/ R   Top )+α  (6)
 
     from geometrical relationship in  FIG. 8 :
 
 S   1   =R   Top  sin(φ 2 −α)− R   Root  sin(φ 1 −α)  (7)
 
     The gearing law leads to the shifting of a trapezoidal generating rack tangential to the pitch circle of a gear blank (see  FIG. 7 ) in order to generate an involute tooth profile. The work gear rotation is equal to s/d 0  [rad] in order to achieve rolling without slippage between the pitch circle of the work gear and the pitch line of the generating rack. A rotation of the work and the cutter disc, drawn in  FIG. 7 , in clockwise direction by an angle α, results in the cutter-work relationship in  FIG. 8 . 
     S 1  is in the direction of generating gear shift. S 1  relates to φ WorkRoll  from start roll to center roll since it is equal S Pitch . 
     work roll angle from start roll to center roll:
 
φ WorkRoll   =S   1   /R   Pitch (generating law) [rad]  (8)
 
φ 3 =φ 2 −φ WorkRoll   (9)
 
φ 4 =α CL −(φ 1 −α)  (10)
 
φ 5 =φ 1 +φ 4 ( R   Top   −R   Root )/ R   Root   (11)
 
     Interference angle from relationship in  FIG. 8 , using (6) and (11):
 
φ Int =φ 2 −φ WorkRoll −φ 5   (12)
 
     Interference angle per φ WorkRoll  from start roll to center roll results in a sliding factor:
 
 f   Slide =φ Int /φ WorkRoll   (13)
 
     The sliding factor can be used to calculate modification of work roll angle depending on theoretical work roll angle:
 
Δφ= f   Slide ·φ WorkRoll   (14)
 
     The sliding factor can also be used to calculate a ratio of roll which will include the new sliding rotation in the work gear:
 
φ WorkRoll   =Δq·RA   (15)
 
φ WorkRoll   *=Δq·RA (1= f   Slide )  (16)
 
 RA*=RA (1+ f   Slide )  (17)
 
     In summary, it is possible to superimpose Δφ to the work roll angles as the process progresses, or to use RA* from start roll to center roll. The calculated angle Δφ will eliminate the severe interference but will not create any clearance between the blades&#39; clearance side and the blank material. In order to eliminate any clearance cutting edge contact by an additional amount, Δφ 0  has to be added to Δφ. Preferred values for Δφ 0  are 5% to 15% of Δφ(Δφ·0.05&lt;Δφ 0 &lt;Δφ·0.15)
 
Δφ Total =Δφ+Δφ 0   (18)
 
     The gear, shown in  FIGS. 7 and 8  is the virtual cylindrical gear of an observed straight bevel gear. The virtual cylindrical gear shows in a two-dimensional representation the same geometrical properties as the real straight bevel gear would show in a profile section (which of course would be a three-dimensional representation). The two-dimensional virtual cylindrical gear profile allows the application of trigonometric expressions in order to make the interference problem on the clearance side of the cutter blades visible and to allow a corrective angle (i.e. a corrective ratio of roll) to be determined. 
     Rotary disc cutters for the cutting of straight bevel gears generally use a dish angle. In case of a dish angle, the cutting edges are not perpendicular to the cutter axis. The cutter representation in  FIGS. 7 and 8  have been drawn without a dish angle. Since the presence of a dish angle changes the pressure angle α used in  FIGS. 7 and 8 , the graphic would be automatically adjusted to any dish angle introduction. This means also, that the formulas (1) through (16) apply for all dish angles, including 0°. 
     The calculation shown to determine a corrective work roll reduction is only one possible way to quantify a reduction angle which prevents clearance side interference. More complex calculations (e.g. the generation of the entire clearance side slot surface as it would be generated by the blades&#39; clearance edges and the comparison of this surface with the clearance side of the slot as it is formed by the entire clearance side of the blades ( FIG. 2 , position  4 )) may deliver more accurate results. However, the more precise calculation will not lead to an improved overall result, since a certain percentage of Δφ (mentioned as Δφ 0  above) has to be added in order to achieve clearance without any unwanted contact. 
     The inventive method may also be applied to bevel gear cutting processes with face cutter heads in those cases where only one kind of blades is used for slot roughing and finishing of one flank. 
     Although the invention has been explained and illustrated with respect to a reduction of the workpiece roll angle during generation of a tooth slot, it follows that the invention may also be achieved by an increase in the amount of roll movement of the rotary disc cutter (increased with respect to an original theoretical amount) during a portion of the generation of a tooth slot. 
     While the invention has been described with reference to preferred embodiments it is to be understood that the invention is not limited to the particulars thereof. The present invention is intended to include modifications which would be apparent to those skilled in the art to which the subject matter pertains without deviating from the spirit and scope of the appended claims.