Method for selecting and implementing cutting conditions in machining a workpiece
BACKGROUND OF THE INVENTION 
     This invention presents an improvement in the machining art by increasing the ability of the tool operator to select and implement reasonable cutting conditions for any of a variety of materials on machine tools of differing horsepower. This invention lends itself to either manually, or numerically, controlled machining. The term &#34;numerical control&#34; is considered herein as encompassing the control of the operation of a machine tool in response either to directions programmed in machine language on a reuseable programming medium (e.g., a punched tape, a magnetic tape, a floppy disk) or to directions stored in the memory of a computerized numerical control machine tool. 
     However, regardless of whether the machining has been manually controlled or numerically controlled, the selection of the cutting conditions has historically been done in a manner, which underutilizes the capabilities of the machine tool. Thus, directions given to a machine tool operator or introduced into a numerical control program by a programmer will, depending upon the type of machining operation being performed, the material being machined, its hardness and condition and the material of the cutting tool, be based upon recommended values for speed, feed and depth of cut (DOC). These recommended values [as well as selection of cutting fluid, tool geometry (i.e., tool attitude relative to the workpiece) and general information for calculating the power required for the particular operation] are determined from handbooks, such as the Machining Data Handbook [2nd Edition, Machining Data Center, Metcut Research Associates Inc., Cincinnati, Ohio (1972)]. Such an approach has built-in rigidity and the values for speed, feed and DOC provided in this way are, unfortunately, unnecessarily conservative and can result in severe underutilization of the machine tool. The problem is compounded by the fact that many part-programmers (i.e., individuals charged with programming the machining of a part to be made) are not skilled in machining technology. 
     The process of this invention addresses the present problem of machine tool underutilization by enabling the iterative determination of cutting conditions for the particular machining operation (i.e., roughing or finishing) that will, while satisfying certain constraints, more fully utilize the machine tool selected. Further, this process, although it employs simple calculations for the determination of feed and DOC such that a trained operator can carry out the requisite computations and manually adjust the machine tool as appropriate, offers in the case of a numerically controlled machine tool the highly desirable option of placing the programming task in the hands of the machine tool operator. 
     Thus, the iterative method of this invention for selecting and implementing the cutting conditions for each of a series of machining operations to be executed in sequence to manufacture a given part can be made part of an overall computer-aided process. In such a process, once a part has been designed, the machine tool operator charged with producing the part can draw the part (or component thereof) using interactive graphics, divide the part into elements, select the sequence of machining operations, select the cutting conditions, write a numerical control program and then execute it with the machining operations being carried out by the machine tool in accordance with the program. It is expected that in addition to the advantage of better machine tool utilization, the placement of the aforementioned tasks under the control of the machine tool operator will result in increased productivity and reduced costs. 
     DESCRIPTION OF THE INVENTION 
     An iterative method is provided by which a machine tool operator can determine those values for feed and DOC that are consistently effective in the machining of any of a variety of materials on different size machine tools. Once the constraints defined herein have been applied, settings for the resulting values of feed and DOC can be imposed on the machine tool manually by the operator via means for adjusting the feed and means for adjusting DOC. Alternatively, in place of employing manual adjustment of feed and DOC, these adjusting means may be automatically repositioned via control devices responsive to a programming medium, such as a numerical control tape prepared in, or converted to, machine language. The medium programmed with the final feed and DOC data for the part to be machined is downloaded to a controller at the machine to set the cutting conditions for a given number of passes to produce a given change in workpiece configuration. 
     The method is carried out in iterative fashion by applying a series of constraints fixing maximum and minimum feeds and maximum and minimum DOC-to-feed ratios. Final feed and DOC are determined so as to satisfy the constraints with no change in horsepower (HP) requirements. For satisfying the conditions imposed the final feed (f f ) should be equal to √d i  f i  /L and final DOC (d f ) should be equal to √d i  f i  L where L=(d/f) max  and f i  and d i  are the initial feed and initial DOC, respectively, selected after satisfying the minimum (or maximum) feed criterion and the HP requirement. 
     To initiate determination of the feed and DOC for turning, milling, boring or other operation, certain data must be selected or calculated to enable the calculation of the first approximation of feed from the formula: ##EQU1## where 
     HP c  is the horsepower at the cutting edge of the tool insert 
     V is the cutting speed 
     d is the first approximation of DOC and 
     uhp is the unit horsepower 
     HP c  will have a value much smaller than the motor horsepower with the difference representing transmission losses and the power needed to offset the additional load imposed as the tool insert wears. The value of f determined as a first approximation is then compared to the allowable range of values of feed bracketed by f min  (the smallest allowable value for feed) and f max  (the largest allowable value for feed). The type of machining operation (i.e., rough or finish) is determinative of the feed constraint. Thus, f min  is dependent on the value of the minimum cut such that any smaller cut will result in excessive rubbing between the tool and the workpiece and f max  is related to the permissible roughness of the surface produced. The value of the former depends upon both the nose radius of the tool insert and the side cutting edge angle (SCEA); the value of the latter on the nose radius (R) of the tool insert (i.e., feed is proportional to √R×R a , where R a  is the arithmetic average of the finish required). 
     If f is less than f min , then the value of f is increased to the value of f min  and this becomes the initial value of feed, f i . The value of d (first approximation of DOC) will have been determined based on shape of the cutting insert to be used, diameter of the circle that can be inscribed on the insert viewed in plan, the nose radius and the SCEA at which the insert is to be used. 
     Next, an initial value (d i ) of d is set using the relationship: 
     d i  f i  =df where the value of f i  is f min   
     d i  =df/f min . 
     The value of d i  is used to calculate (d i  /f i ) for application of the next criterion, the allowable range of pre-set DOC-to-feed ratios. If (d i  /f i )&gt;(d/f) max , then the value of feed tentatively considered the final value (f f ) is obtained by increasing the value of f i  using the relationship: ##EQU2## where L is (d/f) max  and the value of DOC tentatively considered the final value (d f ) is obtained by decreasing d i  using the relationship: ##EQU3## where L is (d/f) max . 
     If the first approximation of feed (f) is greater than f max , then the value of f is reduced to the value of f max  and this becomes the initial value of feed, f i . 
     Next, the value of d i  is determined from the relationship: 
     d i  f i  =df where the value of f i  is f max   
     d i  =df/f max  and d has the value of its first approximation 
     If (d/f i ) has a value less than (d/f) min , (d/f i ) is given the value of (d/f) min . Because the previous condition applies, d is equal to d max  and cannot have a greater value. It is, therefore, necessary to decrease the value of the feed further such that f f  =d/(d/f) min . The final DOC (d f ) has the value of d. 
     If the value of the first approximation of feed (f) is equal to or greater than f min  and is equal to or less than f max  and if the first value of the DOC-to-feed ratio is equal to or greater than (d/f min ) and is equal to or less than (d/f max ), then no change in the values of f and d is needed. 
     In case it was necessary to reduce f (as where f was greater than f max  or where (d/f i ) had a value less than (d/f) min , the horsepower available at the cutting edge of the insert will not be used to the fullest extent, if these values of feed and DOC are used. If the cutting insert is capable of use in the machining operation at a higher speed (e.g., when aluminum is being machined with a carbide tool insert) and if the machine is capable of operating at a higher speed (V), the operator has the option of doing so. If the option of operating at higher speed is selected, then the foregoing analysis is repeated with the new value of V. 
     Next, knowing the thickness of stock to be removed from the workpiece (d s ) and the final DOC (d f ) the requisite number of machining passes can be determined (number of passes=d s  /d f ). If the value so determined does not have an integer value, then the number of passes should be increased to the next larger integer number and a new DOC (d new ) and new feed (f new ) are determined. The new feed is either d new  /(d/f) min  or d f  f f  /d new , whichever is smaller. However, f new  should not be less than f min  or greater than f max . Under extreme conditions, i.e., when f new  is less than f min  or greater than f max , it is possible that d new  /f new  can be less than (d/f) min  or greater than (d/f) max . This result would violate the general rule that the DOC-to-feed ratio should be equal to or greater than (d/f) min  and equal to or less than (d/f) max . It then becomes a matter of operator judgment as to whether the deviation from the general rule would result in detrimental effects. 
     Having arrived at realistic values for the feed and the DOC to be used, the operator can now reposition the DOC to reflect the operating conditions selected and proceed with the machining operation. In place of employing manual adjustment, if the machine tool is so equipped, these adjusting means could be automatically repositioned once the operator has introduced this operating information into the machining program. With conventional numerical control this is accomplished by having the operator generate the program for machining on numerical control tape, verify the accuracy of the punched tape and then feed the properly punched tape into the controller, which executes the program by actuating servo units that reposition the aforementioned adjusting means. Similarly, in the case of the more advanced computerized numerical control the data on feed and DOC is stored (usually by reading a punched tape) as part of the machining program in a memory residing in the machine tool. When the system is actuated, the program downloads to the controller for execution of the program including actuating of the servo units that reposition the means for setting feed and DOC. 
     By this invention it now becomes feasible to incorporate in the software of the controller the knowledge of the process planner, the production engineer and the part-programmer and supplement this data with the operator&#39;s experience in the determination of the most feasible cutting conditions. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     The features of this invention believed to be novel and unobvious over the prior art are set forth with particularity in the appended claims. The invention itself, however, as to the organization, method of operation and objects and advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying drawing wherein: 
     FIG. 1 is a tool table setting forth the formulas for determining the first approximation of DOC for a series of commonly used tool inserts shapes; 
     FIG. 2 is a schematic view in plan of a rotating workpiece being machined showing the tool insert positioning relative thereto; 
     FIG. 3 is a schematic view partially in section showing cutter and tool insert positioning in a milling operation; 
     FIG. 4 is representative of the manner in which ranges of feed and DOC-to-feed ratios representing the constraints applied in the practice of this invention are graphically displayed; 
     FIG. 5 is a flow diagram schematically representing the sequence by which feed and DOC adjustments are implemented in numerical control by programmed tape; and 
     FIG. 6 is a flow diagram schematically representing the sequence by which feed and DOC adjustments are implemented when computerized numerical control is employed. 
    
    
     MANNER AND PROCESS OF MAKING AND USING THE INVENTION 
     Determining The Horsepower Required At The Cutting Edge Of The Insert 
     Reference to the data (e.g., Machine Characteristics Table) supplied by the machine tool manufacturer will provide the horsepower of the machine tool (HP) and the machine utilization factor (η) based on continuous operation. A typical value for η is 80%. The product of these two quantities (HP×η) provides a measure of the horsepower available at the spindle. 
     Next, the tool wear correction factor (C w ) is determined from the relationship: ##EQU4## This expression is based on the assumption that the expenditure of cutting force increases by 10% for every 0.010 inch of flank wear on the tool insert. An exemplary source of data for the tool wear criterion is TABLE I, which is an excerpt from page 212 of the text &#34;The Machining of Metals&#34; by Armarego and Brown [Prentice-Hall, Inc. (1969)]. Similar data can be obtained in other machining textbooks or from handbooks such as the aforementioned Machining Data Handbook. 
     
                       TABLE I
______________________________________
w (inches)* Tool          Remarks
______________________________________
0.030       Cemented carbide
                          Roughing passes
0.010-0.015 Cemented carbide
                          Finishing passes
0.060 or total
            H.S.S.        Roughing passes
destruction
0.010-0.015 H.S.S.        Finishing passes
0.010-0.015 Cemented oxides
                          Roughing and
                          finishing passes
______________________________________
 *Maximum tolerable flank wear, i.e., the tool wear criterion.
 
    
     The tool wear criterion is a reflection of the tool wear that can be tolerated for a given machining operation using a given tool insert material. 
     With the above information the horsepower at the cutting edge (HP c ) can be calculated from the following relationship: 
     
         HP.sub.c HP×η/C.sub.w 
    
     Determining The First Approximation Of DOC (d) 
     Formulas for the determination of DOC are displayed in FIG. 1 of the drawings and the appropriate formula is applied once the tool insert to be used has been selected. The terms found in FIG. 1 have the following meanings: 
     I.C. is the diameter of the circle that can be inscribed on the insert viewed in plan; 
     R is the nose radius and 
     SCEA is the side cutting edge angle. 
     The various tool insert shapes in FIG. 1 are set forth in hierarchical order of preference. Thus, use of the circular shape tool insert is most preferred (if it can be used in a specific machining operation) relative to the use of any of the succeeding shapes. If the circular shape cannot be used, then the next succeeding shape, the square insert is considered and so forth. 
     The value of SCEA to be used is to be set by the operator based on information supplied by the tool insert manufacturer. Its relationship to feed and DOC (i.e., d) in a turning operation is shown in FIG. 2. It is generally preferable to use the maximum recommended SCEA. However, the exact value may depend on the geometry of the portion of the part being machined. In the case of a milling operation the value of the corner angle (shown in FIG. 3) serves as the SCEA. The value of R is also provided by the tool insert manufacturer. 
     By way of example, the DOC for a given tool would be calculated as follows: 
     Shape: square 
     Size: 1/2&#34; square33 3/16&#34; thick 
     Nose rad, R: 3/64&#34; 
     SCEA: 15 degrees 
     After selecting the appropriate formula from FIG. 1, calculation of the DOC follows: 
     
         d=0.4(I.C.-R) Cos SCEA 
    
     
         d=0.4(0.5-3/64) Cos 15° 
    
     
         d=0.175 in. 
    
     Calculating The First Approximation Of Feed (f) ##EQU5## 
     The value of uhp varies with the type and hardness of the material being machined as is shown in TABLES II, III and IV [all excerpts from page 53 of the Milling Handbook of High-Efficiency Metal Cutting published by the Carboloy Systems Department of the General Electric Company]. These tables are merely offered as representative of the type of information generally available from manufacturers of tool inserts and tool holders and in machining handbooks. Numbers given in the vertical columns of TABLE II for the various hardnesses are uhp values. When machining such materials, as cutting speed increases up to a critical value, the magnitude of the uhp factor is reduced. Increasing the cutting speed beyond this critical cutting speed will not significantly affect the uhp value. 
     The value of V can be the value recommended by the tool insert manufacturer or may be a value arrived at by the machine tool operator based on proven tool life and total cost. Cutting speed V can range as high as the critical value, but is usually a somewhat lower value. 
     
                       TABLE II
______________________________________
FERROUS METALS AND ALLOYS
            BRINNEL HARDNESS NUMBER
            150- 176-   201-   251- 301- 351-
            175  200    250    300  350  400
______________________________________
A.I.S.I
1010-1025     .58    .67    --   --   --   --
1030-1055     .58    .67    .80  .96  --   --
1060-1095     --     --     .75  .88  1.0  --
1112-1120     .50    --     --   --   --   --
1314-1340     .42    .46    .50  --   --   --
1330-1350     --     .67    .75  .92  1.1  --
2015-2115     .67    --     --   --   --   --
2315-2335     .54    .58    .62  .75  .92  1.0
2340-2350     --     .50    .58  .70  .83  --
2512-2515     .50    .58    .67  .80  .92  --
3115-3130     .50    .58    .70  .83  1.0  1.0
3160-3450     --     .50    .62  .75  .87  1.0
4130-4345     --     .46    .58  .70  .83   1.00
4615-4820     .46    .50    .58  .70  .83  .87
5120-5150     .46    .50    .62  .75  .87  1.0
52100         --     .58    .67  .83  1.0  --
6115-6140     .46    .54    .67  .83  1.0  --
6145-6195     --     .70    .83  1.0  1.2  1.3
PLAIN CAST IRON
              .30    .33    .42  .50  --   --
ALLOY CAST IRON
              .30    .42    .54  --   --   --
MALLEABLE IRON
              .42    --     --   --   --   --
CAST STEEL    .62    .67    .80  --   --   --
______________________________________
 
    
     
                       TABLE III
______________________________________
NON-FERROUS METALS AND ALLOYS
                 uhp
______________________________________
BRASS:
HARD               .83
MEDIUM             .50
SOFT               .33
FREE MACHINING     .25
BRONZE
HARD               .83
MEDIUM             .50
SOFT               .33
COPPER             .90
(PURE)
ALUMINUM
CAST               .25
HARD (ROLLED)      .33
MONEL              1.0
(ROLLED)
ZINC ALLOY         .25
(DIE CAST)
______________________________________
 
    
     
                       TABLE IV
______________________________________
HIGH TEMPERATURE ALLOYS
MATERIAL        BRINELL
CLASSIFICATION  HARDNESS NUMBER  uhp
______________________________________
A 286           165              .82
A 286           285              .93
CHROMOLOY       200              .78
CHROMOLOY       310              1.18
HASTELLOY-B     230              1.10
INCO 700        330              1.12
INCO 702        230              1.10
M-252           230              1.10
M-252           310              1.20
Tl-150A         340              .65
U-500           375              1.10
4340            200              .78
4340            340              .93
______________________________________
 
    
     Calculating The Final Feed (f f ) And Final DOC 
     Essential to the arrival at final feed and final DOC is the fixing of constraints for these parameters to be met for the given machining operation. These constraints (which depend upon the work material and type of machining operation, i.e., roughing or finishing and are qualitatively illustrated graphically in FIG. (4) are fixed by the operator. An exemplary set of constraints for f min , f max , (d/f) min  and (d/f) max  for rough turning is as follows: 
     Max feed: 0.025 inch/revolution (ipr) 
     Min feed: 0.005 ipr 
     Max (d/f): 15 
     Min (d/f): 10 
     Two alternate routes can be taken to arrive at values of final feed (f f ) and final DOC (d f ). If a table has been generated taking into account the size (i.e., horsepower) of the machine tool being used and its utilization factor, the material to be machined (i.e., work material), the tool insert material under consideration, the proposed cutting speed (V) and the constraints on feed and DOC for the kind of machining (i.e., rough or finish), then it is merely necessary to refer to the table and select the values for final feed and DOC already calculated. TABLES V through XIV are examples of such prepared tables setting forth reasonable values for f f  and d f . Seven sizes of machine tools and six work materials are considered and values for each of four of these work materials are provided at two machining speeds. The data in these tables typifies the use of two different types of tool insert material (i.e., cemented tungsten carbide and ceramic). 
     Manifestly, if an appropriate table is not available it is necessary to carry out the calculation sequence described hereinabove given the first approximation values of feed and DOC (i.e., thereafter finding f i  and d i  ; d i  /f i  and finally f f  and d f  while adhering to the established constraints). 
     
                                           TABLE V
__________________________________________________________________________
WORK MATERIAL:
             6061 T6 Aluminum
                         uhp:        0.3
CUTTING SPEED:
             1200 sfm    TOOL MATERIAL:
                                     Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0 40.0 50.0 75.0 100.
HP × η
       6.0  12.0 24.0 32.0 40.0 60.0 80.0
 ##STR1##
       4.6  9.23 18.46
                      24.62
                           30.77
                                46.15
                                     61.54
f      0.006
            0.0122
                 0.0244
                      0.0326
                           0.0407
                                0.0610
                                     0.0814
d      0.175
            0.175
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR2##
       29.17
            14.33
                 7.17 5.37 4.30 2.87 2.15
f.sub.final
       0.0084
            No   0.0175
                      0.0175
                           0.0175
                                0.0175
                                     0.0175
d.sub.final
       0.1255
            change
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR3##
       15   required
                 10   10   10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE VI
__________________________________________________________________________
WORK MATERIAL:
             6061 T6 Aluminum
                         uhp:         0.3
CUTTING SPEED:
             2400 sfm    TOOL MATERIAL:
                                      Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)   (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0  30.0 40.0 50.0 75.0 100.
HP × η
       6.0  12.0  24.0 32.0 40.0 60.0 80.0
 ##STR4##
       4.6  9.23  18.46
                       24.62
                            30.77
                                 46.15
                                      61.54
f      0.003
            0.0061
                  0.0122
                       0.0163
                            0.0203
                                 0.0305
                                      0.0407
d      0.175
            0.175 0.175
                       0.175
                            0.175
                                 0.175
                                      0.175
 ##STR5##
       58.3 28.69 14.34
                       10.74
                            8.62 5.74 4.30
f.sub.final
       0.0059
            0.00844
                  No   No   0.0175
                                 0.0175
                                      0.0175
d.sub.final
       0.0887
            0.1265
                  change
                       change
                            0.175
                                 0.175
                                      0.175
 ##STR6##
       15   15    required
                       required
                            10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE VII
__________________________________________________________________________
WORK MATERIAL
            AISI 1045 Steel (200 Bhn)
                          uph:       0.83
CUTTING SPEED:
            500 sfm       TOOL MATERIAL:
                                     Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0 40.0 50.0 75.0 100.
HP × η
       6.0  12.0 24.0 32.0 40.0 60.0 80.0
 ##STR7##
       4.6  9.23 18.46
                      24.62
                           30.77
                                46.15
                                     61.54
f      0.005
            0.011
                 0.021
                      0.028
                           0.035
                                0.053
                                     0.071
d      0.175
            0.175
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR8##
       33.14
            16.53
                 8.33 6.18 4.96 3.3  2.48
f.sub.final
       0.00764
            0.0133
                 0.0175
                      0.0175
                           0.0175
                                0.0175
                                     0.0175
d.sub.final
       0.1146
            0.1699
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR9##
       15   15   10   10   10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE VIII
__________________________________________________________________________
WORK MATERIAL:
             AISI 1045 Steel
                       uph:        0.83
             (200 Bhn)
CUTTING SPEED:
             1000 sfm  TOOL MATERIAL:
                                   Alumina-coated
                                   Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)   (c)   (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0  30.0  40.0 50.0 75.0 100.
HP × η
       6.0  12.0  24.0  32.0 40.0 60.0 80.0
 ##STR10##
       4.6  9.23  18.46 24.62
                             30.77
                                  46.15
                                       61.54
f      0.0026
            0.0053
                  0.0106
                        0.014
                             0.0177
                                  0.0265
                                       0.0353
d      0.175
            0.175 0.175 0.175
                             0.175
                                  0.175
                                       0.175
 ##STR11##
       6.29 33    16.51 12.5 9.89 6.60 4.96
f.sub.final
       0.0055
            0.00786
                  0.01112
                        No   0.0175
                                  0.0175
                                       0.0175
d.sub.final
       0.0826
            0.1180
                  0.1668
                        change
                             0.175
                                  0.175
                                       0.175
 ##STR12##
       15   15    10    required
                             10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE IX
__________________________________________________________________________
WORK MATERIAL:
             AISI 4340 Steel
                       uhp:        1.51
             (300 Bhn)
CUTTING SPEED:
             600 sfm   TOOL MATERIAL:
                                   Alumina-coated
                                   Carbide
       SIZE OF MACHINE TOOL
       (a)   (b)   (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5   15.0  30.0 40.0 50.0 75.0 100.
HP × η
       6.0   12.0  24.0 32.0 40.0 60.0 80.0
 ##STR13##
       4.6   9.23  18.46
                        24.62
                             30.77
                                  46.15
                                       61.54
f      0.0024
             0.0049
                   0.0097
                        0.0129
                             0.0162
                                  0.0243
                                       0.0323
d      0.175 0.175 0.175
                        0.175
                             0.175
                                  0.175
                                       0.175
 ##STR14##
       72.31 36.08 18.04
                        13.52
                             10.82
                                  7.21 5.42
f.sub.final
       0.00529
             0.00756
                   0.0106
                        No   No   0.0175
                                       0.0175
d.sub.final
       0.07937
             0.1134
                   0.1596
                        change
                             change
                                  0.175
                                       0.175
 ##STR15##
       15    15    15   required
                             required
                                  10   10
__________________________________________________________________________
 
    
     
                                           TABLE X
__________________________________________________________________________
WORK MATERIAL:
            Gray Cast Iron (250 Bhn)
                          uhp:        0.72
CUTTING SPEED:
            500 sfm       TOOL MATERIAL:
                                      Carbide
       SIZE OF MACHINE TOOL
       (a)   (b)  (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5   15.0 30.0 40.0 50.0 75.0 100.
HP × η
       6.0   12.0 24.0 32.0 40.0 60.0 80.0
 ##STR16##
       4.6   9.23 18.46
                       24.62
                            30.77
                                 46.15
                                      61.54
f      0.0061
             0.0122
                  0.0244
                       0.0326
                            0.0407
                                 0.0610
                                      0.08140
d      0.175 0.175
                  0.175
                       0.175
                            0.175
                                 0.175
                                      0.175
 ##STR17##
       28.78 14.34
                  7.17 5.37 4.3  2.87 2.15
f.sub.final
       0.00843
             no   0.0175
                       0.0175
                            0.0175
                                 0.0175
                                      0.0175
d.sub.final
       0.1265
             change
                  0.175
                       0.175
                            0.175
                                 0.175
                                      0.175
 ##STR18##
       15    required
                  10   10   10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE XI
__________________________________________________________________________
WORK MATERIAL:
           Gray Cast Iron (250 Bhn)
                        uhp:       0.72
CUTTING SPEED:
           1500 sfm     TOOL MATERIAL:
                                   Alumina-TiC or
                                   Si.sub.3 N.sub.4 Ceramic
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)  (d)   (e)   (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0 40.0  50.0  75.0 100.
HP × η
       6.0  12.0 24.0 32.0  40.0  60.0 80.0
 ##STR19##
       4.6  9.23 18.46
                      24.62 30.77 46.15
                                       61.54
f      0.0020
            0.0040
                 0.0081
                      0.01091
                            0.01360
                                  0.0204
                                       0.0271
d      0.175
            0.175
                 0.175
                      0.175 0.175 0.175
                                       0.175
 ##STR20##
       86.21
            43.0 21.5 16.13 12.91 8.6  6.46
f.sub.final
       0.005
            0.0068
                 0.0097
                      0.0113
                            No    0.0175
                                       0.0175
d.sub.final
       0.07 0.1025
                 0.1458
                      0.1692
                            change
                                  0.175
                                       0.175
 ##STR21##
       14   15   15   15    required
                                  10   10
__________________________________________________________________________
 
    
     
                                           TABLE XII
__________________________________________________________________________
WORK MATERIAL:
            302 Stainless Steel
                        uhp:       1.13
            (Austenitic) (162 Bhn)
CUTTING SPEED:
            400 sfm     TOOL MATERIAL:
                                   Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)  (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0 40.0 50.0 75.0 100.
HP × η
       6.0  12.0 24.0 32.0 40.0 60.0 80.0
 ##STR22##
       4.6  9.23 18.46
                      24.62
                           30.77
                                46.15
                                     61.54
f      0.0049
            0.0097
                 0.0195
                      0.0259
                           0.0324
                                0.0486
                                     0.0648
d      0.175
            0.175
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR23##
       36   18   9    6.76 5.4  3.6  2.7
f.sub.final
       0.0097
            0.0106
                 0.0175
                      0.0175
                           0.0175
                                0.0175
                                     0.0175
d.sub.final
       0.1134
            0.1596
                 0.175
                      0.175
                           0.175
                                0.175
                                     0.175
 ##STR24##
       15   15   10   10   10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE XIII
__________________________________________________________________________
WORK MATERIAL:
             Inco 718 (R.sub.C 42)
                        uhp:       1.87
CUTTING SPEED:
             100 sfm    TOOL MATERIAL:
                                   Carbide
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)  (d)   (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0 40.0  50.0 75.0 100.
HP × η
       6.0  12.0 24.0 32.0  40.0 60.0 80.0
 ##STR25##
       4.6  9.23 18.46
                      24.62 30.77
                                 46.15
                                      61.54
f      0.0117
            0.0235
                 0.047
                      0.06269
                            0.0784
                                 0.1175
                                      0.1567
d      0.175
            0.175
                 0.175
                      0.175 0.175
                                 0.175
                                      0.175
 ##STR26##
       14.96
            7.45 3.72 2.79  2.23 1.49 1.12
f.sub.final
       No   0.0175
                 0.0175
                      0.0175
                            0.0175
                                 0.0175
                                      0.0175
d.sub.final
       change
            0.175
                 0.175
                      0.175 0.175
                                 0.175
                                      0.175
 ##STR27##
       required
            10   10   10    10   10   10
__________________________________________________________________________
 
    
     
                                           TABLE XIV
__________________________________________________________________________
WORK MATERIAL:
           Inco 718 (R.sub.C 42)
                     uhp:       1.87
CUTTING SPEED:
           450 sfm   TOOL MATERIAL:
                                SIALON Ceramic
       SIZE OF MACHINE TOOL
       (a)  (b)  (c)   (d)  (e)  (f)  (g)
__________________________________________________________________________
HP     7.5  15.0 30.0  40.0 50.0 75.0 100.
HP × η
       6.0  12.0 24.0  32.0 40.0 60.0 80.0
 ##STR28##
       4.6  9.23 18.46 24.62
                            30.77
                                 46.15
                                      61.54
f      0.0026
            0.0052
                 0.0104
                       0.0139
                            0.0174
                                 0.0261
                                      0.0348
d      0.175
            0.175
                 0.175 0.175
                            0.175
                                 0.175
                                      0.175
 ##STR29##
       67.31
            33.55
                 16.83 12.59
                            10.06
                                 6.70 5.03
f.sub.final
       0.0055
            0.0078
                 0.01101
                       No   No   0.0175
                                      0.0175
d.sub.final
       0.0826
            0.1168
                 0.1652
                       change
                            change
                                 0.175
                                      0.175
 ##STR30##
       15   15   15    required
                            required
                                 10   10 f
__________________________________________________________________________
 
    
     One further iteration may be necessary depending upon whether or not the number of passes needed to remove the requisite depth of stock is a natural number. The operator can obtain the number of passes by dividing the depth of stock to be removed by the value of d f . If the resulting quotient is not a natural number, then the requisite number of passes is raised to the next higher integer and a new DOC is calculated (d new ). The new feed (f new ) is requisite number of passes is raised to the next higher integer and a new DOC is calculated (d new ). The new feed (f new ) is then either d new  /(d/f) min  or d f  f f  /d new  whichever is the smaller value, but f new  cannot be smaller than f min  or larger than f max  unless in the judgment of the operator the constraint should be waived. 
     As stated hereinabove, the type of machining operation (i.e., rough or finish) is determinative of the feed constraint, f max  being related to the permissible roughness of the surface produced and f min  being dependent on the value of the minimum cut such that taking any smaller cut will result in excessive rubbing between the tool and the workpiece. The criteria for the formulas that are used to determine d take into account the size and strength of the tool, the amount of material to be removed, machine tool stiffness, available horsepower and tolerable deflection of the tool insert with respect to the workpiece under application of the cutting forces. Values of d and f are generally smaller for finishing than for roughing: 
     
         ______________________________________
         Roughing
         f =   0.005 to 0.050
         d/f = 5 to 15
         Finishing
         f =   .001 to 0.050
         d/f = 2 to 25
______________________________________
 
    
     EXAMPLE 
     Type of Machining: Rough turning 
     Work Material: AISI 4340 Steel (300 Bhn) 
     uhp: 1.51 
     Tool: Carbide 
     Tool Specification: 
     1/2 in. square×3/16 in. thick insert 
     15 deg. SCEA, and 
     3.64 in. nose radius 
     Cutting Speed: 600 sfm 
     Machine Tool Rating HP m  : 7.5 hp 
     Machine utilization factor, η:80% 
     Tool wear criterion: 0.03 inch flank wear 
     1. Horsepower at the spindle, HP×η7.5×0.8=6.0 ##EQU6## 3. Horsepower at the cutting edge, HP c  =6/1.3=4.6 ##EQU7## 7. Constraints: f min  =0.005 ipr; 
     f max  =0.025 ipr 
     (d/f) min  =10; 
     (d/f) max  =15 
     8. Observations: 
     f&lt;f min , d/f&gt;(d/f) max   
     Action: increase f to f min  and decrease d appropriately such that the product (df) remains constant. ##EQU8## 12. Calculate the final value of feed, f f , and depth of cut, d f , such that (d f  /f f )=(d/f) max  and d i  f i  =d f  f f , using the following formula: ##EQU9## 
     The operator having determined which values of feed and DOC to use in the given machining operation (e.g., changing workpiece dimensions to a new set of values in the making of a given part) must now adjust the machine tool accordingly. The adjustment of the feed control means and the DOC control means may be manually accomplished or these adjustments may be automatically made in the manner of the flow diagrams of FIGS. 5 and 6. In both cases a numerical control programming medium (e.g., punched paper or polyester tape) is prepared in machine language. This programmed medium may be used over and over to input directly to the controller for the production of each part (FIG. 5) or may be read one time to store the program in the memory of a computerized numerical control machine tool (FIG. 6). In the latter case the chances of errors from repeated use of a programming medium such as a punched tape are greatly reduced. 
     The prime advantage of the process of this invention lies in the increased utilization of machine tool capacity now available, but underutilized. Also, by enabling the machine tool operator to take part in programming the cutting conditions to be used, this invention will overcome any lack of experience in the machining process on the part of the regular programmer, the delay between program generation and production of the first part is reduced and the operator&#39;s expertise and skill in machining is more fully utilized. In addition, programming of the part by the operator (instead of by a separate part programmer) can result in significant savings in costs especially in small job shops where it may be difficult to justify a separate part-programmer.