Abstract:
A method of determining a radius of a cutting end of a tool for a turning machine using a touch probe is provided. One of the cutting end and the touch probe is movable relative to a reference frame having a first axis and a second axis and having a reference point trackable in the reference frame. The method comprises establishing a first contact point and recording a first coordinate of the reference point on the first axis; establishing a second contact point and recording a second coordinate of the reference point on the second axis; establishing a third contact point and recording a third coordinate of the reference point on the first axis and a fourth coordinate of the reference point on the second axis upon contact; and determining a radius of the cutting end based on the first, second, third and fourth coordinates.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation-in-part of U.S. application Ser. No. 14/252,910 filed on Apr. 15, 2014, the entire contents of which are incorporated by reference herein. 
     
    
     TECHNICAL FIELD 
       [0002]    The application relates generally to methods of determining radii of tools, and more specifically of tools for turning machines. 
       BACKGROUND OF THE ART 
       [0003]    Turning machines, such as in-turn, mill-turn, and lathes, CNC use tools to carve channels or sections in a rotating part. The tools include a cutting end which, as sharp as it may be, has a rounded portion at its tip. The positioning of the cutting end of the tool determines a position of the channel or section to be removed. In some application, the position of the tool may be required with greater precision before the tool is used. In order to determine the position of the tool, probes, for example mechanical or optical, may be used. 
         [0004]    Touch probes typically contact the tool at various locations to determine a position of the tool&#39;s cutting end in a plane. A radius of the cutting end&#39;s rounded portion is based on nominal values given by the manufacturer of the tool. The nominal values may not correspond enough to the actual radius of the cutting end which could lead to imprecise cutting. 
         [0005]    Optical sensors such as laser beam detectors can be used to scan the cutting end of the tool in order to determine its radius. The optical methods are however calculation intensive, and can be sensitive to noise coming from chips of material or thin layers of fluids. 
       SUMMARY 
       [0006]    In one aspect, there is provided a method of determining a radius of a cutting end of a tool for a turning machine using a touch probe, one of the cutting end and the touch probe being movable relative to a reference frame having a first axis and a second axis, the one of the one of the cutting end and the touch probe having a reference point trackable in the reference frame, the method comprising: a) establishing a first contact point between the touch probe and the cutting end and recording a first coordinate of the reference point on the first axis, the first contact point having a known coordinate on the first axis; and b) establishing a second contact point between the touch probe and the cutting end and recording a second coordinate of the reference point on the second axis, the second contact point having a known coordinate on the second axis; and c) establishing a third contact point between the touch probe and the cutting end by moving an end point of the one of the cutting end and the touch probe along a predetermined direction at an angle with the first and second axes and recording a third coordinate of the reference point on the first axis and a fourth coordinate of the reference point on the second axis upon contact, the pre-determined direction being dependent on the coordinate of the first contact point on the first axis and the coordinate of the second contact point on the second axis, the end point being offset from the reference point by an amount deduced from the first coordinate and the second coordinate recorded at steps a) and b); and d) determining a radius of the cutting end based on the first, second, third and fourth coordinates. 
         [0007]    In another aspect, there is provided a method of determining a radius of a cutting end of a tool for a turning machine using a touch probe, one of the cutting end and the touch probe being movable relative to a reference frame having a first axis and a second axis, the one of the one of the cutting end and the touch probe having a reference point trackable in the reference frame, the method comprising: a) recording a first coordinate of the reference point on the first axis upon contacting the touch probe and the cutting end at a first contact point having a known coordinate on the first axis; b) calculating a first offset of an end point of the one of the cutting end and the touch probe relative to the reference point on the first axis based on the first coordinate; c) recording a second coordinate of the reference point on the second axis upon contacting the touch probe and the cutting end at a second contact point having a known coordinate on the second axis; and d) calculating a second offset of the end point relative to the reference point on the second axis based on the second coordinate; e) recording a third coordinate of the reference point on the first axis and a fourth coordinate of the reference point on the second axis upon moving an end point of the one of the cutting end and the touch probe along a predetermined direction and contacting the touch probe and the cutting end at a third contact point along the predetermined direction, the third contact point having known coordinates on the first and second axes, the predetermined direction being at an angle with the first and second axes and being determined from the coordinate of the first contact point on the first axis and the coordinate of the second contact point on the second axis, the end point calculated using the first and second offsets; and f) determining a radius of the cutting end based on the first, second, third and fourth coordinates. 
         [0008]    In yet another aspect, there is provided a turning machine comprising: a tool having a cutting end; a touch probe having two flat faces and one of a rounded and angled corner joining the two flat faces; and an electronic control unit (ECU) controlling the one of the tool and the probe to move in a reference frame to establish separate contacts between the probe and the tool at a first point on one of the two flat faces, at a second point on the other one of the two flat faces and at a third point on the one of the rounded and angled corner, the ECU being configured to record coordinates of a reference point of the one of the tool and the probe during the separate contacts so as to calculate a radius of the cutting end. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0009]    Reference is now made to the accompanying figures in which: 
           [0010]      FIG. 1  is a schematic view of a tool for a turning machine; 
           [0011]      FIG. 2 a    is a schematic top plan view of a touch probe according to a first embodiment; 
           [0012]      FIG. 2 b    is a schematic top plan view of a touch probe according to a second embodiment; 
           [0013]      FIG. 3  is a schematic view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a first position relative to each other; 
           [0014]      FIG. 4  is a schematic view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a second position relative to each other; 
           [0015]      FIG. 5  is a schematic view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a third position relative to each other; 
           [0016]      FIG. 6  is a schematic view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a fourth position relative to each other; 
           [0017]      FIG. 7 a    is a close-up view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a fifth position relative to each other; 
           [0018]      FIG. 7 b    is a close-up view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in the fourth position relative to each other shown in  FIG. 6 ; 
           [0019]      FIG. 8  is a flow chart of a method of determining a radius of the tool of  FIG. 1  using any one of the touch probes of  FIG. 2 a    or  2   b ; and 
           [0020]      FIG. 9  is a close-up view of the tool of  FIG. 1  and the touch probe of  FIG. 2 a    shown in a sixth position relative to each other. 
       
    
    
     DETAILED DESCRIPTION 
       [0021]    Referring to  FIG. 1 , a tool  10  for a turning machine is shown. The tool  10  includes a body  12  and a cutting portion  14  for use, for example, in in-turn or mill-turn machines, the machines also being known as lathes, CNC, turning machines etc. The cutting portion  14  has a cutting end  16 . The tool  10  may be used to manufacture parts, such as metallic components, by carving out portions of the rotating part using the tool  10 . The parts may then be used in a variety of industries including the aeronautics industry. In turning machines, the parts are cylindrical, revolve about their centerline with the tool  10  abutting on their external surface. The cutting end  16  of the tool  10  creates an indentation. As the tool  10  is moved deeper into the rotating part, material is removed from the part and various cut-outs and channels can be created. A position of the cut-out is predetermined in function of a desired shape of the part, and the tool  10  is moved by the turning machine in a precise fashion to accomplish the desired shape of the part. This is commonly known as grooving, and other operations are possible as well, such as facing and face grooving. 
         [0022]    The cutting end  16  may have various shapes and be more or less sharp depending on the desired shape of the part. Whatever the sharpness of the cutting end  16 , it includes a rounded portion at the tip. The rounded portion may be approximated by a portion of a circle C (a close-up view on the cutting end  16  showing the circle C is shown in  FIG. 7 a   ). For smaller cut-outs where precision may be even more desired, an actual radius R of the cutting end  16  may be a desirable information. While a radius of the cutting end  16  may be obtained from a manufacturer of the cutting portion  14  (i.e. nominal value), there may be a discrepancy between the nominal value and the actual value of the radius R of the cutting end  16 . This discrepancy may cause a discrepancy between the desired shape of the part and the obtained shape of the part. 
         [0023]    In order to decrease a potential discrepancy between the nominal value and the actual value of the radius R of the cutting end  16 , the tool  10  may be tested to determine the actual value of the radius R of the cutting end  16  prior to use on the part. The method by which the actual value of the radius R of the cutting end  16  is determined will be described below. The method includes the determination of coordinates of various points along the cutting end  16  using a touch probe. 
         [0024]    Turning now to  FIGS. 2 a  and 2 b   ,  FIG. 2 a    shows a first embodiment of a touch probe  22  for use in the determination of the actual value of the radius R of the cutting end  16 . The touch probe  22  has a generally square cross-section with rounded corners and is shown in  FIG. 2  in a top plan view (e.g. cubic shape, rectangular prism shape). The touch probe  22  includes at least four flat sides, namely sides  24 ,  26 ,  28 ,  30  and four rounded corners, namely corners  32 ,  34 ,  36 ,  38 . The corners  32 ,  34 ,  36 ,  38  have a same radius of curvature, but it is contemplated that the corners  32 ,  34 ,  36 ,  38  could each have a different radius of curvature. Typically, the touch probe  22  deflects when touching an object. Touching one side  24 ,  26 ,  28 ,  30  or one corner  32 ,  34 ,  36 ,  38  gives a signal to the machine controller to record the actual positions. The touch probe  22  is linked to an electronic control unit (ECU) (not shown) which may record information every time the touch probe  22  sends a signal corresponding to one of the sides  24 ,  26 ,  28 ,  30  or corners  32 ,  34 ,  36 ,  38  being in physical contact with an object. 
         [0025]    The touch probe  22  includes various sides  24 ,  26 ,  28 ,  30  and corners  32 ,  34 ,  36 ,  38  allowing the use of the touch probe  22  in a variety of direction and positions without having to greatly manipulate it, such as rotating it. With the use of the sides  24 ,  26 ,  28 ,  30  and corners  32 ,  34 ,  36 ,  38 , the touch probe  22  could be used in at least 8 orientations of the tool  10  relative to the touch probe  22  in a 360° circumference. 
         [0026]    The touch probe  22  shown in  FIG. 2 a    is only one example of touch probe adapted for the below method of determining the radius R of the cutting end  16 .  FIG. 2 b    shows a second embodiment of a touch probe  22 ′ for use in the determination of the actual value of the radius R of the cutting end  16 . The touch probe  22 ′ is similar to the touch probe  22  except that it features angled corners  32 ′,  34 ′,  36 ′,  38 ′ in place of rounded corners  32 ,  34 ,  36 ,  38  in between flat sides  24 ′,  26 ′,  28 ′,  30 ′. The angled corners  32 ′,  34 ′,  36 ′,  38 ′ are disposed at 45 degrees of the flat sides  24 ′,  26 ′,  28 ′,  30 ′. Other angular orientations of the angled corners  32 ′,  34 ′,  36 ′,  38 ′ are contemplated. It is contemplated that the touch probe  22  could yet have other shapes. For example, the touch probe  22  could have a triangular or rectangular cross-section instead of a square cross-section. The touch probe  22  could also have only one side. 
         [0027]    Turning to  FIG. 3 , the tool  10  is shown in relation with the touch probe  22  for proceeding to the determination of the radius R of the cutting end  16 . The touch probe  22  is used in a turning machine (not shown) with the tool  10  located as it would be to carve a part. It is however contemplated that the touch probe  22  and the tool  10  could be used outside of the turning machine to determine the radius R of the cutting end  16  of the tool  10 . The turning machine has a fixed reference frame RF which defines a X-axis and an in-plane Z-axis. In the embodiment described in relation to the Figures, the touch probe  22  is oriented to have its sides  24 ,  26 ,  28 ,  30  aligned with the X- and Z-axes of the reference frame RF. The touch probe  22  and the tool  10  may move in a plane of the X- and Z-axes relative to one another. 
         [0028]    The touch probe  22  allows determining coordinates of several points P 1 , P 2 , P 3  of the cutting end  16  (shown best in  FIG. 7 a   ) relative to a reference point P 0  of the tool  10  to later calculate the radius R of the cutting end  16 . In the embodiment described herein, the reference point P 0  is a fixed point of the tool  10  and is movable within the reference frame RF. An ECU (which may or may not be a same ECU as the one linked to the touch probe  22 ) records the position of the reference point P 0  at all times t: (P 0   t (X),P 0   t (Z)). From the position of the reference point P 0  at all times and coordinates of the touch probe  22  which may be known from calibration, can be deduced the coordinates of the points P 1 , P 2 , P 3  of the cutting end  16 . As shown in  FIG. 3 , the tool  10  may use 3 different paths, namely path  1 , path  2 , path  3 , to contact the touch probe  22  at three associated locations, in this embodiment sides  24 ,  26  and corner  32 . 
         [0029]    An out-of-plane Y-axis may also be defined, the X,Y,Z-axes forming together an orthogonal reference frame. The tool  10  has a reference point P 0  which allows determining a position of the tool  10  in the reference frame RF. In the example described herein, the touch probe  22  is fixed relative to the reference frame RF, while the tool  10  is movable relative to the reference frame RF. It is contemplated that the tool  10  could be fixed relative to the reference frame RF, while the touch probe  10  could be movable relative to the reference frame RF. 
         [0030]    Turning now to  FIGS. 4 to 8 , a method  40  of determining the radius R of the cutting end  16  will be described.  FIGS. 4 to 7   b  show different positions of the tool  10  relative to the touch probe  22 , and  FIG. 8  is a flow chart with the different steps of the method  40 . 
         [0031]    The method  40  starts at step  42  by a contact between the tool  10  and the touch probe  22  at a first point P 24  having a known position on the X-axis and recording a coordinate of the reference point P 0  of the tool on the X-axis ( FIG. 4 ). 
         [0032]    Referring more specifically to  FIGS. 3 and 4 , a numerical command moves the tool  10  along the path  1  based on information obtained during calibration. Calibration information include a position of the side  24  in the reference frame RF on the X-axis, X 24 . Motion of the tool  10  stops when the tool  10  contacts the side  24  of the touch probe  22 . As the point P 1  of the cutting end  16  contacts the touch probe  22  (time t=t 1 ) at point P 24 , the touch probe  22  triggers an electrical signal which commands the tool  10  to stop its course. Coordinates of the reference point P 0  are then read and the X-coordinate of the reference point P 0 , P 0   t=t1 (X), is recorded by the ECU. The side  24  being aligned with the Z-axis, any point of the side  24  has a same X-coordinate X 24 . Although the cutting end  16  is shown in  FIG. 4  contacting a middle of the side  24  (i.e. point P 24 ), it should be understood that the cutting end  16  may contact any point along the side  24 . It is also contemplated that the side  28  could have been used in place of the side  24  of the touch probe  22 . 
         [0033]    From the determination of P 0   t=t1 (X), various values can be obtained. These values may be obtained by the ECU at step  42  or at a later step. 
         [0034]    At time t=t 1 , the X-coordinate of the point P 1 , P 1   t=t1 (X) is equal to the X-coordinate X 24  of the point P 24 . 
         [0035]    From P 0   t=t1 (X) and P 1   t=t1 (X) can be deduced a position of the first point P 1  relative to the reference point P 0 , i.e. an offset Off X  of the cutting end  16  on the X-axis. 
         [0000]      Off X   =P   1   t=t1 ( X )− P   0   t=t1 ( X )  (Eq. 1)
 
         [0036]    Since, at time t=t 1 , P 1   t=t1 (X) is equal to X 24 , 
         [0000]      Off X   =X   24   −P   0   t=t1 ( X )  (Eq. 2)
 
         [0037]    The offset Off X  may be used to deduce the radius R of the cutting end  16  in a below step. 
         [0038]    The offset Off X  being known, the X-coordinate of the first point P 1  can be known at all times. 
         [0000]        P   1   t ( X )= P   0   t ( X )+Off X   (Eq. 3)
 
         [0039]    When the value of P 0   t=t1 (X) is recorded and optionally the value of the offset Off X  obtained at this step, the touch probe  22  is moved back to its original position shown in  FIG. 3  so as to undo the contact between the touch probe  22  and the tool  10 . 
         [0040]    From step  42 , the method  40  goes to step  44 , to contact the touch probe  22  at a second point P 26  having a known position on the Z-axis and recording a coordinate of the reference point P 0  of the tool on the Z-axis. 
         [0041]    Referring more specifically to  FIG. 5 , a numerical command moves the tool  10  along the path  2  based on information obtained during calibration. Calibration information include a position of the side  26  in the reference frame RF, Z 26 . Motion of the tool  10  stops when the tool  10  contacts the side  26  of the touch probe  22 . As the point P 2  of the cutting end  16  contacts the point P 26  of the touch probe  22  (time t=t 2 ), the touch probe  22  triggers an electrical signal which commands the tool  10  to stop its course. Coordinates of the reference point P 0  are read and the Z-coordinate of the reference point P 0 , P 0   t=t2 (Z), is recorded by the ECU. The side  26  being aligned with the X-axis, any point of the side  26  has a same Z-coordinate Z 26 . Although the cutting end  16  is shown in  FIG. 5  contacting a middle of the side  26  (i.e. point P 26 ), it should be understood that the cutting end  16  may contact any point along the side  26 . It is also contemplated that the side  30  could have been used in place of the side  26  of the touch probe  22 . 
         [0042]    From the determination of P 0   t=t2 (Z), various values can be obtained. These values may be obtained by the ECU at step  44  or at a later step. 
         [0043]    At time t=t 2 , the Z-coordinate of the point P 2 , P 2   t=t2 (Z) is equal to the Z-coordinate Z 26  of the point P 26 . 
         [0044]    From P 0   t=t2 (Z) and P 2   t=t2 (Z) can be deduced a position of the point P 2  relative to the reference point P 0 , i.e. an offset Off Z  of the cutting end  16  on the Z-axis. 
         [0000]      Off Z   =P   2   t=t2 ( Z )− P   0   t=t2 ( Z )  (Eq. 4)
 
         [0045]    Since, at time t=t 2 , P 2   t=t2 (Z) is equal to Z 26 , 
         [0000]      Off Z   =Z   26   −P   0   t=t2 ( Z )  (Eq. 5)
 
         [0046]    The offset Off Z  may be used to deduce the radius R of the cutting end  16  in a below step. 
         [0047]    The offset Off Z  being known, the Z-coordinate of the point P 2  can be known at all times. 
         [0048]    When the value of P 0   t=t2 (Z) is recorded and optionally the value of the offset Off Z  obtained at this step, the touch probe  22  is moved back to its original position shown in  FIG. 3  so as to undo the contact between the touch probe  22  and the tool  10 . 
         [0049]    Steps  42  and  44  could be performed in any order, and by a same probe or two distinct probes. 
         [0050]    From step  44 , the method  40  goes to step  46 , to contact the touch probe  22  at a third point P 32  having a known position on the X- and Z-axes and record a coordinate of the reference point P 0  of the tool on the X- and Z-axes. The point P 32  is not aligned with the sides  24  or  26 , and as such has a X-coordinate different from the X-coordinate of the point P 24 , and a Z-coordinate different from the Z-coordinate of the point P 26 . 
         [0051]    Referring more specifically to  FIGS. 6, 7   a  and  7   b , a numerical command moves the tool  10  along the path  3  based on information obtained during calibration and information obtained at steps  42  and  44 . Calibration information includes a position of the point P 32 , namely X 32 , Z 32 , in the reference frame RF and the numerical command moves the tool  10  to contact specifically the point P 32 . The point P 32  is in a predetermined direction PD which is in-plane with the X- and Z-axes and at an angle α with respect to the X- and Z-axes. The angle α is determined at calibration. In one embodiment, the angle α is 45 degrees. Information obtained at steps  42  and  44  include Off x  and Off Z  which allow deducing the coordinates of a virtual cutting end point P CE , defined as the intersection of a line parallel to the X-axis passing through P 2  and a line parallel to the Z-axis passing through P 3 . The numerical command includes travelling the point P CE  onto the predetermined direction PD. 
         [0052]    Motion of the tool  10  stops when the point P 3  of the cutting end  16  contacts the point P 32  of the touch probe  22 . As the tool  10  contacts the touch probe  22  at time t=t 3 , the touch probe  22  trigger and electrical signal which commands the tool  10  to stop its course. Coordinates of the reference point P 0  are read and the X- and Z-coordinates of the reference point P 0   t=t3 (X), P 0   t=t3 (Z) and recorded by the ECU. It is contemplated that the corners  34 ,  38  or  38  could have been alternatively used. 
         [0053]    The coordinates of the reference point P 0   t=t3 (X), P 0   t=t3 (Z) may be used to deduce the radius R of the cutting end  16  in a below step. 
         [0054]    From step  46 , the method  40  goes to step  48 , to determine the radius R of the cutting end  16  by the ECU. 
         [0055]    As best seen in  FIG. 7 b   , when the cutting end  16  contacts the corner  32  at the point P 32 , the radius R may be obtained by: 
         [0000]        R=d (1+√{square root over (2)})  (Eq. 6)
 
         [0056]    when the angle α is 45°, d being a distance between third point P 32  and the virtual cutting end point P CE . The virtual cutting end point P CE  is defined as the intersection between a line parallel to the X-axis passing through the point P 2  with a line parallel to the Z-axis passing through the point P 1 . 
         [0000]        d =√{square root over (( P   CE   t=t3 ( X )− X   32 ) 2 +( P   CE   t=t3 ( Z )− Z   32 ) 2 )}  (Eq. 7)
 
         [0057]    The cutting end point P CE  has a same X-coordinate as the first point P 1  and a same Z-coordinate as the second point P 2 : 
         [0000]        P   CE   t=t3 ( X )= P   1   t=t3 ( X )= P   0   t=t3 ( X )+Off X    
         [0000]        P   CE   t=t3 ( Z )= P   2   t=t3 ( Z )= P   0   t=t3 ( Z )+Off Z   (Eq. 8)
 
         [0058]    Which leads to: 
         [0000]    
       
         
           
             
               
                 
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         [0059]    From which the radius R is deduced as: 
         [0000]    
       
         
           
             
               
                 
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         [0060]    when the angle α is 45°. Determination of the radius R when the angle α is not 45° will be given below. 
         [0061]    Step  46  could be performed by the same probe as steps  42  and/or  44  or by a distinct probe. 
         [0062]    The above method relies on the knowledge of the parameters X 24 , Z 26 , X 32 , Z 32 , which may be determined during a calibration step prior to the method  40 . 
         [0063]    During calibration, a calibration tool having known dimensions is used. The calibration tool may or may not be similar to the tool  10 . The calibration tool has the reference point P 0  which coordinates in the reference frame RF are recorded at all time. The cutting end of the calibration tool is brought into contact with the side  24 , the X-coordinate of the reference point P 0  is recorded, and the X-coordinate X 24  is determined to be the sum of the X-coordinate of the reference point P 0  and a known distance between a point of the cutting end contacting the side  24  and the reference point P 0 . Similarly, the cutting end of the calibration tool is brought in a second time into contact with the side  26 , the Z-coordinate of the reference point P 0  is recorded, and the Z-coordinate Z 26  is determined to be the sum of the Z-coordinate of the reference point P 0  and a known distance between a point of the cutting end contacting the side  26  and the reference point P 0 . 
         [0064]    To calibrate the corner  32  and determine the parameters X 32 , Z 32 , the predetermined direction PD is first determined. In one embodiment, the predetermined direction PD is disposed at 45° from the X- and Z-axes. In other embodiment, the predetermined direction PD is disposed at an angle other than 45° from the X- and Z-axes. 
         [0065]    With reference to  FIG. 9 , should the predetermined direction PD not be at 45°, the calibration process would define the radius PR of the arc A formed by the probe corner  32 ,  34 ,  36 ,  38  and the center coordinates PC of the arc A. The position of the contact point P 32  on the touch probe  20  may change according to the approach direction and the tool radius size. It may be identified by the calibration as for the case of 45°. When the tool touches the probe, the coordinate of PCE in X and Z directions are recorded. With reference to  FIG. 9   
         [0000]    
       
         
           
             
               
                 ( 
                 
                   
                     
                       
                         d 
                         z 
                       
                     
                   
                   
                     
                       
                         d 
                         x 
                       
                     
                   
                 
                 ) 
               
               = 
               
                 PCE 
                 - 
                 PC 
               
             
             , 
             
               
 
             
              
             
               
                 d 
                 z 
               
               = 
               
                 
                   PCE 
                   z 
                 
                 - 
                 
                   PC 
                   z 
                 
               
             
             , 
             
               
 
             
              
             and 
           
         
       
       
         
           
             
               d 
               x 
             
             = 
             
               
                 PCE 
                 x 
               
               - 
               
                 
                   PC 
                   x 
                 
                 . 
               
             
           
         
       
     
         [0000]    The angular position of the contact point on the probe arc A depends on the tool radius size. From the geometry, when the probe is in contact with the cutting tool: 
         [0000]      ( PR+R ) 2 =( R+d   z ) 2 +( R+d   x ) 2   (Eq. 11)
 
         [0000]    The unknown parameter in this equation is the tool radius R. The solution of this equation gives TR as: 
         [0000]        R =( PR−d   z   −d   x )+√{square root over (( PR−d   x   −d   z ) 2   +PR   2   −d   x   2   −d   z   2 )}  (Eq. 12)
 
         [0066]    In the case of angle=450, as discussed above, geometrically we have: 
         [0000]      ( R+d ) 2 =( R ) 2 +( R ) 2   (Eq. 13).
 
         [0067]    The solution of this equation gives TR as: 
         [0000]        R=d (1+√{square root over (2)}) where
 
         [0000]    
       
         
           
             d 
             = 
             
               
                 
                   
                     ( 
                     
                       
                         
                           P 
                           0 
                           
                             t 
                             = 
                             
                               t 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                          
                         
                           ( 
                           X 
                           ) 
                         
                       
                       + 
                       
                         Off 
                         X 
                       
                       - 
                       
                         X 
                         32 
                       
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           P 
                           0 
                           
                             t 
                             = 
                             
                               t 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                          
                         
                           ( 
                           Z 
                           ) 
                         
                       
                       + 
                       
                         Off 
                         Z 
                       
                       - 
                       
                         Z 
                         32 
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
     
         [0000]    as discussed above. 
         [0068]    Using the above method, relatively small radii R of the cutting end  16  such as the one commonly found in in-turn and mill-turn applications, can be determined. In one embodiment, the radius R is smaller than 0.1 inch. In one embodiment, the radius R is comprised between 0.01 and 0.1 inch. The above method may be carried within the turning machine which reduces a number of steps to determine the radius R. The relatively non-invasive method described above also allows determining the radius at any time before a turning operation without removing the tool  10  from the machine. 
         [0069]    The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. For example, the method could be used for tool not related to turning machines. The method could be used with any tool having an arcuate portion, and could preferably be used with tools of relatively small radii. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims.