CN111890123A - On-machine detection and calculation method for axial inclination angle of front cutter face of cutter - Google Patents
On-machine detection and calculation method for axial inclination angle of front cutter face of cutter Download PDFInfo
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Abstract
The invention discloses a method for detecting and calculating the axial inclination angle of a tool rake face on machine, which comprises the steps of installing a tool on a rotary main shaft of a machine tool, firstly detecting the overhanging length of the installed tool, then selecting two detection points which are distributed along the axial direction and have the same rotary radius on the tool rake face, controlling the movement of each shaft of the machine tool according to the rotary radius, the overhanging length, the offset distance of the detection points and the distance between the detection points of the two detection points, sequentially triggering the probes at the two detection points, and calculating the axial inclination angle of the tool rake face according to the coordinate values of each shaft of the machine tool when the probes are triggered at the two detection points. The on-machine detection calculation method for the axial inclination angle of the cutter rake face provided by the invention utilizes the position value of the coordinate axis of the machine tool triggered by the probe for multiple times, realizes on-machine automatic detection of the axial inclination angle of the cutter rake face, and provides a technical basis for the integrated process of on-machine detection and numerical control machining of the cutter.
Description
Technical Field
The invention relates to an on-machine detection and calculation method for a cutter angle, in particular to an on-machine detection and calculation method for an axial inclination angle of a cutter rake face.
Background
In the field of tool angle detection and calculation, most of traditional angle detection methods belong to off-line detection, a tool is placed under a tool microscope, the contour of the detected angle of the tool is projected, a curve obtained by projection is fitted by using the tool line microscope, and the angle related to the tool is measured according to the curve obtained by fitting. The off-line detection method increases the time required by the angle detection of the cutter, the cutter generally comprises two or even more than two cutter teeth, the auxiliary time required by the cutter machining is prolonged in a projection mode under a tool microscope, the on-machine detection of the cutter cannot be realized, and the integrated detection and machining process of the manufacturing process is realized.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides an on-machine detection and calculation method for the axial inclination angle of the rake face of a cutter.
The technical scheme of the invention is as follows: an on-machine detection and calculation method for the axial inclination angle of a tool rake face comprises the following steps:
s1, clamping the cutter on a shaft A of a rotary main shaft of the machine tool, and acquiring the overhanging length GProbe (1) of the tip of the clamped cutter on the shaft A and the initial phase GProbe (3) of the front cutter face;
s2, setting a rake face phase deviation value vtN (1) of the A-axis rotary cutter, moving the C-axis to a zero position, and enabling a plane of the detection end side of the probe to be perpendicular to the axis of the A-axis;
s3, respectively calculating an X-axis movement position vtN (4), a Y-axis movement position vtN (2) and a Z-axis movement position vtN (3) of the machine tool, and controlling the X-axis, the Y-axis and the Z-axis of the machine tool to respectively move to an X-axis movement position vtN (4), a Y-axis movement position vtN (2) and a Z-axis movement position vtN (3);
s4, searching speed V according to the preset probe1Controlling the X axis of the machine tool to perform searching movement along the negative direction, and recording the X axis coordinate X when the probe is triggered1And controlling the machine tool to move back to the X-axis movement position vtN (4);
s5, selecting two detection points P on the front tool face of the tool1And P2Selecting two detection points P on the front cutter surface of the cutter1And P2The method comprises the following steps:
setting the maximum radius of the tool base body on the front tool surface as RmaxThe preset radial offset safety value is delta r along the radial outward offset of the cutter, and two detection points P are obtained1And P2Is represented by
GvPMY=Rmax+Δr
Setting a detection point P1Contour boundary near the front end of the rake face, probe point P2The distances from the profile boundary of the front tool face close to the tool shank are axial offset safety values xbMaking an auxiliary line parallel to the rotation axis of the tool at the rotation radius of the measuring pointThe distance between two intersection points of the tool contour is L, and two detection points P on the tool are calculated1And P2The distance in the X-axis direction is expressed as
GProbe(5)=L-2·xb;
S6, recalculating the X-axis movement position vtN (7), the Y-axis movement position vtN (5) and the Z-axis movement position vtN (6) of the machine tool respectively, and controlling the X-axis, the Y-axis and the Z-axis of the machine tool to move to the X-axis movement position vtN (7), the Y-axis movement position vtN (5) and the Z-axis movement position vtN (6) respectively;
s7, searching speed V according to preset axis A3Controlling the A shaft of the machine tool to drive the cutter to rotate anticlockwise, and recording the coordinate theta of the A shaft when the probe is triggered1Calculating an A-axis movement position vtN (8), and controlling the A-axis of the machine tool to move backwards to an A-axis movement position vtN (8);
s8, recalculating the X-axis movement position vtN (9) of the machine tool, controlling the X-axis movement of the machine tool to the X-axis movement position vtN (9), and searching the speed V according to the preset A-axis3Controlling the A shaft of the machine tool to drive the cutter to rotate anticlockwise, and recording the coordinate theta of the A shaft when the probe is triggered2Recalculating the A-axis movement position vtN (10) and controlling the A-axis of the machine tool to move backwards to the A-axis movement position vtN (10);
and S9, calculating the axial inclination angle of the rake face of the cutter.
Further, in step S2, the a-axis rotary tool rake face phase offset value vtN (1) — GProbe (3) is set.
Further, in step S3, the X-axis movement position vtN (4) of the machine tool, which is expressed as GSys (5) which is the distance value between the left side surface of the probe detection end and the a-axis distal end positioning surface in the X-axis direction, the tool distal end overhang length GProbe (1), the probe search start point safety offset distance GMeasure (1), and the projection distance value GSys (6) of the left side surface of the probe detection end with respect to the probe mounting axis on the XY plane, is calculated
vtN(4)=-GSys(5)+GProbe(1)+GMeasure(1)+GSys(6)
Calculating the Y-axis movement position vtN (2) of the machine tool according to the gyration radius GProbe (2) when the end point of the tool is horizontal to the right phase, the chamfering length GSys (1) of the probe tip and the distance value GSys (2) of the probe tip and the axis of the A axis in the Y-axis direction, wherein the distance value is expressed as GPys (2)
vtN(2)=GProbe(2)-GSys(1)-GSys(2)
Calculating a Z-axis motion position vtN (3) according to a distance value GSys (3) of the probe cutting edge and the A-axis in the Z-axis direction and a height deviation value GSys (4) of the probe cutting edge relative to the probe installation axis in the Z-axis direction, wherein the Z-axis motion position is expressed as
vtN(3)=-GSys(3)-GSys(4)。
Further, in the step S6, the trigger time of the probe is determined according to the X-axis coordinate X in the step S41A detection point P1The distance GProbe (4) from the tool tip in the X-axis direction is used for calculating the X-axis movement position vtN (7) of the machine tool, and the calculation is represented as
vtN(7)=X1+GProbe(4)。
From two detection points P1And P2Is calculated from the machine Y-axis motion position vtN (5), indicated as GvPMY, of the revolution radius (c), is shown as
vtN(5)=GvPMY。
The machine tool Z-axis movement position vtN (6) is calculated according to the tool design theoretical rake angle value GProbe (7) and the preset second avoidance angle GProbe (8) of the a-axis during probe detection, and is represented as vtN (6) — GSys (3) -GvPMY · Sin ((GProbe (7) + GProbe (8)).
Further, in the step S7, according to the preset first avoidance angle GMeasure (2) of the a-axis and the coordinate θ of the a-axis during the probe detection1Calculate the A-axis motion position vtN (8), expressed as
vtN(8)=GMeasure(2)+θ1。
Further, in the step S8, the trigger time of the probe is determined according to the X-axis coordinate X in the step S41Two probing points P1And P2Distance GProbe (5) in X-axis direction, probe point P1The distance GProbe (4) from the cutting edge in the X-axis direction is calculated and the X-axis movement position vtN (9) of the machine tool is represented as
vtN(9)=X1+GProbe(4)+GProbe(5)
According to a preset first avoidance angle GMeasure (2) of an A axis and an A axis coordinate theta during probe detection2Calculate the A-axis motion position vtN (10), expressed as
vtN(10)=GMeasure(2)+θ2。
Further, in step S9, two detection points P are determined according to the turning radii GvPMY of the two detection points of the tool1And P2Angle difference delta theta of A axis when triggered, rake angle alpha of tool, and two detection points P1And P2The distance GProbe (5) in the axial direction is used for calculating the axial inclination angle of the rake face of the cutter and is expressed as
ξ=tan-1(GvPMY·sin(Δθ)/(cos(α)·GProbe(5)))。
The invention has the beneficial effects that: the invention combines the hardware structure of the machine tool and the precise probe arranged on the machine tool to realize the on-machine detection of the axial inclination angle of the cutter, and completes the on-machine detection of the axial inclination angle of the cutter according to the shape of the cutter and the specific arrangement form of the machine tool under the condition of not passing through the external detection basis, thereby greatly saving the time required by the cutter detection, and the calculated axial inclination angle can be directly applied to the subsequent processing shaft, realizing the integrated detection and processing process of the manufacturing process and improving the manufacturing efficiency of the equipment.
Drawings
FIG. 1 is a schematic flow chart of the on-machine detection and calculation method for the axial inclination angle of the tool rake face of the tool of the present invention;
FIG. 2 is a schematic diagram of a distribution of probe points according to an embodiment of the present invention;
FIG. 3 shows a probe point P according to an embodiment of the present invention1Probing the schematic in the XY plane;
FIG. 4 shows a probe point P according to an embodiment of the present invention1Probing the schematic in the YZ plane;
FIG. 5 shows a probe point P according to an embodiment of the present invention2Probing the schematic in the XY plane;
FIG. 6 shows a probe point P according to an embodiment of the present invention2Probing the schematic in the YZ plane;
wherein the reference numerals are: 1. probe, 2, tool rake face.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
FIG. 1 is a schematic flow chart of the on-machine detection and calculation method for the axial inclination of the rake face of the tool of the present invention; an on-machine detection and calculation method for the axial inclination angle of a tool rake face comprises the following steps:
s1, clamping the cutter on the axis A of the rotary main shaft of the machine tool, and acquiring the overhanging length GProbe (1) of the tip of the clamped cutter on the axis A and the initial phase GProbe (3) of the front cutter face by adopting a manual recording and inputting mode;
s2, setting a rake face phase offset value vtN (1), specifically vtN (1) — GProbe (3), of the a-axis rotary cutter;
rapidly moving the shaft C to a zero position, so that the plane of the detection end side of the probe is vertical to the axis of the shaft A;
s3, respectively calculating the X-axis movement position vtN (4), the Y-axis movement position vtN (2) and the Z-axis movement position vtN (3) of the machine tool, wherein the calculation mode specifically comprises the following steps:
calculating the X-axis movement position vtN (4) of the machine tool according to the distance value GSys (5) between the left side surface of the probe detection end and the front end positioning surface of the A-axis in the X-axis direction, the overhanging length GProbe (1) of the front end of the cutter, the safety offset distance GMeasure (1) of the probe search starting point and the projection distance value GSys (6) of the left side surface of the probe detection end relative to the installation axis of the probe on the XY plane
vtN(4)=-GSys(5)+GProbe(1)+GMeasure(1)+GSys(6)
Calculating the Y-axis movement position vtN (2) of the machine tool according to the gyration radius GProbe (2) when the end point of the tool is horizontal to the right phase, the chamfering length GSys (1) of the probe tip and the distance value GSys (2) of the probe tip and the axis of the A axis in the Y-axis direction, wherein the distance value is expressed as GPys (2)
vtN(2)=GProbe(2)-GSys(1)-GSys(2)
Calculating a Z-axis motion position vtN (3) according to a distance value GSys (3) of the probe cutting edge and the A-axis in the Z-axis direction and a height deviation value GSys (4) of the probe cutting edge relative to the probe installation axis in the Z-axis direction, wherein the Z-axis motion position is expressed as
vtN(3)=-GSys(3)-GSys(4)
Controlling the X axis, the Y axis and the Z axis of the machine tool to rapidly move to an X axis movement position vtN (4), a Y axis movement position vtN (2) and a Z axis movement position vtN (3) respectively;
s4, searching speed V according to the preset probe1Controlling the X axis of the machine tool to perform searching movement along the negative direction, and recording the X axis coordinate X when the probe is triggered1,X1Namely the real coordinate of the trigger probe at the installation position of the cutter in the X-axis direction of the machine tool, and the real overhanging length GProbe (6) of the cutter installation is L1-X1,L1The distance value between the origin of the X axis of the machine tool and the probe is obtained, and the X axis of the machine tool is controlled to rapidly move back to an X axis movement position vtN (4);
s5, selecting two detection points P on the front tool face of the tool1And P2As shown in fig. 2-6, the detection point P1And P2The position calculation method specifically comprises the following steps:
setting the maximum radius of the tool base body on the front tool surface as RmaxWithin the maximum radius, the detection point and the detection movement path are liable to interfere with the tool base body, and the maximum radius R ismaxOn the basis of the two detection points P, the preset radial offset safety value is delta r along the radial direction of the cutter, so that two detection points P are obtained1And P2Is represented by
GvPMY=Rmax+Δr
Setting a detection point P1Contour boundary near the front end of the rake face, probe point P2The distances from the profile boundary of the front tool face close to the tool shank are axial offset safety values xbMaking an auxiliary line parallel to the rotation axis of the cutter at the rotation radius of the measuring point, wherein the distance between the auxiliary line and two intersection points of the cutter contour is L, and the safety value x of axial offset is preset according to the distance L between the intersection points of the cutter tooth contourbCalculating two detection points P on the tool1And P2The distance in the X-axis direction is expressed as
GProbe(5)=L-2·xb。
S6, recalculating the X-axis movement position vtN (7), the Y-axis movement position vtN (5) and the Z-axis movement position vtN (6) of the machine tool respectively in a specific calculation mode:
according to the X-axis coordinate of the probe triggering in the step S4X1A detection point P1The distance GProbe (4) from the tool tip in the X-axis direction is used for calculating the X-axis movement position vtN (7) of the machine tool, and the calculation is represented as
vtN(7)=X1+GProbe(4)
Wherein, the GProbe (4) is input by an operator according to the actual contour of the tool;
from two detection points P1And P2Is calculated from the machine Y-axis motion position vtN (5), indicated as GvPMY, of the revolution radius (c), is shown as
vtN(5)=GvPMY
According to a theoretical front angle value GProbe (7) of tool design and a preset second avoidance angle GProbe (8) of the A axis during probe detection, a Z axis movement position vtN (6) of the machine tool is calculated and expressed as
vtN(6)=-GSys(3)-GvPMY·Sin((GProbe(7)+GProbe(8))
Controlling the X axis, the Y axis and the Z axis of the machine tool to rapidly move to an X axis movement position vtN (7), a Y axis movement position vtN (5) and a Z axis movement position vtN (6) respectively;
s7, searching speed V according to preset axis A3Controlling the A shaft of the machine tool to drive the cutter to rotate anticlockwise, and recording the coordinate theta of the A shaft when the probe is triggered1Then according to a preset first avoidance angle GMeasure (2) of an A axis and an A axis coordinate theta during probe detection1Calculate the A-axis motion position vtN (8), expressed as
vtN(8)=GMeasure(2)+θ1
And controlling the A shaft of the machine tool to rapidly move back to the A shaft moving position vtN (8);
s8, recalculating the X-axis movement position vtN (9) of the machine tool, specifically according to the X-axis coordinate X when the probe is triggered in the step S41Two probing points P1And P2Distance GProbe (5) in X-axis direction, probe point P1The distance GProbe (4) from the cutting edge in the X-axis direction is calculated and the X-axis movement position vtN (9) of the machine tool is represented as
vtN(9)=X1+GProbe(4)+GProbe(5)
And controlling the X axis of the machine tool to rapidly move to an X axis movement position vtN (9);
then searching the speed V according to the preset A axis3Controlling machineThe A shaft of the bed drives the cutter to rotate anticlockwise, and the coordinate theta of the A shaft when the probe is triggered is recorded2Recalculating the A-axis movement position vtN (10), specifically, according to the preset first avoidance angle GMeasure (2) of the A-axis and the coordinate theta of the A-axis during probe detection2Calculate the A-axis motion position vtN (10), expressed as
vtN(10)=GMeasure(2)+θ2
And controlling the A shaft of the machine tool to rapidly move back to the A shaft moving position vtN (10);
s9, calculating the axial inclination angle of the front tool face of the tool, specifically, two detection points P according to the turning radius GvPMY of the two detection points of the tool1And P2Angle difference delta theta of A axis when triggered, rake angle alpha of tool, and two detection points P1And P2The distance GProbe (5) in the axial direction is used for calculating the axial inclination angle of the rake face of the cutter and is expressed as
ξ=tan-1(GvPMY·sin(Δθ)/(cos(α)·GProbe(5)))。
The two detection points P1And P2The angle difference Delta theta of the A axis during triggering is specifically determined according to the probe at two detection points P1And P2Coordinate theta of machine tool A axis when triggered respectively1And theta2Calculating the angle difference Delta theta of the A axis, and expressing the angle difference Delta theta as
Δθ=|θ1-θ2|
In the above-mentioned on-machine detection process of the axial inclination angle of the tool, because the installation arrangement of the probe on the machine tool is different, the above-mentioned calculation method is taken as an exemplary embodiment to illustrate the function of the present invention, but the content is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention shall still fall within the scope of the present invention.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (7)
1. An on-machine detection and calculation method for the axial inclination angle of a tool rake face is characterized by comprising the following steps:
s1, clamping the cutter on a shaft A of a rotary main shaft of the machine tool, and acquiring the overhanging length GProbe (1) of the tip of the clamped cutter on the shaft A and the initial phase GProbe (3) of the front cutter face;
s2, setting a rake face phase deviation value vtN (1) of the A-axis rotary cutter, moving the C-axis to a zero position, and enabling a plane of the detection end side of the probe to be perpendicular to the axis of the A-axis;
s3, respectively calculating an X-axis movement position vtN (4), a Y-axis movement position vtN (2) and a Z-axis movement position vtN (3) of the machine tool, and controlling the X-axis, the Y-axis and the Z-axis of the machine tool to respectively move to an X-axis movement position vtN (4), a Y-axis movement position vtN (2) and a Z-axis movement position vtN (3);
s4, searching speed V according to the preset probe1Controlling the X axis of the machine tool to perform searching movement along the negative direction, and recording the X axis coordinate X when the probe is triggered1And controlling the machine tool to move back to the X-axis movement position vtN (4);
s5, selecting two detection points P on the front tool face of the tool1And P2Selecting two detection points P on the front cutter surface of the cutter1And P2The method comprises the following steps:
setting the maximum radius of the tool base body on the front tool surface as RmaxThe preset radial offset safety value is delta r along the radial outward offset of the cutter, and two detection points P are obtained1And P2Is represented by
GvPMY=Rmax+Δr
Setting a detection point P1Contour boundary near the front end of the rake face, probe point P2The distances from the profile boundary of the front tool face close to the tool shank are axial offset safety values xbAn auxiliary line parallel to the rotary axis of the cutter is made at the rotary radius of the measuring point, and the distance between the auxiliary line and the two intersection points of the cutter contour isL, calculating two detection points P on the tool1And P2The distance in the X-axis direction is expressed as
GProbe(5)=L-2·xb;
S6, recalculating the X-axis movement position vtN (7), the Y-axis movement position vtN (5) and the Z-axis movement position vtN (6) of the machine tool respectively, and controlling the X-axis, the Y-axis and the Z-axis of the machine tool to move to the X-axis movement position vtN (7), the Y-axis movement position vtN (5) and the Z-axis movement position vtN (6) respectively;
s7, searching speed V according to preset axis A3Controlling the A shaft of the machine tool to drive the cutter to rotate anticlockwise, and recording the coordinate theta of the A shaft when the probe is triggered1Calculating an A-axis movement position vtN (8), and controlling the A-axis of the machine tool to move backwards to an A-axis movement position vtN (8);
s8, recalculating the X-axis movement position vtN (9) of the machine tool, controlling the X-axis movement of the machine tool to the X-axis movement position vtN (9), and searching the speed V according to the preset A-axis3Controlling the A shaft of the machine tool to drive the cutter to rotate anticlockwise, and recording the coordinate theta of the A shaft when the probe is triggered2Recalculating the A-axis movement position vtN (10) and controlling the A-axis of the machine tool to move backwards to the A-axis movement position vtN (10);
and S9, calculating the axial inclination angle of the rake face of the cutter.
2. The method for on-machine detection and calculation of the axial rake angle of the tool rake surface according to claim 1, wherein in the step S2, the a-axis rotary tool rake phase offset value vtN (1) — GProbe (3) is set.
3. The on-machine tool rake face axial inclination angle detection and calculation method according to claim 1, wherein in step S3, a machine tool X-axis movement position vtN (4) is calculated based on a distance value GSys (5) between the probe detection end left side face and the a-axis tip positioning surface in the X-axis direction, a tool tip overhang length GProbe (1), a probe search start point safety offset distance GMeasure (1), and a projection distance value GSys (6) between the probe detection end left side face and the probe mounting axis on the XY plane, and expressed as a machine tool X-axis movement position vtN (4)
vtN(4)=-GSys(5)+GProbe(1)+GMeasure(1)+GSys(6)
Calculating the Y-axis movement position vtN (2) of the machine tool according to the gyration radius GProbe (2) when the end point of the tool is horizontal to the right phase, the chamfering length GSys (1) of the probe tip and the distance value GSys (2) of the probe tip and the axis of the A axis in the Y-axis direction, wherein the distance value is expressed as GPys (2)
vtN(2)=GProbe(2)-GSys(1)-GSys(2)
Calculating a Z-axis motion position vtN (3) according to a distance value GSys (3) of the probe cutting edge and the A-axis in the Z-axis direction and a height deviation value GSys (4) of the probe cutting edge relative to the probe installation axis in the Z-axis direction, wherein the Z-axis motion position is expressed as
vtN(3)=-GSys(3)-GSys(4)。
4. The method for on-machine detection and calculation of the axial rake angle of the tool rake face according to claim 1, wherein in step S6, the X-axis coordinate X is determined according to the trigger of the probe in step S41A detection point P1The distance GProbe (4) from the tool tip in the X-axis direction is used for calculating the X-axis movement position vtN (7) of the machine tool, and the calculation is represented as
vtN(7)=X1+GProbe(4)
From two detection points P1And P2Is calculated from the machine Y-axis motion position vtN (5), indicated as GvPMY, of the revolution radius (c), is shown as
vtN(5)=GvPMY
According to a theoretical front angle value GProbe (7) of tool design and a preset second avoidance angle GProbe (8) of the A axis during probe detection, a Z axis movement position vtN (6) of the machine tool is calculated and expressed as
vtN(6)=-GSys(3)-GvPMY·Sin((GProbe(7)+GProbe(8))。
5. The on-machine detection and calculation method for the axial inclination angle of the tool rake face according to claim 1, wherein in the step S7, the a-axis first avoiding angle GMeasure (2) and the a-axis coordinate θ are determined according to a preset probe detection time1Calculate the A-axis motion position vtN (8), expressed as
vtN(8)=GMeasure(2)+θ1。
6. The tool rake face axial rake angle of claim 1 being tested on-machineThe measuring and calculating method is characterized in that in the step S8, the X-axis coordinate X when the probe is triggered in the step S4 is determined1Two probing points P1And P2Distance GProbe (5) in X-axis direction, probe point P1The distance GProbe (4) from the cutting edge in the X-axis direction is calculated and the X-axis movement position vtN (9) of the machine tool is represented as
vtN(9)=X1+GProbe(4)+GProbe(5)
According to a preset first avoidance angle GMeasure (2) of an A axis and an A axis coordinate theta during probe detection2Calculate the A-axis motion position vtN (10), expressed as
vtN(10)=GMeasure(2)+θ2。
7. The on-machine detection and calculation method for the axial inclination of the tool rake face according to claim 1, wherein in step S9, two probe points P are determined according to the turning radii GvPMY of the two probe points of the tool1And P2Angle difference delta theta of A axis when triggered, rake angle alpha of tool, and two detection points P1And P2Distance GProbe (5) in the axial direction, and tool rake face axial inclination angle is calculated and is expressed as xi to tan-1(GvPMY·sin(Δθ)/(cos(α)·GProbe(5)))。
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