) and 
tool 
off- 
t the 
t cost 
agrees 
n line, 
and 
d be 
of 
r the 
uring 
acing 
and 
aking 
taken 
area 
the 
nworn 
d). 
n of 
the 
light 
ghted 
level 
the 
1:- in 
level 
the 
as: 
image 
aking 
that 
   
  
  
  
picture processed 43 shown as the Fy.3 of the 
appendix. 
3.Bulding gauging coordinate system 
In the theory and practice, the tool orthogonal 
plane coordinate system is often used to gaug, design 
and check the angle of cutting tool according to the 
Internation Oarganization for  Standardizalion. 
Because this research only uses two dimensional 
coordinate for measurement we build the gauging 
coordinate system as follows Fig3.1 
0 > 
  
Cutting Tool 
y Major: Flank 
Fig 3 
In the coordinate, the coordinate point is on the 
tool corner, the axis of abscissa is parallel to 
tool reference plane, and the axis of ardinate is 
vertvcal to tool reference plane. These axes are 
called relative axes. While the axes, which are 
definited by imagion system, are called absolute axes, 
In absolute system, the axis oj refers to vertical 
direction and axis oi refers to line scanning 
direction in the computerimage system, These two 
coordinace systems shoued be posited correctly 
follows as Fig.3.2 
o. + 
/ a 
De 
Fig 3.2 
But, the xoy system often takes correct pasition 
to ioj system showed as Fig3. 3 when taking 
micrograph. In this way, gauging erroes have been 
produced. 
It is nessary to adjust the relative position 
between ioj and xo’y. The o’xy system must be build 
at the practical position of cutting tool in taking 
picture, and then rotated or moved until the axes 
0’xy take correct position to oij system, Taking 
lath cutter with 0° tool cutting edge inclination as 
an example, The processing of building and 
transforming relative coordinate system is given as 
follows. 
Oo". 
Fi4 3.3 
Fig3. 3 shows the position of cutting centre in 
microscope visual field. To  constructe o’xy 
coordinate, the Lines, li and 12, which are the 
projctions of the face and the major flank of cutting 
tool in o’xy plane, should be produced, then the 
intersection point of l|] and l2 could be determind. 
This point could be refered to as cutting corner 
after wearing, 
After cutting procession, the parts of the face 
and the major flank around the corner have been worn 
partly. So the projectors of the two planes in o’xy 
are irregular curve, We take regression method to 
gain l| and 12. 
Cutting corner o’ appears a little curve in 
micrograph. Basing on caculating every slope of the 
point on curve, the point which has the largest 
slope could be selected, Then, the whole picture of 
the wear being taken by camera is rotated around the 
picture’s weight centre until the point with largest 
slope is placed on the highest position of the 
picture, From the highest point to the lowest point 
of the curve, we can make regression respectively in 
the two direction along the right and left of the 
highest point. 
It be supposed that the points which take part in 
regression are on the edge of the worn area. We can 
take several x with unequal values(x],x2,:-,xn) to 
test independently, then we could gain a series of 
the samples: (x1,y1), (x2, y2), =, (xn, yn). IF there are 
2 
y~NCa+bx, ¢ ) for every x, or y=atbxit& i, 8 i-NCo, 
2 
oc), i=l, 2,-,n for every point(xi, yi) , the 
probability density function is: 
  
1 
2 
exp [- —(yi-a-bxi )] 
2 
oon 20 
Because yl,y2,:-, and yn are independent for each 
other their coalition's probability density is: 
  
n 1 1 
2 
L-II —————exp[- —«yi-a-bxi) ] 
2 
i=l oVèT 20 
1 1 n 
n 2 
=( ) exp [- — Z2 (yi-a-bxi>] 3-1) 
2 
om 2g i-1 
In above formula, a and b can be estimated by proble 
method. Obviously, when L has the largest value the 
n 
function QCa, b)= 27 (yica-ixiX has the least value. 
i=1 
The following coupled equations can be obtained by 
deriving Q to a and b respectively: 
20 n 
—=-2 T(yi-a-bxi)=10 (3-2) 
2a i=l