29 n
—-2 2 Cvi-a-bxi)xi=g (3-3)
ab i-i
Then we can gain following equations by soving above
equations;
na+nXb = ny (3-4)
{ n n
2
nXat 2; xi b- 3j xiyi (3-5)
i=l i=1
In these equations, x is the mean of the xi,y is the
mean of the yi, Because the xi are not equal to
zerro at the same time, the coefficient determinant
is:
n nx n
2 2
n Hh 9 xi rd (3-6)
> S :
ne S xi i=1
iz] |
Obviously, the coefficient determinant is not equal
to zerro, so there is only result, The proble value
of a and b are:
$- yx 3-1
n n
T(xiyi-nXy) — Xixi-XXC(yi-y)
^ i=] i=l
b= = (3-8)
n n
2 ia oe
xi ~nx T(xi-X)
i=l $71
So, the line vegression formula could be obtained as
follows;
y- 5x (3-9)
Therefore, we can get two line equations
exprersing l1 and l2 through regressing respectively
from the left and right direction of the highest
point of the cutting corner.These lines represent
approximatively the projects of the face and major
flank of cutting tool before wearing. Basing on the
formulae of lj and 12, the intersection point of 1]
and l2 can be obtained, Then, rotating the pcture of
worn area around the point until l| being horizontal
that is paralled with oi and regarding l1 as o'x
ax'is and the intersection point as corner, the
gauging coordinate system(o’xy) could be built as
showed as Fig4 in appedix.
4.Detecting, classifying and recogniging the wear
state
The worn state of the major flank is often
classified two types: one is refersed to as the
ordinary wear which includes cracking without
sharp deformation, equal wear and corner wear,
another type is refersed to as inordinary wear which
includs — centrical wear and verge wear. The
recognazing models which descrrbe these types of
wear have been built based on the geometric state of
wear, x1 and yl are choiced as characteristic
constants of describing the wear geometric
character. x] and yl are separately defined as:
Xp
xL = (4-1)
Xmax
ymax
i= (4-2)
yave
In the formulae, xp is the coordinate of the
largest wearing point in the worn area, xmax is the
largest coordinate of x’s derection, yave is the
mean of wear value(y), ymax is the largest wearing
point of the worn area, They are showed in Fig4.1
000 v
"
Fig 4.1
xmax, ymax and xp could be obtained by detecting
the worn area with line scanning then yave can be
taken out. So the wear model can be recognized
according to the model schedule made before.
In addition to recognazing wear state, the worn
value would be gauging, in this studing, Worn
value, VB’, is defined as:
ymax
VB? = (4-3)
k
k is the amplification of the optical system,
Comparing practical VB’ to theoritical VB, the
wear degree of the cutting tool could be determined,
then we can ascertain wither the cutting tool should
be changed,
5.Forecasting the tool life and optimizing cutting
process
There are two major ways to forecast tool life: on
line and off line method, The on line method is the
way which could forecast the tool life effectively
by using gauging tool such as microscop for
detecting wear value and state in deferent time of
cutting process, While the off line way uses
theoretical or testing formula for counting wear
value and forecasting tool life based on cutting
data base, In this reseach, on line method has been
tanken to checking wear value, forecasting tool life
and building cutting data bace, Then, off line
method has been taken to optimizing the cutting
process,
5.1 On line method
According to Taylor formula:
bi b2 b3
VB= Ait f v (8-1)
VB is wear value, t is cutting time, f is cutting
feed, v is cutting velocity, A, bi, b2. bj are
constants, It could be abtained by taking lagarithm:
In VB=b1lnt+b2lnf+b3 [nv+ [nA (5-2)
Obviously, this equation indicates a line in
loganithmic paper, If the two points on this line
are known, the equation can be defined, So the VB at
any time can be determined, On the contrany, the
tool-change time(tmax) could be taken out based on
the limit of wearing, VBmax.
Through taking t1,t2 and VB1, VB2, to the two
point equation of line, the followed formula can be
gained
inVB-1nVB1 Int-inti
inVB2- lnVB1 Int2-lnt1
