Predictive Analytical and Thermal Modeling of Orthogonal Cutting ...

Table 2 Cutting conditions for AISI 1045 steel „w=2…†24‡
Test V m/min deg t u mm t c mm a
stress distribution is more complicated. Over the portion of the
tool-chip contact area near the cutting edge, sticking friction occurs,
and the frictional shearing stress int is equal to the average
shear flow stress at tool-chip interface in the chip kchip. Over the
remainder of the tool-chip contact area, sliding friction occurs,
and the frictional shearing stress can be calculated using the coefficient
of friction e. The normal stress distribution on the tool
rake face can be described by
Nx = Nmax1− x a
lc 27
where Nmax is given by Oxley 4 as
Nmax = p B +2k AB − 28
Unknowns in Eq. 27 are lc and a, which require two equations to
solve. Integrating the normal stress along the entire tool-chip contact
length yields the relation in Eq. 29, which is equal to normal
force on the tool rake face
lc lc FN =0
wNxdx =0
wNmax1− x a
dx 29
lc Also taking the moment according to point B
F NX fr =0
and denoting
l c
w Nxxdx =0
l c
I = N max X frw
F N
wNmax1− x a
xdx 30
lc 31
From Eqs. 29 and 30, the contact length along the tool-chip
interface l c and the exponent a can be obtained as
a =−1+ 16I 2 −8I
4I −2
deg a
1 200 −7 0.150 0.33 22
2 200 +5 0.150 0.33 25
3 200 −7 0.300 0.6 24
4 200 +5 0.300 0.6 27
5 300 −7 0.150 0.31 24
6 300 +5 0.150 0.31 26
7 300 −7 0.300 0.58 25
8 300 +5 0.300 0.56 29
a As predicted with the model.
32
Table 3 Force and temperature predictions for AISI 1045 steel
Test
Predicted
F C N
Predicted
F T N
Predicted
T AB
Predicted
max T int
Measured 23
max T int
1 662 466 370 1080 1120
2 596 324 332 1125 1250
3 1206 728 369 1170 1100
4 1097 509 319 1158 1220
5 613 371 370 1241 1310
6 576 288 330 1227 1300
7 1174 671 365 1329 1305
8 1046 430 311 1310 1300
Fig. 10 Comparison of the predictions of the cutting force „a…,
and thrust force „b… with experimental data from †23‡
lc = FN . a +1
33
awNmax The shear stress distribution on the tool rake face illustrated in
Fig. 7 can be represented in two distinct regions: a in the sticking
region intx=k chip and when eNxk chip, 0xlP, b
in the sliding region intx= eNx and when eNx kchip, lPxl c. Here int is the shear stress of the material at
the tool-chip interface, and it is related to the frictional force
between the chip and the tool, FF,as Table 4 Predicted normal stress distribution parameters for
machining AISI 1045 steel
Test Nmax N/mm 2 l p mm l c mm a
1 1380 0.12 0.6 0.75
2 992 0.11 0.54 1.1
3 1305 0.13 1.04 0.89
4 1007 0.28 0.91 1.3
5 1308 0.07 0.52 0.9
6 970 0.11 0.56 1.3
7 1325 0.14 0.98 0.91
8 1039 0.28 0.82 1.4
440 / Vol. 128, MAY 2006 Transactions of the ASME