Civil Engineering Reference
In-Depth Information
where the variable (
Q
) represents the material removal rate, and is expressed in volume per unit time,
and
F
and
F
are the normal force and threshold normal force, respectively. The threshold normal
N
TH
, is the lower limit of the normal force, below which no significant amount of material removal
takes place. The material removal coefficient is a function of many parameters including friction
coefficient, material specific energy and wheel velocity. As several of the measures required to determine
are not easily obtained, the coefficient is usually determined directly from experimental results.
Other early grinding research was conducted in the 1950s and 1960s by Shaw and others, as well as
Preston in 1927. Preston observed the relation between material removal and the abrasive power (the
product of the normal force and velocity) in loose abrasive polishing of optics. The Preston equation
(3.12) has been previously used to define the relationship between the normal grinding force, wheel
contact speed, and the MRR without directly addressing friction and specific energy (Brown, 1990). The
empirically-determined coefficient for the grinding model based on the Preston equation can be expe-
ditiously found. (Note the form is quite similar to that of Eq. (3.11).)
force,
F
TH
(
W
)
W
Q
P
F
N
V
(3.12)
correlates the normal grinding force to expected removal rates, given the relative surface
velocity, for specific materials and conditions of the workpiece and wheel.
The coefficient
K
P
F
is the normal force between
N
the part and the grinding wheel, while
V
is the relative velocity between the surfaces of the grinding wheel
and the part.
Model Complexity
The model developed in Eq. (3.11) has been shown to be adequate for real-time estimation and adaptive
control of the grinding process. However, other more complex formulations have been developed for
grinding force models (Salje, 1953; Shaw, 1956; Konig, 1973). All these grinding force models have a
basic formulation (Konig 1979, 1989) where the normal force (or tangential force) is related to various
combinations of the working engagement,
a
, cutting speed,
V
, feedrate,
V
, wheel diameter,
d
, and
e
c
f
e
specific energy,
u
. The general form of the relationships is given in Eq. (3.13). In this equation the
exponents,
1, 2, 3, 4), vary depending on the author. In some models other terms are also present
in the basic equation. For example, Salje uses the shear strength is a parameter, while a model by Ono
makes use of the average grain distance. The coefficient,
e
(
i
i
K
, and the exponents are determined experi-
o
mentally for particular situations.
V
feed
V
C
el
a
e
2
d
e
3
u
e
4
F
N
or
F
T
K
o
----------
(3.13)
As previously mentioned, these models are based on the chip thickness theory and the grinding contact
length, as well as a power balance. However, the exponents and coefficients of Eq. (3.13) are purely
empirical and depend on the specific grinding conditions and materials.
More recent grinding force models also present a similar formulation to that of Eqs. (3.11) and (3.12),
as given by Malkin (1989) in Eq. (3.14)
F
N
,
C
VA
k
l
u
C
.
Q
------------------
(3.14)
1
(
k
1
u
c
)
of Eq. (3.12) is identical to term in Eq. (3.14). This is also close
to the form of the model proposed by Coes (1972) in Eq. (3.15) accounting for wheel wear,
From this it can be seen that
K
P
q
, and
w
dulling by attrition,
q
.
a
q
w
KF
N
V
Q
------------------
(3.15)
q
a
q
w
