Civil Engineering Reference
In-Depth Information
chip thickness in face grinding for a constant triangular cross-section is
12
-------
V
W
V
3
Cr
h
MAX
-------
.
(3.9)
A typical relationship for estimating material removal based on the average or maximum chip thickness
and contact length is given in (10) (Liang, 1994).
l
C
----
2
Q
p
Cr
g
h
MAX
(3.10)
where
r
is the average grit aspect ratio,
a
is the grinding contact area, and the other variables are
g
p
previously defined.
Despite the advances in theoretical chip models, process variation (caused by wheel and part material
variations, wear, and loading) the main thrust of grinding process modeling has been directed towards
empirical models, especially for real-time applications. An interesting exception to this is precision engi-
neering work where a single-point diamond tip is used to cut surfaces at a nanometric level (Dresher and
Dow, 1990; Fawcett and Dow, 1991). However, most of this nanometric work is limited to research focusing
on precision ductile regime turning and grinding of monocrystalline or amorphous glass optics.
Empirical Models
Although theoretical models have generalizable equations, potentially applicable to a multitude of situ-
ations, their many unknown variables limit their accuracy and appropriateness for control applications.
Therefore, empirical models dominate grinding process modeling, especially in the calculation of forces
and material removal. There are several reasons for this, including the fact that empirical models can be
developed with relative ease. Experimental results can be used to determine process models, parameters
can be based solely on the data correlations. However, the quality of such empirical models can vary and
can be limited, depending on the specific process conditions. Also it is important to establish cause and
effect, rather than correlating effects. Thus, the most successful models, whether theoretical or empirical,
have a relation based on an underlying physical principals as well as empirical correlations.
As the grinding process is time-varying, time-invariant empirical models have limitations to their
applicability. Generally, such models are specific to the type of grinding, material, wheel type and wheel
conditions. With continued grinding, grits dull or drop out, the location and orientation of newly
exposed grits varies, and the wheel can load. With all these potentials for change, the conditions and
time duration of empirical model validity is a significant concern.
Empirical models for grinding and abrasive machining have been dated as early as 1927 (Brown, 1990).
Many empirical models have been used to describe various concerns of the grinding process. Grinding
models, focusing on different process aspects, can be separated into several categories: (1) force and
energy, (2) temperature, (3) roughness, (4) topography, (5) vibration and chatter, and (6) wear.
Force Models
The link between the normal contact force and the material removal rate has been established in
empirical models by several research groups (Salje, 1953; Shaw, 1956; Salmon, 1992; Brown, 1990; Hahn
and Lindsay, 1971). The selection of an appropriate mathematical model of the physical grinding process
for real-time control is the objective of this chapter; therefore, further discussion of empirical models
will be limited to force models. Hahn and Lindsay (1971) are generally regarded as publishing one of
the first modern models relating MRR to normal forces in grinding,
Q
W
F
N
(
F
TH
)
(3.11)
