Heat Transfer Handbook part 126 pptx

BOOKCOMP, Inc. — John Wiley & Sons / Page 1247 / 2nd Proofs / Heat Transfer Handbook / Bejan
MACHINING PROCESSES: METAL CUTTING
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Uncut
chip

Cutting
edge
a
␾
o
␾
o
␥
c
␥
o
␣
c
V

c
V
c
a
c
F
f
F
n
F
s
F
c
Chip
yy

x
x
()a ()b
f
RЈ
s
n
R
c
Figure 17.9 Chip formation during orthogonal metal cutting. (From DeVries, 1992.)
is assumed to be continuous, at least in the vicinity of the cutting tool, characteristic
of a ductile workpiece such as brass, low-carbon steel, or an aluminum alloy.
Plastic shear is the principal mechanism of chip formation. There is a finite volume
to the shear zone; however, at common cutting speeds, the angle between the planes,
which defines the deformation zone, collapses, so that the deformation appears to
occur in a single plane. For this reason, an infinitely thin zone of deformation is
assumed in most models. Figure 17.9b shows the force components between the
cutting tool and the workpiece that are needed to characterize the cutting process,
including the heat generation and temperature distributions.
DeVries (1992) has described the relationships among these forces and the geo-
metrical features of chip formation, all based on the classical literature. Several the-
ories are available to determine the shear plane angle φ
o
. One that minimizes the
cutting power is
φ
o
=
π
4

− 0.5

β − γ
o

(17.21)
where β is the friction angle, defined by tan
−1
µ, and µ is the coefficient of friction
between the chip and the tool, F
f
/F
n
. The resultant force at the shear plane must
equal the resultant force at the tool–chip interface.
R = F
c
+ F
s
− R = F
f
+ F
n
(17.22)
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1248 HEAT TRANSFER IN MANUFACTURING AND MATERIALS PROCESSING
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The shear force is then given by
F
s
= (l
s
b)τ
s
= τ
s
ba

sin φ
0
(17.23)
where τ
s
is the plastic flow stress of the material, l
s
the length of the shear zone, a
the depth of cut, and b the width of cut. Combining this information, one may obtain
results for the force components F
c
and F
n
as
F
c
= F
s
µ cos(φ
0
− γ
0
) + sin(φ
0
− γ
0
)
cos(φ
0
− γ

0
) − µ sin(φ
0
− γ
0
)
(17.24a)
F
n
= F
s
1
cos(φ
0
− γ
0
) − µ sin(φ
0
− γ
0
)
(17.24b)
The x component of the resultant force, F
p
, is also easily obtained.
17.4.2 Thermal Analysis
Typically, the heat sources in orthogonal cutting can be regarded as being localized
in three places in the cutting zone. Mechanical energy dissipated in the shear zone
consists of that needed to cause plastic flow (a relatively small amount) and that
converted into internal energy (heat). Usually, this is modeled as a planar heat source.

The second significant source of heating is the rake face between the moving chip and
the cutting tool face. The heat generated there by sliding friction is usually modeled
as a uniformly distributed planar heat source. A tertiary source is frictional heating
between the flank face of the cutting tool and the moving workpiece. For sharp tools,
the contact area is very small, resulting in the neglect of this source in most models.
The engineering information sought at the simplest analytical level is the temperature
rise at the tool–chip interface, which is due to a combination of the shear plane
heating of the chip and the frictional heating between the chip and the tool face. The
focus in the remainder of this section is on these two processes and is based on the
classical work of Trigger and Chao (1951) as described in DeVries (1992).
Tool–Chip Interface Temperature Rise The (assumed) uniform heating of
the chip as it passes through the shear zone is dealt with in the next section. Its
temperature is assumed to be T
c
and it moves with a velocity V
c
as it passes over
the tool surface through a frictional contact length l
c
. The total rake face heat flux is
given by
q

r
=
F
f
V
c
bl

c
(17.25)
Adapting the solution for the surface temperature rise due to a constant heat flux,
eq. (17.16), we may determine the average temperature rise at the chip/tool interface
to be
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MACHINING PROCESSES: METAL CUTTING
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(T
r
− T
0
)
avg
= (T
c
− T
0
) +
4
3
√
π
B
3
q

r
ρ
c
c
c
V
c


Pe
l
c
(17.26)
where B
3
is the fraction of the frictional heat flux that is conducted into the chip,
which is regarded as being infinitely thick for the short times associated with this
process. Trigger and Chao (1951) provided an ad hoc theory for the value of B
3
;
however, a conservative estimate of the rake face temperature rise is obtained if B
3
is
set equal to 1.
Energy Generation at the Shear Plane The heat flux through the uncut chip
cross section, bl
s
, the area of the shear plane, results in a temperature rise in the chip
as it passes through the shear plane:
q

c
= (T
c
− T
0
)c
c

ρ
c
V (17.27)
In turn, q

c
is given by the following expression:
q

c
=
B
1
(F
s
V
c/s
− F
p
VB
2
)
bl
s
=
B
1
[F
p
V(1 − B

2
) − F
f
V
c
]
bl
s
(17.28)
where B
1
is the fraction of the energy at the shear zone that goes into raising the
temperature of the chip as opposed to plastic deformation energy (typical values:
0.85 <B
1
< 0.95). The quantity B
2
is the fraction of the power dissipated in chip
formation that is conducted into the workpiece (typical values: 0.05 <B
2
< 0.15).
In a more complete numerical study of the thermal field in the vicinity of the shear
plane, Dawson and Malkin (1984) found that the average temperature rise of the chip
as it crosses the shear plane may be expressed approximately as
πkV (T
c,avg
− T
o
)
2αq


c
= 3.11(1 − 0.22e
−2.9φ
o
)e
−0.7φ
o
· Pe
0.5e
−3φ
o
l
s
(17.29)
and the fraction of the shear plane energy removed by the chip in cutting is given by
R = 1 − B
2
=
V(2 sin φ
o
)(ρc)(T
c,avg
− T
o
)
2q

c
(17.30)

A plot of this result is given as Fig. 17.10.
Assessment of Steady-State Metal Cutting Temperature Models This
section concludes with a brief summary of a study by Stephenson (1991) which com-
pared calculations from four steady-state metal cutting temperature models [Loewen–
Shaw (Shaw, 1984); Boothroyd, 1975 (as modified by Tay et al., 1976); Wright et al.,
1980; Venuvinod and Lau, 1986] with experimental results. Both tool–chip interface
temperatures and deformation zone temperatures were considered.
All the models assume that there are two heat sources, as discussed previously.
Differences arise in the method in which heat generation is partitioned among the
tool, chip, and workpiece, whether variations of thermal properties are considered,
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1250 HEAT TRANSFER IN MANUFACTURING AND MATERIALS PROCESSING
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Figure 17.10 Fraction of shear plane energy that enters the chip during metal cutting.
and how the rake face heat source is modeled. The Boothroyd and Wright models
use an energy partition analysis due to Weiner (1955) and thus assume less heat
flow into the workpiece than do the other two models, which use analysis based on
Trigger and Chao (1951). The Loewen–Shaw and Venuvinod–Lau models take into
consideration the variation of thermal properties, whereas the Boothroyd and Wright
models do not. Finally, the Boothroyd and Loewen–Shaw models assume that the rake
face source is a uniform heat source, while the Wright and Venuvinod–Lau models
can be applied with more general source strength distributions. Stephenson (1991)
found that the best results were obtained with the Loewen–Shaw and Venuvinod–Lau
models, while the Boothroyd and Wright models overestimated both rake face and
shear zone temperature rises by approximately a factor of 2 for a variety of materials
and cutting conditions. All models failed when chips produced were discontinuous so
that tool–chip contact length was not constant. Finally, all the models predicted shear
plane temperatures that were too high, probably due to their common assumption of
planar heat generation in the shear zone.
17.5 MACHINING PROCESSES: GRINDING
The goals of this section are to review the mechanisms of heat generation in metal
grinding and to provide an overview of some of the relevant modeling assumptions
BOOKCOMP, Inc. — John Wiley & Sons / Page 1251 / 2nd Proofs / Heat Transfer Handbook / Bejan
MACHINING PROCESSES: GRINDING
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used in thermal analysis. A detailed exposition of mathematical modelingfor grinding
is beyond the scope of this chapter; however, some key references to the literature
are cited.
17.5.1 Background

Grinding is a precision machining process capable of delivering surface roughness
10 times lower than that achieved by metal cutting and with dimensional accuracy
that is 10 times better. Grinding accounts for approximately 20% of all machining in
the United States.
One of the major differences between cutting and grinding relates to the num-
ber and geometry of the cutting edges. Grinding uses an abrasive wheel with many
randomly oriented cutting edges, while metal cutting uses a known number of cut-
ting edges with a controlled geometry. Orthogonal metal cutting involves the use of
positive or “moderately” negative rake angles. In grinding, the small abrasive grits
with random orientation give rise to large negative rake angles. The chips or swarf
produced in grinding are typically an order of magnitude smaller than that produced
in metal cutting. These differences are illustrated in Fig. 17.11. Although surface
grinding is not the most common type of production grinding, it is the simplest to
model, and like orthogonal cutting, has been the focus of most modeling effort, much
of which has occurred since 1990. Conventional grinding is characterized by small
depths of cut (0.005 to 0.05 mm) and fast workpiece velocities (100 to 500 mm/s),
whereas creep-feed grinding yields cut depths of 1 to 20 mm with very slow work-
piece velocities (1 to 50 mm/s). In both cases the wheel velocity (typically, 20 to
Figure 17.11 Schematic of the wheel–workpiece interface for a grinding process. (From
DeVries, 1992.)
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80 m/s) is much larger than the workpiece velocity. Other types of grinding are exter-
nal and internal cylindrical grinding, in which both the workpiece and the grinding
wheel are cylindrical; face grinding, which uses the flat edges of a cylindrical wheel
against a workpiece that moves perpendicular to the wheel motion; and abrasive cut-
off, in which a thin cutting wheel slices through a workpiece. In every case, how-
ever, the basic process involves the cutting action of individual abrasive grains acting
against the workpiece.
In grinding, more of the energy provided at the spindle is converted into heat,
making the potential for thermal damage to the workpiece significant. In orthogonal
metal cutting, the tool cutting edge experiences elevated temperatures. In the case
of grinding, more of the heat generated goes into the workpiece, which can lead to
elevated workpiece temperatures and metallurgical changes and subsurface damage

called burning, as discussed by Malkin (1984) and Guo and Malkin (1992). Addi-
tional review and recent advances in thermal modeling of grinding processes is con-
tained in Jen and Lavine (1995), Guo and Malkin (1996), Zhang and Faghri (1996),
and Ju et al. (1998).
17.5.2 Workpiece Temperatures during Grinding
At the level of an individual grain, heat generation occurs in the shear plane, at
the chip–grain interface due to friction there, and at the grain–workpiece interface.
At this scale, the methods described in Section 17.4 may be used to estimate local
temperatures, which may locally attain over 1000°C. Although these temperatures
may be important with respect to wear of the abrasive, they are not usually indicative
of the effects on workpiece quality, because they are so very localized (temporally and
spatially) and since material experiencing such temperatures will quickly be removed
by another grain. More relevant to workpiece damage is the average interference zone
temperature that results from the overall effect of all the grains in the contact region
and from the grinding fluid that is almost always present.
In this way, Malkin (1984) determined an expression for the maximum grinding
zone temperature rise to be
T
m
− T
o
=
βα
1/2
w
εP
k
w
bd
1/4

s
a
1/4
V
1/2
w
(17.31)
where P is the grinding power, ε the fraction of the grinding power entering the
workpiece as heat, a and b the depth and width of cut, V
w
the workpiece velocity,
d
s
the wheel diameter, k
w
the thermal conductivity of the workpiece, α
w
the thermal
diffusivity of the workpiece, and β a constant that depends on the heat source shape
(1.13 for rectangular and 1.06 for triangular). Malkin used a semiempirical analysis
to determine
ε =
u − 0.45u
ch
u
(17.32)
where the specific grinding energy u is equal to the grinding power divided by the vol-
umetric removal rate, and u
ch
is the chip formation component of this energy, which

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MACHINING PROCESSES: GRINDING
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may be regarded as a material property (about 13.8 J/mm

3
for ferrous materials).
Typical values of ε determined in this way are 0.7 to 0.9. Equation (17.31) neglects
heat transfer to the wheel (through the grains) and the grinding fluid, which may
restrict its validity to dry grinding or to the occurrence of film boiling in the grinding
fluid. However, it does permit determination of the onset of workpiece burn (critical
grinding zone temperature) in terms of a measured level of the grinding power.
If a grinding fluid is present, a very approximate analysis yields the following for
the fraction ε:
ε =
1
1 + (V
s
/V
w
)
1/2
[(kρc)
c
/(kρc)
w
]
1/2
(17.33)
where k
c
and (ρc)
c
in the product (kρc)
c

are weighted volumetric averages of the
thermal properties of the grain, grinding fluid, and air (porosity), and V
s
is the wheel
velocity. When applied to creep-feed grinding conditions, the energy partition to the
workpiece is determined to be a small fraction of that in conventional grinding.
Equation (17.33) may be modified for cubic boron nitride (CBN) grinding wheels
to account for the much higher thermal conductivity of the CBN abrasive grains than
that for aluminum oxide, by neglecting the effects of the grinding fluid (valid for
conventional grinding), to yield
(kρc)
c
= (1 − φ)
2
(kρc)
g
(17.34)
for insertion into eq. (17.33). The average wheel surface porosity φ is difficult to
estimate reliably; however, ad hoc estimates based on experimental measurements
imply that ε ≈ 0.2 and φ ≈ 0.9 for typical conditions with ferrous workpieces.
More recent attempts to predict temperature rise during grinding have sought to
eliminate the need to estimate a partition of the grinding energy or to determine effec-
tive fluid/grinding wheel thermal properties. The analytical details are too involved to
present here. However, the general approach, indicated schematically in Fig. 17.12,
is as follows. Separate analytical solutions are determined analytically for the con-
duction heat transfer to an individual abrasive grain, in terms of a heat flux q

g
;for
conduction into the grinding fluid from the workpiece, in terms of a heat flux q


f
;
Figure 17.12 Heat flow paths in the vicinity of an abrasive grain–workpiece interface. (After
Lavine and Jen, 1991.)
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for the background heat transfer into the workpiece from the entire grinding zone, in
terms of a heat flux q

wb
; and for the heat transfer into the workpiece from an individual
grain, in terms of a heat flux q

wg
. Then an appropriate coupling of these solutions is
established using continuity of temperature and conservation of energy applied in a
mathematically consistent way to each interface. The reader is referred to Jen and
Lavine (1995), Lavine and Jen (1991), and Ju et al. (1998) for additional details.
17.6 THERMAL-FLUID EFFECTS IN CONTINUOUS METAL
FORMING PROCESSES
In this section we review briefly some of the important thermal and fluid consider-
ations in continuous deformation processes such as drawing, rolling, and extrusion.
Metal forming processes exploit the property of metals that allows them to flow plasti-
cally in the solid state. By simply moving the material to the shape desired, as opposed
to removing unwanted regions, there is little or no waste. In general, a temperature
increase in the workpiece brings about a decrease in material strength, an increase
in ductility, and a decrease in the rate of strain hardening (all of these effects tend to
promote the ease of deformation).
17.6.1 Background
Deformation processes tend to be classified as hot working (recrystallization occurs
simultaneously; T
initial
≥ 0.6T

melt
), cold working (T
initial
= 0.3T
melt
), or warm work-
ing. However, because the general principles governing deformation at different tem-
peratures are basically the same, classification according to specific input and output
geometries and material and production rate conditions is often more useful. There-
fore, one may broadly characterize forming operations under the headings of forging,
sheet metal forming, drawing, extrusion, and rolling, the latter three being examples
of continuous processing. An understanding of thermal effects in such systems is
integrally coupled to a characterization of the metal flow, stresses, lubrication, and
material handling and design of the forming equipment, so that a simple thermal
analysis even for generic types of systems may not characterize a process completely.
Among classical references, Altan et al. (1983) and Schey (1983) are detailed and
complete, albeit with limited consideration of thermal and heat transfer effects. Yang
(1992) and Tseng et al. (1990) also provide useful discussions of thermal effects in
extrusion and drawing and in rolling, respectively. The focus of the present section is
on factors associated with the temperature rise of the workpiece and the die (or roll).
17.6.2 Considerations for Thermal–Fluid Modeling in Extrusion
and Drawing
Figure 17.13 includes schematic illustrations of generic continuous deformation pro-
cesses. (Although extrusion is a batch process, it is often studied as a quasi-steady-
state process.) The principal distinctions among these are the delivery of the force to
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THERMAL-FLUID EFFECTS IN CONTINUOUS METAL FORMING PROCESSES
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Figure 17.13 Schematic diagrams of rolling, drawing, and extrusion processes. (After Altan
et al., 1983.)
the workpiece, the reduction in the cross section of the workpiece, and the speed. Heat
generation arises from two sources: plastic deformation heating of the workpiece and
frictional heating between the workpiece and the die (Fig. 17.14).
Deformation Heating Considerations In wire drawing and often in rolling,

the deformation and hence the heating of the workpiece due to the plastic flow of
the material may be considered to be nearly uniform (Wright, 1976). Under these
conditions, the uniform temperature increase of the wire is given by
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Figure 17.14 Surface and core temperature distributions during a drawing process.
∆T
DH
=
W
D
ρ
w
c
w

τ
s
ln(A
o
/A
1
)
ρ
w
c
w
(17.35)
where W
D
is the deformation work per unit volume, τ
s
the flow stress of the work-
piece, A

o
and A
1
the initial and final cross-sectional areas, and ρ
w
c
w
the volumetric
specific heat of the workpiece.
Frictional Heating Considerations Frictional heating is concentrated near the
wire–die interface, resulting in severe temperature gradients. In the simplest physical
model, the latter is regarded as arising from a friction coefficient (assumed known
and constant) and the normal stress on the workpiece, which is usually assumed to
be the yield stress of the workpiece. Apparent friction coefficients can vary from
0.01 (hydrodynamic lubrication) up to 0.5 (boundary lubrication). Then if a suitable
partition coefficient for the transfer of heat between the workpiece and die can be
discerned, an estimate of temperature levels may be obtained. Even though uniform
friction and heat partition coefficients may not be realistic, many modeling efforts are
based on their use (Snidle, 1977; El-Domiaty and Kassab, 1998). Figure 17.15 shows
results for a calculation of two-dimensional temperature distributions in a drawn steel
wire using a similar model for the die–workpiece interface; Fig. 17.16 shows a similar
result for a hot aluminum extrusion process.