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Study of the jet-flow rate of cooling in machining Part 1. Theoretical analysis
JeexaJal ~l'
Materials
FrocessNg
ELSEVIER
Technology
Journal of Materials ProcessingTechnology 62 (1996) 149 156
Study of the jet-flow rate of cooling in machining Part 1. Theoretical analysis Xiaoping Li* Departo:ent of Mechanical end Production I:)~gineermg, National Universit , o/Singapore, 10 Kent Ridge Cresent. Singapore 051 I, Singapore
Received 14 April 1995
lndmtrial summary Coolants are used in most machining processes in industry to prevent cutting tools from overheating. In order to achieve the best results of cooling, general guidelines on the method of applying coolants are needed. One of the issues is how to sele."t the jet-flow rate of cooling to cope with the progress of automation in machining manufacturing, in which high-speed machining is is often performed, and on the other hand how to satisfy environmental concerns which require minimization of using coolant. r o answer this question a detailed understanding of the effect of the jet-flow rate of cooling on the cooling action in machining is needed. In this study, the effect of the jet-flow rate of cooling in machining on the cooling heat-transfer coefficient is analysed theoretically, and the effect of the jet-flow rate of cooling on the temperature distribution in the cutting region is examined through numerical simulation of machining with cooling at different flow rates. In Part 1, mathematical models ale developed for the heat-transfer coefficients of cooling applied in machining with a water coolant in the commonly-used cooling method: overhead-jet cooling and flank-jet cooling. The relationships between the heat-transfer coefficient and the jet-flow rate in the cooling processes ale analysed using these models. The results indicate that the cooling heat-transfer coefficient increases with increasing the jet-flow rate. However, a small percentage increase in the heat-transfer coefficient requires a large percentage increase in the flow rate. In overhead-jet cooling, to increase the heat-transfer coefficient by n times, the flow rate has to be increased by about n ~'~7 times, whilst in flank-jet cooling, to increase the heat-transfer coefficient by n times, the flow rate has to be increased by about ,2 times. KcJ'wonl,~: Machining; Cooling; Heat-transfer coefficient: Modelling
1. Introduction tteat is generated in machining due to chip formation and friction at the t o o l - c h i p and t o o l - w o r k interfaces. The heat results at extremely high temperatures in the cutting region, which reduces the hardness o f the tool materials and enhances chemical reactions at the t o o l chip and t o o l - w o r k interfaces such that the tool life is shortened. In order to reduce the temperature in the cutting region, cooling is conducted in most machining processes. The commonly-used cooling methods are overhead-jet cooling and flank-jet cooling, as shown in Fig. 1. In both methods, a water-based coolant is usually used, and heat is removed from the cooled boundary surfaces o f the cutting region by the coolant flowing over the surfaces. The rate o f removing heat
from tile surfaces depends mainly on the velocity o f the coolant flowing along the surfaces, which is related to the jet-flow velocity o f the coolant at the jet nozzle. The
t Flank let coaling
Work *Corresponding author. Fax: (65) 779 1459; e-mail: [email protected]. 0924-0136/96/$15.00 © 1996 Elsevier Scier,ce S.A. All rights reserved SS DI 0924-0136(95)02197-9
Fig. I. Overhead-jet cooling and flank-jet cooling in machining.
150
X. Li / Journtd of MttWrials Prot'ess#lg Technology 62 (1996) 149-156
Jet flow
J
e
~
Fig. 2. Jet impingingon a flat surface(schematically). shape and size of the jet nozzle fitted to a machine is usually fixed. Therefore, the heat-removing rate is related directly to the flow rate of the coolant from the jet nozzle, i.e. the effectiveness of coo!ing depends on the jet-flow rate. With the progress of automation in machining manufacturing, the cutting speed in many machining operations has been increased considerably. These changes will eventuaIly require the efficiency of cooling to be increased in order to cope with the increase in the cutting temperature. On the other hand, legislation in many countries are closing in restrictions oil machining coolants, because of environmental issues. 'Tllere are limits on the amount of coolant mist and some coolants and coolant-coated chips have been treated as toxic materials. Outside the plant, the rising cost of chip disposal and the potential secondary effects of coolant vented to the atmosphere are new concerns' [1]. As a result, the amount of coolant to be used in machining is expected to be limited to the actual need, which requires accurate estimation on how much coolant is actually needed. Therefore, a knowledge of the ~'elationship between the effectiveness of cooling and the jetflow rate of cooling is needed by machine tool designers and operators to achieve optimum design of the cooling system and ~o determine optimum values of the jet-flow rate. In the literature, very few detailed studies of the effect of coolant flow rate on the machining process can be found. Taylor [2] reported that in cutting with a high-speed steel tool, increasing the cutting ~peed, which resulted in an increase in the production rate from 30 to 40%, was achieved by applying a heavy stream of water poured directly upon the chip and tool
rake face. He also reported that small streams of weater trickled upon the tool and workpiece were utterly inadequate for the purpose of cooling the tool. The effect of a water-based coolant on the average temperature at the tool-chip interface was studied experimentally by Shaw et al. [3], and the effect of a water-based coolant on the temperature distribution in the cutting region of a high-speed steel tool was studied experimentally by Smart and Trent [4]. In both studies, the jet-flow rate of cooling was kept constant and its effect on the efficiency of cooling was not investigated. Mazurkiewicz [5] reported that a water-based coolant applied at the toolchip interface through a high-pressure jet nozzle reduced the contact length and coeficient of friction at the tool-chip interface, which resulted in lower cutting forces, longer tool life and tighter-curled chips, compared with machining with conventional pressure jet cooling. In their study, the focus was on the coolant pressure at the jet nozzle, the jet-flow rate of cooling being kept constant and not being discussed. A theoretical and experimental study of the effects of cooling on the temperature distribution in machining was presented by Childs et al. [6]. In this study, a range of values for the average heat-transfer coefficient along the boundary surfaces of the tool tip and tool holder were assumed for overhead jet cooling actions in machining with a water-based coolant. The temperature distribution in the cutting region and in the tool holder corresponding to the assumed average heat-transfer coefficients in cutting over a range of cutting conditions were calculated with the finite-element method. From comparisons of the calculated temperature distributions and the experimentally measured results, it was found that the assumed heat-transfer coefficient values of
X. Li /,hmr~ml gf MateriaLs' Processbtg Tech,.oh~gy 62 (19!~b) 149-156
103 W/(m 2 K) and 5 x 10-~ W/(m a K) matched the effects of the coolant flow rates of 0.251 I/min and 2.51 l/rain, respectively, on the temperature distribution in the turning of 0.43% carbon steel at a speed of 61 m/rain, a feed-rate of 0.254 mm/rev and a depth of cut of 2.54 mm. From their results, the trend of the effects of coolant flow rate on the cooling action and consequently on the temperature distribution in the cutting region, can be observed. However, quantitatively these effects can hardly be concluded, because there were several limitations associated with their method. In the determination of the cooling heat-transfer coefficient, it is inadequate to describe the cooling action in cutting by an average heat-transfer coefficient for all the boundary surfaces of the tool tip and the tool holder, because the actual value of the local heat-transfer coefficient along the boundary surfaces in overhead jet cooling (the cooling method considered in their study) varies substantially from the central cooling zone to the rest of the surfaces. It has been shown [7] that by using a local heat-transfer coefficient determined through theoretical modelling of the cooling process and using an assumed heat-transfer coefficient, the calculated temperature distributions can be significantly different. Therefore, in the temperature calculations it is more appropriate to consider local heat-transfer coefficients along the cooled boundaries, including the work- and chip-surfaces exposed to coolant. Since these coefficients are a function of the coolant flow and temperatures at the cooled surfaces and in the coolant bulk, their values vary fi'om case-to-case in machining. In determining the coefficients for studying the effect of cooling on machining, it is impractical to assume their values and then perform machining experiments to confirm them through examining Ihe matches between the temperature distributions measured experimentally and calculated using the assumed values, because the experiments for various combinations of machining conditions could be too numerous to conduct. Instead, theoretical models for cooling heat transfer should be developed for this purpose. Also, in their calculation of temperatures in the cutting region, it is unreafistic to assume that heat is generated only from the shear plane and friction along the tool-chip interface. In cutting of steel under most of the cutting conditions the chip will be plastically deformed along the tool-chip interface, and a secondary plastic detbrmation zone is thus formed in the chip, in which a significant amount of heat is generated. This heat-generation source should be taken into account for the temperature calculation. Another heat source which should also be taken into account is the heat generated due to friction along the tool flank-work interface. In the present study, theoretical models for the heattransfer coefficients in overhead-jet cooling and flankjet cooling are developed. The relationships between the
151
jet-flow rate of cooling and the corresponding heattransfer coefficient in the cooling processes are described using the models. The effects of the jet-flow rate of cooling on the heat-transfer coefficients in the cooling processes are then analysed, these are presented in Part 1. In Part 2 [8], realistic models for chip formation and heat generation in the machining of metals will be described and a method for calculating the temperature distribution in the cutting region, when machinipg with cooling at different jet-flow rates will be developed. Using the method, the effects of the coolant flow rate on machining temperature will be tested and the results will be presonted.
2. Modelling heat-transfer of cooling in machining In machining with overhead-jet coolant or flank-jet cooling, part of the heat generated is removed by the coolant flowing over the exposed surfaces of the cutting region. In the cooling processes the rate of removing heat by the coolant depends on the thermal conductivity of the coolant and cook~:at temperature gradient at the cooled surface, the latter depending on the flow field in the coolant. The overall effect of the cooling actions can be described using a heat-transfer coefficient, h, defined by: q = hA(T,, - T 0
(I)
where q is the heat-transfer rate related to the overall difference between the temperature at the exposed surface, 7",,, and the bulk temperature of the coolant, It., and A is the coaled surface area. Therefore, the effect of the jet-flow rate of cooling on heat transfer along the cooled boundary surlaces can be examined by investigating the effect of the flow rate on the corresponding heat-transfer coeffÉcient. For forced-convection heat transfer, a simplified form representing the heat-transfer coefficient is usually used: Nu =f(Re, Pr, generic shape)
(2)
where, the functional relation is a power law, Nu = hl/K is the Nusselt number, Re=pvl/l~ is the Reynolds number and P r = Cr,ll/K is the coolant Prandtl number, where I and v ale the characteristic length and velocity. K, p,/~ and Cp are the coolant properties: conductivity, density, viscosity and specific heat, respectively. In the case of a jet impinging on a surface (see Fig. 2) the heat-transfer coefficient, h, depends also on other parameters: normalized jet nozzle<~-~lane spacing L/D; jet inclination angle, ~3; displac~cnt of the stagnation point from the geometric centre of the jet on the impingement surface, E; normalized distance from the stagnation point to a point considered on the impingement surface, r/D; jet Reynolds number Rej = pUjD/It,
X. Li / Journal of Materials Processing Technology 62 (I 996) 149-156
"152
. ~ N* •
Goldstein and Frankchett [12] on heat transfer from a flat surface to an oblique air jet is considered for determining the heat-transfer coefficients in overheadjet cooling. Goldstein and Franchett [12] proposed a correlation equation for the local Nusselt numbers in the form:
J,~t nozzle
Nu/Rej a'7 = A e x p [ - ( B + C cos q~)(r/D)"]
Tool
I
where D is the diameter of the jet nozzle, and r and ~b are cylindrical coordinates for correlation of contours of constant Nu. For two-dimensional problems, r is the distance from the stagnation point on the cooled surface, whilst ~b is determined according to: I0, n,
Fig. 3. Categorizationof overhead-jetcooling. which latter is based on the diameter of the nozzle, D, and the jet velocity at the exit plane of the nozzle, Uj. Correlation for heat-transfer coefficients in overhead-jet cooling and flank-jet cooling are now considered. 2.1. Overhead-jet cooling
A schematic representation of overhead-jet cooling in machining is shown in Fig. 3. In this method, a coolant is applied on the back of the chip and the tool rake face through a jet nozzle. The boundary surfaces exposed to coolant include the undeformed workpiece surface IA, chip surfaces AH and CG and the tool rake face CM. The cooling is a process of heat transfer from a flat surface to an oblique impinging liquid jet, in which the physical properties of the liquid vary with temperature. Previous investigations on heat transfer from a flat surface to an impinging liquid jet include the work of Smirnov et al. [9] on the average heattransfer coefficient in an axisymmetric normally impinging water jet, and Metzger et al, [10] on the effects of the Prandtl number on the heat-transfer characteristics of impinging liquid jets and the work of Stevens and Webb [11] on local heat-transfer coefficients. Unfortunately, there is no reported work related directly to local heat-transfer coefficients in heat transfer from a flat surface to an oblique impinging liquid jet. In the present study, the experimental work presented by
along the side of surface with % < zr/2 along the side of surface with ~j > n/2
90° 60° 45° 30°
a
A
L/D=4
L/D=6
L/D=
0,159 0,163
0.155 0,152
0.123 0.115
N t t / R e / ' 7 = ,4Prt:3Rej exp [ - ( B + C cos ~b)(r/D)"]
0.161
0.146
0.107
0.136
0.124
0.091
(5)
where ,,i is a coefficient corresponding to A in Eq. (3). From comparison of Eqs. (5) and (3): f f P r 1/3 = A
hence, . 4 = A / P r t/a = 1.122A
(6)
where the value of Pr for air was taken at the temperature used in Goldstein and Franchett's experiments [12], i.e. Pr=0.708. Substituting Eq. (6) into Eq. (5) the modified form of Eq. (3) is obtained:
C
I0
0.37 0.40 0.47 0.54
(4)
The coefficients of this correlation are shown in Table i, where E is the displacement of the stagnation point as described in Fig. 2, Good agreement between the Nusselt numbers calculated from Eq. (3) and the experimental values was shown by Goldstein and Franchett [12]. Unfortunately Eq. (3) is based on experimental data for air jets. However, since the main difference in heat transfer between air and liquid jets results from the physical properties of the two media, it is contented that Eq. (3) can be modified for liquid jets, this modification can be achieved by adding the Prandtl number, Pr, to the correlation. Pr does not appear in Eq. (3), because for air P r ~ 0.7 and Pr ~,'-~(note that N u c z P r ~'3) is close to unity. Therefore, Eq. (3) may be ,ewritten with Pr included:
Table I Correlation coefficie~.t~[8] %
(3)
0.0 0.12 0.23 0.34
E L/D=4
L/D=6
L/D= I0
0.0 0.8 1.2 1.5
0.0 0.6 1.0 1.4
0.0 0.9 1.5 1.9
X. Li / Journal of Ml te'R Is Prot'essing Ter'tolology 62 (1990) 149-156
153
Table 2 Average Nusselt numbers predicled using different equations" Jet inclination angle ~i
A~erage Nusselt number Nu
Equationused lbr prediction
61)°
(Eq. 7) Smirnov et al.'s (Eq. 7} Smirnov et al.'s {Eq. 7) Smirnov et al.'s
45° 30°
Rt3 = 10000
Rej = 20000
Rej = 30000
106 113 100 102 88 88
172 176 162 159 143 138
228 229 215 207 190 179
a The jet nozzle diameter D = 10 mm; the normalized jet nozzle-to-plane spacing L/D = 10; the Prandtl number for water at 22 °C is Pr = 6.78. and the cooled plate diameter d = 48 mm. N u = 1.122APrl/aRej°'7 e x p [ - ( B + C cos q~)(r/D}'"]
(7)
where the coefficients A, B, C and D are the same as those shown in Table 1. With the modified equation, Eq. (7), the local Nusselt numbers for both air jets and liquid jets can be predicted if the relevant value for P r is provided. Since P r is composed entirely o f the physical properties o f the coolant and is a function o f temperature, its value is determined according to the average temperature calculated from the heated surface temperature and the coolant bulk temperature. Information about h o w the values o f P r vary with temperatare for commolfly-used coolant liquid, such as water, is available easily in the literature [13]. Eq. (7) has been checked for accuracy using the results o f Smirnov et al. [9] and Stevens and Webb [11] based on experimental data lbr liquid jets. A comparison o f the average Nusselt numbers predicted for cooling at a range o f jet oblique angles and jet Reynolds numbers using Eq. (7) and the correlation equation by Smirnov et al. is shown in Table 2. (Note that since Eq. (7) gives the local Nusselt number N u calculations o f the values o f the average Nusselt numbers N u using the equation adopted the following procedure. Local Nus180
I
*
I
*
I
I
I
selt numbers was firstly calculated from Eq. (7), these then being averaged over the impingement area.) The results show that discrepancies between the Nusselt numbers determined using the two methods for each condition are less than 6% based on the results by Smirnov et al. [9]. Fig. 4 shows a comparison o f the average Nusselt number predicted using Eq. (7) and Stevens and Webb's [ll] correlation equation from experimental data for heat transfer from a flat surface to a normally (% = 90 °) impinging single-phase water jet for a range o f Prandtl numbers. The predicted result is in good agreement with experimental results. 2.2. Flank-jet cooling
A schematic description o f flank-jet cooling is given in Fig. 5. in this method the coolant is applied on the tool flank face and the machined workpiece surface. Usually, the jet nozzle is set at the end o f the tool flank lace with the axis o f the jet being symmetrical to the gap between the machined workpiece surface and the tool flank, The machined workpiece surface and the tool flank form a wedge-like space with an apex at ffieir joint, The flow o f coolant between the two surfaces is three-dimensional, with the coolant being forced to
'
160 140 ==
Chip
120 100
x~
u0 '
/-"
Tool
60
.~ 40 20 0
I
2
,
I
3
~
I
~
I
I, 5 Prandtt numbers
~
I
6
Fig. 4. Average Nusselt numbers predicted using different equations (the local Nusselt numbers were firstly calculated from an equation, then being averaged over the impingement area): (A) from Ref. [7], and (O) from Ref. [11].
Fig. 5. Categorization of flank-jetcooling.
154
X. Li / Journal of Materials Process#~g Technology 62 (1996) 149-156
change flow direction in the region near to the apex. Since a method for determinin~ the heat transfer from the two surfaces to such a complex flow pattern is lacking, in this study it is assumed that the flow of coolant is parallel to both surfaces. This assumption is reasonable, because the tool clearance angle is usually very small. Therefore, the cooling process can be considered as heat transfer from a flat surface to a parallel liquid flow. It is noted that in this way the approximation made on the coolant flow pattern could result in slightly overestimating the heattransfer coefficient. It should, however, be sufficiently accurate for the present purposes. The process of heat transfer from a flat surface to a liquid which flows in a direction parallel to the surface was investigated by many researchers and typical results for heat-transfer coefficients have been well documented in the literature [14]. Only the equations relevant to the present analysis are given here. For heat transfer from a heated plane at constant temperature to a liquid in laminar boundary layer flow over it, the local Nusselt number at a point with a distance x from the leading edge is: h~x Nu, = ~ = 0.332Pr 1'3Rev i,,2
(8)
where Re.,.<~5 x 105. The average heat-transfer coefficient and Nusselt number may be obtained by integrating over the length L of the plane: NuL = --g-= 0.664Pr I'3ReL t~2
(9)
where Ret. ~<5 × 10s, and, pU~L ReL = ~ g
Similarly to Eq. (7) in overhead-jet cooling, in Eqs. (8) and (9) Pr is a function of temperature and is determined according to the average of the temperatures at the cooled surface and in the coolant bulk. It should be mentioned that the above-considered processes of cooling in machining are limited to singlephase heat transfer, where heat is transferred only by convection. In fact, when the heat flux from the surface cooled by coolant is greater than a particular value, the convective heat transfer is not sufficiently strong to prevent the surface temperature from rising above the saturation temperature of the liquid, and boiling may occur. Boiling may occur in one of two ways, depending upon the surface temperature. If the temperature is not much above the boiling point of the liquid, nucleate boiling occurs; if it is well above, film boiling occurs. In boiling, heat is transported by the boiling bubbles in several ways [15] and is also transferred by single-phase convection between patches of bubbles. Due to these
different mechanisms, the heat-transfer coefficients for boiling could be greater or much greater than those in single-phase convection, depending on the boiling state [13]. For boiling heat transfer from a fiat surface to an impinging jet, experimental results from investigations of the characteristics of nucleate boiling with jet impingement have been presented by Ma and Bergles [16]. The investigations included the effects of velocity, subcooling, flow direction and surface condition on fully developed boiling. The results showed that, in general, much of the experience and procedures developed lbr forced convection boiling inside tubes can be applied to jet impingement boiling. In some machining cases, heat flux from the boundary surface may be sufficiently large for boiling to occur. For these cases the heat-transfer coefficients should be calculated according to boiling heat-transfer. However, since the process of machining is very complex, there has been no way to determine where and when a steady boiling process may occur. As a result, calculation methods for boiling heat transfer are not available. Therefore, in the present work it is assumed that for most cases of cooling in machining, sufficient and continuous coolant supply will naturally keep the cooling action within the range of subcooled forced convection before the incipient boiling point. Thus the heat-transfer coefficients will be calculated from the single-phase convection equations presented in the preceding sections. It should be noted that the results calculated in this way may be conservative for cases where boiling does occur.
3. Relationship between flow rate and heat-transfer coefficient
Using the cooling heat-transfer models developed in Section 2, the relationships between coolant flow rate and the corresponding heat-transfer coefficient in overheadjet cooling and flank-jet cooling are now considered. For overhead jet cooling, from Eq. (7): Nu = 1.122APrl/3Rej °'7 exp[-(B + C cos q~)(r/D)'"]
By definition: hD Nu = - K
(10)
and Rej = p U j O (11) P where h is the heat-transfer coefficient, p and p, the density and viscocity of the coolant, respectively, D the diameter of the jet nozzle, and Uj the velocity of the jet flow, which is given by:
Q
vj = a~
02)
X. Li/ Jouroal ~1"Materials Process#tg Technology 62 (1996) 149-156
where Q is the coolanl jet-flow rate and Aj = ~rD2/4 is the cross-sectiona! area of the jet nozzle. Substituting Eqs. (10)-(12) into Eq. (7) and using symbol g2o to represent all the factors that are indelrendent of Q, the relationship between h and q can be written as: h = 0000.7
(13)
Eq. (13) shows that a large percentage increase in Q results in only a small percentage increase in h. Consider increasing Q from Qola to _On.... so that h becomes h ~ w = n × hold, from Eq. (13)the relationshi F of h and q can be rewritten as: Q = h ~/o.7
(o)
5, Conclusions
(hoo,A,,o. (,,,o=VO.,
n°'=
t~-~)
= t, Q--S-)
(is)
and from Eq. (13): hold = ,.CoQold°'7 therefore, Qn~w= n l/O.TQokl
( t 6)
Similarly, for flank-jet cooling, from Eq. (9): 1/3 = k = 0.664Re, I,r2pt,
and using the same method as used for overhead-jet cooling, an expression for the relationship between h and Q can be obtained: h = OrQ 112
(17)
where g2r represents all the factors that are independent o f q in Eq. (9). An expression similar to Eq. (16) can be derived from Eq. (17): Qn~,,, = n2Qoid
10 l/min to Q .... = 31'°7 × 19 = 48 l/rmin, i.e., to increase the value of heat-transfer coefficient by three times, the flow rate has to be increased by about five times. From Eqs. (17) and (18), a similar trend can be seen in flank-jet cooling. According to Eq. (18), in order to increase the value of the heat-transfer coefficient by n times by increasing the jet-flow rate, the value of the flow rate has to increased by n 2 times. If initially the flow rate is Qo~d= 10 l/min which results in a value of heat-transfer coefficient h, to increase the value to 3 h, the flow rate has to be increased from Qo~d= l0 limin to Qn~w= 32 × 10 = 90 1/min, which is nine times the initial value.
,,4,
According to Eq. (14):
Q
155
(18)
4. Discussion The effect of coolant flow rate on the corresponding heat-transfer coefficient in overhead-jet cooling and flank-jet cooling can now be studied through examination; their relationships are described in Section 3. In overhead-jet cooling, Eq. (13) shows that the heattransfer coefficient increases with increasing the jet-flow rate. According to Eq. (16), in order to increase the value of the heat-transfer coefficient by n times by increasing the jet-flow rate, the value of the flow rate has to be increased by n It°'7 times. For example, if initially the flow rate Q = 10 l/min which results in a value of heat-transfer coefficient h, to increase the value to 3h, the flow rate has to be increased from Qo~d=
1. Theoretical models have been developed for overhead-jet cooling and flank-jet cooling in machining. The models can be used to calculate the local heattransfer coefficients along the tool, chip and workpiece boundary surfaces exposed to coolant in overhead-jet cooling, and to calculated the average heat-transfer coefficients at the tool flank face and the machined work surface in flank-jet cooling. In the models, the physical properties of the coolant are considered as a function of the temperature at the cooled boundary surfaces and in the coolant bulk. 2. Corre!ation equations for relationships between the jet-flow rate of cooling and the corresponding heattransfer coefficient in overhead-jet cooling and flank-jet cooling have been derived fl'om tile developed cooling heat-transfer models. Using these equations, the effect of coolant flow rate on the heat-transfer coefficients in the cooling processes call be determined quantitatively. 3. In overhead-jet cooling or flank-jet cooling, the heat transfer-coefficieaat increases when the jet-flow rate increases. In overhead-jet cooling, to increase the value of the heat-transfer coefficient by n times, the jet-flow rate has to be increased by about n U°'7 times. In flank-jet cooling, to increase the value of the heat-transfer coefficient by n times, the jet-flow rate has to be increased by about n 2 times.
6. List of symbols Cp h K L Nu
n Pr Q q
specific heat of coolant heat-transfer coefficient thermal conductivity length of the tool flank Nusselt number out,xard normal to the boundary Prandtl number jet-flow rate of cooling heat flux
X, Li / Journal of Materials Processing Technology 62 (1996) 149-156
156 r
Re T
Vj
U
X
y
cylindrical coordinate Reynolds number temperature (°C) jet-flow velocity of cooling horizontal component of velocity vertical component of velocity horizontal Cartesian coordinate vertical Cartesian coordinate
Greek letters P II
density cylindrical coordinate viscosity
References [I] R.B. Aronson, Mam~f. Eng., 114 (1995) 33-36, [2] F.W. Taylor, Trans. ASME, 28 (1907) 37. [3] M.C. Shaw, J.D. Pigott and L.P. Richardson, Trans. ASME, 73 (Jan.) (1951) 45-56. [4] E.F. Smart, and E.M. Trent, Proc. 15th hu. Maehine Tool
Design Researeh Col~, Birmingham, UK, Sept. 1974, Macmillan, London. 1975, p. 187. [5] M. Mazurkiewicz, J. Eng. bzd., I11 (1989) 7-12. [6] T.H,C. Childs, K. Maekawa and P. Maulik, Mater. Sei. Technol., 4 (1988) 1006-1019. [7] X. Li, Ph,D. Thesis, University of New South Wales, Australia, 1991. [8] X. Li, .;. Mater. Proc. Teehnol, 620996) 157-165. [9] V.A. Smirnov, P.M. Verevochkin and P.M. Brdlick, Int. J. Heat. Mass. Trans., 2 (1961) I-7. [10] D.E. Metzger, K.N. Cummings and W.A. Ruby, Pine. 5th Int. Heat Transfer Conf., Tokyo, Japan, 1974, Vol. 2, pp. 20-24. [11] J. Stevens and W.B. Webb, 1989 National Heat Transfer Conf., Philadelphia, PA, 6-9 Aug, 1989, HTD-Vol. I1 I, Heat Transfer in Electronics, pp. 113-119. [12] R.J. Goldstein and M.E. Franchett, J. Heat Mass. Trans., 110 (1988) 84-90. [13] J.P. Holman, Heat TransJer, McGraw-Hill, New York, 1986. [14] W. Rohsenow and J.P. Hartnett, Hamlbook o/' Heat TransJbr McGraw-Hill, New York, 1973. [15] L,S, Tong, Boiling Heat Transfer and Two-Phase Flow, Wiley, New York, 1965. [16] C.F. Ma and A.E. Bergles,~in S. Oktay and A. Bar-Cohen (eds.), Heat Transfer in Electronie Equipment, American Society for Mechanical Engineers, New York, 1983 pp. 5-12.
Materials
FrocessNg
ELSEVIER
Technology
Journal of Materials ProcessingTechnology 62 (1996) 149 156
Study of the jet-flow rate of cooling in machining Part 1. Theoretical analysis Xiaoping Li* Departo:ent of Mechanical end Production I:)~gineermg, National Universit , o/Singapore, 10 Kent Ridge Cresent. Singapore 051 I, Singapore
Received 14 April 1995
lndmtrial summary Coolants are used in most machining processes in industry to prevent cutting tools from overheating. In order to achieve the best results of cooling, general guidelines on the method of applying coolants are needed. One of the issues is how to sele."t the jet-flow rate of cooling to cope with the progress of automation in machining manufacturing, in which high-speed machining is is often performed, and on the other hand how to satisfy environmental concerns which require minimization of using coolant. r o answer this question a detailed understanding of the effect of the jet-flow rate of cooling on the cooling action in machining is needed. In this study, the effect of the jet-flow rate of cooling in machining on the cooling heat-transfer coefficient is analysed theoretically, and the effect of the jet-flow rate of cooling on the temperature distribution in the cutting region is examined through numerical simulation of machining with cooling at different flow rates. In Part 1, mathematical models ale developed for the heat-transfer coefficients of cooling applied in machining with a water coolant in the commonly-used cooling method: overhead-jet cooling and flank-jet cooling. The relationships between the heat-transfer coefficient and the jet-flow rate in the cooling processes ale analysed using these models. The results indicate that the cooling heat-transfer coefficient increases with increasing the jet-flow rate. However, a small percentage increase in the heat-transfer coefficient requires a large percentage increase in the flow rate. In overhead-jet cooling, to increase the heat-transfer coefficient by n times, the flow rate has to be increased by about n ~'~7 times, whilst in flank-jet cooling, to increase the heat-transfer coefficient by n times, the flow rate has to be increased by about ,2 times. KcJ'wonl,~: Machining; Cooling; Heat-transfer coefficient: Modelling
1. Introduction tteat is generated in machining due to chip formation and friction at the t o o l - c h i p and t o o l - w o r k interfaces. The heat results at extremely high temperatures in the cutting region, which reduces the hardness o f the tool materials and enhances chemical reactions at the t o o l chip and t o o l - w o r k interfaces such that the tool life is shortened. In order to reduce the temperature in the cutting region, cooling is conducted in most machining processes. The commonly-used cooling methods are overhead-jet cooling and flank-jet cooling, as shown in Fig. 1. In both methods, a water-based coolant is usually used, and heat is removed from the cooled boundary surfaces o f the cutting region by the coolant flowing over the surfaces. The rate o f removing heat
from tile surfaces depends mainly on the velocity o f the coolant flowing along the surfaces, which is related to the jet-flow velocity o f the coolant at the jet nozzle. The
t Flank let coaling
Work *Corresponding author. Fax: (65) 779 1459; e-mail: [email protected]. 0924-0136/96/$15.00 © 1996 Elsevier Scier,ce S.A. All rights reserved SS DI 0924-0136(95)02197-9
Fig. I. Overhead-jet cooling and flank-jet cooling in machining.
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X. Li / Journtd of MttWrials Prot'ess#lg Technology 62 (1996) 149-156
Jet flow
J
e
~
Fig. 2. Jet impingingon a flat surface(schematically). shape and size of the jet nozzle fitted to a machine is usually fixed. Therefore, the heat-removing rate is related directly to the flow rate of the coolant from the jet nozzle, i.e. the effectiveness of coo!ing depends on the jet-flow rate. With the progress of automation in machining manufacturing, the cutting speed in many machining operations has been increased considerably. These changes will eventuaIly require the efficiency of cooling to be increased in order to cope with the increase in the cutting temperature. On the other hand, legislation in many countries are closing in restrictions oil machining coolants, because of environmental issues. 'Tllere are limits on the amount of coolant mist and some coolants and coolant-coated chips have been treated as toxic materials. Outside the plant, the rising cost of chip disposal and the potential secondary effects of coolant vented to the atmosphere are new concerns' [1]. As a result, the amount of coolant to be used in machining is expected to be limited to the actual need, which requires accurate estimation on how much coolant is actually needed. Therefore, a knowledge of the ~'elationship between the effectiveness of cooling and the jetflow rate of cooling is needed by machine tool designers and operators to achieve optimum design of the cooling system and ~o determine optimum values of the jet-flow rate. In the literature, very few detailed studies of the effect of coolant flow rate on the machining process can be found. Taylor [2] reported that in cutting with a high-speed steel tool, increasing the cutting ~peed, which resulted in an increase in the production rate from 30 to 40%, was achieved by applying a heavy stream of water poured directly upon the chip and tool
rake face. He also reported that small streams of weater trickled upon the tool and workpiece were utterly inadequate for the purpose of cooling the tool. The effect of a water-based coolant on the average temperature at the tool-chip interface was studied experimentally by Shaw et al. [3], and the effect of a water-based coolant on the temperature distribution in the cutting region of a high-speed steel tool was studied experimentally by Smart and Trent [4]. In both studies, the jet-flow rate of cooling was kept constant and its effect on the efficiency of cooling was not investigated. Mazurkiewicz [5] reported that a water-based coolant applied at the toolchip interface through a high-pressure jet nozzle reduced the contact length and coeficient of friction at the tool-chip interface, which resulted in lower cutting forces, longer tool life and tighter-curled chips, compared with machining with conventional pressure jet cooling. In their study, the focus was on the coolant pressure at the jet nozzle, the jet-flow rate of cooling being kept constant and not being discussed. A theoretical and experimental study of the effects of cooling on the temperature distribution in machining was presented by Childs et al. [6]. In this study, a range of values for the average heat-transfer coefficient along the boundary surfaces of the tool tip and tool holder were assumed for overhead jet cooling actions in machining with a water-based coolant. The temperature distribution in the cutting region and in the tool holder corresponding to the assumed average heat-transfer coefficients in cutting over a range of cutting conditions were calculated with the finite-element method. From comparisons of the calculated temperature distributions and the experimentally measured results, it was found that the assumed heat-transfer coefficient values of
X. Li /,hmr~ml gf MateriaLs' Processbtg Tech,.oh~gy 62 (19!~b) 149-156
103 W/(m 2 K) and 5 x 10-~ W/(m a K) matched the effects of the coolant flow rates of 0.251 I/min and 2.51 l/rain, respectively, on the temperature distribution in the turning of 0.43% carbon steel at a speed of 61 m/rain, a feed-rate of 0.254 mm/rev and a depth of cut of 2.54 mm. From their results, the trend of the effects of coolant flow rate on the cooling action and consequently on the temperature distribution in the cutting region, can be observed. However, quantitatively these effects can hardly be concluded, because there were several limitations associated with their method. In the determination of the cooling heat-transfer coefficient, it is inadequate to describe the cooling action in cutting by an average heat-transfer coefficient for all the boundary surfaces of the tool tip and the tool holder, because the actual value of the local heat-transfer coefficient along the boundary surfaces in overhead jet cooling (the cooling method considered in their study) varies substantially from the central cooling zone to the rest of the surfaces. It has been shown [7] that by using a local heat-transfer coefficient determined through theoretical modelling of the cooling process and using an assumed heat-transfer coefficient, the calculated temperature distributions can be significantly different. Therefore, in the temperature calculations it is more appropriate to consider local heat-transfer coefficients along the cooled boundaries, including the work- and chip-surfaces exposed to coolant. Since these coefficients are a function of the coolant flow and temperatures at the cooled surfaces and in the coolant bulk, their values vary fi'om case-to-case in machining. In determining the coefficients for studying the effect of cooling on machining, it is impractical to assume their values and then perform machining experiments to confirm them through examining Ihe matches between the temperature distributions measured experimentally and calculated using the assumed values, because the experiments for various combinations of machining conditions could be too numerous to conduct. Instead, theoretical models for cooling heat transfer should be developed for this purpose. Also, in their calculation of temperatures in the cutting region, it is unreafistic to assume that heat is generated only from the shear plane and friction along the tool-chip interface. In cutting of steel under most of the cutting conditions the chip will be plastically deformed along the tool-chip interface, and a secondary plastic detbrmation zone is thus formed in the chip, in which a significant amount of heat is generated. This heat-generation source should be taken into account for the temperature calculation. Another heat source which should also be taken into account is the heat generated due to friction along the tool flank-work interface. In the present study, theoretical models for the heattransfer coefficients in overhead-jet cooling and flankjet cooling are developed. The relationships between the
151
jet-flow rate of cooling and the corresponding heattransfer coefficient in the cooling processes are described using the models. The effects of the jet-flow rate of cooling on the heat-transfer coefficients in the cooling processes are then analysed, these are presented in Part 1. In Part 2 [8], realistic models for chip formation and heat generation in the machining of metals will be described and a method for calculating the temperature distribution in the cutting region, when machinipg with cooling at different jet-flow rates will be developed. Using the method, the effects of the coolant flow rate on machining temperature will be tested and the results will be presonted.
2. Modelling heat-transfer of cooling in machining In machining with overhead-jet coolant or flank-jet cooling, part of the heat generated is removed by the coolant flowing over the exposed surfaces of the cutting region. In the cooling processes the rate of removing heat by the coolant depends on the thermal conductivity of the coolant and cook~:at temperature gradient at the cooled surface, the latter depending on the flow field in the coolant. The overall effect of the cooling actions can be described using a heat-transfer coefficient, h, defined by: q = hA(T,, - T 0
(I)
where q is the heat-transfer rate related to the overall difference between the temperature at the exposed surface, 7",,, and the bulk temperature of the coolant, It., and A is the coaled surface area. Therefore, the effect of the jet-flow rate of cooling on heat transfer along the cooled boundary surlaces can be examined by investigating the effect of the flow rate on the corresponding heat-transfer coeffÉcient. For forced-convection heat transfer, a simplified form representing the heat-transfer coefficient is usually used: Nu =f(Re, Pr, generic shape)
(2)
where, the functional relation is a power law, Nu = hl/K is the Nusselt number, Re=pvl/l~ is the Reynolds number and P r = Cr,ll/K is the coolant Prandtl number, where I and v ale the characteristic length and velocity. K, p,/~ and Cp are the coolant properties: conductivity, density, viscosity and specific heat, respectively. In the case of a jet impinging on a surface (see Fig. 2) the heat-transfer coefficient, h, depends also on other parameters: normalized jet nozzle<~-~lane spacing L/D; jet inclination angle, ~3; displac~cnt of the stagnation point from the geometric centre of the jet on the impingement surface, E; normalized distance from the stagnation point to a point considered on the impingement surface, r/D; jet Reynolds number Rej = pUjD/It,
X. Li / Journal of Materials Processing Technology 62 (I 996) 149-156
"152
. ~ N* •
Goldstein and Frankchett [12] on heat transfer from a flat surface to an oblique air jet is considered for determining the heat-transfer coefficients in overheadjet cooling. Goldstein and Franchett [12] proposed a correlation equation for the local Nusselt numbers in the form:
J,~t nozzle
Nu/Rej a'7 = A e x p [ - ( B + C cos q~)(r/D)"]
Tool
I
where D is the diameter of the jet nozzle, and r and ~b are cylindrical coordinates for correlation of contours of constant Nu. For two-dimensional problems, r is the distance from the stagnation point on the cooled surface, whilst ~b is determined according to: I0, n,
Fig. 3. Categorizationof overhead-jetcooling. which latter is based on the diameter of the nozzle, D, and the jet velocity at the exit plane of the nozzle, Uj. Correlation for heat-transfer coefficients in overhead-jet cooling and flank-jet cooling are now considered. 2.1. Overhead-jet cooling
A schematic representation of overhead-jet cooling in machining is shown in Fig. 3. In this method, a coolant is applied on the back of the chip and the tool rake face through a jet nozzle. The boundary surfaces exposed to coolant include the undeformed workpiece surface IA, chip surfaces AH and CG and the tool rake face CM. The cooling is a process of heat transfer from a flat surface to an oblique impinging liquid jet, in which the physical properties of the liquid vary with temperature. Previous investigations on heat transfer from a flat surface to an impinging liquid jet include the work of Smirnov et al. [9] on the average heattransfer coefficient in an axisymmetric normally impinging water jet, and Metzger et al, [10] on the effects of the Prandtl number on the heat-transfer characteristics of impinging liquid jets and the work of Stevens and Webb [11] on local heat-transfer coefficients. Unfortunately, there is no reported work related directly to local heat-transfer coefficients in heat transfer from a flat surface to an oblique impinging liquid jet. In the present study, the experimental work presented by
along the side of surface with % < zr/2 along the side of surface with ~j > n/2
90° 60° 45° 30°
a
A
L/D=4
L/D=6
L/D=
0,159 0,163
0.155 0,152
0.123 0.115
N t t / R e / ' 7 = ,4Prt:3Rej exp [ - ( B + C cos ~b)(r/D)"]
0.161
0.146
0.107
0.136
0.124
0.091
(5)
where ,,i is a coefficient corresponding to A in Eq. (3). From comparison of Eqs. (5) and (3): f f P r 1/3 = A
hence, . 4 = A / P r t/a = 1.122A
(6)
where the value of Pr for air was taken at the temperature used in Goldstein and Franchett's experiments [12], i.e. Pr=0.708. Substituting Eq. (6) into Eq. (5) the modified form of Eq. (3) is obtained:
C
I0
0.37 0.40 0.47 0.54
(4)
The coefficients of this correlation are shown in Table i, where E is the displacement of the stagnation point as described in Fig. 2, Good agreement between the Nusselt numbers calculated from Eq. (3) and the experimental values was shown by Goldstein and Franchett [12]. Unfortunately Eq. (3) is based on experimental data for air jets. However, since the main difference in heat transfer between air and liquid jets results from the physical properties of the two media, it is contented that Eq. (3) can be modified for liquid jets, this modification can be achieved by adding the Prandtl number, Pr, to the correlation. Pr does not appear in Eq. (3), because for air P r ~ 0.7 and Pr ~,'-~(note that N u c z P r ~'3) is close to unity. Therefore, Eq. (3) may be ,ewritten with Pr included:
Table I Correlation coefficie~.t~[8] %
(3)
0.0 0.12 0.23 0.34
E L/D=4
L/D=6
L/D= I0
0.0 0.8 1.2 1.5
0.0 0.6 1.0 1.4
0.0 0.9 1.5 1.9
X. Li / Journal of Ml te'R Is Prot'essing Ter'tolology 62 (1990) 149-156
153
Table 2 Average Nusselt numbers predicled using different equations" Jet inclination angle ~i
A~erage Nusselt number Nu
Equationused lbr prediction
61)°
(Eq. 7) Smirnov et al.'s (Eq. 7} Smirnov et al.'s {Eq. 7) Smirnov et al.'s
45° 30°
Rt3 = 10000
Rej = 20000
Rej = 30000
106 113 100 102 88 88
172 176 162 159 143 138
228 229 215 207 190 179
a The jet nozzle diameter D = 10 mm; the normalized jet nozzle-to-plane spacing L/D = 10; the Prandtl number for water at 22 °C is Pr = 6.78. and the cooled plate diameter d = 48 mm. N u = 1.122APrl/aRej°'7 e x p [ - ( B + C cos q~)(r/D}'"]
(7)
where the coefficients A, B, C and D are the same as those shown in Table 1. With the modified equation, Eq. (7), the local Nusselt numbers for both air jets and liquid jets can be predicted if the relevant value for P r is provided. Since P r is composed entirely o f the physical properties o f the coolant and is a function o f temperature, its value is determined according to the average temperature calculated from the heated surface temperature and the coolant bulk temperature. Information about h o w the values o f P r vary with temperatare for commolfly-used coolant liquid, such as water, is available easily in the literature [13]. Eq. (7) has been checked for accuracy using the results o f Smirnov et al. [9] and Stevens and Webb [11] based on experimental data lbr liquid jets. A comparison o f the average Nusselt numbers predicted for cooling at a range o f jet oblique angles and jet Reynolds numbers using Eq. (7) and the correlation equation by Smirnov et al. is shown in Table 2. (Note that since Eq. (7) gives the local Nusselt number N u calculations o f the values o f the average Nusselt numbers N u using the equation adopted the following procedure. Local Nus180
I
*
I
*
I
I
I
selt numbers was firstly calculated from Eq. (7), these then being averaged over the impingement area.) The results show that discrepancies between the Nusselt numbers determined using the two methods for each condition are less than 6% based on the results by Smirnov et al. [9]. Fig. 4 shows a comparison o f the average Nusselt number predicted using Eq. (7) and Stevens and Webb's [ll] correlation equation from experimental data for heat transfer from a flat surface to a normally (% = 90 °) impinging single-phase water jet for a range o f Prandtl numbers. The predicted result is in good agreement with experimental results. 2.2. Flank-jet cooling
A schematic description o f flank-jet cooling is given in Fig. 5. in this method the coolant is applied on the tool flank face and the machined workpiece surface. Usually, the jet nozzle is set at the end o f the tool flank lace with the axis o f the jet being symmetrical to the gap between the machined workpiece surface and the tool flank, The machined workpiece surface and the tool flank form a wedge-like space with an apex at ffieir joint, The flow o f coolant between the two surfaces is three-dimensional, with the coolant being forced to
'
160 140 ==
Chip
120 100
x~
u0 '
/-"
Tool
60
.~ 40 20 0
I
2
,
I
3
~
I
~
I
I, 5 Prandtt numbers
~
I
6
Fig. 4. Average Nusselt numbers predicted using different equations (the local Nusselt numbers were firstly calculated from an equation, then being averaged over the impingement area): (A) from Ref. [7], and (O) from Ref. [11].
Fig. 5. Categorization of flank-jetcooling.
154
X. Li / Journal of Materials Process#~g Technology 62 (1996) 149-156
change flow direction in the region near to the apex. Since a method for determinin~ the heat transfer from the two surfaces to such a complex flow pattern is lacking, in this study it is assumed that the flow of coolant is parallel to both surfaces. This assumption is reasonable, because the tool clearance angle is usually very small. Therefore, the cooling process can be considered as heat transfer from a flat surface to a parallel liquid flow. It is noted that in this way the approximation made on the coolant flow pattern could result in slightly overestimating the heattransfer coefficient. It should, however, be sufficiently accurate for the present purposes. The process of heat transfer from a flat surface to a liquid which flows in a direction parallel to the surface was investigated by many researchers and typical results for heat-transfer coefficients have been well documented in the literature [14]. Only the equations relevant to the present analysis are given here. For heat transfer from a heated plane at constant temperature to a liquid in laminar boundary layer flow over it, the local Nusselt number at a point with a distance x from the leading edge is: h~x Nu, = ~ = 0.332Pr 1'3Rev i,,2
(8)
where Re.,.<~5 x 105. The average heat-transfer coefficient and Nusselt number may be obtained by integrating over the length L of the plane: NuL = --g-= 0.664Pr I'3ReL t~2
(9)
where Ret. ~<5 × 10s, and, pU~L ReL = ~ g
Similarly to Eq. (7) in overhead-jet cooling, in Eqs. (8) and (9) Pr is a function of temperature and is determined according to the average of the temperatures at the cooled surface and in the coolant bulk. It should be mentioned that the above-considered processes of cooling in machining are limited to singlephase heat transfer, where heat is transferred only by convection. In fact, when the heat flux from the surface cooled by coolant is greater than a particular value, the convective heat transfer is not sufficiently strong to prevent the surface temperature from rising above the saturation temperature of the liquid, and boiling may occur. Boiling may occur in one of two ways, depending upon the surface temperature. If the temperature is not much above the boiling point of the liquid, nucleate boiling occurs; if it is well above, film boiling occurs. In boiling, heat is transported by the boiling bubbles in several ways [15] and is also transferred by single-phase convection between patches of bubbles. Due to these
different mechanisms, the heat-transfer coefficients for boiling could be greater or much greater than those in single-phase convection, depending on the boiling state [13]. For boiling heat transfer from a fiat surface to an impinging jet, experimental results from investigations of the characteristics of nucleate boiling with jet impingement have been presented by Ma and Bergles [16]. The investigations included the effects of velocity, subcooling, flow direction and surface condition on fully developed boiling. The results showed that, in general, much of the experience and procedures developed lbr forced convection boiling inside tubes can be applied to jet impingement boiling. In some machining cases, heat flux from the boundary surface may be sufficiently large for boiling to occur. For these cases the heat-transfer coefficients should be calculated according to boiling heat-transfer. However, since the process of machining is very complex, there has been no way to determine where and when a steady boiling process may occur. As a result, calculation methods for boiling heat transfer are not available. Therefore, in the present work it is assumed that for most cases of cooling in machining, sufficient and continuous coolant supply will naturally keep the cooling action within the range of subcooled forced convection before the incipient boiling point. Thus the heat-transfer coefficients will be calculated from the single-phase convection equations presented in the preceding sections. It should be noted that the results calculated in this way may be conservative for cases where boiling does occur.
3. Relationship between flow rate and heat-transfer coefficient
Using the cooling heat-transfer models developed in Section 2, the relationships between coolant flow rate and the corresponding heat-transfer coefficient in overheadjet cooling and flank-jet cooling are now considered. For overhead jet cooling, from Eq. (7): Nu = 1.122APrl/3Rej °'7 exp[-(B + C cos q~)(r/D)'"]
By definition: hD Nu = - K
(10)
and Rej = p U j O (11) P where h is the heat-transfer coefficient, p and p, the density and viscocity of the coolant, respectively, D the diameter of the jet nozzle, and Uj the velocity of the jet flow, which is given by:
Q
vj = a~
02)
X. Li/ Jouroal ~1"Materials Process#tg Technology 62 (1996) 149-156
where Q is the coolanl jet-flow rate and Aj = ~rD2/4 is the cross-sectiona! area of the jet nozzle. Substituting Eqs. (10)-(12) into Eq. (7) and using symbol g2o to represent all the factors that are indelrendent of Q, the relationship between h and q can be written as: h = 0000.7
(13)
Eq. (13) shows that a large percentage increase in Q results in only a small percentage increase in h. Consider increasing Q from Qola to _On.... so that h becomes h ~ w = n × hold, from Eq. (13)the relationshi F of h and q can be rewritten as: Q = h ~/o.7
(o)
5, Conclusions
(hoo,A,,o. (,,,o=VO.,
n°'=
t~-~)
= t, Q--S-)
(is)
and from Eq. (13): hold = ,.CoQold°'7 therefore, Qn~w= n l/O.TQokl
( t 6)
Similarly, for flank-jet cooling, from Eq. (9): 1/3 = k = 0.664Re, I,r2pt,
and using the same method as used for overhead-jet cooling, an expression for the relationship between h and Q can be obtained: h = OrQ 112
(17)
where g2r represents all the factors that are independent o f q in Eq. (9). An expression similar to Eq. (16) can be derived from Eq. (17): Qn~,,, = n2Qoid
10 l/min to Q .... = 31'°7 × 19 = 48 l/rmin, i.e., to increase the value of heat-transfer coefficient by three times, the flow rate has to be increased by about five times. From Eqs. (17) and (18), a similar trend can be seen in flank-jet cooling. According to Eq. (18), in order to increase the value of the heat-transfer coefficient by n times by increasing the jet-flow rate, the value of the flow rate has to increased by n 2 times. If initially the flow rate is Qo~d= 10 l/min which results in a value of heat-transfer coefficient h, to increase the value to 3 h, the flow rate has to be increased from Qo~d= l0 limin to Qn~w= 32 × 10 = 90 1/min, which is nine times the initial value.
,,4,
According to Eq. (14):
Q
155
(18)
4. Discussion The effect of coolant flow rate on the corresponding heat-transfer coefficient in overhead-jet cooling and flank-jet cooling can now be studied through examination; their relationships are described in Section 3. In overhead-jet cooling, Eq. (13) shows that the heattransfer coefficient increases with increasing the jet-flow rate. According to Eq. (16), in order to increase the value of the heat-transfer coefficient by n times by increasing the jet-flow rate, the value of the flow rate has to be increased by n It°'7 times. For example, if initially the flow rate Q = 10 l/min which results in a value of heat-transfer coefficient h, to increase the value to 3h, the flow rate has to be increased from Qo~d=
1. Theoretical models have been developed for overhead-jet cooling and flank-jet cooling in machining. The models can be used to calculate the local heattransfer coefficients along the tool, chip and workpiece boundary surfaces exposed to coolant in overhead-jet cooling, and to calculated the average heat-transfer coefficients at the tool flank face and the machined work surface in flank-jet cooling. In the models, the physical properties of the coolant are considered as a function of the temperature at the cooled boundary surfaces and in the coolant bulk. 2. Corre!ation equations for relationships between the jet-flow rate of cooling and the corresponding heattransfer coefficient in overhead-jet cooling and flank-jet cooling have been derived fl'om tile developed cooling heat-transfer models. Using these equations, the effect of coolant flow rate on the heat-transfer coefficients in the cooling processes call be determined quantitatively. 3. In overhead-jet cooling or flank-jet cooling, the heat transfer-coefficieaat increases when the jet-flow rate increases. In overhead-jet cooling, to increase the value of the heat-transfer coefficient by n times, the jet-flow rate has to be increased by about n U°'7 times. In flank-jet cooling, to increase the value of the heat-transfer coefficient by n times, the jet-flow rate has to be increased by about n 2 times.
6. List of symbols Cp h K L Nu
n Pr Q q
specific heat of coolant heat-transfer coefficient thermal conductivity length of the tool flank Nusselt number out,xard normal to the boundary Prandtl number jet-flow rate of cooling heat flux
X, Li / Journal of Materials Processing Technology 62 (1996) 149-156
156 r
Re T
Vj
U
X
y
cylindrical coordinate Reynolds number temperature (°C) jet-flow velocity of cooling horizontal component of velocity vertical component of velocity horizontal Cartesian coordinate vertical Cartesian coordinate
Greek letters P II
density cylindrical coordinate viscosity
References [I] R.B. Aronson, Mam~f. Eng., 114 (1995) 33-36, [2] F.W. Taylor, Trans. ASME, 28 (1907) 37. [3] M.C. Shaw, J.D. Pigott and L.P. Richardson, Trans. ASME, 73 (Jan.) (1951) 45-56. [4] E.F. Smart, and E.M. Trent, Proc. 15th hu. Maehine Tool
Design Researeh Col~, Birmingham, UK, Sept. 1974, Macmillan, London. 1975, p. 187. [5] M. Mazurkiewicz, J. Eng. bzd., I11 (1989) 7-12. [6] T.H,C. Childs, K. Maekawa and P. Maulik, Mater. Sei. Technol., 4 (1988) 1006-1019. [7] X. Li, Ph,D. Thesis, University of New South Wales, Australia, 1991. [8] X. Li, .;. Mater. Proc. Teehnol, 620996) 157-165. [9] V.A. Smirnov, P.M. Verevochkin and P.M. Brdlick, Int. J. Heat. Mass. Trans., 2 (1961) I-7. [10] D.E. Metzger, K.N. Cummings and W.A. Ruby, Pine. 5th Int. Heat Transfer Conf., Tokyo, Japan, 1974, Vol. 2, pp. 20-24. [11] J. Stevens and W.B. Webb, 1989 National Heat Transfer Conf., Philadelphia, PA, 6-9 Aug, 1989, HTD-Vol. I1 I, Heat Transfer in Electronics, pp. 113-119. [12] R.J. Goldstein and M.E. Franchett, J. Heat Mass. Trans., 110 (1988) 84-90. [13] J.P. Holman, Heat TransJer, McGraw-Hill, New York, 1986. [14] W. Rohsenow and J.P. Hartnett, Hamlbook o/' Heat TransJbr McGraw-Hill, New York, 1973. [15] L,S, Tong, Boiling Heat Transfer and Two-Phase Flow, Wiley, New York, 1965. [16] C.F. Ma and A.E. Bergles,~in S. Oktay and A. Bar-Cohen (eds.), Heat Transfer in Electronie Equipment, American Society for Mechanical Engineers, New York, 1983 pp. 5-12.