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Thermal analysis of creep-feed grinding
Journal of
Materials
ELSEVIER
J. Mater. Process. Technol. 43 (1994) 109-124
Processing Technology
Thermal analysis of creep-feed grinding Kuang-Hua Fuh, Jen-Sheuan Huang Department of Mechanical Engineering, Tatung Institute of Technology, Taipei, Taiwan, 10451, ROC (Received March 26, 1993; accepted October 12, 1993)
Industrial summary One of the major problems encountered in industrial experience of creep-feed grinding is thermal damage to the workpiece and grinding wheel. Thus, the application of cutting fluids is especially crucial. In this paper an analytical model of the heat transfer between the wheel, the workpiece surface and the grinding fluids is derived and verified. The model enables the prediction of the maximum surface temperature when grinding fluids are applied, demonstrates the thermal energy partitions between the abrasive wheel, the cutting fluids and the workpiece, and also determines the threshold of the occurrence of film-boiling. Despite its simplicity, the model provides remarkable agreement with published data from experimental investigations and from finite-element analysis, for various creep-feed grinding conditions. The cooling effect of water-based grinding fluids is better than that of oil-based cutting fluids, but the resistance to workpiece burning using water-based cutting fluids is worse than that using oil-based cutting fluids. When cutting fluids are applied in the grinding process, the strong cooling effect of the cutting fluids is apparent. In addition, a CBN grinding wheel shows a better performance than an A120 a grinding wheel in the avoidance of workpiece burning. The cooling effect of grinding fluid, Re, can be improved by decreasing the effective contact ratio. In general, this effective contact ratio can be achieved by selecting a grinding wheel with a higher porosity or structure number. Further, a shorter dressing time-interval is a better choice for decreasing the wear flat area and thus for improving the cooling effect of the coolant on the workpiece. Key words: Cooling effect, creep feed grinding, thermal damage
Notations a Cp
grinding depth of cut (mm) specific heat at constant pressure (J/kg°C)
* Corresponding author. Elsevier Science B.V. SSDI 0 9 2 4 - 0 1 3 6 ( 9 3 ) E 0 1 1 9 - 2
110
D k q' q~ q'b Tw,Tf Ti Vs Vw
P 0
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
wheel diameter (mm) thermal conductivity (W/m K) heat flux (W/mm 2) the portion of the grinding energy removed by the coolant (W/mm 2) the portion of the grinding energy remaining in the workpiece (W/mm 2) temperature of the workpiece and grinding fluids respectively (°C) ambient temperature (°C) wheel speed (m/s) workpiece speed (mm/s) thermal diffusivity burning limits of grinding energy (W/mm 2) density (kg/m 3) temperature difference from the ambient temperature Ti (°C)
Subscripts fluid f g grain maximum max surface s total tot workpiece w workpiece background wb workpiece under grain wg
1. Introduction
Creep-feed grinding is a grinding process in which the workpiece infeed rate is reduced to allow the cutting depth to be increased, typically to hundreds or thousands of times encountered in conventional traverse surface grinding. One of the major problems encountered in industrial experience of such a grinding process is the high temperatures attained by the workpiece. This condition will result in various types of thermal damage, such as burning, phase transformations, softening (tempering) of the surface layer with possible re-hardening, unfavorable residual tensile stresses, cracks, and reduced fatigue strength. Furthermore, thermal expansion of the workpiece during grinding contributes to inaccuracies and distortions in the final product. Consequently, the application of cutting fluids is especially crucial in creep-feed grinding. However, the cooling effect of the grinding fluid has been ignored in research of the shear plane and interference zone temperatures analysis, hence the findings of Jaeger [1], Outwater and Shaw [2] and Malkin [3,4], are not directly applicable to the creep-feed grinding process. The thermal-partition coefficient derived by Outwater and Shaw [2] was based on the shear angle of the cutting grains and the Peclect Number. However, the cutting grains on the wheel surface are distributed randomly and the shapes of the grains are not identical, thus the shear angle of the cutting grains during the grinding process is
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994.) 109-124
111
difficult to visualise. Malkin and Anderson I-3] divided the grinding energy into chip formation, plowing, and sliding energy. Because the fraction of these energies is not constant and is difficult to determine during the grinding process, the thermalpartition coefficient derived by Malkin et al. cannot be applied to the real situation. Stuart [5] suggested that the thermal-partition coefficient is less than 5 percent for the grinding process, but his suggestion was lacking of theoretical support to establish that his results will hold for different grinding conditions. The thermal-partition coefficient developed by Ramanath and Shaw [6] can be applied to dry grinding only, as the thermal property of the coolant was not included. Lavine et al. [7,8] regarded the grinding wheel as a porous material filled with coolant. They developed a series of research investigations into the thermal aspects of the grinding process based on the micro-relationships between the abrasive grains, the grinding fluid and the workpiece. According to their model, reduction of the thermalpartition coefficient is associated with a decrease of wheel porosity, i.e. their models implied that dry-grinding, using a grinding wheel with lower porosity, is the preferred choice: this phenomenon violates the general physical concept. Further, in order to accurately predict the thermal-partition coefficient, the porosity of the grinding wheel should be kept at 99.5 percent, which is not likely to happen in the real world. Yasui et al. [9] and Ye et al. [107 performed experimental investigations on the effect of grinding-fluid type, finding that under some particular conditions the maximum temperature rise could be an order less if a water-based fluid is used rather than dry-grinding being carried out. However, when the surface temperature reached a value slightly over 100 °C, the use of a water-based fluid showed no advantage over dry-grinding. Ohishi and Furukawa [11] recognized that when the maximum surface temperature exceeded 100 °C for water-based fluids or 300 °C for oil, the temperature will rise rapidly, accompanied by the occurrence of grinding burn. As mentioned above, the cutting fluids play an important role in determining the grinding burn. Thus, it is desirable that simple criteria based on the heat transferred between the cutting fluid and the workpiece be derived to clarify the energy-partition relationships between the workpiece, the abrasive grains and the cutting fluid, to elucidate the effects of the grinding fluid, and also to determine the threshold for the occurrence of workpiece burning.
2. Mathematical analysis A geometrical explanation of down-cut creep-feed grinding is shown in Fig. 1. The wheel is a porous medium consisting of abrasive grains, bond material, and pores of irregular shapes and different sizes, and as the wheel surface encounters the fluid application zone its pores will begin to fill with fluid. According to Guo and Malkin [12], as long as the abrasive wheel enters the workpiece with properly placed nozzles and sufficient grinding fluid, the amount of grinding fluid left in the contact zone will be substantial and the grinding fluid trapped in the pores of the grinding wheel will move with the wheel peripheral speed, Vs. Thus, it is reasonable to assume that the fluid is stationary with respect to the wheel, i.e. the interference of cutting grains and
112
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D Wheel \ 1 _ ~ a ~ D J Vs
/ fluid /' 'introduced[
"
"~,~/Vs
wheel diaraeter grindin~ zone length depth o f cut wheel speed
~ _ _ _ _ _V__w_l;°rkpiecespeed
Fig. 1. The grindinggeometry.
/ _ ro:
work-piece x
Fig. 2. Microviewof the contactsurfacebetweenthe fluid,the grains and the workpiece.
fluid moves across the surface of the workpiece at the same peripheral wheel speed, Vs. Clearly, the grinding fluid, surrounded by the abrasive grains, the bonding material and the workpiece, can be regarded as water or oil in a boiler, as shown in Fig. 2. Although thermal damage requires time to take place, and the peak temperature generated during the moment of contact will be probably removed, the residue of grinding energy left on the workpiece will accumulate, which contributes to the thermal damage of the workpiece. To model this phenomenon, energy equations are written for the interference of the workpiece and coolant. In order to simplify the complexity of the grinding process, it is assumed that the thermal properties are constant, viscous dissipation and pressure work are negligible, thermal conduction in the direction of motion is negligible, and boiling does not occur. Fig. 3 demonstrates an idealized model of the contact zone at the contact surface. Using this model, the energy equation in the fluid and workpiece can be described as ~Tf ~-=
~2Tf -0~
O~y~
oo
~Tw a2Tw / 0~
(1)
(2)
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
fF
113
inte~ferenc~zone 9f
coolant anawol~plece
qwg
Fig. 3. Modelof the heat transferto the fluidand the workpieceat a point on the workpiecesurfacewhich is exposed to the coolant.
where Tf is the temperature of the grinding fluid, Tw is the temperature of the workpiece, 0tf is the thermal diffusivity of the coolant, ~tw is the thermal diffusivity of the workpiece, V~is the wheel peripheral speed and Vw is the workpiece speed. The initial conditions can then be represented as Tr(y, O) = T~
(3)
Tw(y, O) = Ti
(4)
where Ti is the ambient temperature. Lavine [7] has demonstrated that the fluid fills the pores throughout the entire thermal boundary layer, hence the boundary conditions can be expressed as ~T~ -- k f - - '
8y r=o
= q~'
Tf(oo,t)
= Ti
(5)
and -
k. 8Tw ~Y
y=o
= ,,
qwb
T w ( ~ , t ) = Ti
(6)
where kf is the thermal conductivity of coolants, kw is the thermal conductivity of the workpiece, q~' is the grinding energy removed by the fluid and the q'b is the grinding energy remaining in the workpiece. Now defined are 0f as the temperature difference between Tf and the ambient temperature Ti, and 0w as the temperature difference between Tw and ambient temperature Ti. By solving the above equations, Of and 0w can be obtained as follows: (7)
0w(y, t) =
qwb ~ ) w
2
exp
(8)
-~
x/~
\x/4awtjj
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K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
where p is the density, and c is the specific heat. The interference surface temperature difference along the length of contact can be obtained easily by substituting y -- 0 into Eqs. (7) and (8). Then
f
4x ,, 0f(0, x) -- q ~(k~p)f Vs qf
(9)
and /
0w(0, x) =
4x
,,
41rkp-~p)wVwqwb
(10)
Hence, as long as the portion of grinding energy removed by the grinding fluid, q~', and the portion remaining in the workpiece, q~,b, are determined, the temperature rise of the fluid as well as that of the workpiece can be predicted easily. Because: (i) heat is generated in the vicinity of the contacts between the abrasive grains and the workpiece; (ii) the thermal conductivity of the grain is much greater than that of the grinding fluid; and (iii) the relative velocity between the abrasive grain and the grinding fluid is approximately zero; it is reasonable to assume that the heat that enters the grain simply conducts further into the grain without being removed by the fluid. Further, the coolant cannot enter the actual contacts between the abrasive grains and the workpiece, i.e. the actual contact points belong indisputably to the dry-grinding type. Hence, it is easy to demonstrate that the heat, q~'ri~d, generated at a grain-workpiece interface conducts into either the workpiece or the abrasive grain. Thus . . .= qgrind
.qwg . +.
(11)
qg
where q~' is the heat flux into the workpiece at the grain location and q~' is the heat flux into the grain. In addition, the portion of the heat flux into the workpiece at the grain location to the total grinding energy can be defined as Rdry =
heat to work under the grain total grinding energy
q;~g
(12)
qgtrind
Once the heat flux which flows into the workpiece at the grain location, q~,,, enters the workpiece at the actual grain-workpiece location, part of q~,, denoted as q~,b will remain in the workpiece and later be distributed uniformly in the apparent contact area, whilst the rest of the heat, denoted as q[', will be carried away by the grinding fluid over the remaining portion of the actual grain-workpiece contact area. The rate at which heat leaves the chip is typically not large, and will be neglected. Thus qwg(-D---- q~b + q['(1 --co)
(13)
where the ratio of the actual grain-workpiece contact area to the total contact area, denoted as co, is defined as the effective contact ratio. In general, the effective contact ratio, co, is a function of the porosity of the grinding wheel, the wear flat area of abrasive grains, and the amount of chips adhering to the wheel surface.
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
115
Based on the continuity of the temperature gradient and from Eqs. (9) and (10), the relationship between the energy removed by the grinding fluid and the energy distributed uniformly over the entire apparent contact area can be expressed as
q:b = q'f' ((kpcp)w Vw~½ \ (kpc,)fvs }
(14)
Substituting this result into Eq. (13) qf' =
~'L\
+ 1 -- co
Rd,yq;'~i.d
(15)
The resultant thermal-partition coefficient with cooling effect of coolant can now be defined and expressed as _ Heattotalremainedgrinding inenergyWOrk= gary ~[1 + (1 Rtot-
. { (kpcp)fVsJ'~¥]j - 1 -a))k(kpcp)wV,
(16)
Finally. the cooling effect of the coolant, Re. can be defined as
go- [i + (i -J
(k'c,)'
(17)
"\(kp%)wVw) J
The thermal-partition coefficient with the cooling effect of the coolant on the workpie~ can now be expressed as
Riot = RdrrR~
(18)
Substituting Eqs. (16), (18) and (14) into Eq. (13), the portion of grinding energy carried away by the coolant, q~', and the portion of grinding energy remaining uniformly in the workpiece, q~,b, can be obtained as q~, =
" qwb
(2) ,, 1--~Rd,y(1 -- n~)qg.i.d
(19)
= o~Rtott4grind -"
(20)
Then the temperature distribution in the grinding fluid, Of(y,t), and the temperature distribution in the workpiece, 0w(y,t), can be predicted by combining Eqs. (7), (8), (19) and (20), the results being 0f(y, t) = 1 7 R d r y ( 1 --
y erfc( y ~l x/(kpcp)f L ~# ~e x p ( \- - ~y 2 ) _ x/af \x/4okt/1
Rc)~F2
(21)
o.o,,,,: o,,,o,,~/(kpq,),,,k X/~ r_,OXl,C\
~
-- ~ >. effc
(22)
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K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Hence, after suitable substitution, the surface temperature of the fluid over the contact zone can be represented as 0f,~(0, x) = ~
4x co ( k ~ , Vs 1 ~
Rdry(1 -- Re)q~'rind
(23)
and the surface temperature of the workpiece over the contact zone can be expressed as ,, f 4x 0w,,(0, x) = 4 ~(kp~p)wVwcoRt°tqgrind
(24)
Finally, the maximum surface temperature of the grinding fluid over the grinding zone can be expressed as
0fs max(0,N//~ ) ""
=
1/- 4(aD)½ co coRary(1 _ R¢)q'g',i.d ~] lr(kpcp)fVs 1 -
(25)
and the maximum surface temperature rise of the workpiece over the grinding zone can be obtained as 0..... ( 0 , x / ~ ) = /-4(aD)½ "" ~/ n( k p cp)w Vw coRt°tq'*'rind
(26)
The grinding energy per unit contact area per unit time, mentioned above, can be expressed as FtV~ " = bx/,~ q,rind
(27)
where the tangential grinding force Ft can be determined by the assignment of grinding condition such as the depth of cut, the wheel speed, the workpiece speed and the wheel diameter. As long as F t has been determined, Eqs. (25)-(27) can be employed to predict the maximum surface temperatures of the grinding fluid and the workpiece, Of...... and 0........ Thus the criterion of workpiece surge is determined. If the maximum surface temperature is defined as 0...... then the resistance to workpiece burning ~Limits can be derived inversely from Eq. (25) and written as
~Limits
/ Tz(kpcp)f Vf 1 - co 1 = X/ 4(aD) ½ ~ Rdry(1--- Re) 0s. . . .
(28)
When the type of grinding fluids has been chosen, the maximum endurance surface temperature rise 0..... and the thermal properties of the grinding fluid can be determined. Then, the burning limits of the grinding energy can be obtained based on the effective contact ratio 09 to determine the optimal selection of grinding conditions to avoid the occasion of workpiece burning.
K.-H. Fuh, J.-S. Huang /Journal of Materials Processing Technology 43 (1994) 109-124
117
Table 1 The thermal properties of the coolant, the wheel and the workpieee Thermal property
Water
Oil
Air
AI20 3
CBN
Steel
Thermal conductivity k (W/m K) Specific heat Cp (J/kg°C) Density P (kg/m 3)
0.662
0.15
0.0262
46
1300
43
4201
2000
1005.7
770
506
473
976.8
820.0
1.1747
4000
3450
7801
3. Discussion and results of the cooling effect, Ro of coolant The energy-partition coefficient plays an important role in the grinding process, this coefficient depending on the material of the cutting grains, the porosity and the structure of the wheel, and the type of coolant used in the grinding process. Thus, the following sections are focused on the investigation of the thermal-partition coefficient. The thermal properties of steel and of various abrasive grains and grinding fluids are listed in Table 1: these will be used in this research to investigate the cooling effect, Re, of the grinding fluid on the workpiece. First, compare the cooling effect of the coolant, Re, between creep-feed grinding and conventional traverse grinding. Fig. 4 elucidates that the cooling effect Rc decreases as the velocity ratio, (V,/Vw) °'5, increases. The velocity ratio, (VJVw) °'5, for creep-feed grinding generally falls into the region above 100, whilst the velocity ratio, (VdVw) °'5, for conventional traverse grinding is usually below 40. This shows that as long as the coolant shoe is at a proper location and the coolant is sufficient, the cooling effect in creep-feed grinding should be better than that in the conventional traverse grinding process. (Note that this does not imply that the temperature of the workpiece in the creep-feed grinding process is lower than the temperature in conventional grinding). When the grinding fluid is applied in the grinding process, the improvement of the cooling effect of the coolant is obvious. Furthermore, the cooling effect of water-based coolant is more obvious than that of oil-based coolant. The effective contact ratio is a function of the wheel structure, the wheel porosity, and the wear flat area of the abrasive grains. Amongst these factors, the structure organization of the wheel is the major factor, having a direct effect on the effective contact ratio. As the structure number indicates the volumetric concentration of the abrasive grains in the wheel, a higher structure number referring to a lower grain density of the wheel, a grinding wheel with a higher structure number or with a more open structure will decrease the effective contact ratio, co. If the grinding wheel is newly dressed, the effective contact ratio can be determined simply by the volumetric concentration of the abrasive grains.
118
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
1.2 1k 0.8
Re
~/no coolantadded
ii',
effective contact ratio 1.0
oil fluid
~ A 0.6 ~- - t l/i\ 0"4 / , ~ 0
60
0.5 0.03 waters°luble
120
180
]
240
300
(VsrVw)°'5 Fig. 4. The cooling effect of the grinding fluid versus the velocity ratio for various effective contact ratios.
1.2
1
....
,,
_~__~t
~__
.....................
0.8 Re0.6 -
oii . . . . . . . . . . . . .
S
/
water soluble....- - - J / ,.
0.4 0.2 0
-
~
.'Or
_:............... ~_~a~r~_.,___~ ........ 1
0
";
.-"
1
,
I
I
0.2 0.4 0.6 0.g Effective Contact Ratio
Fig. 5. The cooling effect of the grinding fluid versus the effective contact ratio.
Fig. 5 shows that the cooling effect of the coolant on the workpiece decreases as the effective contact ratio increases. Such a result is expected, as a grinding process with a lower effective contact ratio can make the coolant flow easily, to remove the grinding energy rapidly. Hence, a grinding wheel with a higher porosity will be a preferred choice to improve the cooling effect of the grinding fluid on the workpiece. As the time or distance of the grinding process increases, the wear flat area of the abrasive grains increases also, which causes the effective contact ratio to increase. Thus, dressing conditions with a shorter time interval or with a coarse infeed rate are preferred: this is also the reason why continuous-dressing creep-feed grinding demonstrates a better performance than the conventional creep-feed grinding process.
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
119
4. Verification of the equations of the maximum surface temperature model Before proceeding with further investigation of the workpiece burning criteria, the validity of the temperature model in Eqs. (25) and (26) should be established. Table 2 compares the maximum surface temperatures obtained from Furukawa's experimental values [11] and Lavine's theoretical values [8] with the values calculated from Eqs. (25) and (26). The ratio of the heat flux that flows into the workpiece under the grain location q~,~,to the total grinding energy, qsri,d, denoted as Rdry, as used for Eqs. (25) and (26), is adopted from results of Ramanath and Shaw [6]. This ratio, Rdry, is derived based on the concept that all of the heat flowing inwards is extracted outwards during the cooling portion of a single wheel revolution, rather than based on the concept of temperature continuity. Hence, the utilization of the following expression is suitable
=
[
1+
]
(29)
As the grinding wheel that Ohishi and Furukawa [11] used was WA60G8AV, the volumetric concentration of the abrasive grain for a newly-dressed grinding wheel was about 46 percent: thus the effective contact ratio, to, for a newly-dressed grinding wheel is chosen as 0.46. From the results listed in Table 2, it is obvious that the maximum surface temperature with water-based coolant, predicted in this research, is satisfactory. However, slight deviations of maximum surface temperature take place with the application of oil-based coolant for the identical effective contact ratio, to. The purposes of the coolant applied in the grinding process are not only the cooling and lubricating effects but also the cleaning away of the chips adhering to pores on the wheel surface. However, the viscosity of the oil-based coolant usually obstructs the accomplishment of the cleaning away of the chips adhering to the pores on the wheel surface and thus increases the actual contact surface between the contact zone of the grinding wheel and the workpiece. Hence, the effective contact ratio with the utilization of oil-based coolant will be higher than that with the use of water coolant under the same grinding conditions for an identical abrasive wheel. If a higher effective contact ratio, to, is chosen, namely 0.60, the maximum surface temperatures listed in Table 2 with the use of oil-based coolant calculated from Eqs. (25),(26) and (29) are approximately identical to the experimental results of Ohishi and Furukawa [11] with the use of oil-based coolant. In addition, the maximum surface temperatures calculated from Eqs. (25), (26) and (29) when the effective contact ratio is chosen as 0.60, demonstrate the same tendency as compared to the results of Lavine [8]. Ohishi and Furukawa [11] suggested that when the maximum surface temperature exceeds 100 °C for water-based fluids or 300 °C for oil-based fluids, the temperature will rise rapidly, and the grinding burn will occur. Thus, further investigation will be focused on the prediction of interference zone temperature to determine whether or not grinding burn will occur. Fig. 6 illustrates the maximum surface temperature
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K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Table 2 Comparison of the present predictions with the data of Ohishi and F u r u k a w a [11] and Lavine et al.[8] for creep-feed grinding 0. . . . pred (presented) q" grind (w/mm ~)
Coolandt type
2.0
water
15
32
16
30
oil
80
78
52
80
water
50
105
52
96
260
253
171
260
75
153
76
140
(burn)
369
249
6.5
oil 9.5
water oil
0max,~xp [11]
0max,prod [8]
Vs = 20 m/s, Vw = 0.33 m/s, diameter = 305 mm, depth =
Effective Contact Ratio ~o 09 = 0.46 oJ = 0.60
380 (film boiling)
1.0 mm.
of creep-feed grinding with oil-based fluids and water-based fluids. Note that the temperatures using oil-based grinding fluid in Fig. 6(a) are higher than those using water-based grinding fluid in Fig. 6(b). This is due to the thermal conductivity of water-based grinding fluid being superior than that of oil-based grinding fluid: the increase of the effective contact ratio will obstruct the grinding fluid carrying away the grinding energy from the grinding zone, and thus decreasing the cooling effect on the workpiece. The maximum surface temperatures will then increase as the effective contact ratio increases as shown in Fig. 6. In addition, a grinding process with higher specific grinding energy is more apt to reach the burning region for a specific effective contact ratio. Hence, a suitable selection of grinding or dressing conditions and wheel porosity is crucial to the maintaining of the desired metal removal rate. That is, the occurrence of grinding burn is determined by: the thermal properties of the abrasive grains, the grinding fluids and the workpiece material; the effective contact ratio, ¢o, which is determined by the time-interval of dressing and the structure number of the grinding wheel; and by the assignment of the grinding conditions which determine the specific grinding energy.
5. Prediction of the burning limits of grinding energy Next, the following will discuss the effects of the variety of grinding fluid and the grinding conditions on the burning limits of grinding energy flux, #Limits, and the validity of the model in Eq. (28) is established. Table 3 demonstrates a comparison of heat flux obtained from Eq. (28), using data listed in Table 1 and Table 2, with the
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121
Vs = 18 m/s; Vw = 0.6 mm/s oC
a = I mm; D = 305 mm q~.~ = 2.0 W/ram 2 5OO q",,~= 6.5 W/ram 2 400 - - q",~ = 9.5 W/ram2 Bumin~ Relfion Os,max 300 2OO 600
100 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Effective Contact Ratio
(a)
°C 200
q"o~ = 2.0 W/ram 2 / = 6.5 W/ram 2 / --q'~ = 9 . 5 W/mm " ~ / ' / " - q".~
160 Os,max120
Burning Region
~
./" /
0.5
0.6
80
40 0 0
0.1
0.2
0.3
0.4
0.7
Effective Contact Ratio (b) Fig. 6. Maximum surface temperature versus effective contact ratio for various specific grinding energies with: (a) oil-based coolant; and (b) water; for creep-feed grinding.
Table 3 Comparison of the present predictions with the data of Ohishi and Furukawa [11] for creep-feed grinding Threshold of energy flux for film boiling 0Li=it (W/mm 2) Depth a(mm)
Work speed V,,(mm/s)
Exp[11]
FEM[11]
Present
0.5
2.4
10.7
11
11.11
1.0
1.2
9.5
9
8.96
2.0
0.6
8.2
7
7.30
experimental data and the finite-element results of Ohishi and Furukawa [11]. From Table 3, it is obviously that the present model, using a simple analytical method, has a reliable predictive ability, when compared to the values obtained by Ohishi and
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K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Furukawa [11] using finite-element analysis. Ohishi and Furukawa did not describe the ambient temperature in their experiments, the ambient temperature is assumed at 25 °C so that the temperature difference, 0...... equals 75 °C with water coolants. The effective contact ratio, co, is chosen according to the volumetric concentration of the abrasive grains for a newly-dressed grinding wheel, namely 0.46. Fig. 7 demonstrates the effects of the grinding depth on the burning limits of grinding energy flux, 0Limits, various combination of grinding wheel and grinding fluids being used in the prediction of these burning limits, for different depth of cut. The metal removal rate is set at 1.2 mm3/mm s for all cases. The effective contact ratio, co, is chosen to be 0.43 with water-based grinding fluids and 0.6 with oil-based grinding fluids. It is obvious from Fig. 7 that the combination of a CBN grinding wheel with oil-based grinding fluids secures a preferred performance: this is due to the thermal conductivity of CBN being superior than that of A1203, and the sufferance of film boiling with oil-based grinding fluids being better than that with water-based grinding fluids. It is also revealed that the burning limits of grinding energy flux, 'i~Limlts,decrease as the depth of cut increases: this does not imply that conventional traverse grinding is the preferred choice, since the contact arc of creep-feed grinding, which is longer than that of conventional traverse grinding, should be considered. However, as long as the depth of cut is increased only to a certain level, decrease of the burning limits of grinding energy flux, 4~Limits,is not apparent. Fig. 8 manifests the effects of the effective contact ratio, co, on the burning limits of grinding energy flux, t~Limits , for different combinations of grinding wheel and cutting fluid, showing that the smaller is the effective contact ratio, the higher will be the burning limits of grinding energy flux, 4'L~m~ts.This means that a grinding wheel with an open structure, or a reduced wheel flat area and a shorter time-interval of dressing, will have improved burning limits of grinding energy flux, 4~L~m~t~.Thus, Fig. 8
40 35 30 25 ¢I)~.. 20 (w/r~)15 10 5 0
Metal Removal Rate 1.2 ran//nun s ",, Dia = 305 nun; Vs = 18 m/s ',~ - --- CBN A[20,
,<
-...... ~
0
/./Oil tUuid~ ~~~~~~ W ~ ~a~t~_'_~s°luble
l
L
I
I
1
2
3
4
5
Depth of Cut (mm) Fig. 7. Threshold of grinding energy for film boiling versus the depth of cut with various combinations of grinding fluid and abrasive grains for a fixed metal removal rate.
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123
60
On
Dia = 305 nun 50 _- ...... CBN ",,, AI~O~ ", a = 1 nun 40 ", ",, Vw = 1.2 mm/s "",, " , Vs = 18 m/s 30 "'.,. "', . ~ O i l fluids 10 0
I
I
I
I
I
I
r
I
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Effective Contact Ratio Fig. 8. Threshold of grinding energy for film boiling versus the depth* of cut with various combinations of grinding fluid and abrasive grains for effective contact ratio.
40
a = 1.0 ram; D i a : 305 ram; Vw =1.2 mm/s ......... CBN
--AI=O~
3O
......... ~
0~.20 (w/rod)
10 0 15
Oil-~_flm_'_~.........
~
ater soluble
I
I
I
I
18
21
24
27
30
Wheel Speed (m/s) Fig. 9. Threshold of grinding energy for film boiling versus the depth of cut with various combinations of grinding fluid and abrasive grains for wheel speed. establishes the best evidence for the application of the continuous-dressing creep-feed grinding process. Fig. 9 indicates the effect of the wheel speed, l/s, on the burning limits of grinding energy flux, #Li=its, an increase of wheel speed causing the burning limits of grinding energy flux, #Limits to increase. In other words, a grinding wheel with a higher speed and a larger diameter will i m p r o v e the burning limits of grinding energy flux, #Limits. However, in reality, the wheel speed is usually subjected to the constraints of the spindle rigidity and the wheel characteristics.
6. C o n c l u s i o n s
The grinding process is quite complicated, and a lot of factors can influence the onset of grinding burning and the m a x i m u m metal removal rate, such as the structure
124
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
number of the grinding wheel, the type of cutting fluid, the assignment of working conditions, the time interval of dressing, and the thermal properties of the workpiece as well as those of the abrasive grains. Some of the results presented in this investigation can be summarized as follows: (1) The cooling effect of water-based grinding fluids is better than that of oil-based cutting fluids. However, the resistance to workpiece burning using water-based cutting fluids is worse than that using oil-based cutting fluids. When the cutting fluids are applied to the grinding process, the strong cooling effect of the cutting fluids is apparent. In addition, a CBN grinding wheel shows better performance than an A 1 2 0 3 grinding wheel in the avoidance of workpiece burning. (2) The cooling effect of the grinding fluid, Re, shown in Eq. (17), can be improved by decreasing the effective contact ratio. In general, this effective contact ratio can be achieved by selecting a grinding wheel with a higher porosity or structure number. Further, a shorter dressing time interval and a coarser dressing type will decrease the effective contact ratio, which will improve the cooling effect of the coolant on the workpiece. (3) A simple model for determining the maximum surface temperature of the grinding fluid and the workpiece is presented, its validity being demonstrated by comparing its predicted numerical values with published experimental and finiteelement results. Similarly, the prediction of the burning limits of grinding energy manifests the same satisfactory results.
References [1] J.C. Jaeger, Moving source of heat and the temperature at sliding contacts, Proc. R. Soc. New South Wales, 76 (1942) 203-224. [2] J.O. Outwater and M.C. Shaw, Surface temperatures in grinding, Trans. ASME, 74 (1952) 73-86. [3] S. Malkin and R.B. Anderson, Thermal aspects of grinding, Part 1 - Energy partition, ASME, J. Eng. Ind., 96 (1974) 1177-1183. [4] S. Malkin, Thermal aspects of grinding, Part 2 - Surface temperatures and workpiece burn, ASME, J. Eng. Ind., 96 (1974) 1184-1191. [5] C.S. Stuart, Creep-feed surface grinding, Ph. D. Dissertation, University of Bristol, UK, 1979. [6] S. Ramanath and M.C. Shaw, Abrasive grain temperature at the beginning of a cut in fine grinding, ASME, J. Eng. Ind., 110 (1988) 15-18. [7] A.S. Lavine, A simple model for convective cooling during the grinding process, ibid., 1-6. [8] A.S. Lavine and T.C. Jen, Thermal aspects of grinding: Heat transfer to workpiece, wheel and fluid, ASME, J. Heat Transfer, 113 (1991) 296-303. [9] H. Yausi and S. Tsukuda, Influence of fluid type on wet grinding temperature, Bull. Jpn. Soc. Prec. Eng., 17(2) (1983) 133-134. [10] N.E. Ye and T.R.A. Pearce, A comparison ofoil and water as grinding fluids in the creep feed grinding process, Proc. Inst., Mech. Eng., 198B(14) (1984) 229-237. [11] S. Ohishi and Y.J. Furukawa, Analysis of workpiece temperature and grinding burn in creep feed grinding, Bull. JSME, 28(242) (1985) 1775-1781. [12] C. Guo and S. Malkin, Analysis of fluid flow through the grinding zone, ASME, J. Eng. Ind., 114 (1988) 427-434.
Materials
ELSEVIER
J. Mater. Process. Technol. 43 (1994) 109-124
Processing Technology
Thermal analysis of creep-feed grinding Kuang-Hua Fuh, Jen-Sheuan Huang Department of Mechanical Engineering, Tatung Institute of Technology, Taipei, Taiwan, 10451, ROC (Received March 26, 1993; accepted October 12, 1993)
Industrial summary One of the major problems encountered in industrial experience of creep-feed grinding is thermal damage to the workpiece and grinding wheel. Thus, the application of cutting fluids is especially crucial. In this paper an analytical model of the heat transfer between the wheel, the workpiece surface and the grinding fluids is derived and verified. The model enables the prediction of the maximum surface temperature when grinding fluids are applied, demonstrates the thermal energy partitions between the abrasive wheel, the cutting fluids and the workpiece, and also determines the threshold of the occurrence of film-boiling. Despite its simplicity, the model provides remarkable agreement with published data from experimental investigations and from finite-element analysis, for various creep-feed grinding conditions. The cooling effect of water-based grinding fluids is better than that of oil-based cutting fluids, but the resistance to workpiece burning using water-based cutting fluids is worse than that using oil-based cutting fluids. When cutting fluids are applied in the grinding process, the strong cooling effect of the cutting fluids is apparent. In addition, a CBN grinding wheel shows a better performance than an A120 a grinding wheel in the avoidance of workpiece burning. The cooling effect of grinding fluid, Re, can be improved by decreasing the effective contact ratio. In general, this effective contact ratio can be achieved by selecting a grinding wheel with a higher porosity or structure number. Further, a shorter dressing time-interval is a better choice for decreasing the wear flat area and thus for improving the cooling effect of the coolant on the workpiece. Key words: Cooling effect, creep feed grinding, thermal damage
Notations a Cp
grinding depth of cut (mm) specific heat at constant pressure (J/kg°C)
* Corresponding author. Elsevier Science B.V. SSDI 0 9 2 4 - 0 1 3 6 ( 9 3 ) E 0 1 1 9 - 2
110
D k q' q~ q'b Tw,Tf Ti Vs Vw
P 0
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
wheel diameter (mm) thermal conductivity (W/m K) heat flux (W/mm 2) the portion of the grinding energy removed by the coolant (W/mm 2) the portion of the grinding energy remaining in the workpiece (W/mm 2) temperature of the workpiece and grinding fluids respectively (°C) ambient temperature (°C) wheel speed (m/s) workpiece speed (mm/s) thermal diffusivity burning limits of grinding energy (W/mm 2) density (kg/m 3) temperature difference from the ambient temperature Ti (°C)
Subscripts fluid f g grain maximum max surface s total tot workpiece w workpiece background wb workpiece under grain wg
1. Introduction
Creep-feed grinding is a grinding process in which the workpiece infeed rate is reduced to allow the cutting depth to be increased, typically to hundreds or thousands of times encountered in conventional traverse surface grinding. One of the major problems encountered in industrial experience of such a grinding process is the high temperatures attained by the workpiece. This condition will result in various types of thermal damage, such as burning, phase transformations, softening (tempering) of the surface layer with possible re-hardening, unfavorable residual tensile stresses, cracks, and reduced fatigue strength. Furthermore, thermal expansion of the workpiece during grinding contributes to inaccuracies and distortions in the final product. Consequently, the application of cutting fluids is especially crucial in creep-feed grinding. However, the cooling effect of the grinding fluid has been ignored in research of the shear plane and interference zone temperatures analysis, hence the findings of Jaeger [1], Outwater and Shaw [2] and Malkin [3,4], are not directly applicable to the creep-feed grinding process. The thermal-partition coefficient derived by Outwater and Shaw [2] was based on the shear angle of the cutting grains and the Peclect Number. However, the cutting grains on the wheel surface are distributed randomly and the shapes of the grains are not identical, thus the shear angle of the cutting grains during the grinding process is
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994.) 109-124
111
difficult to visualise. Malkin and Anderson I-3] divided the grinding energy into chip formation, plowing, and sliding energy. Because the fraction of these energies is not constant and is difficult to determine during the grinding process, the thermalpartition coefficient derived by Malkin et al. cannot be applied to the real situation. Stuart [5] suggested that the thermal-partition coefficient is less than 5 percent for the grinding process, but his suggestion was lacking of theoretical support to establish that his results will hold for different grinding conditions. The thermal-partition coefficient developed by Ramanath and Shaw [6] can be applied to dry grinding only, as the thermal property of the coolant was not included. Lavine et al. [7,8] regarded the grinding wheel as a porous material filled with coolant. They developed a series of research investigations into the thermal aspects of the grinding process based on the micro-relationships between the abrasive grains, the grinding fluid and the workpiece. According to their model, reduction of the thermalpartition coefficient is associated with a decrease of wheel porosity, i.e. their models implied that dry-grinding, using a grinding wheel with lower porosity, is the preferred choice: this phenomenon violates the general physical concept. Further, in order to accurately predict the thermal-partition coefficient, the porosity of the grinding wheel should be kept at 99.5 percent, which is not likely to happen in the real world. Yasui et al. [9] and Ye et al. [107 performed experimental investigations on the effect of grinding-fluid type, finding that under some particular conditions the maximum temperature rise could be an order less if a water-based fluid is used rather than dry-grinding being carried out. However, when the surface temperature reached a value slightly over 100 °C, the use of a water-based fluid showed no advantage over dry-grinding. Ohishi and Furukawa [11] recognized that when the maximum surface temperature exceeded 100 °C for water-based fluids or 300 °C for oil, the temperature will rise rapidly, accompanied by the occurrence of grinding burn. As mentioned above, the cutting fluids play an important role in determining the grinding burn. Thus, it is desirable that simple criteria based on the heat transferred between the cutting fluid and the workpiece be derived to clarify the energy-partition relationships between the workpiece, the abrasive grains and the cutting fluid, to elucidate the effects of the grinding fluid, and also to determine the threshold for the occurrence of workpiece burning.
2. Mathematical analysis A geometrical explanation of down-cut creep-feed grinding is shown in Fig. 1. The wheel is a porous medium consisting of abrasive grains, bond material, and pores of irregular shapes and different sizes, and as the wheel surface encounters the fluid application zone its pores will begin to fill with fluid. According to Guo and Malkin [12], as long as the abrasive wheel enters the workpiece with properly placed nozzles and sufficient grinding fluid, the amount of grinding fluid left in the contact zone will be substantial and the grinding fluid trapped in the pores of the grinding wheel will move with the wheel peripheral speed, Vs. Thus, it is reasonable to assume that the fluid is stationary with respect to the wheel, i.e. the interference of cutting grains and
112
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109--124
D Wheel \ 1 _ ~ a ~ D J Vs
/ fluid /' 'introduced[
"
"~,~/Vs
wheel diaraeter grindin~ zone length depth o f cut wheel speed
~ _ _ _ _ _V__w_l;°rkpiecespeed
Fig. 1. The grindinggeometry.
/ _ ro:
work-piece x
Fig. 2. Microviewof the contactsurfacebetweenthe fluid,the grains and the workpiece.
fluid moves across the surface of the workpiece at the same peripheral wheel speed, Vs. Clearly, the grinding fluid, surrounded by the abrasive grains, the bonding material and the workpiece, can be regarded as water or oil in a boiler, as shown in Fig. 2. Although thermal damage requires time to take place, and the peak temperature generated during the moment of contact will be probably removed, the residue of grinding energy left on the workpiece will accumulate, which contributes to the thermal damage of the workpiece. To model this phenomenon, energy equations are written for the interference of the workpiece and coolant. In order to simplify the complexity of the grinding process, it is assumed that the thermal properties are constant, viscous dissipation and pressure work are negligible, thermal conduction in the direction of motion is negligible, and boiling does not occur. Fig. 3 demonstrates an idealized model of the contact zone at the contact surface. Using this model, the energy equation in the fluid and workpiece can be described as ~Tf ~-=
~2Tf -0~
O~y~
oo
~Tw a2Tw / 0~
(1)
(2)
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
fF
113
inte~ferenc~zone 9f
coolant anawol~plece
qwg
Fig. 3. Modelof the heat transferto the fluidand the workpieceat a point on the workpiecesurfacewhich is exposed to the coolant.
where Tf is the temperature of the grinding fluid, Tw is the temperature of the workpiece, 0tf is the thermal diffusivity of the coolant, ~tw is the thermal diffusivity of the workpiece, V~is the wheel peripheral speed and Vw is the workpiece speed. The initial conditions can then be represented as Tr(y, O) = T~
(3)
Tw(y, O) = Ti
(4)
where Ti is the ambient temperature. Lavine [7] has demonstrated that the fluid fills the pores throughout the entire thermal boundary layer, hence the boundary conditions can be expressed as ~T~ -- k f - - '
8y r=o
= q~'
Tf(oo,t)
= Ti
(5)
and -
k. 8Tw ~Y
y=o
= ,,
qwb
T w ( ~ , t ) = Ti
(6)
where kf is the thermal conductivity of coolants, kw is the thermal conductivity of the workpiece, q~' is the grinding energy removed by the fluid and the q'b is the grinding energy remaining in the workpiece. Now defined are 0f as the temperature difference between Tf and the ambient temperature Ti, and 0w as the temperature difference between Tw and ambient temperature Ti. By solving the above equations, Of and 0w can be obtained as follows: (7)
0w(y, t) =
qwb ~ ) w
2
exp
(8)
-~
x/~
\x/4awtjj
114
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
where p is the density, and c is the specific heat. The interference surface temperature difference along the length of contact can be obtained easily by substituting y -- 0 into Eqs. (7) and (8). Then
f
4x ,, 0f(0, x) -- q ~(k~p)f Vs qf
(9)
and /
0w(0, x) =
4x
,,
41rkp-~p)wVwqwb
(10)
Hence, as long as the portion of grinding energy removed by the grinding fluid, q~', and the portion remaining in the workpiece, q~,b, are determined, the temperature rise of the fluid as well as that of the workpiece can be predicted easily. Because: (i) heat is generated in the vicinity of the contacts between the abrasive grains and the workpiece; (ii) the thermal conductivity of the grain is much greater than that of the grinding fluid; and (iii) the relative velocity between the abrasive grain and the grinding fluid is approximately zero; it is reasonable to assume that the heat that enters the grain simply conducts further into the grain without being removed by the fluid. Further, the coolant cannot enter the actual contacts between the abrasive grains and the workpiece, i.e. the actual contact points belong indisputably to the dry-grinding type. Hence, it is easy to demonstrate that the heat, q~'ri~d, generated at a grain-workpiece interface conducts into either the workpiece or the abrasive grain. Thus . . .= qgrind
.qwg . +.
(11)
qg
where q~' is the heat flux into the workpiece at the grain location and q~' is the heat flux into the grain. In addition, the portion of the heat flux into the workpiece at the grain location to the total grinding energy can be defined as Rdry =
heat to work under the grain total grinding energy
q;~g
(12)
qgtrind
Once the heat flux which flows into the workpiece at the grain location, q~,,, enters the workpiece at the actual grain-workpiece location, part of q~,, denoted as q~,b will remain in the workpiece and later be distributed uniformly in the apparent contact area, whilst the rest of the heat, denoted as q[', will be carried away by the grinding fluid over the remaining portion of the actual grain-workpiece contact area. The rate at which heat leaves the chip is typically not large, and will be neglected. Thus qwg(-D---- q~b + q['(1 --co)
(13)
where the ratio of the actual grain-workpiece contact area to the total contact area, denoted as co, is defined as the effective contact ratio. In general, the effective contact ratio, co, is a function of the porosity of the grinding wheel, the wear flat area of abrasive grains, and the amount of chips adhering to the wheel surface.
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
115
Based on the continuity of the temperature gradient and from Eqs. (9) and (10), the relationship between the energy removed by the grinding fluid and the energy distributed uniformly over the entire apparent contact area can be expressed as
q:b = q'f' ((kpcp)w Vw~½ \ (kpc,)fvs }
(14)
Substituting this result into Eq. (13) qf' =
~'L\
+ 1 -- co
Rd,yq;'~i.d
(15)
The resultant thermal-partition coefficient with cooling effect of coolant can now be defined and expressed as _ Heattotalremainedgrinding inenergyWOrk= gary ~[1 + (1 Rtot-
. { (kpcp)fVsJ'~¥]j - 1 -a))k(kpcp)wV,
(16)
Finally. the cooling effect of the coolant, Re. can be defined as
go- [i + (i -J
(k'c,)'
(17)
"\(kp%)wVw) J
The thermal-partition coefficient with the cooling effect of the coolant on the workpie~ can now be expressed as
Riot = RdrrR~
(18)
Substituting Eqs. (16), (18) and (14) into Eq. (13), the portion of grinding energy carried away by the coolant, q~', and the portion of grinding energy remaining uniformly in the workpiece, q~,b, can be obtained as q~, =
" qwb
(2) ,, 1--~Rd,y(1 -- n~)qg.i.d
(19)
= o~Rtott4grind -"
(20)
Then the temperature distribution in the grinding fluid, Of(y,t), and the temperature distribution in the workpiece, 0w(y,t), can be predicted by combining Eqs. (7), (8), (19) and (20), the results being 0f(y, t) = 1 7 R d r y ( 1 --
y erfc( y ~l x/(kpcp)f L ~# ~e x p ( \- - ~y 2 ) _ x/af \x/4okt/1
Rc)~F2
(21)
o.o,,,,: o,,,o,,~/(kpq,),,,k X/~ r_,OXl,C\
~
-- ~ >. effc
(22)
116
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Hence, after suitable substitution, the surface temperature of the fluid over the contact zone can be represented as 0f,~(0, x) = ~
4x co ( k ~ , Vs 1 ~
Rdry(1 -- Re)q~'rind
(23)
and the surface temperature of the workpiece over the contact zone can be expressed as ,, f 4x 0w,,(0, x) = 4 ~(kp~p)wVwcoRt°tqgrind
(24)
Finally, the maximum surface temperature of the grinding fluid over the grinding zone can be expressed as
0fs max(0,N//~ ) ""
=
1/- 4(aD)½ co coRary(1 _ R¢)q'g',i.d ~] lr(kpcp)fVs 1 -
(25)
and the maximum surface temperature rise of the workpiece over the grinding zone can be obtained as 0..... ( 0 , x / ~ ) = /-4(aD)½ "" ~/ n( k p cp)w Vw coRt°tq'*'rind
(26)
The grinding energy per unit contact area per unit time, mentioned above, can be expressed as FtV~ " = bx/,~ q,rind
(27)
where the tangential grinding force Ft can be determined by the assignment of grinding condition such as the depth of cut, the wheel speed, the workpiece speed and the wheel diameter. As long as F t has been determined, Eqs. (25)-(27) can be employed to predict the maximum surface temperatures of the grinding fluid and the workpiece, Of...... and 0........ Thus the criterion of workpiece surge is determined. If the maximum surface temperature is defined as 0...... then the resistance to workpiece burning ~Limits can be derived inversely from Eq. (25) and written as
~Limits
/ Tz(kpcp)f Vf 1 - co 1 = X/ 4(aD) ½ ~ Rdry(1--- Re) 0s. . . .
(28)
When the type of grinding fluids has been chosen, the maximum endurance surface temperature rise 0..... and the thermal properties of the grinding fluid can be determined. Then, the burning limits of the grinding energy can be obtained based on the effective contact ratio 09 to determine the optimal selection of grinding conditions to avoid the occasion of workpiece burning.
K.-H. Fuh, J.-S. Huang /Journal of Materials Processing Technology 43 (1994) 109-124
117
Table 1 The thermal properties of the coolant, the wheel and the workpieee Thermal property
Water
Oil
Air
AI20 3
CBN
Steel
Thermal conductivity k (W/m K) Specific heat Cp (J/kg°C) Density P (kg/m 3)
0.662
0.15
0.0262
46
1300
43
4201
2000
1005.7
770
506
473
976.8
820.0
1.1747
4000
3450
7801
3. Discussion and results of the cooling effect, Ro of coolant The energy-partition coefficient plays an important role in the grinding process, this coefficient depending on the material of the cutting grains, the porosity and the structure of the wheel, and the type of coolant used in the grinding process. Thus, the following sections are focused on the investigation of the thermal-partition coefficient. The thermal properties of steel and of various abrasive grains and grinding fluids are listed in Table 1: these will be used in this research to investigate the cooling effect, Re, of the grinding fluid on the workpiece. First, compare the cooling effect of the coolant, Re, between creep-feed grinding and conventional traverse grinding. Fig. 4 elucidates that the cooling effect Rc decreases as the velocity ratio, (V,/Vw) °'5, increases. The velocity ratio, (VJVw) °'5, for creep-feed grinding generally falls into the region above 100, whilst the velocity ratio, (VdVw) °'5, for conventional traverse grinding is usually below 40. This shows that as long as the coolant shoe is at a proper location and the coolant is sufficient, the cooling effect in creep-feed grinding should be better than that in the conventional traverse grinding process. (Note that this does not imply that the temperature of the workpiece in the creep-feed grinding process is lower than the temperature in conventional grinding). When the grinding fluid is applied in the grinding process, the improvement of the cooling effect of the coolant is obvious. Furthermore, the cooling effect of water-based coolant is more obvious than that of oil-based coolant. The effective contact ratio is a function of the wheel structure, the wheel porosity, and the wear flat area of the abrasive grains. Amongst these factors, the structure organization of the wheel is the major factor, having a direct effect on the effective contact ratio. As the structure number indicates the volumetric concentration of the abrasive grains in the wheel, a higher structure number referring to a lower grain density of the wheel, a grinding wheel with a higher structure number or with a more open structure will decrease the effective contact ratio, co. If the grinding wheel is newly dressed, the effective contact ratio can be determined simply by the volumetric concentration of the abrasive grains.
118
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
1.2 1k 0.8
Re
~/no coolantadded
ii',
effective contact ratio 1.0
oil fluid
~ A 0.6 ~- - t l/i\ 0"4 / , ~ 0
60
0.5 0.03 waters°luble
120
180
]
240
300
(VsrVw)°'5 Fig. 4. The cooling effect of the grinding fluid versus the velocity ratio for various effective contact ratios.
1.2
1
....
,,
_~__~t
~__
.....................
0.8 Re0.6 -
oii . . . . . . . . . . . . .
S
/
water soluble....- - - J / ,.
0.4 0.2 0
-
~
.'Or
_:............... ~_~a~r~_.,___~ ........ 1
0
";
.-"
1
,
I
I
0.2 0.4 0.6 0.g Effective Contact Ratio
Fig. 5. The cooling effect of the grinding fluid versus the effective contact ratio.
Fig. 5 shows that the cooling effect of the coolant on the workpiece decreases as the effective contact ratio increases. Such a result is expected, as a grinding process with a lower effective contact ratio can make the coolant flow easily, to remove the grinding energy rapidly. Hence, a grinding wheel with a higher porosity will be a preferred choice to improve the cooling effect of the grinding fluid on the workpiece. As the time or distance of the grinding process increases, the wear flat area of the abrasive grains increases also, which causes the effective contact ratio to increase. Thus, dressing conditions with a shorter time interval or with a coarse infeed rate are preferred: this is also the reason why continuous-dressing creep-feed grinding demonstrates a better performance than the conventional creep-feed grinding process.
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
119
4. Verification of the equations of the maximum surface temperature model Before proceeding with further investigation of the workpiece burning criteria, the validity of the temperature model in Eqs. (25) and (26) should be established. Table 2 compares the maximum surface temperatures obtained from Furukawa's experimental values [11] and Lavine's theoretical values [8] with the values calculated from Eqs. (25) and (26). The ratio of the heat flux that flows into the workpiece under the grain location q~,~,to the total grinding energy, qsri,d, denoted as Rdry, as used for Eqs. (25) and (26), is adopted from results of Ramanath and Shaw [6]. This ratio, Rdry, is derived based on the concept that all of the heat flowing inwards is extracted outwards during the cooling portion of a single wheel revolution, rather than based on the concept of temperature continuity. Hence, the utilization of the following expression is suitable
=
[
1+
]
(29)
As the grinding wheel that Ohishi and Furukawa [11] used was WA60G8AV, the volumetric concentration of the abrasive grain for a newly-dressed grinding wheel was about 46 percent: thus the effective contact ratio, to, for a newly-dressed grinding wheel is chosen as 0.46. From the results listed in Table 2, it is obvious that the maximum surface temperature with water-based coolant, predicted in this research, is satisfactory. However, slight deviations of maximum surface temperature take place with the application of oil-based coolant for the identical effective contact ratio, to. The purposes of the coolant applied in the grinding process are not only the cooling and lubricating effects but also the cleaning away of the chips adhering to pores on the wheel surface. However, the viscosity of the oil-based coolant usually obstructs the accomplishment of the cleaning away of the chips adhering to the pores on the wheel surface and thus increases the actual contact surface between the contact zone of the grinding wheel and the workpiece. Hence, the effective contact ratio with the utilization of oil-based coolant will be higher than that with the use of water coolant under the same grinding conditions for an identical abrasive wheel. If a higher effective contact ratio, to, is chosen, namely 0.60, the maximum surface temperatures listed in Table 2 with the use of oil-based coolant calculated from Eqs. (25),(26) and (29) are approximately identical to the experimental results of Ohishi and Furukawa [11] with the use of oil-based coolant. In addition, the maximum surface temperatures calculated from Eqs. (25), (26) and (29) when the effective contact ratio is chosen as 0.60, demonstrate the same tendency as compared to the results of Lavine [8]. Ohishi and Furukawa [11] suggested that when the maximum surface temperature exceeds 100 °C for water-based fluids or 300 °C for oil-based fluids, the temperature will rise rapidly, and the grinding burn will occur. Thus, further investigation will be focused on the prediction of interference zone temperature to determine whether or not grinding burn will occur. Fig. 6 illustrates the maximum surface temperature
120
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Table 2 Comparison of the present predictions with the data of Ohishi and F u r u k a w a [11] and Lavine et al.[8] for creep-feed grinding 0. . . . pred (presented) q" grind (w/mm ~)
Coolandt type
2.0
water
15
32
16
30
oil
80
78
52
80
water
50
105
52
96
260
253
171
260
75
153
76
140
(burn)
369
249
6.5
oil 9.5
water oil
0max,~xp [11]
0max,prod [8]
Vs = 20 m/s, Vw = 0.33 m/s, diameter = 305 mm, depth =
Effective Contact Ratio ~o 09 = 0.46 oJ = 0.60
380 (film boiling)
1.0 mm.
of creep-feed grinding with oil-based fluids and water-based fluids. Note that the temperatures using oil-based grinding fluid in Fig. 6(a) are higher than those using water-based grinding fluid in Fig. 6(b). This is due to the thermal conductivity of water-based grinding fluid being superior than that of oil-based grinding fluid: the increase of the effective contact ratio will obstruct the grinding fluid carrying away the grinding energy from the grinding zone, and thus decreasing the cooling effect on the workpiece. The maximum surface temperatures will then increase as the effective contact ratio increases as shown in Fig. 6. In addition, a grinding process with higher specific grinding energy is more apt to reach the burning region for a specific effective contact ratio. Hence, a suitable selection of grinding or dressing conditions and wheel porosity is crucial to the maintaining of the desired metal removal rate. That is, the occurrence of grinding burn is determined by: the thermal properties of the abrasive grains, the grinding fluids and the workpiece material; the effective contact ratio, ¢o, which is determined by the time-interval of dressing and the structure number of the grinding wheel; and by the assignment of the grinding conditions which determine the specific grinding energy.
5. Prediction of the burning limits of grinding energy Next, the following will discuss the effects of the variety of grinding fluid and the grinding conditions on the burning limits of grinding energy flux, #Limits, and the validity of the model in Eq. (28) is established. Table 3 demonstrates a comparison of heat flux obtained from Eq. (28), using data listed in Table 1 and Table 2, with the
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
121
Vs = 18 m/s; Vw = 0.6 mm/s oC
a = I mm; D = 305 mm q~.~ = 2.0 W/ram 2 5OO q",,~= 6.5 W/ram 2 400 - - q",~ = 9.5 W/ram2 Bumin~ Relfion Os,max 300 2OO 600
100 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Effective Contact Ratio
(a)
°C 200
q"o~ = 2.0 W/ram 2 / = 6.5 W/ram 2 / --q'~ = 9 . 5 W/mm " ~ / ' / " - q".~
160 Os,max120
Burning Region
~
./" /
0.5
0.6
80
40 0 0
0.1
0.2
0.3
0.4
0.7
Effective Contact Ratio (b) Fig. 6. Maximum surface temperature versus effective contact ratio for various specific grinding energies with: (a) oil-based coolant; and (b) water; for creep-feed grinding.
Table 3 Comparison of the present predictions with the data of Ohishi and Furukawa [11] for creep-feed grinding Threshold of energy flux for film boiling 0Li=it (W/mm 2) Depth a(mm)
Work speed V,,(mm/s)
Exp[11]
FEM[11]
Present
0.5
2.4
10.7
11
11.11
1.0
1.2
9.5
9
8.96
2.0
0.6
8.2
7
7.30
experimental data and the finite-element results of Ohishi and Furukawa [11]. From Table 3, it is obviously that the present model, using a simple analytical method, has a reliable predictive ability, when compared to the values obtained by Ohishi and
122
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
Furukawa [11] using finite-element analysis. Ohishi and Furukawa did not describe the ambient temperature in their experiments, the ambient temperature is assumed at 25 °C so that the temperature difference, 0...... equals 75 °C with water coolants. The effective contact ratio, co, is chosen according to the volumetric concentration of the abrasive grains for a newly-dressed grinding wheel, namely 0.46. Fig. 7 demonstrates the effects of the grinding depth on the burning limits of grinding energy flux, 0Limits, various combination of grinding wheel and grinding fluids being used in the prediction of these burning limits, for different depth of cut. The metal removal rate is set at 1.2 mm3/mm s for all cases. The effective contact ratio, co, is chosen to be 0.43 with water-based grinding fluids and 0.6 with oil-based grinding fluids. It is obvious from Fig. 7 that the combination of a CBN grinding wheel with oil-based grinding fluids secures a preferred performance: this is due to the thermal conductivity of CBN being superior than that of A1203, and the sufferance of film boiling with oil-based grinding fluids being better than that with water-based grinding fluids. It is also revealed that the burning limits of grinding energy flux, 'i~Limlts,decrease as the depth of cut increases: this does not imply that conventional traverse grinding is the preferred choice, since the contact arc of creep-feed grinding, which is longer than that of conventional traverse grinding, should be considered. However, as long as the depth of cut is increased only to a certain level, decrease of the burning limits of grinding energy flux, 4~Limits,is not apparent. Fig. 8 manifests the effects of the effective contact ratio, co, on the burning limits of grinding energy flux, t~Limits , for different combinations of grinding wheel and cutting fluid, showing that the smaller is the effective contact ratio, the higher will be the burning limits of grinding energy flux, 4'L~m~ts.This means that a grinding wheel with an open structure, or a reduced wheel flat area and a shorter time-interval of dressing, will have improved burning limits of grinding energy flux, 4~L~m~t~.Thus, Fig. 8
40 35 30 25 ¢I)~.. 20 (w/r~)15 10 5 0
Metal Removal Rate 1.2 ran//nun s ",, Dia = 305 nun; Vs = 18 m/s ',~ - --- CBN A[20,
,<
-...... ~
0
/./Oil tUuid~ ~~~~~~ W ~ ~a~t~_'_~s°luble
l
L
I
I
1
2
3
4
5
Depth of Cut (mm) Fig. 7. Threshold of grinding energy for film boiling versus the depth of cut with various combinations of grinding fluid and abrasive grains for a fixed metal removal rate.
K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
123
60
On
Dia = 305 nun 50 _- ...... CBN ",,, AI~O~ ", a = 1 nun 40 ", ",, Vw = 1.2 mm/s "",, " , Vs = 18 m/s 30 "'.,. "', . ~ O i l fluids 10 0
I
I
I
I
I
I
r
I
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Effective Contact Ratio Fig. 8. Threshold of grinding energy for film boiling versus the depth* of cut with various combinations of grinding fluid and abrasive grains for effective contact ratio.
40
a = 1.0 ram; D i a : 305 ram; Vw =1.2 mm/s ......... CBN
--AI=O~
3O
......... ~
0~.20 (w/rod)
10 0 15
Oil-~_flm_'_~.........
~
ater soluble
I
I
I
I
18
21
24
27
30
Wheel Speed (m/s) Fig. 9. Threshold of grinding energy for film boiling versus the depth of cut with various combinations of grinding fluid and abrasive grains for wheel speed. establishes the best evidence for the application of the continuous-dressing creep-feed grinding process. Fig. 9 indicates the effect of the wheel speed, l/s, on the burning limits of grinding energy flux, #Li=its, an increase of wheel speed causing the burning limits of grinding energy flux, #Limits to increase. In other words, a grinding wheel with a higher speed and a larger diameter will i m p r o v e the burning limits of grinding energy flux, #Limits. However, in reality, the wheel speed is usually subjected to the constraints of the spindle rigidity and the wheel characteristics.
6. C o n c l u s i o n s
The grinding process is quite complicated, and a lot of factors can influence the onset of grinding burning and the m a x i m u m metal removal rate, such as the structure
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K.-H. Fuh, J.-S. Huang/Journal of Materials Processing Technology 43 (1994) 109-124
number of the grinding wheel, the type of cutting fluid, the assignment of working conditions, the time interval of dressing, and the thermal properties of the workpiece as well as those of the abrasive grains. Some of the results presented in this investigation can be summarized as follows: (1) The cooling effect of water-based grinding fluids is better than that of oil-based cutting fluids. However, the resistance to workpiece burning using water-based cutting fluids is worse than that using oil-based cutting fluids. When the cutting fluids are applied to the grinding process, the strong cooling effect of the cutting fluids is apparent. In addition, a CBN grinding wheel shows better performance than an A 1 2 0 3 grinding wheel in the avoidance of workpiece burning. (2) The cooling effect of the grinding fluid, Re, shown in Eq. (17), can be improved by decreasing the effective contact ratio. In general, this effective contact ratio can be achieved by selecting a grinding wheel with a higher porosity or structure number. Further, a shorter dressing time interval and a coarser dressing type will decrease the effective contact ratio, which will improve the cooling effect of the coolant on the workpiece. (3) A simple model for determining the maximum surface temperature of the grinding fluid and the workpiece is presented, its validity being demonstrated by comparing its predicted numerical values with published experimental and finiteelement results. Similarly, the prediction of the burning limits of grinding energy manifests the same satisfactory results.
References [1] J.C. Jaeger, Moving source of heat and the temperature at sliding contacts, Proc. R. Soc. New South Wales, 76 (1942) 203-224. [2] J.O. Outwater and M.C. Shaw, Surface temperatures in grinding, Trans. ASME, 74 (1952) 73-86. [3] S. Malkin and R.B. Anderson, Thermal aspects of grinding, Part 1 - Energy partition, ASME, J. Eng. Ind., 96 (1974) 1177-1183. [4] S. Malkin, Thermal aspects of grinding, Part 2 - Surface temperatures and workpiece burn, ASME, J. Eng. Ind., 96 (1974) 1184-1191. [5] C.S. Stuart, Creep-feed surface grinding, Ph. D. Dissertation, University of Bristol, UK, 1979. [6] S. Ramanath and M.C. Shaw, Abrasive grain temperature at the beginning of a cut in fine grinding, ASME, J. Eng. Ind., 110 (1988) 15-18. [7] A.S. Lavine, A simple model for convective cooling during the grinding process, ibid., 1-6. [8] A.S. Lavine and T.C. Jen, Thermal aspects of grinding: Heat transfer to workpiece, wheel and fluid, ASME, J. Heat Transfer, 113 (1991) 296-303. [9] H. Yausi and S. Tsukuda, Influence of fluid type on wet grinding temperature, Bull. Jpn. Soc. Prec. Eng., 17(2) (1983) 133-134. [10] N.E. Ye and T.R.A. Pearce, A comparison ofoil and water as grinding fluids in the creep feed grinding process, Proc. Inst., Mech. Eng., 198B(14) (1984) 229-237. [11] S. Ohishi and Y.J. Furukawa, Analysis of workpiece temperature and grinding burn in creep feed grinding, Bull. JSME, 28(242) (1985) 1775-1781. [12] C. Guo and S. Malkin, Analysis of fluid flow through the grinding zone, ASME, J. Eng. Ind., 114 (1988) 427-434.