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Evaluation of temperature and heat transfer conditions at the metal forming interface
J o u r n a l of
Materials Processing Technology ELSEVIER
J. Mater. Process. Tcchnol. 45 (1994) 6 3 7 - 6 4 2
Evaluation of Temperature and Heat Transfer Conditions at the Metal Forming Interface W. Nshama, J. Jeswiet, P. H. Oosthuizen Queen's University, Kingston, Canada Abstract During the forming of metals, the contact resistance between the workpiece and the die can have an important influence upon the temperature distribution in the material being formed and on the quality of the end product. In order to predict the contact resistance, a technique is being developed which will enable accurate determination of the contact resistance. This technique involves direct temperature measurement at the die/billet interface during deformation and subsequent use of inverse heat transfer model to calculate the contact resistance. The preliminary results indicate that the method can provide a reliable means of predicting the contact resistance.
1
INTRODUCTION
The process of Metal forming is always accompanied by heat generation. This heat affects, among other parameters, lubrication conditions (lubricant viscosity, reaction rates, and breakdown of lubricants), material behaviour during deformation, and quality of finished product. Accurate determination of temperature during a metal tbrming process is important because it affects interface lubrication conditions and material behaviour during deformation. Variations in workpiece temperature across its thickness may cause inhomogeneous deformation leading to defects such as surface cracking or harmful residual stresses. Increase of temperature in the die lowers the allowable die stress. Fast transfer of heat from the billet to the surface layer of the die results in high thermal stresses. On the other hand, rapid chilling of the billet increases flow stress and high contact-stresses on the die. High temperature at the contact zone results in breakdown of lubrication film and in turn increases heat generated due to increase in friction. In forging, force and power requirements and product properties are influenced by workpiece temperatures. Therefore, due to the importance of temperature conditions in metal forming there is a need for a simple heat transfer model to simulate some metal working conditions when designing for a particular forming process. A number of attempts have been made to measure the temperature condition at the tool-
workpiece interface in bulk forming, however, accurate results have not been obtained. One reason for the lack of accurate temperature measurement is the complexity of the metal forming process. Heat is generated by both internal plastic deformation and interface frictional work. In both cases, a simple theoretical analysis cannot be made easily. Therefore, experimental work is always necessary for any meaningful analysis. On the other hand, temperature measurement in metal forming is difficult because of the harsh conditions which exist both in the bulk metal and at the interface. Toolworkpiece interface conditions are never constant. Moreover, the parameters at the interface are interrelated, for example temperature at the interface depends, among other conditions, on lubrication conditions and heat transfer conditions Lubrication affects both friction and heat transfer conditions. Both friction coefficient and lubricant layer at the interface are also difficult to determine. In most research work involving temperature at the interface, lubricant film thickness and friction coefficient are estima~.xP "3. For instance in an attempt to determine the temperature profile in the billet-lubricant-die zone in forging operations, Bo~r et aP': used upsetting experiments and Finite Element calculations In their experiments, different boundary conditions, volume, and height-to-diameter ratios were used in the assessment of the rate of heat transfer. The variation of temperature in the die and billet was experimentally recorded using thermocouples
0924-0136/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved.
SSD1 0924-0136(94)00253-3
638
mounted away from the die/workpiece interface and the results were compared with an analyticalnumerical analysis by Finite Element (FE) in which the lubricant thickness was chosen to be 0.1 mm with the value of conductivity of the lubricant chosen such that the best fit to experimental data was obtained. The lubricant thickness was arbitrarily chosen due to the impossibility of knowing the real thickness of the lubricant trapped between die and billet. The results show that there is almost no influence of the radiation effect but, instead, there is a greater influence of the conductivity of the lubricant. In a recent paper Pawelski et al 3 used the ring test to study friction conditions in hot metal forming. They used thermocouples to measure the temperature of workpiece. The results of the experiment, using unlubrica~l surfaces, shows that there is a rise in temperature in the centre of the specimen which they attribu~_A to the internal plastic work. In the analysis of the temperature of contact zone, they used the assumption of two semi-infinile bodies that come into contact. The justification given being the short duration of the contact time. In the study of the interface conditions in metal rolling Jeswiet and Zou 7 successfully developed a sensor which measured three rolling temperatures simultaneously: at the billet surface, the roll surface, and inside the roll. Measurement of temperature of the billet was done using the law of intermediate metals in thermometry. A similar technique was also used by Hirao 8 in the determination of temperature distribution on flank face of cutting tool. One other experimental technique lbr temperature measurement, Doremus, et al 9 used an infra-red sensor when studying upsetting tests of steels at high temperatures. The problem with the infra-red technique is its low sensitivity at low temperatures. Also the infra-red sensor cannot provide temperature at a specific point, plus the speed of response is too low. However, it's use is limi~l to regional, slowly changing temperature measurement. Semiatin et al. 5 developed a technique by which the heat transfer coefficient can be estima~l for non-isothermal bulk-forming process based on the measurement of the die temperature brought together under varying pressure. A one-dimensional analysis and a finite-difference model were used in the
evaluation of the heat transfer coefficients giving constant values of the heat transfer coefficient for the given initial conditions This technique was further developed by Butte et al 4 for use in hot forging process. In yet another search tbr the heat transfer coefficient, Malinowski et al. 6 used temperature measurement within two dies in contact and a finite element technique to determine the interracial heattransfer coefficient. They developed an empirical relationship giving the coefficient of heat transti~r as a function of time, temperature and interracial pressure. The difference between this work and others in this review is that the temperatures have been measured directly at billet surface and the die surface giving a temperature jump across the interface which gives the heat transfer coefficient by inverse heat transfer methods.
2
EXPERIMENTAL DESIGN
The present work provides a technique oi evaluating interface heat transfer coefficient during upsetting operations using temperature measured at the interface and area near the interface. For accurate analysis of temperature distribution at the tool-workpiece interface and the amount of heat generated during deformation, temperature measurement were made at different positions Two sets of temperature measurement were done. In the first case thermocouple wires were put in the die only, while in the second case hot billets were used with thermocouple wires both in the die and billet and as shown in Figure 2. In the second case, a low contact pressure was used in order to prevent the thermocouple wires from breaking. Three parameters were measured during the experiment: temperature, force, and displacement. The measurements were recorded by a computer via a high speed A/D board. The system also provided a mechanism to control strain rate during the experiment. 2.1 Experimental Apparatus In this experiment Aluminium (606t-O) .samples were used with a seventy ton hydraulic press. Reduction of up to 75 % were conducted. The press
639
was linked to the data acquisition to provide feedback control (Figure 1). The experiment setup is shown in Figure 2. Temperature measurement was done using eight Type J (Iron-Constantan) thermocouples installed in an insert in the lower die at various depths from the die surface and radial distances from the die centre (Figure 3). There are three sets of thermocouples in the die grouped according to their depth from the surface. The first group, which are normally open, measure billet temperature using it as a third metal. The second set of thermocouples which are located at surface of the die, measure the temperature of die surface. The third and forth set of thermocouples are located at depths of about 1 mm and 2 mm respectively. These measure the subsurface temperature of the die. In the case of the instrumented billet, three thermocouples are inserted along the axis of the billet as shown in Figure 2.
lower die. Inside the hole, the wires were bonded to the die, without electrical contact, using the same binding material. This provided sufficient strength and hardness required at high compressive forces at the die-billet interface. Details of the construction can be found in reference 7. To provide fast temperature response, 0.127 mm diameter wires were used. At the measuring point all thermocouple ends touch the substrate, except the wires measuring the billet surface--which are left open.
@ Legend: O, ~
,; ~LIbSLIFfQC~ thermocouples 12159 m m
5. 8 Subsurface thermoco~lples 1 168 m m 1. 6 - Die surface t h e r m o c o u p l e s 2. 4. 7 - Billet surfoce theH,3oc(,uples
Figure 3 Figure 1 Simplified block diagram tbr control system for the press
4
}~ll~t
(m254×254~m) -
~
} ]hermOCOb~ptes
D ~:-]i~er~c,c o u p t e s
Figure 2 setup
Schematic diagram of the experimental
The thermocouple wires were coated with a thin film Molochile (a mixture of A1203, M20, and SiO:) with sodium silicale as a binder. Each thermocouple wire was then placed in a separate hole inside the
deep/ deep
Thermocouple positions in the lower die
Calibration of the thermocouples was done by immersing the instrumented die in a temperature controlled water bath while recording the water temperature and thermocouple volt output. For the normally open thermocouple, an aluminium strip was clamped on die in order make a joint--similar to an actual upsetting operation. The results of converting the voltage reading to their corresponding temperatures (using standard tables) showed that all thermocouples gave readings within a degree centigrade of that of water bath. Thus, during upset tests the thermocouple voltage readings were converted to temperature measurement by using the standard formulas (a polynomial fit for Type J thermocouples). 2.2 Experimental Procedure Solid cylindrical billets of Aluminium (AI 6061-O) were compressed between tv~ opposite fiat dies. Initial size of the samples were 25.4 nun in diameter by 25.4 mm length. The top and bottom
640
dies were both made of tool steel (4140). Both dies have diameters of 125 mm and a height of 62.5 nun: In the first cold forming case a billet was compressed, at controlled strain rate, to various degrees of percentage deformation. The hydraulic ram velocity was at a constant velocity of about 1.375 mm/s. In the second case, hot instrumen~d billets were used instead. The dies were allowed to touch the billet with sufficient pressure to provide good thermo and electrical contacts without actually undergoing plastic deforming.
and the interior of the die with highest temperature values being that of billet surface. T h e results also show a temperature jump ber~e..en billet surface and die surface. Temperature decreases as the distance increases from the surface. For reasons explained earlier, there were no temperature measurements within the billet.
44 F--T--
ac~42
r..... ~
,
~
/i
-~ ....... r
¢!-
.
•
}!!
, .... i S:Ou
3
RESULTS AND DISCUSSION
i :
In the hot billet test, Figure 4, the temperature measurement shows equal temperature distribution inside the billet with respect to the billet centre indicating equal flow towards both dies. The results show that the heat goes through a temperature jump as it crosses the billet/die interlace. This indicates that there is a thermal resistance at the interface and that once the flux is determined from the internal billet therrnocouples, one can then use inverse heat transfer techniques to find the heat transfer coefficient. 225
--.-___._
200
. . . . . . . . . . . . . . . . . . .
~
T
-
4
-- 4
150
M-I
IO0 E 75
50
4 DETERMINING THE HEAT TRANSFER COEFFICIENT
ij 5/~
/3/
25
• 6 74
7 ___L_ 5
Figure 5 Temperature/Displacement V~ Tinle m cold upsetting test (Percentage reduction: 50%)
£
125 /
i *0
The results also show the temperature sensor to be a viable device for determining the interface temperatures.
2
175 •
/
10
lfl
20
2t~
30
35,
,~,0
Figure 4 Temperature/Displacement Vs Time using a hot billet (Percentage reduction: 0%) In the cold upsetting, Figure 5, the results show temperature variation bet,~e.en that of the interface
One of the main purposes of the present work is to determine the heat transfer coefficient from the temperature measurements. The heat transfer coefficient, h, or contact resistance coefficient is defined by: q ~ h(Th, i~) (0 where q is the rate of heat transfer per unit area across the interface between the billet and the die and T~ and T~ are the die and billet interface temperatures respectively. In general, h will depend on both the interfacial pressure and the mean interracial temperature. However, in order to
641
describe the procedure being used to find h, this variation will be ignored i.e. h will be treated as constant. It has been assumed that the heat conduction in both the die and the billet in the region where measurements are made is one-dimensional. Therefore, the temperature in the billet will be described by:
technique. The method basically involves calculating the temperature using an assumed value of h and then altering h to reduce the mean difference between the measured and calculated temperatures. The mean difference is summed over all points at which measurements are made and over all time steps at which measurements are made, i.e. the following error function is introduced: s
9b Co 0 t
: kb
+ q*
where the subscript b indicates billet properties, T is the temperature at any point in the billet at time t and q* is the internal heat generation. The internal heat generation arises from the work being done on the billet. In general, it will not be uniform in the billet. However, in order to illustrate the method of analysis it will be assumed to be uniform and to be derivable from the rate at which work is being done on the billet. Similarly, the temperature distribution in the die will be given by: ~-0T
_(cST )
At the interface:
k (OT]
: h ( T b _ Ta)
(rc-r,,) 2
(5)
where the subscripts C and M refer to the calcula~xl and measured values at corresponding points and corresponding times, From this it follows that:
dE dh
2 ~ ~ (T c
IM) dT':
(6)
dh
The summation is, as mentioned, carried out over all points and all times considered. The value of h that minimizes the error i.e. that gives:
dE dh
(3)
where the subscript d indicates die properties. There is no internal heat generation in the die because the deformation of the die is assumed to be negligible,
k (cOT]
=
(2)
0
(7)
is the "best" value that can be derived from the experimental data. From eq. (6) it then follows that if a value of h is selected and the temperature values given using this value are Tc then the value of the heat transfer coefficient that minimizes the error will differ from h by Ah where, by virtue of eq.(6),
(4) Z Z ( r c + drCAh - T , . ) drc -- : 0
dh
The above equations can be written in finite difference form and used to solve for the temperature-time variations in the die and billet for any assumed value of h. In carrying out this solution, the mesh in the billet must be amended at each time step to account for the deformation of the billet. In the present work, a simple implicit procedure has been used. In obtaining solutions, it has been assumed that the initial temperatures of both the die and billet are specified and that the temperature distribution is symmetrical about the billet centre-plane and that far from the interface the temperature of the die remains equal to the initial die temperature. Now, the value of h is not known. It is determined using an inverse heat conduction
(8)
From this it follows that: f. . . .
Ah=
dTc~
~-~"~- ~ (~': -: ~T M ) - ~ !
(9)
In order to find dTc/dh, the temperature variation in the die and billet is first calcula~d using the selected value of h. The values of the temperatures so calculated are denoted by Tco. A small increment to h, say ~Sh is then chosen, t$h typically being about 1% of h, and new values of Tc
642
are calculaled. At any point and any time, the following is then used:
ate._ dh
(Tc
Too) 8h
(lO)
Using this in eq.(9), Ah can be calculated. Because the above analysis assumes that Ah is small, an iterative procedure must be used. A value of h, say ho, is guessed and the above procedure is used to find Ah. With h set equal to Ah + ho the process is repeated and continued until the error E as defined in eq. (5) is reduced below a selected value. The accuracy of the procedure is strongly dependent on where the temperature measurements are made. In general, the closer that these measurements are made to the interface, the more accurate will be the derived value of h. In the present experimental procedure, the actual interracial temperatures for the die and billet are measured so very accurate values of h can be derived from the measurements.
5
CONCLUSIONS
Forging interface temperatures have been measured successfully in hot and cold hydraulic forging of 6061 Aluminium. These experimental results can be used to verify the model proposed in this paper.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of NSERC and DAAD.
REFERENCES 1.
Bo~,r, C. R., Rydstad, H., and Schr6der, G., "Choosing Optimal Forging Conditions In
Isothermal and Hot-Die Forging," Journal of Applied Metalworking, Vol. 3, No. 4, 1985, pp 421-431. BoSr, C. R., and Schrrder, G., "Temperature in the Die-Billet Zone in Forging," Annals of the CIRP, Vol. 30/1/1991, pp 153-157. 3. Pawelski, O., Rasp, W., and Hoerster, C. "'Ring compression test as simulation test tbr the investigation of friction in hot metal tbrming," Steel Research, Vol. 60, No. 9, 1989, pp 395-402, 1989. 4. Burte, P. R., Im, Y., Altan, T., and Semiatin, S. L., "Measurement and Analysis of Heat Transfer and Friction During Hot Forging," Transactions of the ASME, Vol. 112, November 1990, pp 332-339. 5. Semiatin, S. L., Collings, E. W., Wood, V. E., and Altan, T., "Determination of the lnterthce Heat Transfi~r Coefficient fbr Non-Isothermal Bulk-Forming Processes," JOurnal oJ" Engineering for Industry, Vol. 109, February 1987, pp 49- 57. 6. Malinowski, Z., Lenard, J. G., Davies, M. E. "A Study of the Heat-transfer Coefficient as a Function of Temperature and pressure," Journal of Materials Processing Technology, Vol. 41, 1994, pp 125-142. 7. Zou, S. and Jeswiet, J , "A Multi-point Temperature Sensor lbr Metal Rolling," Transa~vions of NAMR1/SME, Vol. XX, 1992, pp 19-23. 8. Hirao, M., "Determining "I~mperature Distribution on Flank Face of Cutting Tool," Journal of Material Shaping Technology, Vol. 6, No. 3, 1989, pp 143-148. 9. Doremus, E., Oudin, J., Bricout, J. P., and Ravalard, Y., "New device for upsetting tests of steels at high temperatures," Journal of Materials' Processing Technology, v 26 n 3 Jul 1991 p 257-266, 1991. 2.
Materials Processing Technology ELSEVIER
J. Mater. Process. Tcchnol. 45 (1994) 6 3 7 - 6 4 2
Evaluation of Temperature and Heat Transfer Conditions at the Metal Forming Interface W. Nshama, J. Jeswiet, P. H. Oosthuizen Queen's University, Kingston, Canada Abstract During the forming of metals, the contact resistance between the workpiece and the die can have an important influence upon the temperature distribution in the material being formed and on the quality of the end product. In order to predict the contact resistance, a technique is being developed which will enable accurate determination of the contact resistance. This technique involves direct temperature measurement at the die/billet interface during deformation and subsequent use of inverse heat transfer model to calculate the contact resistance. The preliminary results indicate that the method can provide a reliable means of predicting the contact resistance.
1
INTRODUCTION
The process of Metal forming is always accompanied by heat generation. This heat affects, among other parameters, lubrication conditions (lubricant viscosity, reaction rates, and breakdown of lubricants), material behaviour during deformation, and quality of finished product. Accurate determination of temperature during a metal tbrming process is important because it affects interface lubrication conditions and material behaviour during deformation. Variations in workpiece temperature across its thickness may cause inhomogeneous deformation leading to defects such as surface cracking or harmful residual stresses. Increase of temperature in the die lowers the allowable die stress. Fast transfer of heat from the billet to the surface layer of the die results in high thermal stresses. On the other hand, rapid chilling of the billet increases flow stress and high contact-stresses on the die. High temperature at the contact zone results in breakdown of lubrication film and in turn increases heat generated due to increase in friction. In forging, force and power requirements and product properties are influenced by workpiece temperatures. Therefore, due to the importance of temperature conditions in metal forming there is a need for a simple heat transfer model to simulate some metal working conditions when designing for a particular forming process. A number of attempts have been made to measure the temperature condition at the tool-
workpiece interface in bulk forming, however, accurate results have not been obtained. One reason for the lack of accurate temperature measurement is the complexity of the metal forming process. Heat is generated by both internal plastic deformation and interface frictional work. In both cases, a simple theoretical analysis cannot be made easily. Therefore, experimental work is always necessary for any meaningful analysis. On the other hand, temperature measurement in metal forming is difficult because of the harsh conditions which exist both in the bulk metal and at the interface. Toolworkpiece interface conditions are never constant. Moreover, the parameters at the interface are interrelated, for example temperature at the interface depends, among other conditions, on lubrication conditions and heat transfer conditions Lubrication affects both friction and heat transfer conditions. Both friction coefficient and lubricant layer at the interface are also difficult to determine. In most research work involving temperature at the interface, lubricant film thickness and friction coefficient are estima~.xP "3. For instance in an attempt to determine the temperature profile in the billet-lubricant-die zone in forging operations, Bo~r et aP': used upsetting experiments and Finite Element calculations In their experiments, different boundary conditions, volume, and height-to-diameter ratios were used in the assessment of the rate of heat transfer. The variation of temperature in the die and billet was experimentally recorded using thermocouples
0924-0136/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved.
SSD1 0924-0136(94)00253-3
638
mounted away from the die/workpiece interface and the results were compared with an analyticalnumerical analysis by Finite Element (FE) in which the lubricant thickness was chosen to be 0.1 mm with the value of conductivity of the lubricant chosen such that the best fit to experimental data was obtained. The lubricant thickness was arbitrarily chosen due to the impossibility of knowing the real thickness of the lubricant trapped between die and billet. The results show that there is almost no influence of the radiation effect but, instead, there is a greater influence of the conductivity of the lubricant. In a recent paper Pawelski et al 3 used the ring test to study friction conditions in hot metal forming. They used thermocouples to measure the temperature of workpiece. The results of the experiment, using unlubrica~l surfaces, shows that there is a rise in temperature in the centre of the specimen which they attribu~_A to the internal plastic work. In the analysis of the temperature of contact zone, they used the assumption of two semi-infinile bodies that come into contact. The justification given being the short duration of the contact time. In the study of the interface conditions in metal rolling Jeswiet and Zou 7 successfully developed a sensor which measured three rolling temperatures simultaneously: at the billet surface, the roll surface, and inside the roll. Measurement of temperature of the billet was done using the law of intermediate metals in thermometry. A similar technique was also used by Hirao 8 in the determination of temperature distribution on flank face of cutting tool. One other experimental technique lbr temperature measurement, Doremus, et al 9 used an infra-red sensor when studying upsetting tests of steels at high temperatures. The problem with the infra-red technique is its low sensitivity at low temperatures. Also the infra-red sensor cannot provide temperature at a specific point, plus the speed of response is too low. However, it's use is limi~l to regional, slowly changing temperature measurement. Semiatin et al. 5 developed a technique by which the heat transfer coefficient can be estima~l for non-isothermal bulk-forming process based on the measurement of the die temperature brought together under varying pressure. A one-dimensional analysis and a finite-difference model were used in the
evaluation of the heat transfer coefficients giving constant values of the heat transfer coefficient for the given initial conditions This technique was further developed by Butte et al 4 for use in hot forging process. In yet another search tbr the heat transfer coefficient, Malinowski et al. 6 used temperature measurement within two dies in contact and a finite element technique to determine the interracial heattransfer coefficient. They developed an empirical relationship giving the coefficient of heat transti~r as a function of time, temperature and interracial pressure. The difference between this work and others in this review is that the temperatures have been measured directly at billet surface and the die surface giving a temperature jump across the interface which gives the heat transfer coefficient by inverse heat transfer methods.
2
EXPERIMENTAL DESIGN
The present work provides a technique oi evaluating interface heat transfer coefficient during upsetting operations using temperature measured at the interface and area near the interface. For accurate analysis of temperature distribution at the tool-workpiece interface and the amount of heat generated during deformation, temperature measurement were made at different positions Two sets of temperature measurement were done. In the first case thermocouple wires were put in the die only, while in the second case hot billets were used with thermocouple wires both in the die and billet and as shown in Figure 2. In the second case, a low contact pressure was used in order to prevent the thermocouple wires from breaking. Three parameters were measured during the experiment: temperature, force, and displacement. The measurements were recorded by a computer via a high speed A/D board. The system also provided a mechanism to control strain rate during the experiment. 2.1 Experimental Apparatus In this experiment Aluminium (606t-O) .samples were used with a seventy ton hydraulic press. Reduction of up to 75 % were conducted. The press
639
was linked to the data acquisition to provide feedback control (Figure 1). The experiment setup is shown in Figure 2. Temperature measurement was done using eight Type J (Iron-Constantan) thermocouples installed in an insert in the lower die at various depths from the die surface and radial distances from the die centre (Figure 3). There are three sets of thermocouples in the die grouped according to their depth from the surface. The first group, which are normally open, measure billet temperature using it as a third metal. The second set of thermocouples which are located at surface of the die, measure the temperature of die surface. The third and forth set of thermocouples are located at depths of about 1 mm and 2 mm respectively. These measure the subsurface temperature of the die. In the case of the instrumented billet, three thermocouples are inserted along the axis of the billet as shown in Figure 2.
lower die. Inside the hole, the wires were bonded to the die, without electrical contact, using the same binding material. This provided sufficient strength and hardness required at high compressive forces at the die-billet interface. Details of the construction can be found in reference 7. To provide fast temperature response, 0.127 mm diameter wires were used. At the measuring point all thermocouple ends touch the substrate, except the wires measuring the billet surface--which are left open.
@ Legend: O, ~
,; ~LIbSLIFfQC~ thermocouples 12159 m m
5. 8 Subsurface thermoco~lples 1 168 m m 1. 6 - Die surface t h e r m o c o u p l e s 2. 4. 7 - Billet surfoce theH,3oc(,uples
Figure 3 Figure 1 Simplified block diagram tbr control system for the press
4
}~ll~t
(m254×254~m) -
~
} ]hermOCOb~ptes
D ~:-]i~er~c,c o u p t e s
Figure 2 setup
Schematic diagram of the experimental
The thermocouple wires were coated with a thin film Molochile (a mixture of A1203, M20, and SiO:) with sodium silicale as a binder. Each thermocouple wire was then placed in a separate hole inside the
deep/ deep
Thermocouple positions in the lower die
Calibration of the thermocouples was done by immersing the instrumented die in a temperature controlled water bath while recording the water temperature and thermocouple volt output. For the normally open thermocouple, an aluminium strip was clamped on die in order make a joint--similar to an actual upsetting operation. The results of converting the voltage reading to their corresponding temperatures (using standard tables) showed that all thermocouples gave readings within a degree centigrade of that of water bath. Thus, during upset tests the thermocouple voltage readings were converted to temperature measurement by using the standard formulas (a polynomial fit for Type J thermocouples). 2.2 Experimental Procedure Solid cylindrical billets of Aluminium (AI 6061-O) were compressed between tv~ opposite fiat dies. Initial size of the samples were 25.4 nun in diameter by 25.4 mm length. The top and bottom
640
dies were both made of tool steel (4140). Both dies have diameters of 125 mm and a height of 62.5 nun: In the first cold forming case a billet was compressed, at controlled strain rate, to various degrees of percentage deformation. The hydraulic ram velocity was at a constant velocity of about 1.375 mm/s. In the second case, hot instrumen~d billets were used instead. The dies were allowed to touch the billet with sufficient pressure to provide good thermo and electrical contacts without actually undergoing plastic deforming.
and the interior of the die with highest temperature values being that of billet surface. T h e results also show a temperature jump ber~e..en billet surface and die surface. Temperature decreases as the distance increases from the surface. For reasons explained earlier, there were no temperature measurements within the billet.
44 F--T--
ac~42
r..... ~
,
~
/i
-~ ....... r
¢!-
.
•
}!!
, .... i S:Ou
3
RESULTS AND DISCUSSION
i :
In the hot billet test, Figure 4, the temperature measurement shows equal temperature distribution inside the billet with respect to the billet centre indicating equal flow towards both dies. The results show that the heat goes through a temperature jump as it crosses the billet/die interlace. This indicates that there is a thermal resistance at the interface and that once the flux is determined from the internal billet therrnocouples, one can then use inverse heat transfer techniques to find the heat transfer coefficient. 225
--.-___._
200
. . . . . . . . . . . . . . . . . . .
~
T
-
4
-- 4
150
M-I
IO0 E 75
50
4 DETERMINING THE HEAT TRANSFER COEFFICIENT
ij 5/~
/3/
25
• 6 74
7 ___L_ 5
Figure 5 Temperature/Displacement V~ Tinle m cold upsetting test (Percentage reduction: 50%)
£
125 /
i *0
The results also show the temperature sensor to be a viable device for determining the interface temperatures.
2
175 •
/
10
lfl
20
2t~
30
35,
,~,0
Figure 4 Temperature/Displacement Vs Time using a hot billet (Percentage reduction: 0%) In the cold upsetting, Figure 5, the results show temperature variation bet,~e.en that of the interface
One of the main purposes of the present work is to determine the heat transfer coefficient from the temperature measurements. The heat transfer coefficient, h, or contact resistance coefficient is defined by: q ~ h(Th, i~) (0 where q is the rate of heat transfer per unit area across the interface between the billet and the die and T~ and T~ are the die and billet interface temperatures respectively. In general, h will depend on both the interfacial pressure and the mean interracial temperature. However, in order to
641
describe the procedure being used to find h, this variation will be ignored i.e. h will be treated as constant. It has been assumed that the heat conduction in both the die and the billet in the region where measurements are made is one-dimensional. Therefore, the temperature in the billet will be described by:
technique. The method basically involves calculating the temperature using an assumed value of h and then altering h to reduce the mean difference between the measured and calculated temperatures. The mean difference is summed over all points at which measurements are made and over all time steps at which measurements are made, i.e. the following error function is introduced: s
9b Co 0 t
: kb
+ q*
where the subscript b indicates billet properties, T is the temperature at any point in the billet at time t and q* is the internal heat generation. The internal heat generation arises from the work being done on the billet. In general, it will not be uniform in the billet. However, in order to illustrate the method of analysis it will be assumed to be uniform and to be derivable from the rate at which work is being done on the billet. Similarly, the temperature distribution in the die will be given by: ~-0T
_(cST )
At the interface:
k (OT]
: h ( T b _ Ta)
(rc-r,,) 2
(5)
where the subscripts C and M refer to the calcula~xl and measured values at corresponding points and corresponding times, From this it follows that:
dE dh
2 ~ ~ (T c
IM) dT':
(6)
dh
The summation is, as mentioned, carried out over all points and all times considered. The value of h that minimizes the error i.e. that gives:
dE dh
(3)
where the subscript d indicates die properties. There is no internal heat generation in the die because the deformation of the die is assumed to be negligible,
k (cOT]
=
(2)
0
(7)
is the "best" value that can be derived from the experimental data. From eq. (6) it then follows that if a value of h is selected and the temperature values given using this value are Tc then the value of the heat transfer coefficient that minimizes the error will differ from h by Ah where, by virtue of eq.(6),
(4) Z Z ( r c + drCAh - T , . ) drc -- : 0
dh
The above equations can be written in finite difference form and used to solve for the temperature-time variations in the die and billet for any assumed value of h. In carrying out this solution, the mesh in the billet must be amended at each time step to account for the deformation of the billet. In the present work, a simple implicit procedure has been used. In obtaining solutions, it has been assumed that the initial temperatures of both the die and billet are specified and that the temperature distribution is symmetrical about the billet centre-plane and that far from the interface the temperature of the die remains equal to the initial die temperature. Now, the value of h is not known. It is determined using an inverse heat conduction
(8)
From this it follows that: f. . . .
Ah=
dTc~
~-~"~- ~ (~': -: ~T M ) - ~ !
(9)
In order to find dTc/dh, the temperature variation in the die and billet is first calcula~d using the selected value of h. The values of the temperatures so calculated are denoted by Tco. A small increment to h, say ~Sh is then chosen, t$h typically being about 1% of h, and new values of Tc
642
are calculaled. At any point and any time, the following is then used:
ate._ dh
(Tc
Too) 8h
(lO)
Using this in eq.(9), Ah can be calculated. Because the above analysis assumes that Ah is small, an iterative procedure must be used. A value of h, say ho, is guessed and the above procedure is used to find Ah. With h set equal to Ah + ho the process is repeated and continued until the error E as defined in eq. (5) is reduced below a selected value. The accuracy of the procedure is strongly dependent on where the temperature measurements are made. In general, the closer that these measurements are made to the interface, the more accurate will be the derived value of h. In the present experimental procedure, the actual interracial temperatures for the die and billet are measured so very accurate values of h can be derived from the measurements.
5
CONCLUSIONS
Forging interface temperatures have been measured successfully in hot and cold hydraulic forging of 6061 Aluminium. These experimental results can be used to verify the model proposed in this paper.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of NSERC and DAAD.
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