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Glass to metal heat flow during glass container forming
Journal of Non-Crystalline Solids 38 & 39 (1980) 873-878 G North-Holland Publishing Company
GLASS TO METAL HEAT FLOW DURING GLASS CONTAINER FORMING N. T. Huff, D. M. Shetterly and L. C. Hibbits Owens-Illinois Technical Center P.O. Box 1035 Toledo, Ohio 43666 U.S.A.
A mathematical method of determining the glass to metal heat flux during an I.S. forming cycle is presented. The method utilizes a finite difference model to calculate heat flow within the forming implements which contact the glass. Experimental interior and exterior surface temperatures of these forming implements are used in the calculation of heat flux across the metal surfaces. The calculated heat flux across the glass-metal boundaries is presented for a typical blow and blow cycle on an I.S. machine. The effect upon heat flux of various functions such as settle blow, counter blow, etc., are clearly evident. INTRODUCTION The process of forming a glass container on an I.S. machine involves two simultaneous and interrelated tasks. One task is the shaping of the gob and the parison into the final bottle. The other is the removal of sufficient heat from the gob and parison so that the final blown bottle is rigid when it is removed from the blow mold. The main method by which an I.S. machine removes heat from the glass is by forcing the glass against the forming implements (e.g., molds, baffle, etc.) It is this glass to metal heat flow in the I.S. machine which we will be examining in this paper. There have been several previous experimental and theoretical studies of the rate at which heat is removed from glass in contact with metal. I-~ Naughton and McGraw 2 performed significant work in this area more than 20 years ago. They employed an experimental pressing machine whose cycle could easily be interrupted at specific times. Glass was removed from the machine at these times and its total heat content was determined by calorimetry. From this data they were able to determine the total amount of heat removed at several finite steps throughout the forming cycle. This then allowed them to estimate the rate at which heat was removed from the glass during the forming cycle. Kent, Fellowes and Shaw 3 and others at the British Glass Industry Research Association (BGIRA) also utilized an experimental pressing machine. In the BGIRA work special ribbon type surface thermocouples and a mathematical model were used to determine the rate at which heat is extracted from glass pressed against mold metal. The information they have generated is interesting and useful. However, the mathematical model they used solves the heat flow problem in only one dimension, and in addition, the entire mold is assumed to be at a constant temperature at the start of the experiments. Thus, while the data they obtain is useful in a general sense, their modeling techniques cannot be applied directly to a production glass making machine. Kent 4 has reported additional work in which the ribbon surface thermocouples were installed in the blank mold of a production blow and blow (B&B) container. He utilized this thermocouple data in a one-dimensional electrical analog simulation of the heat flow in the blank mold and determined the rate at which heat is
873
874
N.T.
H u f f et al.
/ Glass
to Metal
Heat F l o w
removed from the glass on a continuous basis throughout the forming cycle. As described in the accompanying paper 5 we also use ribbon type thermocouples to obtain the temperature of the metal surface in contact with the glass. This data is used in a three-dimensional mathematical model employed to calculate the transient heat flow in the various I.S. machine parts. By knowing the heat flow through the forming implements during the forming cycle, one can determine the rate at Q! which heat is removed from the glass by the machine parts on a virtually continuous basis throughout the forming cycle. The mathematical model is sufficiently general that it can be applied to the forming implements on production I.S. machines to determine the rate at which heat is being extracted from glass. Q4 Q2 THEORY Let us first consider a solid made up of a number of small six-sided elements (see Figure i). We shall call this element 0. FIGURE ] SOLID ELEMENT 0 The elements are chosen sufficiently small so that they may be assumed to be isothermal. The heat flowing across the i th face of element 0 is represented by Qi in Figure i. If there is a net heat flow into or out of element 0, its temperature will change as a function of its heat capacity. Within the limit of our approximation we write:
Q3
v At(QI + Q2 + Q3 + Q~ + Q5 + Q6) = Co(T0-T0)
(i)
where At = time interval rate of heat flow across i th face heat capacity of element 0 = CppV = (specific heat) (density) (volume) TO! = original temperature of element 0 TO = temperature of element 0 after At The heat flow across the i th face at a given instant of time can be expressed as: Qi = KiAi
(Ti-T0)
(2)
Ii where I i = distance between the center of element 0 and the center of the element i (element i is that element which has a face common with the ith face of element 0) K i = thermal conductivity of the material between the center of elements 0 and i A. = area of the i th face T~ = temperature of element i If the time increment is sufficiently small we may substitute equation 2 into equation i. This will then give us equation 3. 6 E i=l
K.A. 1 1 = CppV y. (Ti-T O) ~ (To-T O) 1
(31
Rearranging this equation allows the future temperature of each element to be expressed in terms of the thermal conductivity, density and specific heat of mold materials and the initial temperature of each element.
N.T.
H u f f et al.
/ Glass
to M e t a l H e a t
875
Flow
The thermal conductivity, density and specific heat data are well known. However, in order to know the initial temperature of each element, thermocouples would have to be placed within each element. Thus from a practical standpoint, it is impossible to obtain the initial temperature of each element. However, it can be shown 6 that if the elements and time step have the correct relationship, equation 3 can be solved iteratively and will converge to a unique solution. W e may simply guess at the initial temperature of each element and solve the problem in an iterative manner until, on successive iterations, the temperatures of all of the elements remain constant at a given time step. A reasonable initial guess of temperatures will, of course, allow the temperatures to converge more rapidly. This method of solving the equations is known as the forward finite difference method. ? Note that equations 2 and 3 implicitly assume that one is working only with interior elements since a thermal conductivity across each face is assumed. If, however, one is working with an element which is at the surface of the solid, the Ki/li term in equation 2 is replaced by a heat transfer coefficient across face i and a radiation term. If face 1 is assumed to be a surface face in contact with air, equation 2 becomes: Q1 = ham AI(Ta-T o) + R
(4)
where: ham = the air-metal heat transfer coefficient T a = the temperature of the air contacting the metal R = net radiation exchange between the air and metal Equation 3 then becomes: 6 KiAi hamAl(Ta-To ) + R + ~ i=2 i i
(Ti-T o) =
CppV
, (T O - TO)
(5)
&t
The air to metal and glass to metal heat transfer coefficients have only been qualitatively approximated. In addition, the temperature of the glass next to the forming implement can only be crudely approximated. Thus the heat flux across an air-metal or gla~s-metal interface cannot be calculated directly. However, if one knew T O and T O for a surface element, equations 1 and 2 could be used to solve for Q1 for one element. By using the surface thermocouples to determine T O and T~ for particular elements, the value of Q1 can be calculated for those elements. Equation 4 can then be used to calculate the air-metal (or glass-metal) heat transfer coefficient ham (or hgm) for the surface elements containing thermocouples. These heat transfer coefficients are then used in equation 5 for all surface elements in the vicinity of the individual thermocouples. By recalculating the values of the heat transfer coefficients at the end of each iteration of the finite difference procedure, one can accurately calculate the heat flux across all surfaces of the forming implements. RESULTS Some typical results obtained for an I.S. blow and blow process will now be discussed. Heat flux values have been calculated using the temperature data presented in the accompanying paper. 5 Figure 2 is a graph representing the heat flux across the glass contact surface of the blank mold below the load line. The initial and highest peak in the heat flux curve is at gob load. The narrowness of this spike can be attributed to two things. First, the surface temperature of the glass is rapidly dropping while the metal temperature is increasing. This reduces the temperature differential between glass and metal, resulting in a slower rate of heat transfer. Secondly, we believe that the cooling and contracting glass will pull away from the metal very slightly. This results in a less intimate contact between the glass and metal, reducing the glass to metal heat transfer coefficient. The second peak is the result of the application of settle blow.
The settle blow
876
N.T.
H u f f et al.
I'+s.+Z .L
4 I+ so""-
N 4o
g 20 N
0 -5
I I I I 4.0 80 120 160 DEGREES DRUM ROTATION FIGURE 2 HEAT FLUX BELOW LOAD LINE 0
/ Glass
to M e t a l H e a t F l o w
air presses the glass against the mold metal resulting in a more intimate glass to metal contact. This causes a sharp rise in the glass to metal heat transfer coefficient which more than offsets the effect of the lower glassmetal temperature differential. The result is that the glass to metal heat flow increases for a short time before once again decreasing. The third peak (at ~90 ° drum rotation) is the result of counter blow. Once again the increase arises from an increased heat transfer coefficient resulting from the glass being pressed against the metal by the counter blow air pressure. As the blank opens we see a large drop in the heat flux curve. The break in the curve (just before 160 ° drum rotation) is not sharp because the metal is still receiving energy by radiation from the parison. As the blank opens completely and the parison is inverted the heat flux at the mold boundary quickly becomes negative indicating the cooling due to radiation and conduction to the air.
Figure 3 is a graph representing the heat flux across the glass contact surface of the blank mold above the load line. The first small peak is the result of the gob passing by the thermocouple as it loads. This peak demonstrates the great sensitivity of the thermocouples and the model. The very high sharp peak at ~i00 ° drum rotation is the result of counter blow. Note that this peak is much higher than the initial load or settle blow peak for the glass below the load line. This is apparently the result of a very large heat transfer coefficient. We believe that the heat transfer coefficient below the load line is smaller because the glass initially contacting the metal has been chilled by the delivery equipment. A less intimate glass to metal contact is established by this glass than by the glass above the load line which either has reheated or come from the interior of the gob.
270
6(
4c
=: 2C
I I I 40 80 120 160 Figure 4 represents the heat flux curve for DEGREESDRUM ROTATION the baffle. The first small broad peak FIGURE 3 HEATFLUX ABOVELOADLINE occurs during settle blow. It is the result of radiation received by the baffle from the end of the gob as the baffle is seated in the funnel. The dip in the curve is the result of the baffle moving away while the funnel is being removed. When the baffle is seated on the blank (just before 90 ° drum rotation) the radiation again causes the heat flux curve to become positive. When the counter blow pushes the glass against the baffle a very high spike is observed. The valley in the curve appearing just after the baffle is removed from the blank is apparently the result of the rapid motion of the baffle through the air causing a large air-metal heat transfer coefficient.
The heat flux curve for the neck ring is presented in Figure 5. This curve is the most complex of the heat flux curves. The first two peaks are the result of load
N.T.
,65[
H u f f et al.
L
5O
~:e 40
3O ~
2C
:=
le
-10,
I I [ 1/~ 40 80 120 ]60 DEGREES DRUM ROTATION FIGURE 4 BAFFLE HEAT FLUX
/ Glass
to Metal
Heat
Flow
877
and settle blow. The valley and peak at about 65-70 ° drum rotation is the result of the plunger moving down. The peak at about 90 ° is the result of counter blow. Blank open starts before 160 ° while invert starts at about 170 ° • The structure between 170 ° and 240 ° is apparently the result of the glass moving slightly during invert. The last two spikes are apparently related to end of invert and neck ring open. The drop in heat flux to negative values occurs at neck ring open. The effect of neck ring closing at about 280 ° during revert is also apparent. Figure 6 shows the heat flux curve for the side of the blow mold. The radiation which the mold receives from the inverted parison is the cause of the positive value for the heat flux before 20 ° drum rotation. The large initial peak is, of course, the result of final blow pressing the glass out against the mold. Note that the initial peak is significantly lower than the initial peaks for the blank, baffle and neck ring. This is apparently the result of cool glass in the bottle sidewall which results in a lower glass to metal heat transfer coefficient.
Finally, Figure 7 shows the heat flux curve for 380the bottom plate. There .1. are significant differ90 ences between this curve and the blow mold curve. First, the initial rise in the heat flux curve 7C is much larger. This is probably the result of the glass in the bottom of the parison being hotter than the glass in ~ 5c the sidewall. It can also be noted that the ~ 4o peak starts about 5 ° sooner in the bottom plate than in the side~ 30 wall. This shows that the glass was blown 2O against the bottom plate before it contacted the sidewall. The second major difference between the bottom plate and the mold curves is found beyond 160 ° . There is -10 I 80 120 160 200 240 280 320 360 g" 40 an initial drop in the DEGREES DRUM ROTATION heat flux when the mold FIGURE 5 NECK RING HEAT FLUX opens even though the bottle is still sitting on the bottom plate. This implies that even a very small motion can break the intimate glass,metal contact required for a rapid removal of heat from the glass.
878
N.T.
H u f f et al.
/ Glass
to Metal
Heat Flow
255 50
50-
~
40-
30
40
=o -
~ 2C-
B := IC-
-5f,
0
40 80 120 160 DEGREES DRUM ROTATION FIGURE 6 MOLD HEAT FLUX
~-
30
~,
20
~
~O
.sJ
I
z'q
I I I I / [ 40 80 120 160 DEGREES DRUM ROTATION FIGURE 7 BOTTOM PLATE HEAT FLUX
As the bottle continues to sit on the bottom plate the heat flux gradually becomes positive. It again becomes negative as the bottle is taken off the bottom plate. In summary, we now have a very sensitive tool which can give us significant insights into the heat flow processes associated with the formation of a bottle in an I.S. machine. We are now able to quantitatively determine how variations in operating parameters affect both the rate of heat extraction from the glass and also the total amount of heat removed. We wish to thank Owens-Illinois, Inc. for permission to publish the procedures and data presented in this paper. REFERENCES
[1] [2] [3] [4] [5] [6]
[7]
McGraw, D. A. Transfer of heat in glass during forming, J. Am. Ceram. Soc., 44 (1961), 353-63. Naughton, T. J. and McGraw, D. A., Analysis of heat transfer in glasspressing operations, VI Int. Cong. Glass (1962). Fellowes, C. and Shaw, F., A laboratory investigation of glass to mold heat transfer during pressing, Glass Technol., 19 (1978), 4-9. Kent, R., Mould temperature and heat flux measurements and the control of heat transfer during the production of glass containers, IEEE Trans. IA-12 (1976) 432-439. Shetterly, D. M. and Huff, N. T., Mold surface temperatures during glass container forming, These Proceedings (1980). Karplus, W. J., An electric circuit theory approach to finite difference stability, Trans. AIEE 77 (1958). Dusinberre, G. M. Heat-transfer calculations by finite differences (Int. Textbook Co., Scranton, Pa., 1961).
GLASS TO METAL HEAT FLOW DURING GLASS CONTAINER FORMING N. T. Huff, D. M. Shetterly and L. C. Hibbits Owens-Illinois Technical Center P.O. Box 1035 Toledo, Ohio 43666 U.S.A.
A mathematical method of determining the glass to metal heat flux during an I.S. forming cycle is presented. The method utilizes a finite difference model to calculate heat flow within the forming implements which contact the glass. Experimental interior and exterior surface temperatures of these forming implements are used in the calculation of heat flux across the metal surfaces. The calculated heat flux across the glass-metal boundaries is presented for a typical blow and blow cycle on an I.S. machine. The effect upon heat flux of various functions such as settle blow, counter blow, etc., are clearly evident. INTRODUCTION The process of forming a glass container on an I.S. machine involves two simultaneous and interrelated tasks. One task is the shaping of the gob and the parison into the final bottle. The other is the removal of sufficient heat from the gob and parison so that the final blown bottle is rigid when it is removed from the blow mold. The main method by which an I.S. machine removes heat from the glass is by forcing the glass against the forming implements (e.g., molds, baffle, etc.) It is this glass to metal heat flow in the I.S. machine which we will be examining in this paper. There have been several previous experimental and theoretical studies of the rate at which heat is removed from glass in contact with metal. I-~ Naughton and McGraw 2 performed significant work in this area more than 20 years ago. They employed an experimental pressing machine whose cycle could easily be interrupted at specific times. Glass was removed from the machine at these times and its total heat content was determined by calorimetry. From this data they were able to determine the total amount of heat removed at several finite steps throughout the forming cycle. This then allowed them to estimate the rate at which heat was removed from the glass during the forming cycle. Kent, Fellowes and Shaw 3 and others at the British Glass Industry Research Association (BGIRA) also utilized an experimental pressing machine. In the BGIRA work special ribbon type surface thermocouples and a mathematical model were used to determine the rate at which heat is extracted from glass pressed against mold metal. The information they have generated is interesting and useful. However, the mathematical model they used solves the heat flow problem in only one dimension, and in addition, the entire mold is assumed to be at a constant temperature at the start of the experiments. Thus, while the data they obtain is useful in a general sense, their modeling techniques cannot be applied directly to a production glass making machine. Kent 4 has reported additional work in which the ribbon surface thermocouples were installed in the blank mold of a production blow and blow (B&B) container. He utilized this thermocouple data in a one-dimensional electrical analog simulation of the heat flow in the blank mold and determined the rate at which heat is
873
874
N.T.
H u f f et al.
/ Glass
to Metal
Heat F l o w
removed from the glass on a continuous basis throughout the forming cycle. As described in the accompanying paper 5 we also use ribbon type thermocouples to obtain the temperature of the metal surface in contact with the glass. This data is used in a three-dimensional mathematical model employed to calculate the transient heat flow in the various I.S. machine parts. By knowing the heat flow through the forming implements during the forming cycle, one can determine the rate at Q! which heat is removed from the glass by the machine parts on a virtually continuous basis throughout the forming cycle. The mathematical model is sufficiently general that it can be applied to the forming implements on production I.S. machines to determine the rate at which heat is being extracted from glass. Q4 Q2 THEORY Let us first consider a solid made up of a number of small six-sided elements (see Figure i). We shall call this element 0. FIGURE ] SOLID ELEMENT 0 The elements are chosen sufficiently small so that they may be assumed to be isothermal. The heat flowing across the i th face of element 0 is represented by Qi in Figure i. If there is a net heat flow into or out of element 0, its temperature will change as a function of its heat capacity. Within the limit of our approximation we write:
Q3
v At(QI + Q2 + Q3 + Q~ + Q5 + Q6) = Co(T0-T0)
(i)
where At = time interval rate of heat flow across i th face heat capacity of element 0 = CppV = (specific heat) (density) (volume) TO! = original temperature of element 0 TO = temperature of element 0 after At The heat flow across the i th face at a given instant of time can be expressed as: Qi = KiAi
(Ti-T0)
(2)
Ii where I i = distance between the center of element 0 and the center of the element i (element i is that element which has a face common with the ith face of element 0) K i = thermal conductivity of the material between the center of elements 0 and i A. = area of the i th face T~ = temperature of element i If the time increment is sufficiently small we may substitute equation 2 into equation i. This will then give us equation 3. 6 E i=l
K.A. 1 1 = CppV y. (Ti-T O) ~ (To-T O) 1
(31
Rearranging this equation allows the future temperature of each element to be expressed in terms of the thermal conductivity, density and specific heat of mold materials and the initial temperature of each element.
N.T.
H u f f et al.
/ Glass
to M e t a l H e a t
875
Flow
The thermal conductivity, density and specific heat data are well known. However, in order to know the initial temperature of each element, thermocouples would have to be placed within each element. Thus from a practical standpoint, it is impossible to obtain the initial temperature of each element. However, it can be shown 6 that if the elements and time step have the correct relationship, equation 3 can be solved iteratively and will converge to a unique solution. W e may simply guess at the initial temperature of each element and solve the problem in an iterative manner until, on successive iterations, the temperatures of all of the elements remain constant at a given time step. A reasonable initial guess of temperatures will, of course, allow the temperatures to converge more rapidly. This method of solving the equations is known as the forward finite difference method. ? Note that equations 2 and 3 implicitly assume that one is working only with interior elements since a thermal conductivity across each face is assumed. If, however, one is working with an element which is at the surface of the solid, the Ki/li term in equation 2 is replaced by a heat transfer coefficient across face i and a radiation term. If face 1 is assumed to be a surface face in contact with air, equation 2 becomes: Q1 = ham AI(Ta-T o) + R
(4)
where: ham = the air-metal heat transfer coefficient T a = the temperature of the air contacting the metal R = net radiation exchange between the air and metal Equation 3 then becomes: 6 KiAi hamAl(Ta-To ) + R + ~ i=2 i i
(Ti-T o) =
CppV
, (T O - TO)
(5)
&t
The air to metal and glass to metal heat transfer coefficients have only been qualitatively approximated. In addition, the temperature of the glass next to the forming implement can only be crudely approximated. Thus the heat flux across an air-metal or gla~s-metal interface cannot be calculated directly. However, if one knew T O and T O for a surface element, equations 1 and 2 could be used to solve for Q1 for one element. By using the surface thermocouples to determine T O and T~ for particular elements, the value of Q1 can be calculated for those elements. Equation 4 can then be used to calculate the air-metal (or glass-metal) heat transfer coefficient ham (or hgm) for the surface elements containing thermocouples. These heat transfer coefficients are then used in equation 5 for all surface elements in the vicinity of the individual thermocouples. By recalculating the values of the heat transfer coefficients at the end of each iteration of the finite difference procedure, one can accurately calculate the heat flux across all surfaces of the forming implements. RESULTS Some typical results obtained for an I.S. blow and blow process will now be discussed. Heat flux values have been calculated using the temperature data presented in the accompanying paper. 5 Figure 2 is a graph representing the heat flux across the glass contact surface of the blank mold below the load line. The initial and highest peak in the heat flux curve is at gob load. The narrowness of this spike can be attributed to two things. First, the surface temperature of the glass is rapidly dropping while the metal temperature is increasing. This reduces the temperature differential between glass and metal, resulting in a slower rate of heat transfer. Secondly, we believe that the cooling and contracting glass will pull away from the metal very slightly. This results in a less intimate contact between the glass and metal, reducing the glass to metal heat transfer coefficient. The second peak is the result of the application of settle blow.
The settle blow
876
N.T.
H u f f et al.
I'+s.+Z .L
4 I+ so""-
N 4o
g 20 N
0 -5
I I I I 4.0 80 120 160 DEGREES DRUM ROTATION FIGURE 2 HEAT FLUX BELOW LOAD LINE 0
/ Glass
to M e t a l H e a t F l o w
air presses the glass against the mold metal resulting in a more intimate glass to metal contact. This causes a sharp rise in the glass to metal heat transfer coefficient which more than offsets the effect of the lower glassmetal temperature differential. The result is that the glass to metal heat flow increases for a short time before once again decreasing. The third peak (at ~90 ° drum rotation) is the result of counter blow. Once again the increase arises from an increased heat transfer coefficient resulting from the glass being pressed against the metal by the counter blow air pressure. As the blank opens we see a large drop in the heat flux curve. The break in the curve (just before 160 ° drum rotation) is not sharp because the metal is still receiving energy by radiation from the parison. As the blank opens completely and the parison is inverted the heat flux at the mold boundary quickly becomes negative indicating the cooling due to radiation and conduction to the air.
Figure 3 is a graph representing the heat flux across the glass contact surface of the blank mold above the load line. The first small peak is the result of the gob passing by the thermocouple as it loads. This peak demonstrates the great sensitivity of the thermocouples and the model. The very high sharp peak at ~i00 ° drum rotation is the result of counter blow. Note that this peak is much higher than the initial load or settle blow peak for the glass below the load line. This is apparently the result of a very large heat transfer coefficient. We believe that the heat transfer coefficient below the load line is smaller because the glass initially contacting the metal has been chilled by the delivery equipment. A less intimate glass to metal contact is established by this glass than by the glass above the load line which either has reheated or come from the interior of the gob.
270
6(
4c
=: 2C
I I I 40 80 120 160 Figure 4 represents the heat flux curve for DEGREESDRUM ROTATION the baffle. The first small broad peak FIGURE 3 HEATFLUX ABOVELOADLINE occurs during settle blow. It is the result of radiation received by the baffle from the end of the gob as the baffle is seated in the funnel. The dip in the curve is the result of the baffle moving away while the funnel is being removed. When the baffle is seated on the blank (just before 90 ° drum rotation) the radiation again causes the heat flux curve to become positive. When the counter blow pushes the glass against the baffle a very high spike is observed. The valley in the curve appearing just after the baffle is removed from the blank is apparently the result of the rapid motion of the baffle through the air causing a large air-metal heat transfer coefficient.
The heat flux curve for the neck ring is presented in Figure 5. This curve is the most complex of the heat flux curves. The first two peaks are the result of load
N.T.
,65[
H u f f et al.
L
5O
~:e 40
3O ~
2C
:=
le
-10,
I I [ 1/~ 40 80 120 ]60 DEGREES DRUM ROTATION FIGURE 4 BAFFLE HEAT FLUX
/ Glass
to Metal
Heat
Flow
877
and settle blow. The valley and peak at about 65-70 ° drum rotation is the result of the plunger moving down. The peak at about 90 ° is the result of counter blow. Blank open starts before 160 ° while invert starts at about 170 ° • The structure between 170 ° and 240 ° is apparently the result of the glass moving slightly during invert. The last two spikes are apparently related to end of invert and neck ring open. The drop in heat flux to negative values occurs at neck ring open. The effect of neck ring closing at about 280 ° during revert is also apparent. Figure 6 shows the heat flux curve for the side of the blow mold. The radiation which the mold receives from the inverted parison is the cause of the positive value for the heat flux before 20 ° drum rotation. The large initial peak is, of course, the result of final blow pressing the glass out against the mold. Note that the initial peak is significantly lower than the initial peaks for the blank, baffle and neck ring. This is apparently the result of cool glass in the bottle sidewall which results in a lower glass to metal heat transfer coefficient.
Finally, Figure 7 shows the heat flux curve for 380the bottom plate. There .1. are significant differ90 ences between this curve and the blow mold curve. First, the initial rise in the heat flux curve 7C is much larger. This is probably the result of the glass in the bottom of the parison being hotter than the glass in ~ 5c the sidewall. It can also be noted that the ~ 4o peak starts about 5 ° sooner in the bottom plate than in the side~ 30 wall. This shows that the glass was blown 2O against the bottom plate before it contacted the sidewall. The second major difference between the bottom plate and the mold curves is found beyond 160 ° . There is -10 I 80 120 160 200 240 280 320 360 g" 40 an initial drop in the DEGREES DRUM ROTATION heat flux when the mold FIGURE 5 NECK RING HEAT FLUX opens even though the bottle is still sitting on the bottom plate. This implies that even a very small motion can break the intimate glass,metal contact required for a rapid removal of heat from the glass.
878
N.T.
H u f f et al.
/ Glass
to Metal
Heat Flow
255 50
50-
~
40-
30
40
=o -
~ 2C-
B := IC-
-5f,
0
40 80 120 160 DEGREES DRUM ROTATION FIGURE 6 MOLD HEAT FLUX
~-
30
~,
20
~
~O
.sJ
I
z'q
I I I I / [ 40 80 120 160 DEGREES DRUM ROTATION FIGURE 7 BOTTOM PLATE HEAT FLUX
As the bottle continues to sit on the bottom plate the heat flux gradually becomes positive. It again becomes negative as the bottle is taken off the bottom plate. In summary, we now have a very sensitive tool which can give us significant insights into the heat flow processes associated with the formation of a bottle in an I.S. machine. We are now able to quantitatively determine how variations in operating parameters affect both the rate of heat extraction from the glass and also the total amount of heat removed. We wish to thank Owens-Illinois, Inc. for permission to publish the procedures and data presented in this paper. REFERENCES
[1] [2] [3] [4] [5] [6]
[7]
McGraw, D. A. Transfer of heat in glass during forming, J. Am. Ceram. Soc., 44 (1961), 353-63. Naughton, T. J. and McGraw, D. A., Analysis of heat transfer in glasspressing operations, VI Int. Cong. Glass (1962). Fellowes, C. and Shaw, F., A laboratory investigation of glass to mold heat transfer during pressing, Glass Technol., 19 (1978), 4-9. Kent, R., Mould temperature and heat flux measurements and the control of heat transfer during the production of glass containers, IEEE Trans. IA-12 (1976) 432-439. Shetterly, D. M. and Huff, N. T., Mold surface temperatures during glass container forming, These Proceedings (1980). Karplus, W. J., An electric circuit theory approach to finite difference stability, Trans. AIEE 77 (1958). Dusinberre, G. M. Heat-transfer calculations by finite differences (Int. Textbook Co., Scranton, Pa., 1961).