Analysis and Optimization of Compression Glass Molds: Tumbler
A Thesis Presented to
The Faculty of the
Fritz J. and Dolores H. Russ College of Engineering and Technology
Ohio University
In Partial Fulfillment
of the Requirement for the Degree
Master of Science
by
Edgardo E. Amable
March, 1997 ACKNOWLEDGMENTS
Thanks to Dr. Bhavin Mehta, my advisor, for his constant encouragement, advice, and recommendation in performing not only this project but also my academic life.
Thanks to Dr. M.K. Alam, Professor of Mechanical Engineering for his effort in being part of the committee.
'41~0I want to thank Dr. James Fales, chairman of the Department of Industrial
'Technology for his support, helpful encouragement and for all that I learned as a member of the Center for Automatic Identification.
I want to dedicate this project to my parents and brothers in gratitude for their constant support during my academic life. Finally, I want to thank Anamaria for her understanding and caring, and for showing me that love is something that goes beyond the simple physical contact.
Gracias! TABLE OF CONTENTS
1. INTRODUCTION AND STATEMENT OF THE PROBLEM ...... 1
1.1. General introduction ...... 1
1.2. Objective ...... 2
1.3. Glass ...... 2
1.3.1. What is glass ...... 2
1.3.2. Flow at high temperatures ...... 4
1.3.3. Glass manufacturing ...... 7
1.3.4. General glass manufacturing methods ...... 9
1.3.5. Compression glass molding ...... 9
1.3.5.1 . What is compression glass molding ...... 9
1.4. Statement of the problem ...... 15
2 . BACKGROUND ...... 16
2.1 . Factors affecting mold design ...... 16
2.2. Thermal stresses on compression glass molds ...... 21
2.3. Previous studies for establishing optimal mold design ...... 25
2.4. The finite element method ...... 34
3 . METHODOLOGY ...... 46
3.1. Description of the tumbler 176 ...... 48
3.1.1. Soda-lime glasses ...... 48 3.2. 3-D solid modeling ...... 49
3.2.1. Geometric modeling technique ...... 49
3.2.2. 3-D solid modeling of the tumbler- 176 molding equipment ...... 50
3.3 . Thermal stress analysis of the mold bottom and the plunger
using Finite Element Method ...... 53
3.3.1. Application of the Finite Element Method ...... 53
3.3.2. Preprocessing ...... 54
3.3.3. The boundary conditions ...... 56
3.3.4. Analysis runs. postprocessing. and optimization ...... 57
4 . ANALYSIS OF RESULTS ...... 58
4.1. Mold insert ...... 58
4.2. Plunger ...... 60
5 . CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH .. 65
5.1 Conclusions ...... 65
5.1.1. Application of computer techniques to improve mold design ..... 65
5.1.2. System implementation feasibility ...... 65
5.2. Recommendations for further research ...... 67
5.2.1. Finite Element Analysis of the assembly model ...... 67
5.2.2. Possibility of research on the glass forming process ...... 67
5.2.2.1. Viscoplastic behavior ...... 67 5.2.2.2. Flow stress ...... 68
5.2.2.3. General method of analysis ...... 69
5.2.2.4. ANTARES ...... 72
REFERENCES ...... 78
APPENDIX A: GLASS MANUFACTURING TECHNIQUES ...... 80
APPENDIX B: ANTARES 4.0 INPUT FOR COMPRESSION MOLDING ...... 87 LIST OF TABLES
Table 2.1 . Manufacturing tolerances and glass design for pressed glassware ...... 20
Table 3- 1. Characteristics of the tumbler- 176 ...... 47
Table 4.1 . Thermal structural stresses for various shapes analyzed ...... 61 LIST OF FIGURES
Figure 1.1 . Relationship between the viscosity and temperature of glass ...... 6
Figure 1.2 . Flow diagram of a typical glass plant ...... 8
Figure 1.3 . Pressed glass-mold types and pressing operations ...... 10
Figure 1.4 . Examples of pressed glassware ...... 11
Figure 1.5 . Straight mold pressing process ...... 14
Figure 2.1 . Linear element under thermal stresses ...... 24
Figure 2.2 . Standard molds and new design ...... 26
Figure 2.3 . Temperature distributions at the outside wall along the height ...... 27
Figure 2.4 . Nature of variation of heat flow and temperature depending on time ...... 32
Figure 2.5 . Finite elements ...... 35
Figure 2.6 . Distribution of displacement u, temperature T, or fluid head ...... 37
Figure 2.7 . One-dimensional problems ...... 40
Figure 2.8 . Boundary conditions or constraints . Body with constraints ...... 44
Figure 2.9 . Examples of boundary conditions. Beam with boundary conditions ...... 44
Figure 3. 1 . Tumbler- 176 molding equipment. Assembly drawing ...... 47
Figure 3.2 . 3D solid modeling of the plunger ...... 51
Figure 3.3 . 3D solid modeling of the mold insert ...... 52
F igure 3.4 . Tetrahedral elements ...... 55 Figure 4.1 . Thermal structural stress distribution on the mold Insert ...... 59
Figure 4.2 . Thermal structural stress distribution for various plunger shapes analyzed 74
Figure 4-3.Thermal structural stress distribution for an original model of a plunger .. 63
Figure 4.4 . Thermal structural stress distribution for an optimized model of a plunger 64
Figure 5.1 . Design for manufacturing of compression glass molds ...... 66
Figure 5.2 . Forming of a Gudgeon pin ...... 70
FIgure 5.3 . Predicted grid distorsion during Gudgeon pin forming ...... 71
Figure 5.4 . Simulation of the deformation and meshing steps for the molten glass ..... 74
Figure 5.5 . Flow stress contours of the molten glass during compression ...... 75
Figure A.1 . Hartford I.S. narrow neck blow and blow process ...... 82
Figure A.2 . Pressed glass ...... 83
Figure A.3 . Ring roll casting machine ...... 84
Figure A.4 . 200-inch Telescope disk cast in 1934 ...... 86 1. INTRODUCTION AND STATEMENT OF THE
PROBLEM
1.1. General Introduction
Anchor Hocking Glass Company, Lancaster, Ohio, is a division of Anchor Glass
Inc., a major glass manufacturer in the United States. In the past decades the company has been developing mold design and manufacturing techniques by applying empirical methods. Studies in the field of glass molds and their effects on the final product have been done by several researchers in the past, based on field experiments with prototypes.
Some of these previous studies established the need of computer applications as tools of analysis and comparison on the effect, that changes in mold design would make to temperatures and heat flow patterns , as Genzelev et al. (1989) cited.
The situation faced by Anchor Hocking, represents an opportunity for students and faculty to explore the possibility of research in the area of glass mold design and manufacturing. As an initial step in the research, several students took a particular product
(e.g., tumbler, baking plate, dish, etc.) and applied CADICAM techniques to compare procedures and results. This study focused on mold design and optimization for a glass tumbler. 1.2. Objective
This study proposes the application of computer aided design, manufacturing, and engineering methods to obtain optimized and thermally balanced glass molds for Anchor
Hocking Glass Company. The study as developed was not an exhaustive design for a general mold manufacturing system, rather it was limited to axissymetrical models
The main idea of this research was to analyze thermal structural stresses and optimize the mold design, using the existing design drawings of the mold and plunger
(provided by Anchor Hocking) for a glass tumbler and constructing the parametric solid models on the CAD system.
Part of this study introduces a preliminary investigation on the flow of molten glass during forming.
1.3. Glass
1.3.1. What is Glass
Glass is obtained by mixing inorganic materials and melting them together at a high temperature. The resultant molten mix becomes a rigid material without crystallizing.
Its atoms never arrange themselves into an orderly crystalline pattern. Glass is always in this non-crystalline state, no matter how hard and rigid it becomes when cool. Silica sand is the major constituent of almost all common, commercial glasses. According to Jones (1956) the term "glass" has a precise scientific meaning. Glass or a substance in the glassy or vitreous state, is formed by cooling fiom the liquid state. It does not show discontinuous change (such as crystallization or separation into more than one phase) at any temperature, but has become reasonably rigid through a progressive increase in its viscosity. It is a true super-cooled liquid. Even though it appears hard and solid at room temperature, it has the properties of a highly viscous liquid that flow if a load is applied to it. On heating, it becomes more fluid, finally becoming fkee-flowing.
A common definition for glass also refers to a material of great practical use, with a number of unique properties such as transparency, brittleness, and the property of softening progressively and continuously when heated.
Phillips(l960) lists the usual raw materials for the mixture or batch:
Sand(Si02),usually.
Soda(Na20) and lime(CaO), usually.
Potash(K20), lead Oxide(PbO), Boric 0xide(B203),etc.
Excess from a previous melt(cul1et).
Oxidizing or reducing agents
Decolorizing agents.
Coloring, opacifying, or nucleating agents.
Recycled glass.
The main effects of the principal oxide components in glasses are as follows: Silica is the major acidic oxide and combines with the basic components.
Large proportions of silica increase the melting and softening point of glasses
and lower the thermal expansion.
Boric oxide can replace silica to some extent in glasses. It has the advantage of
lowering the melting point, so that by a suitable combination of silica and
boric oxide, a glass of low expansion, but with reasonable working
temperature can be manufactured.
Alumina reduces the melting point, prevents crystallization when cooling and
reduces the solubility of glass in water and other chemicals.
Sodium and Potassium oxide are the principal fluxes in glasses and with silica
form a low melting point liquid. Such glasses have a high thermal expansion.
Lime helps in reducing thermal expansion when it replaces sodium. Magnesia
is used as a replacement for lime but the liquids that it produces are more
viscous, although it crystallizes less readily.
Baria behaves rather like magnesia, but also gives a high brightness to glass.
Lead oxide behaves similarly.
An important fact of glass manufacturing is that the ingredients should be free from iron contamination which causes discoloration of the product.
1.3.2. Flow at High Temperatures
The viscosity and flow properties of glass at high temperatures are very important,
as stated by Grimshaw(l971). A glassy material can flow at low temperatures with the application of a large pressure maintained during a long period of time until any significant deformation occurs. At high temperatures the flow becomes progressively easier with less force involved. The ratio between the applied force and the resultant deformation is related to viscosity. The viscosity decreases as the temperature is increased.
Regarding the relationship between viscosity and temperature of glass, some important areas can be defined (see Figure 1-1):
Rigid Glass: where viscosity is above 1014poises and flow is not significant.
Annealing range: between 1012.j and 1013.4poises, at this point internal stresses
can be relieved and some degree of atomic movement is possible.
Working Range: between lo4 and poises, the glass can be handled and
can be blown or rolled without being too fluid. The upper limit of the working
range is called the softening point.
The Melting range: between 10'' and loz5 poises, is the range of viscosity
over which the glass flows readily and corresponds to its condition in the
melting tank. lI!
II'
li!
i
r:
lil
Figure 1-1. Relationship between the viscosity and temperature of glass.
The temperatures over which these ranges occur differ depending on the composition of the glass. For example alkali glasses are more viscous at a particular temperature than those containing lime and magnesia and, in general, alkali glasses have a shorter working range. 1.3.3. Glass Manufacturing
Figure 1-2 shows the general steps in glass manufacturing according to Phillips
(1960). The operations involved in all forming methods depend upon the peculiar characteristics of glass as a material. Glassmaking requires unique manufacturing techniques because the material must be worked while it is in a red hot liquid at temperatures ranging usually from 1200 to 2500 OF, depending on the method and composition. This very hot, syrupy liquid must be transferred from a pot or melting tank into a mold so that the forming operation be completed. This is not a simple task itself because glass cools rapidly by radiation and by contact with cooler air or metal. In few seconds this cooling increases the viscosity so much that the glass becomes a solid. All primary forming operations must be completed in this critical short period of time. Figure :I-2.Flow diagram of a typical glass plant. (Tooley) 1.3.4. General Glass Manufacturing Methods
Grimshaw(l960) describes five general methods of fabricating glass:
Compression
Blowing
Rolling
Drawing
Casting
1.3.5. Compression Glass Molding
1.3.5.1 What is Compression Glass Molding
Three main mold components are required for compression glass molding: a mold bottom, a plunger, and a ring. Automatic presses generally use multiple molds that are carried on a rotating table machine. There may be 6, 8, 10, 12 or 16 stations. Table diameters vary from 56 to 89 inches, and the sizes and weights of the machines depend on the dimensions of the final product demand.
There are three main types of compression molds:
One-piece "block" type: (see Figure 1.3.a) if no undercut exists in the article.
Two-piece or split-type (see Figure 1-3.b), more than two pieces.
font-type for solid pieces (Figure 1-3.c).
Different glassware shapes require the use of different mold types as shown in
Figure 1-4. Figure 1-3. Pressed glass-mold types and pressing operations. (a) Block mold.
(b) Split mold. (c) Font mold. ( Shand) Figure 1-4. Examples of pressed glassware. (a) Block mold glassware. (b)Split mold
glassware. (c)Font mold glassware. (Corning Glass Works) The molded glassware may be removed from the mold in several ways:
Manually.
Blowing out by a jet of air from the side.
Automatic tongs synchronized with the machine.
Vacuum lifting.
Turning the mold over or at an angle to tip out the piece.
For example, a two-piece split mold can open to let tongs into place, or a one- piece "block" mold will usually have a "push-up" valve to raise the glass article enough to allow the tongs to grasp the molded part.
Figure 1.5 illustrates a typical cycle for a 10-mold press. The gob feeder and the table movements are synchronized and indexed automatically. A takeout device removes the glassware and places it on a conveyor for transfer to the annealing lehr. The cycle would be as follows:
A gob of molten glass is placed in a mold at station 1.
At station 2 it is pressed. One plunger and one ring serve for all the press
molds. The speed of the operation is controlled largely by the time required
under pressure between the plunger and the mold to set up the glass and allow
it to hold its final shape.
At stations 3,4, and 5 a wind blast cools the glassware, holds it out to the mold
and sets it up properly for delivery. At stations 6 or 7 the glassware is removed; and at stations 8,9, and 10 the
molds are recovering to an equilibrium temperature.
This type of equipment is used to make glasses, bowls, ovenware, hse plug bodies, tubes, and several other items. VOU> DEZllGNfi ARE MAtY AHU VAltI@U ONE TABLE, BfBE%:^hi$hNOUPON COMPLEXfTY Of WARE. ROTATES, STOPS EACH STAT~ON. QTS1TE: OFT%% PRESSED ARTlCLES BcRZ 1 PISCE DtWK, OR Z PIE&;&OREX K.ATLR FTRG POLISHED TC) IMPROVE BE^ b~lll~TYPE ~THEQTTOM, 9:rRFACX: OR 'TO REMOVE MOLD MARK5 t PLUNGER &YE3 1 RlNG FOR ALL HEAQ.5, AND SEAMS. b.8, $8,la?, s~k-rrorrs,AND MAT us& 13T1m PourreCVCLW-@&dGQW ART~CLEJ ONLY AtTEWATk ONES FOR LARGE BARE. rafUTOFT bS SilZF3 AND WEtGHTS QF MALHIHES VAXY 6663 IN MDLU t. 5 '@bBELf, TABLES 96-89 INCW D1m. r.2 - rcfTgs-LggBy-Eazns PRESS DOWN 4.a MUTOR OR h9R DRIVEN. SMALL. 1,8 AIR OR CAM ktTtW, htEDIWM 45-50 PRESS 'UP PkS$tMt MECtJMEM DEPENDS WON X.ARCF 447-44 LEAVE ATR STATtWN WEIGHT AND YRESVRE REQUIRED. FIRST 12,ff MAKKS WARE FFfPCIM I @I., r'0 MlUvlY POUWI)S. S ECOHD iLf, &I NDKWAL SPEED RANGE 88 TO bD PEA ME'KTE. AT Z TIIEtD 24.0 CWZPXG'I: Tf&EC)UT 6.6,O YOR %R,Q E2I.CINCER
RsMG SEATS E%fIF&kE PLIMGEW IS
OB SETTLING DO
TYPIC& 10 STATXQR CYCLE MOLD 7.MoU,-- COOLMG -: *I. *I. s" " . \\ Irf LOX Pm55URE GOB ".i.DELXVERY+~) *pr I t , ..i \,A=,
B, ,9. , k--- 1"
P 9 LmBLhSTOR MACHME MmSTABLE WIND CBOLmG AlrlD CYCLES VARY TO t SUIT WWP: vmm'm e-.-. 02- 20s.
Figure 1-5. Straight mold compression process. (Tooley) 1.4. Statement of the Problem
During compression glass molding process, the plunger comes in contact with the molten glass as it compresses the molten glass in the mold. In addition to normal wear and tear, the plunger is subjected to heavy thermal stresses due to high temperature. High temperature levels reduce the life of the plunger and add expenses, as the plunger has to be changed. Uneven temperature distribution and concentration of thermal stresses cause cracks in the mold and consequently, its dismissal. The correction of distortion or the scrapping of defective components are widespread and may be costly in terms of time and money. Methods traditionally used to control these undesirable effects have been empirical in the past. Recent attention has been given to the control of thermal stresses and strains in mold design by means of computer analysis. Since the current design and manufacturing system does not take advantage of existing CADICAM technology, the distortion and fracture of component parts subjected to heat transfer loads may increase the costs of operations that may involve high cooling rates and defective parts. With the support of a well implemented mechanical computer aided design and engineering service,
Anchor Hocking should expect to improve glass manufacturing operation and performance while reducing the expense and time required for manufacturing and exchanging defective molds or using protoype models. 2. BACKGROUND
2.1. Factors Affecting Mold Design
A mold-insert, a plunger, and a ring are the only elements contacting the glass during its shaping. They are the shaping tools as well as the heat exchangers. Optimal characteristics of molds and mold metals involve in most cases an economic compromise that must be reached. Mold design factors include:
Low over-all cost per glass unit produced.
Easy to cast to a dense, homogeneous structure capable of taking and holding a
high surface finish.
Easy to obtain a high dimensional tolerance.
Ability to hold shape, and not warp.
Sufficient strength, hardness.
Low thermal expansion, and high resistance to heat checking.
High thermal conductivity.
Resistance to scaling and oxide formation, and its adherence to the metal.
All like molds are finished precisely and identically to assure interchangeability of
parts. Even so, the molds gradually change size as they are repeatedly cleaned to remove
accumulated oxides. They expand and contract during each press cycle at a rate different from the molded glass. Factories typically have mold repair shops where repair is a specialty using welding and pegging to provide metal to re-form to proper contours. This repair may gradually alter the basic mold shape so that an old mold may be noticeably different from a new one.
Hot molds have a temperature range of operation with the exterior surface running steady or at most a very slight cyclical variation. The interior surface which contacts the glass must run hot enough to avoid the "chill" appearance characteristic of hot glass contacting too cold a metal. It must also be hot enough to avoid such sudden glass cooling as it would "check" the glass. On the other hand, when the mold interior surface gets too hot, the glass will stick, producing a defective glass part. The interior temperature of the mold ranges from 1000 OF up to 1300 OF. The inner wall of the mold may have temperature ranges higher than this. The total effect is a cyclical one for each piece of glassware produced, with the maximum to minimum being functions of various factors, such as:
Size of the glassware.
Mold design and weight.
Type of operation and machne.
Speed of the process.
Glass temperature, etc.
Cyclical spreads of several hundred degrees are responsible for heat checking of the interior mold surface. Mold design involves the fitting of the mold to the machine according to the machine demands, the outside design, shape, and contour for proper cooling application depends on the particular machine; the selection of proper metal thickness, and metal inserts, or other devices to adjust mold temperatures to desired operational features, and the selection of the proper mold shape to make the glassware.
Material thicknesses of a mold vary depending on the machine and process. Very light-weight, thin molds run hotter than massive molds, but they rapidly increase up in temperature on initial glass contact, with the whole mass of mold metal giving greater cyclical variation. On the other hand very heavy molds never reach satisfactory operating temperatures because there is not enough heat fiom the glass to overcome the mass of the metal.
Moderate weight and proper design provide a balance between excessive
"flashing" and the mass effect. The resulting mold is not cold enough when the glass hits it to check the glass by sudden glass shock. Besides, it does not heat up suddenly to give sticking at the removal of the glassware.
Cyclical variations of interior temperature are expected. The temperature of the inner mold wall may be expected to be reasonably stable without cyclical variations. This condition also exists on the exterior of the mold surface, if a cooling wind is applied constantly.
For mold temperature control, the solution for a determined area to run hot enough is to reduce the mold mass by removing metal fiom the exterior section behind this area. It is not easy to do the opposite, by adding material. Thus, one can account for the widespread practice of designing molds with excess metal. This allows either an adjustment by removing metal, or an increase of speed of operation, using a higher glass weight to metal weight ratio. Another correction would be to use higher temperatures of the molten glass load. For example small glassware requires higher glass temperatures.
Ilue to physical limitations, the ratio of mold mass to glass mass cannot be held for large sizes of glassware. Smaller glassware requires hotter molten glass to help offset these mass temperature effects.
Another method to control mold temperature is to use a mold insert. The use of an insert makes a definite area run at higher temperature. The interface barrier of the insert and mold retards the heat flow. The usual practice is to use an insert of a different metal to modify the thermal conductivity, metal hardness, or finish, as well as for temperature control.
The side walls of a block mold and plunger must be tapered to permit withdrawal of the glassware after compressing. Table 2-1 shows the design proportions, sizes, weights and tolerances for a proper press molding. Table2-1. Manufacturing tolerances and glass design for pressed glassware. (Shand) 2.2. Thermal Stresses on Compression Glass Molds
The interactions among molding elements complicate mold design with respect to distributing the glass uniformly to all parts of the mold. Because the gob of molten glass is first placed in the center of the mold bottom, this area will be hotter than the side walls.
The plunger walls also may be at different temperature levels. Other factors such as external bottom cooling, and internal cooling of the plunger hrther complicate optimal mold design.
Boresi and Chong (1987) stated that the classical study of thermoelasticity is concerned with the distribution of stress(strain) in:
A solid subjected to a non linear temperature distribution T(x,y,z) in the xyz
system of coordinates, and
A solid that is physically or geometrically constrained and then subjected to a
temperature change, either uniform or non uniform.
The equations for the distribution of strain in an elastic medium containing temperature gradients were formulated initially in 1837 by Duharnel. In 1885, Neumann presented the theory of thermal stress. The classical Duhamel-Neumann theory of thermal stress states that the heat conduction process in a solid is not affected by the state of elastic strain. This is true if the conditions of the problem exhibit mechanical and thermal equilibrium, this is, steady state. The elastic and thermal equations defined under the
Duhamel-Neumann model are based on steady-state conditions. For time-dependent thermal problems the model is not applicable. To understand the steady-state thermal stress model, consider a small element of an isotropic elastic solid be detached from its surroundings (Boresi and Chong, 1985). If an element is subjected to a temperature change T, the additional straining in the element is given by the components:
e=kT& (2-1)
where k is the coefficient of linear thermal expansion for the solid and dij is the notation
for the Kronnecker delta. The strain produced by the structural load can be characterized by the components:
eij"= e.,1, - kT is], (2-2) eijis the net strain in the body.
'The equation for transient heat transfer can be written as:
where v2denotes the Laplacian operator:
ddd s+dyi+z
p denotes the mass density
a C denotes the specific heat. k denotes the temperature diffusivity (k = -). CP
For thermally isotropic and homogeneous bodies the equation for steady-state or
heat transfer can be expressed as follows : This is the Poisson equation of potential theory.
Alpha (a)denotes the thermal conductivity and it is a constant value since it does not depend on the direction nor the location of the body. Also it is assumed (for small temperature gradients) that it does not depend on temperature or stress level. Q denotes the unit of heat per unit of time and unit of volume that is produced by the heat sources that lie in the interior of the volume element.
With the absence of heat sources in the mold body,Q=O. Hence, the temperature distribution in the body satisfies the equation:
Thermal boundary conditions depend on the effect that the environment of the body exerts on its surface. There are three kinds of boundary conditions.
Initial boundary conditions.
Boundary conditions in terms of heat flow.
Boundary conditions in terms of environment temperature. In general, a temperature change in an element will not produce stress in it unless either the element is physically prevented from expanding or, if physically free to expand, it is unable to expand in a manner compatible with the temperature distribution in the element. For example, if the element is constrained so that its length is under a temperature increase of T, forces P must act at its ends (see Figure 2-1). It can be seen that the first element is able to elongate a distance de. Then, by application of forces P the element is returned to its initial length dx. Hence, to compute the stress induced in the element by the temperature change T when its ends are restrained from moving, the stress induced in the element by forces P under compression can be computed by
where A is the cross sectional area of the element and E is the modulus of elasticity of the material. This can also be written as o= -EkT where the minus sign denotes compression.
-. dl! -p ;. r!~= k 'X' dx , - ef lir Figure 2-1. Linear element under thermal stress. 2.3. Previous Studies for Establishing Optimal Design Based on a review of selected literature, there appears to be no method of calculating the optimal design of a mold. Such method should consider the conditions of use of the mold equipment: Temperature of the glass. Machine operation cycle. Cooling conditions. As stated in chapter one, molding glassware is a complex physicochemical and thermal process in which the mold executes a double function. The mechanical function is to give the final shape to the molten glass. The thermal function is to intensively cool the surface layer of the molten glass, fixing the final shape, consequently. Genzelev et al. (1989) state that mold design parameters do not provide a reasonably uniform heat removal from the working surface. The lack of uniform heat removal leads to uneven thermal stress distribution with the consequences of n~icrocrackingand failure of the molds. They suggest the possibility of improving the working parameters by designing thermally balanced molds. One of Genzelev's experiment was made based on the constancy in the temperature averaged over the thickness at any point of contact. Temperature readings were made in molds for compressed glass domes during standard production. The glass rises, cools, and c:orrespondingly produces a temperature pattern in the mold that decreases from the bottom upwards. Temperatures were measured simultaneously at the inner and outer surfaces of the mold using chromel-alumel thermocouples located at different points along the vertical direction of the mold (see Figure 2-2.a). The measurements were made: 1. During the glass loading, 2. At the start of the pressing, 3. At the end, and 4. When the item was removed (see Figure 2-3). Figure 2-2. (a) Standard mold. (b) New design. (1-6) Thermocouple points. Figure 2-3. Temperature distributions at the outside wall along the height: a) Solid lines, temperatures after 1 h, dashed lines after 3h; b) Solid lines after 2 h, dashed lines after 4h; 1) At time of loading glass. 2) Start of pressing. 3) End of pressing. 4) Workpiece removal. With the results obtained, Genzelev cites that the thickness of the mold was optimized by balancing the temperature differences at the various points by reference to the minimum values. One important assumption made was that the amount of heat transferred from the inner wall to the outer wall was constant during the steady state. 'The heat flux through the wall was taken constant. The mold was taken as a hollow cylinder. The equations used for the stationary temperature distribution: where: t',, is the environmental temperature, t, and to are the temperatures of the inner and outer surfaces, R, and R, the outside and inside radii, Bi the Biot number, h the thermal conductivity, and a the surface heat-transfer coefficient. Equation 2-10 evaluates the mold design. The thickness varies via R2 and R, remains constant as it depends on the size of the workpiece. If the wall thickness at all points is less than necessary for thermal balance, the outer surface temperature raises, affecting servicing conditions. If the thickness is greater than necessary, the temperature difference over the thickness increases, which in turn increases the thermal stresses and reduces the life of the mold. As a result, Genzelev proposed a new mold design (see Figure 2-2.b). The improved mold design was characterized by: significant reduction of mass, reduction of temperature differences as well as thermal stress reduction, more uniform heat loss. Experiments by Drozdov et al. (1975) indicated that for a particular mold, reduction of wall thickness increased the throughput by optimizing the ratio between the rriasses of the mold and the glass component. He proposed a method of experimentally determining the optimum mass of cast-iron molds used in glass-molding to provide a first approach to calculate the optimal design of the mold equipment. Other studies (Kropotov and Kalshnikov, 1976) consider the specific mass of the mold, or ratio of the mass of the mold to the mass of the glassware, as the main parameter. However, these studies made no allowance for the productivity or operational cycle of the machine. Drozdov (1975) suggested that productivity could be included using the ratio of the mass of the mold M, to the mass of the number of glassware produced in the mold per unit of time (one minute) M,. Drozdov suggested that a properly selected operational cycle would provide a reserve for reducing M,/M, of the molds. To determine the optimum value of M, / Ma, on the basis of experimental observations, the maximum temperature of the mold was used. According to Drozdov, this should be between the temperature t, at which the glass is workable and not greater than the temperature tad,at which the glass adheres to the material of the mold. Drozdov's experimental results indicated that the temperatures of the molds were in the t, to tadinterval. As a result of Drozdov experiments established the possibility to reduce the value of the M, 1 M, ratio by reducing the mass of the molds and increasing the productivity of the machines. However, the temperature of the molds may exceed the value of tad, thus, the operational cycle must be selected so that the working mold temperature cannot heat up above tad . Kropotov et al. (1972) stated that weight of a mold is a significant factor affecting the results of the molding. Suggesting that a mold has an optimum weight, which assures the maximum output of the machine and improved quality of glassware. The thermal regime as developed from this experiment is shown (Figure 2-4.a). In the metallic layer of thickness 6, adjacent to the hot molten glass an unsteady thermal field was observed. The depth of this layer was about 5-1 0 mm. In layer 62 of the mold wall a steady state thermal condition exists, and the temperature in this layer decreased exponentially towards the outer surface. Based on the results of this experiment, Kropotov suggested factors that should be considered in designing molds and optimizing molding equipment: Weight and temperature of the glassware. Ratio (in one cycle) of time during which the molten glass is present in the mold to the time during which the molds cool down without glass. Thermophysical characteristics of the mold material, degree of development of outer heat-giving surface. Presence (or absence) of heating cavities inside the wall. Type and intensity of artificial cooling. Type and nature of the lubricant for the working surface. Kropotov observed that these parameters are usually not considered and that the method of trial and error under production conditions, continued to be the method to determine the optimum weight and thickness of the mold walls. Howse (1971) presents the nature of time-dependent variation of heat flow and temperature in one working cycle of a mold (see Figure 2-4.b). The curve indicates that at to of receiving a gob of molten glass, when the mold has the minimum temperature and molten glass has the maximum temperature the heat flow between them drastically increases. At first the temperature of the mold rises rapidly and then gently decreases. r Wall ot s nlofd, d B 'rota1 wall thickness t 81 ?%icknead che unsteaefy gtate layer +- +- 62 Thickness of the stertdy st~&lay~ I t~t. W Consumption of csollng air i_ Figure 2-4. Nature of variation of heat flow and temperature depending on time (a) Thermal regime in the mold. (b) Time dependent variation of heat flow. Based on experiments that take into account the mechanism of heat process of molding the molten glass, Stepanov et al. (1974) proposed theoretical ratios for calculating the basic mold design parameters. These ratios have not found yet application. Other works in compression molding of polypropylene glass composites, and established the importance of preheating molds before molding. The researcher (Giles, 1991) suggested that an optimal time-temperature relationship must be determined to uniformly heat molds in order to achieve the desired molding operation without resin degradation. Short oven preheat time at high temperature yielded suitable mold surface temperatures, but the center of the mold was insufficiently heated. At lower oven temperatures with prolonged heating times, both the wall and bottom center temperatures should reach the desired processing temperature. During the flow formation the press force applied is one of the important processing parameters in determining the degree of flow. The speed at which the force is applied is also important. As pressing speed is increased at a given press force, flow increases until a critical point is reached where the flow may decrease. Increases in mold temperature can substantially change the degree of flow with higher mold temperatures requiring less force, but longer overall cycle time can result. Giles does not believe that mold size, while important, is a significant factor. Berrnisderfer et al. (1981) wrote a computer code for examining the thermal characteristics of molds for glass measuring cups. He made a layout of the mold consisting of small nodal segments defined in a coordinate system. Bermisderfer observed that there was a high level of difficulty in preparation for a computer analysis due to the need of assigning many heat transfer coefficients in the interfaces. He suggested that further research was required using computer aided mold design that would allow the comparison and analysis of the effect of mold changes in the temperature and heat flow patterns. 2.4. The Finite Element Method The theory of the Finite Element Method (FEM) is based on variational calculus. This mathematical basis allows the development of a model in a very short time and makes it a powehl tool for engineers to use in analisys. Pate1 (1993) cites seven steps involved in Finite Element Method: 1. Discretize and select the element configuration. 2. Select approximation hctions. 3. Define strain-displacement and stress-strain relationships. 4. Derive the governing equations. 5. Assemble the global equation including boundary conditions. 6. Solve for the unknowns. 7. Interpretation of results. 1. Discretize and Select the Element Configuration. The body is subdivided into a number of "small" bodies or finite elements. The intersections of the element sides are the nodes or nodal points, and the interfaces between the elements are called nodal lines and nodal planes. For one-dimensional bodies a grid of line elements is used (see Figure 2-5.a). The elements are not necessarily of equal size. Figure 2-5. Finite elements: (a) One-dimensional elements. (b) Two-dimensional elements. (c) Three-dimensional elements. Triangles and quadrilaterals (see Figure 2-5.b) are used for two-dimensional bodies. Many polygonal shapes can be used to define the elements. Rectangles can be used when the problem domain itself is rectangular. However, rectangles do not easily fit well when the domain is irregular. The simplest element that easily accommodates irregular surfaces is the triangle, and it is one of the most popular element shapes used today. For three-dimensional bodies (see Figure 2-5.c) the idealization is done with the tetrahedron and the hexahedron. 2. Select Approximation Functions. A pattern or shape (see Figure 2-6) is chosen for the distribution of the unknown quantity. Over each element the unknown quantity will be approximated using known predetermined functions called shape hnctions. The unknown quantity can be displacement, stress, temperature, fluid pressures, or velocity, depending of the type of problem. A number of mathematical hctions such as polynomials and trigonometric series can be used for this purpose, especially polynomials because of the ease and sin~plificationthat they provide in the finite element formulation. The interpolation function can be defined as: u = Nlul +N,u, +N3u3+...+Nmum (2-1 1) where ul, u2...... , U, are the unknowns at the nodal points and N1, N2,....., N, are shape functions. Degrees of freedom can be defined as independent unknown displacements at a point. For example, in a problem of one-dimensional deformation (see Figure 2-5.a) there is only one way to move in the uniaxial direction, there is only one degree of freedom. I Garner cr hddi'tiona' orimsry node Poade Figure 2-6. Distribution of displacement u, temperature T, or fluid head cp. (a)Discretization of a two-dimensional Body. (b) Distribution of u, over an element e. 3. Define strain-displacement and stress-strain Relationships. This step uses a principle, for example, minimum potential energy, for deriving equations for the element. Appropriate quantities must be defined according to the area of application. Some major areas in which the Finite Element Method has been successfully used are: Solid mechanics: Stresslstrain, structures design fatigue, cracking, deformation, extrusion, and cyclic loading are some of the examples where Finite element analysis is being used. For stress deformation problems, strain or gradient of displacement is to be defined. In the case of deformation in one direction (see Figure 2-7.a) the strain E, is given by: where v is the deformation in the y direction. The stress or velocity is expressed using a stress-strain law. In a solid body the Hooke's law defines the relationship of stress to strain in a solid body: oy= Ey&, (2- 13) where o, is the stress in the vertical direction and E, is the Young's modulus of elasticity. Fluid Flow: Flow of ideal fluids and potential formulation of many problems where frictional or non- conservative effects are neglected; although unrealistic, a great deal of insight can be gained in the simplified analysis. For a fluid flow in one direction, the relation is the gradient gx of fluid head(see Figure 2-7.b): Species transport: Atmospheric, lake and ocean transport of pollutants, gaseous diffusion, multispecies interaction, and chemical kinetics are some of the physical processes involving convective and diffusive transport that can be handled by the Finite Element Method. Ground water transport: Contaminant transport, well drilling, oillgas recovery, boring and multi-phase flow. Lubrication: The Reynolds equation applied to slide bearings and hydrodynamic lubrication involving both compressible and incompressible fluids. Biomechanics: Impact load on the human skull, analysis of the tibia, etc. Figure 2-7.One-dimensional problems. (a) One-dimensional stress-deformation. (b) One- dimensional flow. 4. Derive the Governing Equations. Using governing laws and principles, the equations that model the behavior of the element are defined. The equations are generalized to be used for all the elements in the discretized body. There are basically two procedures that are normally used to formulate and solve equations using finite elements. These are the Rayleigh-Ritz and the Galerkin Methods. Other lesser utilized methods are based on collocation, constant weights, and least squares techniques. All of these procedures are subsets of the method of weighted residuals. The Galerkin method, also called method of weighted residuals, is based on minimization of the residual left after an approximate or trial solution is substituted into the differential equations governing a problem. For example, consider the following differential equation: where u* is the unknown, x is the coordinate, t is the time and f(x) is the forcing function. The differential operator L: The approximate function u for u* is denoted as U= cpO +alcpl +a2cp2 + ...... an cpl , 92,.... cpn are known functions that satisfy the homogeneous boundary conditions; cpO satisfies the essential, geometric or forced boundary conditions; and a, are parameters to be defined . Substituting the approximate solution into equation 2- 17 the residual R(x)= LU - f, (2- 18) to get a minimized residual, the expression: b ~(x)wi(x)dx =O , i = I ,2,. .. ,n (2- I 9) D denotes the domain of a structure or body under consideration.Wi are the weighting functions. The equations describing the behavior of an element arriving from the above method are commonly expressed as [kl{q) ={Q) (2-20) where [k]= element property matrix, {q)= vector of unknowns as the element nodes, and {Q)= vector of element nodal forcing parameters. 5. Assemble the global equation including boundary conditions. Once the element equations are established for a generic element, the rest of the equations are generated recursively for other elements repeatedly, adding them together to find global equations. The assembly process requires that the body remain continuous. The neighboring points should remain in the neighborhood of each other after the load is applied. The displacement of two adjacent or consecutive points should have identical values. The continuity conditions are enforced more severely depending on the type and nature of the problem. In plane deformation applications, it is enough to enforce continuity of the displacements only. In bending problems, the physical properties of the deformed body under the load require that in addition to the continuity of displacements we ensure that the slopes or the first derivative of the displacements are also continuous or compatible at adjacent nodes. The assemblage equations obtained have the following matrix notation: [Kl{rl = {R) (2-2 1) where [K]= assemblage property matrix, {r)= assemblage vector of nodal unknowns, and {R)= assemblage vector of nodal forcing parameters. In stress-deformation applications, these quantities are the assemblage stiffness matrix, the nodal displacement vector, and the nodal load vector respectively. Boundary conditions (see Figure 2-8) are the physical constraints or supports that must exist so that the body can stand in space uniquely. These conditions are commonly applied specified in terms of known values of the unknowns on a part of the surface or boundary S, and gradients or derivatives of the unknowns as SZ. The boundary conditions are applied in a different manner for different problems. In the case of a simple supported beam (see Figure 2-9), the boundaries S1 is the two-end points where the displacements are given. This type of constraint expressed in terms of displacement is called geometric boundary condition. 'The final modified assemblage equations are expressed as Figure 2-8. Boundary conditions or constraints. Body with constraints. Figure 2-9. Examples of boundary conditions. Beam with boundary conditions. 6. Solve for the unknowns. 'The expanded notation of equation 2-2 1 is: Kllrl + K12r2+ ... + Klnrn= R1, ...... Knlrl+ Kn2r2+ ... + Knnrn= R, By means of any iterative method such as Gaussian elimination the solution for the primary unknowns rl, r2, ...,r, is obtained. In most of the problems it is necessary to compute additional or secondary quantities from the primary quantities. 7. Interpretation of Results. This is the final step in the procedure. The results are generally output information from the program. This output can be a tabulation or a plot of results. 3. METHODOLOGY The subjects for the present study are the mold elements for manufacturing a glass tumbler. The technical name of the molding equipment is Tumbler 176. The assembly drawing (see Figure 3-1) for the tumbler 176 shows the following items: Mold Insert: Anchor Hocking specification-11. Stainless steel type AISI 431M. The hardenable alloys can be heat treated to a high hardness and because of their oxidation resistance are used for for high-temperature operations. Mold Cage: Gray Cast Iron Specification ASTM A48 Class30. Mold Bottom: Gray Cast Iron Specification ASTM A48 Class30. Valve: Anchor Hocking Specification-2, chilled Low alloy Gray Iron Casting. Plunger: Anchor Hocking Specification-4, Stainless steel type AISI 420 modified. Other material available is Titanium alloy type Ti-6A1-4V. The models were created based on the design drawings provided by Anchor Hocking. Figure 3-1. Tumbler 176 Molding equipment. Assembly drawing. 3.1. Description of the Tumbler 176 The final product is a soda-lime glass tumbler. Table 3-1 shows the typical characteristics for this particular product. Weight 15.25 ounces Softening point 1333.8 OF Annealing point 1012.6 OF Strain point 947.1 OF Component Si02 Fe203 A1203 CaO MgO Na20 K20 SO3 SrO " " " "..,... ""..... ".... " " % 72.79 0.032 1.32 8.95 1.86 14.21 0.29 0.19 0.11 Table 3-1. Characteristics of the tumbler 176. 3.1.1. Soda-Lime Glasses Soda-Lime was the earliest man-made glass. Today, around 90 per cent of the total glass production is soda-lime based. Next to fused silica, soda-lime products are the simplest glasses. Adding Na20 to Si02drastically lowers the melting temperature and acts as a powerful fluxing agent. The resulting substance is soluble in water. To overcome water solubility, the addition of lime is required. The application of this type of glass is desired if no significant heat resistance or chemical durability is required. With minor variations in composition, we can find them in various applications for sheet and plate glass, containers, lamp bulbs, ophtalmic lenses, construction blocks, bottles, tumblers, novelties, etc. 3.2.3-D Solid Modeling 3.2.1. Geometric Modeling Technique The shape of an object is described to simulate dynamic processes. Complex shapes can be modeled as arrangements of simpler ones. The application of virtual models becomes a substitute for the real object or process. Geometric modeling is a combination of analytic geometry, calculus, topology, sets theory and numerical methods. By applying the concept of associative modeling, geometry and design intent are captured in the definition of the part. By capturing the design intent can be changed quickly allowing an efficient design revision. Associative modeling establishes relationships among the elements that make up the model. The model is also useful in transmitting or conveying design information between engineering and manufacturing. The first step in the application of the CAD process consisted in the creation of master models, this is, a collection of data including geometric representation geometric intent captured through associative relationships, and non geometric data (i.e. color, surface finish). Modifications can be easily done. The master models have been created with the Engineering Modeling Sofhvare.The modeling of the mold elements was completely based on the drawings supplied by Anchor Hocking. 3.2.2.3-D Solid Modeling of the Tumbler-176 Molding Equipment The 3-D Solid models of the following items were created: Plunger (see Figure 3-2) Mold Cage Mold Bottom Mold Insert (see Figure 3-3) Valve The models were created on an Intergraph workstation using Intergraph's Engineering Modeling Sofhvare(I1EMS). The following steps were used in the creation of the final models: All the dimensions were taken directly from the manufacturing drawings. Axissymmetric profile creation and constraining. The profile for one of the elements of the molding system shows the detail of dimensional and geometric constraints. Rotation around axis of symmetry for solid model creation. Once the profile is properly defined, the solid model is generated by simply rotating the profile. Boolean operations for creation of 3-D surfaces. This is an optional procedure. Shading process for the solid models. Figure 3-2. Solid modcling of the plunger. 2D axisymmetric profile and 3D solid model. Figure 3-3. Solid modeling of the Inold insert. 2D axisymmetric profile and 3D solid model. 3.3. Thermal Stress Analysis of the Mold Bottom and the Plunger 3.3.1. Application of the Finite Element Method The methodology applied was the Finite Element Method (FEM). As explained in chapter 2, the Finite Element Method is a numerical technique which gives approximate solutions to differential equations that model problems arising in physics and engineering. The Finite Element Method requires a problem defined in a geometrical space to be subdivided into a finite number of smaller regions (a mesh), each subdivision is unique and not need to be orthogonal. Over each finite element the unknown variables (i.e. temperature) are approximated using known functions; these functions can be linear or higher order polynomial expansions that depend on the geometrical locations (nodes) used to define the finite element shape. The governing equations in the finite element method are integrated over each finite element and the solution summed over the entire problem domain. A set of finite linear equations is obtained in terms of a set of unknown parameters over each element. Solution of these equations is achieved using linear algebra techniques. All these features are provided in the FEM software. The FEM software is a computer aided engineering package for general purpose Finite Element Analysis (FEA). It takes advantage of dedicated computing power to simulate the structural behavior of designs before they are built. The FEM software provides automated mesh routines that convert the geometric definition into a complete, accurate finite element model. It automates analytical modeling, computation and results evaluation to help optimize designs for quality performance and structural integrity. Mechanical and thermal stresses on the parts can be shown. Library of commonality can be developed to eliminate redesign of fixture parts. 3.3.2. Preprocessing The discretization of the geometric models into computational models consisting of elements and nodes was made by using three-dimensional linear tetrahedron elements (see Figure 3-4). Linear elements have straight sides while quadratic and higher order elements can have curved surfaces. Four nodes define the linear three dimensional tetrahedron. The meshing process was completely automated but some precaution had to be made to prevent improper meshing. Mainly, mesh density is an important factor to consider to prevent errors in the analysis. Selecting improper density or tolerances can result in bad meshes with unevenly distributed nodes, or totally invalid meshes. Even when the meshing process is automatic, it is possible to select different values of mesh size for different areas within the same model. The automesher is geometry based . It places nodes based on the surface topology and associates boundary conditions with geometry. Figure 3-4. Tetrahedral elements. Based on the studies presented in the literature research, the following assumptions were established to perform the preprocessing: A steady-state thermal regime was observed. The highest temperature was observed at the bottom of the mold. The wall temperature for the mold and plunger was 1050 OF. The optimum wall thickness depends on the constancy in the temperature averaged over the thickness at any point. The molds were previously preheated. It is only possible to vary the thickness of the plunger from the side that is not controlled by the workpiece size. The material properties for the plunger and mold insert were taken from the documentation provided by Anchor Hocking (See table 3-2). Ti-6A1-4V Properties at 1000°P ksi Tensile Strength 110 Yield Strength 90 Rupture Stress 80-100 Elastic Modulus 14000 Table 3-2. Material properties for Ti-6A1-4V alloy. 3.3.3. The boundary conditions For the application of boundary conditions it had to be considered the fact that the analysis would be done at the moment when the plunger have reached its final position, this is, when it had made contact with the stop ring. To simulate such condition the working pressure of 40 psi was applied over the surfaces in contact with the molten glass. For the plunger, a temperature value of 500 OF at the inner wall and 1050 OF at the outer wall were applied. In the case of the mold insert 1050°F for the wall in contact with the molten glass and 500 OF for the outer wall. For the mold insert, the outer wall was constrained in the radial direction because of the surrounding mold cage. The inner wall was also hlly constrained by the surrounding molten glass. 3.3.4. Analysis Runs, Postprocessing and Optimization In order to speed up the interpretation of the analysis results, a complete postprocessing system that presents numerical data is available with IIFEM. Graphic postprocessing options include isocontours, deformed shapes, vector plots, color coding with legends, animations, and graphs. IV. ANALYSIS OF RESULTS 4.1. Mold Insert For the mold insert one analysis run was made. It was not possible to modifiy its geometry without affecting the surrounding components.The solid model and the cross section of the mold insert show the stress distributions (see Figure 4-1). The maximum stress value is 8.91 x 10' psi and the minimum stress value is 4.01 x lo3 psi. The higher stress concentrations are allocated at the bottom of the mold, this is consistent with the fact that when dropping the glass gob, it lies at the central part at the bottom of the insert. Besides, the effect of the plunging action contributes to increase the stresses at the bottom. The rest of the insert is subjected to a very regular thermal stress distribution. M A X 8.90 e+64 U l hl 4.~lgs+b3 UNIT VS~ r! Figure 4-1. Thermal-structural stress distribution on the mold insert. (a) Profile. (b) Isometric view. (c) Cross section. 4.2. Plunger For the plunger, the design and optimization process started from scratch without considering the original inner shape used by Anchor Hocking at the present time. The process of optimization consisted in varying sidewall and bottom thickness looking forward to reduce the maximum stress and volume. Table 4-1 shows the evolution of results for the plunger for six modifications of the inner shape of the plunger. The geometry of the original plunger was released and the finite element analysis was done. The results for this shape are also tabulated in table 4-1. Figure 4-2 depicts these results in a graph. According to the results, the optimized model correspond to a plunger that has an inner wall contours similar to the outside contour. Figure 4-3 shows the model and stress profilere for the original model whereas Figure 4-4 depicts the stress profile optimized . Reducing the wall thickness produces an stress increase. The cylindrical inner shape is similar to the one presently used by Anchor Hocking. According to the results presented, the optimized model presented an stress reduction of 26.6% and volume reduction of 34.2% with respect to the original model. The application of an inner "thin" at the bottom interior of the plunger may not help to reduce stress significantly. The application of a groove at the bottom interior of the plunger may help to reduce stresses because of the increase of the area in contact with the cooling fluid. PLUNGER PLUNGER MAXIMUM MINIMUM SHAPE VOLUME STRESS STRESS approx. in3 psi psi I 27,4U 6,16E+04 1,85E+02 2 v 339 1,01,E+05 1,84E+02 3 35,lU 5,73E+04 6,48E+02 4 v 35,16 6,20E+04 1,38E+02 5 37.21 8,80E+04 1,50E+03 6 v 47,84 8,71E+Q4 561E+U3 7 483 8,38E+04 4,5E+03 Table 4-1. Thermal-Structural stresses for various shapes analyzed. J7igul-r4-3- Thrmla\ strurttlrrl stress distriblsion for an original mollel of a plunger ,.0.6 in Table 4-1). (a) Profile. (b) Isometric view. (c) Cross section- M A X 5.72?8+04 M I N 6.46Ze+OZ UNIT par Figure 4-4. Thermal structural stress diatrihution for an optimized model of ;l plunger (Shape 110.3in T:il)le 4-1). (a) Profile. (b) Isometric view. (c) Cross section. 65 V. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH & 5.1. Conclusions 5.1.1. Application of Computer Techniques to Improve Mold Design An attempt to create 3-D solid models of the elements of the mold system hwas succesfully completed. The use of parametric models brought the capability of making changes in the design in an easier way. A finite element analysis of the mold and the plunger provided results that were consistent with the results and predictions stated by researchers in the past. It is expected that a mass reduction on the optimized design should reduce cost of materials, machine productivity, handling effort when changing molds, 'and reduce dynamic load on the machine. 5.1.2. System Implementation Feasibility All the information files collected from the previous processes can be stored into a database system. By means of a database it could be possible to retrieve the information to repeat the analysis and manufacturing sequences. The information can be retrieved and changes can be made in order to create new designs based on the existent ones. " -- <* - Figure 5-1. Design for manufacturing of compression glass molds. It is possible to integrate a system consisting of all the procedures mentioned before dedicated to design and manufacturing of compression glass molds. Figure 5-1 shows how does each process interact within this system. 5.2. Recommendations for Further Research. 5.2.1. Finite Element Analysis of the Assembly Model Further work on this project may be performed creating a three-dimensional assembly model of the elements of the mold system, this includes the plunger, the mold insert, the mold bottom, the mold cage, the valve, and the ring. 5.2.2. Possibility of Research on the Glass forming Process The effect of modifying the thickness of the molding elements affects directly to the glass forming process since the heat transfer conditions change. In order to predict the behavior of the molten glass during the forming process, an approach for further research has been made. Since there is no sufficient experimental data for establishing the correct parameters for glass forming, approximations were made. The objective of this approach is to show that with the appropiate experimental data collection is possible to include the glass behavior as a design parameter for optimal molds. 5.2.2.1. Viscoplastic Behavior The viscoplastic model defines a material for which viscous (or liquid) behavior occcurs for stresses exceeding some limiting value and, for stresses below this value, the materials behaves as a solid, this is, supports stresses as a rigid or elastic material. The real phenomena is that practically negligible viscosity and irreversibility of deformation for small stress levels, and predominant viscous properties for large stresses. The critical value of stress will be called the yield point or the yield limit . For multiaxial stress states , rigid or elastic states belong to the interior of the yield surface while all viscous states are represented by points in the exterior domain, as Mroz (1973) cites. This behavior is found in paints, polymer solutions, disperse systems and many other viscoplastic liquids. 5.2.2.2. Flow Stress In general terms, the flow stress of a material can be expressed in terms of stress, strain rate, and temperature. For the present study the behavior of glass in the molten state was assumed as: a= k~ em + C (5-1) o= Flow Stress k= material constant E= strain e= strain rate n=Strain hardening index in the flow stress expression. m= strain rate hardening sensivity index. C= Material Constant This expression of the flow stress data is insufficient in glassforming analysis. In order to incorporate a more complicated flow stress behavior, additional material property subroutines can be included to a particular software. This is beyond the scope of this study and, further experimental research is required to find glass properties not available in the literature researched. 5.2.2.3. General Method of Analysis The software package suitable for the analysis of the glass deformation needs to have the capability of analysis of large plastic deformation using finite element method. The software available at the moment of the present study are software aplicable to rigid-plastic and visco-plastic materials, this is, the programs can be applied to hot and cold metal- forming as well as hot forming of glasses and polymers. The basis of this approach is the finite element analysis of backward forging process for a "gudgeon pin". At the first stage (see Figure 5-2.a) a simple upsetting in a closed container is shown, for this particular case the ratio of the billet length to diameter was 1.5 after cropping. The die was filled by reducing the height of the billet and reducing the lengthldiameter ratio. At the second stage (see Figure 5-2.b) the dumped billet is indented to guide the punch in the backward extrusion operation. The third stage (see Figure 5-2.c) consists in the backward extrusion of the element. The final element analysis of the backward extrusion process was performed on aluminium ,using an axisymmetric, elastic-plastic, isothermal finite element program with eight-node iso-parametric quadrilateral elements. The backward extrusion sequence required a remeshing operation every 5% penetration. The process was laborious due to the lack of availability of automatic remesh packages at the moment of the experiment. For practical use of Finite Element simulations of large deformations, automatic remeshing sofhvare is essential. The predicted grid distortions (see Figure 5-3) for each stage are shown. Figure 5-2. Forming of a gudgeon pin. (a) Upsetting (b) Indenting (c) Backward extrusion. Figure 5-3. Predicted grid distorsion during the gudgeon pin forming. In a similar way, the application of an automatic remesh package is proposed to analyze the effects of the modifications in the mold design in glass forming. The procedure of analysis with this type of software package is as follows: 1. Input data file. 2. Run FEM simulation. 3. Postprocessing. 4. Remeshing. 5. Final run and postprocessing. The input data file consists of die data such as geometry, movement and friction at die surface, the workpiece geometry by elements and nodal points, material properties such as flow stresses of the workpiece as a function of temperature, and conduction heat transfer as a function of time. After running the first FEM simulation and postprocessing it was observed that the deformed mesh is subjected to serious distortion creating convergence problems in the calculations. A remesh process is required. Some software packages support a utility to extract the points that define the boundaries of the deformed billet and collect all these information into a data file. It was necessary to export this file into another package in order to create the new mesh. Simple codes written in some programming language, if not supported by the application, help to get the points into the software package and redraw the shape of the deformed billet. A new mesh was created with quad elements with the proper shape and size for continuing the analysis. A new data file containing the element and nodal information was obtained. If necessary the file has to be edited so that it could be readable in the original package . With this file, a rerun was made. Again at some step the solver would stop running and the process of remeshing and edition had to be made several times until getting the desire final deformation. The procedure is expensive in terms of time. The software packages tested for this purpose were ALPID 2.3. from Batelle's Columbus Division, PATRANIADVANCED FEA and ANTARES 4.0 from UES Inc. The most suitable for the present study was ANTARES. 5.2.2.4. ANTARES Antares 4.0 beta version (A Natural Tool to Achieve the Required Engineering Shape), made by UES Inc., is a finite element based solver for predicting the material flow under the presence of complex geometry die contact, frictional effects, plastic heating, die chilling, and heat loss to the environment. It is suitable to perform analysis of several types of single and multiple step processes such as cogging, radial forging, drawing, extrusion, coextrusion, nosing, heading, closed die forging, edge rolling, shape rolling, radial rolling, and ring rolling. Antares reference guide (1995) mentions that this software package performs tool stress and thermal analysis coupled with the workpiece deformation sequence. The solution data is utilized for prediction of fill pattern, lap formation, tool deformations and tool stresses. The analysis is based upon the workpiece flow stress and thermal data, tool material thermoelastic properties, and interface lubricant material frictional and heat transfer characteristics. The modeling can accurately account for workpiece characteristics. The modeling can accurately account for workpiece forming behavior depending on the processing conditions utilized. As previously explained, there was no enough information about properties of molten glass or similar materials at high temperatures. Properties applied were approximated, using the characteristics of a liquid metal such as aluminium at high temperature. Melting point of aluminium is at 1220 OF and its specific gravity is in the range of 2.37-2.5. These values are compatible with molten glass properties. Considering viscosity , liquid metals have viscosities of the order of 1 poise whereas molten glass is in the order of 100 poises. Figure 5-4. Simulation of compression glass forming process. Figure 5-5. Flow stress cotltours of the molten glass during compression. The geometry and the mesh (see figure 5-4) are generated for the dies as well as the billet. It took 14 remeshing steps to get the final deformation. Figure 5-5 depicts the flow stress contours for the molten glass during compression. Figure 5-6 is a comparison of stress distribution at various deformation steps for both original and modified plunger designs. Stress values for the optimized design appear to be of the order of 50 percent less than those for the original design. Step Figure 5-6. Von Mises stress distribution for original and modified plunger shapes analyzed. REFERENCES 1. Genzelev, S. M. , Dubrovskii, V. V., Fen, G. A., Etelis, L. S., Chernyshova, N. V., Zolotareva, R.S., Boru17ko,V. I. & Zakharov, G. V. (May, 1989) . A vigorously cooled glass mold. Steklo I Keramika, No. 5, pp. 1 1-12. Moscow. 2. Jones , G.O. (1956). Glass (1st ed.) . London: Methuen & Co. Ltd. 3. Phillips, Charles John (1960). Glass: Its industrial applications. New York: Reinhold Publishing Corporation. 4. Grimshaw, R. W. (1971). The chemistry and physics of clays and allied ceramic materials (4th ed. rev.). London: Ernest Benn Limited. 5. Drozdov, V. I., Gurin, S. S., Kalashnikov, G. E., Mokrenskii, E V., Sokolov, A.A., and Pogodin,V. A.(August 1975). Optimum mass for cast-iron molds in the AV-type glass molding machines. Steklo I Keramika, No. 8. pp. 19-20, Moscow . 6. Tooley, Fay V.(1953-1960), Handbook of glass manufacture: A book of reference for the plant executive, technologist, and engineer (Vol.1) New York: Ogden Publishing Company. 7. Boresi, Arthur P. & Chong, Ken P. (1987). Elasticity in engineering mechanics. pp. 276 -280. New York: Elsevier. 8. Kropotov,D. P. & Kalshnikov,G. E. (September, 1976). Significance of the optimum weight of molding equipment. Steklo I Keramika, No.9, pp. 20-21, Moscow, 9. Howse, T.K.G (1971). Glass technology. No. 4, p. 12. 10. Stepanov E. & Gladshtein, 1.E (1974). Designing molds for glass items. Leakava Industriya, Moscow I 1. Giles Jr., Harold F. Compression molding; of Polypropylene glass composites, 36th. International SAMPE Symposium, pp.556-570, April 15-18, 1991. 12. Berrnisderfer, C. & Fisher, R. (May 14, 1981). Computer analysis of 496 measuring CUP inserted mold design. Report presented by D. Miller and C. Conrad from Anchor Hocking Corporation, 13. Pepper, Dare11 W. & Heinrich, Juan C. The finite element method, Taylor & Francis publishers, USA, 1992. 14. Avallone, Eugene A. & Baumeister I11 (1987). Marks' standard book for mechanical engineers (9th ed.). New York: Mc. Graw-Hill. 15. UES, Inc. (1 995). Antares primer & examples manual. Dayton, Ohio: UES, Inc. 16. Mroz Z.(1973). Mathematical models of inelastic material behaviow. Ontario: Solid Mechanics Division University of Waterloo. 80 APPENDIX A: GLASS MANUFACTURING TECHNIQUES Blowing Glassblowing machines are used to manufacture a wide variety of products, including bottles, jars, laboratory beakers and flasks, coffee makers, christmas ornaments, and enclosures for incandescent bulbs and radio tubes. Tooley (1953), describes a typical industrial glassblowing machine, the Hartford- Empire individual section I-S machine. The description of the process with this machine gives a general idea on the glassblowing process. The molds open and close without changing position and following the cycle: a gob of molten glass drops through a guide funnel into the blank mold (see Figure A-1 .a). Under proper loading conditions, the gob settles uniformly and almost entirely into its ultimate shape before settle blow air is applied (see Figure A-1 .b). As quickly as possible after the gob drops, a blow down head is positioned on the funnel, by an arm swinging in and down and blowing air to settle down the gob. A plunger is in place, forming the finish and a small bubble for blow air. One element of timing is to hold the settle blow to as short a duration as possible to form a finish which is sufficiently setup and cooled to withstand the following operations without deformation. If settle blow is excessive, the glass in contact with the lower portions of the inverted blank mold is cooled excessively, resulting in a bad way wave or a sudden change in wall thickness in the middle portions of the bottle body. Therefore, as quickly as possible, the blow-down head is removed, the funnel moves out, and the first head comes back, matching to the blank mold, where it serves as a baffle or bottom plate. Just as it reaches home, the air is applied through the mouth of the finish into the bubble, and the counter blow occurs as shown in Figure A-1.c. At this point the parison is completely formed, so the blank mold opens, and the glass is held in the neck rings, inverted. The ring necks are made to swing 180 degrees in a vertical plane, to a position over the closing blow mold (see Figure A-1.d). Just as the blow mold closes all the way, the neck rings open dropping the parison slightly into the proper position within the blow mold. The neck rings quickly revert to their original relationship with the blank mold, and the blank- mold cycle starts to repeat, as the parison is not touching mold metal during transfer. The reheat of the enamel skin or surface takes place (see Figure A-1 .e). The parison elongates after it is uprighted, and ultimately the bottle is blown by a blowing head setting on the top of the blow mold with a slight clearance to the top of the finish (see Figure A-1 .f). After sufficient cooling, the bottle is removed by the take-out tongs to the dead plate (see Figure A-1 .g). This is a fixed plate to receive the bottle , but with a provision for blowing wind on the bottle to further set it up. In most cases the take-out tongs hold the bottle over the dead plate for a fraction of the available time. A push-off from the dead plate to the cross conveyor occurs as the bottle has had sufficient cooling. Figure A-1. Hartford I.S. narrow neck blow and blow process. Pressing From a large tank, gobs of glass are fed in continuous succession into the molds of a rotating press. The mold containing the hot gob is moved beneath a plunger which forces the glass into final shape (see Figure A-2). At the same time another gob of molten glass is being dropped into the following mold. After pressing, the hot formed piece of glass remains in the mold while it passes under cooling streams of air. Then only seconds after the molten glass has left the furnace, the slightly cooled finished piece is automatically transferred to a moving conveyor belt. Details of compression glass molding will be discussed furtherly in chapter three. FINISHED EMPTY MOLD LOADED NOLO GLASS PRESSEO PfECE Figure A-2. Pressed glass. Rolling The molten glass is poured from a pot onto an iron casting table (see Figure A-3). A water-cooled metal roller, is pulled over the glass to flatten it. The surface of the roll may be smooth or cut in various geometric patterns which will then be embossed in the glass. The resulting product is semitransparent, diffuses light, and affords varying degrees of fuzziness, depending on the pattern. The surfaces can have the natural fire polish, from the rolling operation, or can be mechanically grounded and polished, chemically edged, frosted, silvered, or sandblasted. Figure A-3. Ring roll casting machine. Drawing Glass is drawn at speeds up to 40 miles an hour to form tubing and rod for industrial, scientific and home use-piping, laboratory vials, fluorescent and neon tubing and parts for television tubes. Grimshaw (1971) explains the principle of the drawing processes as follows: molten glass, flowing directly from the furnace, passes around a ceramic or metal cone called a mandrel. The glass is then pulled rapidly by a series of pulleys. Air blowing through the center of the mandrel helps maintaining the glass as a continuous tube. The speed of drawing, the glass temperature and amount of air pressure controls the dimensions. Sheet glass, paper thin ribbon glass and some glass fibers are made by a drawing or rolling process. Casting It is a difficult method of glass forming and is usually restricted to large and simple pieces. The molten glass does not have the fluidity of metals and will not flow through small openings or into intricate patterns. It is also easy to trap air bubbles as the glass cools. The largest piece of glass in the world is the 200-inch telescope disk for Mount Palomar, made by Corning Glass Works in 1934 (see Figure A-4). It was made of a low expansion glass to reduce expansion and contraction with changes in temperature, to minimize residual stresses, and to give maximum chemical durability. Figure A-4.200 inch telescope disk cast in 1934. The largest piece of glass ever fabricated. 8 7 APPENDIX B: ANTARES 4.0 INPUT FOR COMPRESSION MOLDING Equipment Ram Hidraulic ram Name: ram1 Ram axis: -Y Velocity function type:Constant Step at: 0 sec Step value: 1 incWsec Deformation stroke: 4 inch Velocity function scale: 1 Load control: off Material steel: ID steel Material type: linear elastic Material properties: Mechanical: Young's modulus: 2.9 E+4 ksi Poison ratio: 2.8 E- 1 Thermal: Conductivity coef.: 1.1572 E-2 BTUIin F s Heat capacity: 3.07 E-2 BTUIcu - in F Thermal expansion: 6.5 E-6 1/Fahrenheit glass: ID glass Relative density: 2.2 Material type: rigid viscoplastic Material properties: Mechanical: Material type: Kcmn K: 2.6 E-4 Ksi C: 0 Ksi M: 1.36 E-1 N: 2.2 E -1 Thermal: Temperature Conductivity Heat Capacity Fahrenheit BTU/in F s BTUIcu-in F 1.22 E+3 1.24 E-3 3.853 E+l 1.292 E+3 1.23 E-3 3.835 E+l 1.472 E+3 1.17 E-3 3.8 E+l 1.652 E+3 1.14 E-3 3.744 E+l 2.012 E+3 1.12 E-3 3.658 E+l Thermal expansion: Temperature Coefficient Fahrenheit 1/Fahrenheit 1.22 E+3 1.8 E-4 1.292E+3 1.8 E-4 1.472E+3 1.8 E-4 1.652E+3 1.8 E-4 2.012E+3 1.8 E-4 Lubricant Name: autolub Friction type: Shear Shear friction coef.: 0.1 Interface heat transfer coef. table: 0 sec 2E-3 Btulsq-in F s 1 2E-3 3 2E-3 4 2E-3 10 2E-3 Boundary conditions CONTACT billet-with-bot CONTACT billet-with-bot SYMMETRY billet-sym SYMMETRY top-die-sym SYMMETRY bottom-die-sym FIX top-die-fix FIX bot-die-fix Initial conditions billet-temp: 1500 Fahrenheit top-die-temp : 1000 Fahrenheit bot-die-temp: 1000 Fahrenheit Assign HYDR-PRESS ram1 TO DIE top-die MATERIAL glass ID glass TO OBJ billet MATERIAL steel ID steel TO OBJ top-die MATERIAL steel ID steel TO OBJ botdie LUBE autolub TO CONTACT billet-with-top LUBE autolub TO CONTACT billet-with-bot CONTACT billet-with-top BETWEEN OBJECT billet AND OBJ top-die CONTACT billet-with-bot BETWEEN OBJECT billet AND OBJ bottom-die SYMMETRY top-die-sym TO OBJ top- die SYMMETRY bottom-die-sym TO OBJ bottom-die SYMMETRY billet-sym TO OBJ billet IC top- die-temp TO OBJ top-die IC bot-die-temp TO OBJ bottom-die IC billet-temp TO OBJ billet FIX bot-die-fix TO OB J bottom-die FIX top-die-fix TO OBJ top-die ELEM-SIZE 0.3 ASP-RATIO 1 TO OBJ bottom-die ELEM-SIZE 0.3 ASP-RATIO 1 TO OBJ billet ELEM-SIZE 0.3 ASP-RATIO 1 TO OBJ top-die ANALYSIS COUPLED TO OBJ billet-1 ANALYSIS COUPLED TO OBJ bottom-die ANALYSIS COUPLED TO OBJ top-die RUN ABSTRACT AMABLE, EDGARDO E. M.S. March 1997 Mechanical Engineering Analysis and Optimization of Compression Glass Molds: Tumbler (92 pp.) Director of Thesis: Bhavin V. Mehta, PhD. Research in the field of glass molds and its effects on the final product has been done in the past based on field experiments with prototypes. Some previous studies have established the need of computer application packages as tools of analysis and comparison of the effect that the changes in mold design. This study proposes the application of computer aided methods to obtain optimized and thermally balanced glass molds. This particular study, as developed, was limited to axissymetrical models, specifically for a tumbler, and was not an exhaustive design for a general manufacturing system, During compression glass molding process, molten glass, at a temperature of around 1050 OF, is compressed between a plunger and a mold. Since the molten glass is almost in a fluid condition, it readily takes the shape of moldlplunger, as it is squeezed between them. During the mass production of glassware products, using compression glass molding technique, the plunger and the mold are exposed to high temperature and pressure conditions. This, coupled with regular normal wear and tear results in the formation of cracks and distortions on the mold and the plunger, which in turn affect the quality of the molded glass part. The molding process can be simulated on computers using various software programs. In this study the models of molding parts were created using IIEMS (Intergraph Engineering Modeling System). Using Finite Element Analysis, the mold bottom and the plungers were subjected to the actual boundary conditions provided by the manufacturer. Thermal stresses developed can be reduced by design optimization, either increasing the surface area of the plunger and the mold or altering the boundary conditions suitably. After carrying out various iterations, an optimized design was obtained where the stress levels are reduced considerably without altering the product significantly. The bottom portion of the plunger was constrained in all three coordinates. Thermal boundary conditions were applied on the surfaces of the plunger. Since the outside surface of the plunger comes in direct contact with the molten glass, a temperature of 1050 OF was applied on the outside surface, whereas a temperature of 200 OF was applied on the inside surface. Moreover, since the plunger is forced into the mold with pressure, a pressure boundary condition of 35 psi was applied to the top surface of the plunger. By varying the thickness of the plunger walls, it was possible to reduce the difference between the highest and the lowest stress values and get more uniform thermal structural stress contours for the plunger. As an initial attempt for fbrther research, an analysis to study the glass forming process and the effects of changing the thickness of the plunger walls in the die fill, was made. It is still necessary to determine strain-stress characteristics of glass at melting temperatures and discuss the effectivity of this approach.