# Computer-aided design in thermoforming.

Computer-Aided Design in Thermoforming

Predicting material allocation for a given shape and optimizing material allocation for that shape can be done more efficiently by means of computer-aided design.

Thermoforming is considered to be one of the oldest plastics processing techniques. Until recently, however, very little has been written on its technical aspects. The process can be considered as consisting of four elements: 1. Sheet heating without sheet stretching. 2. Sheet stretching without additional heat transfer. 3. Sheet cooling while the sheet is held tightly against the tool. 4. Post-molding operations such as trimming, regrinding, and so on.

Since the development of computers, and their application first to extrusion and now to injection molding, blowmolding, and other processes, process and design engineers have come to rely on computer models to provide insight into the interaction of various processing parameters with polymeric material parameters. Recently, thermoformers have begun to develop similar models. This article presents a brief review of the state of the art of computer-aided design in thermoforming.

Modeling

Status of heating. As noted, thermoforming can be conveniently segmented into unique processing elements. Consider first the heating (and cooling) element. Of primary concern in any thermoforming process is the thermal condition of the sheet as it exits the oven. All three modes of heat transfer--conduction, convection, and radiation--are important in heating thermoformable plastic sheet. During the last decade or so, there has been a concerted effort to understand and explain the interrelationships of these modes in the heating of both thin-gage, roll-fed sheet and heavy-gage, cut sheet. One simple criterion that has evolved from this effort is that of the Biot Number, Bi=hL/k. This is the ratio of the amount of environmental energy input to the sheet surface (h being a representative heat transfer coefficient) to the energy conducted from the polymer sheet surface to its centerline (L/k being the ratio of the half-thickness of the sheet to the polymer thermal conductivity). Typically, if Bi is less than 0.1, the energy uptake by the sheet is controlled primarily by the energy input to the sheet surface. This is the case for thin sheet and high-radiant heating. If Bi is greater than 1, however, the heating characteristics of the sheet are controlled by the energy conduction to the interior of the sheet.

The modeling for these two extremes is well understood. For thin-gage sheet, the sheet temperature can be considered as uniform across its thickness. This model is called a Lumped Parameter Model (LPM). For Bi greater than 1, a transient heat conduction model is needed. This is called a Distributed Parameter Model (DPM). These models have been incorporated in relatively straightforward computer programs for predicting one-dimensional temperature profiles in thermoformable sheet.

Status of stretching. The hot sheet is stretched against or onto a rigid surface and held there until the sheet rigidifies. There are two analytical approaches to sheet stretching. Since the sheet is considered imcompressible and initially flat, deformation can be treated geometrically. That is, differential mass balance can be performed as the sheet is differentially drawn onto the mold surface. With appropriate integration techniques, a closed solution can be found for the sheet thickness as a function of the dimensions of the mold. On the other hand, the process can be considered as deformation of an elastic membrane. Finite Element Analysis, developed for solving similar problems, can be applied to this problem to yield similar or identical results. The former approach has been included in the current CAD program in thermoforming.

Current CAD Model Limitations

As with any early development program, the current computer-aided program contains relatively crude approximations and some substantial limitations. Continuing analysis of the process will undoubtedly alleviate many, but some are fundamental to the general thinking of people working to understand the process and thus deserve airing here.

Heat transfer limitations. Until very recently, the arithmetic used to describe energy input to the thermoformable sheet has been one-dimensional. That is, the sheet has been considered infinitely wide compared with its thickness. More important, the incident radiant energy has also been considered to be infinitely planar in nature. Pattern heating as a way of providing more uniform heating to the sheet is an old technique. Shaping the radiant heater output to minimize center-sheet hot spots is relatively new. The actual problem is substantially more complex than this, however. The following factors also influence the energy uptake of the sheet in question: * Sheet emissivity as a function of temperature. * Sheet sag, changing the relative nature of the view factor. * The effect of ramping heater temperatures on the drawdown characteristics of the part. * Changes in adiabatic sidewall temperature. * The possible change in the radiant character of the sheet from specular to diffuse and back again, during the heating step. * The interrelationship of the oven and heaters and the sheet. * The infrared nature of the sheet.

The last two are worth considering in a little more detail. As mentioned, the sheet and oven heaters are usually considered as stationary coplanar, for the most part "seeing" each other. This is satisfactory for heavy-gage, cut sheet, but thin-gage, roll-fed sheet encounters a somewhat different heating environment. For example, there are usually several shots in the oven at one time. Thus, the incoming sheet is directly exposed to the high-temperature heaters, and the exiting sheet is exposed to the cooler entrance section of the oven. This makes the radiant heat transfer problem very difficult. Then, the sheet is not stationary, but it is usually indexed at relatively high velocities for relatively short times. This results in a disturbance of the thermal boundary layer at the surface of the sheet, an effect that can change the rate of heat removal from the sheet to the ambient oven temperature.

So long as the sheet is a monolayer, the energy uptake can be predicted relatively accurately. When multilayer sheet is heated, the difficulty in modeling increases, sometimes substantially. If the sheets are all opaque to the incident radiation, the difficulty is encountered in conduction energy interchange at the layer interfaces. If the surface layers are thin and semitransparent, on the other hand, volumetric radiation absorption and transmissions to interior layers can lead to substantial processing problems, such as delamination, blistering, and pin-holing.

Stretching limitations. The simplest concept in thermoforming is that of draw ratio. The areal draw ratio is frequently quoted as a way of determining the difficulty of drawing sheet of a given material into a mold of a given configuration. By definition, the reciprocal of the draw ratio is the average sheet thickness. Of course, this value does not relate to all the sheet thickness in three-dimensional corners or shallow-draft part bottoms.

The geometrical and FEM approaches discussed above also have limitations. For irregular shapes, the differential geometry arithmetic is so difficult that wall thickness values appear impossible to obtain analytically. For FEM, the mesh size required in drawdown into three-dimensional corners, stiffening ribs, and rims is so fine that very large computer memory and very long computer times are required. Since the ideal designer device is the microcomputer (PC), current FEM techniques are not practical. Moreover, FEM requires reliable equations describing the polymer response to applied load. These constitutive equations are not very well defined today.

Objectives of CAD in Thermoforming

It may seem peculiar to put the objectives of this work here rather than at the beginning of the article, but here they serve to point up the direction taken in the current version of the CAD TF1 program, as well as the focus for future developments. Simply put, there are two general objectives: * Predict material allocation for a given mold shape. * Optimize material allocation for that shape.

It has been pointed out many times that it is wasteful to increase sheet thickness over the entire part when the thickness only needs to be increased on one small region. This is true whether the part is structural or barrier. First, however, it is necessary to know how to predict wall thickness for a given material in a given shape, beginning with planar sheet. Then, given the various processing variables, including temperature, rate of stretching, differential pressure, sheet material parameters (through stress-strain or constitutive equations), and available mechanical and/or pneumatic assists, one must determine how to move material around in order to meet the necessary part design criteria at minimum initial sheet thickness.

The Current CAD Program--IDES TF1 Module

As a first-generation system addressing the objectives of CAD in thermoforming, TF1 provides the user with a means of quickly determining sheet heating times, draw ratios, and wall thickness distributions. Although the calculations are approximate, agreement with experiment has been demonstrated in most cases. Each new generation of software will continue to address the problems faced by processors and designers of thermoformed parts.

A database of materials and relevant properties is built into the TF1 software. Currently, 19 generic material types with properties collected from various sources are included. End-users can easily add new materials as data becomes available. All calculations in TF1 automatically use properties for a selected material in this database.

An additional feature embedded within TF1 provides the user with complete tutorial information on thermoforming processing and part design. The tutorial is provided as a readily accessible reference to concepts used in the calculations.

The software currently "stands alone" and does not interact with an actual part developed by a 3-D modeling system. Eventually though, the system will contain a complete volumetric description of the thermoformed part, thus providing a more accurate basis for calculations. TF1 has been designed to interact with thermoformers in familiar terminology. All values to be input by the user are clearly defined, and characteristic or default values are provided whenever possible.

TF1 sheet heating module. The sheet heating module predicts the temperature for a specific type and size of polymer sheet. Figure 1 is an actual screen print of a typical sheet heating design. The density, specific heat, thermal conductivity, and upper, normal, and lower forming temperatures for ABS in this example are provided from the internal materials database.

The sheet is further characterized by its emissivity and rectangular dimensions. The sheet emissivity of 0.9 used in this example is a default value that is quite accurate for most polymer sheet materials. The remaining input values are usually known for the heater and sheet and can be readily input. One value serves as an illustration of the flexibility of this model. The heat transfer coefficient (h) provides an estimate of the air motion within the heating oven. The default value of 2 Btu/ft hr [degrees] F assumes that the air is nearly quiescent. If, for example, thin-gage, roll-fed sheet is being heated, there may be substantial air motion within the oven because of sheet movement. In this case, larger values of h can be input to determine the relative effect of air motion on the sheet heating profile.

TF1 uses a finite difference scheme to determine the temperature of the sheet during heating. The resulting temperature/time plot for the sheet surface (top curve) and the sheet mid-plane (bottom curve) is shown in Fig. 1. The time of 78 sec is the time for the average sheet temperature to reach the lower forming temperature of 260 [degrees] F. This represents the minimum forming time. The time of 102 sec is the time for the average sheet temperature to reach the normal forming temperature of 295 [degrees] F. This is the recommended time to form. The inputs can be quickly changed to evaluate the relative effects of material properties, sheet thickness, and oven conditions on the heating time.

TF1 draw ratio module. The geometric approach to the determination of draw ratios has been implemented in TF1. Without a doubt, TF1 will require the incorporation of FEM methodologies to allow more accurate prediction of the sheet stretching phenomenon. The current calculations certainly permit the designer to rapidly try "what if" scenarios, however.

TF1 represents 11 simple geometries in the Draw Ratio Module. These geometries are named in the upper right portion of Fig. 2. As a first approximation, the part to be thermoformed can probably be related to one of these geometries. In fact, one approach considers the modeling of more complex parts as hybrids of primary and secondary features, in which each is analyzed as one of the 11 simple shapes. TF1 currently does not assist the designer in separating a given part design into primary and secondary features.

As with the sheet heating module, TF1's material database provides the appropriate properties, as shown in the upper left portion of Fig. 2. In the example shown, the material is ABS, and the maximum areal draw ratio for that material is 5.5.

In Fig. 2, sheet dimensions are input, followed by the percent of rim material in the drawn sheet. This allows for the volume of material not clamped to participate in the drawdown process. The design areal draw ratio is then effectively decreased by the presence of this additional material in the drawn part. Dimensions for the part shape are then input. The design areal draw ratio for the shape in Fig. 2 is quite low, just 13% of the maximum allowable value for ABS. Thus, forming should be relatively easy. A depth of draw ratio of 0.875:1 is determined, as are sheet, finished part, and trim volumes. Design recommendations based on these values are also available.

TF1 wall thickness module. As with the draw ratio module, wall thickness is based on the geometrical approach. The thickness designer will determine the sheet thickness profile for simple shapes. Figure 3 is a screen print of a thickness calculation for the full-cone mold shape. At this point, thickness calculations are material-independent. Work is under way to utilize constitutive equations and FEM to better predict wall thickness for actual part geometries, as noted below.

First Current Focus--Wall Thickness Prediction

The first problem encountered in using the current programs is with wall thickness prediction for irregular shapes. One way of using the current program is to approximate the current part shape with one or more of the regular shapes given in the IDES program. This approach can be used as a "go/no go" concept, particularly if material type and thickness have yet to be determined. It is not a good idea to completely design the part this way, however, because the current program does not provide for prediction of wall thickness in fine details such as ribs, bosses, feet, undercuts, lettering, or rim design.

It appears that neither the geometrical modeling or FEM can be used alone. One approach under development focuses on a combination of these two models. The FEM is considered for the gross deformation or primary forming shape. Geometry is then considered for the fine deformation or secondary forming shape. Thus, FEM will allow determination of the wall thickness of the sheet in the general part shape, where the mesh size can be relatively coarse. The geometrical approach then allows drawdown of the already-thinned sheet into the fine details of the mold, such as three-dimensional corners, ribs, bosses, and so on. Typically, these geometries are similar to the regular or classic shapes given in the literature and in the current CAD program. It appears that maximum draw ratio data or temperature-dependent stress-strain curves, when available, can be used as a measure of maximum stretching of the sheet. The CAD program would then sound an alarm when the sheet was approaching the material limit on deformation.

Second Current Focus--Prestretching

As noted above, material allocation in simple drawdown or stretch-over thermoforming is quantified by geometry. Rearrangement of material in a part wall is done in practice by prestretching the sheet. Two methods are common--pneumatic inflation of the sheet and mechanical stretching of the sheet by pressing a plug into it. Of course, combinations can be and are frequently employed. In both cases, the arithmetic is already in place for modeling the sheet thickness as a function of the degree of stretching. The addition of prestretching criteria to the current CAD program will allow the process or design engineer to assess the limits that can be achieved in optimizing material allocation with prestretching.

Summary This article has touched on some of the elements that go into the development of a useful CAD program for thermoforming process and product design. As with all useful devices, the early attempt is necessarily limited in its application. However, it appears that the information needed to extend this work to a versatile design tool is available, or can be available shortly. This includes shaped radiant heating, ramping of heater temperatures, wall thickness prediction, and the incorporation of certain elements in prestretching. Really difficult design problems, such as semitransparent multilayer sheet, composite sheet, and crystallizing sheet, are set aside for the next generation programming. [Figure 1, 2, and 3 Omitted]

James L. Throne University of Akron Akron, Ohio Michael Kmetz IDES, Inc. Laramie, Wyoming

Predicting material allocation for a given shape and optimizing material allocation for that shape can be done more efficiently by means of computer-aided design.

Thermoforming is considered to be one of the oldest plastics processing techniques. Until recently, however, very little has been written on its technical aspects. The process can be considered as consisting of four elements: 1. Sheet heating without sheet stretching. 2. Sheet stretching without additional heat transfer. 3. Sheet cooling while the sheet is held tightly against the tool. 4. Post-molding operations such as trimming, regrinding, and so on.

Since the development of computers, and their application first to extrusion and now to injection molding, blowmolding, and other processes, process and design engineers have come to rely on computer models to provide insight into the interaction of various processing parameters with polymeric material parameters. Recently, thermoformers have begun to develop similar models. This article presents a brief review of the state of the art of computer-aided design in thermoforming.

Modeling

Status of heating. As noted, thermoforming can be conveniently segmented into unique processing elements. Consider first the heating (and cooling) element. Of primary concern in any thermoforming process is the thermal condition of the sheet as it exits the oven. All three modes of heat transfer--conduction, convection, and radiation--are important in heating thermoformable plastic sheet. During the last decade or so, there has been a concerted effort to understand and explain the interrelationships of these modes in the heating of both thin-gage, roll-fed sheet and heavy-gage, cut sheet. One simple criterion that has evolved from this effort is that of the Biot Number, Bi=hL/k. This is the ratio of the amount of environmental energy input to the sheet surface (h being a representative heat transfer coefficient) to the energy conducted from the polymer sheet surface to its centerline (L/k being the ratio of the half-thickness of the sheet to the polymer thermal conductivity). Typically, if Bi is less than 0.1, the energy uptake by the sheet is controlled primarily by the energy input to the sheet surface. This is the case for thin sheet and high-radiant heating. If Bi is greater than 1, however, the heating characteristics of the sheet are controlled by the energy conduction to the interior of the sheet.

The modeling for these two extremes is well understood. For thin-gage sheet, the sheet temperature can be considered as uniform across its thickness. This model is called a Lumped Parameter Model (LPM). For Bi greater than 1, a transient heat conduction model is needed. This is called a Distributed Parameter Model (DPM). These models have been incorporated in relatively straightforward computer programs for predicting one-dimensional temperature profiles in thermoformable sheet.

Status of stretching. The hot sheet is stretched against or onto a rigid surface and held there until the sheet rigidifies. There are two analytical approaches to sheet stretching. Since the sheet is considered imcompressible and initially flat, deformation can be treated geometrically. That is, differential mass balance can be performed as the sheet is differentially drawn onto the mold surface. With appropriate integration techniques, a closed solution can be found for the sheet thickness as a function of the dimensions of the mold. On the other hand, the process can be considered as deformation of an elastic membrane. Finite Element Analysis, developed for solving similar problems, can be applied to this problem to yield similar or identical results. The former approach has been included in the current CAD program in thermoforming.

Current CAD Model Limitations

As with any early development program, the current computer-aided program contains relatively crude approximations and some substantial limitations. Continuing analysis of the process will undoubtedly alleviate many, but some are fundamental to the general thinking of people working to understand the process and thus deserve airing here.

Heat transfer limitations. Until very recently, the arithmetic used to describe energy input to the thermoformable sheet has been one-dimensional. That is, the sheet has been considered infinitely wide compared with its thickness. More important, the incident radiant energy has also been considered to be infinitely planar in nature. Pattern heating as a way of providing more uniform heating to the sheet is an old technique. Shaping the radiant heater output to minimize center-sheet hot spots is relatively new. The actual problem is substantially more complex than this, however. The following factors also influence the energy uptake of the sheet in question: * Sheet emissivity as a function of temperature. * Sheet sag, changing the relative nature of the view factor. * The effect of ramping heater temperatures on the drawdown characteristics of the part. * Changes in adiabatic sidewall temperature. * The possible change in the radiant character of the sheet from specular to diffuse and back again, during the heating step. * The interrelationship of the oven and heaters and the sheet. * The infrared nature of the sheet.

The last two are worth considering in a little more detail. As mentioned, the sheet and oven heaters are usually considered as stationary coplanar, for the most part "seeing" each other. This is satisfactory for heavy-gage, cut sheet, but thin-gage, roll-fed sheet encounters a somewhat different heating environment. For example, there are usually several shots in the oven at one time. Thus, the incoming sheet is directly exposed to the high-temperature heaters, and the exiting sheet is exposed to the cooler entrance section of the oven. This makes the radiant heat transfer problem very difficult. Then, the sheet is not stationary, but it is usually indexed at relatively high velocities for relatively short times. This results in a disturbance of the thermal boundary layer at the surface of the sheet, an effect that can change the rate of heat removal from the sheet to the ambient oven temperature.

So long as the sheet is a monolayer, the energy uptake can be predicted relatively accurately. When multilayer sheet is heated, the difficulty in modeling increases, sometimes substantially. If the sheets are all opaque to the incident radiation, the difficulty is encountered in conduction energy interchange at the layer interfaces. If the surface layers are thin and semitransparent, on the other hand, volumetric radiation absorption and transmissions to interior layers can lead to substantial processing problems, such as delamination, blistering, and pin-holing.

Stretching limitations. The simplest concept in thermoforming is that of draw ratio. The areal draw ratio is frequently quoted as a way of determining the difficulty of drawing sheet of a given material into a mold of a given configuration. By definition, the reciprocal of the draw ratio is the average sheet thickness. Of course, this value does not relate to all the sheet thickness in three-dimensional corners or shallow-draft part bottoms.

The geometrical and FEM approaches discussed above also have limitations. For irregular shapes, the differential geometry arithmetic is so difficult that wall thickness values appear impossible to obtain analytically. For FEM, the mesh size required in drawdown into three-dimensional corners, stiffening ribs, and rims is so fine that very large computer memory and very long computer times are required. Since the ideal designer device is the microcomputer (PC), current FEM techniques are not practical. Moreover, FEM requires reliable equations describing the polymer response to applied load. These constitutive equations are not very well defined today.

Objectives of CAD in Thermoforming

It may seem peculiar to put the objectives of this work here rather than at the beginning of the article, but here they serve to point up the direction taken in the current version of the CAD TF1 program, as well as the focus for future developments. Simply put, there are two general objectives: * Predict material allocation for a given mold shape. * Optimize material allocation for that shape.

It has been pointed out many times that it is wasteful to increase sheet thickness over the entire part when the thickness only needs to be increased on one small region. This is true whether the part is structural or barrier. First, however, it is necessary to know how to predict wall thickness for a given material in a given shape, beginning with planar sheet. Then, given the various processing variables, including temperature, rate of stretching, differential pressure, sheet material parameters (through stress-strain or constitutive equations), and available mechanical and/or pneumatic assists, one must determine how to move material around in order to meet the necessary part design criteria at minimum initial sheet thickness.

The Current CAD Program--IDES TF1 Module

As a first-generation system addressing the objectives of CAD in thermoforming, TF1 provides the user with a means of quickly determining sheet heating times, draw ratios, and wall thickness distributions. Although the calculations are approximate, agreement with experiment has been demonstrated in most cases. Each new generation of software will continue to address the problems faced by processors and designers of thermoformed parts.

A database of materials and relevant properties is built into the TF1 software. Currently, 19 generic material types with properties collected from various sources are included. End-users can easily add new materials as data becomes available. All calculations in TF1 automatically use properties for a selected material in this database.

An additional feature embedded within TF1 provides the user with complete tutorial information on thermoforming processing and part design. The tutorial is provided as a readily accessible reference to concepts used in the calculations.

The software currently "stands alone" and does not interact with an actual part developed by a 3-D modeling system. Eventually though, the system will contain a complete volumetric description of the thermoformed part, thus providing a more accurate basis for calculations. TF1 has been designed to interact with thermoformers in familiar terminology. All values to be input by the user are clearly defined, and characteristic or default values are provided whenever possible.

TF1 sheet heating module. The sheet heating module predicts the temperature for a specific type and size of polymer sheet. Figure 1 is an actual screen print of a typical sheet heating design. The density, specific heat, thermal conductivity, and upper, normal, and lower forming temperatures for ABS in this example are provided from the internal materials database.

The sheet is further characterized by its emissivity and rectangular dimensions. The sheet emissivity of 0.9 used in this example is a default value that is quite accurate for most polymer sheet materials. The remaining input values are usually known for the heater and sheet and can be readily input. One value serves as an illustration of the flexibility of this model. The heat transfer coefficient (h) provides an estimate of the air motion within the heating oven. The default value of 2 Btu/ft hr [degrees] F assumes that the air is nearly quiescent. If, for example, thin-gage, roll-fed sheet is being heated, there may be substantial air motion within the oven because of sheet movement. In this case, larger values of h can be input to determine the relative effect of air motion on the sheet heating profile.

TF1 uses a finite difference scheme to determine the temperature of the sheet during heating. The resulting temperature/time plot for the sheet surface (top curve) and the sheet mid-plane (bottom curve) is shown in Fig. 1. The time of 78 sec is the time for the average sheet temperature to reach the lower forming temperature of 260 [degrees] F. This represents the minimum forming time. The time of 102 sec is the time for the average sheet temperature to reach the normal forming temperature of 295 [degrees] F. This is the recommended time to form. The inputs can be quickly changed to evaluate the relative effects of material properties, sheet thickness, and oven conditions on the heating time.

TF1 draw ratio module. The geometric approach to the determination of draw ratios has been implemented in TF1. Without a doubt, TF1 will require the incorporation of FEM methodologies to allow more accurate prediction of the sheet stretching phenomenon. The current calculations certainly permit the designer to rapidly try "what if" scenarios, however.

TF1 represents 11 simple geometries in the Draw Ratio Module. These geometries are named in the upper right portion of Fig. 2. As a first approximation, the part to be thermoformed can probably be related to one of these geometries. In fact, one approach considers the modeling of more complex parts as hybrids of primary and secondary features, in which each is analyzed as one of the 11 simple shapes. TF1 currently does not assist the designer in separating a given part design into primary and secondary features.

As with the sheet heating module, TF1's material database provides the appropriate properties, as shown in the upper left portion of Fig. 2. In the example shown, the material is ABS, and the maximum areal draw ratio for that material is 5.5.

In Fig. 2, sheet dimensions are input, followed by the percent of rim material in the drawn sheet. This allows for the volume of material not clamped to participate in the drawdown process. The design areal draw ratio is then effectively decreased by the presence of this additional material in the drawn part. Dimensions for the part shape are then input. The design areal draw ratio for the shape in Fig. 2 is quite low, just 13% of the maximum allowable value for ABS. Thus, forming should be relatively easy. A depth of draw ratio of 0.875:1 is determined, as are sheet, finished part, and trim volumes. Design recommendations based on these values are also available.

TF1 wall thickness module. As with the draw ratio module, wall thickness is based on the geometrical approach. The thickness designer will determine the sheet thickness profile for simple shapes. Figure 3 is a screen print of a thickness calculation for the full-cone mold shape. At this point, thickness calculations are material-independent. Work is under way to utilize constitutive equations and FEM to better predict wall thickness for actual part geometries, as noted below.

First Current Focus--Wall Thickness Prediction

The first problem encountered in using the current programs is with wall thickness prediction for irregular shapes. One way of using the current program is to approximate the current part shape with one or more of the regular shapes given in the IDES program. This approach can be used as a "go/no go" concept, particularly if material type and thickness have yet to be determined. It is not a good idea to completely design the part this way, however, because the current program does not provide for prediction of wall thickness in fine details such as ribs, bosses, feet, undercuts, lettering, or rim design.

It appears that neither the geometrical modeling or FEM can be used alone. One approach under development focuses on a combination of these two models. The FEM is considered for the gross deformation or primary forming shape. Geometry is then considered for the fine deformation or secondary forming shape. Thus, FEM will allow determination of the wall thickness of the sheet in the general part shape, where the mesh size can be relatively coarse. The geometrical approach then allows drawdown of the already-thinned sheet into the fine details of the mold, such as three-dimensional corners, ribs, bosses, and so on. Typically, these geometries are similar to the regular or classic shapes given in the literature and in the current CAD program. It appears that maximum draw ratio data or temperature-dependent stress-strain curves, when available, can be used as a measure of maximum stretching of the sheet. The CAD program would then sound an alarm when the sheet was approaching the material limit on deformation.

Second Current Focus--Prestretching

As noted above, material allocation in simple drawdown or stretch-over thermoforming is quantified by geometry. Rearrangement of material in a part wall is done in practice by prestretching the sheet. Two methods are common--pneumatic inflation of the sheet and mechanical stretching of the sheet by pressing a plug into it. Of course, combinations can be and are frequently employed. In both cases, the arithmetic is already in place for modeling the sheet thickness as a function of the degree of stretching. The addition of prestretching criteria to the current CAD program will allow the process or design engineer to assess the limits that can be achieved in optimizing material allocation with prestretching.

Summary This article has touched on some of the elements that go into the development of a useful CAD program for thermoforming process and product design. As with all useful devices, the early attempt is necessarily limited in its application. However, it appears that the information needed to extend this work to a versatile design tool is available, or can be available shortly. This includes shaped radiant heating, ramping of heater temperatures, wall thickness prediction, and the incorporation of certain elements in prestretching. Really difficult design problems, such as semitransparent multilayer sheet, composite sheet, and crystallizing sheet, are set aside for the next generation programming. [Figure 1, 2, and 3 Omitted]

James L. Throne University of Akron Akron, Ohio Michael Kmetz IDES, Inc. Laramie, Wyoming

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Author: | Throne, James L.; Kmetz, Michael |
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Publication: | Plastics Engineering |

Date: | Sep 1, 1989 |

Words: | 2829 |

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