Computer based models for webs of materials

Methods of using computer based models for simulating the physical behavior of webs.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. provisional application 61/352,099, filed Jun. 7, 2010, which is hereby incorporated by reference.

FIELD

In general, embodiments of the present disclosure relate to computer based models for webs of material. In particular, embodiments of the present disclosure relate to methods of using computer based models for simulating the physical behavior of a web as the web moves and interacts with a contact surface.

BACKGROUND

It can be difficult to predict the physical behavior of a web as the web moves and interacts with a contact surface.

SUMMARY

However, embodiments of the present disclosure can at least assist in predicting the physical behavior of a web. The present disclosure includes methods of simulating the physical behavior of a web as the web moves and interacts with a contact surface. As a result, the web, the contact surface, and the process for moving the web can be evaluated and modified as computer based models before they are tested as real world things.

DETAILED DESCRIPTION

The present disclosure includes methods of simulating the physical behavior of a web. Embodiments of the present disclosure can at least assist in predicting the physical behavior of a web as the web moves and interacts with a contact surface. As a result, the web, the contact surface, and the process for moving the web can be evaluated and modified as computer based models before they are tested as real world things.

Computer aided engineering (CAE) is a broad area of applied science in which technologists use software to develop computer based models that represent real world things. The models can be transformed to provide various information about the physical behavior of those real world things, under certain conditions and/or over particular periods of time. With CAE, the interactions of the computer based models are referred to as simulations. Sometimes the real world things are referred to as a problem and the computer based model is referred to as a solution. There are several major categories of CAE.

Finite element analysis (FEA) is a major category of CAE. In FEA, models representing mechanical articles, as well as their features, components, structures, and/or materials are transformed to predict stress, strain, displacement, deformation, and other mechanical behaviors. FEA represents a continuous solid material as a set of discrete elements. In FEA, the mechanical behavior of each element is calculated, using equations that describe mechanical behavior. The results of all of the elements are summed up, to represent the mechanical behavior of the material as a whole.

Commercially available software can be used to conduct CAE. Abaqus, from SIMULIA in Providence, R.I., and LSDyna from Livermore Software Technology Corp. in Livermore, Calif., are examples of commercially available FEA software. Alternatively, CAE software can be written as custom software. CAE software can be run on various computer hardware, such as a personal computer, a minicomputer, a cluster of computers, a mainframe, a supercomputer, or any other kind of machine on which program instructions can execute to perform CAE functions.

CAE software can be used to represent a number of real world things, such as a web of material. For example, a web can be represented by a computer based model of the web. Thus, CAE can be used to design, simulate, and/or evaluate the features, performance, and/or interactions of the web. This modeling can be used for any kind of web known in the art, including any kind of web disclosed herein.

CAE software can also be used to represent a contact surface, such as the contact surface of a roller. For example, a roller can be represented by a computer based model of the roller. Thus, CAE can be used to design, simulate, and/or evaluate the features, performance, and/or interactions of the roller. This modeling can be used for any kind of roller known in the art, including any kind of roller disclosed herein.

Any and all of the methods of the present disclosure that use computer based models can be represented as program instructions for causing a device to perform a method, and such instructions can be stored on any form of computer readable medium known in the art. Such instructions can also be stored and used as part of a computer-based system.

FIG. 1is a chart illustrating a method100of steps101-104for using computer based models for simulating the physical behavior of a web as the web moves and interacts with a contact surface. Although the steps101-104are described in numerical order in the present disclosure, in various embodiments some or all of these steps can be performed in other orders, and/or at overlapping times, and/or at the same time, as will be understood by one of ordinary skill in the art.

The method100includes a first step101of representing a web of material with a computer based model of at least a portion of the web. The material can be any type of solid material that can move and interact with a contact surface. A web can have various dimensions for its length, width, and thickness.

The model includes a first web contact layer. A contact layer represents a surface of the web. The first web contact layer includes first contact objects. The model also includes a carrier layer with carrier elements. The first web contact layer is joined to the carrier layer. The model can also include a second web contact layer, opposite the first contact layer, with second contact objects. The second web contact layer can also be joined to the carrier layer. In various embodiments, the model of the web can also include additional layers. The model of the web can be created as described in connection with the embodiments ofFIGS. 2E-2H.

The method100includes a second step102of representing a first contact surface with a computer based model of at least a portion of the first contact surface. A contact surface represents a surface of an object that is configured for contact with the web. The contact surface can be any type of solid surface that can interact with a web of material, such as a surface of: a roller, a conveyor, a folding board, a web guide, etc. Contact surfaces can have various sizes and shapes. For example, a contact surface can be convex or concave, with respect to the web. In various embodiments, additional contact surfaces can also be represented.

Prior to or during the third step103, the model of the web and the model of the contact surface can be brought together. In one embodiment, the model of the web can be brought together with model of the contact surface to simulate a real world start-up process, such as the threading of a web over a roller in a machine. In another embodiment, the model of the web can be brought together with the model of the contact surface before the simulation is begun to simulate a real world running condition, after a start-up process has been completed.

The method100includes a third step103of transforming the computer based model of the web from step101, by modeling a physical behavior of the web as the web moves, and as at least a portion of the web interacts with at least a portion of the first contact surface from step102, to form a transformed web. The transforming of the third step103can include one or more of various forms of interaction, such as mechanical interaction, fluid-structure interaction, electrostatic interaction, magnetic interaction, thermal interaction, or other interactions based on various kinds of forces and/or conditions.

In the transforming of the third step103, FEA program instructions can execute to simulate the movement of the web of material from the first step101with respect to a frame of reference and the interaction between the model of the web and the model of the first contact surface of the second step102. However, the present disclosure contemplates that, in an alternate embodiment, part, or parts, or all of the third step103can be performed using another kind of computer based program instructions, as will be understood by one of skill in the art.

The simulation of the third step103transforms the model of the web to form a computer based model that represents a transformed web. The simulation of the third step103deforms the web and changes the position of the web with respect to its frame of reference. The simulation of the third step103is based on boundary conditions.

Boundary conditions are defined variables that represent physical factors acting within a computer based model. Examples of boundary conditions include forces, pressures, velocities, displacements, and other physical factors. Each boundary condition can be assigned a particular magnitude, direction, location, and duration within the model. These values can be determined by observing, measuring, analyzing, and/or estimating real world physical factors. In various embodiments, computer based models can also include one or more boundary conditions that differ from real world physical factors, in order to account for inherent limitations in the models and/or to more accurately represent the overall physical behaviors of real world things, as will be understood by one of ordinary skill in the art. Boundary conditions can act on the model in various ways, to move, constrain, and/or deform one or more parts in the model.

The method100includes a fourth step104of representing the web as it has been transformed by the third step103. The representation of the fourth step104can be provided on a graphical display and/or as an output of data, on a display screen, as electronic data, or in printed form, or in some other way, as will be understood by one of ordinary skill in the art.

In some embodiments of the method100, one or more environmental objects and/or environmental conditions can physically interact with part, or parts, or all of the model of the web of the first step101, as described herein, during the third step103and/or before, during, or after any of the other steps. For example, during the transforming of the third step103, a model of the ambient atmosphere can physically interact with the model of the web.

FIG. 2Ais a side view illustrating a set-up200awith a web of material220moving with a velocity228and interacting with a contact surface216on a roller210as the roller210rotates around an axis212with an angular velocity218.

The embodiment ofFIG. 2Acan be varied in many ways, as will be understood by one of skill in the art. The web220can be any kind of web, in any configuration known in the art, including any configuration described herein. The web can be a continuous piece of material or the web can be a closed loop of material. The web can be any kind of sheet, ribbon, belt, rope, string, strand, or any other kind of web, or a composite of one or more of any of these, joined together in any way. The web can be of any size and shape. The web can be of any length, any width, and any thickness, any of which can be uniform or variable in the machine direction and/or the cross-direction over part, parts, or all of the web. The web can be made of any material. For example, the web can be made of foil, metal, paper, textile, nonwoven, plastic, film, wire, etc. Part, parts, or all of the web can also be made of multiple materials, joined together in any way. For example, the web can be a laminate with a film layer and a nonwoven layer. The surface of the web can be continuous or discontinuous, over part, parts, or all of the web. For example, a web with a discontinuous surface can be a perforated web with holes through its thickness. Part, parts, or all of either or the surfaces of the web can be smooth, or be textured, or can have recesses, or can have protrusions, or any combination of any of these. Any of the variations described above and any other variations known in the art can be combined in any way, with any embodiment of a machine, in any of the embodiments described herein. In an alternate embodiment ofFIG. 2A, the web220can be replaced with anything that can interact with a contact surface.

The roller210can be any kind of roller, in any configuration known in the art, including any configuration described herein. The roller can be driven or undriven. The roller can be any kind of caster, pulley, sheave, wheel, or any other kind of roller. The roller can be a ball roller, cam roller, conveyor roller, guide roller, track roller, web roller, wheel roller, or any other kind of roller. The roller can be of any size and shape. The roller can be of any width and diameter, either of which can be uniform or variable over part, parts, or all of the roller. The roller can be made of any material. For example, the roller can be made of ceramic, metal, plastic, rubber, etc. Part, parts, or all of the roller can also be made of multiple materials, joined together in any way. For example, the roller can be a metal roller with a rubber coating on its roll face. Part, parts, or all of the roller can be hollow or solid. The surfaces of the roller can be continuous or discontinuous, over part, parts, or all of the roller. For example, the roller can have one or more grooves on its surface. Part, parts, or all of the surfaces of the roller can be smooth, or be textured, or can have holes, or can have recesses, or can have protrusions, or any combination of any of these. Any of the variations described above and any other variations known in the art can be used in any way, with any embodiment of a web, and can be combined in any way, within any embodiment of machine, in any of the embodiments described herein. In an alternate embodiment ofFIG. 2A, the roller210can be replaced with any object that has a contact surface.

Throughout the present disclosure, the real-world embodiments are described and illustrated with the web configured as a sheet-like material and the roller configured as a cylindrical roller, however this particular configuration is not required; the web and the roller can each be in any configuration known in the art, including any configuration disclosed herein.

FIG. 2Bis an enlarged view ofFIG. 2A. For clarity, portions of the roller210and portions of the web220are shown as broken away. The roller210has the contact surface216that is spaced apart from the axis212by a radius214. The web220has a first surface221and a second surface229. The first surface221is configured to come into contact with the contact surface216of the roller210as the web220and the roller210move.

The web220has variations in thickness in the machine direction, which is the direction of the travel of the web220. The web220has a first thickness224for most of the web, but the web220also has a thicker portion227with a second thickness226that is greater than the first thickness224. In various embodiments, a web can include one or more thicker portions and/or one or more thinner portions, with variations in the machine direction and/or the cross direction.

FIG. 2Cis a side plan view illustrating a prior art approach to modeling at least a portion of a web of material interacting with at least a portion of a contact surface of a roller, similar to the embodiment ofFIG. 2B, however, in the model ofFIG. 2C, the web has a uniform thickness. For clarity, portions of the roller and portions of the web are shown as broken away. The approach includes a computer based model200cincluding a model of a web240that is moving and interacting with a model of a roller230. The model of the web240includes a layer250. The layer250includes elements250-1through250-9, which are aligned end to end. These elements are offset from the model of the roller230to represent a layer of the material of the web.

FIG. 2Dis an enlarged view of a portion of the prior art approach ofFIG. 2C. The model of the roller230has a contact surface236that is spaced apart from an axis232by a radius234-1. The contact surface236can be configured in various ways. For example, the contact surface236can be configured as one or more rigid objects, one or more analytical rigid surfaces, one or more solid elements, etc. The model of the roller230rotates around the axis232with an angular velocity238.

FIG. 2Dillustrates a side view of a portion of element250-2, element250-3, and a portion of element250-4in the model240. The elements250-1through250-9are shell elements. Each of the elements250-1through250-9is defined by nodes. The element250-3is defined by nodes255-2and255-3and one or more additional nodes (not shown) in the cross-direction, which is perpendicular with the page. The node255-2is offset from the contact surface236by offset distance244-2. The node255-3is offset from the contact surface236by offset distance244-3. In the embodiment ofFIG. 2D, the offset distances are the same and are equal to half of the thickness of the web. As a result, the nodes255-2and255-3are in the midplane of the web.

In the embodiment ofFIG. 2D, if the shell elements of the model of the web240are in traction (no slip) with the contact surface236of the model of the roller230as the model of the roller230is rotating, then each node of the elements will have an instantaneous velocity that matches the instantaneous velocity at the contacting surface236.

For a location on a rotating object, the instantaneous velocity of that location is equal to the angular velocity of the rotation times the distance from that location to the axis of rotation. For a round roller, the instantaneous velocity at the contact surface is equal to the angular velocity times the radius of the roller. So, in the embodiment ofFIG. 2D, the instantaneous velocity at the contact surface236is equal to the angular velocity238times the radius234-1. The instantaneous velocity258-2of the node255-2is equal to this instantaneous velocity at the contact surface236. However, this is an incorrect representation, since it does not account for the offset distance244-2. The nodes of the elements are actually at an effective radius234-2, represented by the circular reference segment255. The effective radius234-2is the radius234-1plus the offset distance244-2. Since the instantaneous velocity258-2of the node255-2is being based on an incorrectly small radius234-1, the instantaneous velocity258-2will be incorrectly smaller than it should be. For a moving web, this incorrect velocity causes an error in the position of the web. As the web moves, this error accumulates over time and can become significant, such that the web becomes improperly positioned, misaligned, and/or out-of-phase with respect to processes, equipment, and/or materials that are joined to the web (e.g. other webs of material).

One possible solution to this problem would be to offset the shell surface from one of the surfaces of the web. Then when the web would be contacting the roller, the roller surface speed and the speed of the shell element at the surface would be matched and accurately represented. However, there is a problem with this approach if another roller contacts the other side of the web, such as with a pair of rollers with an S-shaped thread up of a web. In this case the web surface speed at one of the rollers in the pair would be incorrect.

Another possible solution to this problem would be to increase the radius of the roller to account for the thickness error. That is, the roller radius would be increased by the offset distance. This could work if the web was of uniform thickness, however it would not work in many scenarios in which there are variations in the thickness of the web, either in the machine direction or the cross direction, as it would be very difficult to continuously adjust the radius of the roller to account for this variation.

The embodiments ofFIGS. 2E-2Hdescribe the invention of the present disclosure, which is a better solution to the problem described above. This solution involves creating and using computer based models with contact objects on either or both sides of carrier elements. The contact objects are intended to interact with contact surfaces. These contact objects are located at the surface of the web and are joined, either directly or indirectly, in a defined positional relationship to the mesh of the carrier elements to maintain the proper offset distance. That is, the locations of the nodes of the carrier elements are defined by the locations of the contact objects. As a result, the carrier elements no longer need to contact the contact surface. When the web is in traction with the contact surface, the contact objects in traction will correctly match the velocity of the roller surface. Since the carrier elements are joined to the contact objects, the velocities at the carrier elements are properly represented, regardless of whether or not the web has a uniform thickness, in the cross-direction and/or the machine direction.

The models in the embodiments ofFIG. 2E-2Hare described and illustrated with the web configured as a sheet-like material and the roller configured as a cylindrical roller, however this particular configuration is not required. The model of the web can be any model in any configuration that represents a web, including any configuration disclosed herein. The model of the roller can be any model in any configuration that represents a roller, including any configuration disclosed herein.

FIG. 2Eis a side plan view illustrating a computer based model200erepresenting a portion of the web and a portion of the roller ofFIGS. 2A and 2B. The computer based model200eincludes a model of the web260that is moving and interacting with a model of the roller230. The model of the roller230inFIG. 2Eis configured in the same way as the model of the roller230of the embodiment ofFIG. 2C. The model of the web260includes a carrier layer270and a contact layer280. The carrier layer270includes carrier elements270-1through270-9, which are connected and aligned end to end. The contact layer280includes contact objects280-1through280-9, which are connected and aligned end to end. The contact layer280represents a first surface of the web of material. Together the carrier layer270and the contact layer280form a layer of the material. The model of the web260also has a thicker portion227, which represents the thicker portion227of the web220fromFIG. 2B. The model of the web260represents half of the thickness of the web, as explained below.

FIG. 2Fis an enlarged view of a portion ofFIG. 2E. In the embodiment ofFIG. 2F, the model of the roller230has a contact surface236that is spaced apart from an axis232by a radius234-1. The roller rotates around the axis232with an angular velocity238.

FIG. 2Fillustrates a portion of the carrier layer270, including a portion of carrier element270-2, the carrier element270-3, and a portion of carrier element270-4. SinceFIG. 2Fis a side view, only one side of each of these elements is shown. The carrier elements270-1through270-9are shell elements, however in various embodiments these carrier elements can be one or more other kinds of elements, such as solid elements, membrane elements, truss elements, etc. Each of the carrier elements270-1through270-9is defined by nodes. The carrier element270-3is defined by nodes275-2,275-3and one or more additional nodes (not shown) in the cross-direction, which is perpendicular with the page. The additional nodes define other sides (not shown) of the carrier element.

FIG. 2Falso illustrates a portion of the contact layer280, including a portion of contact object280-2, the contact object280-3, and a portion of contact object280-4. Again, sinceFIG. 2Fis a side view, only one side of each of these contact objects is shown. The contact objects280-1through280-9are contact elements, however in various embodiments these contact objects can be one or more other kinds of objects, such as one or more point clouds, etc. Each of the objects280-1through280-9is defined by nodes. The contact element280-3is defined by nodes285-2,285-3, and one or more additional nodes (not shown) defining other sides of the contact element, as described above.

The nodes285-2and285-3are located on the contact layer280, and these nodes are touching the contact surface236. In the embodiment ofFIG. 2F, if the contact elements of the model of the web260are in traction with the contact surface236of the model of the roller230as the model of the roller230is rotating, then each node on the contact layer280that is touching the contact surface236will have an instantaneous velocity that matches the instantaneous velocity at the contacting surface236. So, in the embodiment ofFIG. 2F, the instantaneous velocity at the contact surface236is equal to the angular velocity238times the radius234-1. The instantaneous velocity278-1of the node285-2on the contact layer280is equal to this instantaneous velocity at the contact surface236. Since the node285-3is also touching the contact surface236, the node285-3has the same instantaneous velocity as the node285-2. In various embodiments, the model of the web260can also include a second contact layer on the opposite side of the carrier layer270, configured in the same way as the first contact layer280, for contacting one or more other contact surfaces on that opposite side, as will be understood by one of ordinary skill in the art.

The contact layer280is joined to the carrier layer270. The carrier layer270is offset from the contact layer280, to maintain the proper offset distance between the carrier layer270and the contact surface236. This offset distance is set between the layers' corresponding nodes.

The nodes275-2and275-3are located on the carrier layer270. For node275-2, the proper offset distance, as measured to its corresponding node285-2, is the offset distance264-2. Since the node285-2is touching the contact surface236, the node275-2is offset from the contact surface236by the offset distance264-2. For node275-3, the proper offset distance, as measured to its corresponding node285-3, is the offset distance264-3. Since the node285-3is touching the contact surface236, the node275-3is offset from the contact surface236by the offset distance264-3. In the embodiment ofFIG. 2F, the offset distances264-2and264-3are the same. However, in various embodiments, the offset distances of the nodes of a carrier element may differ.

In the embodiment ofFIG. 2F, the offset distances are equal to half of the thickness of the web. As a result, the nodes275-2and275-3are in the midplane of the web. However, in various embodiments, one or more of the offset distances of the nodes of a carrier element may be selected to be one or more other particular values.

The nodes275-2and275-3are at an effective radius234-23, represented by the circular reference segment275. The effective radius234-23is the radius234-1plus the offset distance264-2or264-3. In the embodiment ofFIG. 2F, in the traction condition, for each node on the carrier layer270that has a corresponding node on the contact layer280touching the contact surface236, that node on the carrier layer270will have an instantaneous velocity that is equal to the angular velocity238times its effective radius. The instantaneous velocity278-2of the node275-2is equal to the angular velocity238times the effective radius234-23. Since the nodes275-2and275-3are at the same effective radius234-23, the nodes275-2and275-3have the same instantaneous velocity278-2. This is a correct representation, since it accounts for the offset distances264-2and264-3. As a result of the modeling approach of the embodiment ofFIG. 2F, the velocities at the carrier elements are properly represented.

FIG. 2Gis a variation ofFIG. 2E, with the web220in a different position. InFIG. 2G, the web220has advanced so the thicker portion227of the web220is in contact with the contact surface236of the roller230. Since the web220has advanced, different elements are shown for the portions of the carrier layer270and the contact layer280.

FIG. 2His an enlarged view of a portion ofFIG. 2G.FIG. 2Hillustrates the same general relationships illustrated inFIG. 2F, except that different elements are shown. On the carrier layer270, a portion of carrier element270-6, the carrier element270-7, and a portion of carrier element270-8are shown, with carrier element270-7having nodes275-6and275-7. On the contact layer280, a portion of contact element280-6, the contact element280-7, and a portion of contact element280-8are shown, with contact element280-7having nodes285-6and285-7. The nodes285-6and285-7are touching the contact surface236. The node275-6is offset from its corresponding node285-6and from the contact surface236by offset distance264-6. The node275-7is offset from its corresponding node285-7and from the contact surface236by offset distance264-7. In the embodiment ofFIG. 2H, the offset distances264-6and264-7are the same.

In the embodiment ofFIG. 2H, if the contact elements of the model of the web260are in traction with the contact surface236of the model of the roller230as the model of the roller230is rotating, then an instantaneous velocity278-3of the node285-6on the contact layer280is equal to the instantaneous velocity at the contact surface236. Since the node285-7is also touching the contact surface236, the node285-7has the same instantaneous velocity as the node285-6.

Since the elements inFIG. 2Hrepresent part of the thicker portion227of the web, the offset distances264-6and264-7are larger than the offset distances264-2and264-3. Thus, the nodes275-6and275-7are at a larger effective radius234-67. In the embodiment ofFIG. 2H, in the traction condition, for each node on the carrier layer270that has a corresponding node on the contact layer280touching the contact surface236, that node on the carrier layer270will have an instantaneous velocity that is equal to the angular velocity238times its effective radius. The instantaneous velocity278-4of the node275-6is equal to the angular velocity238times the effective radius234-67. Since the nodes275-6and275-7are at the same effective radius234-67, the nodes275-6and275-7have the same instantaneous velocity278-4. This is a correct representation, since it accounts for the offset distances264-6and264-7. As a result of the modeling approach of the embodiment ofFIG. 2H, the velocities at the carrier elements are properly represented, even though the web does not have a uniform thickness in the machine direction.

FIG. 3Ais a side plan view illustrating a computer based model300aof the present disclosure representing a portion of a web having varying thickness in the machine direction with a model of the web360having a carrier layer370and two contact layers380and390, wherein the model of the web300ais moving and interacting with a model of a roller330. The parts of the model360are configured in the same way as the like-numbered parts in the model260of the embodiment ofFIG. 2F, but with the addition of the second contact layer390, which is configured in the same way as the first contact layer380, but on the opposite side of the carrier layer370. The model of the roller330is configured in the same way as the model of the roller230of the embodiment ofFIG. 2F. By having a contact layer on each side, the model of the web360can appropriately contact one or more contact surfaces on either side and/or both sides of the web, to provide correct velocities in the model of the web360. For example, the model of the web360can be used in a scenario where one roller contacts one side of the web and another roller contacts the other side of the web, such as with a pair of rollers with an S-shaped thread up of a web.

FIG. 3Bis a variation ofFIG. 3A, with the web in a different position; part of a thicker portion of the web is shown contacting the roller330. In the position shown inFIG. 3B, the model of the web360can still appropriately contact one or more contact surfaces on either side and/or both sides of the web, to provide correct velocities in the model of the web360.

FIG. 4Ais an end view illustrating a first embodiment of a computer based model400aof the present disclosure representing a portion of a web having varying thickness in the cross direction495with a model of the web460-1having a carrier layer470-1and two contact layers480-1and490-1, wherein the model of the web400ais moving and interacting with a model of a roller430. The parts of the model460-1are configured in the same way as the like-numbered parts in the model360of the embodiment ofFIG. 3A, but with variation in thickness in the cross-direction495, wherein the variation in thickness is on the side of the web that is not contacting the roller. The model of the roller430inFIG. 4Bis configured in the same way as the model of the roller330of the embodiment ofFIG. 3A. As with the model300aofFIG. 3A, the model400aofFIG. 4Acan appropriately contact one or more contact surfaces on either side and/or both sides of the web, to provide correct velocities in the model of the web460-1.

FIG. 4Bis an end view illustrating a second embodiment of a computer based model400bof the present disclosure representing a portion of a web having varying thickness in the cross direction495with a model of the web460-2having a carrier layer470-2and two contact layers480-2and490-2, wherein the model of the web400ais moving and interacting with a model of a roller430. The parts of the model460-2are configured in the same way as the like-numbered parts in the model360of the embodiment ofFIG. 3A, but with variation in thickness in the cross-direction495, wherein the variation in thickness is on the side of the web that is not contacting the roller. The model of the roller430inFIG. 4Bis configured in the same way as the model of the roller330of the embodiment ofFIG. 3A. As with the model300aofFIG. 3A, the model400bofFIG. 4Bcan appropriately contact one or more contact surfaces on either side and/or both sides of the web, to provide correct velocities in the model of the web460-2.

Each of the computer based models described herein can be created as described below, with general references to a computer based model. A computer based model that represents a web or a contact surface can be created by providing dimensions and material properties to modeling software and by generating a mesh using meshing software.

A computer based model can be created with dimensions that are similar to or the same as dimensions that represent parts of a real world object or structure. These dimensions can be determined by measuring actual samples, by using known values, or by estimating values. Alternatively, a model can be configured with dimensions that do not represent a real world object or structure. For example, a model can represent a new variation of a thing or can represent an entirely new thing. In these examples, dimensions for the model can be determined by varying actual or known values, by estimating values, or by generating new values. The model can be created by putting values for the dimensions of parts of the object or structure into the modeling software.

The computer based model can be created with material properties that are similar to or the same as material properties that represent a real object or structure. These material properties can be determined by measuring actual samples, by using known values, or by estimating values. Alternatively, a model can be configured with material properties that do not represent reality. For example, a model can represent a new variation of a thing or can represent an entirely new thing. In these examples, material properties for the model can be determined by varying actual or known values, by estimating values, or by generating new values.

The computer based model of the absorbent article can be created with a mesh for the parts of the article. A mesh is a collection of small, connected polygon shapes that define the set of discrete elements in a CAE computer based model. The type of mesh and/or the size of elements can be controlled with user inputs into the meshing software, as will be understood by one of ordinary skill in the art.