Itzchak, Zhao
Li, Greenwood
Kurt
Itzchak, Zhao
Li, Greenwood
Kurt
| 1. | A method of designing a flat structure which may be opened up to produce a three dimensional macrostructure comprising the steps of : defining the macrostructure; calculating steps for flattening the macrostructure which do not involve stretching any part of said macrostructure; and selecting an optimal set of steps using a predetermined set of criteria. |
| 2. | A method according to claim 1 in which the three dimensional macrostructure is a preform. |
| 3. | A method according to claim 1 or claim 2 in which the method is performed on a computer. |
| 4. | A method according to any one of the previous claims in which the criteria for selecting the optimal set of steps comprise: matching of the width of the flat structure with the reed width of the loom on which said flat structure is to be woven; rejection of sets of steps resulting in a woven structure comprising a number of layers that exceed a predetermined limit; and uniformity in the number of layers of the woven structure across the width of the structure. |
| 5. | A method according to any of the previous claims in which, in the event that no acceptable pathway is computed, the method is repeated using a three dimensional macrostructure rotated with respect to the previously employed macrostructure. |
| 6. | A method according to any of the previous claims, further comprising the steps of : creating a database defining the three dimensional macrostructure; dividing the macrostructure into a plurality of horizontal baselines and connecting sections connecting adjacent baselines; calculating sets of steps for flattening the macrostructure by successively calculating the results of merging the uppermost baseline with the adjacent lower baseline to produce a new uppermost baseline, the merging comprising computing the effect of rotating a connecting section about the point of contact with said lower baseline so said section is colinear with said lower baseline, and rejecting said merging if any connecting section is stretched during said merging and calculating steps for flattening corresponding to a compression of the three dimensional structure in the vertical direction if all of the sets of steps or steps calculation from rotation of the connecting sections are rejected. |
| 7. | A method of weaving flat structure which may be opened up to produce a three dimensional macrostructure comprising the steps of : deteπnining a sequence of shedding motions that enables at least one pick to be inserted into each section of said structure; determining additional shedding motions that may be required to achieve the desired weft density; deteπnining any additional shedding motions that may be required to accommodate the desired fabric weave; linking the combinations of shedding motions to generate a final weave pattern; and weaving the structure using said final weave pattern. |
| 8. | A method according to claim 7 in which the three dimensional macrostructure is a preform. |
| 9. | A method according to claim 7 or claim 8 in which the determination of the sequence of shedding motions that enable at least one pick to be inserted into each section of the structure comprises calculating possible combinations of said shedding motions, selecting as an optimal combination the combination that produces the most uniform weft density and, further, provides the most coherence to the structure, and selecting a suitable sequence of shedding motions from said optimal combination. |
| 10. | A method according to claim 9 in which the determination of additional shedding motions required to achieve the desired weft comprises identifying the sections requiring additional weft, calculating combinations of shedding motions that supply the required weft to said sections and selecting an optimal combination that maximises the coherence of the structure. |
| 11. | A method according to any one of claims 7 to 10 in which a computer is employed to calculate the final weave pattern and to control the weaving process. |
| 12. | A method according to claim 11 in which the weaving is performed on a conventional loom. |
This invention relates to weaving of three dimensional macrostructures, in particular preforms for use in textile composites.
The use of composites consisting of resins reinforced by woven fabrics is of widespread and expanding importance in the field of textiles, due to the combination of high strength and light weight possessed by these structures.
Before impregnation with resin, the reinforcing fabric must be formed into the shape of the ultimate product, and in this precursor configuration it is referred to as a preform. There are drawbacks with the currently employed methods of preform manufacture, since the creation of preforms from conventional fabrics is a costly manual process, the alternative thus far being direct weaving of the preform on specially developed, high specialised and very costly machines. These problems are in essence due to the fact that the ultimate shape of the preforms is 'three dimensional', in the sense that the thickness of the preform is of similar magnitude to the width thereof. (Structures such as preforms described herein as 'three dimensional macrostructures' are not to be confused with products commonly referred to as three dimensional fabrics, the latter being very thick fabrics whose thickness nevertheless is small compared to the width thereof- such a fabric may, for example, be 10mm thick and 1000mm wide.)
The aim of the present invention is to provide a method of weaving three dimensional macrostructures in a cost effective manner on conventional looms. A
particularly important application is in the weaving of three dimensional preforms. The method circumvents the problem of producing a three dimensional macrostructure directly by permitting the weaving of a two dimensional (e.g. flat) structure which becomes a three dimensional macrostructure following the removal from the loom and the opening up or unfolding of the structure. Previously this "opening up" methodology has been applied only to extremely simple macrostructures such as sacks; the present invention enables much more complicated macrostructures to be produced in a systematic manner.
According to one aspect of the invention there is provided a method of designing a flat structure which may be opened up to produce a three dimensional macrostructure comprising the steps of
defining the macrostructure; calculating steps for flattening the macrostructure which do not involve stretching any part of said macrostructure; and selecting an optimal set of steps using a predetermined set of criteria.
The three dimensional macrostructure may be a preform.
The method may be performed on a computer and the flat structure may subsequently be woven on a conventional loom.
The criteria for selecting the optimal set of steps may comprise:
matching of the width of the flat structure with the reed width of the loom on which said flat structure is to be woven; rejection of sets of steps resulting in a woven structure comprising a number of layers that exceed a predetermined limit; and uniformity in the number of layers of the woven structure across the width of the structure;
In the event that no acceptable pathway is computed, the method may be repeated using a three dimensional macrostructure rotated with respect to the previously employed macrostructure.
The method may further comprise:
creating a database defining the three dimensional macrostructure; dividing the macrostructure into a plurality of horizontal baselines and connecting sections connecting adjacent baselines; calculating sets of steps for flattening the macrostructure by successively calculating the results of merging the uppermost baseline with the adjacent lower baseline to produce a new uppermost baseline, the merging comprising computing the effect of rotating a connecting section about the point of contact with said lower baseline so said section is colinear with said lower baseline, and rejecting said merging if any connecting section is stretched during said merging and calculating steps for flattening corresponding to a compression of the three dimensional structure in the vertical direction if all of the sets of steps or steps calculated from rotation
of the connecting sections are rejected.
According to a second aspect of the invention there is provided a method of weaving a flat structure which may be opened up to produce a three dimensional macrostructure comprising the steps of:
deter-i-ining a sequence of shedding motions that enable at least one pick to be inserted into each section of said structure; determining additional shedding motions that may be required to achieve the desired weft density; determining any additional shedding motions that may be required to accommodate the desired fabric weave; linking the combinations of shedding motions to generate a final weave pattern; and weaving the structure using said final weave pattern.
The three dimensional macrostructure may be a preform.
The determination of the sequence of shedding motions that enable at least one pick to be inserted into each section of the structure may comprise calculating possible combinations of said shedding motions, selected as an optimal combination the combination that produces the most uniform weft density and, further, provides the most coherence to the structure, and selecting a suitable sequence of shedding motions from said optimal combination.
The determination of additional shedding motions required to achieve the desired weft density may comprise identifying the sections requiring additional weft, calculating combinations of shedding motions that supply the required weft to said sections and selecting an optimal combination that maximises the coherence of the structure. The desired weft density across the structure may be uniform.
A computer may be employed to calculate the final weave pattern and to control the weaving process. The weaving may be performed on a conventional loom, and this loom may be a shuttleloom or a shuttleless loom-
Methods in accordance with the present invention will now be described with reference to the accompanying drawings in which:-
Figure 1 shows a first macrostructure with three baselines;
Figure 2 shows a macrostructure with two connectors sloping in the same direction;
Figure 3 shows a macrostructure with two connectors sloping in opposite directions;
Figure 4 shows the flattened structure of Figure 2;
Figure 5 shows the system structure;
Figure 6 shows the flattening and weave pattern software architecture;
Figure 7 shows additional three dimensional macrostructures;
Figure 8 shows a second macrostructure with three baselines;
Figure 9 shows the structure of Figure 8 after flattening;
Figure 10 shows all possible shuttle paths for the flattened structure;
Figure 11 shows acceptable combinations of shuttle paths;
Figure 12 shows sections needing additional shuttle paths and possible additional shuttle paths;
Figure 13 shows the target macrostructure;
Figure 14 shows the flattened structure;
Figure 15 shows all possible shuttle paths for the flattened target structure; and
Figure 16 shows all possible additional shuttle paths for uniform weft density;
1. Flat Structure Design
The first aspect of the present invention provides a method of converting the original, three dimensional macrostructure into a design which is flat enough to be woven on a conventional loom. This process is hereinafter referred to as the flattening of the structure. The macrostructures described herein consist in cross-section entirely of straight lines, and are fully defined by said cross-section since the macrostructures do not change along the warp direction. The term 'macrostructure' therefore can be, and is, freely used herein, but it should be noted that strictly speaking it is the cross-section which is referred to.
Macrostructures which do change along the warp direction, for example, macrostructures that taper along the warp direction, are within the scope of the invention. The three dimensional macrostructure may be a preform.
The method is preferably performed using software, whose architecture is described below.
1.1 Modelling the Macrostructure
A macrostructure as defined above consists of a number of points called nodes which are connected by straight lines called sections. These lines represent the fabric elements. A macrostructure is only fully defined if the x and y coordinates of the nodes and the sections connecting these nodes are known.
With, for example, a three dimensional textile preform, there are many ways to flatten it into a two dimensional shape since the material can be bent, extended and sheared.
However, for the purposes of the method developed here, it is useful to initially assume that the sections included in the macrostructure are rigid bodies.
Therefore, in the first instance, an attempt is made to keep all sections straight and of constant length throughout the flattening or deformation process. The assumption of section rigidity also implies that changes in the orientation of individual sections will only occur at a node. As described more fully below, it is possible in this manner to initially treat the flattening process at first as a problem in solid mechanics, and to introduce the textile character of the macrostructure only when the former approach breaks down and folding of individual sections becomes necessary.
The completely mechanical approach is adequate for all macrostructures consisting of sections which are orientated in only two directions. This is the case with a very large number of preforms used in practise, where typically sections are in horizontal and vertical configurations. Therefore the mechanical approach is valid for a large number of applications.
1.2 Methodology of Flattening
1.2.1. General Concepts of Flattening
In the programming of the flattening procedure the x and y directions are (as usual) the horizontal and vertical direction respectively which, when applied to the fabric in the loom, means that the weft runs in the x-direction.
Horizontal lines are drawn through all nodes where two or more sections meet and these lines are referred to as "baselines". A baseline which coincides with one or more sections of the structure is a real baseline. Where this is not the case it is a virtual baseline. No baselines are drawn through nodes from which only one section emanates because the flattening of such sections can be achieved by direct rotation and requires no additional procedure. Where a virtual baseline crosses a section, a new node is created. The lowest baseline coincides with the x-axis. Sections which connect adjacent baselines are called connectors. During flattening, all connectors undergo some deformation which may be a simple rotation or a rotation combined with a folding. Therefore the space between adjacent baselines is hereinafter called "a level of deformation".
The actual flattening is the process of merging all baselines with the x-axis. This can be done in a variety of ways and the criteria by which the flattening procedure is selected are discussed below.
The division of the macrostructure into separate levels of deformation makes it possible to deal with the individual levels one by one. Thus, one can first merge the highest baseline with the second highest one and then the latter with the next etc.
During the flattening process, each connector is linked to the upper and
lower baseline of the related level of deformation by a node and this link cannot be broken. Where the baseline is real, it is physically impossible to break the link. Where the baseline is virtual, it would be physically possible to break the link but for the purpose of the program it is assumed that this kind of link too is unbreakable. It is further assumed that during flattening the baselines remain straight and horizontal and that, at any particular level of deformation, the lower baseline remains stationary while the upper baseline moves downwards to merge with it.
From these concepts, it follows that during flattening all the nodes on the same baseline do not change their distance from each other. However, each pair of nodes situated at the top and bottom ends of a particular connector may or may not change their distance. The distance between the nodal pair does not change if the connector remains straight during flattening and merely rotates with the lower node as pivot. In relation to such a connector and all other connectors parallel to it, the mechanical approach can be applied.
The movement of a connector which is flattened in this manner fully determines the movement of all other connectors (i.e. the movement of their upper nodes). Therefore such an apparently rigid connector is called the "driver" and the other connectors on the same level are called "followers".
As long as all connectors are parallel, it is immaterial which of them is regarded as the driver. It becomes important, however, if some or all followers are not parallel to the driver. In this instance, the follower movement is still determined by the driver and, therefore, as the driver rotates to merge with the lower baseline the distance
between upper and lower end nodes change. Clearly, under these conditions the mechanical approach breaks down. If the distance becomes smaller the followers cannot remain straight and must be folded. If the distance becomes larger the followers would have to be stretched, an impossibility within a rigid body assumption and, in reality, only feasible to a very limited extent with the fibres generally employed in preforms. Therefore, in this latter situation, flattening is impossible. The stretching condition may be avoided by selecting as driver the longest connector on each level and by rotating said connector in the direction of the acute angle between said connector and the corresponding lower baseline.
1.2.2. Application of General Concepts to Software Design
The general approach outlined above is used in developing the methodology in a step by step process as follows:-
a) Reading in of the database
When the desired macrostructure has been fed to the computer, a database is created where each section is defined by the Cartesian coordinates of the end nodes.
b) Discretisation of the macrostructure
The macrostructure is divided into separate levels of deformation by the creation of horizontal baselines. Each node with a different y coordinate is checked out
and stored in an array Y (i) where i=l,2 n. For each of these y coordinates, the horizontal sections are identified and if no actual horizontal section exists a virtual one is added. The added horizontal section is connected to any section it crosses with a new mode. The new sections and nodes are then treated in the same way as all other sections and nodes.
The example shown in Figure 1 consists of 8 nodes, 1-8, connected by 12 sections. The nodes have three different y coordinates, and therefore three baselines 9-11 are drawn. The highest and lowest baseline are real since they contain actual sections. The middle baseline 10, however, is virtual since it does not contain a real section. Thus, the whole macrostructure has three baselines and two levels of deformation.
c) Identification of baselines and connectors
Each connector is allocated to a lower baseline, and the information on baselines and connectors in each level is stored in two two-dimensional arrays for the baselines and connectors respectively.
d) Checking the length and orientation of the connectors
By analysing the length and orientation of each connector, the computer creates the basis for selecting the driver and the direction of its rotation during flattening.
e) Selection of the driver and direction of rotation
The principle on which the selection of the driver by the computer is based is explained by reference to figures 2 and 3 which show one level of deformation with two connectors, 20, 22 of different length. In Figure 2, both connectors slope in the same direction while in Figure 3 they slope in opposite directions. In both figures, either connector will be considered as a possible driver. The rotation of the driver can be either downward through an acute angle or upward through an obtuse angle. The rotation of the driver about its lower node determines the movement of the upper node of the follower. When the driver is vertical the slope and direction of rotation of said driver are taken to be the same as those of the follower.
Whether a particular combination of driver and direction of rotation is acceptable depends upon its effect on the distance between the upper and lower node of the follower. If that distance remains unchanged or decreases, the combination is acceptable. If it decreases, the combination is unacceptable because it would stretch and break the follower. The changes in distance which have to be considered may only be transient during the actual rotation or they may be permanent when the rotation of the driver is completed. In either case, the same criteria apply. Tables 1 and 2 list all the possible combinations for the two cases shown in Figures 2 and 3. The driver is identified as being either the longer or the shorter of the two connectors. The classifications of "acceptable" or "unacceptable" are based on the above principles and on the application of geometry.
Driver Direction of Rotation Acceptable? longer downward yes longer upward no
shorter downward no shorter upward yes
Table 1. Connectors sloping in the same direction.
Driver Direction of Rotation Acceptable? longer downward yes longer upward no shorter downward yes shorter upward no
Table 2. Connectors sloping in opposite directions.
Although these two tables consider only two connectors per level, they apply to levels with any number of connectors if the terms "Longer" and "Shorter" are replaced by "Longest" or "Shortest".
The tables show that only the combination of using the longest connector as driver and rotating it downward is applicable irrespective of whether all the connectors slope in the same direction or not. Even in a situation where the use of the shortest driver is acceptable, the use of the longest one has the advantage that it leads to the smallest sideways extension during flattening. Where there are two or more connectors which have the greatest length but which slope in opposite directions and where it is immaterial which one is chosen, some arbitrary criterion is applied for choosing one of the two possible directions. Otherwise, the computer chooses the direction which is preferable
in the light of other criteria.
f) Finding additional nodes created by folding
When the distance between the end nodes of a follower diminishes due to the rotation of the driver, the method of flattening is acceptable but the follower has to be folded and the point where it is folded constitutes a new node. The algorithm for finding the location of this additional node is explained with reference to Figure 4 which shows the structure of Figure 2 in both the original and the flattened form. Flattening is obtained with the longer connector 22 acting as driver rotating downward. Details of the way this figure is obtained in spite of all y-coordinates being zero after flattening are given below in section 1.2.3.
Since the y-coordinates of all nodes after flattening are zero, this analysis only concerns the x-coordinates.
For any particular followers, the parameters involved are:
Ld = length of driver
Xd = X-coordinate of lower node of driver xd 1 = X-coordinate of upper node of driver before flattening Xd" = X-coordinate of upper node of driver after flattening Sd = sideways displacement of driver
Lf = length of follower
Xf = X-coordinate of lower node of follower xf = X-coordinate of upper node of follower before flattening Xf' = X-coordinate of upper node of follower after flattening Sf = sideways displacement of follower
Xa = X-coordinate of additional node due to folding
The rotation of the driver results in its upper node undergoing a sideways displacement given by:
Sd = Xd" - Xd' (1)
The lower node of the driver acts as a pivot, and by definition, the length of said driver remains unchanged. Therefore:
Xd" = Xd + Ld (2) substituting for Xd":
Sd = Xd - Xd 1 + Ld (3)
By definition:
Xf ' = Xf 1 + Sf (4)
Where:
Sf + Sd (5)
Therefore:
Xf '=Xf + Xd - Xd' + Ld (6)
The follower is folded at Xa but the total length thereof is not changed. This condition can be satisfied in one of two ways; either:
(X-Xf) + (X-Xf') = Lf (7a) or
(Xf-X)-r-(Xf"-X) = Lf (7b)
Therefore, either:
X = (Xf+Xf + Lf)/2 (8a)
or:
X=(Xf+Xf"-Lf)/2 (8b) where Xf ' is derived from equation 6.
Therefore each follower can be folded in two directions and the choice of direction of one follower does not in itself deteπriine the direction for the other followers.
g) Merging all the baselines
The methodology described thus far is confined to one level of deformation. In order to flatten the whole macrostructure, all baselines must be merged with the lowest one. The merging procedure may be explained by starting with the highest level of deformation which lies between the highest and the second highest baseline. The flattening of this level of deformation is fully covered by the steps outlined above. As a result of this flattening, however, the second highest baseline acquires not only the additional nodes it receives from the highest baseline but also the new nodes due to folding of connectors.
The merging of the second highest baseline with the third highest one again takes place in accordance with the steps described above but the second highest baseline must carry with it not only the nodes it originally had but all the additional nodes it has acquired from the highest baseline and from folding. The movement of these additional nodes is determined by the choice of driver and the direction of rotation in exactly the same way as the movement of the original nodes. This process is continued until the second lowest baseline is merged with the lowest one. In the course of this process more and more nodes are collected into one baseline until all nodes are in the lowest one. Although the final flattening brings all nodes into the lowest baseline, their separate identity is of the greatest importance when it comes to the selection of shuttle paths and the generating of weaving instructions. This can be seen from Figure 4 where the completely flattened structure is presented in accordance with the principles outlined in section 1.2.3.
The architecture of the software and the overall system of flattening, together with the weave pattern generation scheme described in Section 2 are shown in
Figures 5 and 6.
1.2.3. Representation of Flattened Structure
Obviously complete flattening transforms the whole macrostructure into a straight line, rending impossible the identification by an operator of individual sections on, for instance, a monitor screen. To overcome this difficulty, the flattened structure is displayed in Figure 4 as a slightly distorted structure wherein the x coordinates are all correct, but the y coordinates have small and finite values. Within each level of deformation the pictorial presentation involves three different y values, i.e. the coordinate of the lower nodes, the coordinate of the upper nodes which is an arbitrary value, and the coordinate of the new nodes created by folding, which is half of said arbitrary value.
1.3 Methodology for Selection of Optimal Flattening
The methodology of flattening described above leaves a number of choices to be made with regard to the driver at each level, the direction of rotation at each level and the direction of folding for every follower on every level. Thus, depending on the size and nature of the macrostructure the number of options can be very large and therefore it is necessary to select the optimal ones.
1.3.1. The number of flattening possibilities
The derivation of the number of possibilities is explained by reference to the macrostructure shown in Figure 1. This structure has three baselines (two actual and one virtual) resulting in two levels of deformation.
At the top level, there are four connectors (two vertical and two sloping at 45°). With regard to choice of driver and direction of rotation, there are only two options, i.e. the right hand sloping connector 13 to rotate in the anti-clockwise direction or the left-hand sloping connector 12 to rotate in the clockwise direction. In either case, there are three followers and each of these can be folded in two directions. Thus, the number of possibilities involving the use of a driver is 2 4 = 16 in the top level. All of these, however, result in a certain increase in width which may not be acceptable. The use of a driver (i.e. the keeping straight of one or more connectors) may therefore have to be abandoned. Once it has been abandoned, the theoretical number of possibilities becomes infinitely large. The only practical one, however, is to compress the whole structure vertically and thereby fold all connectors. This still leaves every connector free to fold in either direction so that vertical compression too provides 2 4 = 16 options. Thus, the total number of options on the top level is 2 x 16 = 32.
The situation in the bottom level is the same as in the top one so that this level too provides 32 options.
In general, the number of options for the whole structure (Ns) is given by
Ns = Nl x N2 x N3 Nn (9)
For the structure in Figure 1 Ns = 32 x 32 = 1024
1.3.2. The criteria for optimum flattening
The criteria for optimum flattening of the structure are dependent on the constraints imposed by textile and machine parameters. The nature of the most important constraints are summarised as follows:
a) Loom width: Some flattening procedures increase the width beyond the reed width and must therefore be rejected. Conversely, weaving becomes difficult when the width of the flattened structure is very much less than the reed width. In this case, the flattening procedure which produces the greatest increase in width is the most advantageous.
b) Maximum Number of Layers: Even in cases where all sections of the structure remain straight during flattening, the flattened structure is bound to have more than one layer in some or all parts. The number of layers is increased when one or more sections are folded. The maximum number of layers that can be woven depends largely on the microstructure which affects the thickness of the layers and which is determined by yarn linear density, thread densities in warp and weft and weave.
c) Uniformity of number of layers: When the number of layers varies along the width of the flattened structure, the insertion of weft across the whole structure leads to variations in weft density since the latter varies inversely with the number of layers. Since in most structures uniform weft density is required, the variation in the number of
layers necessitates the insertion of additional weft in the areas with more than the minimum number of layers. For similar reasons, the overall warp density has to vary pro rata with the number of layers in order to keep the warp density in individual sections constant.
d) Edge position of sections: When the shuttle leaves the flattened structure at one side, it should re-enter the structure at the point of exit. When the re-entry point is at a different position, some weft will remain outside the structure either before or after re-entry. This should as far as possible be avoided because the alternative is to trim the excess weft which is wasteful.
If no acceptable flattening procedure emerges after all these constraints are applied, the macrostructure is rotated by 90° or some other angle appropriate to the structure (e.g. 45° or 60°) and the selection process is repeated. There will be cases where the constraints are such that flattening is impossible.
1.4 Additional Structures
A flattened structure, derived from the flattening of a given three dimensional target macrostructure, may also be used to produce many other target macrostructures. For example, the macrostructure 70 derived from flattening of the target structure shown in Figure 1 can also be used to produce the various target macrostructures 71 - 74 shown in Figure 7. The ability to derive a plurality of target macrostructures from one flattened structure represents a substantial addition to the versatility of the present invention.
2. Flat Structure Weaving
This aspect of the invention concerns the weaving process itself, i.e. the way the weft is inserted into the warp. In the weaving of three dimensional macrostructures such as preforms, the traditional shuttle loom offers many advantages over the shuttleless counterparts and therefore exclusive reference is made hereinafter to shuttle weaving. However, it should be noted that other forms of weaving are within the compass of the invention. Therefore, where shuttleless weaving is appropriate, the term "shuttle" can be taken to refer to any weft insertion element such as a projectile, rapier or air jet.
During the weaving process, the actual path of the shuttle is always the same and to obtain a particular structure the position of the warp ends relative to the new pick is varied by means of the shedding motion. For the purpose of analysing and computerising the process, however, it is convenient to assume that the situation is reversed, i.e. that the warp ends remain in the same position from pick to pick and that the desired structure is obtained by varying the path by which the shuttle traverses the warp. For this purpose it is assumed that the warp ends occupy the positions which they have in the flattened structure where the latter is presented in the manner previously described, i.e. with all nodes having the x-coordinates which they would have if the structure were completely flattened but with the y-coordinates having finite values instead of zero, which they would have in the completely flattened state.
The weaving of the three dimensional macrostructure requires a certain combination of shuttle paths and this combination determines the weave repeat in the
warp direction. A weave repeat in the weft direction will only exist if two or more repeats of the same structure are woven in parallel. The required combination of shuttle paths is found in four main stages as follows:
1st stage A combination of shuttle paths is found which covers the whole of the macrostructure by inserting at least one pick into each section. This may lead to different weft densities in different sections.
2nd stage If required, additional shuttle paths are added to obtain whatever weft density is required in each section of the macrostructure.
3rd stage If required, further shuttle paths are added so as to provide each section of the macrostructure with the correct number of picks to accommodate the desired microstructure (fabric weave) by making the number of shuttle paths in each section equal to or a multiple of the fabric weave repeat. For example, for a 2/1 twill this number is equal to 3 or a multiple thereof.
4th stage The weave repeat dictated by the macrostructure is combined with the weave producing the microstructure so as to generate the final weave pattern which determines the shedding sequence.
The shuttle path calculation is conveniently performed using software, which takes advantage of the versatility and speed of modem computers. Further details of the calculation and of the software architecture are described below.
2.1 Definition of the Flattened Structure
The principles applied in the selection of the shuttle paths in accordance with an embodiment of the present invention will be explained with reference to the macrostructure shown in Figure 8, which is also shown in Figure 9 in the flattened form. This macrostructure consists of a large square whose side equals 20 units which is divided into four smaller squares with sides equal to 10 units.
The macrostructure has three baselines and two levels of deformation and on both levels all connectors are parallel to each other so that all of them can remain straight and retain their original length after flattening. This is the case in Figure 9, except that, as has been explained in 1.2.3, this pictorial presentation involves a slight distortion so as to give the three baselines slightly different y-coordinates (instead of zero) while using the correct x-coordinates. In Figure 9 the y-coordinates of the three baselines are 0,1,2. The nodes (n) are numbered from 1 to 9 and the section (s) from 1 to 12.
From this notation the flattened structure can be defined by the two tables shown below. Table 3 shows the coordinates of the nodes and table 4 the start and end nodes of each section. The start node is taken to be the one to the left of the particular section.
No. of node x-coordinate y-coordinate
1 0 0
2 10 1
3 10 1
4 20 2
5 20 1
6 20 0
7 30 2
8 30 1
9 40 2
Table 3. Coordinates of the nodes.
No. of Section Start node End node
1 1 2
2 1 3
3 2 4
4 2 5
5 3 5
6 3 6
7 4 7
8 5 7
9 5 8
10 6 8
11 7 9
12 8 9
Table 4. Start and end nodes of sections
It must be emphasised that the structure is fully defined only by reference to both of these tables since said structure contains several pairs of nodes which could be connected but which are not, eg. nodes 2 and 7 are not connected although a connection is possible. The identity of pairs of nodes which are in fact connected by a section is only apparent with reference to Table 4.
For the purpose of further processing, all x coordinates contained in Table 3 are arranged in an array in accordance with their position in Table 4 and in the following sequence: section 1 (start), section 1 (end), section 2 (start), section 2 (end), etc. The array is denoted by X (i) where
i = l,2 n
and n is the total number of x coordinates, n is twice the number of sections, and is therefore always an even number. In the array based on the above Tables n = 24.
All x coordinates with odd values of i relate to the start of a section while those with even values of i relate to an end.
All the y coordinates are arranged in a similar array Y (i). Thus the arrays of the coordinates of Table 4 are:
X(24) = [0,10, 0,10, 10,20, 10,20, 10,20, 10,2020,30, 20,30, 20,30, 20,30, 30,40, 30,40] and
Y(24) = [0,1, 0,0, 1,2, 1,1, 0,1, 0,0, 2,2, 1,2, 1,1, 0,1, 2,2, 1,2]
In Table 4, and therefore in all the resulting arrays all the values of x and y appear more than once. This is due to the symmetry of the structure shown in Figure 9. In all structures, however, although some coordinates may be unique, there will be some which occur more than once. It is therefore always possible and necessary to construct a different array called "unique (j)" which is defined by: unique(j) = 1,2, m where m is the number of different values of x in the array X(i). Thus the array unique(j) based on Table 4 has five different values of x and is given by:
unique (5) = [0,10,20,30,40]
These arrays form the basis for the subsequent analysis of the structure.
2.2 Feature Analysis
When a flattened structure such as the one shown in Figure 9 is scanned horizontally, it is seen that whenever a node is passed, the number of sections counted in the vertical direction may or may not change. Between the passage of nodes, however, this number always remain the same. Regions between nodes will be referred to hereinafter as areas.
Clearly, no shuttle path can supply weft to more than one section within a particular area. Therefore each section within that area must be supplied with weft by
a different shuttle path. It is therefore necessary to determine the number of such areas in the structure and the number and identity of sections within each area.
2.2.1 The Number of Areas
The flattened shape in Figure 9 can be divided into several areas along the x direction by lines parallel to y axis in the positions of every element of unique (j).
The total number of areas (Ta) is given by:
Ta = m - 1 (10) where m = number of elements in unique (j)
In this example, Ta 5-1 = 4.
The areas are numbered consecutively from left to right and the number of each area is denoted by t where:
t = l, 2 Ta
Ta serves as a basic index of the geometry. Together with unique(j), Ta provides the information as to where the number of fabric layers (sections) or their identity changes. Clearly, the bigger of the value of Ta, the more complicated is the structure.
2.2.2 The Number of Sections per area
The number of sections (Tt) in a particular area is determined by what happens at the left-hand boundary. Here, some sections start and some sections are passed on from the previous area. Tt is given by:
Tt = St + Pt (11) where: St = number of starting sections
Pt = number of passed-on sections
To find the individual values of St, Pt and hence Tt, the computer, beginning from unique (i), searches through the array X(i) and records the number of starting and passed-on sections for each element in unique(j). For the last element, St and Pt are always zero so that the effective number of elements equals m - l which is the number of areas (Ta). The values of Tt are put into a one dimension matrix L(t) with t = l, 2, Ta.
For the structure in Figure 9 the values of St, Pt and Tt are shown in table
5.
Number of area (ft Si Et B
1 2 0 2
2 4 0 4
3 4 0 4
0
Table 5. Number of sections per area.
It follows that:
L(t) = [Tl, T2, T3, T4]
= [2, 4, 4, 2]
2.2.3 Possible Shuttle Paths
In considering the possible shuttle paths, it is necessary to bear in mind that it is the paths of the weft that are referred to . This means that, in the context of the present analysis, a shuttle path can start or end at any node. It can, for instance, reverse direction halfway across the reed width.
As a first step, however, it is proposed to consider only those shuttle paths which start at a start node which is not an end node and which finish at an end node which is not a start node. For the structure shown in Figure 9, the information required for this selection is presented in table 4. The computer is programmed to produce an equivalent table for any structure. Table 4 shows that the only start node which is not an end node is node 1 and the only end node which is not a start node is node 9. Therefore only shuttle paths which start from node 1 and which end at node 9 are considered. The paths themselves are more usefully expressed in terms of the sections which they traverse and this is done in table 6 where the possible shuttle paths for the structure of Figure 9 are presented by columns numbered 1 to 6 and the sections are presented by rows
numbered 1 to 12.
When a particular section forms part of a particular path, this is indicated by a 1. When this is not the case, it is indicated by a 0. The right-hand column shows how many shuttle paths serve a particular section.
Shuttle Path?
Section No. 1 2 3 4 5 6 No, of Paths
1 1 1 1 0 0 0 3
2 0 0 0 1 1 1 3
3 1 0 0 0 0 0 1
4 0 1 1 0 0 0 2
5 0 0 0 1 1 0 2
6 0 0 0 0 0 1 1
7 1 0 0 0 0 0 1
8 0 1 0 1 0 0 2
9 0 0 1 0 1 0 2
10 0 0 0 0 0 1 1
11 1 1 0 1 0 0 3
12 0 0 1 0 1 1 3
Table 6. Distribution of sections over shuttle paths.
Table 6 shows that, for the present example, there are six possible
shuttle paths. Four sections (3,6,7,10) are served by only one shuttle path, four sections (4,5,8,9) by two paths and four sections (1,2,11,12) by three paths. All the possible shuttle paths are shown in Figure 10.
2.3 The Necessary Shuttle Paths
In choosing the combination of shuttle paths which have to be in the weave repeat, various criteria have to be applied. Some of these apply to all preforms and others are specific to particular ones. These criteria are discussed below.
2.3.1 Supplying weft to all sections
Clearly, a structure cannot be complete unless each section receives at least one pick per weave repeat. To meet this requirement, two criteria are applied.
a) All shuttle paths which are the sole supplier of weft to one or more sections must form part of the combination.
b) The number of shuttle paths included in the combination must be at least equal to the maximum number of sections per area.
It follows that the actual number of shuttle paths included in the combination must be the higher one of the two numbers resulting from these two criteria.
With regard to the present example, table 6 shows that shuttle path number 1 is the sole supplier of weft to sections 3 and 7 while shuttle path number 6 is the sole supplier of weft to sections 6 and 10. Therefore, these two shuttle paths must form part of the combination.
Table 5 above shows that the maximum number of sections per area is
Thus, criterion a leads to two shuttle paths while criterion b leads to 4. Therefore the combination must consist of four shuttle paths including paths 1 and 6.
To make up the required number of shuttle paths, two more paths must be chosen from a possible total number of 6 - 2 = 4. The number of combinations of two paths out of four is six.
Table 7 shows the possible combinations of shuttle paths.
No. of combination Shuttle paths in the combination
1 1,2,3,6
2 1,2,4,6
3 1,2,5,6
4 1,3,4,6
5 1,3,5,6
6 1,4,5,6
Table 7. Shuttle path combinations.
All these combinations are examined by the computer and in the present example it is found that only two combinations (3 and 4) supply weft to all sections. Therefore one of these two combinations must be selected. The two combinations are shown in figures 11a and 1 lb.
2.3.2. Selecting the best shuttle path combination
The criteria for selecting the best combination are:-
a) The number of shuttle paths per section should be as uniform as possible resulting in the most uniform weft density. b) The combination of shuttle paths should give maximum coherence to the whole structure.
Applying criterion a to the combinations shown in Figures 11(1) and 11(2) it is found that with both possible shuttle path combinations there are eight sections which are traversed by the shuttle only once and four sections which are traversed twice. Therefore, this criterion does not lead to any preference.
Applying criterion b, however, to these figures, it is found that the combination shown in Figure 1 lb gives better coherence than the one in Figure 11a because, with the latter combination, there is very little connection between the two halves of the structure.
2.3.3. Shuttle path direction and sequence
For weaving, the structure shown in Figure 9 with the combination shown in Figure 1 la, the sequence of shuttle paths within the combination and hence the direction in which the shuttle follows a particular path is immaterial because all paths start and end at the same node and the combination consists of an even number of shuttle paths. This, however, is not the case with all structures and therefore the computer is programmed to select the correct sequence of paths within the combination.
2.3.4. Creating the desired weft density in all sections
The above mentioned example shows that the selected combination of shuttle paths does not necessarily create the same weft density in all sections. In general, this non-uniformity exists when the number of sections per area (Ta) varies. In that case, the weft density varies inversely with the value of Ta.
In some instances this may be acceptable but usually it is not. There may also be cases where the non-uniformity of weft density created by the selected combination is too large but a somewhat lesser non-uniformity is acceptable. The most common demand, however, is for creating the same weft density in all sections. The procedure described herein concerns the last of these cases (completely uniform weft density), although all of said cases may be catered for by the software. To meet this requirement, additional shuttle paths have to be introduced. In selecting these, the procedure is similar to the one described above. At first, all sections needing
additional shuttle paths are found. Then all possible shuttle paths supplying weft to these sections are identified and the number of shuttle paths required to supply weft to all these sections is determined. All possible combinations of that number of shuttle paths are then found and the acceptable and optimal ones are selected.
For the structure in Figure 9 the sections needing additional shuttle paths are shown in Figure 12a while Figure 12b shows the six possible additional shuttle paths. In Figure 12b all sections are indicated by dotted lines except those which are part of the particular shuttle path. The latter are shown by full lines. The number of sections per area is four and therefore a combination of four paths is required. There are two possible combinations of four paths of which one gives better coherence and is therefore selected.
2.3.5 Incorporation of the microstructure (fabric weave .
The analysis described thus far is only concerned with the supply of weft at the desired density to all sections of the macrostructure. It has not concerned itself with the microstructure i.e. with the way the weft will be interlaced with the warp. The latter problem is dealt with in stages as follows :-
a) The fabric weave is selected. b) If necessary, the shuttle path repeat is adjusted to accommodate the weave pattern. c) The programmes for the micro and macrostructure are linked so as to form the detailed weaving instructions.
These steps are illustrated by reference to the structure in Figure 9. For this structure, the analysis up to now has yielded the following data relating to the size of the pick repeat.
No. of Picks Required
To supply weft to each section 4
To obtain uniform weft density 4
Total pick repeat 8
If it was decided to use plain weave in all sections, there would be no need for any further adjustment of the pick repeat because plain weave repeats after two picks and the pick repeat required for uniform weft density already provides two picks in each section.
For microstructures with a four-pick repeat such as a 2/2 twill, 3/1 twill, 2/2 hopsack etc., the overall pick repeat would have to be doubled to sixteen so as to provide four picks for each section.
If it was decided to use a 2/1 twill which repeats after three picks, the number of picks in each section would have to be increased to the lowest common multiple of two and three which is six and this means that the overall pick repeat would have to be trebled to twenty-four.
The linking of the micro and the macrostructure is carried out by the computer in accordance with the general principles of weave design.
2.4. Weaving
The software described above was applied to the weaving of a preform with a H-shaped cross-section, shown in Figure 13. The flattened structure is shown in Figure 14 to consist of four areas where the two outer areas have one fabric layer each and the two inner areas have two layers each.
The weaving particulars were as follows:-
Loom : Dobcross 4 x 4 drop box shuttle loom
Reed width : 120cm
Shedding : Jacquard with 1334 hooks (1200 active hooks)
1 heald per hook Warp: 74tex Cotton, 60cm between beam flanges, 20 ends/cm on the beam, Reed: 5 dents/cm
Denting: 2 ends/dent (10 ends/cm) in the single-layer areas, (alternate ends from the beam were cast out) 4 ends/dent (20 ends/cm) in the two-layer areas. Weft: 480dtex c.f. Polyester Weave: plain Thread densities in each layer : 10 ends/cm, 10 picks/cm
It will be seen from Figure 14 that the flattened fabric occupies one half of the available reed space. When opened up, the cross-section of the preform occupies an area of approximately 30cm x 30cm, a fact which illustrates the truly three-dimensional character of this technology.
The non-uniformity in the number of layers per area (see Figure 14) necessitated special steps to ensure uniform thread densities in all sections and in the warp and weft directions.
With regard to warp density, this was done by preparing a weaver's beam where the overall warp density corresponded to the overall density required in the double layer areas. The reduced warp density required in the single layer areas was obtained by casting out alternate warp ends. A possible alternative would have been to use more than one warp beam.
For the purpose of obtaining uniform weft density, the procedures described in section 2.3 above were used. The shuttle paths which start from nodes which are not end nodes and which end at nodes which are not start nodes are shown in Figure 15 and the additional shuttle paths required for uniform weft density in the double layer areas are shown in Figure 16. It had originally been thought that the rate of cloth take up would have to be reduced while the additional picks were inserted but this proved to be unnecessary. The main difficulties which emerged and which required a considerable amount of development work were caused by the additional picks in the middle areas of the fabric.
The total width of these areas was only one quarter of the total reed width which meant that at the end of each shuttle traverse more weft had to be pulled out of the shuttle than could be consumed at the next pick. This difficulty was overcome by paying the weft out from the middle of the shuttle instead of from one end and - more important still - by designing a novel tensioning system which pulled
the excess weft back into the shuttle.
A further problem arose from the fact that the additional picks pulled the outer edges of the middle areas towards the centre of the loom, thus creating a lengthways gap between each of the middle two areas and its adjacent outer area. This problem was solved by developing a kind of crow-hop for the affected points to take the strain of the additional picks, thus eliminating the sideways pull. To prevent these crow-hops engaging the new pick after insertion, special weft deflectors were developed.
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