Computer simulation for warp-knitted brushed fabric with patterned piles

Abstract

Warp-knitted brushed fabrics are special pile fabrics with uneven and declining piles that consist of broken filament ends. It is difficult to predict the finial pattern of the pile surface in the process of the design of patterned fabric. There are few researches on computer simulation of the fabric because of their complicated and fuzzy characteristic. This paper focuses on computer simulation of this group of pile fabrics. Firstly, the characteristics of warp-knitted brushed fabric and the factors that influence the pile are discussed. Secondly, a simplified line model is proposed to represent the shape of the pile by some lines in a certain titling angle, radial angle and length. A two-dimensional matrix is used to describe the position and color of piles in one pattern repeat. Finally, based on the mathematic model, a program is developed by VC++.NET to realize the simulation of the brushed fabric with a patterned pile. By the input of some parameters that were adjusted according to the craft, the two-dimensional computer simulation of the pile surface was found to be similar to the actual patterned pile fabric. It is proved that the method is feasible and contributes to the development of a computer-aided design system to realize the design and simulation of the warp-knitted brushed fabric.

Keywords

warp knitted brushed fabric patterned pile computer simulation mathematical model

Warp-knitted pile fabrics can be classified into three categories according to different processes. Plush or fleece fabric is produced on a double-needle bar Raschel machine and gray fabric with connected pile yarns is cut into two pieces of pile fabric by a cutting machine.¹ Cut pile fabric is produced by warp-knitted terry fabric.² Both of the mentioned pile fabrics have even and protruding piles. Brushed fabric is normally produced on a Tricot warp-knitting machine with three or four guide bars. The long underlaps of knitted fabric are broken up and raised into piles on a raising machine. Different from the other two kinds of pile fabrics, piles on this brushed fabric are uneven and declining. Due to the high speed of the Tricot machine, the production of brushed fabric is highly efficienct.^3,4 With plump fluff, good dimensional stability and diversity of styles, the brushed fabric has been widely used for automotive interiors, sofa fabric, garment fabric and so on, so it is an irreplaceable product with increasing market demands and great development potential.⁵ A variety of fabric constructions and yarn combinations are employed for producing patterned brushed fabric to make the fabric more attractive. A Tricot machine with four guide bars and an electronic shog device makes the case easier.

Computer-aided design (CAD) and simulation software is a useful tool to help us forecast the construction and pattern of the fabric in the course of design.^6–8 A number of studies have been carried out to simulate pile fabric and some achievements have already been made. Xiuli⁹ developed a method of texture synthesis realistic simulation of pile-knitted fabric. The pile-knitted fabric texture library based on a SQL Server relational database was established, and combined with CAD technology to realize the realistic simulation of pile-knitted fabrics. This method needed to search huge amounts of image information and is not suitable for fabrics not including in the SQL Server. Hui et al.¹⁰ used image processing methods, such as image graining processing and radial blur, to obtain an entire vague image to simulate the brushed state of real objects. Shuangwu et al.¹¹ investigated the technique of true sense effectiveness fabric simulation, which is based on the light model. At the same time, random curves extended from the yarn, simulating the fuzzy effect.

Generally, the methods of fabric simulation include many kinds of modeling building. Xiaogang¹² reviewed the mathematical modeling of different types of three-dimensional (3D) weaves that have been successfully used in developing CAD software for 3D fabrics. Goktepe and Harlock¹³ developed a 3D cylindrical and uniform solid yarn model to create single warp-knit loops and fabrics. Özdemir and Güngör¹⁴ simulated fabric surface appearance from achieved yarn properties based on digital video camera recordings of moving yarns. However, these researches are focused on 3D fabric simulation, which are too complex for warp-knitted brushed fabric. In another work, Guangfeng et al.¹⁵ devised a solution to simulate the color appearance of tufted carpet to preview the final appearance. The simulation started from traversing the control pattern to get the pile height level information and adopted color blocks to represent a single loop pile in the carpet surface. The paper provides a feasible solution of two-dimensional (2D) simulation for loop pile.

Based on the existing researches, it can be summarized that the methods of pile fabric simulation were focused on the image simulation by texture synthesis or image vague, or even on the 3D simulation by building a yarn model or illumination model. These methods are appropriate to simulate ordinary fabrics, even velvet. However, as a possible condition of the Tricot fabrics with raised finish, the piles have certain directions. Nobody has yet focused on the simulation of this special attractive pile fabric and developing an appropriate CAD program. Therefore, the research on warp-knitted brushed fabric simulation is of practical significance.

The characteristics of warp-knitted brushed fabric

The characteristics of pile

The technical back of warp-knitted fabric should have long floats to provide the minimum length suitable for breaking up and brushing into piles. Currently, the majority of pile yarns are polyester multi-filament. The pile yarns are threaded in the front guide bar to form underlaps longer than three stitches on the technical back. Due to the mostly strongest stress on the middle of the underlap in the raising finish, most fibers of pile yarn break from the middle part. The broken multi-filament float then forms two clusters of piles tilting to the lapping direction. The finishing, such as combing and ironing, may erect the piles, but the piles still have some slope. Figure 1 indicates the long underlaps in Figure 1(a), broken underlaps in Figure 1(b) and piles after finishing in Figure 1(c). Uneven height and tilt of the piles are the characteristics of this group of warp-knitted pile fabric. It makes the computer simulation of the fabric more complicated.
Figure 1.
The formation of pile: (a) long underlap; (b) the underlap after raising; (c) the piles after finishing.

Figure 2 shows the sharp of real piles on the patterned brushed fabric. Figure 2(a) shows the colored pile fabric that was produced on the three guide-bar Tricot machine with one full threading pile bar. Figures 2(b) and (c) show two pique and colored pile fabrics with different threading, which were produced on a four guide-bar Tricot machine. Two colored pile yarns are threaded in GB1 (guide bar 1) and GB2 individually, according to a certain rule. It is very difficult to predict the end pile effect of above-mentioned pile fabrics in the course of design.¹⁶ Therefore, the study focuses on the simulation of this group of pile fabric. As shown in Figure 2, piles have been marked and classified into two types. A represents the pile tilting left direction, while B represents the pile tilting right direction. Based on abundant observation and analysis of the pile, the characteristics of the warp-knitted brushed fabric can be summarized as below. Firstly, every pile consists of two clusters of broken filament ends for two feet of every pile loop. The broken filament ends with different lengths radiate from the head of the stitch. Secondly, the pile is not upright, but leaning to the direction in which the underlap is pulled. For example, when the underlap is from right to left, the pile on its right will lean to the left, shown as A, and the pile on its left will lean to the right, shown as B. Thus, piles of adjacent two courses are in different directions. At the same time, the tilting angle is influenced by the loop structure, type of pile yarn and other factors that will be discussed in the next part. Thirdly, there is a positive correlation between the length of the underlap and pile. Generally, the features of pile can be described by several parameters, that is, pile length, pile radial angle, the angle between pile and fabric surface and angle between the pile and stitch course.
Figure 2.
Details of colored pile fabric: (a) full threading; (b) three quarters threading; (c) half threading.

Discussion of influence factors on patterned pile

Due to the fluffy appearance of pile products, there are many factors influencing the pile effect, such as material of the pile yarn, loop structure and finishing.

Material

Polyester multi-filament is usually used in warp-knitted brushed fabric as the pile yarn. The conventional yarns are polyester DTY (drawn textured yarn) and FDY (fully drawn yarn).¹⁷ Due to the different elasticity and bulkiness of the yarns, the piles formed are different, too. Because DTY is textured yarn with curl, the fluffy angle is larger. The fineness of the filament and the number of filaments of pile yarn positively influence the radial angle. The cross-section of the fiber also influences the angle. The profiled cross-section, such as flat, triangular or trefoil, makes bulked piles because there are more interspaces among filaments.

Construction of the fabric

The lapping of the pile bar is the crucial factor to determine the final pile effect.¹⁸ The length and direction of lapping dictate whether underlap can be raised as pile and the shape of the pile, such as length and slope. Long underlap results in long pile, but the long pile easily falls down, with an obvious tilting trend.

The adjacent piles can support each other. More dense pile fabric has more erect piles with fewer slopes. So the rate of threading of the pile bar and the loop density of the fabric determine the density of the pile and hence influence the erection of piles. As shown in Figures 2(a)–(c), with the decrease of the threading rate of pile bar, the slope of the pile increases.

Dyeing and finishing

The gray fabric experienced some processes, such as presetting, raising, dyeing, combing, shearing, ironing and heat-setting, to turn into the end pile fabric. These processes also influence the shape of the pile and further influence the end effect of the fabric.

The temperature in presetting should be controlled to obtain the appropriate stiff fabric for raising high-quality pile. Then six raising machines are arranged in a set to brush the technical back of the fabric and comb the piles. The fabric surface is fluffy and disordered after being raised, so Shearing and ironing processes are generally needed to make the pile more upright. In the ironing process, the fabric goes through a polishing roll under high temperature to make the pile upright, and increases the luster of the fabric. The shearing process can be performed several times according to the height and evenness of the pile.

Warp-knitted brushed fabric simulation model

Pile simulation model

Microscopic observation shows that every filament of the pile is generally linear. Therefore, when building a model, every short line is on behalf of a filament, and the piles are expressed by a cluster of lines within a certain space angle. Taking a 1-0/4-5// float as an example in Figure 3(a), after being brushed, the piles represented by solid lines are distributed like cluster in 3D space, and the dotted lines represent the piles’ projection on the floor plane.
Figure 3.
Pile simulation model: (a) the three-dimensional model of pile; (b) the two-dimensional model of pile.

To get a simple and efficient simulation image, the piles in 3D space are simplified to a 2D model. The pile is projected onto the fabric surface as shown in Figure 3(a) and the angle between the pile and fabric surface is not shown, but the angle will play a role in the simulation of pile length. The 2D simulation model of pile is shown in Figure 3(b), where x represents the course direction, y represents the wale direction and lines in a certain range represent the pile. Two limit positions, OA and OB, are defined as boundaries, and OC is defined as the trunk line of ∠AOB. When it is necessary, OC could represent the whole pile. ∠AOB is the concentrated area of the pile, and within ∠AOB the filaments are random distribution. ∠COD is the angle between the pile and the course, and it is adjustable according to the kind of pile. Finally, it is summarized that in the model the pile has two angles: the radial angle α(∠AOB) of the pile cluster and the tilting angle β(∠COD) between the pile and the course.

Pile parameters and their settings

Factors such as pile angle, pile length and pile density need to be determined in pile simulation. Information including fabric density, raw materials, pattern height and width, lapping and threading, etc., can be obtained from the fabric parameters. Taking advantage of the information and the general mathematical model of warp-knitted brushed fabrics, some calculations and discussions on parameters needed in simulation are as follows:

Pile angle

As mentioned in the pile simulation model, the pile angle includes the angle between the pile and fabric surface, the angle β between piles and course and the radial angle α of the pile cluster.

The angle between the pile and fabric surface is mainly controlled by raised, combing and ironing finishing. The angle between the pile and fabric is generally in the range of 20°–80° as a matter of experience.

Because of the influence of the finishing process, the angle β between the pile cluster and course needs a correction factor a, as shown in Equation (1):
$β = a \cdot \arctan \frac{P A}{P B \cdot UL (k, j)}$
(1)
where P_A is latitudinal density (wales/cm), P_B is longitudinal density (courses/cm) and UL(k,j) is the underlap length of the jth course in the kth guide bar. The positive and negative value of the pile angle is given in the repeat design of the pattern.

By measuring and summarizing, the angle β is in the range of 15° to 75°.

The pile cluster radial angle α is in the range of 15°–45°, which is closely related to the finishing process, yarn fineness and the number of filaments.

Pile length L

The pile length of warp-knitted brushed fabric is determined by the underlap length of pile yarn. As a matter of experience, after raising and shearing, a 1-0/3-4// float forms a 0.5 mm pile, a 1-0/4-5// float forms a 1 mm pile, a 1-0/5-6// float forms a 1.5 mm pile, and so on, which is also related to process parameters setting. The theoretical pile length is on half of the underlap length, and the length can be obtained through Equation (2):
$L = b \cdot 5 UL (k, j) / P B$
(2)
where L (mm) is pile length, b is the scale factor from the theoretical pile length to the simulation, UL(k, j) is the underlap length of the jth course in kth guide bar and P_B is longitudinal density (courses/cm),

Pile density

Pile density is determined by stitch density, yarn fineness and the number of filaments. Among them, the stitch density influences the number of raising points, but yarn fineness and the number of filaments determine the fineness and number of lines in the simulation. According to the yarn specification, the suitable density can be obtained by repeated drawing of the line when undergoing simulation. Regarding the sharp of yarn as approximately cylindrical, the diameter d (mm) of each filament is expressed in Equation (3):
$d = c \cdot 0.002 \sqrt{D / π}$
(3)
where c is the scale factor from filament fineness to the drawing segment fineness, and D is yarn linear density (tex).

Mathematical description for repeat of fabric pattern

Mathematical models

To realize the mathematical description for repeat of fabric pattern, basic mathematical models, such as the threading circulation mathematical model (Equation (4)), lapping digital mathematics model (Equation (5)) and repeat of pile pattern mathematics model, are developed (Equation (6)):
$G pm = [g 1 m \dots g 11 : g ki : g pm \dots g p 1]$
(4)
where $k = 1, 2, \dots, p$ , $i = 1, 2, \dots m$ . k is the total number of involved guide bars, m is the number of wales in one repeat of pattern and the value of g_ki represents the yarn’s information of the loop in the ith wale of the kth guide bar. g_ki = 0, a, b, $\dots .$ g_ki = 0 indicates the current guide needle without yarn. When $g ki = a, b \dots$ , and so on, it represents the current guide needle with yarn, and what the color code is
$a, b, \dots L k = [l n, 1 l n, 2 : : l j, 1 l j, 2 : : l 1, 1 l 1, 2]$
(5)
where $j = 1, 2, \dots, n$ . n is the number of courses in one repeat of pattern. l_j,₁ = L(k, j, 1), where the value of l_j,₁ represents the lapping digital before overlap shog in the jth course of the kth guide bar and l_j,₂ = L(k, j, 2), where the value of l_j,₂ represents the lapping digital after overlap shog in the jth course of the kth guide bar.

In order to judge the direction and length of the underlap, setting UL(k, j) represents the stitch number of underlap shog in the jth course of the kth guide bar. UL(k, j) = L(k, j + 1, 1)–L(k, j, 2), if UL(k, j) > 0, means that the underlap shogs from right to left in the jth course of the kth guide bar, and if UL(k, j) < 0, the underlap shogs from left to right. In addition, |UL(k, j)| represents the underlap length.

A 2D matrix R containing the information of pile position and pile color in Equation (6) is used to describe the repeat of pile pattern:^19–21
$R = [r mn \dots r in \dots r 1 n : : r mj \dots r ij \dots r 1 j : : r m 1 \dots r i 1 \dots r 11]$
(6)
where r_i,j = R(k, i, j), and the value of r_ij represents the pile information of the loop in the jth course and ith wale of the kth guide bar. r_ij = 0, ±a, ±b, $\dots .$ r_ij = 0 indicates the current loop without pile. When r_ij =a, b…, and so on, it means that the current loop has pile, and the color code of the pile is a, b….; “+” indicates the pile leans to the left, and “−” indicates the pile leans to the right.

When there are several guide bars that could be brushed, the matrix R should be recombined to a matrix E_mn:
$E mn = \sum_{k = 1}^{p} R k$
(7)

Assignment of the repeat pattern

With the design of threading and lapping of all guide bars, the value of every element in the above 2D matrix can be calculated or judged.

First of all, a guide bar is selected as the brushed one, named k_A, which has to fulfill the condition of |UL(k_A,j)| ≥ 2. Then the element value of the pile pattern matrix is calculated, starting from the first course of the brushed guide bar, which is the same as the value of threading.

$r i, 1 = g k A, i$ $i = 1, 2, \dots$ , m, $k = 1, 2, \dots, p$ , and the value of the second course can be judged by the underlap of the first course.

$r i, 2 = g k A, i - UL (k A, 1)$ , where the equation obtained by analogizing is as follows:
$r ij = {g k A, i - UL (k A, j - 1) when i \leq UL (k A, j - 1) + n g k A, i - UL (k A, j - i) - n when i > UL (k A, j - 1) + n$
(8)

The assignment discussed above is just the color value of fabric with full pile, so there are some additional situations that need to be judged.

When the underlap length of one course does not fulfill the condition of |UL(k_A, j)| ≥ 2, this course will not be brushed to form a pile, namely r_i,j = 0. Every course should be judged to complete the assignment.

The direction of piles judged by the expression of WL(k, j) = |UL(k, j)|/2–L(k, j, 2), WL(k, j + 1) = |UL(k, j)|/2 – L(k, j + 1, 1), where the sign of value will match up with the sign of r_i,j_.

Computer simulation

Program of simulation

According to the discussed model of pile and repeat design of pattern, VC++.NET language was used to develop a program to execute the simulation.²² Graphics statements were employed to simulate the pile morphology of warp-knitted brushed fabric.²³

Firstly, create a brush:
$BOOLCreatePen (intnPenStyle, intnWidth, COLORREF crColor);$
where brush style nPenStyle is chosen as PS_SOLID, brush width nWidth is determined according to the diameter d of each filament and brush color crColor is consistent with the color value r_ij.

The line drawing statement is
$BOOLLineTo (intx, inty);$

It is assumed that the r_ij pile position coordinates are O(x_ij₀,y_ij₀), and the coordinates of the pile’s trunk line OC endpoint are C(x_ij₁,y_ij₁). According to O point coordinates, the angle β between pile and course, and the pile length L, the endpoint coordinates of this segment can be determined by Equation (5):
${y 1 = y 0 + L \cdot \sin β {x 1 = x 0 + \frac{L}{\sec β}, if r ij < 0 x 1 = x 0 - \frac{L}{\sec β}, if r ij > 0$
(9)

The repeated drawing segment needs to return to the original position, namely pile point O, so the statement is:
$CPointMoveTo (POINTpoint);$

The angle between the other segment and the course can be randomly selected within the range of $(β - \frac{1}{2} α, β + \frac{1}{2} α)$ . Then the coordinates of the end points are determined according to Equation (9).

Simulation module

A relatively complex pile fabric with a colored pattern was selected to test the program. The height and width of the pattern repeat is 34 courses and 20 wales, knitted on an E28 four guide-bar Tricot machine. The finished product’s latitudinal density is 15 wales/cm, and longitudinal density is 23 courses/cm.

During the computer design of this pile fabric, some technical parameters, including chain notation and threading of all guide bars (Table 1), the fineness and type of yarns (Table 2) and stitch density of fabric, are input into the CAD system.
Table 1.
The structure process parameters

Guide bar Chain notations Threading

GB1 2- 1/ 1- 2/ 2- 1/ 1- 2/ 2- 1/ 5- 6/ 1- 0/ 6- 7/ 2- 1/ 7- 8/ 3- 2/ 8- 9/ 4- 3/9-10/ 5- 4/10-11/ 6- 5/11-12/ 7- 6/11-12/ 6- 5/10-11/ 5- 4/ 9-10/ 4- 3/ 8- 9/3- 2/ 7- 8/ 2- 1/ 6- 7/ 1- 0/ 5- 6/ 2- 1/ 1- 2// 13 out,(1B,1A) × 3,1B

GB2 1- 0/ 5- 6/ 1- 0/ 6- 7/ 2- 1/ 7- 8/ 3- 2/ 8- 9/ 4- 3/ 9-10/ 5-4/10-11/6-5/11-12/7-6/10-11/11-10/10-11/11-10/10-11/11-10/10-11/ 7- 6/11-12/ 6- 5/10-11/5- 4/ 9-10/ 4- 3/ 8- 9/ 3- 2/ 7- 8/ 2- 1/ 6- 7// (1A,1B) × 3,1A, 13 out

GB3 1- 0/ 1- 2// 20C

GB4 2- 3/ 1- 0// 20C

Table 2.
The information of the yarns

Yarn code Specification

A 83.3 dtex 144F polyester DTY

B 83.3 dtex 72F cationic dyeable polyester FDY

C 55.6 dtex 24F polyester FDY

DTY: drawn textured yarn; FDY: fully drawn yarn.

According to the structure process parameters, such as threading and lapping inputted and the pile judgment methods discussed in the Assignment of the repeat pattern section, the system automatically judges which stitch has the pile and what kind of pile it has, including the pile color and pile direction. The value will be assigned to every element of the pile pattern matrix. In the next step, the pile parameters are inputted into the dialog box artificially, as shown in Figure 4. A numerical value is assigned to corresponding parameters, pile angle β, radial angle α, pile length L, and pile number based on the characteristics of pile and finishing. Taking uneven pile length of the actual fabric into account, three length parameters, long, medium and short, should be set according to the proportion. The total number of lines is equal to the filament number of the pile yarn. When the OK key is pressed, the simulation image of the pile fabric appears. The flow chart of the simulation process is shown in Figure 5.
Figure 4.
Design of pile parameters.

Figure 5.
Flow chart of the simulation process.

Three images of the pile fabric were put together to compare the effect of simulation, as shown in Figure 6. Figure 6(a) is the photo of the selected pile fabric. Figure 6(b) is the original simulation without taking the broken pile yarn into account. Figure 6(c) is the modified simulation generated by the mathematic method discussed above.
Figure 6.
Comparison of two simulation effects with real fabric: (a) photo of pile fabric; (b) original simulation; (c) modified simulation.

There are obvious differences between the original simulation and real fabric. The unbroken floats of the original simulation represent the trend and direction of pile yarns, but occupy the area of piles and could not exhibit the details of the pile. On the other hand, the modified simulation is very similar to the photo of the fabric in many respects, such as pile position, pile color and pile direction, especially the whole pile pattern. It is proved that the modified simulation is feasible, and it is more similar to real fabric than the original simulation.

Conclusions

Based on the characteristics of warp-knitted brushed fabric, the line model described the shape of pile simply and effectively. With the multiple parameters setting of angle and length in the model, it reflected the influence that the process parameters would have on the pile shape, such as pile length, pile cluster radial angle and pile tilting angle.

According to the construction and threading of the brushed fabric, a 2D pattern matrix was used to describe the position and color of piles in one pattern repeat. Combined with the line model of the pile, a program was developed by VC++.NET to realize the simulation of the brushed fabric with patterned piles. The facts prove that the simulation effect on the fabric’s overall appearance and texture pattern of this model is satisfied, which is much better than general simulation method. Therefore, this research result has reference value to product design and effect estimation of warp-knitted brushed fabric.

The model realized the 2D simulation of the pile’s shape feature and entire pattern effect of warp-knitted brushed fabric. However, as the pile is a 3D structure, the current simulation remains to be further studied through the illumination model or further 3D model in order to improve the sense of reality of the brushed fabric simulation.

Guide bar	Chain notations	Threading
GB1	2- 1/ 1- 2/ 2- 1/ 1- 2/ 2- 1/ 5- 6/ 1- 0/ 6- 7/ 2- 1/ 7- 8/ 3- 2/ 8- 9/ 4- 3/9-10/ 5- 4/10-11/ 6- 5/11-12/ 7- 6/11-12/ 6- 5/10-11/ 5- 4/ 9-10/ 4- 3/ 8- 9/3- 2/ 7- 8/ 2- 1/ 6- 7/ 1- 0/ 5- 6/ 2- 1/ 1- 2//	13 out,(1B,1A) × 3,1B
GB2	1- 0/ 5- 6/ 1- 0/ 6- 7/ 2- 1/ 7- 8/ 3- 2/ 8- 9/ 4- 3/ 9-10/ 5-4/10-11/6-5/11-12/7-6/10-11/11-10/10-11/11-10/10-11/11-10/10-11/ 7- 6/11-12/ 6- 5/10-11/5- 4/ 9-10/ 4- 3/ 8- 9/ 3- 2/ 7- 8/ 2- 1/ 6- 7//	(1A,1B) × 3,1A, 13 out
GB3	1- 0/ 1- 2//	20C
GB4	2- 3/ 1- 0//	20C

Yarn code	Specification
A	83.3 dtex 144F polyester DTY
B	83.3 dtex 72F cationic dyeable polyester FDY
C	55.6 dtex 24F polyester FDY

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Fundamental Research Funds for the Central Universities (JUSRP51404A), China.

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