Design Method of Circular Weft-Knitted Jacquard Fabric Based on Jacquard Module

To illustrate a knitting pattern, a raster graphics image [13] with different colors is used and referred to as a pattern notation, as it shown in Figure 2. Pattern notation is mainly used to express the technological face of a fabric in circular weft-knitted jacquard fabrics [17]. Generally, the smallest pattern cycle on the face of a fabric is used as a stitch cycle. Pattern notation is a 2D plane graphic that 2D data are converted into a 2D matrix to describe the color information, and the matrix P (Pattern) is shown in equation (1). Let w and h be the width and height of pattern notation, respectively. P_j,k represents the color information at the k^th wale and j^th course and is assigned by color code. The specific values of color code are 0, 1, ..., 255: (1)P=[P1,1⋯P1,w⋮Pj,k⋮Ph,1⋯Ph,w]{\boldsymbol P} = \left[ {\matrix{{{P_{1,1}}} & \cdots & {{P_{1,w}}} \cr \vdots & {{P_{j,k}}} & \vdots \cr {{P_{h,1}}} & \cdots & {{P_{h,w}}} \cr}} \right]

Figure 2

After the design of pattern notation, the width (w), height (h), and 2D matrix P can be obtained. The color sequence is an important reference when decomposing the pattern. Therefore, the following one-dimensional matrix C (Color) is used to store different color codes, which are used in matrix P with a certain order. Taking the first pattern grid's information P_1,1 as the starting point, and the last pattern grid's information P_h,w as the end point to traverse the matrix P. Finally, different color codes are sequentially stored in the matrix C. Let n be the sum of different colors in the pattern notation. C_i represents the color code of i^th color: (2)C=[C1 ⋯ Ci ⋯ Cn]{\boldsymbol C} = \left[ {{C_1}\,\,\,\, \cdots \,\,\,\,{C_i}\,\,\,\, \cdots \,\,\,\,{C_n}} \right]

In fact, the information of knitting actions is the real determinant of machine knitting. Knitting diagram illustrated in Figure 3 is used to describe the abstract shape of yarns formed by actions of needles in each knitting row. To display the pattern and knitting information simultaneously, a knitting diagram consists of colorful grids and different stitch icons. In a double-circular weft-knitted jacquard fabric, a group of knitting action consists of actions from a pair of cylinder and dial needles. A jacquard stitch is usually knitted from yarns of different colors or types. Each dyed yarn is knitted at least once in each course to form the front pattern, so it takes n knitting rows to form a single pattern course, where n is the number of different colors in pattern notation. H is defined as the rows of knitting diagram and contains the following mathematical relationship relative to pattern courses h: (3)H=n×hH = n \times h

Figure 3

To conveniently convert the information of pattern notation into a knitting diagram, it is necessary to split and copy the pattern information of each course according to knitting rows n. A 2D matrix T of technological pattern information is defined for storage. The transformational relation between matrix T and P is Tj,k=PINT(jn),k{T_{j,k}} = {P_{{\rm{INT}}\left({{j \over n}} \right),k}} , and the process of transformation from pattern notation to technological notation is illustrated in Figure 4. To store the generating knitting information, a 2D matrix K is created to describe it. Let w and H be the width and height of knitting diagram, respectively. T_j,k represents the color information at the j^th row and k^th wale and is assigned by color code. K_j,k represents the knitting information at the j^th row and k^th wale and is assigned by the loop code: (4)T=[T1,1⋯T1,w⋮Tj,k⋮TH,1⋯TH,w]{\boldsymbol T} = \left[ {\matrix{{{T_{1,1}}} & \cdots & {{T_{1,w}}} \cr \vdots & {{T_{j,k}}} & \vdots \cr {{T_{H,1}}} & \cdots & {{T_{H,w}}} \cr}} \right](5)K=[K1,1⋯K1,w⋮Kj,k⋮KH,1⋯KH,w]{\boldsymbol K} = \left[ {\matrix{{{K_{1,1}}} & \cdots & {{K_{1,w}}} \cr \vdots & {{K_{j,k}}} & \vdots \cr {{K_{H,1}}} & \cdots & {{K_{H,w}}} \cr}} \right]

Figure 4

A jacquard module is a jacquard needle-selected model with specific jacquard type [18, 19], which is designed according to the structural characteristics of different jacquard types circular jacquard fabrics [20, 21]. The commonly used jacquard colors are 2 to 4 [14]. There is a two-colored bird's eye backing jacquard module illustrated in Figure 5. According to the knitting rule of yarns, the number of colors in a jacquard module is required to be the same as the number in pattern notation, but the colors do not necessarily correspond. Colors in a jacquard module do not specifically represent actual knitting colors and notation colors, which is only used to distinguish different knitting rows in a pattern course. To distinguish colored yarns knitting in different color regions, the background color of jacquard module is in a staggered arrangement of light and dark gray. The light and dark gray in Figure 5 means that decomposing Region A with knitting rule of wales 1–2 and decomposing Region B with knitting rule of wales 3–4. In the horizontal direction, the number of light gray or dark gray wales is the number of pattern wales for each color; longitudinally, each pair of light gray or dark gray forms a jacquard course, and in this case, n is 2. When designing, firstly, the smallest courses and wales cycles should be found according to the back effect. The number of smallest rows cycle represents the pattern courses, and the number of smallest columns cycle means the pattern wales of each color in a jacquard module, and they are two important factors need to be identified in the jacquard module. Then, it is necessary to analyze the knitting actions of each color in the same color area and the rule of loop shape in different color area according to the jacquard type. Finally, these actions are edited into a jacquard module with combining different colors and icons.

Figure 5

To generate a tricolor bird's eye backing effect shown in Figure 6 (a), there is a certain mathematical relationship between knitting rows’ height (JMH) of a designed jacquard module and the minimum cycle pattern's courses (JMh) as equation (6), and the width (JMW) of a jacquard module is calculated by equation (7): (6)JMH=n×JMh{JMH} = n \times {JMh}(7)JMW=n×JMw{JMW} = n \times {JMw}

Figure 6

It can be seen that the number of jacquard colors is three by analyzing Figure 6(a). Furthermore, viewing Figure 6(a) from bottom to top, there are two rows of each color in the minimum cycle that the value of JMh is 2; looking from right to left, JMw is 2. The reason for looking from right to left is that the direction is from left to right when looked at the front of a fabric. When the fabric is turned over, that is equal to flip the fabric along the Y-axis, the serial number of wales is also reversed. After the discussion above, JMH is 6 and JMW is 6. The color sequence of pattern is sort by colors A, B, C, which, respectively, corresponds to color A1, B1, C1 of the jacquard module. The reverse pattern rule is AB|CA|BC from right to left and bottom to top. As shown in Figure 6(b), the jacquard module can be made according to the needle-outed rule of a tricolor bird's eye backing jacquard fabric. Each pattern course of this kind of fabric has two knitting rows in the front side; however, in the back side, it has three knitting rows. So, the fabric has a characteristic that the ratio of the front to reverse pattern courses is 2:3. In the front pattern course of the jacquard module, each color is knitted by needles in the same color region to form front loops, and needles of dial are arranged in ABC with one interval one needle-outed. As for the reverse side, which is knitted by dial's needles, Yarn A loops at odd needle positions [21] in the first knitting row, and Yarn B loops at even needle positions in the second row to form the first course. Yarns C and A are staggered to form the second course. Yarns B and C are staggered to form the third course. There are several common ordinary jacquard modules shown in Figure 7. To conveniently select and make use of various jacquard modules, a jacquard module database is built to store them:

Figure 7

It is important to mention that the jacquard module mainly sets the knitting actions in each color areas according to the color array. The 2D matrix JM of the jacquard module's knitting information is established as equation (8), JM_j,k represents the knitting actions at the j^th row and k^th wale, and the actions are assigned by loop code: (8)JM=[JM1,1⋯JM1,JMW⋮JMj,k⋮JMJMH,1⋯JMJMH,JMW]{\boldsymbol {JM}} = \left[ {\matrix{{JM}_{1,1} & \cdots & {{JM}_{1,JMW}} \cr \vdots & {{JM}_{j,k}} & \vdots \cr {{JM}_{JMH,1}} & \cdots & {{JM}_{{JMH,JMW}}} \cr}} \right]

The design of the jacquard module includes its same color area and different color area, and each color area is distinguished with stagger light and dark grays. In the process of converting pattern notation into a knitting diagram, it is necessary to get the knitting actions of the jacquard module according to the color of the pattern notation. To distinguish the knitting rule of each color in a certain color area, matrix JM is split according to the color areas. A block matrix JM(i) of the jacquard module's knitting information in different color area is established as equation (9), where i is the serial number of the color region: (9)JM(i)=[JM(i)1,JMw×(i-1)+1⋯JM(i)1,JMw×i+1⋮JM(i)j,k⋮JM(i)JMH,JMw×(i-1)+1⋯JM(i)JMH,JMw×i+1]{\boldsymbol JM}\left(i \right) = \left[ {\matrix{{{\bf JM}{{\left(i \right)}_{1,{\bf JMw} \times \left({i - 1} \right) + 1}}} & \cdots & {{\bf JM}{{\left(i \right)}_{1,{\bf JMw} \times i + 1}}} \cr \vdots & {{\bf JM}{{\left(i \right)}_{j,k}}} & \vdots \cr {{\bf JM}{{\left(i \right)}_{{\bf JMH},{\bf JMw} \times \left({i - 1} \right) + 1}}} & \cdots & {{\bf JM}{{\left(i \right)}_{{\bf JMH},{\bf JMw} \times {\bf i} + 1}}} \cr}} \right]

After a pattern notation is completed by using drawing tools, the corresponding pattern data can be obtained. It is necessary to design an appropriate jacquard module and get matrix JM and block matrix JM(i). According the conversion flowchart in Figure 8, matrix P can be converted into matrix K according to matrix JM. First of all, matrix T is traversed from the starting point of T_1,1. Secondly, the obtained color information of matrix T_j,k is compared with each color code in matrix C. If the color is the same as C_i, the knitting information of matrix JM(i)_j%JMH,k%JMw is obtained and assigned to K_j,k. Finally, matrix K is obtained and saved. If the pattern notation is changed, it is necessary to re-decompose matrix P to obtain a new knitting information matrix K.

Figure 8

To illustrate the implemental effect of the design method more simply and lucidly, the design of tricolor bird's eye backing jacquard and four-color air-layer jacquard are shown in Figure 9. By means of the above decomposition process, the three-color bird's eye backing jacquard module (Figure 7(h)) can be used to decompose the intended pattern notation in Figure 9(a) to obtain the knitting diagram, and Figure 9(b) shows the partial knitting diagram. The four-color pattern (Figure 9 (c)) adopts a four-color air-layer jacquard module to get a knitting diagram like Figure 9(d). Only small parts of two knitting diagrams are shown in (b) and (d) to clearly present the knitting actions and color information.

Figure 10

The circular weft-knitted technology is mature, and types of equipment are abundant. However, the circular-knitting CAD system is always in the basic pattern design stage, lacking a unified and standard design model, and the design difficulty is intricate for non-professionals. This study compares the design efficiency of a jacquard module method, with three commonly used jacquard design software in the market, and the result is shown in Table 2. The evaluation index of design efficiency is the time it takes for three professional designers to design the same pattern using different software. It can be seen that four methods of two-color pattern design are equally simple. For three- and four-color jacquards, both Paint Knit and AutoPaint need to choose the color block or knitting action according to the jacquard effect, which has certain requirements on the theoretical basis of designers. The more the number of colors, the greater the challenge to designers. WAC Designer easily designs the front pattern, but the back pattern is controlled by triangles on the machine. Therefore, it is difficult to design complex patterns and multi-color patterns. Through comparison, it can be found that the method of the jacquard module is relatively simple in the design of multi-color jacquard fabrics, and the designed jacquard module can be stored in the database for subsequent calls.