Determination of Sewing Thread Consumption for 602, 605, and 607 Cover Stitches Using Geometrical and Multi-Linear Regression Models

A double stitch consists of complex interlacing of looper and needle threads. By investigating the shape of 602 cover stitch, it was found that different parts could be separately investigated successfully to calculate the total amount of the stitch during seaming (C_{n1 602}, C_{n2 602}, C_{ul 602}, and C_{ll 602}). Figure 4 indicates the actual seam configuration and the positions of interlacing points formed by needles and loopers threads.

Figure 4

So, sewing thread consumption to make a single stitch can be calculated by using Eq. (1).

The amount of sewing thread C₆₀₂ needed for the 602 cover stitch, whose geometry is represented previously in Figure 4, is estimated by the following formula 1.

Where: C_{n1 602} is the consumption of needle 1 thread, C_{n2 602} is the consumption of needle 2 thread, C_{ul 602} is the consumption of upper looper thread, and C_{ll 602} is the consumption of upper looper thread.

Where: (2)Cn1 602=SL+2MT+12(π×(d+d2))2×d2{C_{n1\,602}} = SL + 2MT + {1 \over 2}\left({\pi \times \left({d + {d \over 2}} \right)} \right)2 \times {d \over 2}(3)SL+2MT+d(32π+1)SL + 2MT + d\left({{3 \over 2}{\rm{\pi}} + 1} \right)

Where C_{n1 602} =C_{n2 602}

We used the general equation supposed by Sohanur [22] as a function of the thread linear density Tex to calculate a sewing thread diameter supposed as circular (d) (Eq. 4).

When investigating the shape of 605 cover stitch, it was found that different parts can be separately investigated successfully to calculate the total amount of the stitch during seaming (C_{n1 605}, C_{n2 605}, C_{n3 605}, C_{ul 605}, and C_{ul 605}). This type of stitch is formed with five threads: three needle threads, a looper thread, and an upper thread. 605-stitch type produces very elastic seams, and requires a larger average amount of yarn.

The amount of sewing thread C₆₀₅ needed for the 605 chain stitch, whose geometry is represented previously in Figure 5, is estimated by the following Equation. (7). (7)C605=(Cn1 605+Cn2 605+Cn3 605+Cul 605+Cul 605)×n×L{C_{605}} = \left({{C_{n1\,605}} + {C_{n2\,605}} + {C_{n3\,605}} + {C_{ul\,605}} + {C_{ul\,\,605}}} \right) \times n \times L where: C_{n1 605}, C_{n2 605} and C_{n3 605} are the consumption thread of needle 1, 2, and 3, respectively. Moreover, C_{ul 605} and C_{ul 605} are the consumptions threads of upper and looper threads, respectively. (8)C605=SL+2MT+12(π×(d+d2))+2×d2{C_{605}} = SL + 2MT + {1 \over 2}\left({{\rm{\pi}} \times \left({d + {d \over 2}} \right)} \right) + 2 \times {d \over 2}(9)=SL+2MT+d(32π+1) = SL + 2MT + d\left({{3 \over 2}{\rm{\pi}} + 1} \right) where C_{n1 605} = C_{n2 605} = C_{n2 605}(10)Cul 605=B2+(B1+B2)2+SL2+B12+(3d)2+2×(π×(d+d2)){C_{ul\,605}} = {B_2} + \sqrt {{{\left({{B_1} + {B_2}} \right)}^2} + S{L^2}} + \sqrt {B_1^2 + {{(3d)}^2}} + 2 \times \left({{\rm{\pi}} \times \left({d + {d \over 2}} \right)} \right)(11)4×1n+SL+((1n)2+B12)1/2+((1n)2+B22)1/2+B1+B2+6×1n×(π×(d+d2))+2×d24 \times {1 \over n} + SL + {\left({{{\left({{1 \over n}} \right)}^2} + B_1^2} \right)^{1/2}} + {\left({{{\left({{1 \over n}} \right)}^2} + B_2^2} \right)^{1/2}} + {B_1} + {B_2} + 6 \times {1 \over n} \times \left({{\rm{\pi}} \times \left({d + {d \over 2}} \right)} \right) + 2 \times {d \over 2}

Figure 5

Based upon the geometrical model of cover stitch type 607, the different parts that are investigated to calculate the total amount of the stitch are C_{n1 607}, C_{n2 607}, C_{n3 607}, C_{n4 607}, C_{ul 607}, and C_{ul 607}. The amount of sewing thread C₆₀₇ needed for the 607 chain stitch, whose geometry is represented previously in Figure 6, is estimated by the following formula 12. (12)C607=(Cn1 607+Cn2 607+Cn3 607+Cn4 607+Cul 607+Cul 607)×n×L{C_{607}} = \left({{C_{n1\,607}} + {C_{n2\,607}} + {C_{n3\,607}} + {C_{n4\,607}} + {C_{ul\,607}} + {C_{ul\,607}}} \right) \times n \times L where: C_{n1 607}, C_{n2 607}, C_{n3 607}, and C_{n4 607} are the consumption thread of needle 1, 2, and 3 and 4, respectively. Moreover, C_{ul 607} and C_{ul 605} are the consumptions thread of upper and looper threads, respectively. (13)Cn1 607=SL+2MT+12(π×(d+d2))+2×d2{C_{n1\,607}} = SL + 2MT + {1 \over 2}\left({{\rm{\pi}} \times \left({d + {d \over 2}} \right)} \right) + 2 \times {d \over 2}(14)=SL+2MT+d(32π+1) = SL + 2MT + d\left({{3 \over 2}{\rm{\pi}} + 1} \right) where C_{n1 607} = C_{n2 607} = C_{n3 607} = C_{n4 607}

Figure 6

Please note that 72 samples were prepared by varying the different factors for cover stitch 602 and 36 samples were prepared for cover stitch 605 for verification of these models.

The industrial sewing machine type SIRUBA F007 (WL22-356) (Speed: 2000 rpm/min, 3 needles) was used for both cover stitch types 602 and 605.

Table 3 presents the different factors and levels for each type of cover stitch point.

Table 4 presents the levels of each factor for preparing the samples of each type of cover stitch class 600.

Each sample with 10 cm seam length was investigated. Then, the seam was unstitched to get the needle; upper looper and lower looper thread consumed in 5 cm length. After unstitching, the sewed thread length was determined to measure the value of the consumed thread per cm.

Table 5 presents a comparison between the experimental (C_Exp) and the theoretical (C_Th) thread consumptions within their absolute errors based on the cover stitch type 602 and 605.

The average absolute relative error, Error¯\overline {{\rm{Error}}} (Eq. 23) between the theoretical (C_Th) and experimental values (C_Exp) was determined to improve the obtained results. The limit of the mean absolute error values used in the modeling is estimated to be 6% [23].

Table 6 presents the average error for each type of cover stitch class 600.

The average absolute error does not exceed 4.07%, which means the result of testing thread consumption is widely verified. Regarding the findings, the error values ( Error¯\overline {{\rm{Error}}} (%)) are much lower than 6%. Thus, the studied models are well justified and the findings are highly significant.

Comparing the experimental and theoretical values showed a good agreement between geometrical and experimental consumption values. Moreover, the coefficient of regression ranged from 98.78% to 99.38% (Figure 4), which reflects significant and efficient relationships between experimental and theoretical findings.

Comparisons between the theoretical and experimental consumption values for cover stitch type 602 and 605 are shown in Figures 4a and 4b. Experimental thread consumption (x-axis) is plotted against theoretical thread consumption (y-axis). Linear regression is applied and a line is fitted to the data. The R² value of the fitted line is ranging from 98.78% to 99.38%, which means that the difference between the two data sets is insignificant. The high value of R² verifies the model accuracy and depicts that the model has taken into account all the variables on which the thread consumption depends. This result is similar to Abher who used geometrical models and concluded that the difference between the actual and predicted thread consumption, for 504 over edge stich, sets is insignificant (R² value of the fitted line is 0.992) [11].

As the error rate is very low and the regression coefficients values are very high (98.78%–99.38%), it was concluded that the obtained geometrical models are worthwhile and effective, and could be recommended for the prediction of thread consumption in the experimental design.

The results obtained for cover stitch types 602 and 605, respectively, are effectively proved and sufficiently by applying geometrical technique. Based on these findings, it was concluded that the proposed models of cover stitch type 607 is also successfully proved.

After determining the regression models, the effect of each input parameter is determined. Figure 8 presents the influence of material thickness, stitch density, yarn linear density, and the seam width for the different stitches (602 and 605).

Figure 7

Figure 8

Considering the Figures 8a and 8b, stitch density is found to be the most important parameter. In fact, the increase of stitch density from 3 to 5 stiches/cm increases the thread consumption percentage by 38.01% and 37.93% for 602 and 605 cover stitches, respectively. Thus, the increase of stitch density increases thread consumption. Besides, the increase of the consumption amount of sewing thread results from the increase in interlacing zone number inside assembled fabric layers. This result is in accordance with the findings of Jaouachi, Kennon, Hayes, and Abher [6, 24, 25, 26] and confirms our finding, i.e., the quantity of thread required when the fabric feed in motion to form the upper and lower lengths during stitch length modification. Moreover, this result is in good agreement with the findings of Lauriol's study [4] which proves that if the sewing length decreases from 2.5 mm to 2 mm (from 4 stitches/cm to 5 stitches/cm), thread consumption increases, approximately, by 10%. According to Sharma study, the stitch density is the second most influential parameter on seam thread consumption because, in his case, the stitch density has a small interval (from 2 to 3.5 stitches/cm) [9]. Besides, Abhar calculated the contribution ratio percentage for stitch class 504 and concluded that the contribution ratio of stitch density was around 62% [11]. The stitch density has more impact because our studied stitches class 600 are made up of 4, 5, and 6 different threads. Each thread has its own path but the path of lopper thread is very curvy therefore, a little increase in stitch density contributes significantly toward the total thread consumption.

According to Figures 8a and 8b, Yarn linear density has little impact on thread consumption. But, the increase of yarn diameter from 0.024 to 0.036 cm (relative to increase of yarn linear density from 63.5 to 95 tex) increases thread consumption by 4.93% and 6.93% for 602 and 605 cover stitches, respectively. This result is similar to Jaouachi results [24]. In addition, if 100% PES thread composition is used instead of 100% cotton yarn, thread consumption becomes much less significant. In fact, the increase of its linear density does not have an important effect on thread consumption in the case of polyester thread composition.

Based on Figures 8a and 8b, it is found that that the increase of material thickness from 0.075 to 0.123 mm increases thread consumption by 3.05% and 4.02% for 602 and 605 cover stitches, respectively. Thus, material thickness does not have a very important effect, but it remains an influential factor in thread consumption. It is observed that the increase of material thickness increases thread consumption for the three studied cover stitches. It is noted that the increase of material thickness increases seam thickness as well as thread consumption. So it is deduced that less thick fabric requires less thread, but thicker fabric requires more thread. This result is confirmed by Jaouachi and Abher's finding that consumption values increase with the increase of material thickness [1, 6, 11]. This means that the thickness of fabric samples affects the consumed thread considerably. This finding is also in accordance with the findings of other researchers [24]. Besides, a heavy fabric consumes more sewing thread than an average fabric according to Jaouachi. This consumption is estimated for heavy fabrics that are thicker than the average fabrics [24]. However, Sharma proved that the material thickness has the most important influence on seam consumption because in his case, the material thickness has a very large interval (from1.64 to 6.56 mm) [9].

From the Figure 8a for 602-cover stitch, it is found that the seam width is an important parameter. Note that the increase in the seam width value (B₁) increases the thread consumption. In fact, increasing S_W from 0.3 to 0.6 cm, thread consumption is increased by 30.29% for 602-cover stitch. This is because the increase of width increases the stitch length. This result seems to be similar to the result found by Goldnfiber [27], who reported that higher width of seam requires more thread to sew the garments.