Calculation in Weft Knitting 14.1 PRODUCTION CALCULATIONS Among the various factors those are to be considered in the manufacture of knitted fabrics, it is very important for the knitter to calculate the productivity of a machine in order to be able to schedule production and specify the delivery dates to the customer. Selected examples are given in this chapter to understand the methods of calculating production and efficiency of machines used for weft knitting Productively in weft knitting terms refers to the length of the fabric that comes out of the machine the width of the fabric both single and double width and the weight of the fabrics produced in unit time. The following are the important parameters which decide the production calculations of circular weft knitting. Machine Parameters i. Machine speed (rpm) ii. Machine diameter (inches) iii. Machine gauge (Needles/inch) iv. Number of feeders. v. Machine efficiency vi. Number of needles Yarn and fabric parameters i. Yarn count ii. Stitch length iii. Stitch density iv. Wales per inch v. Courses per inch Gauge or cut is the number of tricks per circumferential inch of the machine. Though the machine gauge and yarn count are approximately interdependably, knitting a large range of yarn counts on a specific machine gauge is impossible. Similarly with a given yarn number. Knitting different stitches is also limited. The following simple formulae are used to calculate the knitting machine productivity. i. Fabric production in yards/Hour is, s × f × 60 CPI × 36
ii. Fabric production in pounds/hour is
s × f × N × l × 60 36 ×840 × Ne
iii. Fabric weight per liner yard (lbs)is
N × l × CPI × 36 36 × 840 × Ne
iv. Fabric width (in inches) = Number of Needles/WPI
or
Number of needles x Wale spacing
Where, Wale spacing=4 x yarn diameter. v. Fabric weight (lbs) per square yard =
Weightperl inearyard ×36 fabricwidt hininches
=
Weghtperli nearyard × 36 Fabricwidt hininches × 2
where S=Machine speed in rpm F=Number of feeders in the machine N=Number of needles in the machine L=Stitch length in inches CPI=Courses per inch WPI=Wales per inch Example 1: calculate the production of knitted fabrics in terms of (i) Yards per hour,(ii) pour per hour (iii) Fabric weight per liner yard (iv) Fabric width and (v) Fabric weight per square yard a knitting machine running with the following data . Machine speed Number of needles Stitches per foot Numbers of feeders Yarn count CPI WPI
20rpm. 490 72 12 25n 24 29
The calculation can be made by substituting the respective values in the formulae as give above. The machine efficiency also can be incorporated in this production calculation. Ins of directly by giving the stitch length, some-time the stitches per foot length is also given. Parameter is generally obtained by making two marks of 1 foot space in the yarn be knitting. After the yarn is knitted into fabric, number of loops between these two mark noted down, which gives the stitches per foot length . from this the stitch length of calculate as (as per the above example)
Stitch length
=
(i) Yards per hour
= =
12 = 0.17 inches 0.17 s × f × 60 CPI ×36
20 ×12 × 60 = 16 .67 24 × 36
(ii) Pounds per hour
=
s × f × N × l × 60 36 × 840 × Ne
=
20 ×12 × 490 × 0.17 × 60 36 × 840 × 25
=1.59 (iii) Fabric weight (lbs) per linear yard =
N × l × CPI × 36 36 × 840 × Ne
=
490 × 0.17 × 24 × 36 36 ×840 × 25
= 0.095 (iv) Fabric width
= 490/29 =16.9 inches (open width) =8.45 inches (folded width) (v) Fabric weight per square yard = =
Weight per linear yard ×36 Fabric width in inches
0.095 = 0.0056 lbs 16 .9
14.1.1 Fabric Length The factor F is to be considered in calculating the linear length of knitted fabrics from the circular weft knitting machines. This factor is determined by the respective fabric structure. The factor F is taken into account the fact that a full course of loops is not always knitted at each feeder. For example, with plain knit fabric a complete course will be knitted at each feeder, therefore F=1. However for a double jersey structure, such as interlock, each feeder only knits half a course of loops, therefore two feeders are required to knit a full course, so F = 0.5. For any structure, F can be calculated as, 1
F = Number of feeders required to knit one full course of loops Therefore, by incorporating the factor F, Fabric length in yard/hour =
s × f × 60 × F CPI × 36
14.1.2 Fabric weight The constant C is important while calculating the production of knitted fabrics in terms of fabric weight. This constant also varies according to the fabric structure. The constant C can be incorporated as Fabric weight (lbs) per square inch =
WPI × CPI × l × C 36 × 840 × Ne
Since the number of courses and wales per centimeter are measured on only one side of the fabric and double jersey structures have two sets of loops, the constant C has to be included in the equation to allow for the second set of loops. For single jersey structures, where there is only one set of loops, C = 1. For balanced double jersey structures, C = 2. For other structures, C has to be determined individually. Example.2: Given a 14 gauge, 20 inch diameter, 40 feedercircular weft knitting machine operating at 25 rpm and 90% efficiency, calculate the length, width and weight of the fabric that could be produced per hour using a two fold resultant yarn count of 12 Ne, Knitted to the following structures and specifications. (i) 1×1 Rib, loop length = 0.2 inch, CPI = 27.0 WPI = 20 (ii) Interlock, loop length = 0.12 inch, CPI = 37, WPI = 30 For 1×1 Rib, (F = 1, C = 2): Length (yards)
=
Width (inches)
=
Weight (lbs / inch 2 ) For interlock (F = 0.5, C = 2): Length (yards) Width (inches) Weight (lbs / inch 2 )
40 × 25 × 60 × l = 61 .73 27 × 36
14 × 20 × 3.14 = 43 .96 20 27 × 20 × 0.2 × 2 = 0.000595 = 36 × 840 ×12 40 × 25 × 60 × 0.5 = 22 .52 37 × 36 14 × 20 × 3.14 = 29 .30 = 30 37 × 30 × 0.12 × 2 = 0.000734 = 36 × 840 ×12
=
14.2 OPTIMUM KNITTING CONDITIONS Though the right choice of knitting machine for the knitting of appropriate knitted fabric is essential, the selection of fibers and yarns are also important. Moreover the emphasis is to be given on optimum knitting conditions by which the knitting takes place to maintain the product uniformity. The following parameters are to be given due weightage during knitting. (i) Tightness factor,
K=
tex where l is loop length in cm. l
Tightness factor ranges from 11 (for slack fabrics) to 19 (for tight fabrics) and an average of 15 is preferable, which is optimum in general. (ii) Machine Gauge: It is the number of needles per inch arranged on the needle bed. Yarn number and machine gauge are related as (a) Yarn Tex
100 G
=
2
G2 where G = Needles/inch 10 0.1gms = tex
(b) Worsted count
=
(iii) Input tension (iv) Loop length (l )
=
tex cms, where K is tightness factor K
(v) Course length, L = Loop length × number of needles per course. Course length is the length of yarn consumed for full course during knitting. (vi) Run-in and run-in ratio: Run in is the yarn in take (inches per minute) at each feed for a given machine speed. It can be calculated by knowing the loop length, number of needles and machine speed. Run-in = course length × rpm Run-in ratio is the simple ratio between sets of feeders, feeding yarn at different run-ins. For a knitted structure produced with two feeders F1 and F2 which are supplying yarns at deferent run-ins. Course length of F1
Run-in ratio
= Course length of F 2
In order to calculate the run-in for structures other than plain knits the following assumptions can be made. (a) For rib gated structures, consider all the loops as plain loops Fig. 14.1 (b) For interlock gated structures, loops are produced on both dial and cylinder and they are considered to be rib loops. Fig. 14.2 (c) The knitted loops produced on dial needles only or cylinder needles only are considered to be plain loops. Fig. 14.3 (d) For both rib and interlock gated structures, the calculation for loop lengths of miss stitch and tuck stitches are, 1
Miss stitch length = Gauge Fig. 14.4 Tuck stitch length can be assumed as plain loop length in case of rib gaiting and rib loop length incase of interlock gating. Fig. 14.5
(vii) Fabric width (in cm)
=
Number of needles L = , where L = Course length wales / cm kw
(viii) Course per centimeter, Cpcm =
kc l
ix. Wales per centimeter, wcpm =
kw l
x. Stitch density, S = cpcm x wpcm xi. Fabric weight (gsm/m2) GSM =
ks ×tex 100 ×l
Where ks = kc x kw Where kc, kw and ks are constant for the geometry of the plain knitted fabric in various stable states, such as dry relaxed, wet relaxed and finishes relaxed sates. Or
GSM =
S ×l ×T 100
S= stitch density (loop / cm2) l = loop length (mm) T = yarn tex. Example 3: for a circular plain knitting machine of 24 gauge, 30” diameter, 96 feeders and 35 rpm speed, find out the optimum knitting conditions. Where
(i) Tex = (
100 2 100 2 ) =( ) = 17.3 tex G 24
≈ 18 tex ≈ 32 Ne
(ii) Loop length : for a optimum knitting, tightness factor = 15 i.e.,
15 =
Loop length
=
(iii)Input tension = (iv)
18 = 0.28 cm 15
0.1gmspertex tex
Course length
(v) Run in
tex l
= 1.8 gms
= loop length x number of needles. = 0.28 x π DG = 633.4 cm
= Course length x rpm =
633 .4 x35 = 221.7 m / min 100
(vi)
Cpcm
=
kc kw , wpcm = l l
cpcm =
5.5 = 19.5 0.28
4. 2 = 14.9 0.28
wpcm = (vii)
Fabric width ( at relax state ) = Number of needle / wpcm =
(viii)
Fabric length ( at relax state) =
Numberoffe eder × rpm × time ×η% cpcm
= (ix)
2262 = 151 cm 14 .9
96 × 35 × 60 × 0.9 = 93 meter/hour 19 .5 ×100
GSM ( at relax state) =
cpcm × wpcm × l × tex × c 10
19 .5 ×14 .9 ×0.28 ×18 ×1 10
=
= 147.48 gms
also, GSM = ks x tex / 10l where
ks = kc x kw = 5.5 x 4.2 = 23.10
Therefore GSM =
23 .10 x18 10 x 0.28
GSM = 148 gms /m2 Example 4 : It is require to knit a plain knit fabric to finished fabric to a finished weight of 150 gm / m2 and a finished width of 160 cm on a 20 gauge machine with 30 inch diameter, 96 feeder and 30 rpm speed. Assuming the finished state constant kc = 5.5 and kw = 4.2, Calculate, i. Optimum yarn tex ii. Optimum loop length iii. Optimum input tension iv. Run-in
v. Length and width shrinkage i.
Optimum yarn tex = (
100 2 100 2 ) =( ) = 25 tex G 20
ii. Optimum stitch length
Assume optimum tightness factor, K = 15 i.e,
k=
Tex l
Therefore
l=
0.1gsm per tex tex
iii. Optimum input tension
=
iv. therefore, input tension
= 2.5 gms
v. Course length
vi. Run-in
= l x needle = l x π DG = 0.33 x 3.14 x 30 x 20 = 621.7 cm =course length x rpm =
vii. Cpm = viii.
25 = 0.33 cm 15
kc l
Wpcm =
=
5.5 = 16.67 0.33
kw l
ix. Finished relax fabric width
=
4.2 = 12.72 0.33
= Needles / wpcm =
x. Finish relax fabric length
621 .7 ×30 = 186.51 m / min 100
=
3.14 × 20 ×30 = 148.11 cm 12 .72
feeders × rpm × time × π % × F cpcm
=
96 ×30 × 60 × 0.9 ×1 16 .6 ×100
= 93.69 mts / hr. xi. Length shrinkage and width shrinkage :
given, finished width therefore,
=160 cm
percentage width shrinkage
=
160 −148 .11 148 .11
Given finished weight i. e
x 100 = 8.02%
=150 gms 150
=
cpcm × wpcm × l × tex .C 10
= cpcm ×πDG / 160 × 0.33 × 25 × l 10
Therefore cpm
= 15.44
Finished length
=
feeders × rpm × time × π % cpcm
=
% length shrinkage
Width shrinkage
96 × 30 × 60 ×8 × 0.9 = 100.74 mts / hr 15 .44 ×100
100 .74 − 93 .69 = 7.52 % 93 .69 1884 wpcm = Needles/finished width = 160 12 .72 −11 .77 = = 8.06 % 11 .77
=
Length shrinkage
=
= 11.77
16 .67 −15 .44 = 7.51 % 15 .44
Example 5: For a double jersey machine of 20 gauge, 48 feeder, 30 inch diameter, knitting acrylic spun yarn at a speed of 18 rpm, calculate the most suitable count ( worsted, cotton count and tex ), optimum input tension and optimum run in and run in ratio for the following double knit structures. (a) Punto-di-roma (b) Swiss double pique (i)
Optimum worsted count is given by Wc=
20 × 20 G2 = = 40 s worsted count 10 10
For cotton count, Cc = 2/3 Wc = 40 × 2/3 = 27 Ne For Tex,
Tex = 885.8/ Wc = 22.0 tex
(ii)
Optimum input tension : T
(iii)
i
=
0.1gms per tex = 0.1 × 22 = 2.2 grams tex
Run- in and Run- in ratio: The optimum conditions for knit ability occurs at tightness factor, K = 15.
(a) As the Punto-di-roma structure (Fig. 14.6) is made up from both Rib and Plain knits only, the difference in Tightness K between these two units is approximately 20%
i.e., K plain = 16.2 and K rib = 13.8 Now, the respective loop lengths are calculated as, lp
tex 4.71 = = 0.291 cm Kp 16 .2
=
lr =
4.71 tex = = 0.342 cm Kr 13 .8
Referring the Punto-di-roma structure, When knitting with dial and cylinder needles (feeder 1 and 2) the course length, Lr = n. l r
When knitting with dial or cylinder needles (feeder 3, 4) the course length, L p = n. l p Where n is the number of needles forming the loops For Punto-di-roma, n=N/2 Where N is the total machine needles of dial and cylinder i.e.,
N=2 (30 π20 ) =3772 3772 =1886 2 Lr = 0.342 ×1886 cm L p = 0.291 ×1886 cm
n= Now course length,
Therefore, Run-in
Ir = Ip
=
0.342 ×1886 × speed = 381 feet / min 2.54 ×12
0.291 ×1886 ×18 = 324 feet / min 2.54 ×12
Therefore, Run-in ratio
=
381 =1.2 324
(b) As Swiss Double Pique is knitted with rib gaiting, all the loops are considered to be plain loops. i.e., K p = 16.2 and loop length, l p =
tex = 0.291 cm 16 .2
At the feeders (1, 3) where dial and cylinder needles form loops, the total number of needles forming the loops are,
n + n = 2829 2 Therefore, Course length produced with both dial and cylinder needles, Ld , c = 2829 × 0.291 cm Fig 14.7 At the feeders (2, 4) where dial only form the loops, n/2 needles form knit stitches and the same n/2 needles form the miss stitches. 1 1 × 2.54 = 0.127 cm inches = G 20 n n Ld = × 0.291 + × 0.127 = 943 ( 0.291 + 0.127 ) = 943 × 0.418 2 2
For miss stitches,
l=
Run in,
Id , c =
Id =
Therefore Run-in ratio
=
2829 × 0.291 ×18 = 486 ft / min 2.53 ×12
943 × 0.418 ×18 = 233 ft / min 2.54 ×12
486 = 2 .1 233
14.3 ANALYSIS OF WEFT KNITTED FABRICS To, understand the history of the fabric as well as for its reproducibility, analyzing the fabric structure is important. Type of machine used and design principles can also be revealed by analyzing the knitted fabrics. For fabric analysis a piece glass (i.e., a counting glass), a pair of scissors, ruler and calculator are needed. The following analysis sheet (Table 14.1) can be completed after having thoroughly analyzed the fabric. The following procedure may assist in carrying out the analysis. These are only guidelines and it takes time and practice to acquire the skill in the analysis. (i)
Fabric Name: To find out to which type of the knitted structure the given sample belongs viz, single jersey, rib purl, interlock etc. For single jersey fabrics, loops are seen at the face side and yarn lines are visible at the back as shown below: Fig. 14.8
Double jersey fabrics have similar appearance on both sides. By holding the fabrics horizontally, in such a manner to observe its cross section, the rib and interlock structures can be found by their cylinder and dial loop arrangements as given below: Fig 14.9 (ii) (iii) (iv)
(v)
Fabric Appearance: To find out the technical face and technical back of the fabrics. The top of the fabric is the edge that was knitted last. The face of the fabric is always the side with the most knit stitches. Yarn Type: The last knitted yarn is unraveled from the fabric and is observed for its types such as single, double, blend, mélange, staple yarn, filament yarn s/z twisted, 2/3 plyed etc., Wales/cm and courses/cm: With piece glass, the Wales per inch can be measured and converted into per centimeter. It is advisable to analyze always the back of the fabric, and particularly for unbalanced fabric, the back is obvious. c = courses/cm and w = Wales/cm Loop length: Unravel 12 yarns from the sample and measure the total length, LT cm ( i.e., L1+L2+L3…) Weigh all the 12 yarns together, in grams(wy) Find out the average length LAV =
LT 12
Count the number of Wales occupied by LAV Now, the average loop length = LAV / (vi)
Grams per square meter: Cut a piece of 10 cm × 10 cm from the fabric sample Find out the weight of the sample, w Now, GSM = w ×100
(vii)
Yarn Tex : Using the total yarn length and weight as found above, Yarn number can be calculated as, Yarn Tex
(viii)
w y ×10 5 LT
Tightness Factor : Using the values of tex and loop length as found above, tightness factor can be calculated as , TF
(ix)
=
tex , where l = loop length in cm’s l
Fabric construction: By carefully analyzing the fabric using a pick needle, the full design repeat of the structure, number of feeders used, needle gating etc., can be found. The repeat can be drawn either as point paper design (symbolic nation) or yarn path diagram (diagrammatic notation).
To prepare the fabric for the analysis, first a wale line is to be marked at the centre of the fabric sample, which is the starting point. Using a pick needle, highest stitches are to be pulled out, which is the yarn that was knitted last. Ensure that one yarn is pulled at a time; continue the de knitting until a yarn is reached that goes completely across the fabric. Now the sample is completely prepared for analysis. Now start de knitting the yarn that was last one knitted. Starting from the marking line, observe the type of stitches (knit, tuck, miss), the yarn is made into at each Wales positions. Record them in a point paper from right to left (Fig. 14.10) as the yarn is de knitted from right to left. The next yarn is de knitted and recorded in the same manner. This process is repeated until two repeats are seen on the paper.
