# Automation of stitch length cams in high speed flat weft knitting machines: Online control system and numerical modeling method.

IntroductionWeft knitting technique is one of the most popular methods to produce the fabric. In this process the feeding yarns forms stitches which interlace one another in horizontal direction so called walls. We must note that in the simplest case, the fabric can be knitted with only one yarn, the fabric can be produced as flat or circular and is stretchable in two vertical and horizontal direction, designing and making these machines specially the cams which control the needles are very important and precision [1 and 2]. Several famous companies have offered semi and full automatic flat knitting machines, but few of them tried to automation the simple machines [3, 4 and 5].

In this work, we have tried to automate simple machines. The automation of these machines can be achieved by automation of skip, tuck and knit cams, stitch length cams, yarn selection mechanism, fabric take -up mechanism and needle selection mechanism.

The rate of production in automatic machines are greater than non automatic ones; while the problems which existed through the design and operation, are approximately omitted and consequently wasted times is decreased in automated machines. By the automation, altering the knit design which has been done by the worker in each course during 3 to 4 seconds is decreased to lower than one second. Adding to this, it is possible to control the machine activities with the computer and change the complicated designs during operations. By automation fabric quality and production efficiency will be increased and wastes are decreased. Automation could be done in the below parts of machine: 1)automation in the needle selection device, 2)specify the position of stitch cam length, 3)fabric take -up mechanism, 4)system of knit cams movement, 5)cylinder traversing system, 6)selection of yarn guides and amount their movements, 7) programming knit design and 8)automation in the needle selection mechanism, in three different cases, stitch convection,stitch receiving, needle selection [6 and 7].

For determine those three case, we can control the relevant cams by using of several electro mechanical devices such as magnetic, electromotor and pneumatic forces. For selection of stitch convection we can use special sensors. Automation in selection of yarn guide is base on machine design. In some cases, it travels by the rail and its movement could be controlled by the magnetic selection system.

Automation in the stitch length control could be done by control the position of stitch length cams by using these devices: a) stitch length roller in the form of teeth, b) take up mechanism, c) magnet and d) stitch receiving device.

In new industrial flat knitting machines, addition to the electrical forces for moving,and control the different parts, by the electrical circuits, makers also use of special cam design, to impart the minimum amount of force to the needles that trends to increase machine speed.

The effective factors on fabric quality are yarn parameters, machine parameters and fabric parameters. Yarn parameters are included, yarn structure( staple or filament) tensile strength,yarn twist, yarn evenness, linear density, knots within the yarn,yarn friction,package quality. Machine parameters are included of :machine gauge, needle arrangement,sequencing,,distance between flat and cylinder and between two cylinder, fabric tension,machine speed,knitting tools, cam design, temperature and design structure. Fabric parameters are knit structure and fabric dimension.

Stitch length or rate of yarn feeding is an important factor that affects the factors of used yarn, fabric weight, walls and courses density, yarn tension, yarn rubbing rate, forces imparted to yarn and type of design.

The height of needle falling determines the stitch length. In other words each needle comes down after forming a stitch and this motion determine the stitch length. By altering the stitch length during the operation in different courses, it is possible to form special features on the fabric. This technique causes varied tension in different courses.

Also, it is possible to impart different adjustment in stitch length cam, or it is possible to use different stitch length in different course design, while compensates evenness yarn tension and obtain almost equal tension on those courses that trend to reinforce the dimensional setting.

The main factor is position of cam length but there are some other factors which affect the stitch length such as knit design, position of cam length, yarn count, yarn components, machine gauge, machine sequencing, kind of needle, humidification, yarn resiliency, stitch mechanism and production speed.

"Munden" proved that fabric dimensional structure is a function of stitch length in accordance with below relations [8]:

CPC = Kc/L, WPC =Kw/L and S.D =Kc*Kw/L (1)

Where, CPC, WPC and SD are course/cm, walls/cm and stitch density/[cm.sup.2]. Kc, Kw and l are course density coefficient, walls density coefficient and stitch length in cm.

Besides these factors, there are two other factors which affect stitch length and their significances are more than of those factors. These two important factors are tension of feeding yarn and rate of fabric take -up [9 and 10].

It is not possible to deduce that how much these tensions affect the stitch length exactly, but we can use of a practical experiment to predict this phenomena. During the stitch forming, some forces acting on the yarn [11 and 12]. One of these forces is the yarn tension which is determined by the feeding mechanism and fabric tension. Other forces are basically friction forces or the forces that are related the yarn elastic properties. The yarn tension and fabric tension forces opposites each other and if the first one will be greater the later, stitch becomes smaller and if the second will be greater the yarn package feeds more. Finding the optimum case (equal stitch lengths) to omit the rubbed yarn is difficult because the yarn rubbing phenomena is not a destructive factor at all [13, 14 and 15].

Design and Experiments

Analyze the forces imparted to stitch cam

Whenever a needle moves along the cam path, its position varies each moment to the former position, therefore the point of forces and also their sum is changed. In addition in each point of the needle path (because of changing the force imparted to the needle tip by the stitch) the force imparted to the cam will be changed [15, 16 and 17]. For analyzing these forces, first it supposed that there is only one needle in the cam path and the forces are constant as figure 1. If "[F.sub.1]" is the forces acted to the knit device by motor and "[F.sub.2]" is the force acted on the needle by stitch, following equation is proposed where, the frictional forces have been ignored as ideal lubricated cam.

[SIGMA] Fx = 0, [F.sub.1]-Fsin[theta] = 0 (1)

[SIGMA] Fy = 0, [F.sub.2] = F cos [theta] (2)

F = [F.sub.2] cos [theta] + [F.sub.1] sin [theta] (3)

[FIGURE 1 OMITTED]

It is appear that cam slope is affected the force and its maximum is in 90 degree. The tension on the needle is changed during knitting functions. Therefore, equation 2 can be presented as equation 4.

[F.sub.2] = A f(y) (4)

Where "A" is a coefficient and "y" is position of needle in vertical axis.

F = [F.sub.1] sin [theta] + A f(y) cos [theta] (5)

From figure 1:

Y = X tan [theta] (6)

So:

F=[F.sub.1] sin [theta] + A f(x tan [theta]) cos [theta] (7)

By modification of primary assumption that "n" needle contact the cam, relation 8 is presented.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

F = n[F.sub.1] sin[theta] + A [SIGMA]xi tan [theta] cos [theta] (9)

For simplicity we suppose "f" is a linear function with coefficient of "B". Therefore, equation 9 can be presented as equation 10.

F = nF1 sin[theta] + A B tan [theta] cos [theta] [SIGMA] xi (10)

F = nF sin[theta] + AB ([x.sub.1] + [x.sub.2] + ... + [x.sub.n]) sin[theta] (11)

F = {n[F.sub.1] + C([x.sub.1] + [x.sub.2] + ... + [x.sub.n])} sin[theta] (12)

"C" could be found by experiments and is based on the feeding yarn tension and fabric tension.

F = {[([G.sup.*]L).sup.*][F.sub.1] + C [[SIGMA].sup.n] x} sin [theta] (13)

Where, "G" is machine guage in centimeters, "L" is cam length in centimeter and "F" is force acting the cam in each moment.

In zero time for two needles in cam path:

[x.sub.1] = 0, [x.sub.2] = x = 2/G (14)

F = (2[F.sub.1]+2 C/G) sin [theta] (15)

After "t" seconds for "v" linear velocity of knitting device equation 16 is acceptable.

[x.sub.1] = vt, [x.sub.2] = 2/G+vt (16)

F = (2[F.sub.1] + C(2/G+vt)) sin [theta] (17)

Equation 17 can be presented as equation 18 for "n" needles.

F=n[F.sub.1] sin [theta] + C sin[theta] {[nvt+n/G]+[(n-1)vt+ (n-1)/G]+ ... +[vt+1/G]} (18)

As seen in equation 18, cam force based on three factors: 1)C: tension constant which is a function of yarn and fabric tension, 2) [theta]: cam angle slope, 3)n: the number of needle which is based on the machine gauge and cam length and 4) v: knitting device speed

Speed of knitting device is not constant, in the first half it is decreasing and in the second half it is increasing. About motor it must be analyzed the crank arms. By experiments, we found "f" function is not pure linear and we must obtain the function which describe the cam forces.

In equation 7, it approached that " F=n [F.sub.1] sin [theta] + A [SIGMA] f(xi tan[theta])* cos [theta]". By using Euler-Lagrange equation, it is possible to calculate the "x" for different "f" [18 and 19].

Therefore, with suppose that "k" is number of needles in cam path, for needles 1 to k the coefficients of equations 19 is written

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

from "LAGRANGE" theory for each parametric function of Pn(x) [10]:

[f.sub.1] = [beta] [x.sub.1] tan[theta], [f.sub.2] = [beta] [x.sub.2] tan[theta], [f.sub.[mu]] = [beta] ([x.sup.[mu]] / [mu] !)tan[theta], [f.sub.K-1] = [beta] [[x.sup.k-1] (k-1)/(k-1)!], [f.sub.k] = ([x.sup.k] x k/k !)tan[theta] (20)

[SIGMA]f = [beta] tan[theta] ([x.sub.1]+[x.sub.2]2/2! +[x.sub.3]3/3! +.. ... [x.sub.n]n/n !) (21)

Whereas, each point of cam path "x" has constant phase difference based in the motion speed therefore:

[SIGMA]f = [beta] tan [theta] [[([x.sub.2]-[x.sub.1]).sup.2]/2! + [([x.sub.3]-[x.sub.2]).sup.2]/3! +. ... + ([x.sub.n]-[x.sub.n-1])]/n! (22)

if the speed of knitting device is controlled constant "[x.sub.n]-[x.sub.n-1]=vt" and the equation 23 is converted to equation 24.

[SIGMA]f = [beta]tan [theta] {[nv.sup.2][t.sup.2]/n! (n ! /2! +n !/3 !+ ... +1)} (23)

With substitution in equation 23, equation 24 is obtained.

F=[nf1+[Cv.sup.2][t.sup.2] (n /2! +n /3! + ... +1) sin[theta] (24)

With respect to this equation we reach to a paradox about the cam angle where, if the cam angle is equal to zero, sin [theta] = 0 and F=0.

But the needles move in a horizontal path if cam angle would be equal to zero In other words the needles will move in a horizontal path after exit from cam path. Therefore, the problem of their vertical motion disappeared and they will have no contact to anyplace and no force imparted them. In actual case there is force imparted to cam because the yarn and fabric tension imply force in horizon direction to the needles and naturally buts imply force in the same direction to the cam surface "[F.sub.2]cos[theta] = [F.sub.2]" and the maximum load imply the cam.

It means that the assumption of "[F.sub.2]= A f(y)" seems true, but in practice we see a paradox in analyzing the forces .Therefore we can not simply accept linear relation "Y=X tan[theta]".

With precise surveying on this relation we conclude that it is a cinematic relation that means; needle path based on its position cinematically, and this is true when needle position has a dynamically relation with the forces and vice versa, more correctly we must (Y) a function of X and [theta].

Ideas

For automation of each non automated machine the best way is the simplest one because with respect to the four factors of time, cost, work and tools, the most useful system is obtained by the simplest way. For automation of cam length in weft knitting machine (its characteristics will be describe later) some limitations must be noted which are using the minimum amount of energy, the mechanism must be simple as possible, total number of component must be minimum, no especial mechanical and electrical instrument use, minimum time should be used, minimum expenses should be used, the minimum tensions be applied the cam, easy computer controlling, use of the facilities on the machine,

Machine characteristics

Flat weft knitting machine made by "UNIVERSAL COMPAUY "in Germany with needle gauge of 12/inch and racking 9 needles and two knitting device was prepared for experimental works. The feeding system was negative. The knitting devices had 4 length cams and 2 knit cams totally 12 cams in each side. Stitch length can be adjusted 0.05-2mm [20].

Design of mechanical parts

Cam stitch length is the last cam among the available cams and its motion is on the surface and is not normal to it is necessary to impart a tangential force to move it.

After complete surveying, it concluded that the best way for movement of stitch length is "step motor" because of its high precision, that of programmable and controllable abilities by computer.

The force by the step motor is named "F", "T" is its momentum and "f" is the required force for moving the stitch length cam. From plan of figure 2 the needed force of cam adjustment is calculated. In figure 2 "[alpha] = [??] 32", "[beta]=42 [??]", "[gamma]=72 [??]" and F=T/R. Also, "F tan [alpha] [L.sub.1] cos [gamma] = f [L.sub.2] cos(180 - [beta] - [gamma])".

The amount of "f" force and the moment of step motor was calculated as: "f=2.1 Kg.force=20.6 N" and "F=37.47 N".

With respect to calculation and step motor catalogs, the motor was selected as Model of SANYO-1037710-50(51) with rotation angle 1.8 degree, voltage 12 volt, 0.7 ampere, resistance 16 ohm and nominal moment 6 cm/kg [21].

[FIGURE 2 OMITTED]

The experiments for adjusting stitch length

The adjusted position of stitch length cam does not present actual stitch length of fabric. In industry, the estimation of suitable position of stitch length cam is an objective action based on try and error method. In the present automated system, it was needed to find an equation that relates degree of cam stitch length to the real stitch length .As it has been shown, the position of cam varies according with different structural yarn and fabric factors. Hence we can not except that by determining one degree of stitch length and different yarn count the equal stitch length obtained. Here the two important factors effected the stitch length, have been discussed. First, degree of stitch length and second fabric tension while, yarn tension will be nearly constant in negative feeding system. Two experiments of cam position and fabric tension were done for estimating stitch length functions. The calculations and stitch determining relation were done by the mathematical assessment functions.

Five samples of different stitch length cam of available position and five samples of different fabric tension were knitted by the automated knitting machine. The samples were weighted and the stitch length was calculated by the equation of "L= (1000W/CPC*WPC* tex)" for every knitted samples [8].

To obtain the function that show the relation between cam degree and stitch length, the "NEWTON RAPHSON" method was used. In this method, divided subtraction procedure was applied for the case that the distances are equal [18 and 22].

Result and Discussion

The calculations were done by using the below tables 1 and 2. The equation of 25 was calculated by the numerical method of "Newton-Raphson" for finding stitch length "P" from fabric tension cam degree "x".

P(x)=6.35+0.73[x-14]-0.09[x-14][x-15]+ 0.032[x-14][x-15][x-16]-0.012[x-14][x-15][x-16][x-17] (25)

Equation 25 can be a good assessment for "x" and "P" that is the cam degree and stitch length, respectively.. This calculation is for constant fabric tension. By development of calculation in various fabric tension many relations such as equation 25 is performed to the control system. After experiments for other fabric tensions, calculated stitch length and real length has been compared. The maximum error of estimation is 3.43% for tension of 20kg and stitch cam degree of 14.

In the normal design such as rib 1-1 or rib 2-1, the stitch length is adjusted in beginning of production. Therefore, in simple fabrics the stitch length is not changed during knitting. Of course, in flat knitting machine for knitting of shoulder, wriest, waist, etc. patterns the stitch length is adjusted. Also, In some fabrics with patterned appearance various methods are applied to make special effects on the fabric appearance. Variation of stitch length change is noticeable in cases stitch length change with changing in design simultaneously in one wall, stitch length change with change the colors, stitch change length with change the traversing gear and stitch change length in several wall which is very beautiful in fantastic fabrics. By changing stitch length in different areas, special effects are occurred in fabric appearance.

Conclusion

In present work, it has been attempted to perform an intelligent controlling system to the stitch length cam tools in a flat knitting machine. Also, the stitch length during knitting process has been modified based on numerical modeling of stitched length and cam degrees relationship.

The relation between stitch length cam and actual stitch length has been estimated as linear regression of "Newton-Raphson" method by experiment. Samples of different stitch length cam of available position and five samples of different fabric tension were knitted by the automated knitting machine. After that, the results were applied to find the relationship function of cam adjusting and stitch length in different tensions.

The results of practical works show that the designed system can control stitched length with low error coefficient about lower than four percent. This system is useable in all flat and circular knitting machines. The stitch length can be changed during knitting process in both case of stability control and designing various appearances.

References

[1] CH. Richman, 1965, Knitted stretch Technology, National Knitted Outerwear Association, New York.

[2] Raz S., 1993, Flat knitting technology, Universal Machinenfabrik.

[3] Stoll-GmbH-and-Co-H; Goller-E; Ploppa-J; Stoll-T; Walker F., "Flat-bed knitting machine having an electronic control for the movement of the needle sinker", USP 4 723 423: 9 February 1988 Priority applications: Germany (FRG), 3336368, 6 October 1983.

[4] Universal-Maschinenfabrik-Dr-Rudolf; Kuhnert G.; Lutz-A, "Knitting cam unit and transfer cam unit combination for V-bed flat knitting machines with slider needles", USP 4 526 018: 2 July 1985 Priority application: Germany (FRG), 3220049, 27 May 1982.

[5] Shima-Seiki-Manufacturing-Ltd: Miyamoto M., "Knitting cam and cam apparatus", EP 0 698 679: 28 February 1996 Priority application: Japan, 198890/94, 24 August 1994.

[6] Hashimoto T., Nagao Y., Doi T., "Needle selection mechanism for an automatic knitting machine ", USP 4222247: Japan, Sep 16, 1980.

[7] Enomoto T.; Watanabe T.; Watanabe K.; WAC-Data-Service-Kabushiki-Kaisha, "Needle selector for knitting machine", USP 6220062: Japan, 10193634, 25 Jun 1998: 486091, 18 Feb 2000.

[8] Munden D.L., 1959, "The geometry and dimensional properties of plain-knit fabrics", Journal of Textile Institute, 46, 587-605.

[9] James J. F. Knapton and Dennis L. Munden, 1966, " A Study of the Mechanism of Stitch Formation on Weft-Knitting Machinery: Part I: The Effect of Input Tension and Cam Setting on Stitch Formation", Textile Research Journal, 12(36): 1072-1080.

[10] James J. F. Knapton and Dennis L. Munden, 1966, " A Study of the Mechanism of Stitch Formation on Weft-Knitting Machinery: Part II: The Effect of Yarn Friction on Yam Tensions in Knitting and Stitch Formation", Textile Research Journal, 12(36), 1081-1091.

[11] P.K. Banerjee and T.S. Alaiban, 1987, " Mechanism of Stitch Formation at Extreme Cam Settings on a Sinker Top Machine: Part I: Relationship Between Count, Gauge, and Tightness Factor", Textile Research Journal, 9(57), 513-518.

[12] T. Dias and G. Lanarolle, 2002, " Stitch Length Variation in Circular Knitting Machines Due to Yarn Winding Tension Variation in the Storage Yarn Feed Wheel ", Textile Research Journal, 11(72), 997-1001.

[13] Knapton, J.J.F, Truter E. V. and Aziz A.K.M.A., 1975, "The geometry, dimensional properties and stabilization of the cotton plain-knit fabrics", Journal of the textile Institute, 66, 413-419

[14] Shanahan W.J. and Postle R., 1973, "Jamming of knitted structures", Textile research journal, 43, 532-538.

[15] Blach D.H. and Munden D.L, 1970, "Increasing the rates of fabric production of weft knitting machinery. III. Measurement of the needle forces, Journal of the Textile Institute, 61(7), 340-348.

[16] Blach D.H. and Munden D.L, 1970, "Increasing the rates of fabric production of weft knitting machinery. II. An analysis of high-speed knitting cam systems ", Journal of the Textile Institute. 61(7), 235-339.

[17] Blach D.H. and Munden D.L, 1970, "Increasing the rates of fabric production of weft-knitting machinery. I. The design and performance of high-speed knitting cams", Journal of the Textile Institute, 61(7), 313-324.

[18] Gerald C.F and Patrick O.W., 1999, Applied numerical analysis, 6th edition, Addison-Wesley Inc.

[19] Agrawal O.P. 2002, "Formulation of Euler-Lagrange equations for fractional variation problems", Journal of Mathematical Analysis and Applications, 272(1), 368-379.

[20] Universal GMBH, Manual of flat knitting machine, KA12.

[21] http://www.sanyo.co.jp/products.

[22] Tjalling J. Ypma, 1995, "Historical Development of the Newton-Raphson Method", SIAM Review, 37(4), 531-551.

Dariush Semnani *, Kamran Matin *, Mohammad Sheikhzadeh * and Masoud Latifi **

* Deptt. of Textile Engg., Isfahan University of Technology, Isfahan, 84156 Tel:+98 311 391 5006, Fax:+98 311 391 2444, Email: dariush_semnani@hotmail.com d_semnani@cc.iut.ac.ir

** Deptt. of Textile Engg., Amirkabir University of Technology, Tehran

Table 1 : Relation of stitch length with cam degree Cam Sample Cps Wps Yarn Stitch degree weight count length (gr) (tex) (mm) 14 7.49 100 100 118.2 6.35 15 9.21 100 100 118.2 7.81 16 10.3 100 100 118.2 8.73 17 11.65 100 100 118.2 9.88 18 12.45 100 100 118.2 10.55 Table 2 : Relation of stitch length with tension (cam degree=15) Tension Sample Cpc Wpc Yarn Stitch (kg) weight count length (gr) (tex) (mm) 5 9.145 100 100 118.2 7.75 10 9.215 100 100 118.2 7.81 15 8.838 100 100 118.2 7.94 20 9.581 100 100 118.2 8.12 25 9.687 100 100 118.2 8.21

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Author: | Semnani, Dariush; Matin, Kamran; Sheikhzadeh, Mohammad; Latifi, Masoud |
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Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jun 1, 2008 |

Words: | 3917 |

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