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Report | October 2018

A study of double jersey knitting

Systematic scientific studies on double jersey knitting are very limited, moreover, those are mainly concerned with circular machines. In the present research by Sandip Mukherjee, Sadhan Ray and SK Punk, an attempt has been made to investigate insight on the loop forming process of the knitted fabrics produced on a double jersey flat bed machine equipped with 1x1 rib gaiting.

Properties of knitted fabrics are mainly governed by the length of yarn forming a loop and the shape of the loop. The length of the loop is mostly decided on the machine during the loop formation and depends upon the stitch cam setting and the yarn tension. The shape of the loop on the other hand is finalised after the relaxation treatment of the knitted fabric. It is possible to determine a pre-determined length of the loop if the variables governing the length of loop as well as the mutual interaction between the variables inside the knitting zone are known.

The basic purpose of modeling of a rib loop unit or Structural Knitted Cell (SKC) is to establish the length of yarn forming a loop and to study the shape and configuration of the loop at the knitting point. Several authors have given their views regarding the modeling of loops of single and double jersey knitted fabrics. Although Tompkins first dealt with 1 x 1 rib fabric, relatively little work on structures other than single jersey was carried out until Nutting and Leaf proposed a generalised geometry for structures other than single jersey structures.

They opined that, in a relaxed state, a relation between courses / unit length and loop length, for structures other than plain – knitted ones, would not be of the simple form. They proposed that such a relation would contain a term involving yarn diameter. Smirfitt concentrated his attention on 1 x 1 rib structure and performed experimental work on wool fabrics. He concluded that these fabrics in a “tumble-relaxed” state were described by

“K” factors analogous to those proposed by Munden for single jersey fabrics.

Smirfitt experimentally showed, for practical purpose, the construction of a geometrical model of 1x1 rib repeating unit based on Leaf’s model for the plain knitted loop and relying on empirically established K-values. This model led Smirfitt to an estimation of the angle between the linking portion of a face and back loop and the fabric plane. Natkanski also reported a theoretical model based on the elastica approach of Postle and Munden. The resultant two-dimensional model yielded theoretical K values, which were in poor agreement with the experimental values, indicating that the model did not represent the true rib stitch in relaxed form.

Woolfardt and Knapton introduced a three dimensional loop model based on the principle introduced by Munden but modified by the introduction of certain assumptions relating to the geometrical configuration of knitted stitch. The significant difference between theoretical loop length and the actual loop length which is due to robbing back was first justified by Knapton and Munden. The work of Ray and Banerjee only deals with theoretical calculation of length of 1 x 1 rib loop out of many double jersey structures. Their model of 1x1 rib loop formation on dial and cylinder type machine can predict theoretical length of loop. Ray and Banerjee derived formula for expressing instantaneous length of a rib loop inside the knitting zone. Jeddi et.al developed the ideal model of knitted loop for the fully relaxed 1x1 rib structure. This model is based on the classic curve as the loop shape of face and back loops are improved by adopting an elastica configuration. Another feature of their analysis is the assumption of minimum energy position of the loops in fully relaxed structures. However neither any model of loop formation on a flat bed double jersey machine nor any geometrical expression of length of yarn contained in a rib loop unit (SKC) at knitting point or at any other point inside the knitting zone is available in the accessible literature.

Mukherjee and Punj developed a Geometrical model of 1x1 rib loop unit in a flat bed double jersey knitting machine and derived simple equations of the front and back bed stitch cam profiles. In the current paper, the entire study related to the knitting zone geometry including the loop arm configuration, stages of loop arm configuration and study of the front and back bed cam profile is highlighted.

Study of cam profiles
Cams are devices which are used in knitting machine for the movement of the needles along the axis of the same. In flat bed knitting machine the linear motion of the cam from one side of the bed to the other causes to and fro motion of the needles along their axis. The cams are carefully profiled to produce precisely-timed movement and dwell periods. The movements may be represented in the form of a time-displacement graph. The profile of the cam system incorporated in the front and back bed of the power driven, computerized flat bed double jersey knitting machine of M/S Brothers, Japan of gauge 5.5 and width 40 inches is studied. The front bed and back bed cam systems along with their profiles and needle path are shown in figure 1. The figures show the underside of the cam carriage and the cams forming the tracks which guide the needle butts for the knitting action. A set of cams consisting of raising or clearing cam, guard cam, cardigan cam and two stitch cams forces the needles to knit a course of loops in either direction of carriage traverse is shown.

The symmetrical camming arrangement is typical of flat bed machines as it enables a similar action to be achieved in both directions of carriage traverse.

The front and back bed cam profiles are drawn after removing the carriage from the machine and the length and angles of the individual components of both the cam systems are physically measured. Figure 1 show the profile of the cam systems and the path of the needles in both different directions for the front bed and the back bed respectively. It has been observed that the stitch cam of the front bed cam system has got a flat base while the stitch cam of the back bed cam system has got a pointed base. This type of profile of the stitch cam for the front bed signifies that after the knitting point the needle remains in bottom most position for sometimes, while the needle for the back bed immediately starts its upward journey after crossing the knitting point. Such observation is essential for developing the knitting zone geometry.

Thereafter the simplified profile of the front bed cam (only the path of needle movement) has been placed in conjunction with the same of the back bed cam system. The combined profiles are shown in figure 2. This has been done in order to get the simplified needle movement path in both the beds as well as to observe the loop arms configuration between the front bed and the back bed needles. This simplified combined profile of the cam systems in front and back beds helps to model the 1x1 rib loop unit (SKC) for a flat bed double jersey knitting machine for the prediction of theoretical loop length inside the knitting zone (KZ) at the knitting points.

The rib loop is formed in multiple planes due to positioning of the needles in the two beds in different planes as well as the beds are making different angles with the ground. The actual loop formation can be observed in figure 3(a). It is basically the side sectional view of the knitting zone in the flat bed double jersey rib knitting machine while the needles are at their knitting point. The front bed is inclined at an angle 1 to the horizontal and the back bed is inclined at an angle 2 to the horizontal.

From the said figure it is seen that the horizontal gap between the two beds is Hg, the maximum displacement of the front bed needle from the verge of the bed is Hf and that of the back bed one is Hb. ‘S’ is the intersection point of the needles in front and back bed, a and b are the angles of the loop in front bed and back bed respectively with the needle axes. TFN and TBN are the thickness of the front bed and back bed needles respectively and COL represents the cast off loops.

So in order to study the knitting zone geometry and formulate the loop arm configuration while the neighboring needles in the front and back bed are at knitting point, both the front and back beds should be brought at the same vertical plane. To bring both the beds in a same plane following steps are undertaken and their corresponding figures are cited:

  • Step 1. Figure 3(b): Keeping the front bed in the original position the back bed is rotated by an angle 2 at an anticlockwise direction centering at the top.
  • Step 2. Figure 3(b): The back bed is again rotated by an angle 1 at an anticlockwise direction.
  • Step 3. Figure 3(b): The back bed is shifted laterally by an amount Hg and also longitudinally by an amount Hg.
  • Step 4. Figure 3(c): The entire system is then rotated by an angle (90°- 1) in an anticlockwise direction to bring the two beds in the same vertical plane of the knitting zone.

  • Knitting zone geometry in flat bed double jersey rib knitting machine
    Geometry of the knitting zone (KZ) in a single jersey machine is described by the properties of and relations between magnitude in space enclosed by the sinker lines connecting sinker and the needle hooks. As there is no sinker in a flat bed rib machine, the enclosed space is generated by the boundary elements, namely front bed needles and back bed needles. In between the front and back bed needles, yarn comes in contact with front bed verge and back bed verge. Hence these contact points also influence the geometry of the knitting zone. The position of the boundary elements as well as the geometry of the KZ changes with change in contour of the stitch cams. The geometry also changes with the change in machine gauge and stitch cam settings due to change in number of knitting elements in the knitting zone. During the process of knitting, the geometry assumes a dynamic nature as the needles keep on moving with yarn along the cam track.

    The geometry of the knitting zone in the flat bed double jersey rib knitting machine based on simplified side view of the KZ shown in figure 4. The needle paths in both front and back beds are obtained from the study of their cam profile in order to obtain a simplified needle movement path in both the beds. From the geometry it is possible to show the position of the needle inside the knitting zone and the configurations of the loop arms as well as to device a simple model of 1x1 rib loop unit on a flat bed machine and to derive an equation for expressing the length of a rib loop unit at the knitting point inside the knitting zone KZ.

    From the figure 4 it is seen that YBm is the tuck height which is the distance of tucking point or yarn catching point from the reference line RR’. DFK and DBK are the distance of front and back bed needles at knitting point from RR’ respectively. DMF and AMF are the magnitude of the slopes of the descending and ascending side respectively of the front bed stitch cam. DMB and AMB are the magnitude of the slopes of the descending and ascending side respectively of the back bed stitch cam. Half the space between the adjacent front bed or back bed needles is denoted by ‘a’. The sinker line has been replaced by the reference line drawn by adjusting the intersecting points (S) of the two sets of needles projected on YZ plane. The position of any needle inside KZ can be determined from the equations of the stitch cam profiles of the front and the back bed. The equations of the stitch cam profiles are derived in terms of angles of the descending and ascending side of the front and back bed stitch cams, tuck height, needle spacing and some other parameters of the KZ.

    The theoretical loop length would be obtained from the length of the yarn contained between either two neighboring front bed needles while the back bed needle in between those needles is stationed at the back bed knitting point or two neighboring back bed needles while the front bed needles in between those needle is situated at front bed knitting point. Further there is a change in configuration of the rib loop inside the knitting zone during its formation in multiple planes. The configuration of the loop arms is highly influenced by the gap between the front and back bed, descending side angle of the stitch cam and the machine gauge. Thus different formulae would be needed to express the instantaneous loop length inside KZ according to the configuration of the loop. In the present work the loop length is calculated at the knitting point only, both in the case of front bed and back bed.

    In a flat bed machine there would be two theoretical loop length values – one occurring at front bed knitting point FKP and other at back bed knitting point BKP. The theoretical loop length at FKP would be the length of yarn held by a front bed needle FN situated at FKP across two neighboring back bed needles BN. Similarly, the theoretical length of the loop at BKP would be the length of yarn held by a back bed needle positioned at BKP across two neighboring front bed needles.

    Equations of cam profiles
    Equations of the front bed stitch cam profiles:

  • For descending side O’A (O < X < OA1) DMF = tanØ1 Thus, Equation of the line O’A : Y = X * DMF --------(4.1.1)
  • For the part AB which is the flat portion of the cam (OA1 < X < OB1) Equation of the line AB : Y = YBm + DFK ---------(4.1.2)
  • For the part BC along the ascending side of the front bed stitch cam (OB1 < X < OC1) X at B = {(YBm + DFK) / DMF + 4a} AMF = tanØ2 Thus, Equation of the line BC Y = (YBm + DFK) – {X – (YBm + DFK) / DMF + 4a} * AMF ------(4.1.3)

  • Equations of the back bed stitch cam profiles :
    For descending side (OH < X < OE1) X (at A1) = (YBm + DFK)/DMF X (at E1) = {(YBm + DFK)/DMF} + a In triangle EE1H : tanØ3 = EE1/E1H Again, EE1= DBK & tanØ3 = DMB Therefore, E1H = DBK/DMB X (at H) = {(YBm + DFK)/DMF + a - DBK/DMB} Now ‘Z’ is 0 upto H & for OH < X < OE1 Equation of the line HE : Z = { X - (YBm + DFK)/DMF + a - DBK/DMB} * DMB ----------(4.2.1) (ii) For the part EF along the ascending side of the back bed stitch cam (OE1 < X < OF1) X at E1 = {(YBm + DFK) / DMF + a} tanØ4 = AMB Thus, Equation of the line EF :Z = DBK – [ X – {(YBm + DFK) / DMF + a}] * AMB -------(4.2.2)

    Loop arm configuration
    Assumptions for loop arm configuration: The following assumptions for loop arm configuration are made in order to frame the knitting zone geometry:

  • At their mutual contact points yarn and needles are circular in cross section.
  • The line of contact between yarn and needles follows the path of an arc of a circle.
  • Although the line of contact between yarns in new and cast off loops follows the path of an arc of a circle, it is neglected.
  • Below the bed verge lines the half wrap angle around any needle is 90 degree.
  • Yarn segment between two successive contact zones, namely yarn-needle, yarn-yarn or yarn-verge lies along a straight line.
  • The co-ordinates of a needle correspond to that of the tip of the crown.

    Stages of loop arm configurations: In order to identify the various configurations of the loop arms, observation was carried out since the catching of the yarn by any particular needle till its reaching in the knitting point. As the catching takes place by front bed needle FN4 at or around tuck height, the feed yarn at the instant of being caught is in contact with only one back bed needle BN4. So only the leading arm is visible. With gradual downward movement of FN4, the feed yarn bends and ultimately touches the previous back bed needle BN5 and trailing arm of the loop under formation becomes visible. So in the present study loop arm configurations have been identified only from that very point of loop formation. Subsequently the front bed needle FN4 reaches the FKP and during this movement five different types of loop arm configuration has been observed. It was found that loop arm configuration passes through five stages. The stages are shown in the figures 5 and 6.

    Stage I: The needle FN4 has caught the new or feed yarn and moved down to some extent so that the yarn comes in contact with both BN4 and BN5. As a result, the leading and trailing arms are just visible and same in length.

    Stage II: The needles FN4 and BN4 has moved beyond the reference line with yarn in hook but their crowns are yet to reach the front bed verge FBV and back bed verge BBV respectively. Needle BN5 is still in the reference line. The wrap angle which is the angle subtended by the yarn around the needles increases. The yarn lies on the stem of the needle without any deflection. Leading arm of FN4 is longer than the trailing arm.

    Stage III: The needles FN4 and BN4 have moved further below the reference line with yarn in their hook and crossed the front bed verge FBV and back bed verge BBV respectively as well as casting off the old loops have taken place. The crown of BN5 has moved below the reference line but is yet to reach the BBV and is positioned between the reference line and back bed verge. Hence the leading arm of FN4 is longer than the trailing arm.

    Stage IV: The needles FN4 and BN4 has moved further below the their respective verges i.e. FBV and BBV respectively moving towards their knitting points. The half wrap angles become 90°. The crown of BN5 has just touched the BBV but still not in a position to deflect the yarn for loop formation.

    Stage V: Figure 6 shows the loop arm configuration while the needle in the front bed is at the knitting point. The crown of all three needles FN3, BN4 and BN5 are positioned at their respective verges. FN4 and BN4 are at their knitting points and BN5 is placed just at its verge level casting off the old loop. However, depending on the relative position of crowns of BN4 and BN5 it is observed that the leading arm is longer than the trailing arm. Figure 7 shows position of the crown of all three needles BN4, FN4 and FN3 in connection with the theoretical loop length at back bed knitting point. The needles BN4 and FN4 are positioned at their respective knitting points and needle FN3 is positioned beyond the knitting point. From the cam profile of the front bed it is evident that due to a flat portion of the stitch cam it is possible for two or more front bed needles to be at the depth or level of knitting point simultaneously. The typical configuration of the loop arms consisting of straight portions and curves are visible.

    The length of yarn between one front bed needle and neighboring back bed needle or vice versa forming either leading or trailing arm is neither straight nor in the same plane. The yarn bends wherever it comes in contact with any element inside the knitting zone and generally it takes the shape of a curve. The portion of the yarn wrapping any needle is in the form of curve and as the total amount of wrap may be up to 180 degree, the curves may be semicircle also. In addition to the straight segments, which are in between two curved segments around the connecting needles, there would be some more curved segments of each loop arm at the contact point of the cast off loops (COL) with the new loop.

    The expressions of the length of loop arms can be derived segment wise from the values of needle and yarn dimensions, machine gauge, contact angles between yarn and needle (angle of wrap), stitch cam settings and cam angles. The theoretical loop length represents the maximum length of yarn contained in a repeating unit when a needle is situated at knitting point. Hence, on a double jersey flat bed knitting machine there would be two theoretical loop length values, first occurring at the front bed knitting point FKP and the other at the back bed knitting point BKP as mentioned earlier.

    Conclusion
    The knitting zone geometry derived from the machine parameters is useful for the modeling of 1x1 rib loop unit (SKC) during its formation in a flat bed double jersey machine at the knitting point.

    The equation of the ascending and descending sides of both the front and back bed stitch cams, as derived, determine the coordinates of the needle positions and help to calculate the length of yarn under the control between the two neighboring needles. Five different types of loop arm configuration have been observed inside the knitting zone since the catching of yarn and reaching of the needle to the respective knitting point. The final configuration of the loop at the knitting point is considered to be divided into eight segments for front bed nine segments for back bed. The segments consist of five straight portions and remaining three curvilinear portions for front bed and six straight and three curvilinear for back bed.

    References
  • Tompkins, F., “Science of Knitting”, Wiley, New York, (1914).
  • Nutting, T. and Leaf, G.A.V., J. Textile Inst. 55, T45-53 (1964).
  • Smirfitt, J.A., J. Textile Inst. 56, T 248-259; T298-313 (1965).
  • Munden, D.L., J. Textile Inst. 50, T448-471 (1959).
  • Leaf, G.A.V. , J. Textile Inst. 51, T-49 (1960).
  • Natkanski, K.B., Ph.D. Thesis, University of Leeds, (1967).
  • Postle, R. and Munden, D.L., J. Textile Inst. 58, T329-351; T352-365 (1967).
  • Woolfardt, C. and Knapton, J.J.F., J. Textile Inst. 62, 561-584 (1971).
  • Knapton, J.F. and Munden, D.L., Textile Res. J.,36, 1072-1080 (1966).
  • Ray, S.C. and Banerjee, P.K., Indian Journal of Fibre and Textile Research, Vol.25, P 97-107, (2000).
  • Ray, S.C. and Banerjee, P.K., Indian Journal of Fibre and Textile Research, Vol.28, P 185-196, (2003).
  • Jeddi A.A.A., & Zareian A., J. Textile Inst. 97(6), P475-482(2006).
  • Mukherjee, S. and Punj, S.K. Melliand International, Worldwide Textile Journal, (Germany) Vol-17, P-143-144, August 2011.
  • Sandip Mukherjee is with the Department of Fashion Design, National Institute of Fashion Technology, Kolkata. Sadhan Chandra Ray is with the Department of Jute & Fibre Technology, University of Calcutta (Retired).

    SK Punj is with the Department of Textile Technology, The Technological Institute of Textile & Sciences, Bhiwani (Retired).

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