Knitted for better understanding

1. (4d2)

2.  The important loop dimensions are:
 loop length,
 loop width (wale spacing) and
 loop height (course spacing).
 After fabric relaxation either dry or hot and also after washing there is a
reduction in wale and course density due to a reduction in loop length
and this actually will affect the fabric properties.
Geometry of knitted fabrics

3.  Early concepts of fabric geometry were based on
• models having maximum cover therefore,
• adjacent loops are touched each other with a constant ratio of
stitch length to yarn diameter.
 Most theoretical models of knitted loops are based on an
adaptation of a geometrical shape known as an ‘elastica’.
 The geometrical models of knitted fabrics parameter is depend on
stitch length to achieve the required fabric dimensions.

4.  yarn count
 WPC: Wales per cm
 CPC: Courses per cm
 SD: Stitches density
(S/cm2)
 𝑅: Radius of loop head
 𝑊: Wale space
 𝐶: Course space
 𝑙: Loop length (mm)
 T.F: Tightness factor
 𝑑: Yarn diameter
 F.W: Fabric weight (g/m2)
 F.B: Fabric bulkiness (g/cm3)
 ℎ: Fabric thickness (mm).
Geometrical Parameters

5.  Idealized General Mathematical Model of Plain Single Jersey
Knitted Fabrics.
 In this model, the general assumptions are:
(1) Yarns are circular cross section and can be touched but they cannot be
compressed.
(2) Yarns are formed in straight lines and half circles.

6. Estimation of loop length of single jersey knitted fabric
 In most of geometrical knitted loop models
 The loop length is defined as the function of parameters other than
loop width (1/W) and height (1/C), and yarn thickness. But Peirce’s
loop model in normal structure loop length (L) depends only on yarn
thickness (d).
 Presumed that a knitted structure is
normal when the adjacent yarns
within the knitted fabric are in
contact (Figure 1). Figure 1: Peirce’s loop model (1) – normal structure
Peirce’s loop
model

7.  projection of the loop onto the fabric plane is composed of the circular needle
and sinker arcs connected with straight lines, i.e. loop legs (Figure 2).
 loop is three-dimensional, which means that the loop arcs and legs lie on the
cylinder surface with the curvature radius R and the axis parallel to the course
direction (Figure 3).
Figure 2: Construction of needle and
sinker arc, and loop legs (projection
onto fabric plane)
Figure 3: Curvature of loop legs

8.  where A is loop width, B loop height, ℓ
loop length and dpr yarn diameter, we
have for the normal knitted structure
 From Figure 2, take quarter of the loop
length ℓ/4 then develop (Equation 3) and
(Equation 4).
From figure 2 develop (Equation 1 and 2).
………………………………. (Eq 1).
……. (Eq 2).
………………………………. (Eq 3). ……………………………….
(Eq 4).
 From Eq 4 Peirce estimated that the knitted structure becomes
compact (crammed) when the ratio between the loop length
and yarn diameter (linear loop module) attains the value ℓ /
dpr = 16.66

9.  The loop length of the open knitted structure (ℓ) defined
by Peirce.
 According to Dalidovich , loop length (L) is a function of loop
width (A), loop height (B) and yarn thickness (d). Assuming that
when the loop is planar,
 Vekassy also defined a simplified equation for the loop length of a normal
knitted structure in which the needle and sinker arcs are in contact.
• The loop length (l) of the normal structure is only dependent on yarn
thickness (d):
……………………………….
(Eq 5).
……………………………….
(Eq 7).
……………………………….
(Eq 6).

10. Moreover, Vekassy anticipated the structure being more closed than
the normal structure.
 The loop height of the closed structure is smaller than the height
of the normal loop structure.
 The loop length (L) of the close knitted structure is as follows:
From the derivation of the original Morooka and Matsumoto and
Morooka’s loop model.
……………………………….
(Eq 8).
……………………………….
(Eq 9).

11. The mathematical models valid for both conventional & elasticized single knitted
structures.
The impact of independent variables to loop length studied with the multiple
linear regressions.
 The general linear model with four predictors are
Cont.…
……………………………….
(Eq 10).
In order to simplify the calculation eliminate the fabric thickness
measurements and from Eq 5, 6 and 9 to develop Eq 11.
……………………………….
(Eq 11).
 loop width (A)
 loop height (B)
 yarn thickness (d) and
 knitted fabric
thickness (t)
• obtained for all knitted fabrics, elasticized and conventional
in (Eq 10)

12. Cont.…
 loop length for conventional can be calculated as:
The loop length of elasticized made from various types of elastomeric
yarns can be calculated as:
……………………………….
(Eq 12).
……………………………….
(Eq 13).
 Finally they concluded that, the structures made from conventional yarns
without elastane show the best agreement with the studied geometrical loop
models for open structures, and
 Elasticized structures cannot be modeled well with the existing geometrical
loop models.

13. Estimation the loop length for both conventional and
elastomeric yarn in case of normal, compact and super
compact.
Estimation of the knitted loop length for open to
normal structure
 Assume that the knitted loop for open to normal structure has the shape as
shown in Fig. 4.
Fig 4. Loop shape of single jersey
knitted fabric for open to normal
structure.
• Loop width= 1/Wales per unit length
=1/w = A
• Loop height =1/courses per unit length=
1/c =B
• For normal to compact structure A ≤ 4d & B ≤
3.46d.
……….. (Eq 14).
Therefore substitute A= 4d & B =3.46d in Eq (14)
loop length will be 16.63d.
 So the loop length for open structure will be larger

14. Estimation of the loop length for normal to
compact structure
Fig 5. Loop shape for normal to
compact single jersey knitted
fabric.
• The loop length can be calculated as
follows:
• From normal to compact structure A ≤ 4d & B ≤ 3.46d
……….. (Eq 15).

15. 15
For super compact Single Jersey Knitted Fabric
A = 2d and B = d From Eq.(15), L = 5.14d.
 Based on the above estimations
 A normal to open structure converts to a compact or a very compact
structure after the dry and wet relaxation.
 The values of the loop width (A) for open, normal, compact and super
compact are larger than 4, equal to 4, from 2 to 4, less than 2 respectively.
 The values of the loop height (B) are larger than 3.46 for open, equal to
3.46 for normal, from 3 to 3.46 for compact and from 1 to 3 for super
compact.
 The loose knitted fabrics made from yarns without the elastane core are

16. Estimation of tightness factor of the knitted fabric
 The tightness factor of the knitted fabric is given by:
Where,
L = loop length in mm.
 The above equation is true, when the loop length is constant at any
state after knitted fabric manufacturing,
 But not after fabric finishing and during washing at end-use,
because the loop length is contracted.
..……………… (Eq
16).
 Hence, substitute the values of loop length in conjunction with the value of
Wales & courses at the two mentioned (Eq 14 and 15) of loop length, the
tightness factor will be as follows:
……….. (Eq 17).
……….. (Eq 18).

17.  If tightness factor considered the ratio of the area covered by the fabrics to
the total area
………………………. (Eq 19).
……………………………………..
(Eq 20).
……………………………………..
(Eq 21).
Cont.…
To simplify the Eq. (20) by ignoring the area repeated by the yarn
(4d2), the Eq. (20) will be the following:
• Loop length * yarn diameter * Wales/unit length *
courses/unit length

18. Estimation of knitted fabric porosity