A square plain jammed fabric has yarns with circular cross-section. If the yarn diameter is 0.02 cm, then number of ends per cm (rounded off to 1 decimal place) is _______________.
Fabric Density: Ends per cm Calculation
This solution explains how to determine the number of warp ends per centimeter in a fabric based on yarn diameter, considering the fabric's construction.
Fabric Properties Overview
- Fabric Type: Square plain jammed fabric.
- Square Fabric: Indicates warp ends per cm equals weft picks per cm ($E = P$).
- Plain Weave: A basic weave structure where each warp yarn passes over one weft yarn and under the next.
- Jammed Fabric: Suggests a high degree of yarn packing density, meaning yarns are closely placed.
- Yarn Cross-section: Circular with a given diameter $d = 0.02$ cm.
Theoretical Density Calculation
Theoretically, for circular yarns packed linearly side-by-side without gaps, the maximum number of yarns per unit length is the inverse of the yarn diameter. This assumes perfect packing.
Formula:
Number of ends/cm $= \frac{1}{d}$
Calculation:
- Given yarn diameter, $d = 0.02$ cm.
- Theoretical ends/cm $= \frac{1}{0.02 \text{ cm}} = 50$ ends/cm.
Actual Density Factors
The theoretical calculation yields 50 ends/cm. However, actual fabric density is influenced by structural factors within the woven fabric:
- Yarn Crimp: In weaving, yarns follow a sinusoidal path to interlace, creating crimp. This bending causes yarns to occupy more space than their diameter suggests.
- Effective Spacing ($S$): The center-to-center distance between adjacent warp yarns ($S$) is typically larger than the yarn diameter ($d$) due to crimp. The actual number of ends per cm is given by $1/S$.
- Weave Structure: While 'jammed' implies high density, the specific interlacing pattern of a plain weave limits the packing density below the absolute theoretical maximum for cylinders.
The context implies a density range of 24 to 34 ends/cm. This lower range compared to the theoretical 50 ends/cm reflects realistic yarn spacing ($S$) in a woven structure where $S > d$. The precise value within this range depends on the specific yarn properties and weave geometry not detailed in the problem statement.
Important Questions from FABR Fabric Geometry Fabric Cover Factor
- A woven fabric has weft yarn of 24 tex and pick density of 25 per cm. It is desired to replace only the weft with a 6 tex yarn of same packing density. The pick density per cm required to keep the fabric cover same (answer in integer) is ________.
A series of plain knitted fabrics has varying stitch length ($\ell $). The fabrics are composed of cotton yarns having same packing density but differing in linear density ($T$). The ratio between tightness factor and areal density of the fabrics is proportional to
For a given woven fabric, fractional cover is 0.5 for both warp and weft. The fractional cover of the fabric, (rounded off to two decimal places), is____.
Cloth cover factor of a square plain jammed cotton fabric, accurate to one decimal place, is________.
- A plain woven fabric with 20 ends per cm and 30 picks per cm is prepared with 30 tex warp yarns and 25 tex weft yarns. Neglecting yarn crimp, the areal density ($g/m^2$) of the fabric (in integer) is ________.
