Common Calculation Formulas for Woven Fabrics
1. Raw Material Quantification Calculation:
The factors involved in raw material quantification are numerous, and many of the process shrinkage calculations are quite complex. To facilitate understanding, a smaller range of values is provided for reference.
1.1 Warp Yarn Quantification:
Warp yarn quantification per meter (g/m) = per centimeter warp density × finished fabric width (cm) × (1 + process shrinkage rate) × (1 + fabric shrinkage rate) × raw material fineness (D) ÷ 9000 (or 1/N, 0.59/s)
1.2 Weft Yarn Quantification:
Weft yarn quantification per meter (g/m) = finished fabric width (cm) × per centimeter weft density × (1 + weft fabric shrinkage rate) × (1 + process shrinkage rate) × raw material fineness (D) ÷ 9000
The "process shrinkage rate" in the above formulas refers to both raw material shrinkage rate and twist shrinkage rate.
(1) Process Shrinkage Rate 1—Raw Material Shrinkage Rate:
Shrinkage rates for various yarns (silk) with different properties and processing methods are as follows:
(2) Process Shrinkage Rate 2—Twist Shrinkage Rate:
When yarn passes through twisting, it shortens because the yarn changes from straight to a spiral shape. As the yarn shortens, its diameter naturally increases.
Therefore, for a constant length, the fineness of the yarn will increase accordingly. The twist shrinkage rate varies depending on the fineness and twist of the yarn. Twist shrinkage can be calculated using a formula or referring to a commonly used twist shrinkage table.
Generally, for 75D filament, adding 10 twists per centimeter results in a twist shrinkage rate of about 2-3%; for 75D filament, adding 20 twists per centimeter results in a twist shrinkage rate of about 11-12%; for 150D filament, adding 10 twists per centimeter results in a twist shrinkage rate of about 5-6%; for 150D filament, adding 20 twists per centimeter results in a twist shrinkage rate of about 13-15%.
(3) Process Shrinkage Rate 3—Warp Direction Shrinkage Rate:
During weaving, the warp yarn forms a bend when interlacing with the weft yarn. As a result, one meter of warp yarn does not correspond to exactly one meter of fabric. The ratio of yarn length to fabric length is the fabric shrinkage rate.
The fabric shrinkage rate can also be calculated using a formula. The size of the shrinkage rate is related to the yarn fineness, weft density, and fabric structure. The coarser the weft yarn, the larger the shrinkage rate; the denser the weft yarn, the larger the shrinkage rate; the smaller the number of structural cycles, the larger the shrinkage rate.
Generally, for standard products (single-layer fabric where the weft density is neither too sparse nor too dense), the shrinkage rate is around 3-8%. (The specific shrinkage rate can be selected between 3-8% based on the above-mentioned yarn fineness, weft density, and fabric structure).
2. Fabric Weight Calculation:
The purpose of fabric weight calculation is to understand the approximate weight of the fabric, which can then be used to estimate the fabric's cost and price.
Weight per meter: Refers to the weight in grams of each meter of finished fabric. The calculation method is:
Finished fabric weight per meter (g/m) = (Warp yarn quantification × refining ratio + Weft yarn quantification × refining ratio) ÷ Dyeing and finishing shrinkage rate
(1) Refining Ratio:
The refining ratio refers to the net weight of the yarn (or filament) after dyeing and finishing. The impurities contained in different fibers vary, and different processes can result in different refining ratios for the same raw material.
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The common refining ratios for raw materials are as follows:
(2) Dyeing and Finishing Shrinkage Rate:
The dyeing and finishing shrinkage rate refers to the length ratio before and after the fabric undergoes dyeing and finishing.
Dyeing and finishing shrinkage rate = Fabric width in gray fabric ÷ Finished fabric width = Finished length ÷ Gray fabric length
Square meter fabric weight (g/m2):
Square meter fabric weight (g/m2) = Weight per meter of fabric (g) ÷ Fabric width (m)
3. Raw Material Content Calculation:
For fabrics woven or blended with two or more types of raw materials, it is necessary to calculate the proportion of each raw material. The calculation method is as follows:
A. Raw Material Content = (Weight of A raw material × Proportion of A raw material × Refining ratio of A raw material) ÷ (Weight of A raw material × Refining ratio + Weight of B raw material × Refining ratio) × 100%
Example: A product has warp yarn as 120N/2 silk-linen blended yarn (70% silk, 30% linen) and weft yarn as 40S/2 high-gloss rayon yarn.
Finished fabric width: 140 cm Plain weave structure Finished warp density: 28 threads/cm Finished weft density: 24 picks/cm Gray fabric weft density: 23 picks/cm
Next, considering multiple factors, estimate the weaving shrinkage rate at 5%, the silk processing shrinkage rate at 2.5%, the weft shrinkage rate at approximately 10%, and the viscose staple fiber processing shrinkage rate at 2.0%. Therefore:
For silk content calculation:
Silk raw material content = (Weight of silk raw material × Proportion of silk × Refining ratio of silk) ÷ (Weight of silk raw material × Refining ratio + Weight of rayon yarn × Refining ratio) = (65 × 0.7 × 0.95) ÷ (70 × 0.95 + 109 × 0.97) × 100% = 43.2 ÷ 167.5 × 100% = 26%
For linen content calculation:
Linen raw material content = (Weight of linen raw material × Proportion of linen × Refining ratio of linen) ÷ (Weight of linen raw material × Refining ratio + Weight of rayon yarn × Refining ratio) = (65 × 0.3 × 0.95 × 100%) ÷ (65 × 0.95 + 109 × 0.97) = 18.5 × 100% ÷ 167.5 = 11%
For viscose content calculation:
Viscose raw material content = (Weight of viscose raw material × Refining ratio of viscose) ÷ (Weight of warp yarn × Refining ratio + Weight of viscose yarn × Refining ratio) = (109 × 0.97 × 100%) ÷ (109 × 0.97 + 65 × 0.95) = 105.73 × 100% ÷ 167.5 = 63%
From the above calculations, we can conclude that the warp yarn raw material quantification is 65g/m, and the weft yarn raw material quantification is 109g/m.
Based on this, the raw material cost can be accurately estimated by adding a certain percentage of yarn return rate based on the product process (white woven, color woven, stripes, checkered).
This cost, along with the weaving and dyeing labor costs, gives the final base price of the product.
(NOTE: The term "weight" in this text is the traditional terminology, while the standard term should be "mass.")