| Summary: | The needle of the industrial sewing machine is its most important part. During the sewing process, the needle is subjected to various actions and interactions between these actions. One of the factors that are most related to these interactions is the lateral elastic resistance – spring effect – of the sewn fabric on the needle during its penetration in the layers of fabric. In the present work, this effect has been investigated via a special formula, where the spring constant is incorporated. It was found that the equivalent length coefficient of the sewing needle (γ) ranged between 0.7, where the lower end of the needle still has not penetrated the fabric and 2, where the lower end has already penetrated the fabric. The elastic stability factor (η) was changed from 2.46 to 20.35, to create a critical axial compressive load Pcr=5 for a 39 cN of the sewing needle. This means that the spring constant (S) changed from S=0 to S=∞, which enhanced the critical load by 8 folds. For S=0, the angle has two options, the first is ≤π2λloand the second ≥π2λl/o. The values ofγ, η, and Pcr for (λl)o were not reasonable, while values of these variables for λl/o were acceptable. The future vision of the present work is to design and construct a stand to experimentally check the theoretical work suggested in this paper and to find its experimental values.
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