Abstract:

In this work a sewing needle of an industrial commercial sewing machine is investigated from the different points of view of geometrical and critical elastic statistical balance. The dimensions of the sewing needle are  = 60 mm, and  = 2.5 mm and 1.45 mm diameter for the two stepped needle. The needle is treated as a fixed – free end column, with two sections: I0 (I1) = 1.9615 (E – 12) m4 and (I2) = 2.0516 (E – 13) m4. The upper partial length a = 31.2 mm, while the lower partial length b = 28.2 mm. The value of the critical load is 110 N, while the Euler load Pe = 1112 N, then γ = 3.1796. Another approach was used for a line diagram of the truncated cone of the sewing needle, where the critical load Pcr = 57 N, the Euler load Pe = 118 N, and γ = 3.13. For the line diagram of a sewing needle with a constant cross-section  = 1.965 mm, I = 7.3185 (E – 13) m4,  = 41.8778 N & η = 2.467. Then Pcr = 103 N, Pe = 413 N & γ =  = 2. For a sewingneedle with a constant cross-section and the penetration load is uniformly distributed, the geometric characteristic is found to be  = 7.839, γ = 1.22, Pcr = Pcr()cr = 328 N & q = 5472 N/m (6 N/mm). The present work aims to open as yet untouched areas for more and intensive academic and experimental studies, in the field of how penetration forces affect critical loads. The work is the first step in the evaluation of the mechanics of the industrial sewing needle.