The Application of the Secant's Equation to the Sewing Machine Needle

S.H. El Gholmy, I.A. El Hawary
2015 Alexandria Engineering Journal  
The sewing needle of the industrial sewing machines is an essential element. Its' target is to penetrate the sewn fabric layers by a penetrating axial compressive force, which, coincides with the sewing needle geometrical axis. Author wise, it will cause stress on the needle's cross section. Practically, there is always a shift -eccentricity-between the effective action line of the force and the sewing needle geometrical axis. In the present work a mathematical approach has been carried out to
more » ... tudy the mathematical relationship between the eccentricity ec r 2 À Á and the penetration force ðP a Þ, taking into consideration the critical load (P cr ) (Euler load) of the sewing needle. This relationship is named the "Secant formula", where it was computerized and graphed. It was found that; the limiting values for the ec r 2 À Á was 0.7 and for the ratio P a =P cr was 0.8 to make the needle to run in its design stress 538 MPa (steel). When the ratio P a =P cr was equal to unity, the sewing needle max stress r max changed from 101 MPa to 58 GPa i.e. the working penetration force P a must be far enough from the critical load by about 20%. The required value of P a must be equal or less than 0.8 P cr . This work focused on the static case. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
doi:10.1016/j.aej.2015.03.005 fatcat:wh4n3i7qwngx3dnsee5cfydice