V. Scherban, O. Kolisko, G. Melnyk, M. Goldberg, A. Kirichenko, V. Kalashnyk. Determination of velocities of thread axis points when interacting with a direct large curvature taking into account the deformation in the contact zone
Description: The theoretical study of the process of the movement of the thread, which is deformed in the contact zone with the guide, from the point of view of determining the speed, is of great importance for solving a number of specific applied problems. When determining the speed, it was assumed that the start of the Lagrangian and Euler coordinates coincided. Taking into account that the crumpling of the thread in the contact zone occurs at forces much lower than the forces required to stretch the thread, the thread was considered as non-extensible. To determine the law of the distribution of the speed of the points of the thread, an independent vector, which is always connected to the main triangle, was introduced into consideration. The relationship between the vector of total curvature and the vector of absolute angular velocity is obtained. The obtained values of the speed at an arbitrary point of the axis of the thread as a function of the deformation vector, which determines the degree of twisting of the thread in the contact zone. The obtained results can be used to study various technological processes in the sewing, knitting, and textile industries, where the movement of the thread takes place along the guide surface of great curvature.