Development of a Method for Estimating the Resistance of Fibers and Threads to a Sliding Bend Based on Energy Consumption for External and Internal Friction

We present materials for constructing an instrumental method for assessing resistance of threads to the sliding bend relative to cylindrical surfaces in order to solve tasks on control and prediction of conditions for their processing at minimal cost of production. Underlying the method is the differential accounting of energy consumed to overcome the internal and external friction.The main objective of this study was to improve informativeness of the results obtained in the analysis of fires and threads through manifestations of physical- mechanical properties predetermined by patterns in their structure and composition, as well as by characteristics of the streamlined surfaces. It has been proposed to test the thread based on the simulated actual conditions for frictional interaction when bending radius r of the working bodies' edges should be commensurate with the thickness of the thread. Given such a variant of testing, we have identified conditions that ensure the manifestation of parameters for the internal and external friction, which made it possible to devise a technological scheme of tests and to conduct comparative analyses of threads in materials with different structure and properties.We have proposed, as an estimate that characterizes the manifestation of only the external friction at a cylindrical surface of curvature 1/r, the magnitude of energy Аext. consumed to displace a thread (of rigidity EI and with a stretched force) under condition 2T(r)2/El ≥ 1500. To account for the total energy A due to the external and internal friction, as an estimate that characterizes the resistance of a thread against a sliding bending, the test conditions imply the application of a bending surface with elevated curvature 1/r1, that is r1<<r.In order to calculate the estimate D as the proportion of energy Аintern required to overcome the internal friction, the dependence D=[(А–Аext.)/A]·100, %, is used. It has been proposed to perform tests in two stages, each of which implies that a thread, stretched by a constant force, should streamline cylindrical surfaces at an unchanged capture angle, while the radius of the curvature varies at each stage.Effectiveness of the proposed method for assessing resistance against a sliding bend has been confirmed by the results of experiments. We have established a possibility to differentiate the tested threads and yarn based on the magnitude of estimates Аext and D under different conditions for interaction with a cylindrical surface. The results obtained allow us to recommend the proposed method for practical implementation, specifically, to control the degree of thread passability through the machine thread-guiding gea

An Approximating Mathematical Model of Interaction Between a Freely Rotating Disk and Soil

A generalized mathematical model of disk interaction with soil was built under general assumptions regarding the mode of the disk knife motion in soil, namely, in a mode of slippage, skidding or rolling without slippage and skidding. Previously constructed models follow from it as particular cases at certain values of parameters. However, because of computational complexity of this model for the case of a freely rotating disk knife consisting in the need for a preliminary numerical solution of a transcendental equation to determine the mode of disk motion, the generalized mathematical model has not found wide application. Therefore, an analytical two-dimensional approximation of a generalized model of disk interaction with soil which is a new model of approximation type was constructed on the basis of a computer experiment using the least squares method.An explicit expression was obtained for the kinematic parameter of a freely rotating disk knife which determines its mode of motion. It was established that this parameter is a rational function of relative depth of the disk penetration and the dimensionless dynamic coefficient characterizing soil properties. Also, explicit expressions were obtained for the projections of the resultant soil reaction forces acting on the blade of the disk knife and its side faces depending on the data of dimensionless parameters. It has been established that the horizontal component of the reaction which determines tractive resistance of the disk is also a rational function of the relative penetration depth and the dimensionless dynamic coefficient. It was established that the magnitude of the kinematic parameter significantly affects the magnitude and direction of the resultant soil reactions to the disk. The expressions obtained make it possible to significantly simplify experiments to determine the resultant soil reaction forces to a freely rotating disk knife and reduce their required number. These expressions make it possible to carry out strength calculations of soil-cultivating working tools with disks and determine their optimal parameters according to the strength criteria and the minimum specific energy consumption with accuracy sufficient for engineering practice. Adequacy of the obtained expressions was confirmed by comparison with experimental data of the disk knife dynamometr