The article presents the theoretical foundations of the fiber separation process from the seed in a newly developed laboratory roller gin intended for ginning small samples of raw cotton. The gin design includes a working roller and a double-knife system, consisting of a stationary and a movable knife located in the ginning zone. Based on a force analysis of the fiber section clamped between the stationary knife and the ginning roller, expressions are derived for the friction forces, the normal pressing force, and the resultant force tending to detach the fiber from the seed. It is shown that, with friction coefficients of 0.463 between the fiber and the leather roller and 0.32 between the fiber and the knife surface, the detaching force amounts to about 14.3% of the normal pressing force. It is established that the movable knife introduces a periodic dynamic component into the detaching force, while the alternating stresses in the fiber attachment zone cause fatigue weakening of the bond between the fiber and the seed. The conditions for effective fiber separation and for avoiding fiber damage are formulated, defining the permissible combinations of system parameters. On the basis of the force analysis, a mathematical model is constructed that describes the dynamics of fiber separation under the action of the working elements of the double-knife system. In this model, the fiber tuft (lint fly) is treated as a material point moving under friction, aerodynamic drag, and damping forces. An analytical solution of the linearized equation of motion is obtained, which makes it possible to determine the trajectory of the fiber tuft and to distinguish the transient, uniform, and oscillatory components of its motion. Expressions are derived for the critical displacement of the fiber tuft and for the fiber separation time, which is inversely proportional to the normal pressing force and to the difference between the friction coefficients, and directly proportional to the mass of the fiber tuft and the bond strength between the fiber and the seed. Optimality criteria and an expression for gin productivity that includes an intensification coefficient are proposed, providing a basis for optimizing the design and operating parameters while ensuring the required fiber quality.
Theoretical Foundations of The Fiber Separation Process in A Laboratory Roller Gin of a New Design
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Abstract
References
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