Calculation of power parameters of the process of formation wire knot "Braid" for increasing reliability of lift and transport operations

. In lifting and transport operations with rolling products, the quality of the strapping is of great importance. An important role here is played by the method of connecting the ends of the strapping material. Due to its successful shape and high load-bearing capacity, the “braid” wire knot is today the most promising way to connect the ends of the binding wire in automated tying of heavy-duty riots. The absence of protruding elements makes this type of assembly less vulnerable to contact with surrounding objects. For effective design of the mechanism for the formation of the “braid” knot, it is necessary to express the dependence of the torque on the geometric parameters of the knot, the mechanical properties of the wire material and the knot formation conditions.


Introduction
In the process of forming the "braid" knot, the two ends of the wire are bent along a helix and twisted.Moreover, the deformation occurs simultaneously on both sides of the working element of the knotter, forming two symmetrical bundles.As an assumption, we accept that the deformation of the wires along the length of each of the bundles is uniform.
The geometric parameters that affect the torque of the knotter drive include (Fig. 1): lay angle α, wire diameter d, lay pitch t, bundle length lzh.The lay angle is the angle at which the axis of the wire is inclined relative to the axis of the knot.

Methods and result
The lay pitch is the length t of the section enclosed between the two nearest similar points of the same wire.The length of the bundle lzh will be considered the distance between the points of application of the torques that form it.To determine the lay angle, consider a helix formed by wires in a bundle (Fig. 2).Since the lay diameter is equal to the wire diameter, the lay angle is determined from the expression The length of the wire in the bundle increases with an increase in the angle α.The difference Δl between the length of the wire in the bundle l and the length of the bundle lzh determines the tightening of the wire on the section being tied and is determined by the formula: .
When the "braid" knot is formed, two wires are twisted twice (see Fig. 1).Thus, the torque required for the formation of such a node is the sum of the moments necessary for the shape change of each of its four branches.Moreover, in the general case, these terms of the torque are not equal to each other -their difference is due to the conditions of knot formation.Usually, one of the branches of the knot does not have a fixation and is freely pulled out during twisting, in the other two, covering the section being tied, the tension increases during knot formation, while in the fourth -the tension is constant, depending on the pressing force by the front end clamping mechanism .A straight binding wire, when a knot is formed, turns into a spatial beam, taking the form of a helix.The stresses that occur in the wire are caused by bending, torsion and stretching deformations.
According to V. T. Kozlov [1], since when the wires are twisted into a bundle, their deformation along the length is uniform, the stresses at the corresponding points of the cross section are the same.In this case, to determine the torque required to form a knot, it is enough to consider the internal force factors in any cross section of the wire in the bundle of the knot (Fig. 3).
The values of deformations from the action of bending are , where z is the distance from the fiber to the neutral axis; χ -is the curvature of the wire (constant coefficient of the kinematic curvature of the helix [2]).
The curvature of twisted wires is determined by the formula [2], [3] where α is lay angle (see Fig. 2); rw is the lay radius (when two wires are twisted, the lay radius is equal to the wire radius).
The amount of deformation from the action of torsion , where ρ is the distance from the neutral axis to the considered point; γ -shift angle for this point; l is the length of the wire in the knot bundle; φ -the angle of twisting of the wire in the bundle (approximately equal to the angle of rotation of the working body of the knotter).Tensile strains caused by wire tension are negligible compared to bending and torsional strains, therefore, according to N. I. Bezukhov [4], the generalized strain for our deformed state can be quite accurately expressed as where μ is the Poisson's ratio (for the elastic zone μ=0.3).
Whence the area of the elastic zone, calculated at σТ=300 MPa, G=0.8•105 MPa, α=45° and the twist radius equal to the radius of the binding wire, is 0.0023% of the cross-sectional area of the wire.
Thus, neglecting the elastic core, we will take into account only plastic deformations.In we will assume that the hardening of the wire material is linear.Then the functional dependence of the generalized stress on the generalized strain will have the form Based on the physical equations of the theory of plasticity [4], we express the normal and shear stresses acting in the cross section of the binding wire Since the volumetric deformation during plastic deformation is practically equal to zero [4], the term εav from equation ( 2) can be excluded.
The mean normal stress is Then, taking into account (1) + П; (3) The values of bending and torque caused by internal forces acting in the cross section of the wire: To determine the first terms in expressions ( 5) and ( 6), let's move on to the polar coordinate system (Fig. 4).After integrating the second terms in expressions ( 5) and ( 6), we obtain the final expressions for the bending and torque moments: In the process of laying, tensile forces P (Fig. 7) act on the wire, directed along the knot axis at an angle α to the direction of wire tension T. The magnitude of these forces depends on the knot formation conditions.
For a wire branch not fixed in the longitudinal direction, the tensile force is zero.The tensile force in the branch fixed by the clamping mechanism of the front end of the wire is a value that depends on the characteristics of this mechanism and does not change during the formation of the knot (the clamping mechanism poisons the wire -the option with rigid fixation is excluded as extremely unfavorable).In the branches covering the section being tied, the tensile forces increase in the process of knotting, which is caused by the tightening of the wire during its shape change.The reaction RT arising from the action of the tensile force P is determined from the condition of equilibrium of the moments Then the expression for determining the moment caused by the tension of the wire, reduced to the working element of the knotter, will have the form The torque M, necessary for the shape change of each of the four branches of the node, is determined from the vector sum of the moments (see Fig. 3 .
where Pi -is the tensile force in each of the four branches of the node.Formula connects the parameters of the knot, the strapping material and the conditions of knot formation with the torque on the working body of the knotter.This makes it possible to use it for theoretical substantiation of the choice of parameters of the elements of the mechanism for the formation of the "braid" knot and for solving problems of their optimization.

Fig 2 .
Fig 2. Scheme for determining the lay angle

Fig. 3 .
Fig. 3. Scheme for determining the internal force factors in the cross section of the binding wire

Fig. 4 .. 6 Fig. 5 .Fig. 6 .
Fig. 4. Geometrical parameters of the elementary cross-sectional area of the wire in polar coordinates Then of inertia and the polar moment of inertia of the wire cross section;