DIAGNOSTICS OF STABILIZATION MODES OF SHAPE STRAND ROPES

The work is devoted to the diagnostic issues of the possibilities of technological balancing of steel shaped strand ropes of lifting and transport equipment, which is of great scientific and practical importance, since it will improve their performance. A literature review showed that this topic is practically not covered and only the issues of straightening (bending) strands, which are not effective enough, are considered. The research objective and the problem that must be solved to obtain ropes with better quality characteristics (greater durability and strength) have been formulated. A more accurate expression for the technological torque of shaped strands is presented. The ways of reducing the torque as a harmful factor are indicated. Diagnostics of possible options for technological balancing of ropes was carried out. Rational modes of manufacturing shaped strand ropes have been determined


INTRODUCTION
Steel ropes and reinforcing strands are widely used in industrial engineering. The first designs of twisted products were wound wires on round cylinders.
The long period of operation of such ropes has led engineers to the need to increase their performance and strength.
The cross section of the round strand and shaped strand ropes is shown in Fig.1. It turned out to be practically impossible to increase the operational capabilities of the ropes due to the quality of the wire materials because of the absence of the corresponding metals in nature.
A way out for this problem was found by the engineers (for the first time in Germany) in the creation of ropes with a new geometry. Structures of steel shaped strand ropes appeared, where wires were wound on cylinders of triangular and oval sections.
It turned out that this design allows to reduce the frictional force of individual wires on the pulleys and drums (that is, to increase the lifetime of the ropes by 42%) and to increase the strength due to the high value of the cross-sectional utilization factor by 33% [1,2].
The manufacture of such ropes has also been mastered in Ukraine at the Khartsyzk Steel Wire Rope Plant.
The shaped cylinder will have variable geometry (lay angle, curvature and torsion) and stress state. Existing works on the geometry and stress state of wires describe their behavior only approximately and with a distortion of the actual state.
For this reason, it is very difficult to diagnose and obtain sufficiently accurate optimal parameters of technological balancing and additional processing of steel shaped strand ropes.
In this regard, the determination of the optimal parameters of the manufacturing technology and additional processing of shaped strand ropes on the basis of more accurate solutions for the geometry and stress state of wires is an urgent scientific and practical problem in the mechanics of steel ropes [3][4][5].

ANALYSIS OF RECENT RESEARCH AND PUBLICATIONS
The laying stresses, being summed up over the cross section of the wires, are integrally given to both the main vector and the main moment of internal forces.
The zones of elastic and plastic strains in the cross section of the wires of the shaped strand, depending on the laying mode, are shown in Fig. 2. a b c d Fig. 2. Zones of elastic plastic strains in the cross section of the rods when winding on a shaped cylinder: a -bending + torsion + tension; bbending + torsion with twisting + stretching; cbending + torsion with twisting; d -bending If we project the main vector and the main moment on the axis of the Frenet trihedron associated with the center of gravity of the wire section, then the normal and transverse forces Qn, Qb, bending Mn, Mb and torque Mt moments (t, n, b are the axes of the Frenet trihedron) are obtained.
These forces and moments form the so-called technological torque, which is a harmful factor. It causes twisting of the strands and the structure of the strands in sections may be disrupted [3]. Therefore, it is necessary to either eliminate ℎ or reduce it in all possible ways. In [4], the value of ℎ is presented in the form of an approximate expression Rjiwire lay radius; γjiangle between the curvature radius and the lay radius; wire curvature.
Here it is assumed that the lay angle is a constant value, and the curvature and torsion of the wires change abruptly, which does not correspond to the actual behavior of the wires. It can be seen that the values of ℎ calculated by (1) will have significant errors [5][6].
One of the effective methods of reduction of ℎ is the use of technological torsional strain. By adjusting its value, which is quite simple to implement, the value of ℎ can be changed in very wide aisles. With regard to the winding of wires onto shaped cylinders, the optimal design for the technological torque has not been studied at all and is of scientific and practical interest [7].
This paper discusses the issues of reducing the value of ℎ during the technological balancing of steel shaped strand ropes. It is noted that these issues do not yet have even an approximate coverage in the technical literature.

THE PURPOSE OF THE RESEARCH
In this regard, the purpose of the paper is to obtain the most accurate solutions for diagnostics of technological balancing of steel shaped strand ropes. This goal is achieved by solving the following tasks: 1. Determine the internal bending and torque moments of the wires, taking into account the variable geometric parameters. 2. Construct a more accurate expression for the technological torque. 3. Optimize the technological parameters of balancing shaped strand ropes. 4. Formulate recommendations for improving the properties of shaped strand ropes during manufacturing.

Diagnostics and theoretical substantiation of technological balancing of shaped strands
The value of ℎ of the shaped strand is equal to the sum of the moments of the internal force factors of the wires relative to the axis of the cylinder [6,7]. According to [8], the technological torque of the shaped strand is determined by the expression: where: mnumber of wires in the layer; technological torque of the strand core, which is determined by the formula [9]: where: number of wires of the core; core wire lay angle; number of layers of core wires; bending moment and torque in the core wires; mnumber of layers of shaped strand wires; technological torque of the layer of shaped strand wires. The value of is determined by the expression [8]: where: coefficients determined for triangular strands by the formulas: k=3 for the triangular strand functions of the lay radius and layer wire lay angle; ( ), Ɵkcurvature and kinematic torsion of layer wires; γ(φ)angle between the lay radius and the curvature radius of the shaped cylinder contour.
The moments are determined by integration over the plastic and elastic zones of the wire sections [8]: (7) where: axial moment of the wire section inertia; moment of inertia of the elastic zone ellipse.
Semi-axes of the elastic zone ellipse in the wire cross-section: Coefficients: (13) where: Gelasticity modulus of the 2nd row of wire material; kinematic torsion of wires on a shaped cylinder.
The moments , , , are determined by integration over the plastic and elastic zones of the wire cross sections [8].
A 2b = ∫ in this formula, "+" is the sign to calculate and «-» is for Calculation of the values of ℎ according to the formula (2) for some shaped strand ropes gave the following values: for a rope strand with a diameter of 27. . (17) In (17), it is denoted: ɳ -twisting coefficient; R(φ)wire lay radius function (radius of the shaped cylinder contour in the normal section); hwire lay pitch.
It is obvious that the wire, when wound on a shaped cylinder, will not experience torsion strain if The values of the twisting coefficient for a rope with a diameter of 27.5 mm are presented in Table 1.  Equation (17) can be solved with respect to the twisting coefficient ɳ: This equation is transcendental and can be easily solved by the method of successive approximations. The initial value ɳ can be selected from the interval -1.3 ≤ ɳ ≤ -1.2, and moments can be calculated using expressions (7) and (14). For wire layers of triangular strands, the numerical solution of equation (20) shows that condition (16) is fulfilled if the twisting coefficient is equal to ɳ = -1.34 (20) Of great practical interest is the simultaneous fulfillment of the criteria of durability and aggregate strength of shaped strands. In this case, the internal force factors, the wire layer technological torque and the strain intensity in the outer wire layers can be provided as functions of one argument ɳ and its values can be obtained for various criteria of durability and aggregate strength of shaped strands [12][13][14].
The various technological modes for the manufacture of shaped strands are considered.
First option. Strands with the highest possible aggregate strength.
This requirement is satisfied when the strain intensity in the outer wire layers: where = √ 2 + 3 2the intensity of stresses in the wire outer fibers has a minimum.
The solution of equation (21) shows that the value ɳ corresponds to this condition. ɳ=-0.96, The moment of elastic recoil of the strand will change by 15-20%. It is seen that the existing lay mode, when ɳ = -(0.9-0.9167), does not correspond to the optimal one. Therefore, by bringing the value of ɳ layers of strand wires to ɳ = -0.96 (which can be done quite simply by changing the gears of the stranding machine unwinding mechanism), it is possible to increase the strength and balance of three-sided strand ropes.
Second option. Strands with the greatest possible balance and strength equal to the ropes being produced [15,16].
This requirement is satisfied when ( ) is equal to the strain of the wires of the ropes being produced, i.e. at ɳ = -0.9.
In this case, the total torsional strain Ɵ must be opposite in sign of the kinematic torsional strain. The numerical solution of equation (20) shows that this can be achieved when ɳ=-1.08. (23) The moment of elastic recoil is reduced by 35-50%.
This mode of stranding strands is the most appropriate for modern rope manufacture. On the one hand, the strength of the ropes will practically not change, but on the other hand, the balance and stability of the geometry of the wires of the strands will improve to a greater extent than in the 1st option [17,18].
The third option. Strands with the highest possible strength and balance at the same time.
This option corresponds to the minimum of simultaneous changes of and . The solution to equation (20) shows that ɳ=-1.18. (24) With such twisting coefficients, the strength of the ropes decreases in relation to those produced, but decreases significantly by 4-5 times. The value ɳ (20) corresponds to this case. With such values of ɳ, the wire will experience significant torsional strain.
At the same time, the strength of the ropes decreases [19,20].
The values of the bending moment, the torque of the wire sections, the torque in the layer of wires and the intensity of strains in the outer fiber of the wires are presented in Table 1. Graphs of these values are presented in Fig. 3. The change in the geometry of the lay of wires in the rope strand with a diameter of 27.5 mm is shown in Fig. 5.
The main difference between formulas (26) -(28) from (29) is the dependence of the lay radius on angle . As a result, the exact determination of the geometry of the wires on the shaped cylinder becomes much more complicated. If (29) is differentiated on one, two and three times, then general formulas are obtained for: the length of the wires on the shaped cylinder = ∫ √ ( ) 2 + ( ) + ( (33) If the lay radius of wires in a triangular strand is represented by the formula  36) and (37) most accurately describe the actual geometry of the wires on the shaped cylinder. In this work, these formulas are used to describe the elastoplastic state of the wire material, which subsequently made it possible to develop the optimal parameters for technological balancing of steel shaped ropes.

CONCLUSIONS AND RECOMMENDATIONS FOR DIAGNOSTICS OF TECHNOLOGICAL BALANCING WHEN MANUFACTURING SHAPED STRAND ROPES
As a result of the research, the following conclusions can be drawn. 1. Expressions for internal bending and torque moments are constructed, taking into account the variable geometric parameters of winding shaped strand wires.
2. Based on the formula (2), the most accurate expression for the technological torque (elastic recoil moment) of shaped strands is given. 3. Recommendations for improving the properties of shaped-strand ropes when manufacturing are formulated (see options 1-4). 4. Additionally, it can be noted that condition (16) can be achieved only due to a significant value of the axial twisting of the wires. In this case, the elastic plastic stresses in the wires reach dangerous values and, therefore, this method has significant limitations. Thus, in the manufacture of shapedstrand ropes, it is necessary to use the values of the twisting coefficients of options 1 and 2, and to significantly reduce the moment of elastic recoil and neutralize the lay stresses, subject the ropes and strands to additional processing.