Expert paper POSSIBILITIES FOR OPTIMIZATION OF STEEL ROPE CROSS-SECTION AND THEIR VERIFICATION. Stanova Eva 1, Molnar Vieroslav 2

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1 UNDERGROUND MINING ENGINEERING 14 (2005) UDK 62 FACULTY OF MINING AND GEOLOGY, BELGRADE YU ISSN ABSTRACT Expert paper POSSIBILITIES FOR OPTIMIZATION OF STEEL ROPE CROSS-SECTION AND THEIR VERIFICATION Stanova Eva 1, Molnar Vieroslav 2 The problem area of optimization for metallic cross-section for steel rope is solved in the paper. Optimization is processed by wire diameter calculation by using three methods and results are verifyied graphically by using 3D model created by application software Pro/ENGINEER Wildfire 2. Key words : steel rope, cross-section, structure SEAL, wire. 1. INTRODUCTION Often used steel ropes are ropes with concurrent construction type SEAL which in comparison with classical ropes by the same diameter have bigger metallic cross-section and so bigger tonnage. By optimization of geometrical construction by the given rope diameter it is possible to achieve the biggest metallic cross-section. For term optimization it is considered finding the most appropriate construction elements for given rope type. Let us consider the rope of type SEAL with geometrical composition 6x(1+9+9)+v with diameter d = 16 mm. There are stated nominal values of basic parameters of the rope in the table 1. The values are determined by the standard STN according to Slovak technical standards. The rope is composed of 114 wires and fabric insertion. Table 1. The basic parameters of the rope SEAL 6x(1+6+9)+v Rope diameter 16 mm Bearing rope cross-section 99,71 mm 2 Rope tonnage wire core diameter Diameter for wires from 1 st layer Diameter for wires from 2 nd layer 156,5 kn 1,6 mm 0,71 mm 1,25 mm 2. OPTIMIZATION OF METALLIC CROSS-SECTION 1 Technical University, Faculty of Civil Engineering, Department of Descriptive Geometry, Vysokoškolská 4, Košice, Slovak Republic. 2 Technical University, Faculty of Mining, Ecology, Process Control and Geotechnologies, Department of Logistics and Production Systems, Letná 9, Košice, Slovak Republic.

2 152 Stanova E.; Molnar V.; Optimization of metallic rope cross-section can be achieved by appropriate geometric construction of strands. Let us assume that rope diameter d and winding angle of rope strands are constant values. There is possible to determine by calculation the most appropriate wires diameters for the core, 1 st and 2 nd layer of strand as well as winding angles of wires for individual layers in strand. There exist various methods for calculation of the parameters. We selected methods described in [3] and [2]. 1 st method In [3] J. Hankus describes determination of construction parameters of circular strand with point contact of wires. We determined strand diameter by the method d pr. For the diameter was calculated by the G. J. Jozef method [3] value of strand core diameter δ 0, wires diameter for the 1 st layer δ 1, wires diameter for 2 nd layer δ 2 and values of winding angles α 1, α 2 of the wires. Calculated values are shown in the table 2. 2 nd method There is described method for calculation the basic parameters of one strand layer in [2]. The real wire cutting is assumed. There are stated values calculated by the method in the table 2. 3 rd method By verification of applicability of calculated parameters the 2 nd method was found as inaccurate. Therefore we selected the following procedure. First we calculated by the method described in [2] strand diameter d pr and by using it wires diameters of the second layer δ 2 and from these values by using homothety and similarity other parameters. Result parameters are in the table 2. There were calculated metallic cross-sections of steel ropes and percent utilisation of metallic cross-sections with regard to circular rope cross-section from achieved values. The values are in the table 2 compared with values given by the standard STN Table 2. Calculated parameters for steel rope SEAL 6x(1+6+9)+v

3 Possibilities for optimization of steel rope SEAL 6x(1+9+9)+v Rope diameter d = 16 mm Optimization method STN 1.method 2.method 3.method Wire core diameter δ 0 [mm] 1,6 1,4 1,6 1,3868 Diameter for wires from 1 st layer δ 1 [mm] 0,71 0,7238 0,7845 0,7142 Diameter for wires from 2 nd layer δ 2 [mm] 1,25 1,3152 1,3283 1,3283 Strand diameter d pr [mm] - 5,2305 5,2359 5,2359 Winding angle for strands in the rope β [ ] - 15, , ,7684 Winding angle for wires from 1 st layer α 1 [ ] - 6,583 7,2238 6,6732 Winding angle for wires from 2 nd layer α 2 [ ] - 12,1 12, ,2762 Cross-section of circumscribed circle [mm 2 ] 201,06 201,06 201,06 201,06 Metallic rope cross-section [mm 2 ] 99,71 105, ,53 Gross-section utilisation 49,59% 52,26% 56,20% 52,49% Rope tonnage [kn] by the σ m =1570 MPa 156,54 164,96 177,41 165,68 Tonnage increase in comparison with STN. - 5,38% 13,33% 5,84% 3. VERIFYING OF PARAMETERS APPLICABILITY Applicability of calculated parameters was graphically verified. We created 3D model for strand part and rope for all the three calculation methods. Strand sections by the plane normal to the rope axis uniquely show not applicability of parameters determined by the 2nd method (fig. 2). There are shaded sections of wires in strands in fig. 1 and fig. 3. Their parameters are determined by the 1 st and 3 rd method. Graphical models of the strands are generated in fig. 4a, b and rope part model in fig. 5. Fig. 1 Wires cross-sections in a strand determined by the 1 st method Fig. 2 Wires cross-sections in a strand determined by the 2 st method

4 154 Stanova E.; Molnar V.; Fig. 3 Wires cross-sections in a strand determined by the 3 st method a) b) Fig. 4 Graphical model of a strand for rope SEAL 6x(1+9+9)+v created by parameters calculated: a) by the 1 st method, b) by the 3 rd method Graphical models are generated by software Pro/ENGINEER Wildfire by using rope mathematical model described in details in [5]. The rope mathematical model can be applied for various constructions of contra-directional as well as directional ropes with any number of strands and wires.

5 Possibilities for optimization of steel rope Fig. 5 Graphical model of a part from rope SEAL 6x(1+9+9)+v 4. CONCLUSION Achieved results show that by optimization of construction parameters for a steel rope by preserving its diameter it can be enlarged metallic cross-section and so rope tonnage or it can be used the rope with lower diameter by the remaining its tonnage and so the rate D/d will be increased as well as rope lifetime growth. Using the graphical model for individual steel rope construction for verifying its calculated values offers the possibility to achieve invaluable information about applicability of setting of concrete geometrical parameters already in the phase of rope geometrical construction design. The paper was created as a part of solution for grant project 1/1005/04, grant project 1/3307/06 and grant project 1/2162/05. REFERENCE [1] Boroška,J., Hulín,J., Lesňák,O.: Oceľové laná. Alfa Bratislava 1982, 479 s. [2] Maligda,J., Stanová,E., Baranová,E.: Geometrická konštrukcia lana z optimálnych prameňov. Transactions of the Universities of Košice 1994/1, s [3] Hankus, J.: Budowa i wlasnosci mechaniczne lin stalowych, Glówny instytut górnictwa, Katowice 2000 [4] Molnár,V.: Využitie výpočtovej techniky pri navrhovaní konštrukcie oceľových lán a modelovanie ich namáhania. Doprava a logistika, mimoriadne číslo 2004/6, s

6 156 Stanova E.; Molnar V.; [5] Stanová,E., Molnár,V.: The Steel Rope and the Possibilities of the Mathematical Modeling. Transactions of the Universities of Košice 2003/3, s [6] Katalóg Oceľové laná. Drôtovňa, a.s. Hlohovec [7] Molnár, V. - Knežo, D.: Simulácia únavových skúšok oceľových lán. In: Výskum, výroba a použitie oceľových lán, Podbanské, máj 2002, s , ISBN [8] Bindzár, P.: Možné metódy hodnotenia kvality oceľových lán pomocou výpočtovej techniky, Doprava a logistika Transport & Logistics mimoriadne vydanie - LOADO, september 2003, s , ISSN X [9] Al Hakim, H., Andrejčák, I.: Experimentálne metódy, FVT TU Košice, KPS Prešov, ISBN