100 B. Tovt Fig. 3. Objective function of the problem of 7-bar truss optimization Рис. 3. Целевая функция задачи оптимизации 7-балочного ростверка Table The results of 7-bar truss weight optimization Initial design Diminishing objective function, % Iteration number a1 51 a2 56 Progress of optimization procedure for a structure B illustrated by the graphs of change objective function depending on iteration (Fig. 4), and also designs variables depending on an iteration (Fig. 5, 6). On the objective function changes graph is not shown optimization progress from an initial design which were in a prohibitive zone.
Analysis of results of weight optimization 6-bar truss confirmed again that the choice of different initial designs does not influence on the receipt of optimal solution of problem (Fig. 4 - 6). Thus at the choice of initial design b40 in a prohibitive zone (Fig. 5, 6) as a result of optimization the same eventual design was done as well as at the choice of initial designs in a possible zone which testifies to algorithm procedure convergence. An optimal design was attained after 4, 7, 12 and 5 iterations, depending on an initial design. As a result of optimization 6-bar truss it succeeded to get 114% diminishing of structure weight (Tab. 2).
Table The results of 6-bar truss weight optimization Initial design Diminishing objective function, % Iteration number 11,4 b 10,8 b 10,8 b – bImprovement of design technique of track machines bodies… Fig. 4. Objective function of the problem of 6-bar truss optimization Рис. 4. Целевая функция задачи оптимизации 6-балочного ростверка Fig. 5. Design variable b2 of the problem of 6-bar truss optimization Рис. 5. Переменная проектирования b2 задачи оптимизации 6-балочного ростверка 3. THE RESEARCH OF THE DEFLECTED MODE AND OPTIMIZATION OF THE BEARING STRUCTURE OF BALLAST LEVELING MACHINE SPZ-5/UA 3.1. The research of the deflected mode of ballast levelling machine SPZ-5/UA A ballast leveling machine is used in the track facilities and is designed for making the final shaping of the track ballast .
The ballast leveling machine SPZ-5 has three operating mode: worker, self-propelled and transport.
The research of the deflected mode of the bearing structure of ballast leveling machine SPZ-5/UA was 102 B. Tovt conducted by five types of loading: loading from forces of own weight of the bearing structure and equipment set on it in a transport mode (there is the mode of the static loading recognition to the dynamic factor) and also from four varieties of loading in operating modes (“А”, “B”, “C”, “D”), depending on technological operations which are executed.
Fig. 6. Design variable b4 of the problem of 6-bar truss optimization Рис. 6. Переменная проектирования b4 задачи оптимизации 6-балочного ростверка By the aim of research of deflected mode of bearing structure of ballast leveling machine SPZ5/UA by the FEM  is verification of accordance of construction to the terms of durability and determining the locations of establishment of strain transducer is for realization of working durability tests of machine. Except that on results the calculation of bearing structure of ballast leveling machine by FEM static stresses st were defined with a following estimation to the safety factor of fatigue resistance n. The general view of FE-model of truss of planner together with loading from forces of own weight and working equipment set on a truss is shown on Fig. 7.
The research of deflected mode of bearing structure of ballast leveling machine SPZ-5 in a transport mode showed that middle part of structure was the most loaded. In the stress concentration zone a maximal value of equivalent stresses is in the theory of durability of von Misses recognition to the dynamic factor, which was accepted k =1,5 , makes about 82,5 MPa (Fig. 8, а) which is considerably below than allowable stress, that is 155 MPa for the steel 09Г2 [6, 7].
Fig. 7. FE-model of the truss of the ballast leveling machine SPZ-5/UA Рис. 7. КЭ-модель рамы планировщика балластной призмы СПЗ-5/UA Improvement of design technique of track machines bodies… In operating modes the most values of stresses were observed in the places of fastening of lateral and middle ploughs. Exactly the operating mode “D”, which two central ploughs work at, appeared most unfavorable for a structure from between other operating modes. The values of main stress in the mode “D” attained 68 MPa (Fig. 8, b), equivalent stress – 72 MPa, which is considerably below than possible tensions of 155 MPa.
b) a) Fig. 8. Equivalent stresses fields in most loaded part of bearing truss: a) static loading mode (MPa); b) working mode «D» (MPa) Рис. 8. Поля эквивалентных напряжений в наиболее нагруженных участках несущей рамы: a) режим статической нагрузки (МПа); b) рабочий режим «D» (МПа) By the Branch Research Laboratory of Dynamics and Durability of Rolling Stock of the Dnipropetrovsk National University of Railway Transport named after Ac. V. Lazaryan were conducted working dynamic tests on durability of the experienced machine of ballast leveling machine SPZ-5. The aim of tests were verification of accordance of structure of pre-production model of machine of SPZ-5 and its durability indexes to the requirements of the Requirement specification, normative documents, that determine the terms of safety of motion and work. Working dynamic tests on durability were conducted in obedience to the program-methodology worked out on the basis of the Requirement specification and .
The estimation of durability of bearing structure of ballast leveling machine SPZ-5/UA for the working modes conducted by allowable stresses, for a transport mode of loading – by allowable stresses and safety factor of fatigue resistance . The fatigue resistance of bearing truss of the experienced machine is considered provided, if in all range of speeds, for which tested, got values of safety factor of fatigue resistance does not exceed a normative value which concordantly accepted n =1,5. As a result of processing of experimental data minimum value to the safety factor of fatigue [ ] resistance 2,84, that not less normative value. Therewith, as evidently from a Tab. 3 results of FEMstudy well conform with the results of working dynamic tests on durability.
Table The safety factor of fatigue resistance of bearing structure ballast leveling machine SPZ-Allowable Characteristic Working dynamic tests FEM-study value [n] structure places on durability С1 2,41 2,С2 3,73 3,С4 3,04 2,80 1,Р4 3,51 4,Р5 3,51 4,The results give a right to predict, that bearing structure of ballast leveling machine SPZ-5/UA keeps a considerable reserve of durability. Such results specify on possibility of optimization of structure of bearing truss of the investigated machine.
104 B. Tovt 3.2. Optimization of ballast levelling machine SPZ-5/UA The simplified FE-model of truss of planer, which is shown on Fig. 9, was created for realization of optimality calculations. The structure of the simplified model was accompanied by the special control calculations with the aim of obtained results, identical to plate model.
Fig. 9. FE-model of the truss of the ballast leveling machine SPZ-5/UA Рис. 9. КЭ-модель рамы планировщика балластной призмы СПЗ-5/UA Problem statement of optimization of bearing structure of ballast leveling machine: the area of cross-section of lateral crosstop of truss = 2Bt + Hd, cm2 came forward as objective function. As design variables came forward height H and width B of cross-section of lateral crosstop of truss.
There were the imposed stress constraints in this bar =, and also design variable constraints [ ] B 10 cm, 0 < H 30 cm. Except that, there was imposed constraint what value of bar thickness less defined value set from the stability condition could not change in obedience to d 0,7 cm and d 0,6 cm. Thereby, there was the imposed constraint on the value of thickness of shelf t 1 cm. As initial design the real design of structure was selected with the next values of design variables and parameters of structure: H = 30 cm, B0 = 30 cm, t =1,9 cm, d =1,1 cm from the value of objective function =147 cm2. With the aim of control of work of optimization procedure additional optimization calculations were executed with an initial design which had such values: H = 20 cm, B = 20 cm, t =1,9 cm, d =1,1 cm.
The cross-beams of truss it was decided to exclude from optimization, as a change of their sizes is inadvisable on the technological consideration.
On Fig. 10 – 12 shown graphs of change of objective function and design variables of problem during optimization of bearing structure of ballast leveling machine SPZ-5 depending on a select initial design.
Fig. 10. Objective function of optimization problem ballast leveling machine SPZ-5/UA Рис. 10. Целевая функция задачи оптимизации планировщика балластной призмы СПЗ-5/UA Improvement of design technique of track machines bodies… Fig. 11. Height H change under optimization Рис. 11. Изменение высоты H в ходе оптимизации Fig. 12. Width B change under optimization Рис. 12. Изменение ширины B в ходе оптимизации As a result of numerical optimization of bearing truss of machine SPZ-5 (Fig. 10) 235% diminishing to the area of cross-section of lateral crosstop (Tab. 4) was done. In a count on metal mass, it had 1101 kg of economy (taking into account that an existent structure has mass of 1529 kg and optimized are 428 kg). It follows to underline that these results are attained at implementation of 106 B. Tovt state variables constraints, in other words real stresses in a structure do not exceed a normative value.
Rational design of structure of bearing truss of ballast leveling machine SPZ-5, got as a result of optimization, is accepted on the engineering and technological consideration On Fig. 13 visual comparison of initial (real) is shown and rational designs of cross-sections of longitudinal bar of planer. For the final rational designs stability is provided in obedience to a calculation by БНіП ІІ-2381*.
a) b) c) d) Fig. 13. Real and rational designs of cross-sections longitudinal bar of machine SPZ-5/UA a) real design;
b) double-T №30 GOST 8239-89;c) rational design with d = 7 mm; d) rational design with d = 6 mm Рис. 13. Реальный и рациональные проекты поперечного сечения продольной балки машины СПЗ-5/UA a) реальный проект; b) двутавр №30 ГОСТ 8239-89; c) рациональный проект с d = 7 мм;
d) рациональный проект с d = 6 мм For the rational bearing structure of the investigated machine the estimation of durability was executed on the criterion of possible stresses and criterion to the safety factor of fatigue strength. The results give a right for assertion what the bearing structure of ballast leveling machine SPZ-5/UA is optimized keeps a sufficient reserve of durability.
Table The results of optimization of the bearing structure of the ballast leveling machine SPZ-5/UA Double-tee №Real design Rational design Rational design GOST 8239-( d =1,1cm, ( d = 0,6 cm, ( d = 0,7 cm, ( d = 6,5cm, t =1,9 cm) t =1cm) t =1cm) t =1,02 cm) opt – H, cm – 13,5 11,0 10,Bopt, cm Wz, cm1612 465 382, MPa 72 147 155, MPa [ ] opt, cm 147 46,5 40,0 41,, % – 216 268 Improvement of design technique of track machines bodies… 4. CONCLUSIONS In the paper on the basis of the conducted theoretical and experimental researches are offered solution of actual scientific and technical problem on the improvement of technique of designing bearing structures of track machines bodies. Next new results obtained in the paper:
1. Numerical optimization procedure of bearing structures of track machines, that is based on the general use of FEM and one of widespread optimization methods – Gradient Projection Method;
2. Approbation of the offered numerical optimization procedure on the number of problems of optimization of structures similar to the widespread variants of implementation of bearing structures of modern track machines, in particular 7-bar and 6-bar trusses;
3. Research of number of mathematical aspects of the use of the offered numerical optimization procedure, in particular research of procedure algorithm convergence;
4. Research of deflected mode of bearing structures of ballast leveling machine SPZ-5/UA.
Justification of necessity of realization of optimization of bearing structures of bodies of the selected machines;
5. Rational design of bearing structure of ballast leveling machine SPZ-5/UA, done as a result of optimization researches which were conducted by means of the numerical optimization procedure offered in paper;
6. Research of deflected mode of the offered rational bearing structure of ballast leveling machine SPZ-5/UA by an analytical way (FEM-study) on the action of the operating loading.
Results done in paper found the use on Public Corporation “Kakhovka plant of electric welding equipment” (KZESO) and in Senior management of track facilities of “UZ” at improvement of bearing structure of body of ballast leveling machine SPZ-5/UA.
Bibliography 1. Haftka R.T., Gurdal Z.: Elements of Structural Optimization. Springer, 1992.
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