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Оптимизация прессового инструмента при производстве низкотемпературных сверхпроводников..pdf

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ȼȿɋɌɇɂɄ ɉɇɂɉɍ
Ɇɟɯɚɧɢɤɚ
2013
ʋ1
ɍȾɄ 621.777
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
ɉɟɪɦɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ
ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ, ɉɟɪɦɶ, Ɋɨɫɫɢɹ
ɈɉɌɂɆɂɁȺɐɂə ɉɊȿɋɋɈȼɈȽɈ ɂɇɋɌɊɍɆȿɇɌȺ
ɉɊɂ ɉɊɈɂɁȼɈȾɋɌȼȿ ɇɂɁɄɈɌȿɆɉȿɊȺɌɍɊɇɕɏ
ɋȼȿɊɏɉɊɈȼɈȾɇɂɄɈȼ
ɉɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ
ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɫɛɨɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɡɚɝɨɬɨɜɨɤ. ȼ ɨɫɧɨɜɭ ɨɩɬɢɦɢɡɚɰɢɢ ɩɨɥɨɠɟɧɨ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɦɢɧɢɦɚɥɶɧɵɟ ɷɧɟɪɝɨɡɚɬɪɚɬɵ ɜ ɯɨɞɟ ɩɪɨɰɟɫɫɚ. Ⱥɤɬɭɚɥɶɧɨɣ
ɹɜɥɹɟɬɫɹ ɡɚɞɚɱɚ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɢ ɨɩɬɢɦɢɡɚɰɢɢ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɨɛɴɟɦɨɜ ɜɵɩɭɫɤɚ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɢɢ ɬɪɟɛɨɜɚɧɢɹɦ ɤɚɱɟɫɬɜɚ. ȼɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɪɚɡɪɚɛɨɬɤɚ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɨɫɧɨɜ ɢ ɦɟɬɨɞɢɤ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɟɯɧɨɥɨɝɢɢ
ɩɪɨɢɡɜɨɞɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ, ɧɚɭɱɧɨ ɨɛɨɫɧɨɜɵɜɚɸɳɢɯ
ɜɵɛɨɪ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɨɫɧɚɫɬɤɢ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɤɚɱɟɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɢɯ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɯ
ɩɨɤɚɡɚɬɟɥɟɣ ɢɯ ɩɪɨɢɡɜɨɞɫɬɜɚ. ɉɪɨɰɟɫɫ ɩɪɟɫɫɨɜɚɧɢɹ ɧɚɯɨɞɢɬ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɩɪɢ ɨɛɪɚɛɨɬɤɟ
ɦɟɬɚɥɥɨɜ ɞɚɜɥɟɧɢɟɦ. ɋɭɳɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɩɪɟɫɫɨɜɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɜɵɞɚɜɥɢɜɚɧɢɢ ɦɚɬɟɪɢɚɥɚ,
ɩɨɦɟɳɟɧɧɨɝɨ ɜ ɡɚɦɤɧɭɬɵɣ ɨɛɴɟɦ, ɱɟɪɟɡ ɤɚɧɚɥ, ɨɛɪɚɡɨɜɚɧɧɵɣ ɩɪɟɫɫɨɜɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ. Ⱦɨɫɬɨɢɧɫɬɜɨɦ ɩɪɨɰɟɫɫɚ ɩɪɟɫɫɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɛɥɚɝɨɩɪɢɹɬɧɚɹ ɫɯɟɦɚ ɧɚɩɪɹɠɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫ ɩɪɟɨɛɥɚɞɚɸɳɢɦ ɜɥɢɹɧɢɟɦ ɫɠɢɦɚɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɨɜɵɲɟɧɧɭɸ ɩɥɚɫɬɢɱɧɨɫɬɶ
ɩɪɟɫɫɭɟɦɨɝɨ ɦɚɬɟɪɢɚɥɚ. ɉɨɷɬɨɦɭ ɩɪɨɰɟɫɫ ɩɪɟɫɫɨɜɚɧɢɹ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɞɚɜɥɟɧɢɟɦ ɦɚɥɨɩɥɚɫɬɢɱɧɵɯ ɬɪɭɞɧɨɞɟɮɨɪɦɢɪɭɟɦɵɯ ɦɟɬɚɥɥɨɜ ɢ ɫɩɥɚɜɨɜ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɩɪɟɫɫɨɜɚɧɢɟ, ɨɩɬɢɦɢɡɚɰɢɹ, ɦɢɧɢɦɢɡɚɰɢɹ, ɭɝɨɥ ɤɨɧɭɫɧɨɫɬɢ, ɩɪɟɫɫɨɜɵɣ
ɢɧɫɬɪɭɦɟɧɬ.
G. L. Kolmogorov, N.A. Kosheleva, T.V. Chernova
Perm National Research Polytechnic University, Perm, Russian Federation
OPTIMIZATION OF THE PRESS TOOL BY PRODUCTION
OF LOW-TEMPERATURE SUPERCONDUCTORS
In this article the technique of definition of optimum angles of the technological tool is offered at
pressing combined composite preparations. In an optimization basis the pressure of pressing providing
the minimum power inputs is necessary. The problem of improvement and optimization of the production technology of low-temperature composite superconductors for achievement of necessary production volumes of release is actual at compliance to quality requirements. Development of theoretical
bases and techniques of design of technological processes in relation to the production technology of
the low-temperature composite superconductors which are scientifically proving a choice of technological modes and industrial equipment for improvement of quality of low-temperature composite supercon-
106
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
ductors and providing high technical and economic rates of their production is important. The pressing
process is widely used in metal forming.The essence of the pressing process is extrusion of material
placed in an enclosed area through the channel formed by the pressing tool. The advantage of process
of pressing is the favorable scheme of a tension with prevailing influence of the squeezing tension providing increased plasticity of the pressed material. Therefore process of pressing is widely used when
processing by pressure of low-plastic hardly deformed metals and alloys.
Keywords: pressing, minimization, an optimum angle, the pressing tool.
ȼ ɪɚɛɨɬɟ ɩɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɦɨɧɨ-, ɛɢ- ɢ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɢɯ ɡɚɝɨɬɨɜɨɤ. ȼ ɨɫɧɨɜɭ ɨɩɬɢɦɢɡɚɰɢɢ ɩɨɥɨɠɟɧɨ ɦɢɧɢɦɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɦɢɧɢɦɚɥɶɧɵɟ ɷɧɟɪɝɨɡɚɬɪɚɬɵ. Ɂɚɞɚɱɚ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɢ ɨɩɬɢɦɢɡɚɰɢɢ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɨɛɴɟɦɨɜ ɜɵɩɭɫɤɚ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɢɢ ɬɪɟɛɨɜɚɧɢɹɦ ɤɚɱɟɫɬɜɚ ɹɜɥɹɟɬɫɹ ɚɤɬɭɚɥɶɧɨɣ. ȼɚɠɧɵɦ ɹɜɥɹɟɬɫɹ
ɪɚɡɪɚɛɨɬɤɚ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɨɫɧɨɜ ɢ ɦɟɬɨɞɢɤ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ, ɧɚɭɱɧɨ ɨɛɨɫɧɨɜɵɜɚɸɳɢɯ ɜɵɛɨɪ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɨɫɧɚɫɬɤɢ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɤɚɱɟɫɬɜɚ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ
ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɢɯ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɢɯ ɩɪɨɢɡɜɨɞɫɬɜɚ [9].
ɉɪɢ ɨɛɪɚɛɨɬɤɟ ɦɟɬɚɥɥɨɜ ɞɚɜɥɟɧɢɟɦ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɧɚɯɨɞɢɬ ɩɪɨɰɟɫɫ ɩɪɟɫɫɨɜɚɧɢɹ. ɋɭɳɧɨɫɬɶ ɩɪɟɫɫɨɜɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɜɵɞɚɜɥɢɜɚɧɢɢ ɦɚɬɟɪɢɚɥɚ, ɩɨɦɟɳɟɧɧɨɝɨ ɜ ɡɚɦɤɧɭɬɵɣ ɨɛɴɟɦ, ɱɟɪɟɡ ɤɚɧɚɥ, ɨɛɪɚɡɨɜɚɧɧɵɣ ɩɪɟɫɫɨɜɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ [1, 6]. Ⱦɨɫɬɨɢɧɫɬɜɨɦ ɩɪɟɫɫɨɜɚɧɢɹ
ɹɜɥɹɟɬɫɹ ɛɥɚɝɨɩɪɢɹɬɧɚɹ ɫɯɟɦɚ ɧɚɩɪɹɠɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫ ɩɪɟɨɛɥɚɞɚɸɳɢɦ ɜɥɢɹɧɢɟɦ ɫɠɢɦɚɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɨɜɵɲɟɧɧɭɸ ɩɥɚɫɬɢɱɧɨɫɬɶ ɩɪɟɫɫɭɟɦɨɝɨ ɦɚɬɟɪɢɚɥɚ. ɉɨɷɬɨɦɭ ɩɪɟɫɫɨɜɚɧɢɟ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɞɚɜɥɟɧɢɟɦ ɦɚɥɨɩɥɚɫɬɢɱɧɵɯ ɬɪɭɞɧɨɞɟɮɨɪɦɢɪɭɟɦɵɯ ɦɟɬɚɥɥɨɜ ɢ ɫɩɥɚɜɨɜ [2].
Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɟɫɫɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɭɫɢɥɢɟ
ɩɪɟɫɫɨɜɚɧɢɹ. ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɦɢɧɢɦɚɥɶɧɨɟ ɭɫɢɥɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɫ ɰɟɥɶɸ ɫɧɢɠɟɧɢɹ ɷɧɟɪɝɨɡɚɬɪɚɬ. ɉɨɥɧɨɟ ɭɫɢɥɢɟ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ ɫɭɦɦɵ ɫɨɫɬɚɜɥɹɸɳɢɯ [1, 7]:
P Tɤɪ Ɍ ɦ Ɍ ɩɥ Ɍ ɤ Ɍ ɲ r Q ,
(1)
ɝɞɟ Ɍɤɪ – ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɫɢɥɚ ɬɪɟɧɢɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɟɣɧɟɪɚ; Ɍɦ –
ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɫɢɥɚ ɬɪɟɧɢɹ ɜ ɡɨɧɟ ɞɟɮɨɪɦɚɰɢɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɚɤɬɚ ɩɪɟɫɫɨɜɨɣ ɦɚɬɪɢɰɵ ɢ ɡɚɝɨɬɨɜɤɢ; Ɍɩɥ – ɭɫɢɥɢɟ, ɡɚɬɪɚɱɟɧɧɨɟ ɧɚ
107
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
ɩɥɚɫɬɢɱɟɫɤɭɸ ɞɟɮɨɪɦɚɰɢɸ; Ɍɤ – ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɫɢɥɚ ɬɪɟɧɢɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɥɢɛɪɭɸɳɟɝɨ ɩɨɹɫɤɚ ɦɚɬɪɢɰɵ; Ɍɲ – ɭɫɢɥɢɟ, ɡɚɬɪɚɱɢɜɚɟɦɨɟ
ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɫɢɥ ɬɪɟɧɢɹ ɦɟɠɞɭ ɦɟɬɚɥɥɨɦ ɢ ɩɪɟɫɫ-ɲɚɣɛɨɣ; Q – ɭɫɢɥɢɟ ɩɪɨɬɢɜɨɞɚɜɥɟɧɢɹ ɢɥɢ ɩɟɪɟɞɧɟɝɨ ɧɚɬɹɠɟɧɢɹ (±Q).
ɉɨɥɧɨɟ ɭɫɢɥɢɟ ɩɪɟɫɫɨɜɚɧɢɹ (1) ɩɪɢɜɨɞɢɬɫɹ ɤ ɫɪɟɞɧɟɦɭ ɧɚɩɪɹɠɟɧɢɸ ɩɪɟɫɫɨɜɚɧɢɹ,
ıɩɪ P / F0 ,
(2)
ɝɞɟ F0 – ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ ɢɫɯɨɞɧɨɣ ɡɚɝɨɬɨɜɤɢ.
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɬɞɟɥɶɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɪɚɜɧɟɧɢɹ (1) ɩɪɢɜɨɞɹɬɫɹ ɤ ɭɞɟɥɶɧɵɦ ɧɨɪɦɚɥɶɧɵɦ ɢ ɤɚɫɚɬɟɥɶɧɵɦ ɧɚɩɪɹɠɟɧɢɹɦ ɫɢɫɬɟɦɵ
ɜɧɟɲɧɢɯ ɫɢɥ (ɪɢɫ. 1).
Ɋɢɫ. 1. ɋɯɟɦɚ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ
ɂɡ ɩɪɚɤɬɢɤɢ ɩɪɟɫɫɨɜɚɧɢɹ ɢɡɜɟɫɬɧɨ ɧɚɥɢɱɢɟ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ
ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɤɨɧɢɱɟɫɤɨɣ ɦɚɬɪɢɰɵ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ Į ɦ . Ɉɬ
ɭɝɥɚ Į ɦ ɜ ɫɨɨɬɧɨɲɟɧɢɢ (1) ɡɚɜɢɫɹɬ ɫɨɫɬɚɜɥɹɸɳɢɟ Ɍɩɥ ɢ Ɍɦ, ɩɨɷɬɨɦɭ
ɨɩɬɢɦɢɡɚɰɢɹ ɝɟɨɦɟɬɪɢɢ ɩɪɟɫɫɨɜɨɣ ɦɚɬɪɢɰɵ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɨɩɬɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ Į ɦ . ȼ ɪɚɛɨɬɟ ɢɡɥɚɝɚɟɬɫɹ ɦɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ Į ɦ ɢɡ ɭɫɥɨɜɢɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɢɡɞɟɥɢɣ ɤɪɭɝɥɨɝɨ ɫɟɱɟɧɢɹ.
ɇɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɩɪɢ ɩɥɚɫɬɢɱɟɫɤɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ [1]
ı ɩɥ
İ
³ ı dİ ,
s
(3)
0
ɝɞɟ ı s – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɟɮɨɪɦɚɰɢɢ ɩɪɟɫɫɭɟɦɨɝɨ ɦɚɬɟɪɢɚɥɚ; İ – ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ.
108
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
ȼ ɪɚɛɨɬɚɯ [3, 4] ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ ɨɩɪɟɞɟɥɟɧɚ ɫ ɭɱɟɬɨɦ ɜɵɬɹɠɤɢ ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɞɟɮɨɪɦɚɰɢɣ ɫɞɜɢɝɚ ɧɚ ɜɯɨɞɟ ɜ ɤɨɧɢɱɟɫɤɢɣ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɣ ɢɧɫɬɪɭɦɟɧɬ ɢ ɜɵɯɨɞɟ ɢɡ ɧɟɝɨ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:
İ ɫɪ ln Ȝ 4 tgĮɦ ,
3 3
(4)
ɝɞɟ Ȝ R02 / R12 – ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɬɹɠɤɢ; R0 ɢ R1 – ɪɚɞɢɭɫɵ ɢɫɯɨɞɧɨɣ ɡɚɝɨɬɨɜɤɢ ɢ ɩɪɟɫɫ-ɢɡɞɟɥɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ⱦɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɫɨɫɬɚɜɥɹɸɳɚɹ ɧɚɩɪɹɠɟɧɢɹ ɩɪɟɫɫɨɜɚɧɢɹ, ɫɜɹɡɚɧɧɚɹ ɫ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɟɣ, ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɹ (4), ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɫɥɟɞɭɸɳɢɦ
ɨɛɪɚɡɨɦ:
ı ɩɥ ı s §¨ ln Ȝ 4 tgĮɦ ·¸.
(5)
3
3
©
¹
ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɪɨɟɤɰɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɫɢɥ ɬɪɟɧɢɹ ɧɚ ɨɫɶ
ɩɪɟɫɫɨɜɚɧɢɹ ɞɥɹ ɤɨɧɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɦɚɬɪɢɰɵ ɜɵɝɥɹɞɢɬ ɬɚɤ:
Tɦ Fɦ ˜ f ˜ ı s ˜ cosĮɦ ,
(6)
ɝɞɟ f – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɜ ɡɨɧɟ ɞɟɮɨɪɦɚɰɢɢ; IJɦ – ɤɚɫɚɬɟɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ; Fɦ – ɩɨɜɟɪɯɧɨɫɬɶ ɤɨɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɦɚɬɪɢɰɵ.
ɂɡ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɞɥɹ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɭɫɚ ɢɦɟɟɦ
ʌR12 § R02 ·
(7)
S
¨ 1¸ .
sinĮ ɦ © R12 ¹
ɋ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɹ (7) ɩɪɨɟɤɰɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɫɢɥɵ ɬɪɟɧɢɹ ɧɚ ɨɫɶ ɩɪɟɫɫɨɜɚɧɢɹ ɛɭɞɟɬ ɜɵɝɥɹɞɟɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
Tɦ ı s ˜ ʌR12 (Ȝ 1) f ctgĮɦ ,
(8)
ȼ ɨɛɳɟɟ ɫɪɟɞɧɟɟ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɜɤɥɚɞ ɨɬ ɩɪɟɨɞɨɥɟɧɢɹ
ɫɢɥ ɬɪɟɧɢɹ ɜ ɡɨɧɟ ɞɟɮɨɪɦɚɰɢɢ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ
ı ɦ ı s (Ȝ 1) fctgĮ ɦ / Ȝ .
(9)
Ɉɩɬɢɦɚɥɶɧɵɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɦɚɬɪɢɰɵ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɩɨɥɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɩɪɟɫɫɨɜɚɧɢɹ:
109
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
w ı ı
ɩɪ ɦ 0.
wtgĮɦ
(10)
ɉɨɫɥɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɫɨɨɬɧɨɲɟɧɢɣ (5) ɢ (9), ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢ ɭɩɪɨɳɟɧɢɣ ɩɨɥɭɱɢɦ
tgĮɨɩɬ
1,14
ɦ
f (Ȝ 1)
Ȝ
(11)
ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
§
f (Ȝ 1) ·
Į ɨɩɬ
arctg
1,14
¨
¸.
ɦ
Ȝ ¹
©
(12)
ɇɚ ɪɢɫ. 2 ɩɪɢɜɟɞɟɧɵ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ
ɦɚɬɪɢɰ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɵɬɹɠɤɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ
ɡɧɚɱɟɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ. ɂɡ ɪɢɫ. 2 ɫɥɟɞɭɟɬ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ Ȝ
ɢ ɭɦɟɧɶɲɟɧɢɟɦ f ɨɩɬɢɦɚɥɶɧɵɟ ɭɝɥɵ ɦɚɬɪɢɰ ɜɨɡɪɚɫɬɚɸɬ.
Ɋɢɫ. 2. Ɋɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ
ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɵɬɹɠɤɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɬɪɟɧɢɹ: 1 – f = 0,01; 2 – f = 0,05; 3 – f = 0,1; 4 – f = 0,2
Ɋɚɫɫɦɨɬɪɢɦ ɞɟɮɨɪɦɚɰɢɸ ɩɪɟɫɫɨɜɚɧɢɟɦ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɨɣ ɫɛɨɪɧɨɣ ɡɚɝɨɬɨɜɤɢ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɫɟɪɞɟɱɧɢɤɚ (Nb-Ti
ɢɥɢ Nb) ɢ ɦɟɞɧɨɣ ɨɛɨɥɨɱɤɢ (ɪɢɫ. 3). ɉɨɥɚɝɚɟɦ, ɱɬɨ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ
ɫɨɫɬɚɜɧɨɣ ɡɚɝɨɬɨɜɤɢ ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɬɹɠɤɢ ɨɞɢɧɚɤɨɜ ɢ ɞɥɹ ɫɟɪɞɟɱɧɢɤɚ, ɢ ɞɥɹ ɨɛɨɥɨɱɤɢ.
110
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
Ɋɢɫ. 3. ɋɯɟɦɚ ɩɪɟɫɫɨɜɚɧɢɹ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɛɨɪɧɨɣ ɡɚɝɨɬɨɜɤɢ:
1 – ɩɪɟɫɫ-ɮɨɪɦɚ; 2 – ɨɛɨɥɨɱɤɚ; 3 – ɫɟɪɞɟɱɧɢɤ
Ⱦɥɹ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ (ɫɟɪɞɟɱɧɢɤɚ) ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ [2]
İ ɫ lnȜ 4 tgĮcɦ ,
3 3
(13)
ɝɞɟ Įcɦ – ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɫɟɪɞɟɱɧɢɤɚ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ; Ȝ –
ɜɵɬɹɠɤɚ.
ɂɡ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɪɢɫ. 3 ɫɥɟɞɭɟɬ
tgĮcɦ
Rc
tgĮ ɦ ,
R0
(14)
ɝɞɟ Rɫ – ɪɚɞɢɭɫ ɫɟɪɞɟɱɧɢɤɚ; R0 – ɧɚɪɭɠɧɵɣ ɪɚɞɢɭɫ ɡɚɝɨɬɨɜɤɢ.
ɋ ɭɱɟɬɨɦ ɭɪɚɜɧɟɧɢɹ (14) ɫɪɟɞɧɹɹ ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ
ɨɩɢɫɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
R
İ ɫ lnȜ 4 c tgĮɦ .
3 3 R0
(15)
Ⱦɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɧɚɩɪɹɠɟɧɢɹ, ɫɜɹɡɚɧɧɚɹ ɫ ɟɝɨ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɟɣ, ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɹ (15), ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
R
§
·
(16)
ı ɫɩɥ ıɫs ¨ lnȜ 4 c tgĮ ɦ ¸.
R
3
3
0
©
¹
ɇɚɩɪɹɠɟɧɢɸ (16) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɞɨɥɹ ɩɨɥɧɨɝɨ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ (ɫɟɪɞɟɱɧɢɤɚ) ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ [3]:
§
·
R
Pc ʌRc2 ısc ¨ lnȜ 4 c tgĮ ɦ ¸ .
3 3 R0
©
¹
(17)
111
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
Ⱥɧɚɥɨɝɢɱɧɵɣ ɪɚɫɱɟɬ ɜɵɩɨɥɧɟɧ ɞɥɹ ɧɚɪɭɠɧɨɣ ɱɚɫɬɢ (ɨɛɨɥɨɱɤɢ)
ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ.
ɇɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɨɛɨɥɨɱɤɢ ɞɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ
ı oɩɥ ı os §¨ lnȜ 4 tgĮɦ ·¸ ,
3 3
©
¹
(18)
ɝɞɟ ıos – ɭɫɪɟɞɧɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɦɚɬɟɪɢɚɥɚ
ɨɛɨɥɨɱɤɢ.
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɨɥɹ ɨɛɳɟɝɨ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ, ɡɚɬɪɚɱɟɧɧɨɝɨ
ɧɚ ɞɟɮɨɪɦɚɰɢɸ,
§
·
Pc ʌ R02 Rc2 ıos ¨ lnȜ 4 tgĮ ɦ ¸ .
3 3
©
¹
(19)
Ⱦɥɹ ɨɛɨɥɨɱɤɢ ɧɟɨɛɯɨɞɢɦ ɭɱɟɬ ɫɢɥ ɬɪɟɧɢɹ ɜ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɡɨɧɵ
ɞɟɮɨɪɦɚɰɢɢ. ɉɪɨɟɤɰɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɫɢɥ ɬɪɟɧɢɹ ɧɚ ɨɫɶ ɩɪɟɫɫɨɜɚɧɢɹ ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ ɮɨɪɦɭɥɵ
Tɦ ıos ʌR12 (Ȝ 1)fctgĮɦ ,
(20)
ɝɞɟ R1 – ɪɚɞɢɭɫ ɧɚɪɭɠɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ ɧɚ
ɜɵɯɨɞɟ.
ȼɤɥɚɞ ɨɬ ɩɪɟɨɞɨɥɟɧɢɹ ɫɢɥ ɬɪɟɧɢɹ ɜ ɡɨɧɟ ɞɟɮɨɪɦɚɰɢɢ ɜ ɨɛɳɟɟ
ɫɪɟɞɧɟɟ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ı ɨɦ ıos (Ȝ 1)fctgĮɦ /Ȝ .
(21)
Ɉɩɬɢɦɚɥɶɧɵɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɦɚɬɪɢɰɵ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ ɨɩɪɟɞɟɥɟɧ ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɩɨɥɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɩɪɟɫɫɨɜɚɧɢɹ, ɢ Į ɦ ɡɚɜɢɫɢɬ ɥɢɲɶ ɨɬ ı ɫɩɪ , ıɨɩɪ , ı ɨɦ , ɩɨɷɬɨɦɭ
w (ı ɫ ıɨ ı ɨ ) 0.
ɩɪ
ɩɪ
ɦ
w tgĮɦ (22)
ɉɪɢ ɷɬɨɦ ɫɭɦɦɚɪɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ, ɜɤɥɸɱɚɸɳɟɟ
ɥɢɲɶ ɜɟɥɢɱɢɧɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ Į ɦ
112
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
ıȈ
· ɨ § Rc2 ·
Rc2 §
Rc
4
ı 2 ¨ lnȜ tgĮɦ ¸ ı s ¨1 2 ¸ u
R0 ©
3 3 R0
¹
© R0 ¹
c
s
R
§
·
u¨ lnȜ 4 tgĮɦ ¸ ı os Ȝ 1 fctgĮ ɦ .
R
3 3
©
¹
2
1
2
0
(23)
ȼɵɪɚɠɟɧɢɟ (23) ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
§
·
§
·
ı Ȉ ı cs Rc2 ¨ lnȜ 4 Rc tgĮ ɦ ¸ ı ɨs §¨1 1 ·¸ ¨ f 1 lnȜ 4 tgĮ ɦ ¸ , (24)
© Ȝ ¹ © tgĮɦ
3 3
3 3
©
¹
¹
ɝɞɟ Ȝ R02 R12 – ɜɵɬɹɠɤɚ; Rc Rc R0 .
ɉɨɫɥɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɹ (24) ɩɨ tgĮɦ, ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢ ɭɩɪɨɳɟɧɢɣ ɩɨɥɭɱɢɦ
ª
º
f (Ȝ 1)
«
».
Į ɨɩɬ
arctg
1,97
ɦ
Ȝ 1 Rc2 ıcs ıos Rc3 »
«¬
¼
(25)
ɇɚ ɪɢɫ. 4 ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɨ ɮɨɪɦɭɥɟ (25) ɩɪɢ
ɤɨɷɮɮɢɰɢɟɧɬɟ ɬɪɟɧɢɹ f = 0,1 ɢ ɨɬɧɨɲɟɧɢɢ ıcs ıos 3,33. Ⱦɚɧɧɨɟ ɨɬɧɨɲɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ ɢ ɨɛɨɥɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɝɨɪɹɱɟɦɭ ɩɪɟɫɫɨɜɚɧɢɸ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɜɟɪɯɩɪɨɜɨɞɹɳɟɣ ɡɚɝɨɬɨɜɤɢ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɧɢɨɛɢɟɜɨɝɨ ɫɟɪɞɟɱɧɢɤɚ ɢ ɦɟɞɧɨɣ ɨɛɨɥɨɱɤɢ, ɞɥɹ
ɬɟɦɩɟɪɚɬɭɪɵ 600 °C. ɉɪɢ ɷɬɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɞɥɹ Nb ı cs 30 Ɇɉɚ, ɞɥɹ
ɦɟɞɢ ı os 9 Ɇɉɚ [5].
Ɋɢɫ. 4. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɝɥɚ ɤɨɧɭɫɧɨɫɬɢ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɵɬɹɠɤɢ
ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ f = 0,1
ɢ ɩɪɢ ɨɬɧɨɲɟɧɢɢ ıcs ıos 3,33 ; 1 – Rɫ = 0,25; 2 – 0,45; 3 – 0,65; 4 – 1
113
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɪɢɫ. 4, ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ ɪɚɡɦɟɪ ɭɝɥɚ ɤɨɧɭɫɧɨɫɬɢ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɜɵɬɹɠɤɢ, ɧɨ ɢ ɨɬ ɫɨɨɬɧɨɲɟɧɢɣ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɪɚɡɦɟɪɨɜ ɡɚɝɨɬɨɜɤɢ ɢ ɭɫɥɨɜɢɣ ɬɪɟɧɢɹ.
ɇɚ ɪɢɫ. 5 ɪɚɫɫɦɨɬɪɟɧɚ ɞɟɮɨɪɦɚɰɢɹ ɩɪɟɫɫɨɜɚɧɢɟɦ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɨɣ ɫɛɨɪɧɨɣ ɡɚɝɨɬɨɜɤɢ [8, 10], ɫɨɫɬɨɹɳɟɣ ɢɡ ɫɟɪɞɟɱɧɢɤɚ (ɦɟɞɶ) ɪɚɞɢɭɫɨɦ R2; ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɫɥɨɹ ɢɡ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɨɝɨ ɦɚɬɟɪɢɚɥɚ (Nb-Ti ɢɥɢ Nb) ɪɚɞɢɭɫɨɦ R1 ɢ ɦɟɞɧɨɣ ɨɛɨɥɨɱɤɢ ɪɚɞɢɭɫɨɦ R0.
Ɋɢɫ. 5. ɋɯɟɦɚ ɩɪɟɫɫɨɜɚɧɢɹ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɛɨɪɧɨɣ ɡɚɝɨɬɨɜɤɢ: 1 – ɩɪɨɦɟɠɭɬɨɱɧɵɣ
ɫɥɨɣ ɢɡ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɨɝɨ ɦɚɬɟɪɢɚɥɚ (Nb-Ti ɢɥɢ Nb); 2 – ɫɟɪɞɟɱɧɢɤ ɢɡ ɦɟɞɢ; 3 –
ɨɛɨɥɨɱɤɚ; 4 – ɩɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ
Ⱥɧɚɥɨɝɢɱɧɨ ɪɚɫɱɟɬɚɦ ɞɥɹ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ ɜɵɩɨɥɧɢɦ
ɪɚɫɱɟɬɵ, ɩɨɥɚɝɚɹ, ɱɬɨ ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɫɨɫɬɚɜɧɨɣ ɡɚɝɨɬɨɜɤɢ ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɬɹɠɤɢ ɨɞɢɧɚɤɨɜ ɢ ɞɥɹ ɫɟɪɞɟɱɧɢɤɚ, ɢ ɞɥɹ ɨɛɨɥɨɱɤɢ. Ⱦɥɹ ɫɟɪɞɟɱɧɢɤɚ ɢɡ ɦɟɞɢ (ɫɦ. ɪɢɫ. 5) ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ [1]
İ ɫɪ ln Ȝ 4 tgĮcɦ ,
3 3
(26)
ɝɞɟ Įcɦ – ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɫɟɪɞɟɱɧɢɤɚ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ.
ɂɡ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ
tgĮcɦ
R2
tgĮɦ ,
R0
(27)
ɝɞɟ R2 – ɪɚɞɢɭɫ ɫɟɪɞɟɱɧɢɤɚ ɢɡ ɦɟɞɢ; R0 – ɧɚɪɭɠɧɵɣ ɪɚɞɢɭɫ ɡɚɝɨɬɨɜɤɢ.
Ⱦɥɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɫɥɨɹ ɢɡ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɨɝɨ ɦɚɬɟɪɢɚɥɚ
ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ
İ ɫɪ ln Ȝ 4 tgĮcɦ ,
3 3
ɝɞɟ Įcɦ – ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɫɟɪɞɟɱɧɢɤɚ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ.
114
(28)
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
ɂɡ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ
tgĮcɦ
R1
tgĮ ɦ ,
R0
(29)
ɝɞɟ R1 – ɪɚɞɢɭɫ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɫɥɨɹ; R0 – ɧɚɪɭɠɧɵɣ ɪɚɞɢɭɫ ɡɚɝɨɬɨɜɤɢ.
Ɍɨɝɞɚ ɫɪɟɞɧɹɹ ɫɬɟɩɟɧɶ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ ɢɡ ɦɟɞɢ [4]
R
İ ɫɪ ln Ȝ 4 2 tgĮɦ .
3 3 R0
(30)
Ⱦɥɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɫɥɨɹ
Ⱦɥɹ ɨɛɨɥɨɱɤɢ
R
İ ɫɪ ln Ȝ 4 1 tgĮɦ .
3 3 R0
(31)
İ ɫɪ ln Ȝ 4 tgĮɦ .
3 3
(32)
Ⱦɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɧɚɩɪɹɠɟɧɢɹ, ɫɜɹɡɚɧɧɚɹ ɫ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ɫɟɪɞɟɱɧɢɤɚ, ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɣ (31) ɢ (32), ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
§
·
R
ı ɫɩɥ ıɫs 2 ¨ ln Ȝ 4 2 tgĮ ɦ ¸.
3 3 R0
©
¹
(33)
§
·
R
ı ɫɩɥ ı ɫs1 ¨ ln Ȝ 4 1 tgĮ ɦ ¸.
3 3 R0
©
¹
(34)
ɇɚɩɪɹɠɟɧɢɸ (33) ɢ (34) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɞɨɥɹ ɩɨɥɧɨɝɨ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ ɫɟɪɞɟɱɧɢɤɚ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ:
ª §
·º
ª §
§R ·
·º
R
Pc F2 «ı ɫs 2 ¨ ln Ȝ 4 2 tgĮɦ ¸» F1 «ıɫs1 ¨ ln Ȝ 4 ¨¨ 1 ¸ tgĮɦ ¸» , (35)
¸»
3 3 R0
3 3 © R0 ¹
«¬ ¨©
¹¼
¬ ©
¹¼
ɝɞɟ F1 ɢ F2 – ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɥɨɳɚɞɢ.
Ⱥɧɚɥɨɝɢɱɧɵɣ ɪɚɫɱɟɬ ɜɵɩɨɥɧɟɧ ɞɥɹ ɧɚɪɭɠɧɨɣ ɱɚɫɬɢ (ɨɛɨɥɨɱɤɢ)
ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ.
ɇɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɨɛɨɥɨɱɤɢ ɞɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ
115
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
ı oɩɥ ıos 0 §¨ ln Ȝ 4 tgĮɦ ·¸ ,
3 3
©
¹
(36)
ɝɞɟ ıos 0 – ɭɫɪɟɞɧɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɦɚɬɟɪɢɚɥɚ
ɨɛɨɥɨɱɤɢ.
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɨɥɹ ɨɛɳɟɝɨ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ, ɩɨɲɟɞɲɟɝɨ ɧɚ
ɞɟɮɨɪɦɚɰɢɸ, ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
§
·
Pc ʌ ˜ R02 ª¬ R22 R12 º¼ ˜ ıos 0 ¨ ln Ȝ 4 tgĮɦ ¸ .
3 3
©
¹
(37)
Ⱦɥɹ ɨɛɨɥɨɱɤɢ ɧɟɨɛɯɨɞɢɦ ɭɱɟɬ ɫɢɥ ɬɪɟɧɢɹ ɜ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɡɨɧɵ
ɞɟɮɨɪɦɚɰɢɢ. ɉɪɨɟɤɰɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɫɢɥ ɬɪɟɧɢɹ ɧɚ ɨɫɶ ɩɪɟɫɫɨɜɚɧɢɹ ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ
Tɦ ıos 0 ˜ ʌ ˜ R32 (Ȝ 1) f ctgĮɦ ,
(38)
ɝɞɟ R3 – ɪɚɞɢɭɫ ɧɚɪɭɠɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ.
ȼ ɨɛɳɟɟ ɫɪɟɞɧɟɟ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ ɜɤɥɚɞ ɨɬ ɩɪɟɨɞɨɥɟɧɢɹ
ɫɢɥ ɬɪɟɧɢɹ ɜ ɡɨɧɟ ɞɟɮɨɪɦɚɰɢɢ ɫɨɫɬɚɜɢɥ
ıoɦ ıos 0 (Ȝ 1) f ctgĮɦ / Ȝ .
(39)
Ɉɩɬɢɦɚɥɶɧɵɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɛɪɚɡɭɸɳɟɣ ɦɚɬɪɢɰɵ ɤ ɨɫɢ ɩɪɟɫɫɨɜɚɧɢɹ ɨɩɪɟɞɟɥɟɧ ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɩɨɥɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɩɪɟɫɫɨɜɚɧɢɹ, ɩɪɢ ɷɬɨɦ ɨɬ ɭɝɥɚ Įɦ ɡɚɜɢɫɹɬ ɥɢɲɶ ıɫɩɥ , ıɨɩɥ , ıɨɦ , ɩɨɷɬɨɦɭ ɭɫɥɨɜɢɟ
ɦɢɧɢɦɭɦɚ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɩɨɥɭɱɟɧɨ ɜ ɜɢɞɟ
w (ı ɫ ıɨ ıɨ ) 0.
ɩɥ
ɩɥ
ɦ
w tgĮɦ (40)
ɉɪɢ ɷɬɨɦ ɫɭɦɦɚɪɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɩɪɟɫɫɨɜɚɧɢɹ, ɜɤɥɸɱɚɸɳɟɟ
ɥɢɲɶ ɜɟɥɢɱɢɧɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ Įɦ ,
ı6
· c R12 §
R22 §
R2
4
4 R1 tgĮ · ı
ln
Ȝ
tgĮ
ı
ln
Ȝ
¨
¸
¨
ɦ
1
ɦ¸
s
R02 ©
R02 ©
3 3 R0
3 3 R0
¹
¹
c
s2
§ R22 R12 · §
· o R32
o
4
ı s 0 ¨1 2 2 ¸ ¨ ln Ȝ tgĮ ɦ ¸ ı s 0 2 Ȝ 1 f ctgĮɦ .
R
R
R0
3
3
©
¹
0
0
©
¹
ȼɵɪɚɠɟɧɢɟ (41) ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɜɢɞɟ
116
(41)
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
§
·
§
·
ı 6 ıcs 2 R22 ¨ ln Ȝ 4 R2 ˜ tgĮɦ ¸ ı cs1 R12 ¨ ln Ȝ 4 R1 ˜ tgĮɦ ¸ 3 3
3 3
©
¹
©
¹
§
·
ıos 0 1 ª R22 R12 º ¨ ln Ȝ 4 tgĮɦ ¸ ı os 0 1 Ȝ 1 f ctgĮɦ ,
¬
¼ ©
Ȝ
3 3
¹
R02
R1
ɝɞɟ Ȝ
–
ɜɵɬɹɠɤɚ;
R
; R2
1
R32
R0
(42)
R2
.
R0
ɉɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɢɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɫɟɪɞɟɱɧɢɤ ɢ ɨɛɨɥɨɱɤɚ ɢɡɝɨɬɚɜɥɢɜɚɸɬɫɹ ɢɡ ɦɟɞɢ, ɚ ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɫɥɨɣ
(ɫɦ. ɪɢɫ. 5) ɢɡ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɚ (Nb-Ti ɢɥɢ Nb).
ɉɨɫɥɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɜɵɪɚɠɟɧɢɹ (42) ɩɨ tgĮɦ, ɭɱɢɬɵɜɚɹ, ɱɬɨ
ı cs 2 ıos 0 , ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢ ɭɩɪɨɳɟɧɢɣ ɩɨɥɭɱɢɦ
Į ɨɩɬ
ɦ
ª
º
«
»
f (Ȝ 1)
«
».
arctg 1,97
c
«
§ı
·»
Ȝ ¨ os1 R13 R1 R23 R2 1 ¸ »
«
«¬
© ıs 0
¹ »¼
(43)
ɇɚ ɪɢɫ. 6 ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɨ ɮɨɪɦɭɥɟ (43) ɩɪɢ
ɤɨɷɮɮɢɰɢɟɧɬɟ ɬɪɟɧɢɹ f = 0,1 ɢ ɨɬɧɨɲɟɧɢɢ ısc ıso 3,33 . Ⱦɚɧɧɨɟ ɨɬɧɨɲɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɟɮɨɪɦɚɰɢɢ ɫɟɪɞɟɱɧɢɤɚ ɢ ɨɛɨɥɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɝɨɪɹɱɟɦɭ ɩɪɟɫɫɨɜɚɧɢɸ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɫɜɟɪɯɩɪɨɜɨɞɹɳɟɣ ɡɚɝɨɬɨɜɤɢ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɧɢɨɛɢɟɜɨɝɨ ɫɟɪɞɟɱɧɢɤɚ ɢ ɦɟɞɧɨɣ ɨɛɨɥɨɱɤɢ, ɞɥɹ
ɬɟɦɩɟɪɚɬɭɪɵ 600 °C [5].
Ɋɢɫ. 6. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɝɥɚ ɤɨɧɭɫɧɨɫɬɢ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɵɬɹɠɤɢ
ɩɪɢ ɩɪɟɫɫɨɜɚɧɢɢ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ f = 0,1
ɢ ɩɪɢ ɨɬɧɨɲɟɧɢɢ ıcs ıos 3,33 ; 1 – R1 = 1; R2 = 0, 75; 2 – R1 = 0,75; R2 = 0,5;
3 – R1 = 0,55; R2 = 0,3; 4 – R1 = 0,5; R2 = 0,25
117
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɡ ɭɫɥɨɜɢɣ ɦɢɧɢɦɭɦɚ ɭɫɢɥɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɨɩɪɟɞɟɥɟɧɵ ɨɩɬɢɦɚɥɶɧɵɟ ɭɝɥɵ ɦɚɬɪɢɰ ɞɥɹ ɩɪɟɫɫɨɜɚɧɢɹ ɦɨɧɨ-, ɛɢ- ɢ ɬɪɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɡɚɝɨɬɨɜɤɢ. ɉɪɢ ɷɬɨɦ ɭɱɢɬɵɜɚɸɬɫɹ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɫɢɥɢɹ
ɩɪɟɫɫɨɜɚɧɢɹ, ɫɨɞɟɪɠɚɳɢɟ ɭɝɨɥ ɤɨɧɭɫɧɨɫɬɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ. ȼɵɹɜɥɟɧɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ, ɜɥɢɹɸɳɢɟ ɧɚ ɭɫɢɥɢɟ
ɩɪɟɫɫɨɜɚɧɢɹ. ɉɨɤɚɡɚɧɨ ɜɥɢɹɧɢɟ ɜɵɬɹɠɤɢ ɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɧɚ
ɡɧɚɱɟɧɢɹ ɨɩɬɢɦɚɥɶɧɵɯ ɭɝɥɨɜ. ɉɪɢɦɟɧɟɧɢɟ ɦɚɬɪɢɰ ɫ ɨɩɬɢɦɚɥɶɧɵɦ ɭɝɥɨɦ
ɤɨɧɭɫɧɨɫɬɢ ɩɨɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɷɧɟɪɝɨɟɦɤɨɫɬɶ ɩɪɨɰɟɫɫɚ ɩɪɟɫɫɨɜɚɧɢɹ ɩɪɢ
ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɵɯ ɢɡɞɟɥɢɣ.
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣ ɫɩɢɫɨɤ
1. ɉɟɪɥɢɧ ɂ.Ʌ., Ɋɚɣɬɛɚɪɝ Ʌ.ɏ. Ɍɟɨɪɢɹ ɩɪɟɫɫɨɜɚɧɢɹ ɦɟɬɚɥɥɨɜ. –
Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ. 1975. – 448 ɫ.
2. Ƚɢɞɪɨɩɪɟɫɫɨɜɚɧɢɟ ɬɪɭɞɧɨɞɟɮɨɪɦɢɪɭɟɦɵɯ ɬɭɝɨɩɥɚɜɤɢɯ ɦɟɬɚɥɥɨɜ ɢ ɫɩɥɚɜɨɜ / Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ȼ.Ƚ. Ɇɢɯɚɣɥɨɜ, ɘ.Ʌ. Ȼɚɪɤɨɜ, ȼ.Ʌ. Ʉɚɪɥɢɧɫɤɢɣ. – Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ, 1991. – 142 ɫ.
3. Ʉɨɥɦɨɝɨɪɨɜ Ƚ.Ʌ. Ƚɢɞɪɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɦɚɡɤɚ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɦɟɬɚɥɥɨɜ ɞɚɜɥɟɧɢɟɦ. – Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ, 1986. – 168 ɫ.
4. Ʉɨɥɦɨɝɨɪɨɜ Ƚ.Ʌ., Ʉɭɡɧɟɰɨɜɚ ȿ.ȼ. Ɉ ɫɬɟɩɟɧɢ ɞɟɮɨɪɦɚɰɢɢ ɩɪɢ
ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ // ɂɡɜ. ɜɭɡɨɜ. ɑɟɪɧɚɹ ɦɟɬɚɥɥɭɪɝɢɹ. –
2000. – ʋ 1. – ɋ. 31–33.
5. Ɍɪɟɬɶɹɤɨɜ Ⱥ.ȼ., Ɂɸɡɢɧ ȼ.ɂ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɦɟɬɚɥɥɨɜ ɢ
ɫɩɥɚɜɨɜ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɞɚɜɥɟɧɢɟɦ. – Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ, 1973. – 224 ɫ.
6. Ɇɟɯɚɧɢɤɚ ɩɥɚɫɬɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɬɪɚɧɫɜɟɪɫɚɥɶɧɨ-ɢɡɨɬɪɨɩɧɵɯ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜɵɯ ɦɚɬɟɪɢɚɥɨɜ / Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ȼ.ɇ. Ɍɪɨɮɢɦɨɜ, Ɇ.Ƚ. ɒɬɭɰɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ. – ɉɟɪɦɶ: ɂɡɞ-ɜɨ
ɉɟɪɦ. ɧɚɰ. ɢɫɫɥɟɞ. ɩɨɥɢɬɟɯɧ. ɭɧ-ɬɚ, 2011. – 217 c.
7. Ʉɨɥɦɨɝɨɪɨɜ Ƚ.Ʌ., Ɏɢɥɢɩɩɨɜ ȼ.Ȼ., Ʌɚɬɵɲɟɜɚ Ɍ.ȼ. Ɉɛ ɨɩɬɢɦɚɥɶɧɨɣ ɝɟɨɦɟɬɪɢɢ ɜɨɥɨɱɢɥɶɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ // ɂɡɜ. ɜɭɡɨɜ. ɑɟɪɧɚɹ ɦɟɬɚɥɥɭɪɝɢɹ. – 2007. – ʋ 4. – ɋ. 41–43.
8. Ʉɪɢɫɬɟɧɫɟɧ Ɋ. ȼɜɟɞɟɧɢɟ ɜ ɦɟɯɚɧɢɤɭ ɤɨɦɩɨɡɢɬɨɜ: ɩɟɪ. ɫ ɚɧɝɥ. –
Ɇ.: Ɇɢɪ, 1982. – 334 ɫ.
9. Ɇɟɬɚɥɥɨɜɟɞɟɧɢɟ ɢ ɬɟɯɧɨɥɨɝɢɹ ɫɜɟɪɯɩɪɨɜɨɞɹɳɢɯ ɦɚɬɟɪɢɚɥɨɜ:
ɩɟɪ. ɫ ɚɧɝɥ. – Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ, 1987. – 560 ɫ.
10. Ɋɚɡɪɚɛɨɬɤɚ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ ɞɥɹ ɦɚɝɧɢɬɧɨɣ ɫɢɫɬɟɦɵ ɂɌɗɊ
ɜ Ɋɨɫɫɢɢ / Ⱥ.Ʉ. ɒɢɤɨɜ [ɢ ɞɪ.] // ɂɡɜ. ɜɭɡɨɜ. ɐɜɟɬɧɚɹ ɦɟɬɚɥɥɭɪɝɢɹ. –
2003. – ʋ 1. – ɋ. 36–43.
118
ɉɪɟɫɫɨɜɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ
References
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119
Ƚ.Ʌ. Ʉɨɥɦɨɝɨɪɨɜ, ɇ.Ⱥ. Ʉɨɲɟɥɟɜɚ, Ɍ.ȼ. ɑɟɪɧɨɜɚ
Ɉɛ ɚɜɬɨɪɚɯ
Ʉɨɥɦɨɝɨɪɨɜ Ƚɟɪɦɚɧ Ʌɟɨɧɢɞɨɜɢɱ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɞɨɤɬɨɪ
ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɡɚɫɥɭɠɟɧɧɵɣ ɪɚɛɨɬɧɢɤ ɜɵɫɲɟɣ ɲɤɨɥɵ ɊɎ, ɡɚɜɟɞɭɸɳɢɣ ɤɚɮɟɞɪɨɣ ɞɢɧɚɦɢɤɢ ɢ ɩɪɨɱɧɨɫɬɢ ɦɚɲɢɧ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (614013, ɝ. ɉɟɪɦɶ, ɭɥ. ɉɪɨɮ. ɉɨɡɞɟɟɜɚ, 13, ɤɨɪɩ. Ƚ, ɤ. 206,
207, e-mail: dpm@pstu.ru).
Ʉɨɲɟɥɟɜɚ ɇɚɬɚɥɶɹ Ⱥɥɟɤɫɚɧɞɪɨɜɧɚ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɚɫɩɢɪɚɧɬ ɤɚɮɟɞɪɵ ɞɢɧɚɦɢɤɢ ɢ ɩɪɨɱɧɨɫɬɢ ɦɚɲɢɧ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (614013,
ɝ. ɉɟɪɦɶ, ɭɥ. ɉɪɨɮ. ɉɨɡɞɟɟɜɚ, 13, ɤɨɪɩ. Ƚ, ɤ. 206, 207, e-mail: nataly.kosheleva@gmail.com).
ɑɟɪɧɨɜɚ Ɍɚɬɶɹɧɚ ȼɹɱɟɫɥɚɜɨɜɧɚ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɤɚɧɞɢɞɚɬ
ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɞɢɧɚɦɢɤɢ ɢ ɩɪɨɱɧɨɫɬɢ ɦɚɲɢɧ
ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ
ɭɧɢɜɟɪɫɢɬɟɬɚ (614013, ɝ. ɉɟɪɦɶ, ɭɥ. ɉɪɨɮ. ɉɨɡɞɟɟɜɚ, 13, ɤɨɪɩ. Ƚ,
ɤ. 206, 207, e-mail:dpm@pstu.ru).
About the authors
Kolmogorov Herman Leonidovich (Perm, Russian Federation) –
Doctor of Technical Sciences, Professor, Honored Worker of Higher Education of the Russian Federation, Head of the dynamics and strength of machines, Perm National Research Polytechnic University (13, Building G,
room 206, 207, st. Pozdeeva Professors, 614013, Perm, Russian Federation,
e-mail: dpm@pstu.ru).
Kosheleva Natalia Alexandrovna (Perm, Russian Federation) –
postgraduate student Dynamics and strength of machines, Perm National
Research Polytechnic University (13, Building G, room 206, 207, st. Pozdeeva Professors, 614013, Perm, Russian Federation, e-mail: nataly.kosheleva@gmail.com).
Chernova Tatiana Vyacheslavovna (Perm, Russian Federation) –
Ph.D., assistant professor of Dynamics and strength of machine, Perm National
Research Polytechnic University (13, Building G, room 206, 207, st. Pozdeeva
Professors, 614013, Perm, Russian Federation, e-mail: dpm@pstu.ru).
ɉɨɥɭɱɟɧɨ 15.02.2013
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