title: ÐÐ½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¸ Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¸Ñ ÑÑÐµÑÐ¸Ð½ Ð´Ð»Ñ Ð³Ð¸Ð±ÐºÐ¾Ð¹ ÑÐ¾ÑÐ¾Ñ-Ð¿Ð¾Ð´ÑÐ¸Ð¿Ð½Ð¸ÐºÐ¾Ð²Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ
title: Ð½Ð°ÑÑÐ½ÑÐ¹ Ð´Ð¾ÐºÐ»Ð°Ð´
titleType: Subtitle
Creators: name: ÐÐ±ÐµÐ´ Ð¡Ð°Ð»Ð°Ð¼ ÐÑ Ð¼ÐµÐ´ ÐÐ±ÐµÐ´
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: Ð Ð¾ÑÐ¾ÑÑ Ð³Ð¸Ð±ÐºÐ¸Ðµ
Ð Ð¾ÑÐ¾ÑÑ
ÐÐ¾Ð´ÑÐ¸Ð¿Ð½Ð¸ÐºÐ¸

description: ÐÑÐ½Ð¾Ð²Ð½Ð°Ñ ÑÐµÐ»Ñ ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ - Ð²ÑÑÐ²Ð¸ÑÑ ÑÑÐµÑÐ¸Ð½Ñ Ð¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÑÐµÑÐ¸Ð½, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´ÑÑ Ð²Ð¾ Ð²ÑÐµÐ¼Ñ ÑÐ°Ð±Ð¾ÑÑ, Ð·Ð½Ð°Ñ Ð³Ð»ÑÐ±Ð¸Ð½Ñ ÑÑÐµÑÐ¸Ð½Ñ Ð¸ ÐµÐµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½Ð° ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ, Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð¸ ÑÑÐ°Ð±Ð¸Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÐ¾ÑÐ¾ÑÐ°, Ñ ÑÐµÐ¼ ÑÑÐ¾Ð±Ñ Ð¾Ð±Ð½Ð°ÑÑÐ¶Ð¸ÑÑ ÑÐ°Ð½Ð½ÐµÐµ Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¸Ðµ Ð´ÐµÑÐµÐºÑÐ¾Ð² Ð´Ð¾ Ð¸Ð·Ð±ÐµÐ¶Ð°ÑÑ ÐºÐ°ÑÐ°ÑÑÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ±Ð¾Ñ.
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ÐÑÐµÐ½ÐµÐ½Ð° ÑÑÐ¶ÐµÑÑÑ ÑÐ¾ÑÐ¾ÑÐ¾Ð² Ñ ÑÑÐµÑÐ¸Ð½Ð¾Ð¹. ÐÑÐºÐ»Ð¸Ðº ÑÐ¼ÐµÑÐµÐ½Ð¸Ñ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ, Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¼ÐµÐ½ÑÑÐ°ÐµÑÑÑ Ñ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸ÐµÐ¼ Ð³Ð»ÑÐ±Ð¸Ð½Ñ ÑÑÐµÑÐ¸Ð½Ñ. ÐÐ¾Ð³Ð´Ð° Ð¾ÑÐºÐ»Ð¸Ðº ÑÐ¼ÐµÑÐµÐ½Ð¸Ñ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ð¾Ñ 3.5% Ð´Ð¾ 5%, Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¼ÐµÐ½ÑÑÐ°ÐµÑÑÑ Ñ 3% Ð´Ð¾ 4%, ÑÑÐ¾ Ð¾Ð·Ð½Ð°ÑÐ°ÐµÑ, ÑÑÐ¾ Ð³Ð»ÑÐ±Ð¸Ð½Ð° ÑÑÐµÑÐ¸Ð½Ñ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ Ð´Ð¾ 0.2Ð . ÐÑÐ»Ð¸ Ð¾ÑÐºÐ»Ð¸Ðº ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ñ 8% Ð´Ð¾ 13%, Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¼ÐµÐ½ÑÑÐ°ÐµÑÑÑ Ñ 7% Ð´Ð¾ 14%, ÑÑÐ¾ Ð¾Ð·Ð½Ð°ÑÐ°ÐµÑ, ÑÑÐ¾ Ð³Ð»ÑÐ±Ð¸Ð½Ð° ÑÑÐµÑÐ¸Ð½Ñ ÑÐ°Ð²Ð½Ð° 0.4Ð . ÐÑÐ»Ð¸ Ð¾ÑÐºÐ»Ð¸Ðº ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ñ 20% Ð´Ð¾ 28%, Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¼ÐµÐ½ÑÑÐ°ÐµÑÑÑ Ñ 13% Ð´Ð¾ 17 %, ÑÑÐ¾ Ð¾Ð·Ð½Ð°ÑÐ°ÐµÑ, ÑÑÐ¾ Ð³Ð»ÑÐ±Ð¸Ð½Ð° ÑÑÐµÑÐ¸Ð½Ñ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ 0.6Ð , Ð¸ ÐµÑÐ»Ð¸ Ð¾ÑÐºÐ»Ð¸Ðº ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ñ 28% Ð´Ð¾ 34%, Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¼ÐµÐ½ÑÑÐ°ÐµÑÑÑ Ñ 17% Ð´Ð¾ 21%, ÑÑÐ¾ Ð¾Ð·Ð½Ð°ÑÐ°ÐµÑ, ÑÑÐ¾ Ð³Ð»ÑÐ±Ð¸Ð½Ð° ÑÑÐµÑÐ¸Ð½Ñ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ 0.8Ð , Ð¸ ÑÑÐ¾ Ð¼Ð°ÐºÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð°Ñ Ð³Ð»ÑÐ±Ð¸Ð½Ð° ÑÑÐµÑÐ¸Ð½Ñ. Ð­ÑÐ¾ Ð²Ð°Ð¶Ð½Ð¾ Ð´Ð»Ñ Ð´Ð¸Ð°Ð³Ð½Ð¾ÑÑÐ¸ÐºÐ¸, Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¸Ñ ÑÑÐµÑÐ¸Ð½ Ð¸ ÑÑÐ¶ÐµÑÑÐ¸ Ð½Ð° ÑÐ°Ð½Ð½ÐµÐ¹ ÑÑÐ°Ð´Ð¸Ð¸, ÑÑÐ¾Ð±Ñ Ð¸Ð·Ð±ÐµÐ¶Ð°ÑÑ ÐºÐ°ÑÐ°ÑÑÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¾ÑÐºÐ°Ð·Ð°.
description: The main objective of this work is to detect the cracks and determine the effect of cracks which take place during operation by knowing the crack depth and its effect on the static, dynamic behavior and the stability of the rotor system so as to early defect detection to avoid the catastrophic failure. 
 This work focuses on the study of the static and dynamic behavior of cracked and uncracked rotor, the crack is placed in a position near the disk on the rotor shaft for many depths. Finding the effect of the crack on the rotor by finding the response, critical speed, stress distribution and the stability in both cracked and uncracked rotors.
 Analytical and numerical techniques has been done and found new equations for finding the stiffness of two cracked shaft in vertical, horizontal and cross directions with making mathematical model representation for rotor and compared the results of analytical and numerical, it found in good agreement. Numerical models to simulate the behavior of cracked shafts during operation and to attempt correlate the observed vibration signature with the presence of cracks on selected location on the shaft.
Assumed cracks in position near the disk (15 mm from disk) with different depths for single crack and for two cracks we studied two cases, firstly, with slant angles (30, 60, 90 degree) for first crack while second crack transverse with 90 degrees and the orientation angle between two cracks fixed zero degrees and secondly, the slant angle of cracks fixed while the orientation angle between two cracks changed (0, 90, 180 degree), both cases took with different depths of cracks. The first crack located 15 mm to the right side of disk while the second crack is located15 mm to the left of disk has been studied. By measuring dynamic responses for each excitation and estimating the critical speed, determine the effect of crack on the critical speed, response and stress which gives a good indication to avoid the catastrophic failure. 
The investigation has been done by analyze actual system dynamic displacement response, the effect of crack on static and dynamic behavior and the stability of dynamic rotor system verifying analytical and numerical by studying 353T steam turbine which operates in Daura Refinery.
 The severity of cracked rotors has been estimated. The response displacement increases and the critical speed decreases with increasing the crack depths. When the displacement response increases from 3.5% to 5% and the critical speed decreases from 3 to 4% that means the crack depth is up to 0.2R. If the response increases from 8% to 13% and the critical speed decreases from 7% to 14% that means the crack depth is 0.4R. If the response increases from 20% to 28% and the critical speed decreases from 13% to 17% that means the crack depth is 0.6R and If the response increases from 28% to 34% and the critical speed decreases from 17% to 21% that means the crack depth is 0.8R and itâs the maximum crack depth. That is important for diagnosis or crack detection and severity in early stage to avoid catastrophic failure.