و هوا فضا و رفتار مكانيكي مواد(مجله مكانيك 3723 الي23، از صفحه88، تابستان2، شماره5، جلد)سازه

، دواريهامحوردر براي رديابي تركديجديروش

به كمك تغييرات شكل مد3مهدي راغبي2محمد حسين زاده1انوشيروان فرشيديان فر

گروه مهندسي مكانيك دانشگاه فردوسي مشهد

و مهندسي دانشكده فني مشهد، واحددانشگاه آزاد اسالمي

گروه مهندسي مكانيك دانشگاه فردوسي مشهد

)23/09/1388:؛ تاريخ پذيرش14/02/1388:خ دريافتتاري(

چكيده

در،در اين مقاله و تشخيص موقعيت ترك هـاي دوار، بـا اسـتفاده از روش مـاتريس محـور روشي غير مخرب جهت تعيين فركانستيتيو بر اساس تئور4انتقال ا. ارائه شده است،موشنكوير م،محورنيدر مي ترك ها ختلفي نسبت بـه يكـديگر توانند تحت زواياي

نتـايج. فركانس طبيعي را به دنبال خواهـد داشـت كاهشو داده تغيير را انعطاف پذيري محلي ها محوردر وجود ترك. قرار گيرندها حاصل از اين روش براي وي متنوعي مثال ا مورد بررسي قرار گرفته در.ت ترك به دست آمـده اسـتيل موقعين تحلي به كمك

ازيت، نتاينها هايبا نتاس انتقالي به كمك روش ماتريل فركانسي تحلج حاصل سه شده كه توافقي مقاي تجربيج حاصل از پژوهشميب . باشدين پاسخ ها نشان دهنده صحت روش به كار برده شده

5 اورهنگمحور، دار، تحليل فركانسي، مد شيپ، روش ماتريس انتقال تركمحور: كليديواژه هاي

A Novel Way for Crack Detection in Rotors, Using Mode Shape Changes M. Raghebi M. Hoseinzadeh A. Farshidianfar

Mech. Eng. Group Ferdowsi Univ. of Mashhad

School of Eng. Islamic Azad Univ., Mashhad Branch

Mech. Eng. Group Ferdowsi Univ. of Mashhad

ABSTRACT In this article, a non-destructive method for the frequency analysis and multi-crack detection in rotating shafts is presented, using transfer matrix method (TMM) and based on the Timoshenko beam theory. The cracks can be placed in different angles with respect to each other. The presence of cracks in structures change the local flexibility and results in reduction of natural frequency. The TMM is exerted for the frequency analysis of the shafts with discrepant boundary conditions. The resultant frequencies are used for requiring the mode shapes of the shaft corresponding to the two perpendicular planes (x-z and y-z). Subtracting these two mode shapes gives the position of the crack or cracks. Finally, the required frequencies by TMM are compared with some available experimental results. Close adaptation between these results is representing the high accuracy of the transfer matrix method.

Key Words: Cracked Shaft, Frequency Analysis, Mode Shape, Transfer Matrix Method (TMM), Overhang Shaft

Farshid@um.ac.ir): نويسنده پاسخگو(دانشيار-1 Hosein2004@yahoo.com:)عضو باشگاه پژوهشگران جوان(كارشناس ارشد-2 دانشجوي دكتري-3

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[

1

Dimarogonas, A.D. and Paipetis, S.A., Analytical Methods in Rotor Dynamics , Applied Science Pub., London, 1983.

2

Dimarogonas, A.D., Vibration of Cracked Structures: A State of the Art Review , Eng. Fracture Mech., Vol. 55, No. 5, pp. 831- 857, 1996.

3

Papadopoulos, C.A. and Dimarogonas, A.D., Coupled Longitudinal and Bending Vibrations

of a Rotating Shaft with an Open Crack , J. Sound and Vibration, Vol. 117, No. 1, pp. 81- 93, 1987.

4

Papadopoulos, L.A. and Dimarogonas, A.D., Coupling of Bending and Torsional Vibration of

a Cracked Timoshenko Shaft , Ingenieur-Archiv, Vol. 57, No. 4, pp. 257- 266, 1987.

5. Papadopoulos, C.A. and Dimarogonas, A.D., Coupled Vibration of Cracked Shafts, J.

Vibration and Acoustics , Vol. 114, No. 1, pp. 461- 467, 1992.

6. Sekhar, A.S., Vibration Characteristics of a Cracked Rotor with Two Open Cracks , J. Sound and Vibration, Vol. 223, No. 4, pp. 497- 512, 1999.

7. Gasch, R., Dynamic Behaviour of the Laval Rotor with a Transverse Crack , Mech. Systems and Signal Processing, Vol. 22, No. 1, pp. 790- 804, 2008

8. Chondros, T.G. and Labeas, G.N. Torsional Vibration of a Cracked rod by Variational Formulation and Numerical Analysis , J. Sound and Vibration, Vol. 301, No. 2, pp. 994- 1006, 2007.

9. Sekhar, A.S., Multiple Cracks Effects and Identification , Mech. Systems and Signal Processing, Vol. 22, No. 1, pp. 845- 878, 2008.

10. Bachschmid, N., Pennacchi, P., Tanzi, E., and Vania, A., Identification of Transverse Crack Position and Depth in Rotor Systems , Meccanica, Vol. 35, No. 1, pp. 563- 582, 2000.

11. Tsai, T.C. and Wang, Y.Z., Vibration Analysis and Diagnosis of a Cracked Shaft , J. Sound and Vibration, Vol. 192, No. 3, pp. 607- 620, 1996.

12. Tsai T.C. and Wang Y.Z., The Vibration of a Multi-crack Rotor , Int. J. Mech. Sciences, Vol. 39, No. 9, pp. 1037-1053, 1997.

13. Haris, C.M. and Crede, C.E., Shock and Vibration Handbook , 2nd Ed., McGraw-Hill, New York, 1976.

14. Shames, H.I. and Dym, C.L., Energy and Finite Element Methods in Structural Mechanics , McGraw-Hill, New York, pp. 200, 1985.

15. Murigendrappa, S.M., Maiti, S.K., and Srirangarajan, H.R., Frequency-based Experimental and Theoretical Identification of Multiple Cracks in Straight Pipes Filled with Fluid , NDT&E Int., Vol. 37, No. 1, pp. 431- 438, 2004.

16. Xiang, J., zhong, Y., Chen, X., and He, Z., Crack Detection in a Shaft by Combination of Wavelet-based Elements and Genetic Algorithm , Int. J. Solids and Structures, Vol. 45, No. 17, pp. 4782-4795, 2008.

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