Joural of Techology, Vol. 3, No., pp. 47-56 (07) 47, * LabView ANSYS A STUDY OF VIBRATION MEASURING AND FATIGUE ANALYSIS FOR CANTILEVER BEAMS Yuo-Ter Tsai, * Hsie-Yag Li Departmet of Mechaical Egieerig De Li Istitute of Techology New Taipei City, Taiwa 36, R.O.C. Departmet of Creative Product Desig De Li Istitute of Techology New Taipei City, Taiwa 36, R.O.C. Key Words: vibratio measurig, frequecy respose, fatigue life. ABSTRACT Mechaical vibratio will cause fatigue failure, iduced maily by ubalaced revolutio of rotatioal parts. I order to aalyze the effects of vibratio to mechaical structure, this paper combied vibratio measurig with fiite elemet methods (FEM) to evaluate the fatigue life of catilever beams. Vibratio is created usig a cool fa by settig ubalaced revolutios. The measured values of vibratio are applied ot oly i idetifyig the quality of a fa but also i calculatig the dyamic loadigs geerated by ubalaced revolutios. A catilever beam was desiged to measure the * e-mail: yttsai@dlit.edu.tw Correspodig author: Yuo-Ter Tsai, e-mail: yttsai@dlit.edu.tw
48 vibratio geerated by a cool fa. ANSYS software is used to aalyze the modals of the structure for fidig out the atural frequecies of structure. The measured system was desiged by LabView software for acquirig vibratio sigals icludig time ad frequecy domais. The frequecy respose fuctio (FRF) of the catilever beam was derived to formulate the relatioship betwee the vibratio acceleratios agaist the dyamic loadigs. The stress amplitudes are evaluated by ANSYS aalysis accordig to the dyamic loadigs obtaied by the FRF. The studied results show that the vibratio loadigs iduced by the fa are too small, so that the catilever beam would ot fail. However, the proposed methods of fatigue life evaluatio of vibratio may be useful i vibratio-based predictive maiteace. [8] PM) [] (predictive maiteace, [] desity, PSD) [9] (power spectrum [4] [3] fatigue) (low-cycle fatigue) [0] (high-cycle 04-05 [5] 04-05 S-N [] [6] [7] (curve fittig) []
49 LabView SolidWorks (fiite elemet methods, FEM) [3]. ANSYS respose) (harmoic (SUS 304) ANSYS ( Boudary Coditios) (harmoic force) ( WHL = 5. 80 mm) (75 75 5 cm) 00 g 6 6 {.5, 96, 5, 443,
50 3 54, 967} Hz.5 Hz mode 3, 4 4. (FRF) 750 rpm (.5 Hz) H a H a (6) A F (6) (frequecy respose fuctio, FRF) (trasfer fuctio) [4] () f ( t) i t Fe () () x( t) i t Xe () A H a (7) ( 4) mx cx kx f ( t ) (7) m c k f(t) (8) (receptace) (3) H x X F (3) k F 3EI 3 l (8) ) F (4) ( 3 l H a k m i c E (9) I (9) f t F e m e e (4) i t i t F (N) m e (kg) (m) = f (rad/sec) (rpm) (Accelerace) (5) i t i t a t X e A e (5) A (m/sec ) k m c m (FRF) /, (0) H a m (Dampig ratio) () (0)
5 8 Hz 5 9 6.5 mm 7 8 Hz 7 Labview 9 USB 934 H () a ta (DFT). N ANSYS 5 (,, 5, 6) (3, 4) 6 (over all, OA) (progostic maiteace)
5 OA RMS (root mea square) 0-peak peak-peak ( equivalet 0-peak equivalet peak-peak) (peak to peak) (peak) (average) (RMS) [8] (a) - (c) 0 T T RMS a ( t) dt 0 (a) Peak RMS (b) Peak to Peak RMS (c) (time domai) (frequecy domai) (discrete fourier trasform, DFT) DTFT DFT. 0 PCB333B NI USB934 (acceleratio meter) 4 5 V TEDS NIST NI CompactDAQ CompactRIO (IEPE) IEPE V 3.5 V 650 rpm 800 rpm 00-400 rpm LabVIEW (read out) 5.6 k/s DFT RMS V 7500 rpm (g) (mm) NI USB934 4 C IEPE (0 ma) 5. ks/s AC (0.5 Hz) 4 0 db 3 V (800 rpm) 3 (a)
53 4 3 5, 4, 7 3 (b) 4 (a) (.5 Hz) 0 Hz.5 Hz mode 4 (b) S Wohler ) 5. N N S-N (S-N Curve
54 (3) S-N Basqui. T D time (6) S S ( N ) b (3) ' a f f ANSYS S a (stress amplitude) S f (fatigue stregth coefficiet) b (fatigue stregth expoet) (4) b b ' log( N f ) log S f log Sa (4) SUS304 [5] (S a, N f ) {(300, 0 4 ) (70, 0 7 )} 70 Mpa 0 7 Cycle b = 0.08 S f = 639.7 MPa (7) log( N ) 34.6.6log S (7) f a Gerber Goodma R = R [] ANSYS (643 rpm) me =.5764E 05 N m V S-N Mier S N S /N D S S-N S-N (A) (Peak) (me) (H) (F) S a ( V) = 560 rpm A =.3 g () Peak =.44 (9.8*.3) = 8.04 m/s () Eq. (0) H = 0.94 (m = 0., = 0.0, =.5) (3) F = Peak/H =.647 N (4) me = F/ = 0.0009 Nm (5) S a = 3.7 MPa ANSYS Harmoic respose 70 MPa /N D = /N S S D = /N i N fi D S i D time F =.647 N.5 0.009700346 89 ( =.5) S a = 355 MPa N f = 89 Cycle T D 03 sec time (5) D time K i N i fi (5) (6)
55 Volt rpm A (g) (Hz) Peak (m/s ) H F(N) me (N-m) S a (Mpa) 3.5 650 0. 0.8 3.0486 9.989 0.305 0.006 9.5 4 830.55 3.8.479 53.47 0.40 0.00 63.7 5 086 0.38 8. 5.657 9.09 0.76 0.0008 5.7 6 345 0.45.4 6.357 4.5 0.43 0.0009 3.6 7 600 0.55 6.7 7.65.8 0.595 0.0008 4. 8 806 0.7 30. 9.7.08 0.803 0.0009 3.9 9 00 0.8 33.5.086.6 0.954 0.0009 3.8 0 95 0.83 36.6.50.3.06 0.0008 3.3 390. 39.8 6.69.09.499 0.0009 4 560.3 4.7 8.04 0.94.647 0.0009 3.7 0954406JMES588. 3. 99 3 45-78 4. 993 ( ) () LabView () CAD FEM NSC 0--E-37-006. Orha, S., N. Aktürk, ad V. Celik. 006. Vibratio Moitorig for Defect Diagosis of Rollig Elemet Bearigs as a Predictive Maiteace Tool: Comprehesive Case Studies. NDT & E Iteratioal 39 (4): 93-98. doi: 0.06/j.dteit.005.08.008.. Tsai, Y. T. 009. Applyig a Case-based Reasoig Method for Fault Diagosis Durig Maiteace. The Istitutio of Mechaical Egieers, Part C: Joural of Mechaical Egieerig Sciece 3 (0): 43-44. doi: 0.43/ 49-58 5. 00 6. Tsai, Y. T., K. S. Wag, ad H. Y. Li. 00. Performace States Estimatio of System Usig Bayesia Method ad Fuzzy Sigal Iformatio. Joural of Chiese Society of Mechaical Egieers 3 (5): 403-4. 7. Tsai, Y. T., ad Y. Y. Hsu. 0. A Study of Fuctiobased Diagosis Strategy ad Testability Aalysis for a System. The Istitutio of Mechaical Egieers, Part C: Joural of Mechaical Egieerig Sciece 6 (): 73-8. doi: 0.77/0954406407. 8. Tsai, Y. T., C. C. Che, ad Z. X. Liao. 0. A Study of Performace Degradatio Predictio ad Fault Diagosis for Mechaical Systems. Joural of Techology 7 (3): -9. 9. Moo, S. I., I. J. Cho, ad D. Yoo. 0. Fatigue Life Evaluatio of Mechaical Compoets Usig Vibratio Fatigue Aalysis Techique. Joural of Mechaical Sciece ad Techology 5 (3): 63-637. doi: 0.007/s06-0-04-6. 0. Lee, Y. L. 005. Fatigue Testig ad Aalysis: Theory ad Practice. Oxford: Butterworth-Heiema.. Tsai, Y. T., K. S. Wag, ad J. C. Woo. 03. Fatigue-life ad Reliability Evaluatios for Detal Implats Based o Computer Simulatio ad Limited Test Data. The Istitutio of Mechaical Egieers, Part C: Joural of Mechaical Egieerig Sciece 7 (3): 554-564. doi: 0.77/ 095440646353.. Tsai, Y. T., ad K. S. Wag. 05. A Study of Reliability
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