A priedas. Diagnostikoje naudojami tarptautiniai ISO standartai
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1 Priedai A priedas. Diagnostikoje naudojami tarptautiniai ISO standartai B priedas. Patikslintas tiesiakrumplės pavaros matematinis modelis C priedas. Patikslintas tiesiakrumplė pavaros matematinis modelis D priedas. Duomenys išskaidyti į dažnio intervalus E priedas. Bendraautorių sutikimai teikti publikacijų medžiagą disertacijoje F priedas. Autoriaus mokslinių publikacijų disertacijos tema kopijos 113
2 114 PRIEDAI A priedas. Diagnostikoje naudojami tarptautiniai ISO standartai A.1 lentelė. ISO standartai ISO 2954: 1975 Mechanical vibration of rotating and reciprocating machinery Requirements for instruments for measuring vibration severity ISO 5348: 1998 Mechanical vibration and shock Mechanical mounting of accelerometers ISO : 1996 Mechanical vibration of non-reciprocating machines Measurements on rotating shafts and evaluation criteria Part 1: General guidelines ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on rotating shafts Part 2: Land-based steam turbines and generators in excess of 50 MW with normal operating speeds of r/min, r/min, r/min and r/min ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on rotating shafts Part 3: Coupled industrial machines ISO :2009 Mechanical vibration Evaluation of machine vibration by measurements on rotating shafts Part 4: Gas turbine sets with fluid-film bearings ISO : 2005 Mechanical vibration Evaluation of machine vibration by measurements on rotating shafts Part 5: Machine sets in hydraulic power generating and pumping plants ISO : 1995 Reciprocating internal combustion engine driven alternating current generating sets Part 9: Measurement and evaluation of mechanical vibrations ISO : 1993 Asseptance code for gears Part 2: Determination of mechanical vibrations of gear units during acceptance testing ISO : 1995 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 1: General guidelines ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 2: Land-based steam turbines and generators in excess of 50 MW with normal operating speeds of r/min, r/min, r/min and r/min ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 3: Industrial machines with nominal power above 15 kw and nominal speeds between 120 r/min and r/min when measured in situ
3 PRIEDAI 115 A.1 lentelės tesinys ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 4: Gas turbine sets with fluid-film bearings ISO : 2000 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 5: Machine sets in hydraulic power generating and pumping plants ISO : 1995 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 6: Reciprocating machines with power ratings above 100 kw ISO : 2009 Mechanical vibration Evaluation of machine vibration by measurements on non-rotating parts Part 7: Rotodynamic pumps for industrial applications, including measurements on rotating shafts ISO : 2004 Condition monitoring and diagnostics of machines Vocabulary ISO : 2002 Condition monitoring and diagnostics of machines Vibration condition monitoring Part 1: General procedures ISO : 2005 Condition monitoring and diagnostics of machines Vibration condition monitoring Part 2: Processing, analysis and presentation of vibration data ISO : 2003 Condition monitoring and diagnostics of machines Data processing, communication and presentation Part 1: General guidelines ISO : 2007 Condition monitoring and diagnostics of machines Data processing, communication and presentation Part 2: Data processing ISO/DIS Condition monitoring and diagnostics of machines Data processing, communication and presentation Part 3: Communication ISO :2003 Condition monitoring and diagnostics of machines General guidelines on data interpretation and diagnostics techniques ISO/DIS Condition monitoring and diagnostics of machines Data interpretation and diagnostics techniques Part 1: General guidelines ISO : 2004 Condition monitoring and diagnostics of machines Prognostics Part 1: General guidelines ISO : 2004 Rolling bearings Measuring methods for vibration Part 1: Fundamentals ISO : 2004 Rolling bearings Measuring methods for vibration Part 2: Radial ball bearings with cylindrical bore and outside surface ISO : 2006 Rolling bearings Measuring methods for vibration Part 3: Radial spherical and tapered roller bearings with cylindrical bore and outside surface
4 116 PRIEDAI A.1 lentelės tesinys ISO : 2007 Rolling bearings Measuring methods for vibration Part 4: Radial cylindrical roller bearings with cylindrical bore and outside surface ISO 17359: 2003 Condition monitoring and diagnostics of machines General guidelines ISO : 2004 Condition monitoring and diagnostics of machines Requirements for training and certification of personnel Part 1: Requirements for certifying bodies and the certification process ISO : 2003 Condition monitoring and diagnostics of machines Requirements for training and certification of personnel Part 2: Vibration condition monitoring and diagnostics ISO : 2008 Condition monitoring and diagnostics of machines Requirements for qualification and assessment of personnel Part 3: Requirements for training bodies and the training process ISO : 2008 Condition monitoring and diagnostics of machines Requirements for qualification and assessment of personnel Part 4: Field lubricant analysis ISO/DIS Condition monitoring and diagnostics of machines Requirements for qualification and assessment of personnel Part 5: Lubricant laboratory technician/analyst
5 PRIEDAI 117 B priedas. Riedėjimo diagnostinių parametrų reikšmės B1 lentelėje pateiktos diagnostinių parametrų kitimo skaitinės reikšmės, kai sūkiai yra 1484 aps/ min. Matuojami pagreičiai vertikalia kryptimi. B1 lentelė. Virpesių signalo statistiniai duomenys X1 X2 X3 X4 X5 X6 X7 8 be pažaidos 0, , , , , , , ,10334 Išorinio žiedo pažaida 2, , , , ,0012 0, , ,57438 Vidinio žiedo pažaida 53, ,4975 5, ,7487 0, , , ,03509 X9 X10 X11 X12 X13 X14 X15 X16 be pažaidos 1, , , , , , , ,17108 Išorinio žiedo pažaida 3, , , , ,4457 6, ,8983 8,53492 Vidinio žiedo pažaida 9, , ,4997 5, , , ,621 34,5839 B2 lentelėje pateiktos statistinių parametrų kitimo santykinės reikšmės (kiek kartų padidėjo reikšmė, kai atsirado pažaida, lyginant su reikšmėmis, kai guolis neturi pažaidos). Kai sūkiai yra 1484 aps/ min, guolyje yra išorinio žiedo pažaida. Duomenys išskaidyti į dažnio intervalus. B2 lentelė. Virpesių signalo statistiniai duomenys, esant išoriniam žiedo pažaidai Dažnio intervala s X1 X2 X3 X4 X5 X6 X , , , , ,0557 1, , ,4169
6 118 PRIEDAI B2 lentelės tesinys Dažnio intervala s X1 X2 X3 X4 X5 X6 X , , , , ,563 2, , , , , , , ,8168 4, , , , , , , ,0984 8, , , , , , , , ,702 8, , , , ,5 17, , , ,2274-2, , ,2807 1, ,62 781,25 17, , , ,4337 6, ,0466 9, , ,31 390,62 6, , , , ,3694 3, , , ,31 5, , , , ,9385 4, ,1444 1,07505 X9 X10 X11 X12 X13 X14 X15 X , , , , , , , , , , , , ,7318 0, , , , , , , ,0868 0, , , , , , , ,0451 0, , , , , , , ,3389-3,4966 2, , , , ,5 1, , , ,3160 1,1721 1, , , ,62 781,25 1, , , ,0609 0,2471 1, , , ,31 390,625 1, , ,8807 4, ,0544 1, , , ,31 1, , , , ,732 1, , ,16129 B3 lentelėje pateiktos statistinių parametrų kitimo santykinės reikšmės (kiek kart, padidėjo reikšmė, kai atsirado pažaida, lyginant su reikšmėmis, kai guolis neturi pažaidos). Kai sūkiai yra 1484 aps/min, guolyje yra vidinio žiedo pažaida. Duomenys išskaidyti į dažnio intervalus.
7 PRIEDAI 119 B3 lentelė. Virpesių signalo statistiniai duomenys esant VŽP Dažnio intervala s X1 X2 X3 X4 X5 X6 X , , ,17 552,779 1, ,78 115,422 0, , , ,47 508,586-0, ,32 161,286 0, , , , ,204-2, ,85 373,179 0, , , , ,161-3, , ,893 1, , , , , , ,43 382, ,352 1, , ,5 453, , , , , , ,640 1, ,62 781,25 226, , , ,137-22,001 98, ,6747 1, ,31 390,625 49, , , , , , ,0076 1, ,31 32, , , ,2594 1, , ,8606 1,24193 X9 X10 X11 X12 X13 X14 X15 X , , , ,18-0,0152 0, , , , , , ,48 0, , , , , , , ,094-0,0366 0, , , , , , ,2146-0,0509 0, , , , , , , ,905-6,1924 4, ,1164 1, , ,5 1, , , ,424-1,3233 2, , , ,62 781,25 1, , , ,138 1, , , , ,31 390,625 2, , , ,4603-4,4449 2, , , ,31 2, , , , ,13 2, ,6720 1,82994 B4 lentelėje pateiktos statistinių parametrų kitimo santykinės reikšmės (kiek kartų padidėjo reikšmė, kai atsirado pažaida, lyginant su reikšmėmis, kai guolis
8 120 PRIEDAI neturi pažaidos). Kai sūkiai yra 1000 aps/ min, guolyje yra išorinio žiedo pažaida. Duomenys išskaidyti į dažnio intervalus. B4 lentelė. Virpesių signalo statistiniai duomenys, esant IŽP, apsukos 1000 aps/min Dažnio intervalas X1 X2 X3 X4 X5 X6 X ,7548 4,0410 2,5382 4,0410 0,8609 1,3240 1,1010 1, ,3390 5,3707 3,8627 5,3707 0,8985 1,7411 1,0156 2, ,7862 6,7014 5,0362 6,7014 3,5484 3,2053 1,8120 1, ,6973 8,4103 5,0833 8,4103 3,6649 3,4519 2,1370 1, , ,8300 7,9986 4,7679 7,9986-4,2905 3,3134 2,1902 1, , ,5 6,9303 7,0511 4,3338 7,0511 2,5390 3,2690 2,5203 1, ,62 781,25 5,2687 5,2903 3,3949 5,2903-0,7399 2,4843 1,9833 1, ,31 390,625 2,4639 2,6363 1,5926 2,6363-2,1359 1,2680 1,0783 1, ,31 1,3094 1,1773 0,7996 1,1773-0,5514 0,6774 0,6028 1, , , ,5 390,62 781,25 195,31 390,625 X9 X10 X11 X12 X13 X14 X15 X16 1,4793 2,8360 3,4105 2,5382 0,3700 2,9460 5,8778 1,5921 1,3822 3,0664 5,2568 3,8627-0,0831 2,0239 3,3808 1,3904 1,3475 2,1172 3,7452 5,0362-0,2812 1,6501 2,6830 1,3306 1,7109 2,5196 4,0698 5,0833-0,8746 2,1995 5,4707 1,6545 1,6422 2,3631 3,5750 4,7679-0,6931 2,4590 6,6585 1,6776 1,5991 2,1200 2,7498 4,3338 4,4059 2,2975 5,6783 1,6270 1,5519 2,1208 2,6565 3,3950 2,3528 2,7028 7,0119 1,5583 1,5471 1,9430 2,2850 1,5926 0,7150 2,4080 6,4514 1, ,31 1,6375 1,9331 2,1722 0, ,323 2,0125 4,8697 1,4723
9 PRIEDAI 121 B5 lentelė. Virpesių signalo statistiniai duomenys, esant IŽP, apsukos 2000 aps/min Dažnio intervalas X1 X2 X3 X4 X5 X6 X ,5196 2,5609 2,0378 2,5609-0,5313 1,3777 1,1340 1, ,3417 2,2050 2,6020 2,2050-0,9192 1,7346 1,1575 1, ,9301 3,3529 2,6242 3,3529-1,0851 1,6870 1,0306 1, ,6115 3,5145 2,0604 3,5145-0,5639 1,3935 0,9546 1, , ,8227 2,8268 1,5155 2,8268-1,8483 1,1927 1,0581 1, , ,5 2,0227 2,0356 1,4749 2,0356-0,1632 1,3359 1,2642 1, ,62 781,25 2,0208 2,1354 1,6389 2,1354-0,0577 1,4539 1,3568 1, ,31 390,625 1,4894 1,4461 1,0780 1,4461-1,3555 0,9698 0,8999 1, ,31 1,2056 1,4711 5,3984 1,4711-4,3883 6,6278 6,6418 0, , , ,5 390,62 781,25 195,31 390,625 X9 X10 X11 X12 X13 X14 X15 X16 1,2364 1,8289 2,2220 2, ,9773 1,6602 2,5701 1,2567 0,9000 1,3500 2,0231 2,6020-0,3288 1,6194 1,8316 0,8474 1,1165 1,7369 2,8431 2,6242-1,6222 2,3730 5,2486 1,2777 1,7528 2,5917 3,7833 2,0604-0,9449 2,6713 7,4359 1,7057 1,8625 2,3665 2,6678 1,5155-2,0969 2,6935 8,8252 1,8652 1,3714 1,5140 1,6000 1,4750-2,6782 1,6425 3,0195 1,3801 1,2330 1,3899 1,4894 1,6389-0,1731 1,6715 2,8484 1,3030 1,3817 1,5358 1,6552 1,0780-2,7904 1,6079 2,9717 1, ,31 0,2233 0,1819 0,1815 5,3985 0,0899 0,0991 0,0056 0,2725
10 122 PRIEDAI C priedas. Patikslintas tiesiakrumplės pavaros matematinis modelis Tiesiakrumplės pavaros matematinio modelio, masių matrices ir vidinių jėgų vektoriaus detalus išvedimas. Lygtims sudaryti pasinaudojama ryšio funkcijomis i-tojo krumplio, n-tojo baigtinio elemento poslinkių ryšio funkcija: Rp, = R + [A(ψ )]r, + ; u, (C.1) R, čia vektorius R = R,. 0 cosψ sinψ 0 Posūkio matrica Aψ = sin ψ cosψ r + nl + ξl Vektorius r, = 0 0, daroma prielaida, kad krumpliaračio vainikas nesideformuoja, L - n-to elemento ilgis. Vektorius: u, = u,, u,, 0 = Nq,, = u,, v,, N 0 0 N 0 0 w,, = 0 N N 0 N N u = (C.2),, v,, w,, N u,, + N u,, = N v,, + N w,, + N v,, + N w,, ; 0 ξ bedimensis dydis, kinta 0 ξ 1.
11 PRIEDAI 123 Įvedame: r + nl + ξl R, = r, + u, = r + nl + ξl + N u, + N u, 0 + N v, + N w, + N v, + N w,. 0 Skaičiuojama deviacija: u, u, = δrp, = δr + δψ [A(ψ )]R, + Aψ δu., Pertvarkome išraišką: δrp, = δr [A(ψ )]R, δψ + Aψ δu ;, čia: δr, δr = δr, ; 0 R, = 0 0 R,, ; 0 0 R,, R,, R,, 0 čia R,, = N v, + N w, + N v, + N w, ; R,, = r + (n 1) L + ξl + N u, + N u, ; kadangi vertinamas sukimas tik apie z ašį: 0 δψ = 0 ; δψ vektoriaus u, išvestinė skaičiuojama: (C.3) (C.4) (C.5) (C.6) (C.7) (C.8) (C.9) (C.10) δu,, δu, = δu,, = Nδq,, = 0
12 124 PRIEDAI δu,, N 0 0 N 0 0 δv,, δw,, = 0 N N 0 N N ; (C.11) δu,, δv,, δw,, čia N formos funkcijos N = x arba naudojant bedimensį dydį: + ;(C.12) N = 1 ξ 0 0 ξ ξ + 2ξ Lξ 2ξ + ξ 0 3ξ 2ξ L ξ + ξ.(c.13) Galutinė išraiška atrodo: δrp, = [[E], [A(ψ )]R, ]δq, + Aψ [N]δq ;,, Čia E vienetinė matrica: E = Vektorius δq, turi pavidalą: (C.14) δr, δr, δq, = 0. (C.15) 0 0 δψ Išskleistas vektorius δrp, turi pavidalą: cosψ sinψ 0 δrp, = [0 1 0, sinψ cosψ
13 PRIEDAI 125 δr, 0 0 R,, δr, 0 0 R,, 0 + R,, R,, δψ cosψ sinψ 0 +sinψ cosψ ξ 0 0 ξ ξ + 2ξ Lξ 2ξ + ξ 0 3ξ 2ξ L ξ + ξ δu, δv, δw,. (C.16) δu, δv, δw, Įvedame: B, = [[E], [A(ψ )]R, ]; tada: δrp, = [B, ]δq, + Aψ [N]δq.,, Greitis Rp, = [B, ]q, + Aψ [N]q.,, Pagreitis Rp, = B, q, + [B, ] q, + Aψ Parametras: [B, ] + Aψ [N]q.,, [N]q,, = [0, Aψ ψ R, [A(ψ )]R, ]; čia R, = 0 + =Nq u.,, (C.17) (C.18) (C.19) (C20) (C.21) (C.22)
14 126 PRIEDAI Po pertvarkimų gauname: Rp, = B, q, + B, q, + ψ Aψ [N]q,, + Aψ Nq,, = = B, q, + [B, ] q, Aψ [[N]q,, ] ψ + Aψ Nq.,, Įvedame: a = [B, ] Aψ [[N]q,, ] ψ. q, Pagreičio išraiška: Rp, = B, q + Aψ Nq+a,,.(C.25) Naudojant Dalambero principą galima užrašyti: δrp, Rp, dm F = 0; įšskleista forma: (C.23) (C.24) (C.26) δr R dm = (δq, [B, ] + δq,, [N] Aψ ) (B, q, + Aψ Nq+a,, )dm. (C.27) Krumpliaračio masė: δq, [B, ] B, q dm, = δq, [B, ] B, dmq, = δq E E, Aψ R,, R, Aψ, R, R dmq, ; (C.28), [B, ] B, dmq, = [M ]q., Krumpliaračio n krumplio i-ojo elemento masė: δq,, N Aψ ) Aψ Nqdm,, = N Aψ ) Aψ Nqdm,, = = δq,, = δq,, ρsξn NL dξq,,. Galutinė išraiška: (C.29) (C.30) ρs(ξ)[n] NL dξq,, = [M,, ]q,,. (C.31)
15 PRIEDAI 127 Kitų narių daugybą: δq, B, Aψ Nqdm,, = = δq, [B, ] Aψ Nqdm,, ; (C.32) δr Aψ Nq,, R dm = (δq, B, + δq,, N Aψ ) (B, q, + + [B, ] Aψ [[N]q,, ] ψ )dm ; (C.33) q, Jėgos vektoriaus formavimas Naudojant Delambero principą mūsų lygčių sistemoje (C.26) yra vidinės jėgos Vidinių jėgų nustatymas δr R dm = (δq, [B, ] + δq,, [N] Aψ ) (B, q, + Aψ Nq+a,, )dm; (C.27) a = B, Aψ [[N]q,, ] ψ = q, = B, q, + ψ Aψ [N]q ;,, (C.28) -F= (B, + N Aψ ) (B, q, + ψ Aψ [N]q )dm,, ; (C.29) [B, ] = [0, ψ Aψ R, [A(ψ )]R, ]; (C.30) R, = 0 + u =Nq,, ; (C.31) [B, ] = 0, ψ Aψ R, [A(ψ )] Nq,, ; (C.32) F= (B, + N Aψ ) (0, ψ Aψ R, [A(ψ )] Nq,, + q, δψ Aψ [N]q )dm;,, (C.33) 1 = [B, ] 0, ψ Aψ R, [A(ψ )] Nq,, q, dm ;(C.34)
16 128 PRIEDAI 1 = [B, ] 0, ψ Aψ R, [A(ψ )] Nq,, S(ξ)dξq, ;(C.35) 2 = [B, ] ψ Aψ [N]q dm,, ; (C.36) 2 = [B, ] ψ Aψ [N]S(ξ)dξq,, ; (C.37) 1 = N Aψ 0, ψ Aψ R, [A(ψ )] Nq,, q, dm ;(C.38) 1 = N Aψ 0, ψ Aψ R, Aψ Nq,, S(ξ)dξ q, ; (C.39) 2 = N Aψ ψ Aψ [N]q,, ] dm ; (C.40) 2 = N Aψ ψ Aψ [N]S(ξ)dξ q.,, (C.41)
17 PRIEDAI 129 D priedas. Duomenys išskaidyti į dažnio intervalus Riedėjimo guolių su pažaidomis matematinio modeliavimo skaitiniai rezultatai D1 pav. Veleno pagreitis vertikalia kryptimi, kai guolis neturi pažaidos (signalas išskleistas naudojant DB5 Vilnelę) D2 pav. Veleno pagreitis vertikalia kryptimi, kai guolis turi pažaidą išoriniame žiede (signalas išskleistas naudojant DB5 Vilnelę)
18 130 PRIEDAI D3 pav. Veleno pagreitis vertikalia kryptimi, kai guolis turi pažaidą vidiniame žiede (signalas išskleistas naudojant DB5 Vilnelę) Riedėjimo guolių su pažaidomis eksperimentinių tyrimų skaitiniai rezultatai D4 pav. AE signalas be pažaidos a) išmatuotas signalas; b) Išskleistas signalas naudojant DB5 Vilnelę
19 PRIEDAI 131 D5 pav. AE signalas, išorinio žiedo pažaida a) išmatuotas signalas; b) Išskleistas signalas naudojant DB5 Vilnelę D6 pav. AE signalas, vidinio žiedo pažaida a) išmatuotas signalas; b) Išskleistas signalas naudojant DB5 Vilnelę
20 132 PRIEDAI Cilindrinės tiesiakrumplės pavaros matematinio modeliavimo rezultatai D7 pav. Išskleistas signalas, pavara be pažaidos D8 pav. Išskleistas signalas, pavaroje 1 mm pažaida
21 PRIEDAI 133 D9 pav. Išskleistas signalas, pavaroje 2 mm pažaida D10 pav. Varančiojo krumpliaračio išskaidytas signalas
22 134 PRIEDAI Pavaros eksperimentiniu tyrimu rezultatai D11 pav. Išskleistas VS be pažaidos D12 pav. Išskleistas VS su 1mm pažaida
23 135 PRIEDAI D13 pav. Išskleistas VS su 2 mm pažaida D14 pav. Išskleistas AE signalas, be pažaidos
24 136 PRIEDAI D15 pav. Išskleistas AE signalas, sistemoje 1 mm pažaida D16 pav. Išskleistas AE signalas, sistemoje 2 mm pažaida
25 137 PRIEDAI Hipoidinės pavaros eksperimentinių tyrimų rezultatai D17 pav. Hipoidinės pavaros virpesių signalas išskaidytas į dažnio intervalus D18 pav. AE signalo skaidymas į dažnio intervalus
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