Technique Of Research Uncertainty Dynamic Measurements Of Vibration Acceleration Of Rotating Machines

Transcription

1 IOSR Joural of Electrical ad Electroics Egieerig (IOSR-JEEE) e-issn: ,p-ISSN: , Volue 11, Issue 5 Ver. III (Sep - Oct 16), PP Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig Machies О. М. Vasilevsyi 1, P. I. ulaov 1, V. M. Didych 1 Viytsia Natioal Techical Uiversity, 95 helitsoyeshose, Viytsia, 11, Uraie, Viytsia Natioal Medical Uiversity aed after M. I. Pirogov Аabstract: Developed ethodology for estiatio of dyaic easureet ucertaity, which correspods to the iteratioal stadards for evaluatig the quality of easureets - the cocept of ucertaity. It is proposed to estiate the ucertaity of dyaic easureets o the basis of the frequecy characteristic easurig eas ad the spectral fuctio of the iput sigal. This ethod was tested i the evaluatio of the dyaic easureet of vibratio of rotatig achies that helped cofir its correctess ad efficiecy. It is foud that the axiu value of the dyaic ucertaity vibratio acceleratio easureet of,5 /s for a observatio tie of 3 s ad the oial value sigal of vibratio acceleratio.35 /s at a frequecy of 6 z. eywords: dyaic ucertaity of easureet devices, quality assurace of dyaic easureets, spectral fuctio, frequecy characteristic, vibratio acceleratio. I. Itroductio Experiets coducted usig Measureet Meas (MM) uder dyaic coditios are becoig ore coo i ay fields icludig scietific research, techology, aufacturig idustry, coerce, ad edicie. Dyaic easureets are i the first istace cocered with the study of the cofority of the path of the physical processes i subjects uder ivestigatio. As a result, the role of such easureets is particularly sigificat, firstly i the areas of sciece related to the ivestigatio of the structure of atter, the aalysis ad sythesis of ew substaces ad aterials, where the study of taes place uder experietal coditios, ad secodly, i the fields of egieerig, especially i aufacturig ad edicie, which are which characterized by the creatio of ew techological processes ad the testig of ew MM usig high precisio equipet. Whe reportig o the results of dyaic easureets, it is ecessary to provide a quatitative assesset of the quality of the experiet i order that its reliability ay be correctly appraised [1-5]. Without such a referece value, the results of dyaic easureet ca either be copared with other equivalet studies, or with stadard referece values. It is therefore ecessary to develop a uifor ad uderstadable assesset ethodology of the quality characteristics of dyaic easureets. I this cotext, is ecessary to tae ito accout the fact that durig dyaic easureet there is always a trasitio period durig the operatio of the MM, durig which the output sigal of the MM chages sigificatly over tie. This set of circustaces ay be explaied give the iertial properties of the MM, because they coprise, o the whole, of copoets with differet asses ad sprigs, capacitace ad iductace or other iertial eleets, that lead to the eergece of dyaic ucertaity. This leads to the fact that the eas of easurig the coversio equatio that aps its statics is uacceptable i a dyaic ode. I this case, we eed to use differetial equatios that describe the dyaic relatioship of the output, y t, ad the iput x t values of easurig istruets [6]. Give the above, it is ecessary to develop a sigle approach to the expressio of dyaic ucertaity i easureet eas, which would eet iteratioal requireets that apply to the evaluatio of the characteristics of the quality of easureets, ad this is see as the core scietific proble i the field of etrology. The objective i writig this paper: is the developet ad atheatical descriptio of a ew approach to the expressio of the dyaic ucertaity of easureet eas, that would allow us to tae ito accout the iertial properties of the easureet eas ad the easureet sigal passig through it, which will esure a uified estiatio of dyaic easureets i accordace with existig regulatios i etrology, eve if produced i differet coutries, differet laboratories ad differet etrological orgaizatios. DOI: 1.979/ Page

2 Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig.. II. Aalysis of the status of research ad publicatios I drawig up relevat differetial equatios, iput sigals are recorded o the right, i.e. the reaso that led the MM to fuctio, while the left side of the differetial equatio, describes the output sigal (or respose of the MM), ad for liear trasducers, it is writte i the for [6, 7] i a i t b x t, (1) i y x t, t where y are respectively the iput ad output values; i, are the order derivatives; ad a, b are the coefficiets that characterize the properties of the MM. To express the differetial equatio i the area of frequecy, the differetiatio sybol as the tie coordiate, ad the the equatio (1) taes the for: y x j S j b a or j jx j where y j, j 1 j b1 j... 1 j a j y, () 1, j ay replace d dt x are respectively the spectral fuctios of the iput ad output easureet sigal; b a is the static sesitivity, i.e. the sesitivity to the costat iput value (whe j j is S ); the trasfer fuctio of the MM or operatioal sesitivity. The ost typical properties of the MM are dyaic characteristics, which are described by differetial equatios of the first or secod order, although i soe cases, the third or higher order [4-7]. Iforatio about the dyaic characteristics should be foud i the regulatory ad techical docuetatio of the MM, although if data is ot available, it ca be obtaied o the basis of a priori data o the MM. To express the experietal ucertaity of the results of dyaic easureets, it ay be coveiet for practical use to refer to the frequecy characteristics of the easurig eas [4, 8], listed i Tab. 1. Frequecy characteristics of the MM j where is the trasissio coefficiet j 1 j Table 1 where is the tie costat deteried by the paraeters of the MM j j j 1 j j exp j j 1 j 1 j 1 Typical Uits No-iertial (ideal easureet trasducer) Aperiodic (teperature trasducer) Itegrated (itegrated aplificatio) Forcig (differetial aplificatio) Delay (aalog-to-digital coverters) Oscillatig (electroechaical trasducers) It is also ow that the existig iteratioal experiece i the cocept of evaluatio ad expressio of easureet ucertaity [1] does ot describe how to udertae estiatio of dyaic ucertaities i the perforace of etrological wors (or experiets i dyaic odes of MM). [1] oly aes it apparet that i existece there are ways of estiatio as deostrated by type A ad type B, ad i additio ways to deostrate ucertaities, which ay be stadard, cobied or ehaced. The defiitios of these ucertaities are give i [1]. A well-ow approach, as ivestigated i the papers [4 6], is that dyaic ucertaity is calculated as a stadard ucertaity of type B, itself deteried by the dyaic error value divided by the square root of 3 (assuig a uifor distributio law). DOI: 1.979/ Page

3 Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig.. Usig classical theory i the easureet of dyaic error i the expressio of dyaic ucertaity is uacceptable, give the cocept of easureet ucertaity expressio, which, as set out i the iteratioal stadard [1], is ovig away fro the cocept of easureet error, as such, which does ot use ow values, ad caot have absolute values. This is as opposed to easureet ucertaity, which ca be evaluated, ad for a particular easureet result is ot a sigle value, but has a ifiite uber of values, which are scattered aroud the result. osequetly, there is a eed to develop a ew approach to the expressio of dyaic ucertaity that ca be evaluated without usig the classic dyaic errors used i error theory. III. The presetatio of the base aterial If the equatio of the easurig trasitter is Y =, (3) where a physical quatity to be easured (iput sigal); trasforatio coefficiet of the easurig device; Y easureet result (output sigal). The atheatical expectatio of the iput sigal equals to M[], ad atheatical expectatio of the output sigal will equal M[Y] = M[], (4) where M[Y] ad M[] atheatical expectatios of the output ad iput sigals of easurig device correspodigly. Spectral desity of the iput sigal (t) has the equatio [4] 1 (ω) = li T j whe T, (5) where (jω) fourier iage, received by substitutio of the eaigs o jω i the operator iage (s); T observatio tie; ω = πf. Siilarly the equatio for spectral desity of output sigal ca be represeted as 1 Y (ω) = li T Y j whe T. (6) Iages ratio of output ad iput eaigs results i the equatio of easurig device trasfer fuctio [4, 7] B s Y s s, (7) s q A s q q where Y(s), (s) operators iages of output Y(t) ad iput (t) sigals correspodigly;, q derivative orderfro Y и correspodigly; A q, B coefficiets of differetial equatio. Therefore it follows that [7] Y j, (8) where (jω) frequecy characteristics of easurig trasforer. We ca deterie the ucertaity of output sigal o dyaic easureets as a square root fro itegral of output sigal spectral desity accordig to all available frequecies [7] u D j d T j j DOI: 1.979/ Page d 1, (9) where j odulus of easurig device frequecy characteristics beig used for dyaic easureet. Modulus of easurig device frequecy characteristic is deteried by the forula where j a b 1, (1) a, b real ad iagiary parts of frequecy characteristic correspodigly j Spectral fuctio of the iput sigal (jω) is lied to its tie fuctio (t) by Laplace equatio j t jt e dt, (11) where ω circular frequecy of iput sigal [4 9]. Ifiity sig ca be substituted by suary observatio tie T whe tie iterval is fial. [9].

4 Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig.. So the ucertaity itroduced by the liited capacity of the easurig device o dyaic easureets ca be evaluated o the basis of the odel equatio of iput sigal spectral fuctio ad frequecy characteristics of the used device by the forula (9). IV. The ethod of dyaic vibratio acceleratio easureet ucertaity estiatio Whe easurig thevibratio acceleratio of operatig echaiss actig o the basis of the acceleroeter echaical vibratios lead to the fact that the piezo is affected by dyaic force that is the product of the acceleratio of the seisic ass to the appropriate weightultiplicatio. Piezoeleets geerate a electrical charge proportioal to the curret dyaic force for it. Seisic ass of the acceleroeter virtually uchaged, which eas that the electric charge that occurs at the electrodes of the piezoeleets is proportioal to the acceleratio of the asses. Sice the aplitude ad phase of acceleratig seisic ass i a broad frequecy rage are idetical to the aplitude ad phase of acceleroeter bases acceleratio, the overall electric charge, give to the latter is proportioal to the acceleratio of its foudatios ad therefore acceleratio of the echaical vibratios of the objectsurfaces, to which acceleroeter is fixed [1]. Differetial equatios describig the dyaic relatioship of iput ad output variables of acceleratio easurig chael has the for d ) d ) c ) F(t ), (1) dt dt where F(t) = F si t is haroic forced oscillatios power of the object surfaces(iput value); F is power aplitude; ω is agular frequecy of forced power; Х s (t) is echaical vibratios of the iertial ass; is acceleroeter ass; c is dapig paraeter; is piezoeleets equivalet stiffess [1]. Let us write the differetial equatio (1) i the for of cooexpretio d ) d ) F h h ) si t, (13) dt dt where h c is dapig coefficiet; h is critical dapig coefficiet. The trasfer fuctio of the easurig tool has a loo ( s ) MM s hs h, (14) where MM is proportioality factor of vibratio acceleratio easurig chael. Turig to the frequecy doai ad separatig the real ad iagiary parts, we obtai a expressio of the odule of frequecy easurig vibratio acceleratio characteristics ( j MM MM ). (15) 4 4 h h 4 h h j h j 1 Iput sigal F si t j j F j of the vibratio acceleratio has iage -1-1, (16) where is cyclic frequecy of iput vibratio acceleratio sigal, which rages fro 6 to 1 z, that is, its iiu value is 18,849.5 rad/s, ad the axiu value is rad/s. The odule of iput vibratio acceleratio iage described by 1 1 j F. (17) Fro the literature [1-1], it is ow that the aplitude of the forced haroic force F is 4,3, which correspods to 3 1. Weight acceleroeter is = 4 g, correspodig to 41 g. Dapig paraeter c for piezoelectric acceleroeters is,5, equivalet stiffess piezoeleets is =, the observatio tie is T = 3 s. The proportioality factor (gai) MM of vibratio acceleratio easurig chael is 1 5. Substitutig the foud values of frequecy characteristics odule (15) ad iput sigal iage (17) i equatio (9) we obtai a expressio for the estiatio of easureet ucertaity dyaic vibratio acceleratio 1 DOI: 1.979/ Page

5 Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig.. u D MM F T d. (18) 4 4 h 4 h h For the solutio of equatio (18) atheatical pacage Maple 1 was used. Substitutig i the expressio (18) the etioed above factors there was obtaied the ueric value of easureet ucertaity dyaic acceleratio, which is,33 /s at the frequecy of the iput sigal 1 z ad acceleratio tie of observatio T = 3 s. If the observatio tie icreases to 6 s at the sae frequecy as the iput vibratio acceleratio, the value of dyaic ucertaity reduces to,3 /s. Rated otor acceleratio sigal fro electrospidles is,35 /s [1-1]. At the iiu frequecy of the vibratio acceleratio iput sigal which is 6 z ad at the tie of observatio with 3 s, the value of dyaic ucertaity is,49 /s. If the observatio icreases to 6 s with the frequecy of the iput sigal vibratio acceleratio 6 z, the value of dyaic ucertaity is reduced to,35 /s (oial otor vibratio acceleratio sigal fro electric spidel is,35 /s). Dyaic ucertaity chages characteristics depedig o the observatio tie T (fro 1 to 15 s) are obtaied usig atheatical pacage Maple 1 ad preseted i Figure 1 at iiu 6 z ad 1 z axiu values of the iput sigal of frequecy vibratio acceleratio. Figure 1 Thus, o basis of the proposed ethod of evaluatio of dyaic easureets ucertaity there has bee estiated the ucertaity of vibratio acceleratio dyaic easureet of electric otor based o atheatical odels of the spectral fuctio of the iput acceleratio ad frequecy respose of easurig chael acceleratio.it resulted i the opportuity, together with the values of the stadard ucertaity type A, stadard ucertaity type B that due to the liited properties of easurig trasducers, which are part of easurig chael acceleratio, cosider the value of dyaic ucertaities i assessig the cobied (total) easureet ucertaity acceleratio. As a result of studies it has bee foud out (Fig. 1), that the saller the observatio tie of vibratio acceleratio sigal of a ovig object, is the bigger is value of dyaic easureet ucertaity. Therefore, to DOI: 1.979/ Page

6 Techique Of Research Ucertaity Dyaic Measureets Of Vibratio Acceleratio Of Rotatig.. reduce the ipact of dyaic easureet ucertaity i the assesset of the easureet result of vibratio acceleratio is ecessary to icrease observatio tie of at least 3 s. V. oclusios The techique of estiatio of dyaic easureets ucertaity allows to calculate the value of dyaic ucertaities, taig ito accout that iteratioal requireets for perforace evaluatio of the accuracy of easureet - the cocept of ucertaity. It helps to esure traceability ad eables copariso of the results of dyaic easureets ade by differet easureet ad testig laboratories of the leadig coutries. The ethod was tested i the assesset of dyaic easureet ucertaity of electric otor vibratio acceleratio with electric spidel, which cofired its validity ad effectiveess. Refereces [1]. ISO/IE Guide 98-1:9 «Ucertaity of easureet Part 1: Itroductio to the expressio of ucertaity i easureet». Geeva (Switzerlad): ISO p. (Eg). []. IE GUIDE «Applicatio of ucertaity of easureet to cofority assesset activities i the electrotechical sector». Geeva (Switzerlad): IE p. (Eg). [3]. ISO/IE 175:5 «Geeral requireets for the copetece of testig ad calibratio laboratories». Geeva (Switzerlad): ISO р. (Eg). [4]. Eichstädt S. Aalysis of Dyaic Measureets. Evaluatio of dyaic easureet ucertaity. Berli: Fraeberg, р. (Eg). [5]. Esward T. J., Elster., esslig J. P. Aalysis of dyaic easureets: ew challeges require ew solutios // I IMEO World ogress o Fudaetal ad Applied Metrology. 9. PP (i Portugal). (Eg). [6]. Elster., Eichstädt S., Li A. Ucertaity evaluatio of dyaic easureets i lie with GUM // I IMEO World ogress o Fudaetal ad Applied Metrology. 9. PP (i Portugal). [7]. Vasilevsyi O. M. A frequecy ethod for dyaic ucertaity evaluatio of easureet durig odes of dyaic operatio // Iteratioal Joural of Metrology ad Quality Egieerig. 15. Vol. 6. Nuber.. (i Uited igdo). [8]. Vasilevsyi O., ucheru V., uryti I. A approach to the evaluatio of dyaic ucertaity i easureet usig o-statistical techiques // Poiary. Autoatya. otrola. 14. Vol. 6. Nuber PP (i Polish). [9]. Vasilevsyi O. M. Assesset of the ucertaity of dyaic easureets // Visy Viytsogo politehichogo istytutu С (Ur.). [1]. Vasilevsyi O. M., Podzhareo V. O. Aalysis of dyaic etrological characteristics of easurig vibratio trasducer // Nau. pr. ІV Мizharodoy auovo-tech. of. [ Мetrologiya ta vyiryvala techia ]. hariv: NNTS «Іstytut etrologii», 4. Т.. P (Ur.). [11]. Podzhareo V. O., Vasilevsyi O. M., Sevastyaov V. M. Evaluatio of static etrological characteristics of easurig vibratio chael // Uraisyy etrologichyy zhural P (Ur.). [1]. Vasilevsyi O. M. Iforatio-easurig syste for autoatic cotrol of asychroous rotatio ad vibratio diagostics of electroechaical systes // Vibratsiya ashi: izereie, sizheie, zaschita. Doets P (Ur.). DOI: 1.979/ Page