577. Estimation of surface roughness using high frequency vibrations

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1 577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str , LT-5368 Kauas, Lithuaia Kauas Techical College Tvirtoves av. 35, LT-555 Kauas, Lithuaia (Received 5 September ; accepted 9 December ) Abstract. Surface roughess is a importat parameter for evaluatig the quality of material surfaces. It affects the tribological ad optical properties of the materials. The paper proposes a ew method for estimatio of surface roughess, which is based o measuremet of high frequecy vibratios that are geerated whe air flow iteracts with the surface of a solid body. It was determied that itesity of high frequecy vibratios depeds o surface roughess. Sadpapers with differet magitudes of surface roughess were used for the experimetal study. Keywords: Surface roughess, high frequecy vibratios Itroductio Surface roughess is a importat parameter for evaluatig the quality of material surface. This parameter affects the tribological ad optical properties of the materials []. Methods that are curretly i use ca be divided ito two major groups: cotact ad o-cotact []. Cotact methods are based o the iteractio betwee probe ad surface. The methods of stylus profilig, atomic force microscope ad others are classified as cotact methods. Optical, microscope, iterferometry, peumatic, capacitace ad others are o-cotact measuremet methods [ 5]. Methods ca also be classified ito three categories: profilig, area-profilig ad area-averagig []. Profilig techiques provide quatitative assessmet of surface peaks ad valleys through poit-by-poit measuremet with a high-resolutio probe. Three-dimesioal represetatios of the surface roughess ca be produced by usig a procedure kow as area-profilig. Area-profilig gives a much more complete represetatio of the surface roughess tha profilig. The area-averagig techique probes the surface over a fiite area all at oce to produce a measured property that represets a statistical average of peaks ad valleys. Area-averagig techiques offer the potetial for high speed ispectio, but most of them have limited effectiveess. May methods metioed above have disadvatages ad therefore are ot appropriate for practical applicatios. Relevace of the preseted work is to demostrate possibility of applicatio of high frequecy vibratios (HFV) as a measuremet method for estimatio of surface roughess. This method ca be attributed to the area-averagig category. The purpose of the preseted work is VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

2 to ivestigate possibility of the applicatio of HFV measuremet method for estimatio of the surface roughess. Evaluatio of surface roughess Surface roughess is a measure of topography of the surface. It is quatified by the vertical deviatios of a real surface from its ideal form. If these deviatios are large, the surface is rough; if they are small the surface is smooth. There are may parameters of the surface roughess that ca be used to aalyze the surface [, 6]. The most commo parameter used i idustry is the average roughess. The average roughess ca be calculated as: R = l y ( x) dx= a Y i l i=, () where is the umber of sample poits; Yi or y (x) is the value of the profile deviatio from the mea lie; l is the basic legth. The geometrical iterpretatio of surface roughess is preseted i Fig.. Other commo parameters of the surface roughess are R, R, R, R, R, R ad R ku [6]. Some of them are used oly i certai idustries or withi certai coutries. R q is root mea square roughess. It is the root mea square of the measured value deviatios take withi the evaluatio legth ad measured from the mea lie. It ca be calculated: R q = Y i i=. () R t defies maximum peak-to-peak-valley height. It is the absolute value betwee the highest ad lowest peaks ad ca be evaluated as: R t = mi Y + max Y. (3) i i i i q t z v p sk R a Fig.. Geometrical iterpretatio of the surface roughess: lie; l basic legth R a average roughess; m mea Rz is the average absolute value of the five highest peaks ad the five lowest valleys over the evaluatio legth. Rv is the depth of the deepest valley i the roughess profile over the evaluatio legth. R is the height of the highest peak i the roughess profile over the p evaluatio legth. Rsk ad R ku are skewess ad kurtosis respectively. Both of them describe the shape of the amplitude distributio fuctio of surface roughess. Skewess measures the symmetry of the variatio of a profile about its mea lie. Kurtosis relates to the spikiess of the profile. 43 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

Applicatio of HFV measuremet method for estimatio of surface roughess Acoustical HFV measuremet method may be used for estimatio of the surface roughess.

The formatio of HFV is based o the iteractio betwee the air flow ad the surface of a solid body. It was estimated that itesity of HFV depeds o the roughess of the surface of a solid body.

Therefore experimetal ivestigatio is performed here. The block diagram of the measuremet system is preseted i Fig.. Air from the compressor is applied to a ozzle, where the air pressure is measured.

Afterwards measured sigals are amplified ad stored i the oscilloscope. Fially, the sigals are trasferred to the computer, where Matlab programme is used for data processig. Fig.

3 Applicatio of HFV measuremet method for estimatio of surface roughess Acoustical HFV measuremet method may be used for estimatio of the surface roughess. This estimatio is based o the measuremet of high frequecy vibratios. The measuremet trasducer i the frequecy bad of 3 khz is used. The formatio of HFV is based o the iteractio betwee the air flow ad the surface of a solid body. It was estimated that itesity of HFV depeds o the roughess of the surface of a solid body. The priciple of the formatio of the HFV is based o the assumptio that the air flow moves alog the surface ad forms the air whirls. The theoretical ivestigatio of the formatio of HFV is complicated. Therefore experimetal ivestigatio is performed here. The block diagram of the measuremet system is preseted i Fig.. Air from the compressor is applied to a ozzle, where the air pressure is measured. Air flow from the ozzle iteracts with the surface of a solid body. This iteractio results is the formatio of HFV aroud. The HFV are measured by trasducer. Afterwards measured sigals are amplified ad stored i the oscilloscope. Fially, the sigals are trasferred to the computer, where Matlab programme is used for data processig. Fig.. Experimetal measuremet system: C air compressor; PS pressure sesor; N ozzle with air flow; TR HFV trasducer; A amplifier; O oscilloscope; PC computer; L distace betwee ozzle ad surface; M distace betwee surface ad HFV trasducer; d diameter of the ozzle; α agle betwee the HFV trasducer ad rough plate; β agle betwee the ozzle ad rough plate; γ agle betwee the HFV trasducer ad the ozzle Experimetal results ad discussio The experimets were performed with the plates of differet roughess. Sadpapers with various grit sizes were used for this purpose. Grit size refers to the size of the particles of abradig materials embedded i the sadpaper. The parameters ad examples of the ivestigated surfaces are preseted i Table ad Fig. 3. The average roughess R a decreases whe the sadpaper grit umber (size) icreases. a) b) VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

Table. The parameters of the ivestigated surfaces. Sadpaper grit size, No 36 5 6 8 5 8 4 8 36 4 Average particle diameter, µm * 538 336 69 6 5 8 59 5 4 35 Average roughess, µm * - 3 9 67 54 3 3 7,4 6.

4 c) d) e) Fig. 3. Examples of the ivestigated roughess of the surface: a) sadpaper with grit size ; b) sadpaper with grit size 5; c) sadpaper with grit size ; d) sadpaper with grit size 4; e) sadpaper with grit size 4 Table. The parameters of the ivestigated surfaces. Sadpaper grit size, No Average particle diameter, µm * Average roughess, µm * , * Naovea test results [7] ad measuremets by TR [8]. It ca be stated that the sigals measured by HFV trasducer are oise type sigals. The example of the measured sigal is show i Fig. 4. Amplitude, V Time, ms Number of value 8 x Amplitude, V Fig. 4. Represetative example of the measured Fig. 5. Distributio of the measured sigal ; sigal Gaussia distributio (results are obtaied for stable air flow) The distributio of the measured sigal (Fig. 4) ca be approximated by Gaussia distributio (Fig. 5). The root mea square (RMS) value ad the average of the RMS value ca be used for the evaluatio of itesity of HFV sigal [9]. The RMS value of the HFV sigal is calculated accordig to the followig equatio: RMS = N N = U T ( ), (4) where U T () is the digitized time sigal; N is a umber of poits. 43 The average of the RMS values ( RMS AVE ) is calculated as follows: VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

5 RMS AVE = K K k= RMS( k), (5) where K is the umber of the RMS values. Sigal characteristics i the frequecy domai are also importat. The example of the spectrum of the measured sigal is preseted i Fig. 6. I order to evaluate the maximum speed of the measuremet, it is ecessary to establish the miimum measuremet duratio [9], which esures statistically reliable ad o-correlated measuremet result. The miimum measuremet duratio τ mi is evaluated accordig to the followig equatio [9]: mi = ρ τ ) τ ( d τ, (6) Rτ ( ) 5 where ρ ( τ ) = is the stadard autocorrelatio fuctio. I our case τ mi s. It ca R() be oted that sigals, obtaied by dividig the measured sigal ito time itervals of a legth τ mi, do ot correlate with each other [9]. The stadard autocorrelatio fuctio of the stochastic trasducer sigal is preseted i Fig x -3 Magitude of spectrum, V/Hz Frequecy, khz Fig. 6. Spectrum of the measured sigal Fig. 7. Stadard autocorrelatio fuctio of the measured sigal The calibratio curve showig the depedece betwee the output sigal RMS of the HFV trasducer ad sadpaper grit size was obtaied. Air pressure (i the ozzle) is costat durig this experimet. The relatioship betwee measured RMS values of the HFV trasducer sigals ad sadpaper grit size is preseted i Fig. 8. The RMS values are measured times at the each poit of the calibratio curve. The measuremet duratio for each RMS value is ms. The averages of the RMS values ( RMS AVE ) are used for the calibratio curve (Fig. 8). Sadpaper roughess ca be assessed by aother parameter the average roughess. The a liear relatioship betwee measured RMS values of the output sigals of the HFV trasducer ad average roughess was obtaied (Fig. 9). VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

6 RMSAVE, mv Sadpaper grit size Fig. 8. Relatioship betwee measured RMS values of the output sigals of the HFV trasducer ad sadpaper grit size RMSAVE, mv y =,3864x + 94,69 R =, Average roughess, µm Fig. 9. Relatioship betwee measured RMS values of the output sigals of the HFV trasducer ad average roughess (the parameters of the sadpaper are preseted i Table ) The relatioship betwee the itesity of HFV sigals ad ozzle diameter was ivestigated. Whe diameter of the ozzle icreases (air flow icreases too) RMS value of HFV sigals also icreases. Air pressure ad the plate of roughess are costat durig this experimet. The relatioship betwee RMS value of HFV sigals ad ozzle diameter is preseted i Fig.. The relatioship betwee the itesity of HFV sigals ad air pressure was ivestigated. Whe air pressure icreases (air flow icreases too) RMS value of HFV sigals also icreases. The ozzle diameter ad the plate roughess are costat durig this experimet. The relatioship betwee RMS value of HFV sigals ad air pressure is preseted i Fig.. RMS value, mv ,,,3,4,5,6,7 Nozzle diameter, mm Fig.. Relatioship betwee RMS value of HFV sigals ad ozzle diameter RMS value, mv Air pressure, Pa Fig.. Relatioship betwee RMS value of HFV sigals ad air pressure The relatioship betwee the calculated power spectrum desity of measured HFV sigals ad sadpaper grit size is preseted i Fig.. It is demostrated that the positios of the frequecy bad resoaces do ot deped upo sadpaper grit size. Accordig to Fig. the optimum ozzle ad trasducer positios were ivestigated. Optimality is associated with a higher itesity of HFV. The agle γ=9, the surface roughess, air pressure ad ozzle diameter are costat durig the experimet. I this case agle β (betwee the ozzle ad rough plate) was costat while the agle α (betwee the HFV trasducer ad rough plate) was varied. The experimetal results are preseted i Fig. 3. HFV itesity is ormalized with respect to the maximum value. Fig. 3 idicates that the most appropriate agle β is equal to 9 or 5. Whe β is equal to 9, α should be equal to 5 degrees. Whe β is equal to 5, α should be equal to VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

7 Fig.. Relatioship betwee power spectrum desity of the measured sigals ad sadpaper grit size Fig. 3. Directioal diagram of HFV: β is agle betwee ozzle ad rough plate; α is agle betwee the HFV trasducer ad rough plate (otatios are used accordig Fig. ) Cocludig remarks New method for the measuremet of surface roughess is proposed i the paper. It is based o the applicatio of high frequecy vibratios ad ca be used for practical purposes. The preseted method is based o measuremet of itesity of HFV, which are formed as a result of iteractio betwee air flow ad surface of a solid body. The proposed method eables cotactless measuremet ad evaluates average roughess of solid body i the rage of ca. µm. Experimetal results demostrate that geerated HFV sigals are oise-type sigals. The basic measured parameters of HFV sigals are RMS value, average RMS value ad power spectrum. Ackowledgemets We would like to thak Dr. Vytautas Jureas for his help durig the measuremet process by surface roughess aalyzer TR. Refereces [] Surface roughess ad mechaical processes, Available: [] Czadera A. W. Beam effects, surface topography, ad depth profilig i surface aalysis. Higham. MA. USA: Kluwer Academic Publishers, 998, p. 75. [3] Whitehouse D. J. Surface metrology. Meas. Sci. Techol., Vol. 8, 997, p [4] Beet J. M. Recet developmet i surface roughess characterizatio. Meas. Sci. Techol., Vol. 3, 99, p [5] Xiao Mei X., Hog H., Developmet of No-cotact Surface Roughess Measuremet i Last Decades, Vol., 9 Iteratioal Coferece o Measurig Techology ad Mechatroics Automatio, 9, p. -3. [6] Oe-dimesioal roughess parameters, Available: [7] Topography & Roughess Study of Various Sadpaper Grits, Available: [8] Portable Surface roughess tester TR, Available: [9] Augutis S. V., Sauoris M. A method for air flow measuremet usig high frequecy vibratios // Joural of Vibroegieerig/Vilius: Vibromechaika. ISSN , Vol., o., p VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER. VOLUME, ISSUE 4. ISSN

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