Roughness parameters

Transcription

1 Joural of Materials Processig Techology ) 133±145 Roughess parameters E.S. Gadelmawla a, M.M. Koura b, T.M.A. Maksoud c,*, I.M. Elewa a, H.H. Solima d a Productio Egieerig ad Mechaical Desig Departmet, Faculty of Egieerig, Masoura Uiversity, Masoura, Egypt b Desig ad Productio Egieerig Departmet, Faculty of Egieerig, Ai Shams Uiversity, Cairo, Egypt c School of Desig ad Advaced Techology, Uiversity of Glamorga, Wales, UK d Electroics ad Commuicatios Egieerig Departmet, Faculty of Egieerig, Masoura Uiversity, Masoura, Egypt Accepted 14 Jauary 2002 Abstract Surface roughess evaluatio is very importat for may fudametal problems such as frictio, cotact deformatio, heat ad electric curret coductio, tightess of cotact joits ad positioal accuracy. For this reaso surface roughess has bee the subject of experimetal ad theoretical ivestigatios for may decades. The real surface geometry is so complicated that a ite umber of parameters caot provide a full descriptio. If the umber of parameters used is icreased, a more accurate descriptio ca be obtaied. This is oe of the reasos for itroducig ew parameters for surface evaluatio. Surface roughess parameters are ormally categorised ito three groups accordig to its fuctioality. These groups are de ed as amplitude parameters, spacig parameters, ad hybrid parameters. This paper illustrates the de itios ad the mathematical formulae for about 59 of the roughess parameters. This collectio of surface roughess parameter was used i a ew software computer visio package called Surf Visio developed by the authors. I the package, these de itios were exteded to calculate the 3D surface topography of differet specimes. # 2002 Elsevier Sciece B.V. All rights reserved. Keywords: Surface roughess; Surface topography; Computer visio 1. Itroductio Roughess parameters ca be calculated i either twodimesioal 2D) or three-dimesioal 3D) forms. 2D pro le aalysis has bee widely used i sciece ad egieerig for more tha half a cetury. I recet years, there was a icreased eed for 3D surface aalysis. Recet publicatios [1±4] emphasised the importace of 3D surface topography i sciece ad egieerig applicatios. 3D roughess parameters are calculated for a area of the surface istead of a sigle lie. Hece, i order to calculate the 3D roughess parameters, the SurfVisio software cosiders a area from the surface to be tested ad divides it ito a umber of sectios. These sectios represet a umber of cosequet pro les from the surface. The 2D roughess parameters the calculated for each sectio separately, ad the average of each parameter is take for all sectios. This research presets all roughess parameters ad their calculatio methods. Abbreviatios: 2D, two-dimesioal; 3D, three-dimesioal; ADC, amplitude desity curve; BAC, bearig area curve; BMP, type of graphics format stads for widows bitmap; CCS, Cartesia coordiate system; CA, cetre lie average; CPP, cotact probe pro lometry; EVC, Elf VGA capture board; FFT, fast Fourier trasformatio; GIF, type of graphics format stads for graphics iterchage format; h/v, horizotal/vertical resolutio; HS, hue, saturatio, lightess * Correspodig author. Fax: The amplitude parameters Amplitude parameters are the most importat parameters to characterise surface topography. They are used to measure the vertical characteristics of the surface deviatios. The followig sectios give a brief descriptio for each parameter Arithmetic average height R a ) The arithmetic average height parameter, also kow as the cetre lie average CA), is the most uiversally used roughess parameter for geeral quality cotrol. It is de ed as the average absolute deviatio of the roughess irregularities from the mea lie over oe samplig legth as show i Fig. 1. This parameter is easy to de e, easy to measure, ad gives a good geeral descriptio of height variatios. It does ot give ay iformatio about the wavelegth ad it is ot sesitive to small chages i pro le. The mathematical de itio ad the digital implemetatio of the arithmetic average height parameter are, respectively, as follows: R a ˆ 1 Z l jy x j dx l R a ˆ 1 0 X jy i j /02/$ ± see frot matter # 2002 Elsevier Sciece B.V. All rights reserved. PII: S )

2 134 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 Nomeclature ACF ADF g H s H u HSC k l o m 0) P c P s P u PSD r p R a R ku R p R pm R q R sk R t, R max R ti R tm R v R vm R y R z R 3y R 3z RMS S S f S m S.D. t p W f auto correlatio fuctio mm) amplitude desity fuctio ±) umber of iflectio poits Iflectios) roughess height skewess ±) roughess height uiformity ±) high spot cout cout s)) profile solidity factor ±) relative legth of the profile ±) umber of peaks i profile peaks) umber of itersectios of the profile at the mea lie itersectios) peak cout cout/cm) roughess pitch skewess ±) roughess pitch uiformity ±) power spectral desity ±) mea peak radius of curvature mm) arithmetic average height mm) Kurtosis ±) maximum height of peaks mm) mea height of peaks mm) root mea square roughess mm) skewess ±) maximum height of the profile mm) maximum peak to valley height mm) mea of maximum peak to valley height mm) maximum depth of valleys mm) mea depth of valleys mm) largest peak to valley height mm) te-poit height mm) third poit height mm) mea of the third poit height mm) root mea square mm) mea spacig of adjacet peaks mm) stepess factor of the profile ±) mea spacig at mea lie mm) stadard deviatio ±) bearig lie legth ad bearig area curve %) waviess factor of the profile ±) Greek symbols b correlatio legth mm) g profile slope at mea lie 8) D a mea slope of the profile 8) D q RMS slope of the profile 8) l a average wavelegth mm) RMS wave legth mm) l q 2.2. Root mea square roughess R q ) This parameter is also kow as RMS. It represets the stadard deviatio of the distributio of surface heights, so it is a importat parameter to describe the surface roughess by statistical methods. This parameter is more sesitive tha the arithmetic average height R a ) to large deviatio from the mea lie. The mathematical de itio ad the digital implemetatio of this parameter are as follows: s Z 1 l R q ˆ fy x g 2 dx l 0 s 1 X R q ˆ y 2 i The RMS mea lie is the lie that divides the pro le so that the sum of the squares of the deviatios of the pro le height from it is equal to zero Te-poit height R z ) This parameter is more sesitive to occasioal high peaks or deep valleys tha R a. It is de ed by two methods accordig to the de itio system. The Iteratioal ISO system de es this parameter as the differece i height betwee the average of the ve highest peaks ad the ve lowest valleys alog the assessmet legth of the pro le. The Germa DIN system de es R z as the average of the summatio of the ve highest peaks ad the ve lowest valleys alog the assessmet legth of the pro le. Fig. 2 shows the de itio of the te-poit height parameter. The mathematical de itios of the two types of R z are as follows: R z ISO ˆ 1 X p i X v i R z DIN ˆ 1 2 X p i X v i where is the umber of samples alog the assessmet legth Maximum height of peaks R p ) R p is de ed as the maximum height of the pro le above the mea lie withi the assessmet legth as i Fig. 3. I the gure, R p3 represets the R p parameter Maximum depth of valleys R v ) R v is de ed as the maximum depth of the pro le below the mea lie withi the assessmet legth as show i Fig. 3. I the gure R v4 represets the R v parameter Mea height of peaks R pm ) R pm is de ed as the mea of the maximum height of peaks R p ) obtaied for each samplig legth of the

3 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± Fig. 1. Defiitio of the arithmetic average height R a ). Fig. 2. Defiitio of the te-poit height parameter R z ISO), R z DIN) ). assessmet legth as show i Fig. 3. This parameter ca be calculated from the followig equatio: R pm ˆ 1 X R pi where is the umber of samples alog the assessmet legth of the pro le. From Fig. 3, R pm ˆ R p1 R p2 R p3 R p4 R p5 = Mea depth of valleys R vm ) R vm is de ed as the mea of the maximum depth of valleys R v ) obtaied for each samplig legth of the assessmet legth as show i Fig. 3. This parameter ca be calculated from the followig equatio: R vm ˆ 1 X v i where is the umber of samples alog the assessmet legth of the pro le. From Fig. 3, R vm ˆ R v1 R v2 R v3 R v4 R v5 = Maximum height of the profile R t or R max ) This parameter is very sesitive to the high peaks or deep scratches. R max or R t is de ed as the vertical distace betwee the highest peak ad the lowest valley alog the assessmet legth of the pro le. From Fig. 3, R max ˆ R p R v ˆ R p3 R v Maximum peak to valley height R ti ) R ti is the vertical distace betwee the highest peak ad the lowest valley for each samplig legth of the pro le. As the assessmet legth is divided ito ve samplig legths, the maximum peak to valley height R ti ) ca be de ed, as Fig. 3. Defiitios of the parameters R p, R v, R pm, R vm, R t R max ).

4 136 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 Fig. 4. Defiitio of the maximum peak to valley height parameters R ti ). show i Fig. 4, as follows: R ti ˆ R pi R vi where i rages from 1 to 5. From the gure, R t1 ˆ R p1 R v1, R t2 ˆ R p2 R v2, etc Mea of maximum peak to valley height R tm ) R tm is de ed as the mea of all maximum peak to valley heights obtaied withi the assessmet legth of the pro le. From Fig. 4, the mathematical de itio of this parameter is as follows: R tm ˆ 1 X R ti where is the umber of samples alog the assessmet legth of the pro le. From the gure R tm ˆ R t1 R t2 R t3 R t4 R t5 = argest peak to valley height R y ) This parameter is de ed as the largest value of the maximum peak to valley height parameters R ti ) alog the assessmet legth. From Fig. 4, R y ˆ R t Third poit height R 3y ) To calculate this parameter, the distace betwee the third highest peak ad the third lowest valley is calculated for each samplig legth, the the largest distace is cosidered as the third poit height R 3y ). From Fig. 5 the third poit height parameter R 3y ) is the maximum value of the ve values of R 3y1, R 3y2, R 3y3, R 3y4, R 3y5, that is R 3y Mea of the third poit height R 3z ) This parameter is the mea of the ve third poit height parameters R 3y1, R 3y2, R 3y3, R 3y4, ad R 3y5 ). As show i Fig. 5 R 3z is equal to R 3y1 R 3y2 R 3y3 R 3y4 R 3y5 =5. The mathematical de itio of this parameter is as follows: R 3z ˆ 1 X 5 R 3yi Profile solidity factor k) The pro le solidity factor k) is de ed as the ratio betwee the maximum depth of valleys ad the maximum height of the pro le. The mathematical de itio of this parameter is as follows: k ˆ Rv R max Skewess R sk ) The skewess of a pro le is the third cetral momet of pro le amplitude probability desity fuctio, measured over the assessmet legth. It is used to measure the symmetry of the pro le about the mea lie. This parameter is sesitive to occasioal deep valleys or high peaks. A symmetrical height distributio, i.e. with as may peaks as valleys, has zero skewess. Pro les with peaks removed or deep scratches have egative skewess. Pro les with valleys lled i or high peaks have positive skewess. This is show i Fig. 6. The skewess parameter ca be used to distiguish Fig. 5. Defiitios of the third poit height parameters R 3y, R 3z ).

5 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± Fig. 6. Defiitio of skewess R sk ) ad the amplitude distributio curve. betwee two pro les havig the same R a or R q values but with differet shapes. The value of skewess depeds o whether the bulk of the material of the sample is above egative skewed) or below positive skewed) the mea lie as show i Fig. 6. The mathematical ad the umerical formulas used to calculate the skewess of a pro le, which has umber of poits N, are as follows: R sk ˆ 1 Z 1 R 3 y 3 p y dy q 1 R sk ˆ 1 NR 3 q X N 3 Y i where R q is the RMS roughess parameter ad Y i the height of the pro le at poit umber i. The skewess parameter ca be used to differetiate betwee surfaces, which have differet shapes ad have the same value of R a. I Fig. 6, although the two pro les may have the same value of R a, they have differet shapes Kurtosis R ku ) Kurtosis coef ciet is the fourth cetral momet of pro le amplitude probability desity fuctio, measured over the assessmet legth. It describes the sharpess of the probability desity of the pro le. If R ku < 3 the distributio curve is said to be platykurtoic ad has relatively few high Fig. 7. Defiitio of kurtosis R ku ) parameter.

6 138 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 peaks ad low valleys. If R ku > 3 the distributio curve is said to be leptokurtoic ad has relatively may high peaks ad low valleys. Fig. 7 shows these two types of kurtosis. The mathematical ad the umerical formula used to calculate the kurtosis of a pro le with a umber of poits N are as follows: R ku ˆ 1 Z 1 R 4 y 4 p y dy q 1 R ku ˆ 1 NR 4 q X N 4 Y i where R q is the RMS roughess parameter ad Y i the height of the pro le at poit umber i. The skewess parameter ca also be used to differetiate betwee surfaces, which have differet shapes ad have the same value of R a. I Fig. 7, although the two pro les may have the same value of R a, they have differet shapes Amplitude desity fuctio ADF) The term amplitude desity correspods exactly to the term probability desity i statistics. The ADF represets the distributio histogram of the pro le heights. It ca be foud by plottig the desity of the pro le heights o the horizotal axis ad the pro le heights itself o the vertical axis as show i Fig. 8. To calculate the desity of the pro le heights, the amplitude scale is divided ito small parts d y. The measure of the amplitude values foud withi d y, ca be made by calculatig all amplitude values betwee y ad d y relative to the assessmet legth of the pro le. The Amplitude desity is hece de ed by the followig equatio: P y; y d y p y ˆ lim dy 0 d y For surfaces produced by a truly radom process, the ADF would be a Gaussia distributio of surface heights give by the followig equatio: q ADF y ˆ 2pR 2 q exp y2 2R q Auto correlatio fuctio ACF) The ACF describes the geeral depedece of the values of the data at oe positio to their values at aother positio. It is cosidered a very useful tool for processig sigals because it provides basic iformatio about the relatio betwee the wavelegth ad the amplitude properties of the surface. The ACF ca be cosidered as a quatitative measure of the similarity betwee a laterally shifted ad a ushifted versio of the pro le. The mathematical ad umerical represetatios of this fuctio are as follows: Z ACF dx ˆ1 y x y x dx dx ACF dx ˆ 1 X N y i y i 1 N 1 0 where dx is the shift distace ad y i the height of the pro le at poit umber i. The ACF ca be ormalised to have a value of uity at a shift distace of zero. This suppresses ay amplitude iformatio i the ACF but allows a better compariso of the wavelegth iformatio i various pro les Correlatio legth b) This parameter is used to describe the correlatio characteristics of the ACF. It is de ed as the shortest distace i which the value of the ACF drops to a certai fractio, usually 10% of the zero shift value. Poits o the surface pro le that are separated by more tha a correlatio legth may be cosidered as ucorrelated, i.e. portios of the surface represeted by these poits were produced by separate surface formig evets. Correlatio legths may rage from the i ite correlatio legth for a perfectly periodic wavelegth to zero for a completely radom waveform Power spectral desity PSD) The PSD fuctio is a importat fuctio for characterisig both the asperity amplitudes ad spacig. It is calculated by Fourier decompositio of the surface pro le ito its siusoidal compoet spatial frequecy f). For a 2D surface Fig. 8. The ADF.

7 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± pro le it ca be calculated from the followig equatio: Z 2 PSD f ˆ1 y x exp i2pfx dx 0 " # PSD ˆ 1 X N 1 2 y i e j2pbi=n N 1 iˆ0 where b is the correlatio legth. 3. The spacig parameters The spacig parameters are those which measure the horizotal characteristics of the surface deviatios. The spacig parameters are very importat i some maufacturig operatios, such as pressig sheet steel. I such case, evaluatig the spacig parameters is ecessary to obtai cosistet lubricatio whe pressig the sheets, to avoid scorig ad to prevet the appearace of the surface texture o the al product. Oe of the spacig parameter is the peak spacig, which ca be a importat factor i the performace of frictio surfaces such as brake drums. By cotrollig the spacig parameters it is possible to obtai better boudig of ishes, more uiform ish of platig ad paitig. The SurfVisio software calculates the most kow spacig parameters. The followig sectios give more iformatio about the spacig parameters High spot cout HSC) The HSC parameter is de ed as the umber of high regios of the pro le above the mea lie, or above a lie parallel to the mea lie, per uit legth alog the assessmet legth. Fig. 9 shows how to calculate the HSC parameter above a selected level. The pro le show i the gure has eight HSC Peak cout P c ) The importace of the peak cout parameter appears i some maufacturig processes such as formig, paitig, or coatig surfaces. It is de ed as the umber of local peaks, which is projected through a selectable bad located above ad below the mea lie by the same distace. The umber of peak cout is determied alog the assessmet legth ad the result is give i peaks per cetimetre or ich). If the assessmet legth is less tha 1 cm, the results should be multiplied by a factor to get the peak cout per cetimetre. As show i Fig. 10 the peak cout is determied oly for the closed areas of the pro le, i which the pro le itersects each the upper ad the lower bads i two poits at least. The pro le show i the gure has four peak couts Mea spacig of adjacet local peaks S) This parameter is de ed as the average spacig of adjacet local peaks of the pro le measured alog the assessmet legth. The local peak is de ed as the highest part of the pro le measured betwee two adjacet miima ad is oly measured if the vertical distace betwee the adjacet peaks is greater tha or equal to 10% of the R t of the pro le. Fig. 11 shows how to measure this parameter. This parameter ca be calculated from the followig equatio: S ˆ 1 X S i N Fig. 9. Calculatig HSC above a selected level. Fig. 10. Calculatig the peak cout P c ) parameter withi a selected bad.

8 140 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 Fig. 11. Calculatig the mea spacig of adjacet local peaks S). where N is the umber of local peaks alog the pro le Mea spacig at mea lie S m ) This parameter is de ed as the mea spacig betwee pro le peaks at the mea lie ad is deoted as S m ). The pro le peak is the highest poit of the pro le betwee upwards ad dowwards crossig the mea lie. Fig. 12 shows how to measure the mea spacig at mea lie parameter. This parameter ca be calculated from the followig equatio: S m ˆ 1 X S i N where N is the umber of pro le peaks at the mea lie. The differece betwee the two types of mea spacig parameters, S ad S m, is that the rst parameter S) i s measured at the highest peaks of the pro le, whilst the secod parameter S m ) is measured at the itersectio of the pro le with the mea lie Number of itersectios of the profile at the mea lie 0)) This parameter calculates the umber of itersectios of the pro le with the mea lie measured for each cetimetre legth of the pro le. As show i Fig. 13, the umber of itersectios of the pro le at the mea lie ca be calculated from the followig equatio: X 0 ˆ1 c i where is the pro le legth i cm) Number of peaks i the profile m) This parameter calculates the umber of peaks of the pro le per uit legth cetimetre or ich). Peaks are couted oly whe the distace betwee the curret peak ad the precedig oe is greater that 10% of the maximum height of the pro le R t ). I Fig. 14 the three little peaks, which follow the peaks m 2, m 3 ad m 4 are eglected because the distace betwee each peak ad the precedig oe i too small. The umber of peaks ca be calculated from the followig equatio: m ˆ 1 X m i where is the pro le legth i cm) Number of iflectio poits g) This parameter calculates the umber of i ectio poits of the pro le per uit legth cetimetre or ich). A Fig. 12. Calculatig the mea spacig at mea lie S m ).

9 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± Fig. 13. Calculatig the umber of itersectios of the profile at mea lie. Fig. 14. Calculatig the umber of peaks alog the profile. i ectio poit occurs whe the pro le chages its directio at ay poit as show i Fig. 15. This parameter ca be calculated from the followig equatio: g ˆ 1 X g i where is the pro le legth i cm) Mea radius of asperities r p ) The mea peak radius of curvature parameter is de ed as the average of the priciple curvatures of the peaks withi the assessmet legth. This parameter ca be calculated by calculatig the radius of curvature for each peak alog the pro le, the calculatig the average of these radii of curvatures. The radius of curvature for a peak r pi ) ca be calculated from the followig equatio: r pi ˆ 2y i y i 1 y i 1 l 2 where y i is the height of the peak at which the peak radius of curvature r pi ) is to be calculated, y i 1 the height of the precedig peak, ad y i 1 the height of the ext peak. Fig. 15. Calculatig the umber of iflectio poits alog the profile.

10 142 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 The mea peak radius of curvature r), the ca be calculated from the followig equatio: r p ˆ 1 X r pi 4. The hybrid parameters The hybrid property is a combiatio of amplitude ad spacig. Ay chages, which occur i either amplitude or spacig, may have effects o the hybrid property. I tribology aalysis, surface slope, surface curvature ad developed iterfacial area are cosidered to be importat factors, which i uece the tribological properties of surfaces. The followig sectios describe the most commo hybrid parameters Profile slope at mea lie g) This parameter represets the pro le slope at the mea lie. It ca be calculated by calculatig the idividual slopes of the pro le at each itersectio with mea lie, the calculatig the average of these slopes as show i Fig. 16. The umerical equatio for calculatig the pro le slope at the mea lie is as follows: g ˆ 1 1 X 1 ta 1 dy i dx i where is the total umber of itersectios of the pro le with the mea lie alog the assessmet legth Mea slope of the profile D a ) This parameter is de ed as the mea absolute pro le slope over the assessmet legth. May mechaical properties such as frictio, elastic cotact, re ectace, fatigue crack iitiatio ad hydrodyamic lubricatio affect this parameter. This parameter ca be calculated by calculatig all slopes betwee each two successive poits of the pro le, the calculatig the average of these slopes. As show i Fig. 17, the mathematical ad umerical formulas of calculatig the mea slope parameter are as follows: D a ˆ 1 Z dy dx dx; 0 D a ˆ 1 X 1 d yi 1 d xi 4.3. RMS slope of the profile D q ) This parameter is the root mea square of the mea slope of the pro le. The mathematical ad umerical formulas for calculatig this parameter are as follows: s Z 1 Z D q ˆ y x y _ 2 dx; y _ 1 ˆ y x dx 0 0 Fig. 16. Calculatig the profile slope at mea lie. Fig. 17. Calculatig the mea slope of the profile.

11 v u 1 X 1 d 2 yi D q ˆ t y m ; y m ˆ 1 1 d xi 1 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± X 1 y i y i 1 x i x i 1 the dividig the summatio of these legths by the assessmet legth as show i Fig. 18. This parameter ca be calculated from the followig equatio: 4.4. Average wavelegth l a ) The average wavelegth parameter is a measure of the spacig betwee local peaks ad valleys, takig ito cosideratio their relative amplitudes ad idividual spatial frequecies. This parameter ca be calculated from the followig equatio: l a ˆ 2pR a D a where R a is the arithmetic average height ad D a the mea slope of the pro le RMS wave legth l q ) The RMS wavelegth parameter is similar to the average wavelegth l a ) parameter. It is de ed as the root mea of the measure of the spacig betwee local peaks ad valleys, takig ito cosideratio their relative amplitudes ad idividual spatial frequecies. It ca be calculated from the followig equatio: l q ˆ 2pR q D q 4.6. Relative legth of the profile l o ) The relative legth of the pro le l o ) is estimated by calculatig the legths of the idividual parts of the pro le l o ˆ 1 X l i where l i is the legth of lie umber i i the pro le, ad it ca be calculated from the followig equatio: q l i ˆ y i 1 y i 2 dx 2 i where y i is the pro le height at poit umber i, ad dx the horizotal distace betwee each two successive poits Bearig area legth t p ) ad bearig area curve The bearig lie legth parameter is de ed as the percetage of solid material of the pro le lyig at a certai height. This parameter is a useful idicator of the effective cotact area as the surface wear. From Fig. 19, the bearig area legth ca be calculated from the followig equatio: t p ˆ 1 X l i where is the assessmet legth of the pro le. By calculatig the bearig lie legth at differet heights of the pro le, the bearig area curve BAC) ca be draw, as show i Fig. 20. The horizotal axis represets the bearig area legths as a percet from the total assessmet legth of Fig. 18. Calculatig the relative legth the profile l o ). Fig. 19. Calculatig the bearig area legth t p ) of the profile.

12 144 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133±145 legth, the the average of the stadard deviatios is take. With referece to Fig. 1, the H u ) parameter ca be calculated from the followig equatio: H u ˆ 1 XNS 1 S:D: y inps 1 ;y inps 2 ;y inps 3 ;...;y inps NPS NS iˆ0 where NS is the umber of samples alog the assessmet legth, NPS the umber of poits i each sample, Y inps # the pro le's height at poit umber inps #) Roughess height skewess H s ) the pro le ad the vertical axis represets the heights of the pro le. The iterpretatio of the BAC is that if the surface wor dow to a certai height the appropriate gure would represet the fractio of solid cotact at that height. The bearig curve has the S-shape appearace for may surfaces. It represets the cumulative form of the height distributio histogram described i sectios 1± Stepess factor of the profile S f ) The stepess factor of the pro le is de ed as the ratio betwee the arithmetic average height R a ) ad the mea spacig of the pro le S m ). It ca be calculated from the followig equatio: S f ˆ Ra S m 4.9. Waviess factor of the profile W f ) The Waviess factor of the pro le is de ed as the ratio betwee the total rage of the etire pro le ad the arithmetic average height R a ). From Fig. 18 this parameter ca be calculated from the followig equatio: W f ˆ 1 X 1 R a l i Fig. 20. The BAC of a profile. where is the umber of poits alog the pro le Roughess height uiformity H u ) The roughess height uiformity of a pro le H u ) i s de ed as the stadard deviatios of the idividual height values of the pro le costitutig the arithmetic average height R a ). To calculate this parameter the stadard deviatio is calculated for the pro le heights i each samplig The roughess height skewess H s ) of a pro le is de ed as the media of the histogram height values divided by the arithmetic average height R a ). To calculate this parameter the media is calculated for the pro le heights i each samplig legth, the the average of the medias is take ad divided by R a. With referece to Fig. 1, the H s ) parameter ca be calculated from the followig equatio: H s ˆ 1 NS 1 X media NSR a iˆ0 y inps 1 ;y inps 2 ;y inps 3 ;...;y inps NPS where NS, NPS, Y inps # are de ed as i the previous sectio Roughess pitch uiformity P u ) The roughess pitch uiformity P u ) of a pro le is de ed as the stadard deviatio of the idividual mea spacig values costitutig the mea spacig parameter S m ). With referece to Fig. 12, the roughess pitch uiformity parameter ca be calculated from the followig equatio: P u ˆ S:D: S 1 ; S 2 ; S 3 ;...; S Roughess pitch skewess P s ) The roughess pitch skewess P s ) of a pro le is de ed as the media of the mea spacig values, alog the pro le, divided by the mea spacig parameter S m ). With referece to Fig. 12, the roughess pitch skewess parameter ca be calculated from the followig equatio: P s ˆ media S 1 ; S 2 ; S 3 ;...; S 5. Results sample The proposed visio system SurfVisio is divided ito two parts, hardware ad software. The hardware icludes a IBM compatible persoal computer with Widows 95 operatig system, frame grabber as a capturig board, charge coupled device CCD) camera, ad a microscope. The

13 E.S. Gadelmawla et al. / Joural of Materials Processig Techology ) 133± software was writte especially to perform differet aalysis o the captured images. The proposed software was writte usig Microsoft Visual C versio 5.0 ad it could ru uder Widows 95, Widows 98 or Widows NT operatig systems. The software package was developed totally i-house such that it ca be used idepedetly without referrig to ay other software. The package icludes the uique feature of cotaiig a multitude of surface roughess parameters that are ot icluded i ay other package hitherto. Also, the software allows the buildig up of a data base iformatio system durig surface ispectio. This database was made to allow the future iclusio of arti cial itelligece module for automated calibratio of the system. The software is fully itegrated with AutoCAD ad MS Word. The software has the professioal look iterface that is used by most Widows 95 applicatio. Stadard surface roughess specimes were used to test the proposed visio system. These specimes are the RUBERT surface roughess scales o. 24 MK II, which has 12 pieces with differet values of R a for differet machiig operatios. Three specimes with the same maufacturig process ad differet values of R a were selected as show i the table below. The values of R a for the three specimes were give i mi. The correspodig values i mm were calculated by multiplyig each value by ) as show i the table below. Specime umber Value of R a mi.) Calculated R a mm) Maufacturig process Accuracy %) appig appig appig 10 After checkig the accuracy of the system for calculatig the R a parameter, 59 roughess parameters were calculated for the six sectios usig both the imperial ad the metric uits. The above table shows the symbols, the descriptio ad the value of the calculated roughess parameters for the 2 mi. specime. 6. Coclusio Differet maufacturig processes produce differet surface characteristics. Also, differet applicatios require differet surface properties. Surface parameters are therefore differet ad wide-ragig. Each of these parameters idicates a particular property of the surface ad it could be the most importat for the particular applicatio. This research preseted the de itios ad the mathematical formulae for about 59 of the surface roughess parameters. This collectio of surface roughess parameter was used i a ew software computer visio package called SurfVisio developed by the authors. I the package, these de itios were exteded to calculate the 3D surface topography of differet specimes. Refereces [1] U.B. Abou El-Atta, Surface roughess assessmet i three-dimesioal machied surfaces for some maufacturig operatios, M.Sc. Thesis, Idustrial Productio Egieerig Departmet, Uiversity of Masoura, Egypt, [2] E.C. Teague, F.E. Scire, S.M. Baker, S.W. Jese, 3-Dimesioal stylus profilometry, Wear 83 1) 1982) 1±12. [3] T. Pacewicz, I. Mruk, Holographic cotourig for determiatio of three-dimesioal descriptio of surface roughess, Wear 199 1) 1996) 127±131. [4] B.G. Rose, Represetatio of 3-dimesioal surface topography i CAD-systems ad image processig, It. J. Mach. Tools Mauf. 33 3) 1993) 307±320.