APPLICATION GUIDE MANUAL FOR SURFCOM SERIES SURFACE ROUGHNESS & WAVINESS PARAMETERS

Transcription

1 DT00300-R00-E7 APPLICATION GUIDE MANUAL FOR SURFCOM SERIES SURFACE ROUGHNESS & WAVINESS PARAMETERS TOKYO SEIMITSU CO., LTD. TOKYO, JAPAN

2 No part of this documet shall be reproduced i ay form or by ay electroic or mechaical meas icludig iformatio storage ad retrieval system without permissio i writig from us, Tokyo Seimitsu Co., Ltd., Tokyo, Japa.

3 PREFACE You may have a few acquaitace with the termiologies ad symbols which are used i the messages ad the output parameters of surface texture measurig istrumet. The explaatios about those defiitio ad usage, parameter symbols, ame ad the way of calculatio of surface roughess ad waviess are metioed i this maual. Refer to the separate user's maual for hadlig of the measurig istrumets. Applicable rage This maual applies to the followig models of Surfcom. Surfcom 30A Surfcom 480A Surfcom 400 series Surfcom 500 series Surfcom 800 series Surfcom 900 series Surfcom 2800 series Surfcom 2900 series Surfcom 3000 series Please be oted that the symbols of parameters ad the calculatio method may vary i the other models. CAUTION The symbols, termiologies or their meaig of the surface parameters are sometimes varied accordig to the atioal stadard o which their defiitios are based. Whe omial values of the surface parameter are specified o a drawig, please check carefully the refereced atioal stadard. The, select the value of cutoff, traversig legth ad surface parameter which are correct ad suitable to the refereced stadard before startig the measuremet. - i -

4 - CONTENTS - Page STANDARD OF SURFACE ROUGHNESS AND WAVINESS... - Surface Roughess... - Roughess ad Waviess Parameters... - Fuctio ad Parameters of Surface SAMPLED CURVES Profile Curve, Primary Profile (P) Mea Lie Roughess Profile (R) Mea Lie Ceter Lie Waviess Profile/Filtered Waviess Curve (W, W C ) Filtered Ceter Lie Waviess Curve (W CC, W-profile) Rollig Circle Waviess Curve (W E ) Rollig Circle Ceter Lie Waviess Curve (W EC ) DIN4776 Special Roughess Curve (Rg 2 ) Tilt Correctio / Referece Lie Referece Profile/Datum Lie Ushifted Origial Profile Least Squares Straight Mea Lie Least Squares Polyomial Mea Lie B-Splie Mea Lie First Half Correctio Latter Half Correctio Begiig ad Ed Port Coected Straight Lie ii -

5 Page 3 CUTOFF VALUE A Itroductio to "Cutoff" Value RC Filter Phase Correct Filter RC Phase Correct Filter Gaussia Phase Correct Filter Short wavelegth cutoff value (λs) ad cutoff ratio Necessity of short wavelegth cutoff (λs filter) ROUGHNESS ANALYSIS TERMINOLOGY AND DEFINITION Samplig Legth (L) Evaluatio Legth (L) Measurig Legth (Lm) Pre-travel Legth (Lpe) Post-travel Legth (Lpo) Traversig Legth (Lt) Horizotal Magificatio i Recordig Chart (Vh) Vertical Magificatio i Recordig Chart (Vv) Vertical Magificatio Directio (z) Profile Peak Profile Valley Top of Profile Peak Bottom of Profile Valley Lie of Profile Peaks Lie of Profile Valleys Cuttig Level (c) Local Peak of Profile Local Valley of Profile Top of Local Peak of Profile Bottom of Local Valley of Profile iii -

6 Page 5 PARAMETERS FOR AMPLITUDE Arithmetic Average/Mea Lie Average Value (Ra,Ramax,WCA,Wa,WEA,Pa) Root-Mea-Square Value (Rq,Rqmax,RMS,Wq,Pq) Maximum Height (Ry,Rymax,Rmax,Rt,Rz,Pt,W,Wt,W CM,W EM,Wz) Te-poit Height of Irregularities[JIS, ISO] (Rz,RzISO,RzJ ) Base Roughess Depth/Averaged Middle Peak-To-Valley Height (R3z) Mea Height of Elemets (Rc,Rcmax,Pc,Wc) Maximum Profile Peak Height (Rp,Rpmax,Rpm,Rp5,Pp,Wp) Maximum Profile Valley Depth (Rv,Rvmax,Rvm,Rm5,Pv,Wv) Height of Step (AVH, Hmax, Hmi, AREA) FPD waviess (Wfpd) PARAMETERS FOR WAVELENGTH AND SLOPE Mea Spacig of Profile/Average Spacig of Roughess Peaks (Sm,Smmax,RSm,PSm,WSm) Peak Cout (Pc,PPI,HSC) Mea Spacig of Local Peaks of the Profile (S,Smax) Arithmetical Mea Slope of Profile/Average Absolute Slope ( a) Root-Mea-Square Slope of Profile ( q,p q,r q,w q) Average Wavelegth of Profile (λa) Root-Mea-Square Wavelegth of Profile (λq) Average Slope Agle (TILT A) Profile Legth Ratio (Lr,SL) Power Graph/Power Spectrum iv -

7 Page 7 PARAMETERS FOR BEARING AREA CURVE Profile Bearig Legth Ratio/ Profile Bearig Ratio (tp), Material Ratio of the Profile (tp,mr,rmr,pmr,wmr).. 7- Bearig Area Curve (BAC)/Abbott-Firestoe Curve/ Material Ratio Curve(MRC)/Curve of the Profile Bearig Legth Ratio(BC) Method of Cut Level () % (2) µm Method of Legth Referece () Evaluatio Legth Method (2) µm Display Referece Legth Method (3) % Display Referece Legth Method Bearig Legth Ratio 2/Profile Bearig Ratio (tp2,rmr2,pmr2,wmr2) Differece of Bearig Legth Ratio (tp(c-c 0 ), Rδmr) Profile Sectio Level Separatio Rδc/Height of Plateau (Hp) ISO3565 (DIN4776) Special Bearig-Area Curve Parameters () Bearig Legth Ratio - Iitial Wear Ratio - (Mr) (2) Bearig Legth Ratio 2 - Oil retetio Bearig Ratio (Mr2) (3) The Reduced Peak Height (Rpk) (4) The Reduced Valley Depth (Rvk) (5) Core Roughess Depth (Rk) (6) Oil Retetio Volume (V O ) (7) Reduced Valley Depth Ratio (K) PARAMETERS FOR AMPLITUDE DISTRIBUTION Amplitude Desity Fuctio/Amplitude Distributio Curve/ Distributio of Profile Departure Desity (ADC, ADF) Skewess (Rsk,Sk) Kurtosis (Rku,Kurt) PARAMETER FOR MOTIF What is the motif calculatio? Motifs upper limit legth What is the motif? How to calculate the motifs v -

8 Page 0 SELECTION & EVALUATION METHOD OF CUTOFF VALUE SAMPLING LENGTH Pursuat to JIS () Cutoff Value ad Measurig Legth for Ra (Ra75) (2) Referece Legth for Rmax,Rz (3) Evaluatio Method of Measured Value Pursuat to JIS () Cutoff Value, Samplig Legth ad Evaluatio Legth for Ra, Ry ad Rz (2) Cutoff Value, Samplig Legth ad Evaluatio Legth for Sm ad S (3) Evaluatio Method of Measured Value (ISO4288) Pursuat to ISO84/BS/ANSI () Cutoff Value, Samplig Legth ad Evaluatio Legth for Radom Waveform Curve without Periodicity (2) Cutoff Value, Samplig Legth ad Evaluatio Legth for Periodic Curve (3) Evaluatio Method of Measured Value I coformity to the former DIN () Cutoff Value, Samplig Legth ad Evaluatio Legth for Radom Waveform Curve without Periodicity (2) Cutoff Value, Samplig Legth ad Evaluatio Legth for Periodic Curve (3) Evaluatio Method of Measured Value Pursuat to ISO97/ASME/DIN () Cutoff Value, Samplig Legth ad Evaluatio Legth for Radom Waveform Curve without Periodicity (2) Cutoff Value, Samplig Legth ad Evaluatio Legth for Periodic Curve (3) Evaluatio Method of Measured Value (ISO4288:996) Exceptio of Samplig Legth ad Evaluatio Legth: I case of uavailable measuremet with stadard value () Uavailable to get Stadard Value of Evaluatio Legth (2) Uavailable to get Multiple of Cutoff Value for Evaluatio Legth (3) Smaller Workpiece Surface Legth tha the added Legth of Cutoff Value ad Preparatory Legth (Lt<λc+Lpe+Lpo) vi -

9 Page Average value process of the parameter... - Average value process... - MAX rule % rule Miimum value PARAMETER LIST Roughess ad Waviess Parameters with SURFCOM () Parameters related to Amplitude (2) Parameters related to Wavelegth & Slope (3) Parameters related to Bearig Ratio Curve (4) Parameters related to Amplitude Distributio Aex A. JIS 200. A- B. Splie correctio.. B- - vii -

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11 STANDARD OF SURFACE ROUGHNESS AND WAVINESS Surface Roughess Surface roughess is defied it as follows: "Roughess is a surface irregularities that occurs at small itervals ad is the sesory base o which we recogize somethig as 'smooth' or 'rough'. For machie surface, it shows irregularities caused by tool edges ad abrasive grais." I geeral, a surface is three-dimesioal ad composed of complex forms. Besides, it cotais so much iformatio that a parameter or two are ot eough to eable complete evaluatio of a surface. For example, see Fig... For example, see Fig... Whe the maximum height Rmax of Curve A ad that of Curve B are H ad H2 respectively, eve the coditio H=H2 could ot always assure that the characteristics of both surfaces are idetical. Compared with B surface, A surface has superior lubricat capability ad agreeable touchig ad it is hard to be wor away. H A H 2 B Fig.. Therefore, to evaluate surface roughess ad waviess form practical viewpoits, the optimal determiatio of parameters for a purpose must be made. Roughess ad Waviess Parameters O a machie drawig, it is required to specify dimesios, agles ad the degree of the surface irregularities of a material with umeric values. Without covertig them ito umeric values, the material is ot cotrolled quatitatively ad besides the machie drawig is useless as measured for evaluatig the quality upo busiess. For roughess ad waviess, a evaluatio method with the dimesios i the height directio as measure is the stadard of roughess. Ad wavelegth of peak ad valley ad distictive features of waveform may also be the stadard. This is parameters of roughess ad waviess. Except for the amplitude to height directio which is geerally used, there are followig roughess ad waviess parameters which are coected to wavelegth ad slope agle of roughess, bearig curve to idicate lubricat capability ad amplitude distributio, etc. -

12 Fuctios ad Parameters of Surface Mechaical performace is sometimes greatly chaged by the coditios of surface; some workpieces produce fuctioal problems i both cases whe the surface roughess is too large or too small. Evaluatio parameters are differet whe the fuctio to be objected is differet. The followig table shows the roughess parameters that are cosidered to be i correlatio with the fuctios required for the surface of workpiece as referece. Please bear i mid that the relatios described below are merely physical estimatios ad they are ot based o aythig defiite. Fuctio Descriptio Relevat workpiece Evaluatio Parameter Sealig Tightess Leakage from gap betwee cotact Valve, Cock, Cylider Ra, Rp, Sm, Rpk surfaces Abrasio Force to be caught by roughess Clutch, Kock pi a, q, Ry, Rz, Rp resistace peak Abrasio Loads cocetrated o a covex upo slidig Shaft, Bearig Cylider hole, Pisto rig, Rp, Bearig legth ratio curve, tp, Rpk, Rsk Guide surface Burig, Lubricatig ability Deposit lubricatig oil i valleys Plateau hoig surface of cylider block bore Rv, Bearig legth ratio curve,tp, Rvk, Rδc, Hp, Mr2, Vo, K Adhesio Wrigig Optimum Blockgauge PC Board Flatess, Ry, Rmax Bodig Form for bodig aget, Ueasiess to peel off Bodig surface, Platig Rz, Ry, a, q, Lr foudatio Peel ability Ability to remove moldig from mold Die Rz,Ry, a, q,lr Appearace, Gloss Scatterig i reflectio of light, Glarig, High quality feelig Glossy surface (Brightess of coated surface) Turbulece of beam reflectio, Scatterig Easiess to be wet due to capability Platig surface Raibow surface Patter fiish Mirror surface q, Rq, Ra, W CM, W CA, Power graph, Rku, Rpk Cold-rolled steel for car W CA, Ra, Pc, PPI Optical performace Mirror, Les, Prism q, Rq, Ra Corrosio Weatherproof parts, Ra, a, q, Rv, Mr2 resistace, Electric parts Isulatio ability Fatigue stregth Cocetratio of stress due to the Crak shaft Rmax, Rv, Rvk form of otch Electromagetic Disturbace of ski effect by flows Waveguide, Magetic Ra, Ry, Rz characteristic ad roughess core Electric resistace Electric resistace due to cotact Relay, Switch tp, Mrl, Ra, Lr of cotact surface, surface, heat trasfer Coector, Radiator Heat resistace Rigidity of juctio Deflectio due to excessively small Bolt clampig portio Parallelism, W EM, tp, Rz, surface cojuctio surface Rp, Rpk Accuracy of Measuremet error due to Micrometer, Air Parallelism, Ry, Rp, Rpk dimesioal roughess, deformatio of micrometer Calipers measuremet roughess due to meas. pressure Texture The touch Kurlig tool, Sati Rp, a, q, Sm, Pc, surface Power graph Pritig quality Fittig of ik ad paper Pritig paper Ra, Rv, Rvk, Sm, Pc, Power graph Noise, Vibratio Vibratio of rollig surface at high Gear, Roller bearig, Rp, Rmax, W EM, Sm, speed Guide surface Power graph -2

13 2 SAMPLE CURVES Profile Curve, Primary Profile (P) A cotour appears o a cut ed, whe a surface to be measured has bee cut with a plae which is perpedicular to that surface. (JIS B ,982) This istrumet records raw profile curves which are ot made tilt correctio. I the figure of below, the Z-axis directio ad X-axis directio are called as vertical directio ad horizotal directio respectively. Mea lie I a profile curve, the mea lie is the same as the geometric profile of the measured surface ad is the curve that the sum of squares of the deflectio from the profile curve becomes miimum(iso4287/-984). This is ormally a straight lie because the measuremet is made o a plae surface, but there is a case that the mea lie becomes a circle or specified curve o the curved surface or desigated cotour. I this istrumet, the mea lie is show as X-axis which was made the "Straight lie correctio" to the profile curve. (Refer to Tilt-correctio/referece lie) Mea lie of phase correct filter (Filtered waviess profile) Z Mea lie of profile curve (Least square mea lie) Profile curve Roughess Profile (R) This is a curve which has bee cut off ay loger surface waviess compoet tha a wavelegth of the specified cutoff value λc(mm) from the profile curve by meas of high-pass filter. (Refer to Chapter 3 for the filter.) Mea lie The mea lie i roughess profile passed the phase correct high-pass filter is the "Filtered waviess curve" by meas of the same phase correct type filter. The roughess profile is the oe which was removed filtered waviess curve from the profile curve, ad the mea lie at this time becomes a straight lie to become Z=0 of the roughess profile. Ceter lie The ceter lie is the straight lie that whe the straight lie parallel to the mea lie of a roughess curve passed 2RC filter is draw, the areas surrouded by this straight lie ad roughess curve o both sides of the straight lie are equal to each other. Z X Mea lie (phase correct) Ceter lie (2RC) X Roughess profile Note ) The differece of selectio to choose a mea lie or a ceter lie comes from the type of filter i its stadard, but the both cotets are the same. 2-

14 Waviess Profile/Filtered Waviess Curve (W, Wc) This is the curve obtaied by removig the surface roughess compoets with short wavelegth is called filtered waviess curve. A 2RC low-pass filter of -2db/oct Note ) atteuatio is employed. (JIS B ) I the filtered waviess curve for calculatig a mea lie of roughess profile by meas of phase correct filter, a phase correct type low-pass filter is employed. (JIS B ) Z Mea lie (phase correct) Filtered waviess curve X Mea lie of profile curve (Least square mea lie) Filtered Ceter Lie Waviess Curve (Wcc, W-profile) This is the curve obtaied by removig the short ad log wavelegth compoets from a profile curve. 2RC high-pass filter of -2db/oct atteuatio is employed. (JIS B , DIN4774) Mea lie (phase correct) Z Ceter lie (2RC) X Filtered ceter lie waviess curve Note ) db is called as decibel ad it is explaied as follows. Whe the dampig factor of iput ad output sigal is set to A (output amplitude / iput amplitude), it is show as follows. Trasfer factor (dampig factor) db = 20 log 0 A If the dampig factor is assumed as A = / 4, it becomes 2dB. oct is called as octave ad it shows two times of a wavelegth. Therefore 2dB / oct shows that whe the wavelegth becomes 2 times, the amplitude becomes / 4 times. 2-2

15 Rollig Circle Waviess Curve (W E ) This is the locus of the circle ceter with a specified radius that traces a profile curve. This circle is called as Rollig Circle ad its radius correspods to that of the stylus tip. Namely, a profile curve obtaied by measurig with a stylus tip of 8mmR for waviess measuremet is the rollig circle waviess curve. (JIS B ) Z Rollig circle waviess curve X Profile curve Rollig Circle Ceter Lie Waviess Curve (W EC ) This is a curve obtaied by removig the log wavelegth compoets from the rollig circle waviess curve. A 2RC high-pass filter of 2 db/oct is employed. (JIS B ) Z Rollig circle ceter lie waviess curve X 2-3

16 ISO3565 (DIN4776) Special Roughess Curve (Rg 2 ) I the stadard of ISO3565- (ad DIN ), special roughess curve Rg2 which is removed the waviess is employed. ( Rg2 is the temporary sig of this machie.) As this machie is determied to calculate the bearig area curve i accordace with ISO3565 or DIN4776, it is calculated i accordace with the stadard of ISO3565 by the followig procedure. Step Obtai a phase compesatio filtered waviess curve (Mea lie) Wg from the profile curve P by usig Gaussia phase correct filter. 5.0 µm Step 2 Coect the profile curve, P with the higher waviess positios of the phase correct filtered waviess curve, Wg obtaied i Step, ad create a curve i which valleys are removed. 5.0 µm Step3 Apply the curve obtaied by Step 2 to the phase correct filter i Step to obtai a referece mea curve, Wg µm Step4 Subtract the referece mea curve, Wg 2 i Step 3 from the profile curve ad obtai the special roughess curve, Rg µm

17 Tilt Correctio / Referece Lie Referece Profile/Datum Lie: This is a lie to become referece of a profile curve, which is selected from the followig methods of determiig the referece. Ushifted Origial Profile: This is a actual profile curve without shiftig or correctio. This profile is used for measuremet of height ad tiltig agle from the referece lie beig set at the begiig. Measurig legth Lt Origial profile curve L t / 2 L t / 2 Least squares straight mea lie: This is a mea lie to be used i a profile curve from the plae surface profile. This method is based o the stadard for roughess measuremet. Straight lie correctio curve Measurig legth Lt L t / 2 L t / 2 Origial profile curve Correctio curve Least Squares Polyomial Mea Lie: Whe a omial profile is a curved surfaces of a circle ad a ivolute fuctio, etc., the evaluatio must be made by usig the referece lie correspodig to the omial profile. I this istrumet, it is approximated by a curve of fourth degree polyomial expressio i the least square method. Curve correctio curve Measurig legth Lt Origial profile curve Curve correctio curve B-Splie mea lie: I case of a existece of a sudde curve chagig poit i the omial profile, it uses a method which is approximated by B-Splie mea lie as its stadard. The superiority compared with the least squares polyomial mea lie is deped o the profile, so that apply the oe which the curved lie after correctio is closer to the straight lie for the actual use. 2-5

18 First Half Correctio (Before half least squares mea lie): This is a method to make correctio of the least square mea lie i the left portio (first half) of the step profile. This is used for measuremet of the log step amout i the first half portio. Before half Measurig legth Lt L t / 2 L t / 2 Correctio rage Origial profile curve Latter Half Correctio (Latter half least squares mea lie): This is a method to make correctio of the least square mea lie i the right portio (latter half) of the step profile. This is used for measuremet of the log step amout i the latter half portio. Latter halt Measurig legth Lt L t / 2 L t / 2 Correctio rage Origiall profile curve Begiig ad ed port coected straight lie: This is a method to make a referece lie which is a straight lie to coect the right ad left eds of the measuremet legth i order to obtai the height of a projectio i the sate like a belt o a plae surface board or the depth of a depressed portio. Begiig ad ed port Measurig legth Lt Start poit Ed poit Origial profile curve I case of a applicatio of ay oe of the above correctio methods, calculatios for all the parameters are available from the profile curve i coected with the referece lie. But the straight lie correctio oly is properly based o the roughess measuremet stadard. 2-6

19 3 CUTTOFF VALUE A Itroductio to "Cutoff" Value Irregularities of a object surface geerally show complex patters as show i the figure ofa. Take a close look at the figure, the you will fid that it is cosisted of a compoet with a fie short cycle of Fig. B ad a compoet with a gradual-slope log cycle of Fig. C, ad they are overlapped. Cutoff is to separate Profile Patter A ito Roughess B ad Waviess C ad sample out oly the ecessary compoet. Referece wavelegth that divides the patter ito "Roughess" ad "Waviess" compoets is called as "Cutoff value λc(mm)". I order to make the cutoff, a Filter (Wavelegth filter) is employed. A B C 2RC Filter This is the filter defied i JIS B , JIS B , ANSI B ad ISO A two-rc filter cosists of two R-C circuits with a equal time costat i series coectio, ad it provides with amplitude trasmissio characteristics as follows. a2 a0 = + λ 2 3 (λc75) 2 Where a 2 : Amplitude after cutoff of relevat wavelegth compoets a 0 : Origial amplitude of relevat wavelegth compoets λ : Relevat wavelegth (mm) λc 75 : Cutoff value (mm) Whe λ=λc 75, the trasmissio rate is a 2 /a 0 = 75%. I this case, the power of 2RC filter waviess curve (Square mea value(rms) 2 ) which has the same cutoff value ad the value which was added the power of this curve are early the same as the power of the profile curve. The chagig ratio of the atteuatio rate i the atteuatio area is -2db/oct. But a waveform has a characteristic to chage the phase similar to the chage of the amplitude trasmissio rate caused by a chage of the wavelegth. This should be oted that it causes a distortio of the waveform to the roughess profile. There is a case that a outlook of the waveform is largely differ from the roughess parameter or the bearig ratio curve is drastically chaged whe they are compared with the result obtaied from the profile curve. 3-

20 Phase Correct Filter By passig a phase correct filter, the phase shift which occurs i the trasmissio characteristic ca be solved. Followig figures show the phase shift which occurs whe a rectagular wave is peetrated each of a filter with phase correctio ad a filter with o-phase correctio (2RC filter). Measurig profile (without filter) Example of Roughess Profile i Case of 2RC Filter Example of Roughess Profile i Case of Phase Correct Filter P R 3-2

21 There are followig two types of the characteristic i the phase correct filter: 2RC Phase Correct Filter This has the same cutoff characteristic as the 2RC filter ad it is a filter without phase shift. The trasmissio ratio at λ = λc is a 2 / a 0 = 75%. Gaussia Phase Correct Filter This will be adopted hereafter as a iteratioal stadard of a filter which is pursuat to JIS B , DIN ad ISO The parameter values are determied accordig to the procedure as follows:- () As weighed fuctio for the ormal probability desity (Gauss Distributio) fuctio, the curve which was made covolutio itegral to the profile curve is made as the phase correct filtered waviess curve Wg. The formula of the weight fuctio becomes as follows; S(χ) λc S ( x ) = α λc e κ X 2 κ = π ( α λc ) Where X : Distace from the ceter of the weight fuctio λc : Cutoff value of the filter α : χ / λc Weight Fuctio of Gaussia Filter The trasmissio characteristic of the Phase Correct Filtered Waviess Profile (a / a 0 ) is show as follows; a a0 =e π( α λ c ) 2 λ Where a 0 : Amplitude of a sie profile curve before the filter a : Amplitude of a sie curve o waviess curve λ : Wavelegth of a sie curve 3-3

22 (2) Subtract the phase correct filtered waviess profile from the profile curve. The the roughess profile (Rg) ca be obtaied. The trasmissio characteristic of the roughess profile (a 2 / a 0 ) becomes as follows; a2 a0 = a a0 Phase correct filter 2RC filter Amplitude Trasmissio Ratio (%) Wavelegth / Cutoff value Trasmissio characteristics of roughess curve with Gaussia phase correct filter ad 2RC filter (3) The trasmissio ratio at λ = λc is a 2 / a 0 = 50%. Therefore, the profile curve ca be restored by addig the phase correct filtered waviess curves of the same cutoff value. 3-4

23 Short wavelegth cutoff value(λs) ad cutoff ratio I the Gaussia phase correct roughess curve ad profile curve, short wave cutoff filter ca be used i order to remove the ifluece of microwave area error caused by the stylus tip radius. The cutoff value is called as λs. λs filter is determied as follows. () Gaussia phase correct filter is used as a filter. (2) Trasmissio characteristic is followed to the trasmissio characteristic a / a 0 of above Gaussia phase correct filtered waviess curve. (3) Short wavelegth cutoff value λs is selected from the followig umeric values. 0.25, 0.8, 2.5, 8, 25, 80µm (4) Cutoff ratio meas the ratio of log wavelegth cutoff value λc agaist short wavelegth cutoff value λs of its provided trasmissio zoe (λc/λs), which stadard values are 30, 00 ad Note - Depedig o the istrumet, there are types which is ecessary to set λs filter before measuremet ad which ca be calculated by chagig the value of λs filter at the time of beig executed the recalculatio. With the type of beig required settig before measuremet, recalculatio is executed with λs filter value which was set before measuremet eve the value was chaged at recalculatio. Please check with the maual comig together with the machie for which fuctio your istrumet has. Relatios betwee log wavelegth cutoff ad stylus tip radius, ad cutoff ratio I case of ot beig specified, the relatios of cutoff ratio agaist the stadard values of stylus tip radius R tip ad the stadard values of log ad short wavelegths cutoff are recommeded to use as show i the table of below. (ISO ) Table 3. Stylus tip radius ad Cutoff λ c (mm) λ s (µm) λ c /λ s R tip (µm) or or , 5 or 2 Necessity of short wavelegth cutoff (λs filter) No cosideratio of short wavelegth filter is required, because of large basic periodic compoets of waviess or machiig streaks ad egligibly miute profiles i roughess curves of ormal machied surfaces. However, the depth of valleys chages by the cutoff value of short wavelegth ad radius value of stylus tip, whe deep, sharp ad miute streaks remai o high-precisio machied surfaces by lappig, etc. The larger grows amplitude of roughess i geerally speakig, as the larger is the cutoff ratio, or the smaller is the radius of stylus tip. I such a case, required is the measuremet by specifyig the cutoff value of short wavelegth filter i order to obtai comparable data. 3-5

24 3-6

25 4 ROUGHNESS ANALYSIS TERMINOLOGY AND DEFINITION I this chapter, it explais about the termiology ad defiitio used i this maual which have ot bee explaied i Chapter 2 ad 3. Samplig Legth (L): This is the legth of a sampled part from a surface curve for makig calculatio of parameters of the surface curve. I a roughess profile, the samplig legth is the same value as the cutoff value λc i priciple. (JIS B ) I a profile curve, the samplig legth is the legth determied accordig to which has bee obtaied by the value of profile parameter. (JIS B ) Evaluatio Legth (L): This is the legth which icludes oe or more samplig legth for makig evaluatio of a surface roughess. The stadard value of the evaluatio legth is five times of the samplig legth. (JIS B ,ISO4288) Measurig Legth (Lm): This is a evaluatio legth i order to calculate Ra(JISB ), Ra75(JIS B Aex). The stadard value is three times of the cutoff value. Pre-travel Legth (Lpe): This is the measurig legth i frot of the evaluatio legth. Loger legth is required to be set for the pre-travel i liger waviess compoet. For this settig with the phase correct filter, select it from the cutoff values of λc,λc/2 ad λc/3. For settig with the 2RC filter, it is set to two times of the value of the phase correct filter. Post-travel Legth (Lpo): This is the measurig legth i the rear of the evaluatio legth. This is ecessary to remove a error caused by the trasitioal respose of the phase correct filter. For this settig with the phase correct filter, select it from the cutoff values of λc,λc/2 ad λc/3. For settig with the 2RC filter, it is set zero because it is ot ecessary. Traversig Legth (Lt): This is the total legth of icludig the pre-travel, evaluatio legth ad post-travel which is the pickup traversig legth for measuremet of roughess. Be oted ot to cofuse the traversig legth with the measurig legth defied i the above JIS-'82. Measuremet start positio Pickup The way to traverse Measuremet ed positio Pretravel legth (Lpe) Samplig legth L L2 L3 L4 L Eval.legth L = Lx ( = or more) Traversig legth Lt = L + Lpe + Lpo Posttravel legth (Lpo) Fig. 4. Relatio betwee Traversig Legth, Evaluatio Legth ad Samplig Legth Horizotal Magificatio i Recordig Chart (Vh): This is a elargemet magificatio of recordig chart to the displacemet i traversig directio of the pickup. 4-

26 Vertical Magificatio i Recordig Chart (Vv): This is a elargemet magificatio of recordig chart to the displacemet i vertical directio agaist to the pickup traversig directio. Vertical Magificatio Directio (z): This is the vertical directio agaist to the pickup traversig directio. Profile Peak: A outwardly directed etity of profile surrouded by the roughess profile ad the mea lie coectig two adjacet poits of the itersectio made whe cuttig the roughess profile with the mea lie. Whe the startig ad ed portios of the samplig legth are i upper side of the mea lie, the part is regarded as the profile peak. (JIS B , ISO4287/) Profile Valley: A iwardly directed portio of space surrouded by the roughess profile ad the mea lie coectig two adjacet poits of itersectio made whe cuttig the roughess curve with the mea lie. Whe the startig ad ed portios of the samplig legth are i lower side of the mea lie, the part is regarded as the profile valley. (JIS B , ISO4287/) Top of Profile Peak: A poit of the highest altitude i the profile peak of roughess profile. (JIS B ) Bottom of Profile Valley: A poit of the lowest altitude i the profile valley of roughess profile. (JIS B ) Lie of Profile Peaks: Of the referece legth sampled from the roughess profile, the lie parallel to the mea lie passig through the highest top of profile peak. (JIS B ,ISO4287/) Lie of Profile Valleys: Of the referece legth sampled from the roughess profile, the lie parallel to the mea lie passig through the lowest bottom of profile valley. (JIS B ,ISO4287/) Cuttig Level (c): A vertical distace betwee the top of profile peak lie ad the lie parallel to the top of profile peak lie itersectig the roughess profile. (JIS B ) The cuttig level ca be determied by a uit of µm or percetage of Ry. Local Peak of Profile: A part of etity betwee two adjacet miima of the roughess profile. (JIS B ,ISO4287/-984) Local Valley of Profile: A part of space betwee two adjacet maxima of the roughess profile. (JIS B ,ISO4287/-984) Top of Local Peak of Profile: A poit of the highest altitude i the local peak of profile. (JIS B ) 4-2

27 Bottom of Local Valley of Profile: A poit of the lowest altitude i the local valley of profile. (JIS B ) Lie of profile peaks Top of profile peak Top of local peak of profile Local peak of profile Profile peak Mea lie(m) Local valley of profile Bottom of local valley of profile Bottom of profile valley Sampig Legth (L) Lie of profile valleys Profile valleys Fig. 4.2 The ame of roughess profile (Top of profile peak Bottom of profile valley, etc) 4-3

28 4-4

29 5 PARAMETERS FOR AMPLITUDE Arithmetic Average/Mea Lie Average Value (Ra, Ramax, WCA, Wa, WEA, Pa) This meas the value obtaied by the followig formula whe samplig oly the samplig legth, L from the sampled curve i the directio of mea lie, takig X-axis i the directio of mea lie ad Y-axis i the directio of logitudial magificatio of this sampled curve is expressed by y=f(x). L Ra= f(x) dx L 0 Namely, i the figure of below, the arithmetic average represets the average deflectio obtaied by dividig the area of the portio surrouded by the sampled curve ad the mea lie by the measurig samplig legth. Sampled curve f(x) Z Mealie (phase correct) Ceter lie (2RC) Ra X Samplig legth (L) TABLE 5. Parameter Names ad Sampled Curves uder Various Stadards Stadard (Coutry) Roughess Profile R & Phase Correct Roughess Profile Rg Profile Curve P Filtered C-Lie ISO4287:997 (It l Stadard) ISO ISO4287/-984 (It l Stadard) Div. - Arithmetical Mea Deviatio of Profile Ra, Rai Ceter Lie Mea Roughess Ra75 (Note 3) Max. per Samplig legth Arithmetical Mea Deviatio of the Assessed Profile Ramax Arithmetical Mea Deviatio of the Profile Ramax Average per Samplig legth Arithmetical Mea Deviatio of the Assessed Profile Ra Arithmetical Mea Deviatio of the Profile Samplig legth Arithmetical Mea Deviatio of the Assessed Profile Pa - Waviess Curve Wcc Div. Arithmetical Mea Deviatio of the Assessed Profile Wa Rollig Circle C-Lie Waviess Curve W EC Div. Ra, Ra 5 (Wa) (Wa) JIS B Arithmetic Average Filtered Rollig Circle (Japaese - Roughess - Ceter Lie C-Lie Waviess idustrial Ra (Note 4) Waviess Curve Stadard) W CA W EA JIS B Ra (Note 3) JIS B060 JIS B060 B.S (UK) ASME B (USA) DIN4768/-990 (Germay) Note Note 2 Note 3 Note 4 Arithmetical Mea Deviatio of the Profile Ra Roughess Average Value Ra, (AA) Mitterauhwert Ra (Note 4) Arithmetical Mea Deviatio of the Profile Ra Mitterauhwert Ra (Note 4) : Marked ( ) are previous stadards or referece stadards. : Ra is a value of arithmetic average of profile irregularities i the etire samplig legth, therefore a partial large chip does ot affect to the result. : 2RC Filter is used. : Gaussia Phase correct filter is used. - 5-

30 Root-mea-square Average (Rq, Rqmax, RMS, Wq, Pq) This meas the value obtaied by the followig formula whe samplig the samplig legth, L from the sampled curve i the directio of mea lie, takig X-axis i the directio of mea lie ad Z-axis i the directio of logitudial magificatio of this sampled curve is expressed by Z=f(x). Z Rq= L L f 2 (x)dx 0 f 2 (X) Mea Lie(phase correct) Ceter lie(2rc) X Samplig legth (L) Namely, i the above figure, the root-mea-square represets the root mea square average deflectio obtaied by dividig the area of the portio betwee the curve, which is obtaied by squarig the distace betwee the sampled curve ad the ceter-lie, ad the ceter-lie by the traversig legth. This is equivalet to stadard deviatio σ i statistics. TABLE 5.2 Parameter Names ad Sampled Curves uder Various Stadards Stadard Roughess Profile R & Phase Correct Roughess Profile Rg Profile Curve P Filtered C-Lie (Coutry) Max. of Root Mea Average of Root Mea Samplig legth Waviess Average Div. Square obtaied i each Samplig Legth Square obtaied i each Samplig Legth per Samplig legth Wcc ISO4287:997 (It l Stadard) - Rqmax Root-mea-square deviatio of the assessed profile Rq ISO Root-mea-square ISO4287/-984 deviatio of the profile (It l Stadard) (Rq) (Rqmax) (Rq, Rq 5 ) ASME B (USA) DIN4768/-990 (Germay) Root-mea-square roughess Rq, (RMS) Quadratischer mitterauhwert des profile (Rq) Root-mea-square deviatio of the assessed profile Pq Root-mea-square deviatio of the assessed profile Wq (Rq) - - Note : Marked ( ) are stadards of before for referece. 5-2

31 Maximum Height (Ry, Rymax, Rmax, Rt, Rz, Pt, W, Wt, W CM, W EM, W z ) This is the distace betwee the lie of profile peaks ad the lie of profile valleys measured i the vertical magificatio directio withi a portio extracted from the sampled curve Z=f(x) as the samplig legth, L. Ry = max (f(x))- mi (f(x)) Z Lie of profile peaks Sampled curve Mea lie(phase correct) Ceter lie(2rc) Ry X Stadard (Coutry) Samplig legth (L) Lie of profile valleys TABLE 5.3 Parameter Names ad sampled Curves uder Various Stadards Roughess Profile R & Profile Filtered Filtered C-Lie Phase Correct Roughess Profile Rg Curve P Waviess Waviess Max. value of Average of Samplig Curve W Average per Div. Max. height Max. height legth Evaluatio Samplig legth obtd. per obtd. per legth Wcc Samplig Samplig Legth Legth Rollig Circle Waviess Curve Evaluatio legth ISO04287:997 Max. height Max. height Max. height Max. height - - of profile of profile of profile - of profile (It l Stadard) Rzmax Rz Pz Wz ISO4287/-984 ISO Max. height of profile Max. height of profile Max. height of profile (It l Stadard) Ry Rymax Ry (Ry 5 ) JIS B (Japaese idustrial Stadard) - - Maximum height Ry - Filtered Max. Waviess - Rollig Circle Maximum Waviess JIS B Max. height Rmax W CM JIS B060 W EM JIS B060 BS.34/-988 Max. height - Max. height (UK) Ry Ry ASME B (USA) Max. peak-to-valley roughess Rt Max. height of the profile Rmax Average max.height Rz - Waviess height Wt - - DIN477 DIN4774 DIN4768/-990 (Germay) Maimum roughess Rt Maximale rauhtiefe Rmax (Rmax DIN) Gemittelte rouhtiefe Rz Profiltiefe Pt Welletiefe Wt - - Note : For the maximum height, it is required to measure the workpiece surface excludig the outstadig flaw, because the system reads the value durig the samplig. It is also required to measure more tha oe poits ad average them. I ISO 4288 ad JIS B , the maximum height is obtaied i each legth ad average them by the total evaluatio legth. This is called as Te Poit Average Roughess, Rz, i DIN stadard. Note 2 : Normal processig faces cotai surface waviess to a certai degree; This causes the maximum height from roughess curve, Rt to be smaller tha the maximum height form profile curve, Rmax (Pt). But i some cases like cross sectios with small waviess ad complex waveform such as groud surface ad hoig surface, Rt is larger tha Rmax/Pt due to the effect of the trasiet characteristic of filter. 5-3

32 Te-poit Height of Irregularities [JIS, ISO] (Rz, RzISO, RzJ) Oly the samplig legth is sampled from the sampled curve i the directio of its mea lie, the sum of the average value of absolute values of the heights of five highest profile peaks (yp) ad the depths of five deepest profile valleys(yv) measured i the vertical magificatio directio from the mea lie of this sampled portio. 5 5 Rz= ( ypi + yvi ) 5 i= i= Sampled curve Z Mea lie (m) yp yp3 yp4 yp2 yp5 yv5 yv4 yv3 Samplig legth (L) TABLE 5.4 Parameter Names ad sampled Curves uder Various Stadards Aalysis Methode Former JIS ISO New JIS DIN Stadard (Coutry) ISO ISO4287/-984 (It l Stadard) JIS B (Japaese Idustrial Stadard) JIS B (Note 4) Calculate Samplig Legth from Profile Curve P - Calculated Average per Samplig Legth from Roughess R 0 poit height of irregularities Rz yv yv2 Max.of Calculated Value per Spmplig Legth from Roughess Curve 0 poit height of irregularities Rzmax poit average roughess Rz (RzJ) B.S (UK) - ANSI B (USA) - DIN4768/-990 (Germay) - X Average of calculated Value per Samplig Legth from Roughess Curve Rg - 0 poit average roughess Rz Average of Max. Height per Samplig Legth from Roughess Curve Rg Average value of maximum height Ry (Ry 5 ) Maximum height poit height of irregularities Rz 0 poit roughess height (Rz) (Rz ISO) Ry Maximum height - - Ry Mea Rt - - (Rtm) - - Gemittelte Rauhtiefe Rz Note : The ISO 468 stadard specifies as criterio for peak ad valley that values uder 0% of Ry shall ot be recogized as a idepedet peak ad valley. This machie follows it i JIS94, DIN ad ASME, ad provides vertical dead bads which are 0% of Ry o each sides of the mea lie. Note 2 : I case a log referece legth is ot take, sometimes 5 peaks ad valleys are ot foud i it. I such a case, measuremet results may ot be obtaied. This machie calculate oly the recogized peaks ad valleys, ad idicate it with*. Note 3 : It provides the vertical dead bads of 0.5mm / measurig magificatio both above ad below the mea lie, i order to ward off such fear that oise compoets are judged as peaks or valleys i the JIS82 mode. (I Surfcom 30A/480A, it provides the each dead bad of ±0.5µm i measurig rage of ±400µm, ±0.05µm i measurig rage of ±40µm, ±5m i measurig rage of ±4µm ad ±2.5m i measurig rage of ±2µm.) Note 4 : I JIS ad ISO 468, the evaluatio legth which cosists of cotiuous five referece legths (same legth as the cutoff value) is take out from the roughess profile ad above calculatio is made i each referece legth, the the arithmetical mea value of the five values is Rz. Note 5 : This parameter has bee disused i ISO

33 Base Roughess Depth/Averaged Middle Peak-to-valley height (R3z) Extract the evaluatio legth which cosists of five cotiuous samplig legths (same as the legth of cutoff value) from a samplig curve. The height betwee the 3rd highest peak ad the 3rd lowest peak i each of the divided samplig legths. The average value i the evaluatio legth is defied as base roughess depth/averaged middle peak-to-valley height. This parameter is a private stadard. (Daimler-Bez-Specificatio N ) R3z= R3zi i= Sampled curve Mea lie(m) yp yp3 yp2 R3z yv3 yv yv2 X Samplig legth (L) The figure of above shows oe samplig legth. I the evaluatio legth, there are "" set of the samplig legth ad their average value is calculated. Dead bad is specified i Note below. Mea Height of Elemets (Rc, Rcmax, Pc, Wc) Extract the samplig legth, L from the sampled curve z = f(x), ad the sum of the average value of absolute values of the heights from the mea lie ad of the depths from the mea lie is the mea height of elemets. m Rc= ypi + yvj m i= j= "m" ad "" i the above formula show each umber of the top of the peak ad the bottom of the valley i the rage of the samplig legth. Z Sampled curve yp yv yp2 yp3 yp4 yp5 yv2 yv3 yv4 yp6 yp7 yp8 yv5 yv6 Samplig legth (L) yv7 yv8 yp9 yv9 Mea lie (m) TABLE 5.5 Parameter Names ad Sampled Curves uder Various Stadards Stadard Roughess Profile R & Phase Correct Roughess Profile Rg Profile Curve P Filtered C-Lie (Coutry) Evaluatio Legth Samplig legth Average value obtd. Samplig legth Waviess i each Samplig Legth Wcc ISO4287/-984 ISO (It l Stadard) Mea height of profile irregularities (Rc) ISO4287:997 (It l Stadard) - Maximum mea height of profile irregularities (Rcmax) Mea height of profile elemets Rcmax Average mea height of profile irregularities (Rc) Mea height of profile elemets Rc X - - Pc Average per Samplig legth Wc Note : It provides the vertical dead bads of 0.5mm / measurig magificatio both above ad below the mea lie, i order to ward off such fear that oise compoets are judged as peaks or valleys i the JIS82 mode. (I Surfcom 30A/480A, it provides the each dead bad of ±0.5µm i measurig rage of ±400µm, ±0.05µm i measurig rage of ±40µm, ±5m i measurig rage of ±4µm ad ±2.5m i measurig rage of ±2µm.) 5-5

34 Maximum Profile Peak Height (Rp, Rpmax, Rpm, Rp5, Wp, Pp) Extract the samplig legth, L from the sampled curve z = f(x) ad measure the distace betwee the lie of profile peaks withi the legth of L ad the mea lie to the directio of vertical magificatio. This is defied as maximum profile peak height. Rp = max (f(x)) Z Lie of profile peaks Sampled curve Mea lie (phase correct) Ceter lie (2RC) Rp X Samplig legth (L) TABLE 5.6 Parameter Names ad Sampled Curves uder Various Stadards Stadard Roughess Profile R & Phase Cor. Roughess Profile Rg Profile Curve P Filtered mea lie (Coutry) Evaluatio Legth Samplig legth Average value obtaied i each Samplig Legth Samplig legth Waviess curve W CC ISO4287/-984 (It l Stadard) Maximum profile peak height (Rp) ISO4287:997 (It l Stadard) - BS34/-988 (UK) ASME B (USA) DIN477 DIN4774 DIN4768/-990 (Germay) Levelig depth (Rp) Max. profile peak height Rp Maximale höhe der Profilerhebug (Rp) Maximum profile peak height (Rpmax) Maximum profile peak height Rpmax Levelig depth (Rp) - Maximale höhe der Profilerhebug (Rp) Average value of maximum profile peak height (Rp, Rp 5 ) Maximum profile peak height Rp Mea levelig depth (Rpm) Average max profile peak height Rpm (Rpm) - (Wp) Maximum profile Maximum profile peak height peak height Average per Samplig legth Pp Wp Note : Marked ( ) is a stadard for referece oly, which is ot a official stadard. Note 2 : A surface which is measured by a air micrometer ad a electric capacitace type displacemet meter is equivalet to the above mea lie, ad a surface which is measured by a micrometer is equivalet to the profile peak lie. So that 2xRp is equivalet to the differece of their dimesioal measuremet values. 5-6

35 Maximum Profile Valley Depth (Rv, Rvmax, Rvm, Rv5, Wv, Pv) Extract the samplig legth, L from the sampled curve z = f(x) ad measure the distace betwee the lie of passig through the lowest peak withi the legth of L ad the mea lie to the directio of vertical magificatio. This is defied as maximum profile valley depth. Rv = mi (f(x)) Z Sampled curve Mea lie (phase correct) Ceter lie (2RC) Rv X Samplig legth (L) Lie of profile valleys TABLE 5.7 Parameter Names ad Sampled Curves uder Various Stadards Stadard Roughess Curve R & Phase Cor. Roughess Curve Rg Profile Curve Fil. Mea lie (Coutry) Evaluatio Legth Samplig legth Average value obtaied i each Ref. legth P Samplig legth Waviess curve Wcc ISO4287:997 (It l Stadard) - ISO4287/-984 (It l Stadard) ASME B (USA) DIN477 DIN4774 DIN4768/-990 (Germay) Maximum profile valley depth (Rm) Maximum profile valley depth Rv Maximale höhe der Profilerhebug (Rv) Maximum profile valley depth Rvmax Maximum profile valley depth (Rmmax) Maximum profile valley depth Rv Average value of maximum profile valley depth (Rm, Rm 5 ) Maximum profile valley depth Pv - Maximum profile valley depth Average per Samplig legth Wv Maximale höhe der Profilerhebug (Rv) (Rvm) (Wv) - - Note : Marked ( ) is a stadard for referece oly, which is ot a official stadard. 5-7

36 Height of Step (AVH, Hmax, Hmi, AREA) This is the parameter to idicate a iterval i the directio of vertical magificatio of the protruded top ed ad sectio area of the protruded portio toward the referece lie. (The same processig is available for the cocave portio, too.) () Iput parameter:. Height of step calculatio mode deletio legth: Start out portio of a step which is uecessary for calculatio ad deletig legth of fallig dow portio are specified. 2. Height of step calculatio mode referece height: Threshold value of the protruded height which becomes the subject of height of step calculatio is iput. 3. Area calculatio legth The area which become the subject of Area calculatio are specified. (2) Tilt correctio: Correctio of both eds A straight lie which is coected recordig start poit ad recordig ed poit is defied as a correctio lie. (3) Calculatio of step differece parameter calculatio rage I the protruded portio which is bigger tha the umerical value of the height of step calculatio mode referece height, the rage of beig deleted the both eds of deleted legth umerical portio is defied as step differece parameter calculatio rage. (4) Calculatio parameter Three types of parameter of below are calculated.. AVH... Average height value withi the rage of step differece parameter calculatio k AVH= Zi Zi : All data withi parameter calculatio rage k i= k : Its data umber 2. Hmax... Maximum height value toward the referece lie withi step differece parameter calculatio 3. Hmi... Miimum height value toward the referece lie withi step differece parameter calculatio 4. AREA... Sectio area surrouded by profile withi step differece parameter calculatio ad the referece lie Referece height Area calculatio legth Delete legth Step height calculatio area Delete legth Area calculatio legth (5) Uses This is used for cotrollig thickess of prited circuit board ad thick film IC, etc. ad electric resistace. Note : This parameter is ot icluded i the atioal stadard. 5-8

37 FPD waviess Wfpd (= Movig miimum zoe method straightess of waviess) FPD waviess Wlcd is the maximum value of straightess amog the samplig legths of the filtered ceter lie waviess withi the rage of the evaluatio legth. The procedure for fidig the value by maual operatio is as uder. () Prepare a template with a widow havig the width of samplig legth. (2) Let the template trace alog the curve i the rage of the evaluatio legth of filtered ceter lie waviess. (3) Read the straightess value withi the scope of widow at all positios i the process. (4) The maximum value out of all readigs is Wfpd. The followig is the evaluatio stadard of glass board for LC. (SEMI Iteratioal Stadard D5-296) The measure coditios are set as follows. () Radius of stylus tip: Sphere R 5µm or above (2) Evaluatio curve: Filtered ceter lie waviess Wcc (3) Wavelegth filter: 2RC filter or Phase Correctio Filter of Gaussia Distributio Characteristics (4) Low-area cutoff wavelegth λl: 8 mm or 25 mm (5) High-area cutoff wavelegth λc: 0.8 mm (6) Evaluatio legth Le: Full legth i the measurig directio i the quality rage of glass board (7) Samplig legth Ls: Ls = 20 mm whe λl = 8 mm Ls = 25 mm whe λl = 25 mm The samplig legth meas the legth of a sigle stroke of repetitive waviess calculatios executed little by little from oe ed to aother over the full rage of evaluatio legth. (8) Pre-Travel Lp: 2RC filter takes 2λL s at the head ed of evaluatio legth. Phase correctio filter takes a λl at both eds of evaluatio legth. fpd Explaatio of Le, Lp ad Ls Note : This parameter is ot icluded i Surfcom 30A/480A. 5-9

38 5-0

39 6 PARAMETERS FOR WAVELENGTH AND SLOPE Mea Spacig of profile irregularities/average Spacig of Roughess peaks (Sm, Rsm, Smmax, PSm, WSm) Extract the samplig legth, L from the samplig curve to the directio of the mea lie. Whe the sum of the legths of the mea lie correspodig to oe of the profile peaks ad its adjacet oe profile valley (spacig of profile irregularities) is calculated, the mea spacig of profile/average spacig of roughess peaks is the arithmetical mea value of may spacig of those irregularities. Whe the spacig of irregularities betwee the poit which goes across the mea lie i the directio from the oe profile peak to oe profile valley ad the poit of crossig i directio from the ext oe profile peak to oe profile valley is made to Smi ad the total umbers of the itervals are made to N, it ca be obtaied by the followig formula. Sm= Z N N Smi i= Sm Sampled curve f(x) Sm2 Mea lie (phase correct) Ceter lie (2RC) Smi Sm X Stadard (Coutry) Samplig legth (L) TABLE 6. Parameter Names ad Sampled Curves uder Various Stadards Roughess Profile R & Profile Curve Phase Correct Roughess Profile Rg P Curve W Value per oe Value per Each Mea value of -Samplig legth Samplig Legth Samplig Legth values obtaied per JIS B Mea spacig of profile irregularities Sm (Note 3) ISO4287:997 (It l Stadard) - ISO4287/-984 (It l Stadard) ASME B (USA) DIN4762 (Germay) B.S.34/-988 (UK) Mea Spacig of Profile Irregularities Smi (RSmi) Mea Spacig of Profile Irregularities Sm Mittelerer Abstad der Profilumregelma Bigkeite (Sm) Mea Spacig of Profile Sm - RSmmax Sm max Samplig Legth Mea spacig of profile irregularities Sm (Note 3) Mea width of the profile elemets RSm Filtered Waviess -Samplig legth - - Mea width of the profile elemets RSm Mea width of the profile elemets Average per Samplig legth WSm Mea Spacig of Profile Irregularities Sm (RSm) (PSm) (WSm) Mittelerer Abstad - der Profilumregelma Bigkeite (Sm) - Mea Spacig of Profile Sm Note : I ISO 468 ad JIS B stadard, the height of less tha 0% of Ry is ot regarded as oe idividual profile peak or valley as the coditio for judgemet. Because of this limitatio, eve if a small compoet of the wavelegth is icluded i the waveform, the Sm value is geerally apt to become the value which correspods to the wavelegth of the biggest amplitude. This machie follows it i ISO, DIN, ASME ad JIS94 modes. Note 2 : It provides the vertical dead bads of 0.5mm / measurig magificatio both above ad below the mea lie, i order to ward off such fear that oise compoets are judged as peaks or valleys i the JIS82 mode. (I Surfcom 30A/480A, it provides the each dead bad of ±0.5µm i measurig rage of ±400µm, ±0.05µm i measurig rage of ±40µm, ±5m i measurig rage of ±4µm ad ±2.5m i measurig rage of ±2µm.) Note 3 : I JIS B , the roughess profile, Rg, passed by phase correct filter is used. 6-