Numerical assessment employed using a light-section microscope However, if one compares the profiles shown in Fig 4.1c and 4.1f the same numerical value would be obtained for each, although it is obvious that the two surfaces are completely different Therefore the simple system described above is not suitable for the types of surface produced in practical situations and it becomes necessary to devise some system which will give an average height of the profile along with some indication of the roughness of the surface One such system in practical use is the ‘R,’ or ‘10-point height’ method of assessing average peak-to-valley height as laid down in BS 1134: 1972 This is defined as the separation of the average of the five highest peaks and the average of the five lowest valleys within a single sampling length More involved peak-to-valley definitions have been devised, notably the Allison system (Hydell 1967/68) developed by General Motors, and the Swedish H-system Each system positions the peak and valley reference lines by truncating the higher peaks and lower valleys The Allison or “general surface texture’ (GST) system (Fig 4.12), truncates the 10 per cent highest peaks and the lowest valleys, similarly the Swedish technique involves a per cent truncation to position the reference lines In the Allison system the reference lines are termed the upper and lower GST lines and enclose the general surface texture which is considered as the workable surface between initial wear-in and a severe wear condition The difference between the two reference lines is used as the roughness parameter (GST) Outside the GST reference lines the system is reported to offer a control on the highest peaks and lowest valleys by specifying a permissible peak height and a permissible valley depth Other peak-to-valley roughness parameters more or less widely used are listed and defined in Tables 4.1 and 4.2 and sect 4.4.1 The Allison system of profile char- Upper GST reference line ¬— ho Waviness depth Permissi ermissible oxture (Gs | peak height General surface texture (GST) aX ———~—T _ Me- 7) Permissible _.Ắ— —+ valley depth Evaluation length Average parameters The two most widely used mean-line roughness parameters are rootmean-square (RMS) and arithmetic or centre-line average R, As a mathematical technique, each can be used to define the mean line or mean plane, and in fact they are equivalent The RMS technique which involves minimizing the sum of the squares defines the same mean as the 81 Profile description R, condition of equal areas or volumes of surface and void, above and below the mean Of these two parameters the RMS roughness has now almost gone out of practical usage The most universally used parameter is that of the average roughness R,, which may be defined mathematically as: R, = — + where z is measured from the mean line and L is the profile sample length in the x-direction (Fig 4.13) To determine the average roughness from a given graphical profile it is first necessary to draw the mean line Referring to Fig 4.13: Draw straight line A~A parallel to general slope of graph Using some suitable method (e.g planimeter) find the areas above the line, A,, A3 denoting these positive; and also the areas below the line A,, Ay denoting these negative Sum these areas algebraically The resulting sum divided by the length of the graph gives the distance by which the true centre-line lies from line A—A Draw in the true centre line To determine the R, value: Sum the areas above and below the centre line, irrespective of sign and divide by the length of graph This gives the average height of the graph Now the height of the graph has been increased by some magnification factor, therefore to find the true average height of the actual profile the value obtained in (6) must be divided by this factor From a practical point of view deriving the R, value by this method is tedious and time consuming Most modern instruments are of the stylus type as described in Chapter 2, and these electronically establish the mean line and derive the R, value Also in contrast to the peak-to-valley height, the average roughness reveals neither the greatest extent nor the nature of the irregularities Indeed, it is one of the main disadvantages of the measure that it is quite Determination of mean Fig 4.13 line and R, value in the M-system C) 82 z Numerical assessment O capable of giving identical values for surfaces of vastly different charac- teristics, as might quite well be expected from the nature of an average Nevertheless, where the characteristics of a surface have been found to be satisfactory, the average roughness provides a workable control, providing always that the conditions which produced the satisfactory surface are maintained Bearing area curves A frequent requirement in industry is to be able to estimate the area in contact between two mating surfaces, and to assess the rate of wear The area of real contact is known as the bearing area and may be obtained from a graphical profile as follows Referring to Fig 5.7: Some distance from a reference line draw a parallel line (the bearing line) as shown Measure the length of each metal intercept (land) along this line and sum them together The proportion of this sum to the total length of bearing line being considered represents the proportion of true area of contact to the nominal area after some process such as lapping, etc If this procedure is repeated along a number of bearing lines and plotted as shown in Fig 5.7 a curve is obtained which is commonly known as the Abbott bearing area curve (Abbott & Firestone 1933) and this gives an indication of the rate of wear which may be expected Strictly, of course, this procedure gives a bearing length along a profile, whereas what is required is a bearing area over a surface However, it can be shown (e.g Finkin 1968) that for a random surface the bearing length and bearing area fractions are numerically identical The bearing area curve is in fact the integral of the height probability density function, as discussed in sect 5.2.4 If the height distribution is approximately Gaussian then the Abbott curve is the well-known cumulative error function of classical statistics, and the bearing area fraction at any height relative to the mean line may be obtained by simple inspection of tables 4.3.2 Horizontal descriptors It has been suggested above that as well as the average roughness the openness or closeness of the texture should also be quoted There are a number of possible parameters which might specify this They mostly reduce either to the number of peaks per unit length of the profile (peak density) or the number of times the profile intersects its own mean line (zero-crossing density) Unfortunately, neither of these parameters is an intrinsic property of a profile If the profile exhibits self-similarity as Suggested in sect 4.2 above, then the peak density is infinite and the number of peaks actually observed is a function of the measuring instrument; a sharper stylus will reveal more peaks, as is well known (Jungles & Whitehouse 1970) The same argument may be applied, 83 Profile description C though a little less containing infinitely each ‘macroscopic’ an infinite number problem could be obviously, to the zero-crossing density If a profile high frequencies intersects its own mean line then intersection will on close enough inspection reveal of ‘microscopic’ zero crossings However, this resolved to some extent by digital technology if an international standard sampling interval were agreed (see Chs 5, and 7) Other parameters suggested include the mean slope, mean profile curvature (i.e the second differential of the profile) and various random-process parameters such as the correlation length All these are functions of the peak and zero-crossing densities and their mathematical behaviour is discussed in the next chapter A parameter which has been Proposed for instrumental use is the so-called average wavelength (Spragg & Whitehouse 1970/71), defined in Table 4.2, as illustrated in Fig 4.14 which shows some typical surfaces OC) Fig 4.14 Average wavelengths for some typical surfaces (Spragg & Whitehouse 1974), 1m } > je Average 0.1mm wavelength sum ay pl «+ _»ð i Average wavelength "` .e 0.1 mm 0.1mm > F— Average wavelength In some profiles there may be present numbers of very shortwavelength components which could prove difficult to assess in the practical situation This may be overcome by rejecting the very short wavelengths and is very easily accomplished in instruments using meter cut-off filters These filters can be designed to reject long wavelengths and short wavelengths and therefore the instrument can be made to accept only the wavelengths which occur within a given band Experiment has shown that rejection of the very short wavelengths gives meaningful results as regards average wavelength, yet has little or no effect on the value of R, An interesting observation is that the average wavelength is always very close or equal to the feedmark of the tool used in the manufacturing process and is particularly noticeable in turned surfaces O34 SE 20 m } Roughness standards ro i 4.4 Roughness standards Most countries with an industrial or partly industrial society have their | own national roughness standards These enshrine a bewildering variety of roughness parameters and definitions, such that it is quite difficu lt to specify unambiguous descriptions which will be valid across nation al ` boundaries Difficulties of comparing standards are of several sorts Firstly, two national standards may use different symbols or nomen- clature for the same parameter, for example the total rough ness depth is R, in the French standard, but R,,,, in the J apanese Secondly and more confusingly, two standards may use the same symbol for quite different T able 4.1 Some national roughness stand ards parameters, for example the West German R, is the average of the maximum peak-to-valley heights in five successive sample length s, s2 Whereas the British R, is the difference in height between the average of the five highest peaks and the average of the five lowest valleys in a £ © % ‹ %s \®o\S\ “\E\SA\ S\e\ S2\%S\ \2 2\S S ` \e\ \e %\E\ %\ e\G8\S\ m5 &° 63 \*%\S\% Do L SD, \e\% eÂ& â \ \ a \Z\ EB\ % \ã \ã \ Ss hin Ry | Rp | Rp R, p| R, Ra R, Ky| Ra | Re R, R, R, Ra | Rp R, R, km R, R, ` R, R, R, R, C ) ——— kọi A, A, | R, Aw | Rmax | R Ay R, Rinax | Ry Argentine Cuba |W R, WR, R, R, R, (Tp)p | Sk | Sw | Rmax | Re | We} H to R, R, R, R, |R, % %^2 Rimax | Denmark R, R, R R, ởs Austria Finland |France e A4 QDa” O Belgium Bulgaria R, ky | Ra | Rp | (Tp)c | An| C) % eB “ R, R, | Rp R, | Rp | %ọ R, R, R, | Ry ` ứ $ \e\e\ ©©, \9-\ \B\e\ \Z\E\'S R, R, ` &€ \B\s\B \S\S\ \2\D ©on < \*\3\% B\S\Se\S ge k, | Ry R, $ ©53 \ \SB\A2SB\e@\%\3\ \4\%.\ Q % và6 e\a\ o\%\% s S.\â\%9đ \ \4\ ằ % $ E\e B\% \% % %\% v đ,â ố IRAM 5065 NBN 863 BDS 782 UNC 03-04 DS 940 SFS 2038 NFE 05-015 Germany, W.| DIN 4768/1 Rmax | Japan MSZ 4721/2 IS 3073 UNI 3963 JIS B0601 Netherlands | NEN 630 New Zealand | as UK Norway NS 981 Poland Pmax | Rumania Spain Rmax | Sweden Turkey UK USA USA ‹% 62 1964 ONORM M1115 | 1974 Germany, E | TGL 0-4762 Germany, W.| DIN 4762 Rmax | Hungary Rmax | India Italy PNM-04251 STAS 730/1 UNE 1037 SMS 671 TS 971 BS 1134 ANSI B46.1 MIL-STD-I0A Rinax | International | ISO R468 1970 1973 1972 1963 1969 1972 1963 1960 1974 1974 1967 1960 1976 1967 — 1969 1973 1975 1951 1975 1971 1972 1978 1955 1966 Profile description © Fig 4.15 Some peak and valley parameters + C Roughness parameters and waviness † Fig 4.16 spacing aw, ¢ W | >ịe aw, aw, a >) a, SUP | Definitions parameters Symbol A, of some —>ờ k—— Definition Roughness width A, = > Lw < Table 4.2 roughness Name ¡ðỌ N Reference Figure DIN 4768 4.16 NFE 05-015 ~ DIN 4762/1 4.16 NFE — n SD =1 n within one roughness sampling length e AR Mean roughness step As for A,, but n within measuring length Ay Waviness width Ay Ay Mean h MAA _ waviness step Bearing length at height c(say) from mean linet =- n > ayi Hj=I As for A,,, but ” within measuring length = > i Mean apparent amplitude Mean of the peak-to-valley heights of 13 consecutive 50 mm sampling lengths P, Profile height Very nearly the same as W (DIN 4762/2), but uncorrected for roughness R, Average roughness R, = T J |z|dx LẺ over 2-20 consecutive sampling lengths 86 05-015 DIN 4762/1 Lackenby (1962) 4.15 — DIN 4771 - BS 1134 4.15 Roughness standards O Table 4.2 (cont.) Symbol Name Kmax Maximum height Rp Depth of surface Ry =¬ + [ (mạ Rg Root-mean-square roughness L _ fl Ry = VL J zdx R, Peak-to-valley height Separation of highest peak and lowest valley DIN 4762/1 4.15 Rim Mean depth of roughness Mean of the roughness depths R, of five consecutive sampling lengths DIN 4768 - Levelling depth Distance between mean line and a parallel line through highest peaks Olsen (1963) 4.15 Average peak-to-valley height Average of single peak-to-valley heights from five adjoining sampling lengths DIN 4768 - R, Ten-point height Separation of average of five highest peaks and five lowest valleys within a single sampling length BS 1134 - Ry, Average roughness depth Mean of separation of third highest peak and third lowest valley in each of five consecutive sampling lengths Sk Skewness ° i ~ R, oo R, » ! ` Definition peak-to-valley smoothness ` Reference Largest single peak-to-valley heightin five adjoining sampling lengths L Sk=— ao ¿ˆ J ~, z)dx Figure DIN 4768 — DIN 4762/1 4.15 MIL-STD-10 4.15 (1949) - zp(z)dz _ where p(z) = height distribution t C) : P “ng i W Waviness height profile ty = _ h DIN 4762/1 4.15 Separation of highest peak and DIN 4762/2 4.16 lowest valley of waviness over a waviness sampling length, corrected for roughness Zi t Single peak-to-valley Separation of highest peak and lowest DIN 4768 _ Rn Mean depth Distance between mean line and a parallel line through the deepest valleys Olsen (1963) 4.15 Aa Average 27 X R,/mean Spragg — height wavelength valley within a single sampling length slope and Whitehouse (1970/71) 87 single sample length Thirdly and most dangerous of all, a number of definitions are intrinsically ambiguous, for example the roughness width A, of DIN 4768 depends on instrumental characteristics in an undefined way An attempt has been made information and to present it comparisons between standards 4.1 is a list of some current here to in such easier, or national bring together some of this a way as to make practical at least less confusing Table and international roughness standards with some (not all) of their defined parameters and corre- sponding symbols In Table 4.2 some (again not all) of the roughness parameters in use are defined and referred back to their sources Finally, some of the terms in common use to describe the measurement of roughness are defined below 4.4.1 Glossary 9f some terms and definitions used in roughness characterization Abbott curve: Bearing area fractions plotted as a function of height Arithmetic average roughness: See R, Average peak-to-valley height: See R, Average roughness: See R, Average wavelength: See A, Bearing area: Also bearing area fraction, bearing line fraction Fraction of surface at a given height above or below the mean line (see ¿,) Centre line: A line representing the form of the geometrical profile and parallel to the general direction of the profile throughout the sampling length, such that the sums of the areas contained between it and those parts of the profile which lie on either side of it are equal Centre-line average roughness: See R, Cut-off: See meter cut-off Deepest maximum roughness: See RmaxDepth of surface smoothness: See Ry Effective profile: The contour that results from the intersection of the effective surface by a plane conventionally defined with respect to the geometrical surface Effective surface: The close representation of a real surface obtained by instrumental means © Electrical mean line: In an electric meter instrument, a reference line established by the circuits determining the meter cut-off, which line divides equally those parts of the modified profile lying above and below it General surface texture: The vertical distance between reference lines formed by truncating the 10 per cent highest peaks and lowest valleys of the surface texture The definition forms part of the Allison system and is said to take account of initial wear-in and represents a measure of the maximum possible surface wear The surface between the upper and lower GST is considered as the workable surface for the service life of the component (Hydell 1967/68) 88 Roughness standards Geometrical profile: The contour that results from the intersection of the geometrical surface by a plane conventionally defined with respect to this surface Geometrical surface: The surface determined by the design or by the process of manufacture, neglecting errors of form and surface rough- ness Land length: Length of intercept with the profile of a line drawn parallel to the profile mean line Lay: The direction of the predominant surface pattern, ordinari ly determined by the production method used I SE TE NI RTES ey” ~ — Least-squares mean line: A reference line representing the form of the “ © geometrical profile within the limits of the sampling length, and so placed that within the sampling length the sum of the squares of the deviations of the profile from the mean line is a minimum Levelling depth: See R,,, Rp Maximum peak-to-valley height: See R max: Mean apparent amplitude: See MAA Mean depth: See R,, Mean roughness index: See R, Mean roughness step: Also mean roughness wavelength or frequency See Ap Mean waviness step: Also mean waviness wavelength or frequency See Ay Measuring traversing length: The length of the modified profile used for measurement of surface roughness parameters It is usual for the measuring traversing length to contain several sampling lengths Meter cut-off: In a profile meter instrument, the conventionally defined wavelength separating the transmitted from the attenuated components of the effective profile Modified profile: The effective profile modified by such defined filter means as are used for suppressing those undulations of the real profile — that are not or are not fully to be included in the measured roughness parameters of the surface Peak roughness: See Rp Peak-to-valley height: See R,, Rmax» Rim, Rz, R3zPermissible peak height: Maximum permissible peak height in the Allison system (see general surface texture) Permissible valley depth: As for permissible peak height Profile height: See P, Proportional profile bearing: See t, Real profile: The contour that results from the intersection of the real surface by a plane conventionally defined with respect to the geometrical surface Real surface: The surface limiting the body, separating it from the surrounding space ° Recording traversing length: The maximum recording movement of the stylus along the surface Reference line: A line chosen by convention to serve for the quantitative evaluation of the roughness of the effective profile 89 Profile description Root-mean-square roughness: See Rg Roughness: The irregularities in the surface texture which are inherent in the production Proc ess, but excluding waviness and errors of form Roughness factor: Ratio of true to projected surface area Roughness width: See A, ` Run-out length: Vertical projection on to the mean line of the last part of the traversing length which is not used for numerical evaluation Sampling length: The length of the effective profi le selected for the evaluation of the surface roughness, with out taking into account other types of irregularities Secondary texture: Irregularities outs ide the bandwidth of wavelengths of the primary texture Shape factor: See smoothness index Single peak-to-valley height: See z, Smoothness index: Ratio of the sepa ration of the mean line and a parallel line through the highest peak to the average roughness Also shape factor Start-up length: Length of the first part of the traversing length projected vertically on to the mean line and not used for numerical evaluation Transient oscillations shall fade out within the start-up length Surface texture: Irregularities which, recurrin g many times across the surf ace, tend to form on it a pattern or texture Also primary texture Surface volume: The volume per unit area encl osed by the surface and a plane located by the highest summits Ten-point height: See R, Traversing length: The length of the effective profi le necessary for the evaluation of surface roughness parameters for the surface inspected The traversing length may include one or more sampling lengths True profile length: The length obtained by foll owing all the undulations of the profile along a sampling length (strictly infin ite) TM Waviness: That component of surface texture upon which roughnes s is superimposed Waviness may result from such factors as machine or work deflections, vibrations, chatter, heat trea tment or warping strains Waviness height: See W Waviness width: See Ay Zone roughness: See R, ... noticeable in turned surfaces O34 SE 20 m } Roughness standards ro i 4.4 Roughness standards Most countries with an industrial or partly industrial society have their | own national roughness standards... C Roughness parameters and waviness † Fig 4.16 spacing aw, ¢ W | >ịe aw, aw, a >) a, SUP | Definitions parameters Symbol A, of some —>ờ k—— Definition Roughness width A, = > Lw < Table 4.2 roughness... but uncorrected for roughness R, Average roughness R, = T J |z|dx LẺ over 2-20 consecutive sampling lengths 86 05-015 DIN 4762/1 Lackenby (1962) 4.15 — DIN 4771 - BS 1134 4.15 Roughness standards