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BS 1134-1:1988

This British Standard, havingbeen prepared under thedirection of the GeneralMechanical EngineeringStandards Committee, waspublished under the authorityof the Board of BSI and comesinto effect on29 February 1988

© BSI 11-1999

BS 1134 first publishedDecember 1950

First revision April 1961

First published as BS 1134-1 August 1972

First revision February 1988

The following BSI referencesrelate to the work on this

standard:Committee reference GME/10

Draft for comment 85/74262 DC

ISBN 0 580 16269 9

Committees responsible for thisBritish Standard

The preparation of this British Standard was entrusted by the General

Mechanical Engineering Standards Committee (GME/-) to TechnicalCommittee GME/10, upon which the following bodies were represented:

Department of Trade and Industry (National Engineering Laboratory)

Department of Trade and Industry (National Physical Laboratory)

GAMBICA (BEAMA Ltd.)

Gauge and Tool Makers’ Association

Institution of Production Engineers

Loughborough University of Technology

University of Warwick

Coopted member

Amendments issued since publication

Amd. No. Date of issue Comments

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Contents

Page

Committees responsible Inside front cover

Foreword iiiSection 1. General

1 Scope 1

2 Definitions 1

Section 2. Determination of surface roughness

3 Sampling lengths 12

4 Graphical determination of parameter values 12

5 Statements of surface roughness 16

Section 3. Instrumentation

6 Stylus-type measuring instruments 17

7 Accuracy 20

Appendix A Parameter values 23 Appendix B Method divergence of instrument reading 24

Appendix C Factors affecting the statement of accuracy 25

Figure 1 — Surface characteristics and terminology 3

Figure 2 — Traversed length 4

Figure 3 — Profile departure 5

Figure 4 — Local peak of the profile 5

Figure 5 — Spacing of local peaks of the profile 6

Figure 6 — Local valley of the profile 6

Figure 7 — Profile peaks 7

Figure 8 — Profile valleys 7

Figure 9 — Spacing of profile irregularities 8Figure 10 — Profile section level 8

Figure 11 — Profile bearing length 9

Figure 12 — Arithmetical mean deviation of the profile (Ra) 9

Figure 13 — Maximum height of the profile (Ry) 10

Figure 14 — Graphical determination of Ra values 13

Figure 15 — Graphical determination of Rz values 13

Figure 16 — Graphical determination of S m values 14

Figure 17 — Graphical determination of S values 15

Figure 18 — Graphical determination of tp values 15

Figure 19 — Stylus acting midway between two skids 17

Figure 20 — Profile instrument frequency response 19Figure 21 — Permissible deviations of the transmission coefficient 21

Figure 22 — Symbols for the direction of lay 22

Figure 23 — Centre arithmetical mean lines (A) and electricalmean lines (B) 25

Table 1 — Sampling lengths 12

Table 2 — Static measuring force of the stylus 17

Table 3 — Evaluation lengths 18

Table 4 — Nominal sinusoidal frequency response characteristics fora profile instrument 19

Table 5 — Upper and lower limits of transmission coefficients 20

Table 6 — Preferred nominal values for arithmetical mean deviationof the profile (Ra) 23


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Page

Table 7 — Preferred nominal values for ten point height of

irregularities (Rz), and maximum height of the profile (Ry) 23Table 8 — Preferred nominal values for mean spacing of profileirregularities (S m), and mean spacing of local peaks of the profile (S ) 24

Table 9 — Comparison of Ra values obtained by graphical andinstrumental means 24

Publications referred to Inside back cover


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Foreword

This Part of BS 1134 has been prepared under the direction of the GeneralMechanical Engineering Standards Committee and is a revision ofBS 1134-1:1972, which is withdrawn.

The definitions given in this Part of BS 1134 supersede those given in BS 6741-1and BS 6741-2. BS 6741-1 and BS 6741-2 are accordingly withdrawn.

BS 1134 was first issued in 1950 and revised in 1961 and 1972. This revisiontakes account of the 1982 edition of ISO 468 “Surface roughness — Parameters,their values and general rules for specifying requirements” published by theInternational Organization for Standardization.

BS 1134-1:1972 dealt with two parameters, Ra and Rz, whereas this edition coversthe additional parameters Ry, S m, S and tp.

Additional parameters may be found in ISO 4287-1:1984 “Surface roughness —Terminology — Part 1: Surface and its parameters” and in ISO 4287-2:1984“Surface roughness — Terminology — Part 2: Measurement of surface roughness parameters” .

BS 1134-2 gives general information and guidance.

A British Standard does not purport to include all the necessary provisions of acontract. Users of British Standards are responsible for their correct application.

Compliance with a British Standard does not of itself confer immunityfrom legal obligations.

Summary of pages

This document comprises a front cover, an inside front cover, pages i to iv,pages 1 to 26, an inside back cover and a back cover.

This standard has been updated (see copyright date) and may have hadamendments incorporated. This will be indicated in the amendment table on theinside front cover.


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Section 1. General

1 Scope

This Part of BS 1134 describes methods for the assessment of surface texture of machined, self-finished and

other surfaces and describes the characteristics and parameters standardized for use in industry.

It embraces the following.

a) The terminology to be employed in statements relating to surface texture and measurement of surfacetexture.

b) Preferred values for the grading of surface texture (see Appendix A).

c) Sampling lengths and cut-off values to be used in graphical procedures and instrument construction.

d) The graphical determination of the following parameters:

1) Ra, arithmetical mean deviation of the profile;

2) Rz, ten point height of irregularities;

3) Ry, maximum height of the profile;

4) S m, mean spacing of profile irregularities;5) S , mean spacing of local peaks of the profile;

6) tp, profile bearing length ratio.

e) The determination of parameter values by instrumental means.

f) The essential instrument requirements to ensure repeatability of performance.

g) The information to be given in statements relating to surface texture requirements.

NOTE The titles of the publications referred to in this standard are listed on the inside back cover.

2 Definitions

For the purposes of this Part of BS 1134 the following definitions apply.

2.1 Terms relating to the surface, profile and datum

2.1.1real surface

the surface limiting the body, separating it from surrounding space

2.1.2real profile

the profile that results from the intersection of the real surface by a plane conventionally defined withrespect to the geometrical surface (see Figure 1)

2.1.3geometrical surface

the surface determined by the design, and defined by the drawing and/or other technical document,neglecting errors of form and surface roughness (see Figure 1)

2.1.4geometrical profile

the profile that results from the intersection of the geometrical surface by a plane conventionally definedwith respect to this surface (see Figure 1)

2.1.5effective surface

the close representation of a real surface obtained by instrumental means (see Figure 1)

2.1.6effective profile

the profile that results from the intersection of the effective surface by a plane conventionally defined withrespect to the geometrical surface (see Figure 1)


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Figure 1 — Surface characteristics and terminology


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2.1.13waviness

that component of surface texture upon which roughness is superimposed (see Figure 1)NOTE Waviness may result from such factors as machine or work deflections, vibrations, chatter, heat treatment or warpingstrains.

2.1.14lay

the direction of the predominant surface pattern, ordinarily determined by the production method used(see Figure 1)

2.1.15traversed length

the complete length of the pick-up movement along the surface being measured (see Figure 2)

2.1.16

reference linethe line chosen by convention as a reference to serve for the quantitative evaluation of the roughness of theeffective profile (see Figure 2)

2.1.17sampling length, l

the length of the reference line used for identifying the irregularities characterizing the surface roughness(see Figure 2). The sampling length is measured in the general direction of the profile

2.1.18evaluation length, ln

the length over which the profile is assessed. It may contain one or more sampling lengths (see Figure 2)

2.1.19profile departure, y

the distance between a profile point and the reference line in the direction of measurement (see Figure 3)

2.1.20mean line system, system M

the calculation system used for the profile evaluation in which a mean line is taken as a reference line

2.1.21least-squares mean line of the profile

a reference line having the form of the geometrical profile and dividing the profile so that, within thesampling length, the sum of the squares of the profile departures from this line is the minimum

Figure 2 — Traversed length


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2.1.22centre arithmetical mean line of the profile

a reference line representing the form of the geometrical profile and parallel to the general direction of theprofile throughout the sampling length, such that the sums of the areas contained between it and thoseparts of the profile that lie on each side of it are equal

NOTE The centre line (centre arithmetical mean line) is defined and used for graphical convenience. When the centre line has adistinguishable periodicity and its general direction is therefore determinate, the “equal area” centre line is unique. When the profileis irregular, the assessment of the general direction becomes uncertain over a certain range. Within this range a family of “equal area”centre lines can be drawn, one of which will be identical with the least-squares mean line.

2.1.23electrical mean line

in an electrical instrument, a reference line that is established by the circuits determining the metercut-off and which divides equally those parts of the transformed profile lying above and below it

2.1.24

local peak of the profilea part of the profile between two adjacent minima of the profile (see Figure 4)

NOTE Figure 3 represents a profile graph which, due to the difference in the vertical and horizontal magnifications, is a distortedrepresentation of the real profile. For this reason, the profile departures should be measured in the same direction as that used todetermine the real profile. On the real profile, the angles, µ , between the reference line and the general direction of the profile withinthe evaluation length are very small. Thus, the difference between the profile departures measured perpendicular to the referenceline and those measured perpendicular to the general direction of the profile may be negligible. Hence, on the real surface, the profiledepartures should be considered perpendicular to the reference line.

Figure 3 — Profile departure

Figure 4 — Local peak of the profile


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2.1.25spacing of local peaks of the profile

the length of a mean line section between the two highest points of adjacent local peaks of the profileprojected on the mean line (see Figure 5)

2.1.26local valley of the profile

a part of the profile between two adjacent maxima of the profile (see Figure 6)

2.1.27local irregularity

a local peak and the adjacent local valley

2.1.28profile peak

an outwardly directed (from material to surrounding medium) portion of the profile connecting twoadjacent points of the intersection of the profile with the mean line (see Figure 7)

Figure 5 — Spacing of local peaks of the profile

Figure 6 — Local valley of the profile


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2.1.32line of profile peaks

a line parallel to the mean line and passing through the highest point of the profile within the samplinglength (see Figure 7)

2.1.33line of profile valleys

a line parallel to the mean line and passing through the lowest point within the sampling length(see Figure 8)

2.1.34profile section level, c

the distance between the line of profile peaks and a line intersecting the profile, the latter being parallel tothe line of profile peaks (see Figure 10)

NOTE The profile section level can be determined in micrometres or in percent of Ry, the maximum height of the profile (see 2.2.2).

Figure 9 — Spacing of profile irregularities

Figure 10 — Profile section level


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2.1.35profile bearing length, ½p

the sum of the section lengths obtained by cutting the profile peaks by a line parallel to the mean linewithin the sampling length (see Figure 11)

2.2 Terms associated with surface roughness parameters

2.2.1arithmetical mean deviation of the profile, Ra

the arithmetical average value of the departure of the profile above and below the mean line (centre or

electrical mean line) throughout the specified sampling length (see Figure 12). The arithmetical meandeviation is given by the equations:

or approximately:

where

l is the sampling length;

y is the profile departure;

n is the number of profile departures.

NOTE In practice, the values of Ra are determined within the evaluation length which includes several sampling lengths. Thesampling length is equal to the cut-off.

Figure 11 — Profile bearing length

Figure 12 — Arithmetical mean deviation of the profile (Ra)


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2.2.2maximum height of the profile, Ry

the distance between the line of profile peaks and the line of profile valleys within the sampling length(see Figure 13)

2.2.3ten point height of irregularities, Rz

the average distance between the five highest profile peaks and the five deepest profile valleys within thesampling length, measured from a line parallel to the mean line and not crossing the profile (see Figure 15)

2.2.4mean spacing of profile irregularities, S m

the mean value of the spacing of the profile irregularities within the sampling length (see Figure 16)

2.2.5mean spacing of local peaks of the profile, S

the mean value of the local peak spacing of the profile within the sampling length (see Figure 17)

2.2.6profile bearing length ratio, tp

the ratio of the profile bearing length to the sampling length

2.3 Terms associated with instruments for the measurement of surface roughness by the profilemethod

2.3.1profile recording instrument

an instrument recording the coordinates of the profile of the surface texture

2.3.2profile instrument

an instrument used for the measurement of surface roughness parameters

2.3.3contact profile instrument, system M

a contact (stylus) instrument of consecutive profile transformation used for the measurement of surfaceroughness parameters according to system M (the mean line system)

NOTE See ISO 3274:1975.

2.3.4modified profile

the effective profile defined by the combination of a stylus and profile filter, the filter being used forselecting a part of the spectrum of the real profile to be taken into consideration in the measurement ofsurface roughness parameters

Figure 13 — Maximum height of the profile (Ry)


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2.3.5profile instrument with predetermined evaluation length

an instrument in which the length used for measurement has a defined beginning and endNOTE These instruments generally indicate and hold the reading of the measured parameter obtained at the end of the statedmeasuring length.

2.3.6profile instrument with “running” evaluation length

a profile instrument with running evaluation length giving a running average

2.3.7static measuring force

the force which the stylus exerts along its axis on the examined surface without taking into account thedynamic components that arise from the traversing of the surface by the stylus

2.3.8

rate of change of the static measuring forcethe change of the static measuring force per unit displacement of the stylus along its axis

2.3.9 cut-off, 2 B

the value of the wavelength 2 numerically equal to the sampling length and conventionally taken as theupper limit of transmission of the instrument

NOTE The given upper limit conventionally separates the nominally transmitted components of the effective profile spectrum fromthose that are nominally suppressed.

2.3.10vertical magnification of a profile record, V v

the ratio of the recorded horizontal displacement to the displacement of the stylus along the surface

2.3.11

horizontal magnification of a profile record, V hthe ratio of the recorded length of the recorder chart to that of the stylus displacement along the surface

2.3.12error of vertical magnification of a profile record

the percentage difference between the nominal and the actual values of the vertical magnification referredto the nominal value

2.3.13error of horizontal magnification of a profile record

the percentage difference between the nominal and the actual values of the horizontal magnificationreferred to the nominal value

2.3.14

basic error of a profile instrument readingthe percentage difference between the instrument reading and the value of the surface roughnessparameter as defined by the stylus and cut-off (without skid) of the instrument

2.3.15method divergence of the instrument reading

for a given measured profile, the percentage difference between the value of the surface roughnessparameter determined with respect to the electrical mean line of the defined wave filter and a successionof straight centre arithmetical mean lines each equal in length to the cut-off, both determinations beingreferred to the same part and overall length of the same cross section (see Appendix B)


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Section 2. Determination of surface roughness

3 Sampling lengths

Normally the appropriate sampling length of surface, which determines the corresponding cut-off to be

used (see 6.3), shall be selected from the range of sampling lengths given in Table 1.

In special cases which require the choice of values of sampling length other than those specifiedin Table 1, sampling and evaluation lengths shall be stated on all records of the test.

Table 1 — Sampling lengths

4 Graphical determination of parameter values

4.1 Graphical determination of Ra values

4.1.1 Observe the procedure in 4.1.2 to 4.1.8 when determining Ra values from graphical recordings.

NOTE If the surface is intentionally curved, the curvature will generally be neutralized, prior to recording, by some form of guidingor filter device.

4.1.2 Assume the surface is nominally flat, and that the record is produced in rectilinear coordinates inwhich a truly flat surface is represented by a straight line.

4.1.3 First determine the centre arithmetical mean line of the profile for each successive sampling length,l, contained within the evaluation length of the record, as given in 4.1.4 to 4.1.6.

4.1.4 Draw a straight line A“B” through the lowest profile valley and parallel to the general course of therecord over the sampling length l [see Figure 14a)].

NOTE 1 The slope of the line A“B” can usually be determined by eye with sufficient accuracy.NOTE 2 Where the texture has a distinguishable periodicity it is essential that the sampling length should be chosen to include awhole number of wavelengths.

4.1.5 Determine the area, P , between the profile and the line A“B” either by measuring equally-spacedordinates or by the use of a planimeter, through the chosen sampling length.

4.1.6 The height, H m, of the centre arithmetical mean line above A“B” (the line of profile valleys) is givenby the equation:

where

4.1.7 Draw the centre arithmetical mean line AB parallel to the line of profile valleys (A“B”) at the heightH m above it [see Figure 14a)].

4.1.8 Determine the areas r1, r2, r3 ... and s1, s2 ... above and below the centre arithmetical mean line[see Figure 14b)]. The value of Ra (in 4m) is calculated from the equation:

where

mm in

0.08 0.003

0.25 0.01

0.8 0.03

2.5 0.1

8.0 0.3

P is the area between the profile and line of profile valleys (A“B”);

l is the sampling length.

ri is the area (in mm2) of the ith profile peak;

si is the area (in mm2) of the ith profile valley;

l is the sampling length (in mm);

V v is the vertical magnification of the profile record.

H m P

l----=


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4.1.9 The required value of Ra over the evaluation length is taken as the mean of the successive values ofthe sampling length.

4.2 Graphical determination of Rz and Ry values

For some purposes it is convenient to have an assessment of average peak-to-valley height of surfaceirregularities. The Rz or “ten point height” method (see Figure 15) is an arbitrary way of avoiding the effectof exceptional peaks and valleys in the final computation, and is used in determining averagepeak-to-valley values. Rz values are generally from four to seven times the corresponding Ra values, theratio depending upon the shape of the profile.

Measure the five highest peaks and five deepest valleys from an arbitrary base line A“B” drawn parallel tothe centre arithmetical mean line AB of the chosen sampling length l. Rz (in 4m) is then given by theequation:

Figure 14 — Graphical determination of Ra values

Figure 15 — Graphical determination of Rz values


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where

Y 1, Y 2, . . . Y 10 is the distance (in mm) of peaks and valleys from the arbitrary base line A“B”;


The value of Ry (in 4m) is calculated from the equation:

where

Y y is the maximum height (in mm) of the profile record;


4.3 Graphical determination of S m values

Draw the centre arithmetical mean line AB (see Figure 16) for the sampling length, l, and identify the

profile peaks, noting that the minimum height of the profile peaks to be taken into consideration isspecified as 10 % of Ry. The mean spacing of the profile irregularities S m (in 4m) is calculated from theequation:

where

S mn is the length (in mm) of mean line section containing the nth profile peak and the adjacent profile

valley;

n is the number of sections included in the determination;

V h is the horizontal magnification of the profile record.

4.4 Graphical determination of S values

Draw the centre arithmetical mean line AB (see Figure 17) for the sampling length, l, and identify the localpeaks, noting that the minimum spacing of the local peaks that is to be taken into consideration is specifiedas 1 % of the sampling length, while the minimum height of the local peaks that is to be taken intoconsideration is specified as 10 % of Ry. The mean spacing of local peaks of the profile, S , (in 4m) iscalculated from the equation:

Figure 16 — Graphical determination of S m values


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where

S 1 . . . S n are the spacing of local peaks of the profile (in mm);

n is the number of spacings included;

V h is the horizontal magnification of the profile record.

4.5 Graphical determination of tp values

Determine the profile bearing length, ½p, which is the sum of the section lengths obtained by cutting theprofile peaks by a line (A“B” in Figure 18) parallel to the arithmetical mean line within the sample length,l, at the profile section level, c, below the line of profile peaks. The profile bearing length, ½p, is given by theequation:

½p + a + b + c + d + e

where

a, b, c . . . are the section lengths.

The profile bearing length ratio, tp, expressed as a percentage, is given by the equation:

where

½p and l are in the same units.

Figure 17 — Graphical determination of S values

Figure 18 — Graphical determination of tp values


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5 Statements of surface roughness

5.1 General

The following information is that which shall be given in statements relating to surface roughness.

5.2 Surface roughness values

For requirements specified by the maximum value (in 4m) of the surface roughness parameter, none of themeasured values of the parameter of the whole surface being inspected shall exceed the value specified onthe drawings or in technical documents. In such cases, the suffix “max” shall be added to the parametersymbol, as shown in the following example:

Ry max 12.5

5.3 Limiting values

When both lower and upper limit values need to be specified, these shall be expressed (in 4m) as shown inthe following examples:

If a single value is stated it shall be the upper limit value and shall be expressed (in 4m) as shown in thefollowing examples:

Ra 0.8, Rz 12.5

NOTE Variations in the value of the surface roughness parameter in most engineering surfaces are found to approximatesufficiently closely to the normal (Gaussian) distribution for the properties of the normal distribution to be applied. Thus, the lowerand upper limits of the roughness parameter values are the limits between which 68 % of all the measured values of the parameterare expected to fall.

For requirements specified by the upper limit of the surface roughness parameter, the surface is considered to be acceptable if notmore than 16 % of all the measured values of the parameter exceed the value specified on the drawings or in technical documents. Incases where the lower limit is specified, the surface is considered to be acceptable if not more than 16 % of all the measured values ofthe roughness parameter can be exceeded by the specified value.

5.4 Cut-off values

When the cut-off value is other than 0.8 mm the value shall be indicated in parentheses following thesurface roughness value (in 4m), as shown in the following example:

Ra 0.2 (2.5)

NOTE Apart from indicating the cut-off to be used in assessment, the cut-off value denotes that dominant peak spacings greaterthan the cut-off are not present on a surface.

5.5 Lay

It is sometimes necessary to specify the direction of lay, in which case it shall be as defined as in Figure 22and expressed in accordance with the following example:

Ra 0.8 C

NOTE C refers to the symbol for lay which is circular (see Figure 22). Unless otherwise specified, the implication is that the surface

roughness should be measured across the direction of the lay.

5.6 Production process

When production of a surface is to be limited to the use of one particular process, the process shall be stated.

Ra 0.8 Rz 12.5Ra 0.4 Rz 6.3


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Section 3. Instrumentation

6 Stylus-type measuring instruments

6.1 Stylus

6.1.1 Tip radius of the stylus. The nominal value of the tip radius of the stylus shall be one of the following:

a) 2 ± 0.5 4m;

b) 5 ± 1 4m;

c) 10 ± 2.5 4m.

See also Appendix C.

6.1.2 Stylus angle. The nominal value of the stylus angle shall be one of the following:

a) 1.57 radians (90°);

b) 1.05 radians (60°).

6.1.3 Static measuring force. The static measuring force shall be sufficient to ensure continuous contactbetween the stylus and the surface being measured and shall be not greater than that given in Table 2.

Table 2 — Static measuring force of the stylus

6.2 Skid

6.2.1 Skid dimensions. If a skid is employed, its radius in the direction of the traverse shall be not less

than 50 times the meter cut-off used.If two simultaneously operative skids, as shown in Figure 19, are used, their radii shall be not less thaneight times the meter cut-off.

NOTE Although the use of the skid may, when applied under suitable conditions, introduce no error of any great practicalsignificance, external datum units should be used in all serious metrological work such as, for example, calibration procedures, andin the case of surfaces of limited area or requiring the use of cut-off values of 2.5 mm or greater.

6.2.2 Skid surface roughness. The surface roughness of the skid as determined by the ten point height ofirregularities, Rz, shall be not greater than 0.1 4m when measured in the direction of traverse.

6.2.3 Skid force. The force exerted by the skid on the surface to be measured shall be not greater than 0.5 N.

6.3 Traverse

In profile instruments with predetermined or running evaluation lengths, the length shall depend on themeter cut-off value 2 B within the limits given in Table 3.

Nominal tipradius of stylus

Maximum staticmeasuring force at mean

level of stylus

Maximum rate ofchange of

measuring force

4m mN N/m

2 ± 0.5 0.7 35

5 ± 1 4.0 200

10 ± 2.5 16.0 800

Figure 19 — Stylus acting midway between two skids


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Table 3 — Evaluation lengths

6.4 Values of vertical and horizontal magnification

The values of vertical and horizontal magnification for profile recording instruments shall be selected fromthe following series:

Vertical (V v): 100, 200, 500, 1 000, 2 000, 5 000, 10 000, 20 000, 50 000, 100 000, 200 000, 500 000,

1 000 000.

Horizontal (V h): 10, 20, 50, 100, 200, 500, 1 000, 2 000, 5 000, 10 000, 20 000, 50 000.

6.5 Transmission characteristics in the long wavelength

6.5.1 Rate of attenuation. The rate of attenuation shall be equivalent to that produced by two independentC-R networks of equal time constant in series. This describes a system in which the maximum slope of thetransmission curve is 12 dB per octave and in which the phase shift at the 75 % cut-off 2 B is 60°.

The transmission coefficient of such a system shall be given by the equation:

where

j = Æ – 1;

2 is the wavelength;

2 B is the meter cut-off.

The effective cut-off wavelengths shall be taken at 75 % transmission. These are deemed to be equivalentto the sampling lengths in Table 1.

NOTE In a practical determination, the values of the transmission coefficients for the characteristics shown are measured relativeto the flat part of the transmission curve (see Figure 20).

6.5.2 Cut-off values. The cut-off values (in mm) to be used in instrument construction shall be selected fromthe following series:

0.08, 0.25, 0.8, 2.5, 8.0.

NOTE 1 A cut-off of 0.8 mm is found adequate for most of the finer surfaces.

NOTE 2 Nominal sinusoidal frequency response characteristics for a profile instrument are shown by the ratios given in Table 4(see also Figure 20).

The permitted deviations from the nominal values of the transmission coefficients shall be as givenin Table 5, and graphically presented in Figure 21, and these allow the cut-off to be assessed atbetween 70 % and 80 % of maximum transmission.

Type of profile meter Cut-off

2 B

Evaluation length

Min. Max.

mm mm mm

Predetermined evaluation length

0.080.250.82.58

0.41.252.45

16

258

1540

Running evaluation length 0.250.8

2.55

1616


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Table 4 — Nominal sinusoidal frequency responsecharacteristics for a profile instrument

Figure 20 — Profile instrument frequency response

Wavelength Percentage transmission

Cut-off 0.25 mm

Cut-off 0.8 mm

Cut-off 2.5 mm

Cut-off 8.0 mm

mm % % % %

0.0250.050.08

99.798.796.7

— — 99.7

— — —

— — —

0.100.250.5

94.975.042.9

99.596.888.5

— 99.798.7

— — —

0.81.0

2.5

22.715.8

2.9

75.065.8

23.5

96.794.9

75.0

99.799.5

96.85.08.0

10.0

0.75 — —

7.12.91.8

42.922.715.8

88.575.065.8

25.050.080.0

— — —

— — —

2.90.75

—

23.57.12.9

NOTE Because of practical difficulties in measurement at the very shortwavelengths involved, the electrical transmission characteristic for 0.08 mmcut-off, although nominally of the same form as for the longer cut-off values, hasnot been tabulated.


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7 Accuracy

7.1 Statement of basic error of calibration of Ra instruments

The basic error of profile instrument reading (as defined in 2.3.14) given within the cut-off by aninstrument in optimum adjustment and use (see C.5), and expressed as a percentage of the designatedvalue of the surface roughness parameter of an instrument calibration specimen complying with BS 6393,shall be determined from the formula:

where

x is the fraction of the range indicated by the instrument;

p is a percentage of full range;

q is a percentage of reading.

NOTE The admissible basic error of calibration thus expressed does not include the effect of deviations in the transmission

characteristic which will be additional thereto.

7.2 Deviations of transmission coefficients

The permissible deviations of the amplitude transmission coefficient (see Table 5 and Figure 21) of a profileinstrument from the nominal transmission coefficient shall be given by the equations:

where

2 is the wavelength;

2 B is the meter cut-off.

Table 5 — Upper and lower limits of transmission coefficients

Wavelength, 2 Transmission coefficient

Cut-off, 2 B Lower limit Upper limit

% dB % dB

0.10.20.30.5

96.695.593.788.4

– 0.30 – 0.40 – 0.56 – 1.07

102.7101.8100.496.0

– 0.23+ 0.15+ 0.03 – 0.26

0.71.01.52.0

81.469.851.737.9

– 1.78 – 3.13 – 5.74 – 8.43

90.279.862.347.7

– 0.90 – 1.96 – 4.12 – 6.44

3.05.0

10.0

21.59.02.4

– 13.5 – 20.9 – 32.3

28.512.5

3.4

– 10.9 – 18.1 – 29.3

NOTE An explanation of the method divergence of the instrument reading (see 2.3.15) isgiven at Appendix B, and factors affecting the statement of accuracy are explained at

Appendix C.

x --- q+


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Figure 21 — Permissible deviations of the transmission coefficient


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Symbol Interpretation

Parallel to the plane of projection of theview in which the symbol is used

Perpendicular to the plane ofprojection of the view in which thesymbol is used

Crossed in two slant directions relativeto the plane of projection of the view inwhich the symbol is used

Multi-directional

Approximately circular relative to thecentre of the surface to which thesymbol is applied

Approximately radial relative tothe centre of the surface to which

the symbol is applied

NOTE Should it be necessary to specify a direction of lay not clearly defined by these symbols, this may be done by a suitable noteon the drawing.

Figure 22 — Symbols for the direction of lay


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Appendix A Parameter values

Values are normally determined as mean results from the measurement of several sampling lengths taken

consecutively along the profile. These may be determined graphically in accordance with clause 4 or bydirect reading instruments. The direction in which the measurement is made should in general beapproximately at right angles to the lay if the surface texture has a directional quality (see Figure 22). Theparameter values specified should be selected from the ranges of preferred values given in Table 6,Table 7 and Table 8.

Table 6 — Preferred nominal values forarithmetical mean deviation of the profile (Ra)

Table 7 — Preferred nominal values forten point height of irregularities (Rz),and maximum height of the profile (Ry)

4m 4in

400200100

16 0008 0004 000

502512.5

2 0001 000500

6.33.21.6

25012563

0.80.40.2

3216

8

0.10.050.0250.0125

4210.5

4m 4in 4m 4in

1 600 64 000 3.2 125

800 32 000 1.6 63

400 16 000 0.8 32

200 8 000 0.4 16

100 4 000 0.2 8

50 2 000 0.1 4

25 1 000 0.05 2

12.5 500 0.025 1

6.3 250


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Table 8 — Preferred nominal values for meanspacing of profile irregularities (S m), and

mean spacing of local peaks of the profile (S )

NOTE The values given in Table 6, Table 7 and Table 8 are expressed as “preferred” in order to discourage unnecessary variationof the values expressed on drawings. It should be realized that in some circumstances, other values may be specified.

Appendix B Method divergence of instrument readingB.1 General

When two methods of measurement which are both standardized give results which are nominally but notprecisely equal, the numerical difference is referred to as “method divergence”.

Thus the two methods referred to in this standard for selecting the texture to be measured (by samplinglength and cut-off), although deemed to be acceptable equivalents of each other, treat the profile in differentways that may lead to slightly different numerical evaluations.

B.2 Effective cut-off

Reference to Figure 20 will show that transition occurs gradually from the fully transmitting to thesubstantially rejecting part of the standardized characteristic. From consideration of filter theory,experimental results and various practices, the effective cut-off has now become rated, by acceptedconvention, at the wavelength for which there is 75 % of the full transmission of a pure sinusoidalwaveform, with a tolerance permitting a range from 70 % to 80 %. This means that for a sine wave havinga wavelength equal to the sampling length, an instrument calibrated in the usual way for a sine waveoccurring on the flat part of the characteristic would indicate an Ra value equal to 75 % of the valueobtained from the profile graph by planimetry. For short wavelengths and most machined surfaces thedivergence is usually small, and this is generally the case for random profiles. It is usual to accept theinstrument reading as the operative basis for grading workpieces in the workshop, and to avoid extremedivergences by use of a sufficient cut-off.

B.3 Range of method divergence

The typical and extremes of method divergence found by comparing metered Ra values with the valuescomputed from the least squares mean line are shown in Table 9.

Table 9 — Comparison of Ra values obtained bygraphical and instrumental means

mm in mm in

12.5 0.500 0.2 0.008

6.3 0.250 0.1 0.004

3.2 0.125 0.05 0.002

1.6 0.062 0.025 0.001

0.8 0.032 0.0125 0.0005

0.4 0.016 0.006 0.0003

Type ofsurface

Cut-off Ra from least squaresmean line of graph

Ra frominstrument

Methoddivergence

mm 4m 4m %

Milled 2.5 0.80 0.86 + 7

Milled 2.5 2.66 2.67 0

End-milled 2.5 0.90 0.81 – 11

Turned 2.5 6.74 6.86 + 2

Turned 2.5 0.83 0.81 – 2

Ground 0.8 0.71 0.66 – 8

Ground 0.8 0.48 0.53 + 9

Lapped 0.8 0.02 0.02 0NOTE Mean method divergence for 2.5 mm cut-off: 0 %; standard deviation: 4 %.

Mean method divergence for 0.8 mm cut-off: 1 %; standard deviation: 7 %.

These mean method divergences and standard deviations were obtained from measurementson 22 surfaces.


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B.4 Electrical mean line

A further point concerns the shape of the self-determined electrical mean line found by the filter. This is

generally not a straight line but an undulating one which weaves its way through the profile as shownin Figure 23. The undulations account for the method divergence. Equations and computing tables for theelectrical mean line found by the standard filter are available from manufacturers, and these can serve asa basis for determining precisely, by computation from digitized profile records, the errors of instrumentscomplying with this standard.

In practice, however, it is generally only in the case of precise instrument calibration that it is necessaryto take the details of filter behaviour fully into account.

Appendix C Factors affecting the statement of accuracy

C.1 General

Many instruments are responsive to a single variable (e.g. length, angle, electric current) and have fewsources of error. These errors can be expressed simply, and it is a normal expectation that this should bedone.

Surface instruments are more complicated, for the quantity to be measured has generally to be derivedfrom a fluctuating signal representing the profile of a sample of the surface. Errors can arise from different

sources having quite different error laws, and the total error does not lend itself to expression in a simpleyet meaningful way.

C.2 Calibration

Workshop calibration is generally effected with the aid of instrument calibration specimens complying withBS 6393. Ideally, in addition to being marked with substantially its full value, assuming negligibleinstrument losses, each specimen should be accompanied by a statement of the reading that should beobtained from it by an instrument having given stylus dimensions and for each mean transmissioncharacteristic. This is a refinement that has still to be treated in a formal way.

The overall amplification is left as an adjustment for the user to make by means of one or morepotentiometers which have to be set in conjunction with an instrument calibration specimen or with acalibrated test specimen. The attainable accuracy therefore starts with the calibration specimen and theuser’s skill in allowing for its characteristics and in securing with it the best overall adjustment of the

instrument. It is envisaged that the use of more than one test specimen will become normal practice.

Figure 23 — Centre arithmetical mean lines (A) and electrical mean lines (B)


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C.3 Instrument error

If the instrument is set up to give the correct reading for the calibration specimen allowing for all relevant

characteristics, the basic instrument error at this point in its range of operation will be that of thespecimen, often assumed to be zero. However, the working range of the instrument may be considerable,extending vertically from around 0.025 4m to several micrometres, and horizontally from around 2 4m toseveral millimetres. Even if there is, after initial adjustment, no error in the calibrated region of the range,there may be errors in other regions unless all parts of the instrument function perfectly. These errorswould be revealed by other precisely calibrated specimens. It is to the expression of the error throughoutthe range, relative to the setting-up point, that 7.1 refers.

Instrument errors can arise from the condition of the stylus and datum device, various electronic sources,and the errors inherent in the output behaviour and reading.

Assuming that the stylus is in good order, the radius of its tip may influence the indication. Differencesbetween a 2 4m and a 10 4m tip, while negligible for many surfaces, may be quite significant for others,and especially for very fine ones. It does not follow that the blunter tip will always give the lower reading,

for on some surfaces (e.g. turned surfaces with sharp peaks) its own radius added to the radii of the peaksmay more than compensate for the losses in the valleys.

Instrument errors, apart from an error in overall amplification, may include errors due to electrical andmechanical noise, to residual non-linearity, to ratio errors in range switching and, where applicable, toerrors in the transmission characteristic.

C.4 Noise

The effect of noise depends mainly on its proportion to the value of the signal. For most purposes, the noisecan be taken as the reading given by a well-polished optical flat, free from scratches. When the proportionof noise in the reading is small, say less than one-third, the noise can be neglected. When the two are equal(as can happen with smooth surfaces) it can account for 70 % to 80 % of the reading. When it is twice asgreat as the signal, it becomes dominant. The noise cannot be allowed for by simple subtraction, for if thetwo signals have values of en and es, the nearest simple assessment of their combination will be givenby Æ . The actual value of the noise, for a given instrument, may vary over a wide range accordingto the rigidity of the set-up and the amount of vibration in the instrument and its environment.

C.5 Optimum adjustment

The reference in 7.1 to optimum adjustment and use may call for qualification. If an instrument wererequired to give maximum accuracy over a small range of operation, its adjustment would naturally beoptimized for that range. On the other hand, if the instrument were required to perform as well as possibleover a wide range without readjustment, the adjustment would be optimized so as to minimize the residualerrors throughout the range.

The concept of optimum use will refer to environmental conditions, rigidity of workpiece mounting, and thefact that readings near the top of the scale will generally be less subject to error than those near the bottom.

C.6 Statement of accuracy

If it is accepted that a useful statement of accuracy should neither under-rate nor over-rate the capability

of an instrument, it becomes clear that no single figure can be expected to give fair information. On theother hand, a specification attempting to cover all possible combinations would become impossibly complexand again meaningless.

en

2 es

2+( )


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Publications referred to

BS 308, Engineering drawing practice.

BS 308-2, Recommendations for dimensioning and tolerancing of size.

BS 1134, Method for the assessment of surface texture1)

.BS 1134-2, General information and guidance.

BS 6393, Specification for calibration of stylus instruments.

ISO 468, Surface roughness — Parameters, their values and general rules for specifying requirements.

ISO 3274, Instruments for the measurement of surface roughness by the profile method — Contact (stylus)instruments of consecutive profile transformation — Contact profile meters, system M.

ISO 4287, Surface roughness — Terminology.

ISO 4287-1, Surface and its parameters1).

ISO 4287-2, Measurement of surface roughness parameters1).

1) Referred to in the foreword only.


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