application guide manual for surfcom series...

DT00300-R001-E7

APPLICATION GUIDE MANUAL FOR

SURFCOM SERIES SURFACE ROUGHNESS & WAVINESS PARAMETERS

TOKYO SEIMITSU CO., LTD.

TOKYO, JAPAN

No part of this document shall be reproduced in any form or by any electronic or mechanical

means including information storage and retrieval system without permission in writing from us,

Tokyo Seimitsu Co., Ltd., Tokyo, Japan.

- i -

PREFACE

You may have a few acquaintance with the terminologies and symbols which are used in the

messages and the output parameters of surface texture measuring instrument.

The explanations about those definition and usage, parameter symbols, name and the way of

calculation of surface roughness and waviness are mentioned in this manual.

Refer to the separate user's manual for handling of the measuring instruments.

Applicable range

This manual applies to the following models of Surfcom.

Surfcom 130A

Surfcom 480A

Surfcom 1400 series

Surfcom 1500 series

Surfcom 1800 series

Surfcom 1900 series

Surfcom 2800 series

Surfcom 2900 series

Surfcom 3000 series

Please be noted that the symbols of parameters and the calculation method may vary in the other

models.

CAUTION

The symbols, terminologies or their meaning of the surface parameters are sometimes varied

according to the national standard on which their definitions are based.

When nominal values of the surface parameter are specified on a drawing, please check carefully

the referenced national standard. Then, select the value of cutoff, traversing length and surface

parameter which are correct and suitable to the referenced standard before starting the

measurement.

- ii -

- CONTENTS -

Page

1 STANDARD OF SURFACE ROUGHNESS AND WAVINESS ............................. 1-1

Surface Roughness .............................................................................................. 1-1

Roughness and Waviness Parameters ................................................................ 1-1

Function and Parameters of Surface .................................................................... 1-2

2 SAMPLED CURVES ............................................................................................ 2-1

Profile Curve, Primary Profile (P) ......................................................................... 2-1

Mean Line ....................................................................................................... 2-1

Roughness Profile (R) .......................................................................................... 2-1

Mean Line ....................................................................................................... 2-1

Center Line ...................................................................................................... 2-1

Waviness Profile/Filtered Waviness Curve (W, WC ) ............................................... 2-2

Filtered Center Line Waviness Curve (WCC, W-profile) ........................................ 2-2

Rolling Circle Waviness Curve (WE )........................................................................ 2-3

Rolling Circle Center Line Waviness Curve (WEC )................................................... 2-3

DIN4776 Special Roughness Curve (Rg2 )............................................................... 2-4

Tilt Correction / Reference Line ............................................................................ 2-5

Reference Profile/Datum Line ......................................................................... 2-5

Unshifted Original Profile ................................................................................. 2-5

Least Squares Straight Mean Line .................................................................. 2-5

Least Squares Polynominal Mean Line ........................................................... 2-5

B-Spline Mean Line ......................................................................................... 2-5

First Half Correction ........................................................................................ 2-6

Latter Half Correction ...................................................................................... 2-6

Beginning and End Port Connected Straight Line ........................................... 2-6

- iii -

Page

3 CUTOFF VALUE .................................................................................................. 3-1

An Introduction to "Cutoff" Value .......................................................................... 3-1

2RC Filter ............................................................................................................. 3-1

Phase Correct Filter ............................................................................................. 3-2

2RC Phase Correct Filter ................................................................................ 3-3

Gaussian Phase Correct Filter ........................................................................ 3-3

Short wavelength cutoff value (λs) and cutoff ratio .......................................... 3-5

Necessity of short wavelength cutoff (λs filter) ................................................ 3-5

4 ROUGHNESS ANALYSIS TERMINOLOGY AND DEFINITION .......................... 4-1

Sampling Length (L) ............................................................................................. 4-1

Evaluation Length (Ln) ......................................................................................... 4-1

Measuring Length (Lm) ........................................................................................ 4-1

Pre-travel Length (Lpe) ........................................................................................ 4-1

Post-travel Length (Lpo) ....................................................................................... 4-1

Traversing Length (Lt) .......................................................................................... 4-1

Horizontal Magnification in Recording Chart (Vh) ................................................ 4-1

Vertical Magnification in Recording Chart (Vv) ..................................................... 4-2

Vertical Magnification Direction (z) ....................................................................... 4-2

Profile Peak ........................................................................................................... 4-2

Profile Valley .......................................................................................................... 4-2

Top of Profile Peak ................................................................................................ 4-2

Bottom of Profile Valley.......................................................................................... 4-2

Line of Profile Peaks .............................................................................................. 4-2

Line of Profile Valleys ............................................................................................ 4-2

Cutting Level (c)..................................................................................................... 4-2

Local Peak of Profile .............................................................................................. 4-2

Local Valley of Profile ............................................................................................ 4-2

Top of Local Peak of Profile................................................................................... 4-2

Bottom of Local Valley of Profile ............................................................................ 4-3

- iv -

Page

5 PARAMETERS FOR AMPLITUDE ...................................................................... 5-1

Arithmetic Average/Mean Line Average Value (Ra,Ramax,WCA,Wa,WEA,Pa) ..... 5-1

Root-Mean-Square Value (Rq,Rqmax,RMS,Wq,Pq) ............................................ 5-2

Maximum Height (Ry,Rymax,Rmax,Rt,Rz,Pt,W,Wt,WCM,WEM,Wz).......................... 5-3 Ten-point Height of Irregularities［JIS, ISO］ (Rz,RzISO,RzJ ) ........................... 5-4

Base Roughness Depth/Averaged Middle Peak-To-Valley Height (R3z) ............... 5-5

Mean Height of Elements (Rc,Rcmax,Pc,Wc) ...................................................... 5-5

Maximum Profile Peak Height (Rp,Rpmax,Rpm,Rp5,Pp,Wp) .............................. 5-6

Maximum Profile Valley Depth (Rv,Rvmax,Rvm,Rm5,Pv,Wv) ............................. 5-7

Height of Step (AVH, Hmax, Hmin, AREA) .......................................................... 5-8

FPD waviness (Wfpd) ........................................................................................... 5-9

6 PARAMETERS FOR WAVELENGTH AND SLOPE ............................................ 6-1

Mean Spacing of Profile/Average Spacing of Roughness Peaks

(Sm,Smmax,RSm,PSm,WSm) ......... 6-1

Peak Count (Pc,PPI,HSC) ................................................................................... 6-2

Mean Spacing of Local Peaks of the Profile (S,Smax) ......................................... 6-3

Arithmetical Mean Slope of Profile/Average Absolute Slope (∆a) ........................ 6-4

Root-Mean-Square Slope of Profile (∆q,P∆q,R∆q,W∆q) ...................................... 6-4

Average Wavelength of Profile (λa) ..................................................................... 6-5

Root-Mean-Square Wavelength of Profile (λq) .................................................... 6-5

Average Slope Angle (TILT A) ............................................................................... 6-6

Profile Length Ratio (Lr,SL).................................................................................... 6-7

Power Graph/Power Spectrum .............................................................................. 6-8

- v -

Page

7 PARAMETERS FOR BEARING AREA CURVE .................................................... 7-1

Profile Bearing Length Ratio/

Profile Bearing Ratio (tp), Material Ratio of the Profile (tp,mr,Rmr,Pmr,Wmr) .. 7-1

Bearing Area Curve (BAC)/Abbott-Firestone Curve/

Material Ratio Curve(MRC)/Curve of the Profile Bearing Length Ratio(BC) ......... 7-3

Method of Cut Level ........................................................................................ 7-3

(1) % ...................................................................................................... 7-3

(2) µm .................................................................................................... 7-3

Method of Length Reference ........................................................................... 7-4

(1) Evaluation Length Method ................................................................ 7-4

(2) µm Display Reference Length Method ............................................. 7-4

(3) % Display Reference Length Method ............................................... 7-4

Bearing Length Ratio 2/Profile Bearing Ratio (tp2,Rmr2,Pmr2,Wmr2) ................. 7-5

Difference of Bearing Length Ratio (tp(Cn-C0), Rδmr) ......................................... 7-6

Profile Section Level Separation Rδc/Height of Plateau (Hp) ............................ 7-7

ISO13565 (DIN4776) Special Bearing-Area Curve Parameters............................. 7-8

(1) Bearing Length Ratio 1 - Initial Wear Ratio - (Mr1) .................................... 7-8

(2) Bearing Length Ratio 2 - Oil retention Bearing Ratio (Mr2) ........................ 7-8

(3) The Reduced Peak Height (Rpk) ............................................................... 7-8

(4) The Reduced Valley Depth (Rvk) ............................................................... 7-8

(5) Core Roughness Depth (Rk) ...................................................................... 7-8

(6) Oil Retention Volume (VO) .......................................................................... 7-9

(7) Reduced Valley Depth Ratio (K) ................................................................ 7-9

8 PARAMETERS FOR AMPLITUDE DISTRIBUTION ............................................ 8-1

Amplitude Density Function/Amplitude Distribution Curve/

Distribution of Profile Departure Density (ADC, ADF) ..................... 8-1

Skewness (Rsk,Sk) .............................................................................................. 8-2

Kurtosis (Rku,Kurt) ............................................................................................... 8-3

9 PARAMETER FOR MOTIF .................................................................................. 9-1

What is the motif calculation? .............................................................................. 9-1

Motifs upper limit length ....................................................................................... 9-1

What is the motif? ................................................................................................ 9-2

How to calculate the motifs .................................................................................. 9-2

- vi -

Page

10 SELECTION & EVALUATION METHOD OF CUTOFF VALUE SAMPLING LENGTH ......... 10-1

Pursuant to JIS82 ................................................................................................ 10-1

(1) Cutoff Value and Measuring Length for Ra (Ra75).................................... 10-1

(2) Reference Length for Rmax,Rz ................................................................. 10-1

(3) Evaluation Method of Measured Value ...................................................... 10-1

Pursuant to JIS94 ................................................................................................ 10-2

(1) Cutoff Value, Sampling Length and Evaluation Length for Ra, Ry and Rz...................................... 10-2

(2) Cutoff Value, Sampling Length and Evaluation Length for Sm and S ............................................. 10-2

(3) Evaluation Method of Measured Value (ISO4288)..................................... 10-2

Pursuant to ISO84/BS/ANSI ................................................................................ 10-3

(1) Cutoff Value, Sampling Length and Evaluation Length for

Random Waveform Curve without Periodicity ....................... 10-3

(2) Cutoff Value, Sampling Length and Evaluation Length for Periodic Curve .................................... 10-3

(3) Evaluation Method of Measured Value .................................................... 10-3

In conformity to the former DIN............................................................................ 10-4

(1) Cutoff Value, Sampling Length and Evaluation Length for Random Waveform Curve without Periodicity......................... 10-4

(2) Cutoff Value, Sampling Length and Evaluation Length for Periodic Curve...................................... 10-4

(3) Evaluation Method of Measured Value .................................................... 10-4

Pursuant to ISO97/ASME/DIN ............................................................................. 10-5

(1) Cutoff Value, Sampling Length and Evaluation Length for Random Waveform Curve without Periodicity......................... 10-5

(2) Cutoff Value, Sampling Length and Evaluation Length for Periodic Curve...................................... 10-5

(3) Evaluation Method of Measured Value (ISO4288:1996) .......................... 10-6

Exception of Sampling Length and Evaluation Length: In case of unavailable measurement with standard value ..... 10-7

(1) Unavailable to get Standard Value of Evaluation Length ......................... 10-7

(2) Unavailable to get Multiple of Cutoff Value for Evaluation Length ............ 10-7

(3) Smaller Workpiece Surface Length than the added Length of Cutoff Value and Preparatory Length (Lt<λc+Lpe+Lpo) ........ 10-7

- vii -

Page 11 Average value process of the parameter ............................................... 11-1

Average value process.................................................................................... 11-1

MAX rule ........................................................................................................... 11-1

16% rule............................................................................................................ 11-2

Minimum value.................................................................................................. 11-3

12 PARAMETER LIST.............................................................................................. 12-1

Roughness and Waviness Parameters with SURFCOM ...................................... 12-1

(1) Parameters related to Amplitude ................................................................ 12-1

(2) Parameters related to Wavelength & Slope ............................................. 12-5

(3) Parameters related to Bearing Ratio Curve ............................................. 12-7

(4) Parameters related to Amplitude Distribution ........................................... 12-8

Annex

A. JIS 2001.……………………………………………………………………………… A-1

B. Spline correction …………………………………………………………………….. B-1

- viii -

1-1

1 STANDARD OF SURFACE ROUGHNESS AND WAVINESS Surface Roughness

Surface roughness is defined it as follows: "Roughness is a surface irregularities that occurs at small intervals and is the sensory base on which we recognize something as 'smooth' or 'rough'. For machine surface, it shows irregularities caused by tool edges and abrasive grains." In general, a surface is three-dimensional and composed of complex forms. Besides, it contains so much information that a parameter or two are not enough to enable complete evaluation of a surface. For example, see Fig. 1.1. For example, see Fig.1.1. When the maximum height Rmax of Curve A and that of Curve B are H1 and H2 respectively, even the condition H1=H2 could not always assure that the characteristics of both surfaces are identical. Compared with B surface, A surface has superior lubricant capability and agreeable touching and it is hard to be worn away.

A

B

H 1

H 2

Fig. 1.1

Therefore, to evaluate surface roughness and waviness form practical viewpoints, the optimal determination of parameters for a purpose must be made.

Roughness and Waviness Parameters

On a machine drawing, it is required to specify dimensions, angles and the degree of the surface irregularities of a material with numeric values. Without converting them into numeric values, the material is not controlled quantitatively and besides the machine drawing is useless as measured for evaluating the quality upon business. For roughness and waviness, an evaluation method with the dimensions in the height direction as measure is the standard of roughness. And wavelength of peak and valley and distinctive features of waveform may also be the standard. This is parameters of roughness and waviness. Except for the amplitude to height direction which is generally used, there are following roughness and waviness parameters which are connected to wavelength and slope angle of roughness, bearing curve to indicate lubricant capability and amplitude distribution, etc.

1-2

Functions and Parameters of Surface Mechanical performance is sometimes greatly changed by the conditions of surface; some workpieces produce functional problems in both cases when the surface roughness is too large or too small. Evaluation parameters are different when the function to be objected is different. The following table shows the roughness parameters that are considered to be in correlation with the functions required for the surface of workpiece as reference. Please bear in mind that the relations described below are merely physical estimations and they are not based on anything definite.

Function Description Relevant workpiece Evaluation Parameter

Sealing Tightness Leakage from gap between contact surfaces

Valve, Cock, Cylinder Ra, Rp, Sm, Rpk

Abrasion resistance

Force to be caught by roughness peak

Clutch, Knock pin ∆a ,∆q, Ry, Rz, Rp

Abrasion Loads concentrated on a convex upon sliding

Shaft, Bearing Cylinder hole, Piston ring, Guide surface

Rp, Bearing length ratio curve, tp, Rpk, Rsk

Burning, Lubricating ability

Deposit lubricating oil in valleys Plateau honing surface of cylinder block bore

Rv, Bearing length ratio curve,tp, Rvk, Rδc, Hp, Mr2, Vo, K

Adhesion Wringing Optimum Blockgauge PC Board Flatness, Ry, Rmax Bonding Form for bonding agent, Uneasiness

to peel off Bonding surface, Plating foundation

Rz, Ry, ∆a, ∆q, Lr

Peel ability Ability to remove molding from mold Die Rz,Ry,∆a,∆q,Lr Appearance, Gloss

Scattering in reflection of light, Glaring, High quality feeling

Plating surface Rainbow surface Pattern finish Mirror surface

∆q, Rq, Ra, WCM, WCA, Power graph, Rku, Rpk

Glossy surface (Brightness of coated surface)

Cold-rolled steel for car WCA, Ra, Pc, PPI

Optical performance

Turbulence of beam reflection, Scattering

Mirror, Lens, Prism ∆q, Rq, Ra

Corrosion resistance, Insulation ability

Easiness to be wet due to capability Weatherproof parts, Electric parts

Ra, ∆a, ∆q, Rv, Mr2

Fatigue strength Concentration of stress due to the form of notch

Crank shaft Rmax, Rv, Rvk

Electromagnetic characteristic

Disturbance of skin effect by flows and roughness

Waveguide, Magnetic core

Ra, Ry, Rz

Electric resistance of contact surface, Heat resistance

Electric resistance due to contact surface, heat transfer

Relay, Switch Connector, Radiator

tp, Mrl, Ra, Lr

Rigidity of junction surface

Deflection due to excessively small conjunction surface

Bolt clamping portion Parallelism, WEM, tp, Rz, Rp, Rpk

Accuracy of dimensional measurement

Measurement error due to roughness, deformation of roughness due to meas. pressure

Micrometer, Air micrometer Calipers

Parallelism, Ry, Rp, Rpk

Texture The touch Knurling tool, Satin surface

Rp, ∆a, ∆q, Sm, Pc, Power graph

Printing quality Fitting of ink and paper Printing paper Ra, Rv, Rvk, Sm, Pc, Power graph

Noise, Vibration Vibration of rolling surface at high speed

Gear, Roller bearing, Guide surface

Rp, Rmax, WEM, Sm, Power graph

2-1

2 SAMPLE CURVES Profile Curve, Primary Profile (P)

A contour appears on a cut end, when a surface to be measured has been cut with a plane which is perpendicular to that surface. (JIS B0601-1994,1982) This instrument records raw profile curves which are not made tilt correction. In the figure of below, the Z-axis direction and X-axis direction are called as vertical direction and horizontal direction respectively.

Mean line In a profile curve, the mean line is the same as the geometric profile of the measured surface and is the curve that the sum of squares of the deflection from the profile curve becomes minimum(ISO4287/1-1984). This is normally a straight line because the measurement is made on a plane surface, but there is a case that the mean line becomes a circle or specified curve on the curved surface or designated contour. In this instrument, the mean line is shown as X-axis which was made the "Straight line correction" to the profile curve. (Refer to Tilt-correction/reference line)

Profile curve

Mean line of profile curve(Least square mean line)

Mean line of phase correct filter(Filtered waviness profile)

Z

X

Roughness Profile (R)

This is a curve which has been cut off any longer surface waviness component than a wavelength of the specified cutoff value λc(mm) from the profile curve by means of high-pass filter. (Refer to Chapter 3 for the filter.)

Mean line The mean line in roughness profile passed the phase correct high-pass filter is the "Filtered waviness curve" by means of the same phase correct type filter. The roughness profile is the one which was removed filtered waviness curve from the profile curve, and the mean line at this time becomes a straight line to become Z=0 of the roughness profile.

Center line The center line is the straight line that when the straight line parallel to the mean line of a roughness curve passed 2RC filter is drawn, the areas surrounded by this straight line and roughness curve on both sides of the straight line are equal to each other.

Mean line (phase correct)Center line (2RC)

Roughness profile

Z

X

Note 1) The difference of selection to choose a mean line or a center line comes from the

type of filter in its standard, but the both contents are the same.

2-2

Waviness Profile/Filtered Waviness Curve (W, Wc) This is the curve obtained by removing the surface roughness components with short wavelength is called filtered waviness curve. A 2RC low-pass filter of -12db/oct Note 1) attenuation is employed. (JIS B0610-1987) In the filtered waviness curve for calculating a mean line of roughness profile by means of phase correct filter, a phase correct type low-pass filter is employed. (JIS B0601-1994)

Mean line of profile curve(Least square mean line)

Mean line (phase correct)Filtered waviness curveZ

X

Filtered Center Line Waviness Curve (Wcc, W-profile)

This is the curve obtained by removing the short and long wavelength components from a profile curve. 2RC high-pass filter of -12db/oct attenuation is employed. (JIS B0610-1987, DIN4774)

X

Filtered center linewaviness curve

Z Mean line (phase correct)Center line (2RC)

Note 1) “dB” is called as “decibel” and it is explained as follows.

When the damping factor of input and output signal is set to “A” (output amplitude /

input amplitude), it is shown as follows.

Transfer factor (damping factor) dB = 20・log10A

If the damping factor is assumed as A = 1 / 4, it becomes “–12dB”. “oct” is called as

“octave” and it shows two times of a wavelength.

Therefore “–12dB / oct” shows that when the wavelength becomes 2 times, the

amplitude becomes 1 / 4 times.

2-3

Rolling Circle Waviness Curve (WE) This is the locus of the circle center with a specified radius that traces a profile curve. This circle is called as Rolling Circle and its radius corresponds to that of the stylus tip. Namely, a profile curve obtained by measuring with a stylus tip of 8mmR for waviness measurement is the rolling circle waviness curve. (JIS B0610-1987)

Profile curve

Rolling circlewaviness curveZ

X

Rolling Circle Center Line Waviness Curve (WEC)

This is a curve obtained by removing the long wavelength components from the rolling circle waviness curve. A 2RC high-pass filter of 12 db/oct is employed. (JIS B0601-1987)

Rolling circle center line waviness curveZ

X

2-4

ISO13565 (DIN4776) Special Roughness Curve (Rg2) In the standard of ISO13565-1 (and DIN4776-1990), special roughness curve Rg2 which is

removed the waviness is employed. (“Rg2” is the temporary sign of this machine.)

As this machine is determined to calculate the bearing area curve in accordance with

“ISO13565 or DIN4776”, it is calculated in accordance with the standard of ISO13565 by the

following procedure. Step ① Obtain a phase compensation filtered waviness curve (Mean line) Wg from the profile

curve P by using Gaussian phase correct filter.

0

5.0

2.5µm

Step ② Connect the profile curve, P with the higher waviness positions of the phase correct

filtered waviness curve, Wg obtained in Step ①, and create a curve in which valleys are removed.

0

5.0

2.5µm

Step③ Apply the curve obtained by Step ② to the phase correct filter in Step ① to obtain a

reference mean curve, Wg2.

0

5.0

2.5µm

Step④ Subtract the reference mean curve, Wg2 in Step ③ from the profile curve and obtain

the special roughness curve, Rg2.

0

5.0

µm

2.5

2-5

Tilt Correction / Reference Line Reference Profile/Datum Line:

This is a line to become reference of a profile curve, which is selected from the following methods of determining the reference.

Unshifted Original Profile: This is an actual profile curve without shifting nor correction. This profile is used for measurement of height and tilting angle from the reference line being set at the beginning.

L t / 2 L t / 2

Measuring length Lt

Original profile curve

Least squares straight mean line:

This is a mean line to be used in a profile curve from the plane surface profile. This method is based on the standard for roughness measurement.

Correction curveOriginal profile curve

Measuring length Lt

L t / 2 L t / 2Straight line correction curve

Least Squares Polynomial Mean Line:

When a nominal profile is a curved surfaces of a circle and an involute function, etc., the evaluation must be made by using the reference line corresponding to the nominal profile. In this instrument, it is approximated by a curve of fourth degree polynomial expression in the least square method.


Measuring length Lt

Curve correction curve

Curve correction curve

B-Spline mean line:

In case of an existence of a sudden curve changing point in the nominal profile, it uses a method which is approximated by B-Spline mean line as its standard. The superiority compared with the least squares polynomial mean line is depend on the profile, so that apply the one which the curved line after correction is closer to the straight line for the actual use.

2-6

First Half Correction (Before half least squares mean line): This is a method to make correction of the least square mean line in the left portion (first half) of the step profile. This is used for measurement of the long step amount in the first half portion.


Measuring length Lt

L t / 2 L t / 2

Correction range

Before half

Latter Half Correction (Latter half least squares mean line):

This is a method to make correction of the least square mean line in the right portion (latter half) of the step profile. This is used for measurement of the long step amount in the latter half portion.

Correction range

Originall profile curve

Latter halt

Measuring length LtL t / 2 L t / 2

Beginning and end port connected straight line:

This is a method to make a reference line which is a straight line to connect the right and left ends of the measurement length in order to obtain the height of a projection in the sate like a belt on a plane surface board or the depth of a depressed portion.


Measuring length Lt

End pointStart point

Beginning and end port

In case of an application of any one of the above correction methods, calculations for all the parameters are available from the profile curve in connected with the reference line. But the straight line correction only is properly based on the roughness measurement standard.

3-1

3 CUTTOFF VALUE An Introduction to "Cutoff" Value

Irregularities of an object surface generally show complex patterns as shown in the figure ofA. Take a close look at the figure, then you will find that it is consisted of a component with a fine short cycle of Fig. B and a component with a gradual-slope long cycle of Fig. C, and they are overlapped. Cutoff is to separate Profile Pattern A into Roughness B and Waviness C and sample out only the necessary component. Reference wavelength that divides the pattern into "Roughness" and "Waviness" components is called as "Cutoff value λc(mm)". In order to make the cutoff, a Filter (Wavelength filter) is employed.

B

A

C

2RC Filter

This is the filter defined in JIS B0601-1982, JIS B0601-1987, ANSI B46.1-1985 and ISO3274-1976. A two-RC filter consists of two R-C circuits with an equal time constant in series connection, and it provides with amplitude transmission characteristics as follows.

= 1+

a2 a0

1 λ2

3× (λc7 5)2

Where a2 : Amplitude after cutoff of relevant wavelength components a0 : Original amplitude of relevant wavelength components λ : Relevant wavelength (mm) λc75 : Cutoff value (mm) When λ=λc75, the transmission rate is a2/a0 = 75%.

In this case, the power of 2RC filter waviness curve (Square mean value(RMS)2) which has the same cutoff value and the value which was added the power of this curve are nearly the same as the power of the profile curve. The changing ratio of the attenuation rate in the attenuation area is -12db/oct. But a waveform has a characteristic to change the phase similar to the change of the amplitude transmission rate caused by a change of the wavelength. This should be noted that it causes a distortion of the waveform to the roughness profile. There is a case that an outlook of the waveform is largely differ from the roughness parameter nor the bearing ratio curve is drastically changed when they are compared with the result obtained from the profile curve.

3-2

Phase Correct Filter By passing a phase correct filter, the phase shift which occurs in the transmission characteristic can be solved. Following figures show the phase shift which occurs when a rectangular wave is penetrated each of a filter with phase correction and a filter with non-phase correction (2RC filter).

Measuring profile (without filter)

Example of Roughness Example of Roughness Profile in Case of 2RC Filter Profile in Case of Phase Correct Filter

P

R

3-3

There are following two types of the characteristic in the phase correct filter: 2RC Phase Correct Filter

This has the same cutoff characteristic as the 2RC filter and it is a filter without phase shift. The transmission ratio at λ = λc is a2 / a0 = 75%.

Gaussian Phase Correct Filter This will be adopted hereafter as an international standard of a filter which is pursuant to JIS B0601-1994, DIN4777-1990 and ISO11562-1996. The parameter values are determined according to the procedure as follows:- (1) As weighed function for the normal probability density (Gauss Distribution) function, the

curve which was made convolution integral to the profile curve is made as the phase correct filtered waviness curve Wg. The formula of the weight function becomes as follows;

1 S ( x ) = eκ α × λc X 2 κ = − π ( ) α × λc

Where X : Distance from the center of the weight function λc : Cutoff value of the filter α : 0.4697

The transmission characteristic of the Phase Correct Filtered Waviness Profile (a1 / a0) is shown as follows;

= e

−π( ) 2 α× λ c λ

a1 a0

Where a0 : Amplitude of a sine profile curve before the filter a1 : Amplitude of a sine curve on waviness curve λ : Wavelength of a sine curve

S(χ)•λc

-1 χ / λc 1

Weight Function of Gaussian Filter

1

3-4

(2) Subtract the phase correct filtered waviness profile from the profile curve. Then the roughness profile (Rg) can be obtained. The transmission characteristic of the roughness profile (a2 / a0) becomes as follows;

= 1 −a2a0

a1a0

Phase correct filter 2RC filter

Ampl

itude

Tra

nsm

issi

on R

atio

(%)

Wavelength / Cutoff value

Transmission characteristics of roughness curve with Gaussian phase correct filter and

2RC filter

(3) The transmission ratio at λ = λc is a2 / a0 = 50% . Therefore, the profile curve can be restored by adding the phase correct filtered waviness

curves of the same cutoff value.

3-5

Short wavelength cutoff value(λs) and cutoff ratio In the Gaussian phase correct roughness curve and profile curve, short wave cutoff filter can be used in order to remove the influence of microwave area error caused by the stylus tip radius. The cutoff value is called as λs.

λs filter is determined as follows. (1) Gaussian phase correct filter is used as a filter. (2) Transmission characteristic is followed to the transmission characteristic a1 / a0 of above

Gaussian phase correct filtered waviness curve. (3) Short wavelength cutoff value λs is selected from the following numeric values. 0.25, 0.8, 2.5, 8, 25, 80µm (4) Cutoff ratio means the ratio of long wavelength cutoff value λc against short wavelength

cutoff value λs of its provided transmission zone (λc/λs), which standard values are 30, 100 and 300.

- Note - Depending on the instrument, there are types which is necessary to set λs filter before measurement and which can be calculated by changing the value of λs filter at the time of being executed the recalculation. With the type of being required setting before measurement, recalculation is executed with λs filter value which was set before measurement even the value was changed at recalculation. Please check with the manual coming together with the machine for which function your instrument has.

Relations between long wavelength cutoff and stylus tip radius, and cutoff ratio

In case of not being specified, the relations of cutoff ratio against the standard values of stylus tip radius Rtip and the standard values of long and short wavelengths cutoff are recommended to use as shown in the table of below. (ISO 3274-1996)

Table 3.1 Stylus tip radius and Cutoff

λc(mm) λs(µm) λc/λs Rtip(µm) 0.08 2.5 30 2 0.25 2.5 100 2 0.8 2.5 2 or 5 2.5 8 300 2 or 5 8 25 10, 5 or 2

Necessity of short wavelength cutoff (λs filter)

No consideration of short wavelength filter is required, because of large basic periodic components of waviness or machining streaks and negligibly minute profiles in roughness curves of normal machined surfaces. However, the depth of valleys changes by the cutoff value of short wavelength and radius value of stylus’ tip, when deep, sharp and minute streaks remain on high-precision machined surfaces by lapping, etc. The larger grows amplitude of roughness in generally speaking, as the larger is the cutoff ratio, or the smaller is the radius of stylus’ tip. In such a case, required is the measurement by specifying the cutoff value of short wavelength filter in order to obtain comparable data.

4-1

4 ROUGHNESS ANALYSIS TERMINOLOGY AND DEFINITION In this chapter, it explains about the terminology and definition used in this manual which have not been explained in Chapter 2 and 3. Sampling Length (L):

This is the length of a sampled part from a surface curve for making calculation of parameters of the surface curve. In a roughness profile, the sampling length is the same value as the cutoff value λc in principle. (JIS B0601-1994) In a profile curve, the sampling length is the length determined according to which has been obtained by the value of profile parameter. (JIS B0601-1982)

Evaluation Length (Ln): This is the length which includes one or more sampling length for making evaluation of a surface roughness. The standard value of the evaluation length is five times of the sampling length. (JIS B0601-1994,ISO4288)

Measuring Length (Lm): This is a evaluation length in order to calculate Ra(JISB0601-1982), Ra75(JIS B0601-1994 Annex). The standard value is three times of the cutoff value.

Pre-travel Length (Lpe): This is the measuring length in front of the evaluation length. Longer length is required to be set for the pre-travel in linger waviness component. For this setting with the phase correct filter, select it from the cutoff values of λc,λc/2 and λc/3. For setting with the 2RC filter, it is set to two times of the value of the phase correct filter.

Post-travel Length (Lpo): This is the measuring length in the rear of the evaluation length. This is necessary to remove an error caused by the transitional response of the phase correct filter. For this setting with the phase correct filter, select it from the cutoff values of λc,λc/2 and λc/3. For setting with the 2RC filter, it is set zero because it is not necessary.

Traversing Length (Lt): This is the total length of including the pre-travel, evaluation length and post-travel which is the pickup traversing length for measurement of roughness. Be noted not to confuse the traversing length with the measuring length defined in the above JIS-'82.

Measurement start position

Pre-travellength(Lpe)

Sampling length Post-travellength(Lpo)

Traversing length Lt = Ln + Lpe + LpoEval.length Ln = Lxn (n = 1 or more)

Measurement end positionPickup

L1 L2 L3 L4 Ln

The way to traverse →

Fig. 4.1 Relation between Traversing Length, Evaluation Length and Sampling Length

Horizontal Magnification in Recording Chart (Vh): This is an enlargement magnification of recording chart to the displacement in traversing direction of the pickup.

4-2

Vertical Magnification in Recording Chart (Vv): This is an enlargement magnification of recording chart to the displacement in vertical direction against to the pickup traversing direction.

Vertical Magnification Direction (z): This is the vertical direction against to the pickup traversing direction.

Profile Peak: An outwardly directed entity of profile surrounded by the roughness profile and the mean line connecting two adjacent points of the intersection made when cutting the roughness profile with the mean line. When the starting and end portions of the sampling length are in upper side of the mean line, the part is regarded as the profile peak. (JIS B0601-1994, ISO4287/1)

Profile Valley: An inwardly directed portion of space surrounded by the roughness profile and the mean line connecting two adjacent points of intersection made when cutting the roughness curve with the mean line. When the starting and end portions of the sampling length are in lower side of the mean line, the part is regarded as the profile valley. (JIS B0601-1994, ISO4287/1)

Top of Profile Peak: A point of the highest altitude in the profile peak of roughness profile. (JIS B0601-1994)

Bottom of Profile Valley: A point of the lowest altitude in the profile valley of roughness profile. (JIS B0601-1994)

Line of Profile Peaks: Of the reference length sampled from the roughness profile, the line parallel to the mean line passing through the highest top of profile peak. (JIS B0601-1994,ISO4287/1)

Line of Profile Valleys: Of the reference length sampled from the roughness profile, the line parallel to the mean line passing through the lowest bottom of profile valley. (JIS B0601-1994,ISO4287/1)

Cutting Level (c): A vertical distance between the top of profile peak line and the line parallel to the top of profile peak line intersecting the roughness profile. (JIS B0601-1994) The cutting level can be determined by a unit of µm or percentage of Ry.

Local Peak of Profile: A part of entity between two adjacent minima of the roughness profile. (JIS B0601-1994,ISO4287/1-1984)

Local Valley of Profile: A part of space between two adjacent maxima of the roughness profile. (JIS B0601- 1994,ISO4287/1-1984)

Top of Local Peak of Profile: A point of the highest altitude in the local peak of profile. (JIS B0601-1994)

4-3

Bottom of Local Valley of Profile: A point of the lowest altitude in the local valley of profile. (JIS B0601-1994)

Local peak of profile Profile peak

Mean line(m)

Local valley of profile

Profile valleys

Top of local peak of profileLine of profile peaks

Top of profile peak

Bottom of profile valley

Samping Length (L)

Line of profile valleysBottom of local valley of profile

Fig. 4.2 The name of roughness profile (Top of profile peak • Bottom of profile valley, etc)

5-1

5 PARAMETERS FOR AMPLITUDE Arithmetic Average/Mean Line Average Value (Ra, Ramax, WCA, Wa, WEA, Pa)

This means the value obtained by the following formula when sampling only the sampling length, L from the sampled curve in the direction of mean line, taking X-axis in the direction of mean line and Y-axis in the direction of longitudinal magnification of this sampled curve is expressed by y=f(x).

R a = ∫ | f ( x ) | d x1L

L

0 Namely, in the figure of below, the arithmetic average represents the average deflection obtained by dividing the area of the portion surrounded by the sampled curve and the mean line by the measuring sampling length.

Meanline (phase correct)Center line (2RC)

Z

X

Sampled curve f(x)

Ra

Sampling length (L)

TABLE 5.1 Parameter Names and Sampled Curves under Various Standards Standard (Country)

Roughness Profile R & Phase Correct Roughness Profile Rg

Profile Curve P

Filtered C-Line

Rolling CircleC-Line

1 Div.

Max. per Sampling

length

Average per Sampling

length

1 Sampling length

Waviness Curve Wcc

1 Div.

Waviness Curve WEC

1 Div. ISO4287:1997

(Int’l Standard)

-

Arithmetical Mean Deviation of the Assessed

Profile Ramax


Profile Ra


Profile Pa


Profile Wa

-

ISO468-1982 ISO4287/1-1984 (Int’l Standard)

Arithmetical Mean Deviation

of Profile Ra, Rai


of the Profile Ramax


of the Profile Ra, Ra5

-

(Wa)

(Wa) JIS B0601-1994

(Japanese industrial Standard)

Center Line Mean Roughness

Ra75 (Note 3)

-

Arithmetic Average Roughness Ra (Note 4)

-

Filtered Center Line Waviness

WCA

Rolling Circle C-Line Waviness

Curve WEA

JIS B0601-1982 Ra (Note 3) - - - JIS B0610 JIS B0601 B.S.1134-1988

(UK) Arithmetical

Mean Deviation of the Profile

Ra

-


of the Profile Ra

-

-

-

ASME B46. 1-1995 (USA)

Roughness Average Value

Ra, (AA)

-

-

-

-

-

DIN4768/1-1990 (Germany)

Mittenrauhwert Ra

(Note 4)

-

Mittenrauhwert Ra

(Note 4)

-

-

-

Note 1 : Marked ( ) are previous standards or reference standards. Note 2 : Ra is a value of arithmetic average of profile irregularities in the entire sampling length,

therefore a partial large chip does not affect to the result. Note 3 : 2RC Filter is used. Note 4 : Gaussian Phase correct filter is used.

5-2

Root-mean-square Average (Rq, Rqmax, RMS, Wq, Pq) This means the value obtained by the following formula when sampling the sampling length, L from the sampled curve in the direction of mean line, taking X-axis in the direction of mean line and Z-axis in the direction of longitudinal magnification of this sampled curve is expressed by Z=f(x).

R q = ∫ f 2 ( x ) d x1L

L

0

Sampling length (L)

Z

X

Mean Line(phase correct)Center line(2RC)

f 2 (X)

Namely, in the above figure, the root-mean-square represents the root mean square average deflection obtained by dividing the area of the portion between the curve, which is obtained by squaring the distance between the sampled curve and the center-line, and the center-line by the traversing length. This is equivalent to standard deviation σ in statistics.

TABLE 5.2 Parameter Names and Sampled Curves under Various Standards

Standard Roughness Profile R & Phase Correct Roughness Profile Rg Profile Curve P Filtered C-Line (Country)

1 Div. Max. of Root Mean Square obtained in

each Sampling Length

Average of Root Mean Square obtained in

each Sampling Length

1 Sampling length Waviness Average per Sampling

length Wcc

ISO4287:1997 (Int’l Standard)

-

Rqmax

Root-mean-square deviation of the assessed profile

Rq

Root-mean-square deviation of the assessed profile

Pq

Root-mean-squaredeviation of the assessed profile

Wq ISO468-1982

ISO4287/1-1984 (Int’l Standard)

Root-mean-square deviation of the profile

(Rq)

(Rqmax)

(Rq, Rq5)

-

-

ASME B46.1-1995

(USA)

Root-mean-square roughness Rq, (RMS)

-

-

-

-


Quadratischer mittenrauhwert des

profile (Rq)

-

(Rq)

-

-

Note 1 : Marked ( ) are standards of before for reference.

5-3

Maximum Height (Ry, Rymax, Rmax, Rt, Rz, Pt, W, Wt, WCM, WEM, Wz) This is the distance between the line of profile peaks and the line of profile valleys measured in the vertical magnification direction within a portion extracted from the sampled curve Z=f(x) as the sampling length, L.

R y = m a x ( f ( x ) ) - m i n ( f ( x ) )

Sampled curveMean line(phase correct)Center line(2RC)

Line of profile valleys

Z

X

Line of profile peaks

Ry

Sampling length (L)

TABLE 5.3 Parameter Names and sampled Curves under Various Standards

Standard (Country)


Profile Curve P

Filtered Waviness

Filtered C-LineWaviness

Rolling Circle

1 Div.

Max. value of Max. height

obtd. per Sampling Length

Average of Max. height

obtd. per Sampling Length

1 Sampling length

Curve W 1 Evaluation

length

Average per Sampling length

Wcc

Waviness Curve

Evaluation length

ISO04287:1997

(Int’l Standard)

-

Max. heightof profile Rzmax

Max. heightof profile

Rz

Max. heightof profile

Pz

-

Max. height of profile

Wz

-

ISO4287/1-1984 ISO4288 - 1985 (Int’l Standard)

Max. height of profile

Ry

Max. heightof profile Rymax

Max. heightof profile Ry (Ry5)

-

-

-

-

JIS B0601-1994 (Japanese

industrial Standard)

-

-

Maximum height

Ry

-

Filtered Max. Waviness

-

Rolling Circle Maximum Waviness

JIS B0601-1982 - - - Max. heightRmax

WCM JIS B0610

WEM JIS B0601

BS.1134/1-1988 (UK)

Max. height Ry

- Max. heightRy

- - - -

ASME B46.1-1995

(USA)

Max. peak-to-valley

roughness Rt

Max. height of the profile

Rmax

Average max.height

Rz

-

Waviness height

Wt

-

-

DIN4771 DIN4774


Maimum roughness

Rt

Maximale rauhtiefe

Rmax (Rmax DIN)

Gemittelterouhtiefe

Rz

Profiltiefe

Pt

Wellentiefe

Wt

-

-

Note 1 : For the maximum height, it is required to measure the workpiece surface excluding the

outstanding flaw, because the system reads the value during the sampling. It is also required to measure more than one points and average them.

In ISO 4288 and JIS B0601-1994, the maximum height is obtained in each length and average them by the total evaluation length. This is called as Ten Point Average Roughness, Rz, in DIN standard.

Note 2 : Normal processing faces contain surface waviness to a certain degree; This causes the maximum height from roughness curve, Rt to be smaller than the

maximum height form profile curve, Rmax (Pt). But in some cases like cross sections with small waviness and complex waveform such as ground surface and honing surface, Rt is larger than Rmax/Pt due to the effect of the transient characteristic of filter.

5-4

Ten-point Height of Irregularities [JIS, ISO] (Rz, RzISO, RzJ) Only the sampling length is sampled from the sampled curve in the direction of its mean line, the sum of the average value of absolute values of the heights of five highest profile peaks (yp) and the depths of five deepest profile valleys(yv) measured in the vertical magnification direction from the mean line of this sampled portion.

R z = (∑| y p i | +∑| y v i | )15

5

i=1

5

i=1

yv1

yp2

yv4 yv3

yp4yp3

yv5

yp1

Sampled curve

Sampling length (L)

yp5

yv2

Mean line (m)

X

Z

TABLE 5.4 Parameter Names and sampled Curves under Various Standards

Analysis Methode Former JIS ISO New JIS DIN Standard (Country)

Calculate 1 Sampling Length

from Profile Curve P

Calculated Average per Sampling Length from

Roughness R

Max.of Calculated Value per

Spmpling Length from Roughness

Curve

Average of calculated Value per

Sampling Length from Roughness

Curve Rg

Average of Max. Height per Sampling

Length from Roughness Curve Rg

ISO468-1982 ISO4287/1-1984 (Int’l Standard)

-

10 point height of irregularities

Rz


Rzmax

-

Average value of maximum height

Ry (Ry5) JIS B0601-1994

(Japanese Industrial Standard)

-

-

-

10 point average roughness

Rz

Maximum height

Ry JIS B0601-1982

(Note 4) 10 point average

roughness Rz (RzJ)

-

-

-

-

B.S.1134-1988 (UK)

-


Rz

-

-

Maximum height

Ry ANSI B46.1-1985

(USA) -

10 point roughness height (Rz)

-

-

Mean Rt

(Rtm) DIN4768/1-1990

(Germany) -

(Rz·ISO) - - Gemittelte Rauhtiefe

Rz

Note 1: The ISO 468 standard specifies as criterion for peak and valley that values under 10% of Ry shall not be recognized as an independent peak and valley. This machine follows it in JIS94, DIN and ASME, and provides vertical dead bands which are 10% of Ry on each sides of the mean line.

Note 2 : In case a long reference length is not taken, sometimes 5 peaks and valleys are not found in it. In such a case, measurement results may not be obtained.

This machine calculate only the recognized peaks and valleys, and indicate it with＊. Note 3 : It provides the vertical dead bands of ‘0.5mm / measuring magnification’ both above and below

the mean line, in order to ward off such fear that noise components are judged as peaks or valleys in the JIS82 mode. (In Surfcom 130A/480A, it provides the each dead band of ±0.5µm in measuring range of ±400µm, ±0.05µm in measuring range of ±40µm, ±5nm in measuring range of ±4µm and ±2.5nm in measuring range of ±2µm.)

Note 4 : In JIS and ISO 468, the evaluation length which consists of continuous five reference lengths (same length as the cutoff value) is taken out from the roughness profile and above calculation is made in each reference length, then the arithmetical mean value of the five values is Rz.

Note 5 : This parameter has been disused in ISO4287-1997.

5-5

Base Roughness Depth/Averaged Middle Peak-to-valley height (R3z) Extract the evaluation length which consists of five continuous sampling lengths (same as the length of cutoff value) from a sampling curve. The height between the 3rd highest peak and the 3rd lowest peak in each of the divided sampling lengths. The average value in the evaluation length is defined as base roughness depth/Averaged middle peak-to-valley height. This parameter is a private standard. (Daimler-Benz-Specification N31007-1983)

R 3 z = ∑R 3 z i1n

n

i=1

yp3

yv3 yv1

yp2

yv2

Sampled curve

Mean line(m)

Sampling length (L)

X

yp1

R3z

The figure of above shows one sampling length. In the evaluation length, there are "n" set of the sampling length and their average value is calculated. Dead band is specified in Note 1 below.

Mean Height of Elements (Rc, Rcmax, Pc, Wc) Extract the sampling length, L from the sampled curve z = f(x), and the sum of the average value of absolute values of the heights from the mean line and of the depths from the mean line is the mean height of elements.

R c = ∑ | y p i | + ∑ | y v j |1m

m

i=1

n

j=1

1n

"m" and "n" in the above formula show each number of the top of the peak and the bottom of the valley in the range of the sampling length.

yp1

yv2 yv3 yv4yv9

yv8yv7yv6yv5

yp5yp6

yp7yp8 yp9yp4yp3yp2

yv1

Sampled curve

Mean line (m)

Z

Ｘ

Sampling length (L)

TABLE 5.5 Parameter Names and Sampled Curves under Various Standards Standard Roughness Profile R & Phase Correct Roughness Profile Rg Profile Curve P Filtered C-Line (Country) 1 Evaluation Length 1 Sampling length Average value obtd.

in each Sampling Length

1 Sampling length Waviness Wcc

ISO4287/1-1984 ISO4288-1985 (Int’l Standard)

Mean height of profile irregularities

(Rc)

Maximum mean height of profile

irregularities (Rcmax)

Average mean height of profile

irregularities (Rc)

-

-


-

Mean height of profile elements

Rcmax

Mean height of profile elements

Rc

Pc

Average per Sampling length

Wc Note 1 : It provides the vertical dead bands of ‘0.5mm / measuring magnification’ both above and below the

mean line, in order to ward off such fear that noise components are judged as peaks or valleys in the JIS82 mode. (In Surfcom 130A/480A, it provides the each dead band of ±0.5µm in measuring range of ±400µm, ±0.05µm in measuring range of ±40µm, ±5nm in measuring range of ±4µm and ±2.5nm in measuring range of ±2µm.)

5-6

Maximum Profile Peak Height (Rp, Rpmax, Rpm, Rp5, Wp, Pp) Extract the sampling length, L from the sampled curve z = f(x) and measure the distance between the line of profile peaks within the length of L and the mean line to the direction of vertical magnification. This is defined as maximum profile peak height.

R p = m a x ( f ( x ) )

Sampled curve Mean line (phase correct)Center line (2RC)

Z

X

Line of profile peaks

Rp

Sampling length (L)

TABLE 5.6 Parameter Names and Sampled Curves under Various Standards Standard Roughness Profile R & Phase Cor. Roughness Profile Rg Profile Curve P Filtered mean line(Country) 1 Evaluation

Length 1 Sampling length Average value

obtained in each Sampling Length

1 Sampling length Waviness curveWCC


Maximum profile peak height

(Rp)


(Rpmax)

Average value of maximum profile peak

height (Rp, Rp5)

-

(Wp) ISO4287:1997 (Int’l Standard)

-


Rpmax


Rp


Pp

Maximum profile peak height Average per

Sampling lengthWp

BS1134/1-1988 (UK)

Leveling depth (Rp)

Leveling depth (Rp)

Mean leveling depth(Rpm)

- -

ASME B46.1-1995 (USA)

Max. profile peak height

Rp

-

Average max profile peak height

Rpm

-

-

DIN4771 DIN4774


Maximale höhe der

Profilerhenbung (Rp)

Maximale höhe der

Profilerhenbung (Rp)

(Rpm)

-

-

Note 1 : Marked ( ) is a standard for reference only, which is not an official standard. Note 2 : A surface which is measured by an air micrometer and an electric capacitance type

displacement meter is equivalent to the above mean line, and a surface which is measured by a micrometer is equivalent to the profile peak line. So that 2xRp is equivalent to the difference of their dimensional measurement values.

5-7

Maximum Profile Valley Depth (Rv, Rvmax, Rvm, Rv5, Wv, Pv) Extract the sampling length, L from the sampled curve z = f(x) and measure the distance between the line of passing through the lowest peak within the length of L and the mean line to the direction of vertical magnification. This is defined as maximum profile valley depth.

R v = m i n ( f ( x ) )

Rv

Sampling length (L)

Line of profile valleys

Sampled curve Mean line (phase correct)Center line (2RC)

Z

X


Standard Roughness Curve R & Phase Cor. Roughness Curve Rg Profile Curve Fil. Mean line (Country) 1 Evaluation

Length 1 Sampling length Average value

obtained in each Ref. length

P 1 Sampling length

Waviness curveWcc


-

Maximum profile valley depth

Rvmax


Rv


Pv

Maximum profile valley depth Average per

Sampling lengthWv



(Rm)


(Rmmax)

Average value of maximum profile

valley depth (Rm, Rm5)

-

(Wv) ASME B46.1-1995

(USA) Maximum profile

valley depth Rv

-

-

-

-

DIN4771 DIN4774


Maximale höhe der

Profilerhebung (Rv)

Maximale höhe der

Profilerhebung (Rv)

(Rvm)

-

-

Note 1 : Marked ( ) is a standard for reference only, which is not an official standard.

5-8

Height of Step (AVH, Hmax, Hmin, AREA) This is the parameter to indicate an interval in the direction of vertical magnification of the protruded top end and section area of the protruded portion toward the reference line. (The same processing is available for the concave portion, too.) (1) Input parameter:

1. Height of step calculation mode deletion length: Start out portion of a step which is unnecessary for calculation and deleting length of

falling down portion are specified. 2. Height of step calculation mode reference height: Threshold value of the protruded height which becomes the subject of height of step

calculation is input. 3. Area calculation length The area which become the subject of Area calculation are specified.

(2) Tilt correction: Correction of both ends A straight line which is connected recording start point and recording end point is defined

as a correction line. (3) Calculation of step difference parameter calculation range In the protruded portion which is bigger than the numerical value of the height of step

calculation mode reference height, the range of being deleted the both ends of deleted length numerical portion is defined as step difference parameter calculation range.

(4) Calculation parameter Three types of parameter of below are calculated.

1. AVH ....... Average height value within the range of step difference parameter calculation

A V H = •∑Z i1k

k

i=1Zi : All data within parameter calculation rangek : Its data number

2. Hmax ..... Maximum height value toward the reference line within step difference

parameter calculation 3. Hmin ...... Minimum height value toward the reference line within step difference

parameter calculation 4. AREA..... Section area surrounded by profile within step difference parameter

calculation and the reference line

Reference height

Deletelength

Step heightcalculation area

Deletelength

Area calculationlength

Area calculationlength

(5) Uses This is used for controlling thickness of printed circuit board and thick film IC, etc. and

electric resistance.

Note 1 : This parameter is not included in the national standard.

5-9

FPD waviness Wfpd (= Moving minimum zone method straightness of waviness)

FPD waviness Wlcd is the maximum value of straightness among the sampling lengths of the filtered center line waviness within the range of the evaluation length.

The procedure for finding the value by manual operation is as under. (1) Prepare a template with a window having the width of sampling length. (2) Let the template trace along the curve in the range of the evaluation length of filtered center

line waviness. (3) Read the straightness value within the scope of window at all positions in the process. (4) The maximum value out of all readings is Wfpd.

The following is the evaluation standard of glass board for LC. (SEMI International Standard D15-1296) The measure conditions are set as follows. (1) Radius of stylus tip: Sphere R 5µm or above (2) Evaluation curve: Filtered center line waviness Wcc (3) Wavelength filter: 2RC filter or Phase Correction Filter of Gaussian Distribution Characteristics (4) Low-area cutoff wavelength λL: 8 mm or 25 mm (5) High-area cutoff wavelength λc: 0.8 mm (6) Evaluation length Le: Full length in the measuring direction in the quality

range of glass board (7) Sampling length Ls: Ls = 20 mm when λL = 8 mm Ls = 25 mm when λL = 25 mm The sampling length means the length of a single stroke

of repetitive waviness calculations executed little by little from one end to another over the full range of evaluation length.

(8) Pre-Travel Lp: 2RC filter takes 2λL’s at the head end of evaluation length. Phase correction filter takes a λL at both ends of

evaluation length.

fpd

Explanation of Le, Lp and Ls

Note 1 : This parameter is not included in Surfcom 130A/480A.

6-1

6 PARAMETERS FOR WAVELENGTH AND SLOPE Mean Spacing of profile irregularities/Average Spacing of Roughness peaks (Sm, Rsm, Smmax, PSm, WSm)

Extract the sampling length, L from the sampling curve to the direction of the mean line. When the sum of the lengths of the mean line corresponding to one of the profile peaks and its adjacent one profile valley (spacing of profile irregularities) is calculated, the mean spacing of profile/Average spacing of roughness peaks is the arithmetical mean value of many spacing of those irregularities. When the spacing of irregularities between the point which goes across the mean line in the direction from the one profile peak to one profile valley and the point of crossing in direction from the next one profile peak to one profile valley is made to Smi and the total numbers of the intervals are made to N, it can be obtained by the following formula.

S m = ∑S m i1N

N

i=1

Sm1 Sm2


Sampled curve f(x)

Z

X

Smi Smn

Sampling length (L)

TABLE 6.1 Parameter Names and Sampled Curves under Various Standards Standard (Country)


Profile Curve P Curve W

Filtered Waviness 1-Sampling length

Value per one Sampling Length

Value per EachSampling Length

Mean value of values obtained per

Sampling Length

1-Sampling length

JIS B0601-1994 Mean spacing of profile irregularities

Sm (Note 3)

-

Mean spacing of profile irregularities

Sm (Note 3)

-

-


-

RSmmax

Mean width of the profile elements

RSm

Mean width of the profile elements

RSm

Mean width of the profile elements Average per Sampling length WSm


Mean Spacing of Profile Irregularities

Smi (RSmi)

Sm max

Mean Spacing of Profile Irregularities

Sm (RSm)

(PSm)

(WSm) ASME B46.1-1995

(USA) Mean Spacing of

Profile Irregularities Sm

-

-

-

-

DIN4762 (Germany)

Mittelerer Abstand der Profilumregelma

Bigkeiten (Sm)

-

Mittelerer Abstand der Profilumregelma

Bigkeiten (Sm)

-

-

B.S.1134/1-1988 (UK)

Mean Spacing of Profile Sm

- Mean Spacing of Profile Sm

- -

Note 1 : In ISO 468 and JIS B0601-94 standard, the height of less than 10% of Ry is not regarded as one individual profile peak or valley as the condition for judgement. Because of this limitation, even if a small component of the wavelength is included in the waveform, the Sm value is generally apt to become the value which corresponds to the wavelength of the biggest amplitude.

This machine follows it in ISO, DIN, ASME and JIS94 modes. Note 2 : It provides the vertical dead bands of ‘0.5mm / measuring magnification’ both above and

below the mean line, in order to ward off such fear that noise components are judged as peaks or valleys in the JIS82 mode. (In Surfcom 130A/480A, it provides the each dead band of ±0.5µm in measuring range of ±400µm, ±0.05µm in measuring range of ±40µm, ±5nm in measuring range of ±4µm and ±2.5nm in measuring range of ±2µm.)

Note 3 : In JIS B0601-1994, the roughness profile, Rg, passed by phase correct filter is used.

6-2

Peak count (Pc, PPI, HSC) A specified reference level, H is set in both negative and positive going directions from the mean line of the roughness profile. Every time the positive reference height is exceeded after the negative reference level is exceeded, the number is counted. A count value when the number is counted to the end of evaluation length, Ln is called as the peak counts. This parameter is specified by The Engineering Society for Advancing Mobility Land Sea Air and Space :SAE J911-JUN86 "SURFACE TEXTURE MEASUREMENT OF COLD ROLLED SHEET STEEL" in the USA. Under the SAE standard, measuring traverse length is 1 inch (=25.4mm) and the parameter is called PPI(Peaks per inch). the length between negative and positive reference heights, 2H is called peak count level and it is generally set to 2H=50µinch. When the negative reference level is set to zero, it becomes high spot count HSC.

1 count

n count

Sampled curve f(x) Mean line(phase correct)Center Line (2RC)

Evaluation length (Ln)

Z

XHH

2 count 3 count

Reset Reset Reset Reset

TABLE 6.2 Name of Parameters and Sampled Curves under Various Standards Sampled curve Roughness Profile R & Phase Correct Roughness Profile Rg

Standard (Country) Peak-Valley Count Blind

zone 50µ inch per 1 inch

Peak-Valley Count with Blind zone per

1cm

Peak-Valley Count without Blind zone in

the range of Sampling Length

Peak Count in the range of specified

length

Valley Count in the range of specified

length

SURFCOM

Pc (Level setting) Meas. length

1inch set

Pc (Level setting) Meas. length

1cm set

Pc (Level H = 0)

Pc (Valley level H2 = 0)

(PPI-P)

Pc (Peak level H1 = 0)

(PPI-V)

ISO468-1982 (Int’l Standard)

- - Profile Peak densityD

- -

ASME B46.1-1995 (USA)

- Peak density Pc

- High Spot Count (HSC)

-

SAE J911-1986 Peaks per inch PPI

- - - -

DIN4762 (Germany)

-

- by former standard

Ti

Dichte der Profilerhebu-ngen

(D)

- by formerstandard

S

-

EURONORM 49-83E

- Peak Count Pc

- - -

Note 1 : The SURCOM defines a peak counting (Symbol: Pc) from roughness curve and

displays the number of peaks per evaluation length. A count level in both negative and positive can be set at any level, which can be cope

with several kinds of standards.

6-3

Mean Spacing of Local Peaks of the Profile (S, Smax) Within a portion extracted from the roughness curve of the sampling length, L, and calculate the mean line length (spacing of local peaks) which corresponds to the spacing between the adjacent local peaks in the extracted portion. The arithmetic mean value of the spacing between many local peaks is the mean spacing of local peaks of the profile.

S = ∑S i1N

N

i=1

S2

Sampled curve f(x) Mean line (phase correct)Center line (2RC)

Sampling length (L)

Z

X

S1 Si Sn


Standard Roughness Profile R & Phase Correct Roughness Profile Rg (Country) Value per one Sampling Length Value per Each

Sampling LengthMean value of values obtained per

Sampling Length JIS B0601-1994 Mean spacing of local peaks

S - Mean spacing of local peaks

S (Note: 3) ISO4287/1-1984 ISO4288-1985 (Int’l Standard)

Mean Spacing of Local Peaks of Profile

Si

Smax


S (S5) DIN4762

(Germany) Mittlerer Abstand der örtlichen

Profilspitzen S

-

Mittlerer Abstand der örtlichen Profilspitzen

S BS1134/1-1988

(UK) Mean Spacing of Local Peaks

of Profile S

-


S

Note 1 : Marked ( ) is a standard for reference. Note 2 : This instrument follows ISO 468 and the height of less than 10% of Ry is not regarded

as one individual profile peak or valley as condition for judgment. The minimum value of the spacing between local peaks is 1% of the sampling length(L)

and the spacing less than that is considered as a peak, so that the value of “S” is limited in the range of L/100 < S < L toward the sampling length..

Note 3 : This parameter has been disused in ISO4287-1997.

6-4

Arithmetical Mean Slope of Profile/Average Absolute Slope (∆a) Within a portion extracted from the sampling curve of the sampling length, L, and differentiate the sampling length portion and obtain the slope curve then calculate the absolute value in each point of the curve. The arithmetic mean value of the many absolute values is the arithmetical mean slope of profile/Average absolute slope.

∆a = ∫ | f ( x ) | d x1L

L

0

ddx

However, a slope at each sampling point on a profile curve is calculated by the formula of below in accordance with ISO4287-1997.

Root-Mean-Square Slope of Profile (∆q, R∆q, P∆q, W∆q)

Within a portion extracted from the sampling curve of the sampling length, L, and differentiate the sampling length portion and obtain the slope curve then calculate the square value in each point of the curve. The arithmetic mean value of the many square values is the root-mean-square slope of profile.

∆ q = ∫ ( f ( x ) ) 2 d x1L

L

0

ddx

However, a slope at each sampling point on a profile curve is calculated by the formula of above in the same manner of ∆a.

TABLE 6.4 Name of Parameters and Sampled Curves under Various Standards Sample Curve Roughness Profile R & Phase Correct Roughness Profile Rg Cal. Method Arithmetical mean Value Root-mean-square Value

Standard (Country)

One sampling Length Value

Max. Value of each

Sampling Length

Mean Value of each Sampling

Length


Max. Value of each

Sampling Length


Length

ISO4287:1997

(lnt’l Standard)

-

-

-

Root mean square slope of the

assessed profileP∆q

R∆qmax W∆qmax

Root mean square slope of assessed

profile R∆q, W∆q

ISO4287/1-1984 ISO4288-1985 (lnt’l Standard)

Arithmetical mean slope of profile (∆a)

(∆amax)

-

Root mean square slope of profile

∆q

(∆qmax)

Root mean square slope of profile

∆q ASME

B46.1-1995 (USA)

Average absolute slope

∆a

-

-

Root mean square slope ∆q

-

-

DIN 4762 DIN 4768/

1-1990 (Germany)

Arithmetischer Mittelwert der Neigung des Profils (∆a)

-

Arithmetischer Mittelwert der Neigung des Profils (∆a)

Quadratischer Mittelwert der Neigung des Profils (∆q)

-

Quadratischer Mittelwert der

Neigung des Profils (∆q)

Note 1 : Marked ( ) is a standard for reference. Note 2 : The mean slope shows scattering of reflected ray of light irradiated on the surface, and it

has a correlation with a visual surface evaluation. The smaller mean slope is the better reflection surface. The smaller mean slope is also better for friction and wear.

On the contrary, the larger mean slope is better for the bonding surface. Note 3 : Refer to the formula of below for making conversion of ∆a and ∆q into the slope angle θa

and θq (degree).

θ a = t a n - 1∆ a , θ q = t a n - 1∆ q

d dx f(x) = d

dx zi = 1 60ΔX

(zi+3 - 9zi+2 + 45zi+1 - 45zi-1 + 9zi-2 - zi-3)

6-5

Average Wavelength of Profile (λa) The average wavelength of profile is the 2π times of the ratio of the arithmetical mean slope of profile ∆a of the same sampling curve as the arithmetic average roughness Ra of the sampling curve.

λ a = 2 πRa∆ a

In the above formula, λa is a kind of the approximate value of spacing between the local peak and local valley points in consideration of the relative amplitude and the individual space frequency.

Root-Mean-Square Wavelength of Profile (λq) The root-mean-square wavelength of profile is the 2π times of the ratio of the square mean slope of profile ∆q of the same sampling curve as the square average roughness Ra of the sampling curve.

λ q = 2 πRq∆ q

In the above formula, λq is a kind of the approximate value of spacing between the local peak and local valley points in consideration of the relative amplitude and the individual space frequency.

TABLE 6.5 Name of Parameters and Sampled Curves under Various Standards

Sample Curve Roughness Profile R & Phase Correct Roughness Profile Rg Cal. Method Arithmetical Mean Value Root-Mean-Square Value

Standard (Country)


Max. Value of each Sampling

Length


Length


Max. Value of each Sampling

Length

Mean Value of each Sampling Length

ISO 4287/1-1984

ISO4288-1985 (Int’l Standard)

Average wavelength of

profile λa

λamax

Average wavelength of

profile λa

Root mean square wavelength of

profile λq

λqmax

Root mean square wavelength of

profile λq

DIN4762 (Germany)

Mittlere Wellenlänge des Profils

(λa)

-

Mittlere Wellenlänge des

Profils (λa)

Mittlere quadratische

Wellenlänge des Profils (λq)

-

Mittlere quadratische

Wellenlänge des Profils (λq)

Note 1 : Marked ( ) is a standard for reference. Note 2 : This parameter has been disused in ISO4287-1997.

6-6

Average Slope Angle (TILT A) The average slope angle is an angle toward the X-axis of the minimum square mean line of a profile curve in the evaluation portion. When the minimum square line is set to y = ax + b, the average slope angle is shown in the formula of below.

T I L T A = t a n − 1 a

The unit is expressed by degree, minute and second ( ° ' " ) or degree ( ° ).


Evaluation length (Ln)

Z

X

Sampled curve f(x)

T I L T A

The relative angle (taper) can be obtained by making measurement of tilting angle of the objective surface after making parallel adjustment as a datum for reference surface. Note 1 : This parameter represents correction angle of least square straight tilt correction, so

that evaluation areas of each tilt correction method are following. (1) No correction : Whole profile (2) Least square straight correction : Whole profile or the area specified by evaluation area set (3) Beginning half correction : Beginning half (4) Latter half correction : Latter half (5) Beginning and End : Beginning and end

Note 2 : When curve compensation and spline compensation are selected as the tilt correction, it is unable to make its calculation.

Note 3 : This parameter is not included in the national standard.

6-7

Profile Length Ratio (Lr, SL) Profile length ratio is the ratio of length to the sampling length which is obtained by extending the sampling curve to the straight line in the sampling length. This is a non-dimensional number.

L r = ∫ 1 + [ f ( x ) ] 2 d xL

0

ddxL

This parameter is defined as Lr in ISO4287/1-1984. Note 1 : As for coating, plating, adhesive surface and heat transmission, the larger actual

surface area has the better efficiency. In order to calculate this area, this parameter is used. This becomes actually the

value of " 1 < Lr < about 1.02 " which is very close to the value of 1 .

6-8

Power Graph/Power Spectrum When Fourier transformation of a sampling curve is made, a function which shows the amount and type of component of the spatial frequency (evaluation length / wavelength) in the sampling curve can be obtained. The power graph (or power spectrum) explained herewith is expressed in a graph which axis of abscissas is for the frequency (1 / wavelength) and the axis of ordinates is for the whole amplitude of the sine wave component of the frequency. < The way to calculate a power graph >

When the sampling curve is set to X(t), the Fourier transformation F(f) becomes as follows:-

T/2 F(f) = ∫ X (t) exp (- j 2πf t ) d t T/2

The above ‘ t ‘ shows an irregular variate in the range of – T / 2 < t < T / 2 , which ‘ T ‘ shows the time for measurement and it is regarded as zero in the sphere of ‘ t ‘ excepting for that. The power spectrum (or power spectrum density function) P (f) at this time is indicated as shown below as an amplitude power of the Fourier transformation.

P( f ) = |F ( f )|² / T

< The way to show in a graph for this instrument >

The axis of ordinates is shown as the whole amplitude value in the unit of μm of the sine wave component in some wavelength of 1 / f . Though the original power spectrum is shown as the value of being squared a half amplitude value, the amplitude of roughness is shown in many cases as the maximum height Rz (Rmax) which is the whole amplitude value. Therefore, it is shown as a graph of the whole amplitude value which is not squared as the exclusive way to indicate the roughness. The axis of abscissas is expressed in a wavelength, however the wavelength becomes shorter when it goes to the right side in the spatial frequency or “Evaluation length / wavelength”. By using this graph, its periodicity of being included in the waveform can be analyzed. And it can be also used for making analysis of chattering of a cutting tool for cutting processing, vibration of a motor and grading of grinding grain, etc.

6-9

Example : In case of the composite sampling curve between two sine waves of 2.0μm for amplitude / 500.0μm for wavelength and 0.25μm for amplitude / 50.0μm for wavelength, the axis of ordinates of the power graph corresponding to the axis of abscissas of 500.0μm becomes 4.0μm. And the axis of ordinates of the power graph corresponding to the axis of abscissas of 50.0μm becomes 0.5μm.

The above figure is the result based on the experimental data. But it actually becomes the graph shown as below.

Measuring result (Power Graph)

1.35µm

0.00µm250µm 0.060µm

< Explanation about a graph > ① Calculation of a power graph is made to the profile curve. However due to the use of FFT

(Fast Fourier Trasform) in the power graph calculation, the data point number of being available for evaluation becomes to N = 2 ⁿ (2 to the integral power). So that the calculation is made by using the N’s data quantity which becomes the maximum but not exceeding the measuring data number from the top of the sampling data. The power graph which was obtained as the above result is therefore not the result from the whole area (or data) of the evaluation but the result from the limited area of ‘Measuring length’ x ‘ N ‘ / ‘Measurement data point number’.

② From the peculiarity of the FFT calculation, results of the quantity of N / 2 are sampled.

Therefore, the quantity of N / 2 are calculated as its data on the graph.

4.0µm

0.00µm500µm 50µm

0.5µm

6-10

③ This explains about a drawing of a figure. The numerical value indicated in upper side of the axis of ordinates means the maximum whole amplitude value in the unit of μm. The numerical value indicated in the left side of the axis of abscissas means the corresponding length or effective measuring length to N , and the numerical value indicated in the right side means ‘ Measurement effective length ‘ / (N / 2) or resolution of the axis of abscissas. The drawing of a figure is made by plotting the result obtained by the FFT at even intervals, and it is not possible to indicate the value excepting for the calculated result. When the coordinates of plotting in the axis of abscissas is set as shown below:

Effective measuring length = LE, N2 = N / 2 It becomes as follows from the left side.

LE / 1, ; (In case of being set to 1 wavelength for the total effective measuring length) LE / 2, ; (In case of being existed 2 wavelengths within the effective measuring length) LE / 3, ・・・ LE / (N2 – 2), LE / (N2 – 1), LE / N2 ; (In case of being existed wavelengths of the quantity of N2 within the

effective measuring length)

7-1

7 PARAMETERS FOR BEARING AREA CURVE Profile Bearing Length Ratio/Profile Bearing Ratio (tp), Material Ratio of the Profile (Mr, Rmr, Pmr, Wmr)

A sampling length, L is extracted from the sampling curve, and the length of the surface cutting portion which was cut by a straight line of being parallel to the mean line of the reference length and of being located at the cutting level C from the maximum highest peak is expressed in percentage toward the whole length L.

T p ( C ) = ∑ b i %100L

N

i=1 The cut level, C can be selected from the following two methods. (1) % method: This is shown as a percentage % when the level of the highest peak is set to 0% and the

deepest valley is set to 100%. In the evaluation length Ln, each tpi is obtained at the cut level being set as 100% for the

maximum height Ry to the each reference length L of the quantity of "n", and it is calculated as the average value of the quantity of "n".

(2) µm method: This is shown as the depth in µm unit from the highest peak or the height (depth) in µm

unit from mean line. In the evaluation length Ln, set the highest (or mean line) point in each reference length of

the quantity of "n" to zero, and each tpi is calculated at the cut level C of the depth (or height/depth) shown in µm, then calculate the average value of the quantity of "n".

C

Ry(100 %)

L

b 3 b i b n

b 1 b 2

7-2

TABLE 7.1 Parameter Names and Sampled Curves under Various Standards Standard Roughness Profile R & Phase Correct Roughness Profile Rg P-Profile Filtered Waviness

1-Sampling length(Country) Mean value of values obtained per

each Sampling Length Value per

Evaluation Length Value per

Evaluation Length Value per

Evaluation LengthISO04287:1997 (Int’l Standard)

-

Material ratio of the profile Pmr

Material ratio of the profile

Rmr

Material ratio of the profile

Wmr JIS B0601-1994 Bearing length ratio tp - - -

ISO468-1982 ISO4287/1-1984

Profile bearing length Ratio tp

(Rmr by the draft of DIS4287/1-1994)

(Pmr by the draft of DIS4287/1-1994)

-

ASME B46.1-1995 (USA)

- Profile Bearing Length Ratio Tp

- -

DIN4768 (Germany)

(Micro-Profile Bearing ratio tpi) - - -

B.S.1134-1988 (UK)

Profile bearing Length Ratio tp

- - -

7-3

Bearing Area Curve(BAC)/Abbott-Firestone Curve/ Material Ratio Curve (MRC)/Curve of the Profile Bearing Ratio (BC)

This is the graphic representation in the relationship between every cut level C (% and µm) in the sampled curve and the bearing length ratio tp (%) in the cut level. In 1933, Abbott and Firestone found that the distributed pattern of surface roughness played a significant role and introduced the concept of bearing length ratio graph. This is equivalent to cumulative density distribution function in statistics. The upper part of the curve represents the operation characteristic upon the trial operation of machine, the mid part represents the prediction of abrasion and service life, and the lower part represents the size of the oil deposit on the bearing surface.

Sampled curve Bearung area curveZ

X

C

Cut level

C %

0 %

50 %

100% 0 % 100 %tp

Note : Profile curve P in JIS82 mode and Gaussian distribution characteristics phase correct

roughness profile Rg in the other modes are used. In case the 2RC roughness profile is employed, some profile curve may cause phase

shifts and distortion in the waveforms by the cutoff, which resulting in the change in the bearing length ratio curve. Thus reliable evaluation will not be expected.

Method of Cut Level Cut level C is expressed by either of the following notations. (1) % Expressed as a percentage where the level of the highest peak is 0% and that the level of

the lowest peak is 100%. (ISO4287/1,DIN4762/1)

(2) µm Expressed in µm unit by the depth from the highest peak where the level of the highest

peak is 0µm. Or expressed by height (depth) in µm unit from the mean line which height is assumed 0 µm.

7-4

Method of Length Reference There are following three types of method for drawing bearing curve according to the calculation method of the bearing length ratio. (1) Evaluation Length Method (ISO13565-1 also uses the evaluation length system. Bearing curve is calculated from

special roughness curve of ISO13565-1.) (2) µm Display Reference Length Method This is drawn as tp by making average in each cut level of the µm method with combined

the peak lines of each reference line. (3) % Display Reference Length Method This is drawn as tp by making average in each cut level % after being normalized with the

maximum height Ryi in each reference length and displayed in %. (Based on JIS B0601-1994, ISO4287/1-1984)

Bearing curves based on the method of length reference

Sampling length (I)

Evaluation Length (Le)

Rt


Sampling length (I)

Sampling length (I)


Rymax

100%

Evaluation length method

µm-display referencelength method

% display referencelength method

7-5

Bearing Length Ratio 2/Profile Bearing Ratio (tp2)/Relative material ratio (Pmr2, Rmr2, Wmr2) The bearing length ratio tp2 (%) means the ratio after abrasion to the depth of Z (= C0-Cn) µm from the cutting level C0 which is equivalent to the bearing length ratio tpC0 (%) after the specified initial abrasion in the bearing area curve.

Notation : t p 2 ( 5 % , 2 µm ) > 7 0 % ↑ ↑ ↑ tp(C0) Z=C0−Cn tp2

As sampled curve, profile curve is employed in JIS82 mode and the roughness curve is employed in the other modes. This parameter is specified only under private standards and not under national standards.

0 %

C0 %

Cn %

100 %

( C0-Cn ) µm

tp

0 % tp ( C0 ) tp 2 100 %

7-6

Difference of Bearing Length Ratio (tp(Cn-C0),Rδmr) This is a value of difference between the bearing length ratio tp (C0) at the reference cut level C0 where a reference length L was extracted from the sample curve and the bearing length ratio tp (C0) at the specified cut level Cn.

t p ( C n −C 0 ) = t p ( C n ) − t p ( C 0 ) The cutting level C is expressed by a percentage % when the maximum peak height is set to 0% and the minimum valley depth is set to 100%, by the depth from the maximum peak height in the unit of µm or the height (depth) of µm unit from the mean line position. Notation : Firstly display as tp0 : t p ( C 0 ) = ✻ ✻ . ✻ % and specify the C0. ① When the tp-val is under the unit of % t p ( ✻ ✻ − ✻ ✻ % ) = ✻ ✻ . ✻ % ② When the tp-val is under the unit of µm t p ( ✻ ✻ ✻ ✻ ✻ − ✻ ✻ ✻ ✻ ✻ µm ) = ✻ ✻ . ✻ % This parameter is specified only under private standards and not under national standards. In this instrument, it is set in the item of "Difference of tp reference value".

Z

0 %

C0 %

Cn %

100 % tp

0 % tp ( C0 ) tp (Cn) 100 %

tp ( Cn - C0 )

7-7

Profile Section Height Difference (Rδc, Pδc, Wδc)/ Height of Plateau (Hp) This is the difference, C0−Cn (µm) between the bearing length ratio tp (C0) (%) after the specified initial abrasion and the bearing length ratio after a long term abrasion, tp (Cn) (%) on a bearing area curve.

Notation : H p ( 7 0 − 2 ) ＜ 0 . 5 µm ↑ ↑ ↑ tp(Cn) tp(C0) Hp

As sampled curve, profile curve is employed in JIS82 mode and the roughness curve is employed in the other modes.

0 %

C0 %

Cn %

100 %

Hp or Rδc

tp

0 % tp ( C0 ) tp (Cn) 100 %

Z

This parameter is specified only under private standards and not under national standards. These parameters of tp2, Rδc(Hp) and tp(Cn-C0) are used to indicate the roughness condition with good abrasion resistance in the drawing with referring to the bearing area curve. When the above bearing area curve is analyzed; the depth (roughness) between 0% - C0% indicates the initial abrasion portion which will be worn away soon by the running-in. The portion between Cn - 100% is equivalent to the oil deposit bearing portion. The portion between C0 - Cn % is the portion representing the abrasion resistance performance, which is called as plateau. The flatter and longer the plateau, the better the abrasion resistance performance. In general, the bearing length ratio of initial abrasion portion, tp (C0) is set at 1 to 5%, and that of plateau tp (Cn) is set at 40 to 80%. Generally, bearing length ratio is gradually improved by abrasion and with the increase in the bearing length ratio, the contact state changes from "point contact" to "contact on surface". The system performs oil lubrication to stop abrasion to progress further more. In this process, large size-reduction due to abrasion will cause troubles such as sooseness in the bearings. Designating the bearing length ratio tp (Cn) after abrasion or the amount of abrasion Z, the surface characteristics is controlled by calculating the abrasion height Z or bearing length ratio tp (Cn) after abrasion.

7-8

ISO13565 (DIN4776) Special Bearing-Area Curve Parameters (Mr1, Mr2, Rpk, Rvk, Rk, V0, K) These are standards to evaluate lubrication characteristics of the bearing are curve by dividing into an initial abrasion portion, material contact portion and oil reservoir portions. (DIN 4776-1990, ISO13565-2) This is mainly for plateau honing processing surfaces. By the special roughness curve Rg2 explained in the chapter 2, the bearing area curve is calculated by the evaluation length method and µm method, then the parameters will be calculated.

(1) Bearing Length Ratio 1 Mr1 (Material portion 1) (Materialanteil 1) Extract the width which becomes 40% in the direction of tp value on the bearing area

curve, and find out the position where different value of the both end heights becomes the minimum (minimum tilt line). And calculate the intersection point 'a' between the line which passes two points of the above and the limit line of tp = 0%.

Set the intersection point between the horizontal line 'ac' from the point 'a' and the bearing area curve as 'c', and set the tp value at this time as Mr1. This represents bearing length ratio after initial abrasion.

(2) Bearing Length Ratio 2 Mr2 (Material portion 2) (Materialanteil 2) Extract the width which becomes 40% in the direction of tp value on the bearing area

curve, and find out the position where different value of the both end heights becomes the minimum (minimum tilt line). And calculate the intersection point 'b' between the line which passes two points of the above and the limit line of tp = 100%.

Set the intersection point between the horizontal line 'bd' from the point 'b' and the bearing area curve as 'd', and set the tp value at this time as Mr2. This represents bearing length ratio after initial abrasion.

(3) The Reduced Peak Height Rpk (The reduced peak height) (Reduzierte Spitzenhohe) Rpk is the height on the limit line of tp = 0% which composes right triangle with the side

'ac', and the area of this right triangle is equal to that of the portion surrounded by the lines of tp = 0% limit line, the side 'ac' and the bearing area curve.

This represents the abrasion height of the initial wear. (4) The Reduced Valley Depth Rvk (The reduced valley depths) (Reduzierte Riefentiefe) Rvk is the height on the limit line of tp = 100% which composes right triangle with the side

'bd', and the area of this right triangle is equal to that of the portion surrounded by the lines of tp = 100% limit line, the side 'bd' and the bearing area curve.

This represents the valley depth of the oil deposit. (5) Core Roughness Depth Rk (Core roughness depth) (Kernrauhtiefe) Rk is the difference of the heights between the 'c' and 'd' obtained in the above. This represents the height of abrasion which plane will be worn away by the long term

abrasion.

7-9

(6) Oil Retention Volume V 0 (Oil retention Volume) This represents volume of oil which is deposited in the oil deposit valley per 1cm2.

V 0 = ( mm3/cm2) ( 1 0 0 −M r 2 )×R v k

2 0 0 0 However, the unit (mm3/cm2) is not displayed due to the limited display space. Be attentive, because it is of irregular expression. Here, in the formula, Mr2 is expressed in %, while Rvk in µm. For these parameters, only those of mm unit notation are applicable, but those of inch are not displayed.

Note) Previous edition of this book for the same equipment described the unit notation changed to the following by the convenience of unit display.

V 0 = (μ m ) ( 1 0 0 −M r 2 )×R v k

2 0 0 This expresses the volume (µm3) of oil retained in the reduced valley depth in each unit area of 1µm2. Convert the numerical values of both unit notations by the following formula.

V 0 = ( mm3/cm2) = V 0 ( µm )／ 1 0

Oil retention

1 cm Rvk(µm)

(100−Mr2)%

1 cm = 100% (7) Reduced Valley Depth Ratio K (Reduced valley depth ratio)

This represents the ratio of oil deposit valley depth to the effective bearing area roughness, and larger the value is the better the lubricating characteristic is.

K = R v k / R k (Non-dimensional number) Note : A parameter of profile coefficient was used before by the same "K" before. Profile coefficient K = R v / R m a x This is the same kind of the parameter as the oil deposit valley depth ratio by

which it can be calculated in manual.

Rvk Rk

a Minimum tilt line

Cut level C

(Unit : µ m

)

c

d

Rpk

0 20 40 60 80 100% Mr1 Mr2

b

Special roughness curve Rg2on the objective surface

Bearing length ratio Mr (Unit: %)

8-1

8 PARAMETERS FOR AMPLITUDE DISTRIBUTION Amplitude Density Function/Amplitude Distribution Curve/ Distribution of Profile Departure Density (ADC, ADF)

This is shown in a graph of probability that all of the cut level 'c' in a sampled curve and the sampled curve becomes equal to the cut level.

X ( c ) = T p ( c ) − t p ( c + ∆ c )∆ c

This is calculated as ∆c = Ry / 100 . (A unit of : 1%) This is that the bearing area curve is differentiated by the cut level 'c'. When the bearing area curve is X = F (c) and amplitude distribution curve is X = G (c), it has the following relations.

G ( c ) = F ( c )dd c

This curve is called as probability density function in statistics, and it comes close to the normal distribution in a random waveform.

Sampled curve Amplitude Density FunctionZ

X

c

cCut level

0 %

50 %

100 % 0 %X (p)

Note 1 : In the JIS82 mode, a profile curve, and the roughness profile in the other mode, is

uses as the sampling curve. When a filtered center line waviness curve in the mode of IS097 is measured, the filtered center line waviness is used as its sampling curve.

Note 2 : This is the curve for reference defined in ISO4287-1997, ISO4287/1-1984 and ANSI B46. 1-84.

Note 3 : The cutting level method and the reference length method are the same as the bearing area curve. Refer to the Chapter 7.

8-2

Skewness (Rsk, Sk) This is the parameter that indicates the symmetric property for the centerline of amplitude density function (ADF) and is expressed by the formula:

R s k = ∫ Z3P ( z ) d z = ∑ yi3 ∞

−∞

1 Rq3

n i=1

1 Rq3×n

Where, Rq : Root-mean-square roughness (square root of the quadratic moment of amplitude density function) ∫Z3P(z)dz : The moment of degree three of an amplitude density function n : Number of samples of measurement data yi : Height from the center-line of the roughness profile of the i-th

measurement data This is the curve for reference defined in ISO4287-1997, ISO4287/1-1984 and ANSI B46. 1-84. Skewness shows whether or not many of the object is on the mean line. When the portion with larger probability density of amplitude density function deflects to; A The upper side of its center-line, Rsk < 0 This shows the surface to have been worn away,

or the hard to be abrasive and good for lubricant surface.

B Being nearly agreed with the mean line, Rsk = 0 This shows the symmetry of upper and lower

sides of the waveform. C The lower side, Rsk > 0 This shows the surface which has not yet been

worn away, or the surface which is easy to be worn away and is deteriorated for the lubrication.

Mean line (phase correct)Center Line (2RC)

１

0

C

X (c)

−1

ADC


１

0

C

X (c)

−1

ADC


１

0

C

X (c)

−1

ADC

8-3

Kurtosis (Rku, Kurt) This parameter indicates the features of the amplitude density curve (ADC) such as whether it is peaked or collapsed, and is expressed by the formula.

R k u = ∫ Z4P ( z ) d z = ∑ yi4 ∞

−∞

1 Rq4

n i=1

1 Rq4×n

Where, ∫Z4P(z)dz : The moment of degree four of an amplitude density function

On the basis of the assumption that the amplitude density function is the normal distribution, Rku value is as follows;


−1

１

0

C

−1

１

0 X(c)

−1

１

0

ADC

0<Rku<3 : Rku=3 : Rku>3 : The broadened peaked Normal distribution The shaped peak of density distribution, or platykurtic distribution. or leptokurtic distribution distribution

9-1

9 PARAMETER FOR MOTIF What is the motif calculation? The motif calculation is prescribed in ISO12085-1997. The motif calculation is the measurement method that is originally defined in the French automobile industry. This method is the individual investigation to distinguish the roughness from waviness, and by using the calculation method, it can evade a difference between the visual evaluation that is caused by a deformation of the waving form that have been occurred frequently in the usual filter method. The pre-travel and post-travel become no need because the filter processing is not done. (The motif calculation is prescribed in ISO12085-1997.) Motifs upper limit length Although it was mentioned that the filter processing is not done in the above, the equivalent process is needed to be performed to separate the roughness from waviness. The details will be mentioned later in this chapter, for the process, the indication value that is equivalent to the cutoff value in the filter processing is needed. The indication values are called as “Roughness motifs upper limit length (the operator A)” and “Waviness motifs upper limit length (the operator B)”. The former shows the fineness of the transverse directional texture (measurement direction) on the roughness motif calculation, and the latter shows the fineness of the transverse directional texture (measurement direction ) on the waviness motif calculation. The following is the combined setting value of the motifs upper limit length, evaluation length, etc. that are recommended by the ISO standard.

Roughness motifs Upper limit length (A)

mm

Waviness motifs Upper limit length (B)

mm

Evaluation Length

mm

λs

µm

Max. radius of The stylus tip

µm 0.02 0.1 0.64 2.5 2±0.5 0.1 0.5 3.2 2.5 2±0.5 0.5 2.5 16 8 5±1 2.5 12.5 80 25 10±2

Reference) ･ The smaller stylus tips can reproduce the finer profiles. ･ The λs filter (a short wavelength cutoff filter) is capable of eliminating the

elements (outside oscillation and flaw) that have a smaller wavelength than the indication value more than 50%.

Note) ･ Although it does not necessarily set the recommended value, set them to become as the evaluation length can be more than twice of the motifs upper limit length. (There is a possibility that the waviness motifs parameter cannot be calculated

when it is less than twice.)

9-2

What is the motif? A portion of the primary profile between the highest points of two local peaks of the profile. The following marks are used to show the characters. Depth :Hj and Hj+1 (Roughness), Wj and Wj+1 (Waviness) Length (Width) :ARi (Roughness), AWi (Waviness) Either of the peaks that is smaller in the depth: T

How to calculate the motifs 1. Roughness motifs and Upper envelope line

Roughness motifs : It is constituted by the consecutive roughness motifs. Upper envelope line: The peaks of the roughness motifs are connected by a straight line.

2. How to find the Roughness motifs

a. eparate the evaluation length at intervals of the setting length (LH = Roughness motifs upper limit length/2). Regard the number of the division as n. Discard the fractions.

b. Find the difference between the maximum value and the minimum value (HRi) at the every

setting length. c. Find the peaks height conditions (Hmin ). (It is 5% of the average value of HRi ).

Peak Peak

Hj+1 (T)

ARi

Hj

Profile curveUpper envelope line

Roughness motifs

9-3

HR i-1

LH LH

HR i

d. Find the peaks and valleys.

Peaks have the valleys that have the difference more than Hmin in the both side.

e. Find the depth of the motifs. The depth of the motifs is the difference of the height between the lower peaks of the both side and the valley.

Peak Peak Motif depth Valley Motif

f. Constitute the segment. (In the whole of the evaluation range.)

When there is the peak that is higher than the front peak, that is the first peak, in the range of the distance within LR from the front peak, the peak becomes the end peak and it makes the one segment from the front to the end motifs. When there is no higher peak in the range, regard the highest peak as the end peak and make the one segment as well. After this, find the end peak repeatedly by regarding the end peaks as the front peaks. By the above way, constitute the segments with the succession of the made up motifs.

Peak Peak

Valle y Valle y

M otifs

∑

• • = n

HRi n

H i=1 min

1 05 . 0

9-4

g. Combine the motifs. (In the each segments.) When the each segments satisfies the following conditions 1~3 among the 1~4, make them combined. To combine means that to make the two adjacent motifs 1 motif. ･ Start from the first motif, operate for the i th motif and i th + 1st motif. When it was

combined, do the same for the i + 2nd one and the i + 3rd one next, if it was not combined, operate for the i + 1st one and the i + 2nd one.

･ When finish the last combination and any combination was made, do the combining operation again from the front, and repeat it until there is no motif to be combined anymore.

P1

P2 P3

T3 T1 T2 Tr ARi

1) Envelope condition

The height of the P2 that is the peak in the center must be less than either of the P1 or P3.

P2 ≦ P1 or P2 ≦ P3 2) Enlargement condition

T3 that is the motif depth after the combination must be deeper than the T1 and T2 that are the motif depth in both side.

T3 ≧ T1 or T3 ≧ T2 3) Depth condition

Either depth of the motifs in both side must be less than Tr that is 60% of T3 that is the motif depth when it assumes that the segment is 1 motif.

T1 ≦ Tr or T2 ≦ Tr 4) Length condition

ARi that is the motif width after the combination must be less than the motifs upper limit length LR.

ARi ≦ LR

h. Combine the motifs. (In the whole evaluation length)

When the above conditions 1~4 are satisfied in the whole evaluation length, make them combined.

In this case, T3 of the depth condition of above 3) becomes the depth of the motif when a

pair of motif under being about to be combined is regarded as having been combined.

9-5

i. Correct the height of the singular peaks and valleys. Correct the independent peaks and valleys not to exert a bad influence on the upper envelope line. (1) Preparation

Find the depth Hj, average of the whole Hj and the standard deviationσHj.

And, find the reference height Hs. Hs=Hj+1.65・σHj Pj-1 P j

Phj

Vhj-1

Vj Vj-1

(2) Correct the peaks

Correct the Phj value with comparing the Hs with Phj * and move the peak point of Pj to become Phj = Hs when Hs ＜ Phj .

* Phj : The height between Pj and the point of intersection of the perpendicular line from Pj and the line that connect Vj-1 with Vj .

(3) Correct the valleys (Correct it after the correction of peaks.)

Correct the Vhj-1 value with comparing the Hs with Vhj-1 * and move the valley point of Vj-1 to become Vhj-1 = Hs when Hs ＜ Vhj-1 .

* Vhj-1 : The height between Vj-1 and the point of intersection of the perpendicular line from Vj-1 and the line that connect Pj-1 with Pj .

j. The preparation of roughness motifs are completed by the above, now calculate

the parameter of roughness motifs next. <Roughness motifs parameter> NCRX (Number of valleys) : Number of the all valleys within the evaluation length

before combining of roughness motifs.

R (Mean depth of roughness motifs)

Rx (Maximum depth of profile irregularity) : Maximum value of the all roughness motifs depth

within the evaluation length. (For all of Hj )

∑=

•=m

jjHm

R1

1: Arithmetical mean value of the all roughness

motifs depth within the evaluation length.

Rx=MAX

∑=

•=n

jjj H

nH

1

1

2

1

)(1 ∑=

−•=n

jjjHj HH

nσ

9-6

AR (Mean spacing of roughness motifs) NR (Number of roughness motifs) : Number of the all roughness motifs within the

evaluation length. CPM (Mean number of valleys) SR (Standard deviation of roughness motifs depth) SAR (Standard deviation of roughness motifs space) ＊ m=2n Note) Rx should be calculated before correction of the height. The others should be calculated

after correction of the height. R and AR are calculated when 3 or more motifs exist.

3. Waviness motifs curve Profile curve Upper envelope line Roughness Waviness motifs motifs

Waviness motifs : It is constituted by the consecutive waviness motifs.

∑=

•=n

iiAR

nAR

1

1: Arithmetical mean value of the all roughness motifs

width within the evaluation length.

NR=n

NRNCRXCPM =

: Arithmetical mean value of the number

of valleys per a roughness motif.

: Standard deviation of the all roughness

motifs depth within the evaluation length.2

2

1

1 RHm

SRm

jj −•= ∑

=

: Standard deviation of the all roughness

motifs space within the evaluation length.∑=

−•=n

ii ARAR

nSAR

1

221

9-7

4. How to find the Waviness motifs

a. Find the peaks and valleys of the waviness motifs. The data sequence that the peaks data were replaced with the evaluation data in the roughness motifs is called the upper envelope line and find the peaks and valleys on this curve by following below. Find the point that the next point is lower than itself and make it the peak, and find the point that the next point is higher than itself and make it the valley.

Peak Peak Peak Peak Peak Valley Valley Valley Valley

b. Combine the waviness motifs The method conforms to the case of the roughness motifs, only LR is replaced with LW (Waviness motifs upper limit length).

c. The preparation of waviness motifs are completed by the above, now calculate

the parameter of waviness motifs next. <Waviness motifs parameter> W (Mean depth of waviness motifs)

Wx (Maximum depth of waviness) : Maximum value of the all waviness motifs

Wx=MAX(Wj) depth within the evaluation length. (For all of Wj )

AW (Mean spacing of waviness motifs)

Wte (Total depth of waviness) : P-P value of the upper envelope line. NW (Number of waviness motifs) : Number of the all waviness motifs within NW=n the evaluation length. SW (Standard deviation of waviness motifs depth)

∑=

•=m

jjWm

W1

1: Arithmetical mean value of the all waviness

motifs

: Arithmetical mean value of the all waviness

motifs ∑=

•=n

iiAW

nAW

1

1

: Standard deviation of the all waviness motifs

depth within the evaluation length. 2

2

1

1 WWm

SWm

jj −•= ∑

=

9-8

SAW (Standard deviation of waviness motifs space)

＊ m=2n Note) W and AW are calculated when 3 or more motifs exist.

: Standard deviation of the all waviness motifs

space within the evaluation length. ∑=

−•=n

ii AWAW

nSAW

1

221

10-1

10 SELECTION & EVALUATION METHOD OF CUTOFF VALUE • SAMPLING LENGTH Select the suitable cutoff value and reference length according to the specified roughness value size on a drawing after confirming the standard which has been pursuant to. Pursuant to JIS82 (JIS B0601-1982 and JIS B0601-1994 Annex)

(1) Cutoff Value and Measuring Length for Ra (Ra75) 2RC roughness curve is used for the sampling length.

Cutoff Value λc75 (mm)

Measuring Traverse Length Lm (mm)

Range of Ra (µm)

0.08 0.24 or more - 0.25 0.75 or more - 0.8 2.4 or more 12.5 or less 2.5 7.5 or more 12.5~100 8 24 or more -

(2) Sampling Length for Rmax, Rz Profile curve is used for the sampling length.

Sampling Length L (mm)

Range of Rmax/Rz (µm)

0.08 - 0.25 0.8 or less 0.8 0.8 ~ 6.3 2.5 6.3 ~ 25 8 25 ~ 100

25 100 ~ 400 (3) Evaluation Method of Measured Value Excepting the part of a scratch, calculate the arithmetic mean value of the parameter in

each part which was sampled at random from the workpiece surface (the objective surface). And make judgment whether or not the value is within the specified tolerance (or upper and lower limit values in case of being specified two positions).

10-2

Pursuant to JIS94 (JIS B0601-1994) The Gaussian distribution characteristic phase correct roughness profile is used for the sampling curve. (1) Cutoff Value, Sampling Length and Evaluation Length for Ra, Ry, Rz

Cutoff Value Sampling Length Evaluation Length Range of Ra (µm) Range of Ry / Rz (µm)λc (mm) L (mm) Ln (mm) Over Under Over Under

0.08 0.08 0.4 (0.006) 0.02 0.025 0.1 0.25 0.25 1.25 0.02 0.1 0.1 0.5 0.8 0.8 4 0.1 2 0.5 10 2.5 2.5 12.5 2 10 10 50 8 8 40 10 80 50 200

(2) Cutoff Value, Sampling Length and Evaluation Length for Sm and S

Cutoff Value Sampling Length Evaluation Length Range of Sm / S (mm) λc (mm) L (mm) Ln (mm) Over Under

0.08 0.08 0.4 0.01 0.032 0.25 0.25 1.25 0.032 0.1 0.8 0.8 4 0.1 0.32 2.5 2.5 12.5 0.324 1.0 8 8 40 1.0 3.2

(3) Evaluation Method of Measured Value

Excepting the part of a scratch, calculate the arithmetic mean value of the parameter in each part which was sampled at random from the workpiece surface (the objective surface). And make judgment whether or not the value is within the specified tolerance (or upper and lower limit values in case of being specified two positions).

10-3

Pursuant to ISO84/BS/ANSI (ISO4288-1985,BS1134-1988 and ANSI B46/1) 2RC roughness curve is used for the sampling curve. (ISO03274-1975/BS1134/1-1988/ANSI B46.1-1985)

(1) Cutoff Value, Sampling Length and Evaluation Length for Random Waveform Profile without Periodicity

Cutoff Value Sampling Length Evaluation Length Range of Ra (µm) Range of Ry / Rz (µm)λc (mm) L (mm) Ln (mm) Over Under Over Under

0.08 0.08 0.4 (0.006) 0.02 (0.025) 0.1 0.25 0.25 1.25 0.02 0.1 0.1 0.5 0.8 0.8 4 0.1 2 0.5 10 2.5 2.5 12.5 2 10 10 50 8 8 40 10 80 50 200

(2) Cutoff Value, Sampling Length and Evaluation Length for Periodic Curve


0.08 0.08 0.4 (0.4~2) 0.01 0.032 0.25 0.25 1.25 (1.25~5) 0.032 0.1 0.8 0.8 4 (2.4~8) 0.1 0.32 2.5 2.5 12.5 (5~15) 0.32 1.0 8 8 40 (16~40) 1.0 3.2

Note : The numerals in the ( ) are listed differencies when they are pursuant to BS1134/1-1988 and ANSI B46/1.

(3) Evaluation Method of Measured Value (ISO4288)

① Check in visual the way of processing, and make judgment of either periodic waveform or random waveform.

② When the tolerance value is specified, measure the parameter after specifing the measurement condition from the table of above.

③ When the tolerance value is not specified, select the appropriated measuring condition from the calculated value. And then make the measurement again.

④ After obtaining the measured value, make judgment by the following method whether or not the value is within the specified tolerance in the drawing. (a) When the upper limit value of the surface roughness parameter is specified, measure

the portion where the roughness seems to be the maximum roughness value. And if the part which exceeds the illustrated value takes part of less than 16% of the all measurement values, or if the value of µ+σ is less than the standard value, it can be accepted. In case of the following result, for example, it can be accepted. • The first measurement value does not exceed 70% of the illustrated value. • The first measurement values for three times does not exceed the illustrated value. • More than one measurement value out of the first six measurement values does not exceed the illustrated value. • More than two measurement values out of the first twelve measurment values do not exceed the illustrated value.

(b) When the lower limit value of the surface roughness parameter is specified, measure the portion where the roughness seems to be the minimum roughness value. And if the part which is lower the illustrated value takes part of less than 16% of the all measurement values, or if the value of µ−σ is more than the standard value, it can be accepted.

(c) When the maximum value of the surface roughness parameter is specified, that is, the "max" is attached to the parameter mark, it can be passed in case of that all of the measurement values on the entire surface under measurement are less than the illustrated value.

10-4

In conformity to the former DIN (DIN4768/1-1990) The Gaussian distribution characteristic phase correct roughness curve is used for the sampling curve. (DIN4777-1990) (1) Cutoff Value, Sampling Length and Evaluation Length for Random Waveform Curve

without Periodicity Cutoff Value Sampling Length Evaluation Length Brange of Ra (µm) Brange of Ry/Rz (µm)λc (mm) L (mm) Ln (mm) Over Under Over Under

0.08 0.08 0.4 - 0.02 0.025 0.1 0.25 0.25 1.25 0.02 0.1 0.1 0.5 0.8 0.8 4 0.1 2 0.5 10 2.5 2.5 12.5 2 10 10 50 8 8 40 10 - 50 200



0.08 0.08 0.4 0.01 0.04 0.25 0.25 1.25 0.04 0.13 0.8 0.8 4 0.13 0.4 2.5 2.5 12.5 0.4 1.3 8 8 40 1.3 4.0

(3) Evaluation Method of Measured Value

① Check in visual the way of processing, and make judgment of either periodic waveform or random waveform.

② When the tolerance value is specified, measure the parameter after specifing the measurement condition from the table of above.

③ When the tolerance value is not specified, select the appropriated measuring condition from the calculated value. And then make the measurement again.

④ After obtaining the measured value, make judgment whether or not the value is within the specified tolerance in the drawings. (Upper and lower values in case of being specified to the two of them.)

10-5

Pursuant to ISO97/ASME/DIN (DIN ISO4288:1996, DIN ISO4288-1996 and ASME B46. 1-1995) The Gaussian distribution characteristic phase correct roughness curve is used for the sampling curve. (ISO4287:1997 and ISO11562:1996) (1) Cutoff Value, Sampling Length and Evaluation Length for Random Waveform Curve

without Periodicity Cutoff Value Sampling Length Evaluation Length Brange of Ra (µm) Brange of Rz (µm)λc (mm) L (mm) Ln (mm) Over Under Over Under

0.08 0.08 0.4 0.006 0.02 0.025 0.1 0.25 0.25 1.25 0.02 0.1 0.1 0.5 0.8 0.8 4 0.1 2 0.5 10 2.5 2.5 12.5 2 10 10 50 8 8 40 10 80 50 200 Note: The range of Ra is effective when the parameters of Ra, Rq, Rsk, Rku and RΔq

are measured. (ISO4288:1996) And the range of Rz is effective when the parameters of Rz, Rv, Rp. Rc and Rt are measured. (ISO4288:1996)


Cutoff Value Sampling Length Evaluation Length Range of RSm (mm) λc (mm) L (mm) Ln (mm) Over Under

0.08 0.08 0.4 0.013 0.04 0.25 0.25 1.25 0.04 0.13 0.8 0.8 4 0.13 0.4 2.5 2.5 12.5 0.4 1.3 8 8 40 1.3 4.0

10-6

(3) Evaluation Method of Measured Value (ISO4288:1996) ① Check in visual the way of processing, and make judgment of either periodic waveform

or random waveform. ② When the tolerance value is specified, measure the parameter after specifing the

measurement condition from the table of above. ③ When the tolerance value is not specified, select the appropriated measuring condition

from the calculated value. And then make the measurement again. ④ After obtaining the measured value, make judgment by the following method whether or

not the value is within the specified tolerance in the drawing. (a) When the upper limit value of the surface roughness parameter is specified, measure

the portion where the roughness seems to be the maximum roughness value. And if the part which exceeds the illustrated value takes part of less than 16% of the all measurement values, or if the value of µ+σ is less than the standard value, it can be accepted. In case of the following result, for example, it can be accepted. • The first measurement value does not exceed 70% of the illustrated value. • The first measurement values for three times does not exceed the illustrated value. • More than one measurement value out of the first six measurement values does not exceed the illustrated value. • More than two measurement values out of the first twelve measurment values do not exceed the illustrated value.

(b) When the lower limit value of the surface roughness parameter is specified, measure the portion where the roughness seems to be the minimum roughness value. And if the part which is lower the illustrated value takes part of less than 16% of the all measurement values, or if the value of µ−σ is more than the standard value, it can be accepted.

(c) When the maximum value of the surface roughness parameter is specified, that is, the "max" is attached to the parameter mark, it can be passed in case of that all of the measurement values on the entire surface under measurement are less than the illustrated value.

10-7

Exception of Sampling Length and Evaluation Length: In case of unavailble measurement with standard value Select the above sampling length, cutoff value, measurement length and evaluation length in accordance with the adopted standard. Depend on the size of the measurement object, it might be changed the length as follows:- (1) Unavailable to get Standard Value of Evaluation Length When the evaluation length is set to Ln and five times of the cutoff value λc are not

available to get, a cutoff value of the integer multiple can be accepted.(ISO4288) Therefore, in this case, select the evalulation length from the integer multiple of the

sampling length. (2) Unavailable to get Multiple of Cutoff Value for Evaluation Length When the evaluation lengths is obliged to change slightly due to the measurement object

and the purpose, it is exceptionally accepted to use the value of longer sampling length L than the cutoff value λc.

In this case, however, clearly indicate the values of λc and L . When these evaluation length is specified in this measuring instrument, the sampling

length will be set as follows; ① In case of that the evaluation length Ln is smaller than λc (Ln<λc), → It becomes to L = Ln . ② In case of that the evaluation length Ln does not become multiple of λc

[nλc>Ln>(n+1)✕λc], → It becomes to L = Ln/n . ③ In case of that the evaluation length Ln is bigger than 150 times of λc (Ln>150✕λc), → It becomes to L = Ln/150 .

(3) Smaller Workpiece Surface Length than the added Length of Cutoff Value and Preparatory

Length (Lt<λc+Lpe+Lpo) Preparatory length is necessary for making cutoff, but in case of the small area where can

be measured, it is not possible to get the parameter calculation specified in the standard. In this case, set the sampling curve to profile curve P only then the preparatory length

becomes the minimum. Under this condition, estimate the specified parameter by calculating the parameters of the maximum profile Rmax, Pt or ten-point-mean roughness Rzj, by making to JIS mode or by reading from the recorded profile curve.

11-1

11 Average value process of the parameter.

In general, surface parameter spreads out unevenly on the same surface depending on parts to

parts.

Measure the points as much as possible on the same level in order to make it equal, and make

statistical evaluation. Then calculate average value of the parameter from several measurements

by average calculation method, and define as measurement value of the surface.

The following are the displayable parameter from average value process. Note）Average value X is the only displayable average value of Surfcom130A, 480A.

Following maximum value and standard deviation, minimum value are displayed by

Surfcom after 1400D.

(1)Average value process：Supposing that 1 parameter is figured per 1 evaluation Length, then

calculate average value, considering this value as a repetitious measurement value for several

evaluation length.

Average value X ：Xi is the data per 1 evaluation length, this average value is calculated by n

times measurement. Compare average value X with tolerance, and judge OK/NG

decision (judge).

n

xX

n

ii

=∑= 1

(2)MAX rule：When evaluation length parameter is attached with character MAX, i.e. 1 parameter

is figured per 1 evaluation length, calculate maximum value, considering this value as a

repetitious measurement value for several evaluation lengths.

Maximum X : Xi is the data per 1 evaluation length, this maximum value is calculated by n times

measurement.Compare maximum value with tolerance and judge OK/NG decision.

11-2

(3)16% rule: In the case that 16 % rule is adapted for evaluation length parameter, i.e. 1

parameter is figured per 1 evaluation length, and take this value for repetitious

measurement value, µ+σ and µ-σ (ISO4288 method)

Specimen standard deviation σn：Xi is the date per 1 evaluation length, this is the standard

deviation for n times measurement.

−= ∑ ∑

= =

n

i

n

iiin xxn

n 1

2

1

22

1σ

Calculate this standard deviation, at the upper value, calculate µ+σ by manual and make

tolerance comparison judgment.

−+

=+=+ ∑ ∑∑

= =

=n

i

n

iii

n

ii

n xxnnn

xX

1

2

1

22

1 1σσµ

Between the range of 1<n<5, calculate converting σ into σ5.

−+

=+=+ ∑ ∑∑

= =

=n

i

n

iii

n

ii

n xxnn

nn

xnX

1

2

1

22

15

155

σσµ

At lower value, calculate µ-σ by manual and make tolerance comparison judgment.

−−

=−=− ∑ ∑∑

= =

=n

i

n

iii

n

ii

n xxnnn

xX

1

2

1

22

1 1σσµ

Between the range of 1<n<5, calculate converting σ into σ5.

−−

=−=− ∑ ∑∑

= =

=n

i

n

iii

n

ii

n xxnn

nn

xnX

1

2

1

22

15

155

σσµ

11-3

Note1) Notice that this standard deviation is σn (Sample standard deviation), this is calculated as

population standard deviation by considering only sample as known population.

−= ∑ ∑

= =

n

i

n

iiin xxn

n 1

2

1

22

1σ

In fact, population is unknown, and calculates average value µ by finite sample extracted from

population. Then standard deviation will be calculated, degree of freedom is n-1, which is

calculated by taking degree of freedom 1 of average value µ from sample number n. Formal

statistic uses following σn-1.

−

−= ∑ ∑

= =−

n

i

n

iiin xxn

nn 1

2

1

21 )1(

1σ

By the definition of standard, here we use specimen standard deviation σn for easy calculation

method.

(4)Minimum value：

Minimum value xmin：Xi is the data per 1 evaluation length, this is the minimum value from n times measurement. There is no minimum evaluation length in the roughness evaluation standard.

12-1

12 PARAMETER LIST Roughness and Waviness Parameters with SURFCOM

Parameters of standards for roughness and waviness which are currently applied by the major countries are as indicated in the chart of below. With the SURFCOM, parameters' group can be set to meet the individual national standard in various countries as shown in the table of below. As a standard of JIS (1982), JIS (1994), ISO (1984), ISO (1997), BS (1988),DIN (1990) and ASME (1995), this can display the parameters to match six types of the national standard. If it is set to a certain national standard, display of some parameters which are not specified in the national standard are also available.

(1) Parameters related to Amplitude

National Standard Parameter SURFCOM Parameter

Name Evaluation

Division

Sampled

Curve

(Note 1)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Center line Ｒ－Ｒa Ｒa －Ｒa Ｒa Ｒa －－－－－Ｒa

mean value ＷＣ－－－－－ＷＣＡＷＣＡ－Ｗa Ｗa Ｗa ＷＣＡＷＣＡ

1 division as total

evaluation length

ＷＥＣ－－－－－ＷＥＡＷＥＡ－－－－ＷＥＡＷＥＡ

ＰＰa －－－－－－Ｐa －－－－－ Arithmetical

mean value Ｗ－－－－－－－Ｗa Ｗa Ｗa Ｗa Ｗa ＷC-a

1 division as total

evaluation length

ＷE －－－－－－－－－－－ＷE-a ＷE-a

R/Rg Ｒamax Ｒamax －－－－－Ｒamax Ｒamax Ｒamax Ｒamax Ｒamax －

Maximum in each

reference length ＷＣＷamax －－－－－－Ｗamax －－－－－

R/Rg －－－－－－－Ｒamin Ｒamin Ｒamin Ｒamin Ｒamin －

Minimum in each

reference length ＷＣ－－－－－－－Ｗamin －－－－－

Average in each R/Rg Ｒa Ｒa －Ｒa －Ｒa －Ｒa Ｒa Ｒa Ｒa Ｒa －

reference length Ｗc Ｗa －－－－－－Ｗa －－－－－

R/Rg －－－－－－－Ｒasd Ｒasd Ｒasd Ｒasd Ｒasd －

Standard dev. σ

Ｗc －－－－－－－Ｗasd －－－－－

12-2

Parameters related to Amplitude (continue 2)


Name Evaluation

Division

Sampled

Curve

(Note 1)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Root mean 1 division as total ＰＰq －－－－－－Ｐq －－－－－

Square Value evaluation length Ｒ－Ｒq －－Ｒq －－－－－－－Ｒq

Ｗ－－－－－－－Ｗq Ｗq Ｗq Ｗq Ｗq ＷC-q

ＷＥ－－－－－－－－－－－ＷE-q ＷE-q

ＷＣ－－－－－－－－Ｗq Ｗq Ｗq ＷC-q ＷCC-q

ＷＥＣ－－－－－－－－－－－ＷEC-q ＷEC-q

R/Rg Ｒqmax Ｒqmax －－－－－Ｒqmax Ｒqmax Ｒqmax Ｒqmax Ｒqmax －

Maximum in each

reference length ＷＣＷqmax －－－－－－Ｗqmax －－－－－

R/Rg －－－－－－－Ｒqmin Ｒqmin Ｒqmin Ｒqmin Ｒqmin －

Minimum in each

reference length Ｗc －－－－－－－Ｗqmin －－－－－

R/Rg Ｒq Ｒq －－－－－Ｒq Ｒq Ｒq Ｒq Ｒq －

Average in each

reference length Ｗc Ｗq －－－－－－Ｗq Ｗq －－－－

R/Rg －－－－－－－Ｒqsd Ｒqsd Ｒqsd Ｒqsd Ｒqsd － Standard dev. σ

Ｗc －－－－－－－Ｗqsd －－－－－

Maximum Maximum in each R/Rg Ｒzmax Ｒymax － Rmax Rmax －－Ｒzmax Ｒymax Ｒmax Ｒmax Ｒymax －

height reference length Ｗc Ｗzmax －－－－－－Ｗzmax －－－－－

Minimum in each R/Rg －－－－－－－Ｒzmin Ｒymin Ｒmin Ｒmin Ｒymin －

reference length Ｗc －－－－－－－Ｗzmin －－－－－

Average in each R/Rg Ｒz Ｒy Ｒy Ｒz Ｒz Ｒy －Ｒz Ｒy Ｒz Ｒz Ｒy －

reference length Ｗc Ｗz －－－－－－Ｗz －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒzsd Ｒysd Ｒzsd Ｒzsd Ｒysd －

Ｗc －－－－－－－Ｗzsd －－－－－

Maximum roughness

1 division as total evaluation length Ｒ－Ｒy －Ｒt Ｒt －－Ｒt Ｒt Ｒt Ｒt Ｒt Ｒt

Maximum profile Ｐ－ (Ｐt) －Ｐt －－ Rmax Ｐt Ｐt Ｐt Ｐt Ｒmax Ｒmax

Maximum 1 division as total Ｗ－－－Ｗt Ｗt ＷＣＭＷＣＭＷt Ｗt Ｗt Ｗt ＷＣＭＷＣＭ

Waviness evaluation length ＷＥ－－－－－ＷＥＭＷＥＭ－－－－ＷEM ＷEM

ＷＣ－ (Ｗt) －－－－－Ｗt Ｗt Ｗt Ｗt ＷC-t ＷCC-m

ＷＥＣ－－－－－－－－－－－ＷEC-t ＷEC-m

10-point JIS height of

1 division of evaluation length Ｐ－－－－－－Ｒz Ｒz･J Ｒz･J Ｒz･J Ｒz･J Ｒz･J Ｒz

irregu- ISO larities

Maximum in each reference length R/Rg －Ｒzmax －－－－－－Ｒzmax RzImax RzImax Ｒzmax －

Minimum in each reference length R/Rg －－－－－－－－Ｒzmin RzImin RzImin Ｒzmin －

Average in each reference length R/Rg －Ｒz Ｒz －－Ｒz －－Ｒz Ｒz.I Ｒz.I Ｒz －

Standard dev. σ R/Rg －－－－－－－－Ｒzsd Rz.Isd Rz.Isd Ｒzsd －

12-3



Name Evaluation

Division

Sampled

Curve

(Note 1)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Base roughness

Average in each reference length Ｒ－－－－－－－Ｒ3z Ｒ3z Ｒ3z Ｒ3z Ｒ3z －

depth Average evaluation length/5 Ｒ－－－－－－－－－－－－Ｒ3z

Mean height 1 division of ＰＰc －－－－－－Ｐc.I －－－－－

of elements evaluation length R/Rg －Ｒc －－－－－－－－－－Ｒc

Maximum in each R/Rg Ｒcmax Ｒcmax －－－－－Ｒcmax Ｒcmax Ｒcmax Ｒcmax Ｒcmax －

reference length Ｗc Ｗcmax －－－－－－Ｗcmax －－－－－

Minimum in each R/Rg －－－－－－－Ｒcmin Ｒcmin Ｒcmin Ｒcmin Ｒcmin －

reference length Ｗc －－－－－－－Ｗcmin －－－－－

Average in each R/Rg Ｒc Ｒc －－－－－Ｒc Ｒc Ｒc Ｒc Ｒc －

reference length Ｗc Ｗc －－－－－－Ｗc －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒcsd Ｒcsd Ｒcsd Ｒcsd Ｒcsd －

Ｗc －－－－－－－Ｗcsd －－－－－

Maximum 1 division of ＰＰp －－－－－－Ｐp －－－－－

profile peak evaluation length R/Rg －Ｒp －Ｒp Ｒp －－－－－－－Ｒp

height Ｗ－－－－－－－－Ｗp Ｗp Ｗp Ｗp ＷC-p

ＷＥ－－－－－－－－－－－ＷE-p ＷE-p

ＷＣ－ (Ｗp) －－－－－－Ｗp Ｗp Ｗp ＷC-p ＷCC-p

ＷＥＣ－－－－－－－－－－－ WEC-p WEC-p

Maximum in each R/Rg Ｒpmax Ｒpmax －Ｒp －－－Ｒpmax Ｒpmax Ｒpmax Ｒp Ｒpmax －

reference length ＷＣＷpmax －－Ｗp －－－Ｗpmax －－－－－

Minimum in each R/Rg －－－－－－－Ｒpmin Ｒpmin Ｒpmin Ｒpmmin Ｒpmin －

reference length ＷＣ－－－－－－－Ｗpmin －－－－－

Average in each R/Rg Ｒp Ｒｐ－－Ｒpm －－Ｒp Ｒp Ｒp Ｒpm Ｒp －

reference length ＷＣＷp －－－－－－Ｗp －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒpsd Ｒpsd Ｒpsd Ｒpmsd Ｒpsd －

ＷＣ－－－－－－－Ｗpsd －－－－－

12-4



Name Evaluation

Division

Sampled

Curve

(Note 1)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Maximum 1 division of ＰＰv －－－－－－Ｐv －－－－－

profile valley evaluation length R/Rg －Ｒv －－Ｒv －－－－－Ｒv －Ｒv

depth Ｗ－－－－－－－Ｗv Ｗv Ｗv Ｗv Ｗv ＷC-v

ＷＥ－－－－－－－－－－－ＷE-v ＷE-v

ＷＣ－ (Ｗv) －－－－－－Ｗv Ｗv Ｗv ＷC-v ＷCC-v

ＷＥＣ－－－－－－－－－－－ＷEC-v ＷEC-v

Maximum in each R/Rg Ｒvmax Ｒvmax －－－－－Ｒvmax Ｒvmax Ｒvmax －Ｒvmax －

reference length Ｗc Ｗvmax －－－－－－Ｗvmax －－－－－

Minimum in each R/Rg －－－－－－－Ｒvmin Ｒvmin Ｒvmin －Ｒvmin －

reference length Ｗc －－－－－－－Ｗvmin －－－－－

Average in each R/Rg Ｒv Ｒv －－－－－Ｒv Ｒv Ｒv －Ｒv －

reference length Ｗc Ｗv －－－－－－Ｗv －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒvsd Ｒvsd Ｒvsd －Ｒvsd －

Ｗc －－－－－－－Ｗvsd －－－－－

Height of step Height of step

average Ｐ－－－－－－－ＡＶＨＡＶＨＡＶＨＡＶＨＡＶＨＡＶＨ

evaluation Max. height of step Ｐ－－－－－－－Ｈmax Ｈmax Ｈmax Ｈmax Ｈmax Ｈmax

range 1 division Min. height of step Ｐ－－－－－－－Ｈmin Ｈmin Ｈmin Ｈmin Ｈmin Ｈmin

Height of step area Ｐ－－－－－－－ AREA AREA AREA AREA AREA AREA

LCD waviness Full evaluation length ＷＣ－－－－－－－Ｗfpd Ｗfpd Ｗfpd Ｗfpd Ｗfpd Ｗfpd

Note 1) R : Roughness profile through 2RC filter

Rg : Roughness profile through Gaussian curve (Temporary mark)

P : Profile

W : Filtered waviness curve

WE : Rolling circle waviness curve

WC : Filtered center line waviness curve

WEC : Rolling circle center line waviness curve

12-5

(2) Parameters related to Wavelength and Slope


Name Evaluation

Division

Sampled

Curve

(Note 2)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Mean spacing 1 division of ＰＰSm (ＰSm) －－－－－ＰSm －－－－Ｓｍ

of profile evaluation length R/Rg －－－－Ｓm －－－－－－－－

Ｗ－－－－－－－ＷSm ＷSm ＷSm ＷSm ＷSm ＷC-Sm

ＷＥ－－－－－－－－－－－ＷE-Sm ＷE-Sm

ＷＣ－ (ＷSm) －－－－－－ＷSm ＷSm ＷSm ＷC-Sm ＷCC-Sm

ＷＥＣ－－－－－－－－－－－ WEC-Sm WEC-Sm

Maximum in each R/Rg ＲSmmax Ｓmmax －－－－－ RSmmax Rsmmax RSmmax RSmmax Smmax －

reference length Ｗc ＷSmmax －－－－－－ WSmmax －－－－－

Minimum in each R/Rg －－－－－－－ RSmmin Rsmmin RSmmin RSmmin Smmin －

reference length Ｗc －－－－－－－ WSmmin －－－－－

Average in each R/Rg ＲSm Ｓm Ｓm Ｓm －Ｓm －ＲSm ＲSm ＲSm ＲSm Ｓm －

reference length Ｗc ＷSm －－－－－－ＷSm －－－－－

Standard dev. σ R/Rg －－－－－－－ＲSmsd ＲSmsd ＲSmsd ＲSmsd Ｓmsd －

Ｗc －－－－－－－ＷSmsd －－－－－

Mean spacing 1 division of

evaluation length R/Rg －－－－－－－－－－－－Ｓ

of local peaks Maximum in each reference length R/Rg －Ｓmax －－－－－－ＲSmax ＲSmax ＲSmax Ｓmax －

of profile Minimum in each reference length R/Rg －－－－－－－－ＲSmin ＲSmin ＲSmin Smin －

Average in each reference length R/Rg －ＳＳＳ－Ｓ－－ＲＳＲＳＲＳＳ－

Standard dev. σ R/Rg －－－－－－－－ＲSsd ＲSsd ＲSsd Ｓsd －

Peak count 1 division of

evaluation length R/Rg －－－－Ｐc －－Ｐc Ｐc Ｐc Ｐc Ｐc Ｐc

Arithmetical 1 division of Ｐ－－－－－－－－－－－－ Δa

mean slope evaluation length

R/Rg －－－－ Δa －－－－－－－－

of profile Maximum in each reference length R/Rg － Δamax －－－－－ RΔamax Rδamax RΔamax RΔamax RΔamax －

Minimum in each reference length R/Rg －－－－－－－ RΔamin Rδamin RΔamin RΔamin RΔamin －

Average in each reference length R/Rg － Δa －－－－－ＲΔa ＲΔa ＲΔa ＲΔa ＲΔa －

Standard dev. σ R/Rg －－－－－－－ RΔasd Rδasd RΔasd RΔasd RΔasd －

12-6

Parameters related to Wavelength and Slope (Continue 2)


Name Evaluation

Division

Sampled

Curve

(Note 2)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Root-mean- 1 division of ＰＰΔq (ＰΔq) －－－－－ＰΔq －－－－ Δq

Square slope evaluation length R/Rg －－－－ Δq －－－－－－－－

of profile Maximum in each R/Rg RΔqmax Δqmax －－－－－ RΔqmax RΔqmax RΔqmax RΔqmax RΔqmax －

reference length Ｗc WΔqmax －－－－－－ WΔqmax －－－－－

Minimum in each R/Rg －－－－－－－ RΔqmin RΔqmin RΔqmin RΔqmin RΔqmin －

reference length Ｗc －－－－－－－ WΔqmin －－－－－

Average in each R/Rg ＲΔq Δq －－－－－ＲΔq ＲΔq ＲΔq ＲΔq ＲΔq －

reference length Ｗc ＷΔq －－－－－－ＷΔq －－－－－

Standard dev. σ R/Rg －－－－－－－ RΔqsd RΔqsd RΔqsd RΔqsd RΔqsd －

Ｗc －－－－－－－ WΔqsd ― WΔqsd WΔqsd WΔqsd －

Average 1 division of

evaluation length Ｐ－－－－－－－－－－－－ λa

wavelength Maximum in each reference length R/Rg － λamax －－－－－ Rλamax Rλamax Rλamax Rλamax Rλamax －

of profile Minimum in each reference length R/Rg －－－－－－－ Rλamin Rλamin Rλamin Rλamin Rλamin －

Average in each reference length R/Rg － λa －－－－－Ｒλa Ｒλa Ｒλa Ｒλa Ｒλa －

Standard dev. σ R/Rg －－－－－－－ Rλasd Rλasd Rλasd Rλasd Rλasd －

Root-mean- 1 division of

evaluation length Ｐ－－－－－－－－－－－－ λq

Square Maximum in each reference length R/Rg － λqmax －－－－－ Rλqmax Rλqmax Rλqmax Rλqmax Rλqmax －

Wavelength Minimum in each reference length R/Rg －－－－－－－ Rλqmin Rλqmin Rλqmin Rλqmin Rλqmin －

of profile Average in each reference length R/Rg － λq －－－－－Ｒλq Ｒλq Ｒλq Ｒλq Ｒλq －

Standard dev. σ R/Rg －－－－－－－ Rλqsd Rλqsd Rλqsd Rλqsd Rλqsd －

Average slope angle

1 division of evaluation length Ｐ－－－－－－－ TILTA TILTA TILTA TILTA TILTA TILTA

Profile length 1 division of Ｐ－－－－－－－－－－－－ｌr

ratio evaluation length R/Rg －ｌｒ－－－－－ｌr ｌr ｌr ｌr ｌr －

Note 2) P, W, WE, WC, WEC : Refer to explanation of curves.

R : Roughness curve through 2RC filter

Rg : Roughness curve through Gaussian filter (Temporary mark)

12-7

(3) Parameters related to Bearing Ratio Curve


Name Evaluation

Division

Sampled

Curve

(Note 3)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Bearing length 1 division of ＰＰmr() (Ｐmr) －－－－－Ｐmr －－－－ｔp

ratio tp & tp1 evaluation length R/Rg/

Rg２Ｒmr() (Ｒmr) －－ｔp －－Ｒmr Ｒmr Ｒmr Ｒmr Ｒmr －

Ｗc Ｗmr() －－－－－－Ｗmr －－－－－

Average in each reference length R/Rg － tp ｔp ｔp －ｔp －－ tp tp tp ｔp －

Bearing length 1 division of ＰＰmr －－－－－－Ｐmr2 －－－－ｔp2

ratio tp2 evaluation length R/Rg/

Rg２Ｒmr －－－－－－Ｒmr2 Ｒmr2 Ｒmr2 Ｒmr2 Ｒmr2 －

Ｗc Ｗmr －－－－－－Ｗmr2 －－－－－

Average in each reference length R/Rg －－－－－－－－ tp2 tp2 tp2 ｔp2 －

Cutting level 1 division of ＰＰδc (Ｐδc) －－－－－Ｐδc －－－－Ｈｐ

difference/ evaluation length R/Rg/

Rg２Ｒδc (Ｒδc) －－Ｈtp －－Ｒδc Ｒδc Ｒδc Ｒδc Ｒδc －

Height of Ｗc Ｗδc －－－－－－Ｗδc －－－－－

Plateau Average in each reference length R/Rg －－－－－－－－Ｒδc Ｒδc Ｒδc Ｒδc －

Core 1 division of Ｐ－－－－－－－－－－－－Ｒk

roughness evaluation length R/Rg/

Rg２Ｒk (Ｒk) －－－－－Ｒk Ｒk Ｒk Ｒk Ｒk －

depth Average in each reference length R/Rg －－－Ｒk －－－－Ｒk Ｒk Ｒk Ｒk －

The reduced 1 division of Ｐ－－－－－－－－－－－－Ｒpk

peak height evaluation length R/Rg/

Rg２Ｒpk (Ｒpk) －－－－－Ｒpk Ｒpk Ｒpk Ｒpk Ｒpk －

Average in each reference length R/Rg －－－Ｒpk －－－－Ｒpk Ｒpk Ｒpk Ｒpk －

The reduced 1 division of Ｐ－－－－－－－－－－－－Ｒvk

valley depth evaluation length R/Rg/

Rg２Ｒvk (Ｒvk) －－－－－Ｒvk Ｒvk Ｒvk Ｒvk Ｒvk －

Average in each reference length R/Rg －－－Ｒvk －－－－Ｒvk Ｒvk Ｒvk Ｒvk －

Bearing length 1 division of Ｐ－－－－－－－－－－－－Ｍr1

ratio 1 evaluation length R/Rg/

Rg２Ｍr1 (Ｒmr1) －－－－－Ｍr1 Ｍr1 Ｍr1 Ｍr1 Ｍr1 －

Average in each reference length R/Rg －－－Ｍr1 －－－－Ｍr1 Ｍr1 Ｍr1 Ｍr1 －

Bearing length 1 division of Ｐ－－－－－－－－－－－－Ｍr2

ratio 2 evaluation length R/Rg/

Rg２Ｍr2 (Ｒmr2) －－－－－Ｍr2 Ｍr2 Ｍr2 Ｍr2 Ｍr2 －

Average in each reference length R/Rg －－－Ｍr2 －－－－Ｍr2 Ｍr2 Ｍr2 Ｍr2 －

Oil retention 1 division of Ｐ－－－－－－－－－－－－Ｖ０

volume evaluation length R/Rg/

Rg２－－－－－－－Ｖ０Ｖ0 Ｖ０Ｖ０Ｖ０－

Average in each reference length R/Rg －－－－－－－－Ｖ０Ｖ０Ｖ０Ｖ０－

12-8

Parameters related to Bearing Ratio Curve (Continue 2)


Name Evaluation

Division

Sampled

Curve

(Note 3)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Reduced valley 1 division of Ｐ－－－－－－－－－－－－Ｋ

depth ratio evaluation length R/Rg/

Rg２－－－－－－－ＫＫＫＫＫ－

Average in each reference length R/Rg －－－－－－－－ＫＫＫＫ－

Note 3) Rg2 : DIN4776 method special roughness curve (Temporary mark)

(4) Parameters related to Amplitude Distribution


Name Evaluation

Division

Sampled

Curve

(Note 3)

ISO

Int'

1997

ISO

Int'

1984

BS

UK

1988

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

ISO

Int'

1997

ISO

Int'

1984

DIN

Ger.

1990

ASME

USA

1995

JIS

JPN

1994

JIS

JPN

1982

Skewness 1 division of ＰＰsk －－－－－－Ｐsk －－－－Ｒsk

evaluation length R/Rg/

Rg２－Ｓk －－Ｒsk －－－Ｒsk Ｒsk Ｒsk Ｒsk －

Maximum in each R/Rg －－－－－－－ Rskmax －－－－－

reference length Ｗc －－－－－－－ Wskmax －－－－－

Minimum in each R/Rg －－－－－－－ Rskmin －－－－－

reference length Ｗc －－－－－－－ Wskmin －－－－－

Average in each R/Rg Ｒsk －－－－－－Ｒsk Ｒsk Ｒsk Ｒsk Ｒsk －

reference length Ｗc Ｗsk －－－－－－Ｗsk －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒsksd －－－－－

Ｗc －－－－－－－Ｗsksd －－－－－

Kurtosis 1 division of ＰＰku －－－－－－Ｐku －－－－Ｒku

evaluation length R/Rg/

Rg２－－－－Ｒku －－－Ｒku Ｒku Ｒku Ｒku －

Maximum in each R/Rg －－－－－－－ Rkumax －－－－－

reference length Ｗc －－－－－－－ Wkumax －－－－－

Minimum in each R/Rg －－－－－－－ Rkumin －－－－－

reference length Ｗc －－－－－－－ Wkumin －－－－－

Average in each R/Rg Ｒku －－－－－－Ｒku Ｒku Ｒku Ｒku Ｒku －

reference length Ｗc Ｗku －－－－－－Ｗku －－－－－

Standard dev. σ R/Rg －－－－－－－Ｒkusd －－－－－

Ｗc －－－－－－－Ｗkusd －－－－－

A-1

Annex A. JIS 2001 In 2001, the Japanese Industrial Standards (JIS) were revised in accordance with the ISO standards (translated standards, referred to as “ISO 97” and JIS revised in 2001 is referred to as “JIS 01”). Therefore, if the text describes that an item is specified in ISO 97, you can judge that the item is also specified in JIS 01. In addition, the JIS uses its own terms, such as “rolling circle waviness”. For this reason, this section describes these terms. 1. Definitions of terms

Profile: Generic name for the primary profile, roughness profile, waviness profile, etc.

Sampling length: Length in the direction of the X-axis and used for obtaining the characteristics (parameters) of the profile. The roughness profile sampling length “lr” and waviness profile sampling length “lw” are equal to the profile filter cut-off lengths “λc” and “λf”, respectively. In addition, the sampling length for primary profile “lp” is equal to the evaluation length “ln”.

Evaluation length: Length in the direction of the X-axis and containing one or more sampling lengths.

Profile filter: Filter that separates the longwave components from the shortwave components included in a profile. There are three filters as described below: λs filter: Filter that defines the intersection between the roughness and the even shorter

wave components present in a surface. λc filter: Filter that defines the intersection between the roughness and waviness

components. λf filter: Filter that defines the intersection between the waviness and the even longer wave

components present in a surface. The transmission characteristics of the roughness and waviness profiles are shown in the following figure. The figure shows that the roughness profile is part of the entire profile; the wavelength λs-λc part of the entire profile.

The filter that eliminates the wave components longer than the cut-off value is referred to as the high-frequency pass filter, high-pass filter, long wavelength cut-off filter, etc. The filter that eliminates the wave components shorter than the cut-off value is referred to as the low-frequency pass filter, low-pass filter, short wavelength cut-off filter, etc.

A-2

Total profile: String of data points obtained by quantizing the profile detected by picking-up. Using the probe, this machine traces the real surface to sample data at the same intervals. This machine sequentially converts the obtained analog data to the digital data, and then quantizes the data to obtain the string of data points.

Primary profile: Profile obtained after applying the short wavelength cut-off filter having the cut-off value λs to the total profile. The primary profile parameters are calculated from the obtained primary profile. However, if the λs filter is not used, this machine will calculate the primary profile parameters from the total profile.

Roughness profile: Profile obtained after applying the long wavelength cut-off filter having the cut-off value λc to the primary profile. The roughness profile parameters are calculated from the obtained roughness profile. However, if the λs filter is not used, this machine will obtain the roughness profile by applying the long wavelength cut-off filter having the cut-off value λc to the total profile.

Waviness profile: Profile obtained after sequentially applying the short wavelength cut-off filter having the cut-off value λc and the long wavelength cut-off filter having the cut-off value λf to the primary profile. The waviness profile parameters are calculated from the obtained waviness profile. The waviness profile is conventionally referred to as the “filtered wave center line waviness profile”.

Filtered wave waviness profile: Conventionally used profile obtained after applying the short wavelength cut-off filter having the cut-off value λf to the primary profile. In JIS 01, this profile is defined as the “mean line for the roughness profile”. According to the conventional machine, this machine can calculate parameters from the filtered wave waviness profile.

2. Parameters

Parameters are numeric values that show part of the profile characteristics. To clarify the profile characteristics, two or more parameters showing different characteristics are needed, and these parameters should be properly selected and used depending on the purpose of measurement or inspection. Fundamentals of the parameters are described below: Parameter symbols:

There are various parameter symbols, such as Px, Rx, and Wx. The first character (left character) of each parameter symbol shows the profile used for parameter calculation. For example, the first character “P” of parameter symbol Px shows that the parameter is calculated from the primary profile. The first character “R” of parameter symbol Rx shows that the parameter is calculated from roughness profile. The first character “W” of parameter symbol “Wx” shows that the parameter is calculated from the waviness profile. The second character (right character) of each parameter symbol shows the characteristic of the parameter. Various characters used for showing the parameter characteristics are listed below:

p: Maximum peak height v: Maximum valley depth z: Maximum height c: Mean height of profile elements t: Total height of profile a: Arithmetical mean deviation q: Root mean square deviation sk: Skewness

A-3

ku: Kurtosis Sm: Mean length of profile elements ∆q: Root mean square slope mr: Material ratio δc: Section height difference

Combination of these first and second characters creates various parameter symbols. For example, if the created parameter symbol is “Pa”, this parameter symbol represents the arithmetical mean deviation of the primary profile. Parameter symbol “Rsm” represents the mean length of the roughness profile elements. Parameter symbol “Wmr” represents the material ratio of the waviness profile. However, for the following parameters, the conventional terms are used:

Rz: Maximum height roughness Wz: Maximum height waviness Ra: Arithmetical mean roughness Wa: Arithmetical mean waviness Rq: Root mean square roughness Wq: Root mean square waviness

For the calculation method used for each parameter, refer to the text. “mr” and “δc” are parameters calculated from the material ratio curves. If a character is added to the left side of these parameters, the added character represents the profile used for calculation of the material ratio curve. For example, “Wδc” represents the section height difference calculated from the material ratio curve that is calculated from the waviness profile.

Parameter calculation range:

Some parameters are calculated from the evaluation length, and the other parameters are calculated from the sampling lengths. If a parameter is calculated from the evaluation length, it can be said that the parameter is calculated from all the data obtained by measurement. To calculate a parameter from the sampling lengths, the evaluation length is divided into several sampling lengths first, and then the parameter is calculated for each sampling length. After that, the mean value of the obtained parameter values is calculated, and this mean value is regarded as the parameter value (mean parameter). This machine can also display the parameter calculated for each sampling length. Parameters calculated from evaluation length:

- All primary profile parameters - Following curves:

Material ratio curve, amplitude distribution curve (probability density function) - Following roughness/waviness parameters:

t, mr, δc

Parameters calculated from sampling lengths: - Following roughness/waviness parameters:

p, v, z, c, a, q, sk, ku, Sm, ∆q

Example: To calculate the arithmetical mean deviation (Ra: arithmetical mean roughness) from the roughness profile (sampling length (λc) = 0.8 mm, evaluation length = 4.0 mm), the following operation will be performed:

(1) The evaluation length is divided into several sampling lengths. In this case, the evaluation length is divided into 5 sampling lengths.

(2) The Rai (i = 1 to 5) value is calculated for each sampling length. (3) From the obtained Rai values, the mean parameter Ra is calculated.

Ra = (Ra1 + Ra2 + Ra3 + Ra4 + Ra5)/5

A-4

Motif parameter: In addition to the above-described parameters, the motif parameter is also defined. For a detailed description, refer to the text. The motif parameter is calculated from the primary profile and used as a supplementary parameter of the above-described filter type parameters. The motif parameter is particularly effective in handling the abrasion/lubrication fields and the other fields related to abrasion or lubrication.

3. Definition of rolling circle waviness

JIS defines the rolling circle waviness, but ISO does not define it. As the rolling circle waviness parameters, JIS specifies maximum height of rolling circle waviness profile WEM and arithmetical mean deviation of filtered rolling circle waviness profile WEA. Note that some terms conventionally used for curves have been changed. For this reason, main terms currently used are defined below: Rolling circle:

Circle having a certain radius and used for tracing of the real surface in measurement. For actual measurement, a sphere is used in place of the rolling circle.

Rolling circle waviness total profile: String of data points obtained by quantizing the locus of the center of the rolling circle that traces the primary profile of real surface.

Rolling circle waviness profile: Profile obtained by eliminating the long wavelength components of the nominal contour, such as the arc, from the rolling circle waviness total profile using the method of least square. For this machine, this profile is conventionally regarded as the “filtered rolling circle waviness profile”.

Filtered rolling circle waviness profile: Profile obtained after applying the long wavelength cut-off filter having the cut-off value λf to the rolling circle waviness profile. For this machine, this profile is conventionally regarded as the “rolling circle center line waviness profile”.

Rolling circle profile parameters: Maximum height of rolling circle waviness profile WEM and arithmetical mean deviation of filtered rolling circle waviness profile WEA are specified as the rolling circle profile parameters.

4. Comparison of measurement value with limit value

If the allowable value (reference value for judgment of acceptance or rejection) is not specified, the mean parameter will be used for acceptance/rejection judgment from the measurement value. If the maximum value is specified as the allowable value, judgment will be made while observing the maximum value rule. If the allowable value is specified but the maximum value is not specified, the judgment will be made while observing the 16% rule. Maximum value rule:

If the maximum value of the parameters is specified as the reference value for acceptance/rejection judgment, all the parameters obtained from the target area should not exceed the maximum value (reference value). After each measurement, parameters of respective sampling lengths will be calculated. This machine compares the maximum value of these parameters with the reference value to make a judgment.

16% rule: If the parameter upper limit value is specified as the reference value for acceptance/rejection judgment, all the parameters calculated for the respective sampling lengths (lengths divided

A-5

from the evaluation length) will be compared with the upper limit value. If the parameters that exceed the upper limit value are 16% or less of all the parameters, the test piece will be accepted. If the parameter lower limit value is specified as the reference value for acceptance/rejection judgment, all the parameters calculated for the respective sampling lengths (lengths divided from the evaluation length) will be compared with the lower limit value. If the parameters that are smaller than the lower limit value are 16% or less of all the parameters, the test piece will be accepted.

5. Parameter evaluation

JIS 01 uses the same parameter (measurement value) evaluation method as ISO 97. Refer to Chapter 10 “Cut-off value/sampling length selection and evaluation in accordance with ISO 97, ASME, or DIN standards” of the text.

6. Standards referred to

For a detailed description of standards specified in JIS 01 and ISO 97, refer to the following standards: JIS B 0601: 2001 / ISO 4287: 1997

Definitions and designation of surface parameters JIS B 0610: 2001

Definitions and designation of rolling circle waviness JIS B 0631: 2000 / ISO 12085: 1996

Motif parameter JIS B 0632: 2001 / ISO 11562: 1996

Characteristics of phase compensation filter JIS B 0633: 2001 / ISO 4288: 1996

Surface evaluation method and procedure JIS B 0651: 2001 / ISO 3274: 1996

Instruments for measurement of surface roughness by stylus method

B-1

B. Spline correction This machine corrects data using the tertiary spline curve to carry out spline correction. Fundamentals of spline correction are described below: 1. Tertiary spline curve

The tertiary spline curve is an interpolation curve that smoothly links data points. This curve is actually a set of partial straight lines linking 2 adjacent points. When these partial straight lines are linked, the slope and the curvature of 2 adjacent lines will be equalized at each linking point. For this reason, the straight lines are smoothly linked at each linking point (refer to Fig. 1).

Fig. 1 Linking points and tertiary spline curve

The advantage of this curve is that this curve can properly express the comparatively large waviness. In other words, this curve can smoothly regenerates the measured form. Using all the sample data obtained by measurement, the tertiary spline curve can be drawn. In this case, the curve shows the actual sectional form itself, and the data correction function described in the next section cannot be used. (The data correction function is used for extraction of comparatively small-waviness form from the comparatively large-waviness form.) If the entire evaluation length is divided properly and the tertiary spline curve is drawn by linking the representative points of respective divisions, the form to be eliminated can be separated from the comparatively small-waviness form. (Refer to Fig. 2. For a detailed description, refer to the next section.)

Fig. 2 Linking points and spline curve when entire length is divided into three

B-2

2. Data correction using tertiary spline curve

As described in the previous section, the tertiary spline curve is used for separation of the form to be eliminated from the comparatively small-waviness form. As shown in Fig. 3, data correction is to eliminate the tertiary spline curve from the sectional form to obtain the components of the comparatively small-waviness form (refer to Fig. 3).

Fig. 3 Spline correction 3. Number of divisions

For the spline correction, the number of divisions can be selected from the following numbers: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

The entire measurement length (evaluation length + front and rear margin lengths) is divided into the set number of divisions at the same intervals to carry out spline correction. If the entire length is divided into more divisions, components of a smaller-waviness form will remain in the form data after spline correction. This means that the entire length should be divided into more divisions to obtain more accurate analysis result. However, this processing should be carefully performed because increase in the number of divisions may eliminate the necessary part of the form. The effect of this processing depends on the form. Therefore, it is necessary to preliminarily check how many divisions is the most effective in correction. The most effective number of divisions can be obtained as described below. Using several numbers of divisions, carry out calculation to obtain the most effective number of division. How to obtain the most effective number of divisions:

(1) Determine the number of division, and calculate the length of one division using the

following formula: (Length of one division) = (Measurement length)/(Number of divisions)

(2) Set the slope correction method to “no slope correction”, and divide the primary curve by the obtained length of one division.

(3) Check each division assuming that the effect is the same as the tertiary curve correction.

B-3

Main applications: Use the above-described correction method in the following cases: (1) The measurement data sampled by contour measurement is subject to roughness analysis

to obtain subtle roughness on the contour (using the TIMS system). (2) The curve correction (R-surface correction) method cannot correct the form in roughness

analysis.

application guide manual for surfcom series...

Documents