Definition of Parameters
ISO 4287: 1997, Amd.1: 2009 (JIS B 0261: 2013)
Amplitude Parameters (peak and valley) Maximum peak height of the primary profile P p Maximum peak height of the roughness profile R p Maximum peak height of the waviness profile W p Largest profile peak height Z p within a sampling length
Amplitude Parameters (average of ordinates) Arithmetical mean deviation of the primary profile P a Arithmetical mean deviation of the roughness profile R a Arithmetical mean deviation of the waviness profile W a Arithmetic mean of the absolute ordinate values Z(x) within a sampling length
Curves, Probability Density Function, and Related Parameters Material ratio curve of the profile (Abbott-Firestone curve) Curve representing the material ratio of the profile as a function of section level c
Mean Line c
l
1
Z(x) dx with l as l p , l r , or l w according to the case. ∫ 0
P a , R a , W a =
l
0 20 40 60 80 100 R mr(c) ,%
Sampling length
Root mean square deviation of the primary profile P q Root mean square deviation of the roughness profile R q Root mean square deviation of the waviness profile W q Root mean square value of the ordinate values Z(x) within a sampling length
Material ratio of the primary profile P mr ( c ) Material ratio of the roughness profile R mr ( c ) Material ratio of the waviness profile W mr ( c ) Ratio of the material length of the profile elements M l ( c ) at a given level c to the evaluation length
Sampling length
Maximum valley depth of the primary profile P v Maximum valley depth of the roughness profile R v Maximum valley depth of the waviness profile W v Largest profile valley depth Z v within a sampling length
l
1
M l(c)
∫
P q , R q , W q =
Z 2 (x)dx
P mr ( c ) , R mr ( c ) , W mr ( c ) =
with l as l p , l r , or l w according to the case. l 0
ln
Section height difference of the primary profile P δc Section height difference of the roughness profile R δc Section height difference of the waviness profile W δc Vertical distance between two section levels of a given material ratio
Skewness of the primary profile P sk Skewness of the roughness profile R sk Skewness of the waviness profile W sk
R δ c = c ( R mr1 ) – c ( R mr2 ); R mr1 < R mr2
Quotient of the mean cube value of the ordinate values Z(x) and the cube of P q , R q , or W q respectively, within a sampling length
c 0
lr
lr 1 ∫
1
R sk =
Z 3 (x)dx
R q 3
c 1
0
Sampling length
The above equation defines R sk . P sk and W sk are defined in a similar manner. P sk , R sk , and W sk are measures of the asymmetry of the probability density function of the ordinate values.
0 10 20 30 40 50 60 70 80 90 100 R mr0 R mr
Maximum height of the primary profile P z Maximum height of the roughness profile R z Maximum height of the waviness profile W z Sum of height of the largest profile peak height Z p and the largest profile valley depth Z v within a sampling length
Relative material ratio of the primary profile P mr Relative material ratio of the roughness profile R mr Relative material ratio of the waviness profile W mr Material ratio determined at a profile section level R δ c related to the reference section level c 0
Kurtosis of the primary profile P ku Kurtosis of the roughness profile R ku Kurtosis of the waviness profile W ku
Quotient of the mean quartic value of the ordinate values Z(x) and the fourth power of P q , R q , or W q respectively, within a sampling length
P mr , R mr , W mr = P mr ( c 1 ), R mr ( c 1 ), W mr ( c 1 ) where c 1 = c 0 – R δ c ( P δ c , W δ c ) c 0 = c ( P m0 , R mr0 , W mr0 )
lr
lr 1 ∫
1
R ku =
Z 4 (x)dx
R q 4
0
The above equation defines R ku . P ku and W ku are defined in a similar manner. P ku , R ku , and W ku are measures of the sharpness of the probability density function of the ordinate values.
Probability density function (profile height amplitude distribution curve) Sample probability density function of the ordinate Z(x) within the evaluation length
Sampling length
In the old JIS and ISO 4287-1: 1984, R z was used to indicate the “ten point height of irregularities”. Care must be taken because differences between results obtained according to the existing and old standards are not always negligibly small. (Be sure to check whether the drawing instructions conform to existing or old standards.)
Mean line
Spacing Parameters Mean width of the primary profile elements PS m Mean width of the roughness profile elements RS m Mean width of the waviness profile elements WS m Mean value of the profile element widths X s within a sampling length
Amplitude density
Evaluation length
Mean height of the primary profile elements P c Mean height of the roughness profile elements R c Mean height of the waviness profile elements W c Mean value of the profile element heights Z t within a sampling length m m P c , R c , W c = Z t i i=1 1 Σ
m
1
i=1 Σ
PS m , RS m , WS m =
X S i
m
JIS Specific Parameters Ten-point height of irregularities, R z JIS
X s1
Xs2
X s3
X s4
X s5
X s6
Sum of the absolute mean height of the five highest profile peaks and the absolute mean depth of the five deepest profile valleys, measured from the mean line within the sampling length of a roughness profile. This profile is obtained from the primary profile using a phase-correct band-pass filter with cutoff values of lc and ls.
J
5 Z p 1 + Z p 2 + Z p 3 + Z p 4 + Z p 5 + Z v 1 + Z v 2 + Z v 3 + Z v 4 + Z v 5
R z JIS =
Sampling length
Peak count number based on the primary profile elements PP c Peak count number based on the roughness profile elements RP c Peak count number based on the waviness profile elements WP c
Sampling length
Sampling length
1
RP c =
Symbol R z JIS82 R z JIS94
Used profile Surface profile as measured Roughness profile derived from the primary profile using a phase-correct high-pass filter
RS m
Total height of the primary profile P t Total height of the roughness profile R t Total height of the waviness profile W t
Hybrid Parameters Root mean square slope of the primary profile P Δ q Root mean square slope of the roughness profile R Δ q Root mean square slope of the waviness profile W Δ q Root mean square value of the ordinate slope d Z / d X within a sampling length
Sum of the height of the largest profile peak height Z p and the largest profile valley depth Z v within the evaluation length
R a 75 = Arithmetic mean deviation of the profile R a 75 Arithmetic mean of the absolute values of the profile deviations from the mean line within the sampling length of the roughness profile (75%). This profile is obtained from a measurement profile using an analog high-pass filter with an attenuation factor of 12db/octave and a cutoff value of λ c. ∫ Z(x) dx ln ln 1
d Z (x) dx
d Z (x) dx
R z
R z
Sampling length R z
d Z (x) dx
Evaluation length
d Z (x) dx
0
d Z (x) dx
J-18
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