There are three basic forms of surface finish analysis types as shown above. A Primary analysis will give a result which includes the Roughness and Waviness elements of the surface. A Roughness result has been filtered with a Roughness filter to remove the Waviness elements of the surface and a Waviness result has been filtered using a Waviness filter such that only the Waviness elements remain.

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Basic Surface Finish Parameters

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Contents
• Parameter Types
• Amplitude
– Ra
– Rq
– Rt
– Rp
– Rv
– Rz
– Rz1max
• Spacing
– High Spot Count (Rhsc)
– Peak Count (Rpc)
– Mean Spacing (Rsm)
• Hybrid
– Slope

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• Roughness
– Prefix R
• Waviness
– Prefix W
• Primary
– Prefix P
Parameter Types
There are three basic forms of surface finish analysis types as shown
above. A Primary analysis will give a result which includes the Roughness
and Waviness elements of the surface. A Roughness result has been
filtered with a Roughness filter to remove the Waviness elements of the
surface and a Waviness result has been filtered using a Waviness filter
such that only the Waviness elements remain.

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Parameter Types
• Amplitude Parameters are Defined from
– Z co-ordinates
• Spacing Parameters are defined from
– X co-ordinates
• Hybrid Parameters are defined from
– X & Z co-ordinates
Profile parameters are divided into three types depending on the
characteristics of the profile being quantified.
Amplitude parameters are determined solely by peak or valley heights, or
a combination of both, irrespective of horizontal spacing. The Ra
parameter is an amplitude parameter.

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Ra
Amplitude Parameters - Ra
This parameter is the most commonly used in surface finish measurement
and has also been known in the past as Centre Line Average (CLA) or in
the USA, Arithmetic Average (AA).
Mathematically, Ra is the arithmetic average value of the profile departure
from the mean line, within a sampling length.
A method of visualising how Ra is derived is as follows:
Graph A: A mean line X-X is fitted to the measurement data.
Graph B: The portions of the profile within the sampling length “l” and
below the mean line are then inverted and placed above the line.
Graph C: Ra is the mean height of the profile above the original mean
line.
The Ra parameter is often misused. It should be noted that Ra is a
controlling parameter,if the Ra value changes then the process it controls
has changed, e.g.Cutting tip, speeds, feeds and cutting fluid (lubricant).
Ra on its own does not tell us anything about the surface characteristics of
the component under test.

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Same Ra - Different Surfaces
Ra
Ra
Ra
Ra
Amplitude Parameters - Ra Limitations
As mention on the previous slide the Ra parameter does not tell us
anything about the characteristics of a surface, the above picture
demonstrates this. There is no distinction between peaks and valleys. The
four profiles shown have totally different shapes and different peak to
valley values but the all have the same Ra value. These profiles would
have very different performance characteristics.
Ra is not very diagnostic.
Medical Analogy:
Measuring Ra is like taking a Patients temperature, a high temperature
indicates that something is wrong. But it does not tell you what is wrong. A
high temperature may be a symptom of mild flu or of malaria.

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ln
= Pa x ln
Area
Amplitude Parameters - Using Pa & ln
to Calculate Area
Pa and ln value can be used to calculate the Area of a
hole
Pa may be used with ln (evaluation length) to calculate area.
Uses : amount of material wear / deposit

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lr = Sampling Length
Amplitude Parameters - Rq (rms)
Rq is the Root Mean Square of Ra.
Rq is more susceptible to spurious peaks and valleys on the surface under
test and in these cases will tend to give a higher value than Ra.
Compared with the Ra parameter, Rq (rms) has the effect of giving extra
weight to the higher values. This can be illustrated with three groups of
values:
3, 4, 5 2, 4, 6 1, 4, 7
The arithmetic average is 4 in each case, the successive increase of one
in the higher value being exactly balanced by the decrease in one in the
lowest value. The respective rms values are √16.6 (4.07), √18.6 (4.31),
√22 (4.69), showing that the increase in the highest figure outweighs the
decrease in the lowest.
For statistical work, Rq (rms) values are more meaningful than arithmetic
averages ones. This parameter is not used very much in general
engineering, but is used more in the optical industry due to it’s ability to
detect spurious peaks and valleys.

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ln = Assessment Lengthlr = Sampling Length
Rt
Amplitude Parameters - Rt
Rt is the maximum peak to valley height of the profile in the assessment
(evaluation) length (ln).
This parameter is particularly useful where components are subjected to
high stresses, any large peak to valley could be areas which are likely to
suffer from crack propagation, however because this is a peak parameter
it is subject to large variations and can be unstable.
From time to time, in older technical documents usually originating from
Germany, one sometimes sees triangle symbols used for Rt specification.
This standard is no longer valid and was cancelled in 1978. Originally DIN
3141, this has been superseded by ISO 1301.

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Amplitude Parameters - Rt Results are
Divergent
Note: A single scratch or peak can affect Rt
Rt is a peak parameter it is subject to large variations and can be
unstable.
Like all peak-valley type parameters, it is divergent: The more times you
measure the part the larger the (Rt) value you will find!

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Sampling Length
Rp
Amplitude Parameters - Rp
Rp is the maximum height of the profile above the mean line within a
sampling length divided by n sample lengths.
Peaks are important when considering friction and wear properties, as the
interaction between surfaces concentrates around them. The presence of
peaks can make dimensional measurements on components that are
subjected to wear unreliable, as wear removes the peaks that were
originally included in the measurement.
It must be noted, that there is no guarantee that a measurement will
include the extremes of a surface. Therefore, the results of this
parameter, obtained from repeated measurements over the same surface,
will tend to vary

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Sampling Length
Rv
Amplitude Parameters - Rv
Rv is the maximum depth of the profile below the mean line within a
sampling length divided by n sample lengths.
Valleys are important for the retention of lubrication. However, fracture
propagation and corrosion start in valleys.
It must be noted, that there is no guarantee that a measurement will
include the extremes of a surface. Therefore, the results of this
parameter, obtained from repeated measurements over the same surface,
will tend to vary

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Rz1
Rz2
Rz3 Rz4
Rz = (Rz1 + Rz2 + Rz3 +Rz4 +Rz5 . . .)
/ n
n = number of sampling lengths
Rz5
Amplitude Parameters - Rz
The Rz parameter has changed its meaning over a number of years.
The Rz parameter definition as shown here is the mean of all the Rt
values taken from each sample length.
The definition of this parameter may change according to the age of the
instrument, care must be taken when carrying out analysis.
This definition is equivalent to the older Rz(DIN) and Rtm(ISO)
parameters. The Rz(DIN) parameter was calculated using a 2CR filter.
This parameter has similar uses to the Rt parameter but is not subject to
high variations caused by spurious features such as dust, burrs or
scratches.

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Rz1max
Rp1m
ax
Rv1ma
x
Amplitude Parameters - Rz1max,
Rp1max, Rv1max
The Rz1max parameter is defined as the largest of the individual peak to
valleys from each sample length. This parameter has change name over
the years, on older instruments it would be known as either Rymax, Ry, or
Rmax.
The Rp1max parameter is defined as the largest of the individual peak to
mean line from each sample length. This parameter has change name
over the years, on older instruments it would be known as either Rpmax or
Rp.
The Rv1max parameter is defined as the largest of the individual mean
line to valleys from each sample length. This parameter has change name
over the years, on older instruments it would be known as Rv.
It should be noted that Rv1max + Rp1max might not equal Rz1max, in
certain cases, because they could be in different sample lengths.

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lr = Sampling Length (Cut-off) ln = Assessment Length
A = Slice Level B = Mean Line
Spacing Parameters - RHSC
(High Spot Count)
The High Spot Count parameter, quantifies the number of complete profile
peaks (within the evaluation length) that project above a pre-set reference
line or slice level that is set parallel to the mean line.
The reference line can be set to a selected depth below the highest peak,
to a selected distance above or below the mean line or at a Material Ratio
% height [ Rmr (c)]. ( Material Ratio dealt with in preceding slides)
This parameter is frequently used in the automobile industry on cylinder
liners, where lubrication is essential. It can be used to predict wear or
lapping requirements and also in circumstances where a certain number of
peaks are required such as brake liners for friction purposes.

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• Hardened Peaks will
eventually break off and
the surface will
Breakdown
• Tall Narrow peaks tend
to work harden
Spacing Parameters - RHSC (High Spot
Count)
If it is known that only the peaks are critical then parameters such as High
Spot Count or Count Peak Count (see preceding slide) can be considered.
When bearing areas are produced the ideal situation would be for the
surface to have plenty of valleys for oil retention and plenty of material to
support load.
However lots of peaks are undesirable and can cause excessive wear
especially if these break off and mix with lubricants.
Manufacturers can measure HSC and consequently control the amount of
peaks allowed through the process.

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A = Selectable Bandwidth B = Mean Line
Spacing Parameters - RPc (Peak Count)
The RPc (Peak Count) parameter is similar to the HSC parameter but has
an additional control based on height as well as frequency of occurrence
and is evaluated on the primary profile.
RPc is the number of local peaks that project through a selectable
bandwidth centred about the mean line. The count is determined over the
evaluation length and the results are given in peaks per cm (or per inch).
The parameter should, therefore be measured over the greatest
evaluation length possible.
The reference line is parallel to the mean line and can be set to a selected
depth below the highest peak, to a selected distance above or below the
mean line.
This parameter is often used where control of surface coating adhesion is
required.
When used by the sheet steel industry it is a good parameter for
controlling characteristics related to bending, forming, painting and
laminating.

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Spacing Parameters - RPc (Peak Count)
• Orange Peal Effect, due to peaks on sheet steel base
Surface
Base Sheet Steel
Painted Surface
This drawing demonstrates the orange peel effect due to peaks on sheet
steel.
When a painted surface exhibits ‘orange peel’ it is often due to peaks
present on the surface. The surface tension of the paint causes
replication of the peaks but with a much reduced sharpness on the
finished surface. Proper use of the RPc parameter can help control this
effect.

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lr=Sampling Length (Cut-off)
Mean
Line
Spacing Parameters - RSm (Mean
Spacing)
The Sm (Mean Spacing) is the mean spacing between profile peaks at the
mean line within the sampling length.
A profile peak is the highest point of the profile between an upwards and
downwards crossing of the mean line.
The general form for defining this parameter is: Sm is the mean value of
the spacing between profile elements within a sampling length.
When this parameter is used in conjunction with the S*
parameter it can
help to differentiate between a Smooth and a Jagged surface.
For a smooth waveform the values of these parameters will be similar to
each other.
Sm is also useful for deciding on the correct filter, for further information
on this subject consult the Taylor Hobson Surface texture parameter
guide. This is also discussed earlier in this presentation.
S*
is the mean spacing of adjacent local peaks, measured over the
evaluation length.

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• Rdq (RDq) - Root Mean Square
Slope
– Very sensitive to any exceptional
values of local slope then Rdq
(RMS Slope)
– Most suitable for extremely fine
surfaces
– More suitable for optical or
electronic parts, where even
small changes are important.
• Rda (RDa) - Arithmetical Mean
Slope
– Less sensitive to any exceptional
values of local slope then Rdq
(RMS Slope)
– Less suitable for extremely fine
surfaces
– More suitable for general
engineering and Automotive
components.
θ
θ
θ θ
Hybrid Parameters - Rda, Rdq, (Wda,
Wdq, Pda, Pdq)
Rda, the Arithmetic Mean Slope, is less sensitive to any exceptional
values of local slope then Rda ( RMS Slope) and is thus less suitable
when analysing extremely fine surfaces where even small changes are
important and need to be highlighted. ‘Rda is more suitable for general
engineering and automotive components.
Rdq, the RMS slope, is very sensitive to any exceptional values of local
slope and is thus most suitable when analysing extremely fine surfaces
where even small changes are important and need to be highlighted.
Typically optical or electronic components.

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Hybrid Parameters - Rda, Rdq, (Wda,
Wdq, Pda, Pdq)
• Slope Parameters
–– FrictionFriction Higher slope : higher friction
–– ReflectivityReflectivity Higher slope : less reflective the surface
–– ElasticityElasticity Higher slope : more likely to deform under
load
–– WearWear Higher slope : greater rate of wear
–– VibrationVibration Lower slope : less vibration / more quiet
–– AdhesionAdhesion Higher slope : better adhesion / less shearing
Slope is a particularly useful parameter and has close correlation to:-
a) Friction : the greater the slope the higher the friction.
b) Reflectivity : the greater the slope the less reflective the surface. The
lower the angle the better the finish will appear but the roughness may still
be higher than a much less shiny surface.
c) Surface Elasticity : the greater the slope the higher the chance of
deformation upon loading.
d) Wear : the greater the slope the greater the rate of wear.
e) Noise : ball and roller bearings with low surface slopes will be quieter
and exhibit less vibration than those with high slope values. This is
because less energy is imparted by the rise and fall of the balls or rollers
on the surface as they roll along. Although there are other factors the
noise level or vibration generated is often proportional to the magnitude of
the surface slopes and can be measured by the Rdq parameter.
f) Adhesion : for good adhesive qualities the slope value needs to be
high.Higher slopes give a better keying surface which resists shearing of
the coating by rubbing or smearing.
Most normal fine machine surfaces read between 3 - 8 degrees slope but
look higher on a graphical display due to compression of the scales.

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No Vibration
> Quiet <
Low Frequency
> Rumble <
High Frequency
> Scream <
Effects of Surface Slopes - Vibration & Noise
Hybrid Parameters - Rda, Rdq, (Wda,
Wdq, Pda, Pdq)
From the above diagram it is clear that the surface which has low surface
slopes will be quieter and exhibit less vibration. This is because less
energy is imparted by the rise and fall of the bearing on the surface.
Although there are many other factors the noise level or vibration
generated is often proportional to the magnitude of the surface slopes and
can be measured by slope parameters

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With low surface slopes
more light is reflected
into the eye and hence
has a good appearance
With high surface slopes
less light is reflected into
the eye and hence has a
poor appearance
Effects of Surface Slopes - Appearance
Hybrid Parameters - Rda, Rdq, (Wda,
Wdq, Pda, Pdq)
The above slide shows the cosmetic Effects of two different surfaces.
Many people judge a the smoothness of a surface by its ability to reflect
light. The surface seen as most reflective will often look and feel (to the
finger) smoother. This can often be proved by measuring something like a
precision ground part (such as a fuel injection nozzle) against a piece of
chrome plated bar stock. The chrome will both look and feel smoother
than the fuel injection nozzle, although the nozzle may be half the Ra
value of the Chromed surface.
Often the cosmetic property of a surface can be measured by slope
parameters

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High Surface Slopes mean greater friction - and greater safety.
Typical
Parameters:
Rz, Rp, Rda, Rsk
Ceramic Tiles
Hybrid Parameters - Rda, Rdq, (Wda,
Wdq, Pda, Pdq)
Effects of Surface Slopes - Slip Resistance
Rda is useful here. Ceramic tiles are treated so as to improve the slip
resistance. When tiles are checked before and after treatment, a
significant change in Rda should be noticed.
Rz is also useful. Minimum roughness requirements are helpful in
assessing floor specification requirements.
The Rp parameter also relates to the bulk of a floors frictional property and
therefore its slip resistance.
The Rsk (skew) parameter also gives an indication of the nature of such
surfaces - whether it has a majority of peaks, valleys or a balance of the
two. Surfaces made up of dominant peaks may provide better slip
resistance qualities.

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Summary
• There are three basic forms of surface finish analysis
types
– Roughness, Waviness & Primary
• Profile parameters are divided into three types
– Amplitude, Spacing & Hybrid
• Some parameters have limitations - relying on a single
parameter can give unstable results
• Some parameters are used in particular industries
– Optics, Fabrication, Automotive, Health & Saftey