Surfaces and Profiles

Transcription

Surface Metrology Guide - Surfaces and Profiles
Surface Metrology Guide
Surfaces and Profiles
Surfaces
Types of Surfaces
Surface
A surface is a boundary that separates an object from another object or
substance.
Nominal Surface
A nominal surface is the intended surface. The shape and extent of a nominal
surface are usually shown and dimensioned on a drawing. The nominal surface
does not include intended surface roughness.
Real Surface
A real surface is the actual boundary of an object. It deviates from the nominal
surface as a result of the process that created the surface. The deviation also
depends on the properties, composition, and structure of the material the object
is made of.
Measured Surface
A measured surface is a representation of the real surface obtained with some
measuring instrument. This distinction is made because no measurement will give
the exact real surface. Later portions of this manual describe many different types
of measuring instruments.
Surface Geometry
Surface geometry and geometric dimensioning and tolerancing are large subfields
of metrology which parallel or exceed surface finish in scope and complexity. This
is the realm of coordinate measuring machines and roundness measuring
instruments and contouring instruments. However, there is an increasing overlap
between geometric measurements and surface finish measurements, so it is
helpful to be aware of some basic concepts in geometric measurement.
Form
Form refers to the intentional shape of a surface which differs from a flat line.
Dimension
Dimensions are the macroscopic sizes of a part, e.g. diameter or length.
Tolerance
A tolerance is an allowable range for a dimension to take, a specified interval of
dimensions where the part will still function acceptably.
Surface Finish Imperfections
Form Error
Form error encompasses the long wavelength deviations of a surface from the
corresponding nominal surface. Form errors result from large scale problems in the
manufacturing process such as errors in machine tool ways, guides, or spindles,
insecure clamping, inaccurate alignment of a workpiece, or uneven wear in
machining equipment. Form error is on the dividing line in size scale between
geometric errors and finish errors.
Texture
Surface texture is the combination of fairly short wavelength deviations of a
si4rface from the nominal surface. Texture includes roughness, waviness, and lay,
that is, all of the deviations that are shorter in wavelength than form error
deviations.
Surface texture includes roughness and waviness. Many surfaces have lay: directional striations
across the surface.
Roughness
Roughness includes the finest (shortest wavelength) irregularities of a surface.
Roughness generally results from a particular production process or material
condition.
Waviness
Waviness includes the more widely spaced (longer wavelength) deviations of a
surface from its nominal shape. Waviness errors are intermediate in wavelength
between roughness and form error. Note that the distinction between waviness
and form error is not always made in practice, and it is not always clear how to
make it. New standards are emerging that define this distinction more rigorously
as developed in later sections.
Lay
Lay refers to the predominant direction of the surface texture. Ordinarily lay is
determined by the particular production method and geometry used.
Turning, milling, drilling, grinding, and other cutting tool machining processes
usually produce a surface that has lay: striations or peaks and valleys in the
direction that the tool was drawn across the surface. The shape of the lay can
take one of several forms as shown below. Other processes produce surfaces with
no characteristic direction: sand casting, peening, and grit blasting. Sometimes
these surfaces are said to have a non-directional, particulate, or protuberant lay.
Several different types of lay are possible depending on the manufacturing and machining
processes.
Lay (or the lack thereof) is important for optical properties of a surface. A smooth
finish will look rough if it has a strong lay. A rougher surface will look more
uniform if it has no lay (it will have more of a matte look).
Flaws
Flaws are unintentional and unwanted problems with a surface. Usually the term
flaw refers to individual and unusual features such a scratches, gouges, burrs, etc.
According to the ANSI B46.1 standard a flaw is defined when agreed upon in
advance by buyer and seller, leaving open all sorts of other types of surface
problems. The ANSI 13211.1 standard defines a number of specific types of
physical flaws including pits, cracks, craters, and fractures. That standard also
defines a number of material or chemical problems that occur in surfaces but are
outside the realm of surface finish.
Surface Profiles
Types of Profiles
Profile
A profile is, mathematically, the line of intersection of a surface with a sectioning
plane which is (ordinarily) perpendicular to the surface. It is a two-dimensional
slice of the three-dimensional surface. Almost always profiles are measured across
the surface in a direction perpendicular to the lay of the surface.
A profile is a two-dimensional picture of a three dimensional surface that may be thought of as the
result of a sectioning place cutting the surface. Profiles are ordinarily taken perpendicular to the
lay.
Nominal Profile
The nominal profile is the straight or smoothly curved line of intersection of the
nominal surface with a plane which is (ordinarily) perpendicular to the surface.
The nominal profile has a known mathematical shape for a known part (most often
a straight line or a circle).
Real Profile
A real profile is a profile of the real surface. It is the (idealized) shape of the
intersection of a surface with a perpendicular sectioning plane.
Measured Profile
A measured profile is a representation of the real profile obtained with some
measuring instrument This distinction between "real" and "measured" is made
because no measurement will give the exact real surface. Later portions of this
manual describe many different types of measuring instruments, emphasizing
profiling instruments.
Profiling Methods
A profiling method is a means of measuring a profile of a surface. The result of the
method is a two-dimensional graph of the shape of the surface in the sectioning
plane created by the profiling instrument.
The most common type of profiling instrument draws a diamond stylus across the
surface and measures its vertical displacement as a function of position. Chapter 5
describes profiling instruments in detail.
Modified Profiles
Modified Profile
A modified profile is a measured profile that has been modified by mechanical,
electrical, optical, or digital filtering. The filtering is ordinarily done to minimize
certain surface characteristics while emphasizing others. A modified profile differs
from a measured profile in the sense that the real profile is intentionally modified
as part of the measurement. The details of the modification are typically
selectable by the user of an instrument. A measured profile is an unintentional
modification of the real profile resulting from the limitations of the measuring
instrument.
Traced Profile
An instrument's raw trace of a surface is always relative to some reference plane.
The traced profile is the raw measured profile with profile height measured
relative to a zero line which is parallel to the instrument's reference plane.
Since an instrument's set-up will vary from measurement to measurement, the
traced profile has little value except as the starting point for leveling or other
form removal.
Form Profile
The form profile is the nominal profile in the coordinate system of the traced
profile. That is, it is the nominal shape of the part relative to the reference line of
the profiling instrument.
Ordinarily form will be a straight line or a circle. It is most often found by a least
squares fit of the traced profile with a straight line or a circle.
Primary Profile
The primary profile is the traced profile alter subtracting the form. The primary
profile is thus the sum of all the deviations of the measured profile from the
nominal profile. The primary profile is the sum of the form error profile, the
waviness profile, and the roughness profile.
Often the primary profile is referred to as the "unfiltered profile" or the "total
profile". In this case, it is the trace of the surface leveled and magnified, but
otherwise unmodified.
Wavelength
Wavelength (almost universally denoted X) refers to the repeat length of a
periodic function.
Wavelength is the distance between similar points of a repeating,
periodic signal.
A real profile can be thought of as the sum of many different individual functions,
each with its own wavelength.
Filter
A filter (for purposes of surface finish measurement) is an electronic, mechanical,
optical, or mathematical transformation of a profile to attenuate (remove)
wavelength components of the surface outside the range of interest for a
measurement.
Form Error Profile
The form error profile encompasses the very long wavelength deviations of the
traced profile from the nominal profile. Form error is the modified profile
obtained by filtering the measured profile to attenuate medium and short
wavelength components associated with waviness and roughness.
Texture Profile
The texture profile is the sum of the waviness profile and the roughness profile,
i.e. the remaining medium and short wavelength deviations of the measured
profile from the nominal profile after form error has been subtracted from the
primary profile.
Measurement of texture is the primary domain of traditional surface finish
analysis.
Waviness Profile
The waviness profile includes medium wavelength deviations of the measured
profile from the nominal profile. The waviness is the modified profile obtained by
filtering a measured profile to attenuate the longest and shortest wavelength
components of the measured profile (i.e. the filter removes form error and
roughness).
An important concept in surface finish is the breaking of a surface profile into
different components by wavelength. There is a hierarchy of components, as shown.
Roughness Profile
The roughness profile includes only the shortest wavelength deviations of the
measured profile from the nominal profile. The roughness profile is the modified
profile obtained by filtering a measured profile to attenuate the longer
wavelengths associated with waviness and form error. Optionally, the roughness
may also exclude (by filtering) the very shortest wavelengths of the measured
profile which are considered noise or features smaller than those of interest.
Roughness is of significant interest in manufacturing because it is the roughness of
a surface (given reasonable waviness and form error) that determines its friction in
contact with another surface. The roughness of a surface defines how that
surfaces feels, how it looks, how it behaves in a contact with another surface, and
how it behaves for coating or sealing. For moving parts the roughness determines
how the surface will wear, how well it will retain lubricant, and how well it will
hold a load.
Reference Mean Lines
Mean Line
A mean line is a reference line from which profile deviations are measured. It is
the zero level for a total or modified profile.
Least Squares Mean Line
A least squares mean line is a line through a profile such that the sum of the
squares of the deviations of the profile from the mean line is minimized. In
practice, this is done with a digitized profile.
A least squares mean line minimizes the sum of the squares of the deviations of a set of points
from the line. This method approximates how your eye would fit a line through a set of points
The most common application of a least squares mean line is to "level" the raw
traced profile. The traced profile is relative to the straight line reference of the
profiling instrument. Unless the instrument is perfectly aligned with the part, that
reference will be tilted with respect to the measured surface. A least squares line
fit through the raw traced profile may be used as a reference line to remove the
misalignment.
More sophisticated instruments give greater control over this leveling process,
either by providing for "releveling" or by providing alternatives to the least squares
mean line. This is because a least squares mean line is distorted by flaws or
unusually shaped profiles.
Filter Mean Line
A filter mean line is the mean line implicit in a profile filter. (Filters are discussed
at length in Chapter 7). For example, the waviness profile may be considered the
mean line of the texture profile. Another name for the filter mean line in analog
instruments is the "electrical mean line".
Center Line
The center line of a profile is the line drawn through a segment (usually a sample
length) of the profile such that the total areas between the line and the profile
are the same above and below the line.
This concept is little used in modern instruments; it mainly served as a graphical
method for drawing a mean line on the output of a profile recording instrument
with no built-in parameter processing.
Profile Peaks and Valleys
Profile Height
The height of a profile at a particular point is the distance from the profile to its
mean line. Profile height is considered positive above the mean line and negative
below the mean line.
Profile Peak
A profile peak is a region of the profile that lies above the mean line and
intersects the mean line at each end. In the figure below, each shaded region is a
peak. The height of a peak is defined to be the point of maximum height within
the region.
Profile peaks are regions above the mean line. Local peaks are regions between two local minima.
Profile Valley
A profile valley analogous to a profile peak is a region of the profile that lies below
the mean line and intersects it at each end. The depth of a valley is the depth of
the lowest point within the valley.
Profile Irregularity
Sometimes it is convenient to speak of one profile peak together with one
adjacent profile valley as a profile irregularity.
Profile Valleys extend below the mean line. Local valleys lie between two maxima (above or below
the mean line).
Local Peak
A local peak is a region of a profile between two successive local minima in the
profile.
Local Valley
A local valley is a region of a profile between two successive "high points" (local
maxima) in the profile.
Few parameters say very much about local peaks or valleys, but very experienced
surface finish experts can tell a great deal about a machining process by looking at
the shape of local peaks and valleys within each larger peak or valley.
Spacing
Spacing
Spacing refers to the distance between features on a profile in the x direction,
parallel to the nominal direction of the trace. The features that determine a
spacing parameter usually relate to peaks and valleys or to average wavelengths,
etc.
Surface Metrology Guide - Drawing Indication of Surface Texture
Drawing Indication of Surface Texture
Specifying surface texture
The following criteria may be used in the specification of surface texture:
Control surface texture only when and where necessary.
Experimentation and experiences are best sources of knowledge in specifying
surface characteristics.
In experimentation, statistical techniques have proved to be helpful for
establishing correlation between surface characteristics and its intended
functions.
Specified surface texture can be produced and measured.
Surface roughness produced by common production methods (ASME B46.1-1995)
Meaning of the surface finish symbol (ASME Y14.36M-1996)
a = roughness value Ra in micrometers
b = production method, treatment, coating, other text or
note callout
c = roughness cutoff or sampling length in millimeters
d = direction of lay
e = minimum material removal requirement in
millimeters
f = roughness value other than Ra in micrometers
preceded by its parameter symbol (e.g. Rz 0.4)
For a detailed explanation of the individual components of the symbol, see the
references listed at the end of this page.
The use of this symbol is illustrated in the next section. The lay symbols are
illustrated in the following table.
Lay symbols and examples
Lay
Symbol
Meaning
Example
Lay approximately parallel to the line representing the
surface to which the symbol is applied.
Lay approximately perpendicular to the line representing
the surface to which the symbol is applied.
Lay angular in both directions to the line representing the
Lay multidirectional.
Lay approximately circular relative to the center of the
Lay approximately radial relative to the center of the
Lay particulate, non-directional, or protuberant.
Examples of Surface Texture Indication
Here are some examples of the surface texture symbol application:
Basic Surface Texture Symbol. Surface may be produced by
any method except when the bar or circle (Symbol b or d)
is specified.
Material Removal By Machining Is Required. The horizontal
bar indicates material removal by machining is required to
produce the surface and material must be provided for
that purpose.
Material Removal Allowance. Value in millimeters for "X"
defines the minimum material removal requirement.
Material Removal Prohibited. The circle in the vee
indicates the surface must be produced by processes such
as casting, forging, hot finishing, cold finishing, die
casting, powder metallurgy and injection molding without
subsequent removal of material.
Surface Texture Symbol. To be used when any surface
texture values, production method, treatment, coating or
other text are specified above the horizontal line or to the
right of the symbol. Surface may be produced by any
method except when bar or circle (Symbol b or d) is
specified or when the method is specified above the
horizontal line.
Roughness average rating is placed at the left of the long
leg and the roughness cutoff rating or sampling length is
placed at the right. The specification of only one rating for
roughness average shall indicate the maximum value and
any lesser value shall be acceptable. Specify the roughness
average in micrometers.
The specification of maximum and minimum roughness
average values indicates a permissible range of roughness.
Specify in micrometers.
Removal of material prohibited.
Roughness sampling length or cutoff rating is placed below
the horizontal extension and is mandatory in all cases
when values are applied to the symbol. Specify in
millimeters.
Example of roughness sampling length or cutoff rating for
Rz (2.5) when different than that for Ra (0.8).
Indication of roughness parameter other than Ra can also
be specified as a range separated by a dash (i.e. 0.4-0.8).
Example of roughness sampling length or cutoff rating (2.5)
applied to Rz
Lay designation is indicated by the lay symbol placed at
the right of the long leg.
Example of maximum roughness spacing, Sm, placed at the
right of the cutoff rating and above the lay symbol. Any
lesser rating shall be acceptable. Specify in millimeters.
Material removal by machining is required to produce the
surface. The minimum amount of stock provided for
material removal is specified at the left of the short leg of
the symbol. Also, "NOTE X" can be used to control
designations other than those covered by defaults in ASME
846.1 - 1995.
Indication on Older Drawings
The common use of Ra is deep-rooted in surface measurement, so much so that
older standards provided ways of specifying Ra only. Today's and upcoming
surface texture standards aim to de-emphasize the special role that Ra has been
taking and attempt to accomodate more parameters and factors affecting their
characterization.
Grade Numbers
Older drawings may use roughness grade numbers to indication Ra values. The
following table is given in ISO 1320:1992.
Roughness values Ra
µm
µin
Roughness Grade
Numbers
50
2000
N12
25
1000
N11
12.5
500
N10
8.3
250
N9
3.2
125
N8
1.6
63
N7
0.8
32
N6
0.4
16
N5
0.2
8
N4
0.1
4
N3
0.05
2
N2
0.025
1
N1
RHR - Roughness Height Range
Another practice in the specification of Ra values on drawings is using the letters
"RHR" with a superscript and subscript indicating the range of Ra value permitted.
The following figure illustrates this practice.
Older drawings may have used this notation to express an allowable range for Ra. This
notation is now obsolete.
For example, the second symbol above means that Ra may fall between 10 µin and
20 µin.
References
ASME Y14.36M-1996; Surface Texture Symbols.
ISO 1302:1994; Technical Drawings - Method of indicating surface texture.
Watch for revisions
ISO CD 1302; Geometrical Product Specifications (GPS) - Indication of Surface
Surface Metrology Guide - Instruments
Surface Measuring Equipment
The Measurement Coordinate System
Profiling Coordinate System
Coordinate System
It Is helpful to use a standard right-handed coordinate system when referencing
profile or surface topography measurements. If x and y are the coordinates in the
plane of the surface and z is displacement from the surface, then the coordinate
system appears as below We have chosen x to be the direction of travel of the
transducer across the surface.
The coordinate system for profiling a surface has x in the trace direction, y normal to the
trace in the plane of the surface, and z perpendicular to the surface. This same coordinate
system is useful for both profiling and 3-D topography. In the past a simpler 2-D, x-y
coordinate system was usually used for profiling.
This coordinate system differs from the 2-D coordinate system often used in simple
profiling, namely x horizontal and y vertical. By making z the vertical
displacement we can use the same coordinate system whether we are discussing 2D profiles or 3-D surfaces.
Which Way is "Up"?
In general the coordinate system above can be oriented in any way with respect to
gravity or the surface of the earth (depending on the capabilities of the measuring
instrument). However, when referring to surface features, it is much easier to
speak of "vertical" and "horizontal", "peak" and "valley", "height" and "depth", and
"up" and "down", rather than trying to express everything as x, y, and z
displacements or distances. Therefore, throughout this work it is assumed that the
positive z coordinate is physically "up" when using such terms, even though a
particular measurement may not fit that assumption.
Units of Measure in Surface Finish
Surface heights are generally measured in microinches or micrometers. A
microinch, abbreviated µin, is one millionth of an inch. Similarly, a micrometer
[µm] is one millionth of a meter.
As points of reference for how small a microinch is, here are the sizes of some
familiar items:
length of a football field
width of a hand
thickness of a pane of glass
diameter of human hair
thickness of paper
diameter of a spider web strand
wavelength of visible light
"diameter" of a hydrogen atom
3,600,000,000 µin
3,000,000 - 4,000,000 µin
80,000 - 120,000 µin
2,000 - 3,000 µin
1,000-2,000 µin
100 - 200 µin
16 - 30 µin
0.004 µin
A microinch is very small!
When converting from µin to µm the conversion 25.4 mm equals 1 inch comes into
play. Depending on whether you live in Europe or in the United States this
conversion is exact or is good enough for all practical purposes. Our conversion is
thus 39.37 µin = 1 µm, but in surface finish it is common to approximate things
even further, 40 µin = 1 µm.
Unit conversion in surface finish
Magnification in Surface Traces
To be of any use to humans, surface traces are magnified moderately in the
horizontal direction and significantly in the vertical direction in order to be
presented on a computer screen or a piece of paper. As a typical example, a 0.15"
trace with a 300 µin height from highest peak to lowest valley might be expanded
to fit on a 6" wide by 3" high plot. This is a 40X magnification horizontally and a
10,000X magnification vertically. This difference leads to a very sharply undulating
trace that easily deceives the uninitiated as to the actual shape of the surface.
For example, here is a surface trace actual size, magnified 40X horizontally and
vertically, and then magnified 40X horizontally and 10,000X times vertically:
The vertical magnification of a surface trace is ordinarily much greater than the horizontal
magnification. A trace that looks jagged and rough to the eye is really a distorted view of a nearly
flat surface with moderate ripples across it.
There is no difference between the 40X vertical magnification and a straight line
with tile resolution of a laser printer. Always keep in mind the extreme vertical
magnification when looking at surface profiles produced by a practical instrument.
Profile Measuring Lengths
Traverse Length
The traverse length (A+B+C) of a profile measurement is the total distance
traveled by the profiling instrument's pick-up during data collection.
In a profile measurement the evaluation length, the length over which data may be collected,
is shorter than the physical traverse length because of end effects in the motor control and
settling times for optional electronic filters. An evaluation length consists of one or more
sample lengths.
Evaluation Length
The evaluation length (B) is the entire length of a profile over which data has been
collected. The evaluation length will ordinarily be shorter than the traverse length
because of end effects in the travel (A) and (C): motors accelerating and
decelerating, electrical filters settling down, etc.
The evaluation length is denoted L.
Sample Length
For roughness measurements one evaluation length consists of several (ordinarily
five) sample lengths. Many roughness parameters are statistical averages of values
for the individual sample lengths.
A standard roughness evaluation length comprises five sample lengths. The sample length is always
equal to the filter cutoff length.
For waviness and form error measurements, the sample length is usually chosen to
be equal to the evaluation length, but there is presently no standard way of
defining the sample length or per-sample-length parameters for these profiles. For
waviness an emerging standard for the the waviness evaluation length (and
waviness filter cut-off) is ten times the roughness cutoff.
A single sample length is denoted l. For the roughness profile the sample length is
almost invariably chosen to be equal to the cutoff length of the roughness filter
(defined later).
There is often not a clear distinction made between the sample length and the
evaluation length, even within a particular instrument manufacturer. Another
term which usually equates to evaluation length is "assessment length". Be very
careful to decipher what is meant when any of these three terms is used.
To add to the confusion, the evaluation length for a modified profile is always
shorter than the evaluation length for the traced profile. Whether analog or
digital, profile filtering requires an extra two cutoffs or so beyond the filtered
profile in order for the filter not to be corrupted by the turn-around areas or by
end effects in digital filtering. The chapter on filtering covers this in detail. For
purposes of this chapter, in order to measure any modified profile, you will need
to measure more of the surface than your final evaluation length, and the portion
of the surface that you measure is always shorter than the portion of the surface
that you physically traverse.
Instrument Resolution and Range
Height Resolution
The height resolution of an instrument is the minimum height deviation in a profile
that can be distinguished from background noise. Height resolution depends on
many factors such as the quality of the electronic circuit (for avoiding noise), the
size of the A to D converter in a digital instrument, the mechanical characteristics
of the transducer and measuring probe, the presence of vibration in the
instrument's environment, and so on.
One way to estimate the height resolution (or vertical resolution) of an instrument
is to take a trace of air or of an optical flat- a surface that has a roughness much
less than the expected resolution.
Height Range
The height range is the maximum peak to valley height that an instrument can
measure accurately. The range is determined by the gain of the electronics and
the electrical and mechanical limitations of the transducer and probe. Some
transducers become nonlinear outside a specified range, some have mechanical
constraints.
Range to Resolution Ratio
The range to resolution ratio is the ratio of the height range of an instrument to
the resolution of an instrument. This is a key measure of the capability of an
instrument. Some instruments allow the user to trade range for resolution,
maintaining a roughly constant range to resolution ratio.
Sampling Interval
Instruments which digitize the profile and store an array of height values have a
particular sampling interval. This is the interval between points in the x direction,
along the trace length. Nyquist theory has as its primary result that the
wavelength of an analog signal which can be represented in a digitized signal is
twice the sampling interval. In practice the sampling interval is chosen to give five
points in each period of the shortest wavelength that is to be measured.
Lateral Resolution
The lateral or horizontal resolution of an instrument is the size of the smallest
feature that can be distinguished on a surface. Lateral resolution depends not only
on the sampling interval but on the physical characteristics of the mechanical or
optical probe (for example the diamond radius of a contact stylus).
The ability of an instrument to distinguish the features of a surface is a
combination of its vertical and horizontal resolution.
Classifications of Instruments
Type I Profiling Contact Skidless Instruments
Type II Profiling Non-contact Instruments
Type III Profiling Nanometer-Level Scanning Microscopy
Type IV Profiling Contact Skidded Instruments
Type V Other Skidded Instruments
Type VI Area Averaging Instruments
Schematic of a Surface Profiling Instrument
The Instrument Measuring Loop
The measuring loop of an instrument comprises all of the components of the
instrument and fixturing that contribute to converting the real surface profile into
an electrical (analog or digital) representation of the profile.
The measuring loop of a profiling instrument consists of all the electrical and mechanical (and
optical) components of the instrument involved in converting a real surface profile into an
electrical signal representing that profile. The pickup consists of the components exclusive of
the traverse and guide mechanisms.
Internal (Skid) Reference Datums
Several methods can be used to establish an instrument reference line from which
profile height can be measured. The simplest approach is to use a skid riding on
the surface itself as a reference. Usually the arm to which the skid is tied pivots a
long distance away from the measurement. The skid assembly and transducer are
designed to measure the difference in height between the skid height and the
stylus tip height. The skid rides over imperfections in the surface and acts as a
mechanical filter of the surface: it smoothes out longer wavelength undulations in
the surface. This approach is therefore suitable for roughness profile measurement
only.
In the simplest skidded profiling instruments the stylus rides on the surface and measures
height relative to a skid which also rides on the surface. The skid can be in line with the
diamond or beside it as the assembly traverses the part.
Several alternatives are in use for the geometry of the skid relative to the stylus
tip. A single skid can ride in front of, behind, or in line with the diamond. More
commonly two skids are used that ride on either side of the diamond. A final
alternative is a single skid with the diamond tip protruding down from its center.
For some applications, for example measuring round parts, it may be desirable to
use two skids to establish the reference height, eliminating the pivot from the
measurement.
Two skids are occasionally used as the reference for round or unusually shaped
parts.
External Reference Datums
More advanced profiling instruments measure a surface relative to an external
datum as shown below.
An external reference is necessary to get a picture of the surface not mechanically filtered by
skids. The external reference is usually a lapped bar or an optical flat.
A vertical mechanical flexure provides a horizontal reference plane. This
geometry has the disadvantage of short travel distance.
An optical interferometric transducer can provide a vertical reference level, or an optical
transducer can be combined with a mechanical reference guide.
Once a profile has been converted to an electrical signal it enters the amplifier of the instrument
where it is not simply amplified, but converted to a digital representation and analyzed for all the
desired surface parameters. Higher capability instruments can display and plot profiles and
parameter results.
Surface Measurement Transducers
Several types of transducers are in use for measuring surface profiles. They fall
into two general types: velocity transducers and displacement transducers.
Moving Coil Transducers
Piezoelectric Transducers
Inductive Transducers
LVDTs
Linear variable differential transformers (LVDT*s) are widely used as high quality
displacement transducers in surface finish measurement.
A linear variable differential transformer (LVDT) consists of two transformers. The relative
efficiency of the two depends on the displacement of a ferrous core. In an actual transducer the
core, primary coil, and secondary coils share a common axis.
LVDT's work by comparing the output of two parallel transformers which have a
common core. As the core moves up or down, one or the other transformer
becomes more efficient because of better magnetic coupling between the primary
and secondary coils. In the simplest wiring scheme the two transformers are wired
in series. Then the voltage out is proportional to displacement and the direction of
displacement from the zero point is indicated by the phase of the output relative
to the input. The output has the opposite phase in one case because the
transformers are wired in opposite directions. More complicated detection
electronics look at both transformers independently.
LVDT's are very linear and repeatable. They have a definite zero point and have
good response as far as the highest frequency (shortest profile wavelength) they
can resolve. They have the disadvantage of being somewhat larger than other
surface finish transducers.
LVDTs are commonly used on profiling instruments and contouring instruments.
Surface Metrology Guide - Calibration and Reference Specimens
Calibration and Reference Specimens
In order to calibrate surface finish measuring instruments, a calibration reference
is needed. For profiling instruments these fall into three categories: specimens
with a known parameter (Ra) value, step height specimens, and specimens
designed to test the integrity of a diamond stylus.
In addition to specimens designed to calibrate instruments) one can buy specimens
of varying Ra designed to be compared with a fingernail to actual surfaces.
Roughness comparison Specimens
...
Less reverent workers in surface finish refer to this type of test as a "scratch-nsniff' test. The test is very subjective and is good only for estimates Of Ra on fairly
rough surfaces.
Instrument calibration Specimens Known Ra
Specimens
Triangle Waves
Sine Waves
Random Patches
Repeated Random Patches
Techniques for Creating
Stylus Check Specimens
Step Height Standards
.
Surface Metrology Guide - Filtering
Surface Profile Filtering
Introduction
What Filters Do
A surface profile may be composed of a range of frequency components. The high
frequency (or short wave) components correspond to those that are perceived to
be rough and hence called "roughness". The low frequency (or long wave)
components correspond to more gradual changes in the profile and are often
associated with the terms "waviness" or even "form". Note that roughness and
waviness are relative terms, just as the words "high", "low", "long" and "short".
Filtering is a procedure to separate certain frequency components of a surface
profile. Depending on what component is desired, the filtering operation may be
short-pass, or high-pass - letting the short wavelength (high frequency)
components through, therefore the roughness profile is extracted;
long-pass, or low-pass - letting the long wavelength (low frequency)
components through, therefore the waviness profile is extracted;
band-pass - extracting a profile of specified bandwidth by applying both
high-pass and low-pass filters, allowing controlled profile data bandwidth
The term "cutoff" numerically specifies the frequency bound below or above which
the components are extracted or eliminated.
wave in, components attenuated, wave out
Frequency Response
The "frequency response" of a filter refers to how the filter attenuates (or
amplifies) a sine wave input. For most useftil filters the attenuation is a ftinction
of the frequency or wavelength of the input, so the frequency response of a filter
is a (complicated) flinction of attenuation (often expressed as percent) versus
wavelength.
Analog 2RC Filter
Background
The 2RC (or 2CR) filter is the oldest standard filter used in surface roughness
measurements. It Is typically implemented as an analog electrical filter, 2 RC
filters in series, separated by a buffer. It Is not phase-correct, and it has a
frequency transmission of 75% at the cutoff wavelength. The 75% level was
apparently chosen because the 2RC filter has a long "tail" in its frequency
response, and, therefore, much of the long wavelength components above the 50%
cutoff remains in the roughness. The cutoff at 75% more accurately retains the
intuitive sense of being the wavelength boundary between roughness and
waviness. However, in almost all others scientific domains, the "cutoff' of a filter
is the 50% transmission point by definition. Newer filters in surface finish revert to
the more accepted 50% definition.
Cutoff Lengths
Standard values. Table
Electrical Definition
If the height, z, of a profile that varies over x distance is translated by transducer
and electronics into a DC voltage, e, that varies over time, t, then the 2RC filter
can be implemented electrically with the following circuit:
The "ideal separation" may be approximated by an electronic "buffer." In practice
the circuit R, and C values must be chosen to give the desired cutoff length. The
values depend on the horizontal velocity of the measuring instrument's pick-up as
it travels across the surface. The electrical filter is therefore only as accurate as
the instrument's horizontal velocity. One can change the cutoff by switching R
values or by changing the speed of the instrument.
Some in surface finish have begun to refer to the above filter as a 2CR filter
because the capacitor comes before the resistor in each pair. However, electrical
engineers refer to either order as an RC filter and distinguish between them by
calling one a high pass filter and one a low pass filter. "Pass" refers to what
frequencies make it through the filter. Thus the filter above is really a high pass
2RC filter; it lets through high frequency (short wavelength) components of the
signal, i.e. the roughness of the profile the signal represents.
Mathematical Definition
Following are useful relationships between distance, velocity, frequency, and
wavelength for a surface profile. Also consult the nomenclature section for
definitions of variables throughout this document.
If the height of the profile is z(x), then the electrical signal corresponding to the
profile is
This is the voltage, em, entering the above filter circuit. Application of Kirchoil's
laws (see an electronics or physics textbook) yields a differential equation for the
output voltage as a function of the input voltage for the circuit:
If we put things back in the domain of profile height versus horizontal distance, we
find a corresponding differential equation for the roughness profile as a function
of the texture profile:
In this equation we have also looked ahead to Section 7.4 and have made use of
the identity
which comes from the criterion of 75% frequency response at the cutoff.
Frequency Response
In the following two sub-sections we rigorously show how to calculate the
frequency response for the 2RC filter, but for now we simply present the result,
which is part of ANSI and ISO standards.
The meaning of this graph is that wavelengths considerably smaller than the cutoff
get through the filter completely, while long wavelengths are attenuated to zero.
There is a gradual transition between these two extremes.
Phase Lag in the Frequency Response
Digital Filters
Advantages of Digital Filters
Modern surface finish measuring instruments no longer rely on electronics to do
the roughness filtering. Instead they digitize the raw trace of the surface and
mathematically (computationally) filter this raw data after it has been collected
and stored in a computer memory. The first advantage of this approach is that the
same raw data can be filtered multiple times with different cutoffs to compare
the results. Another advantage is that it becomes possible to compare the
roughness or waviness to the original surface trace which it is a part of;
Weighting Functions
The most common way of performing digital filtering is to convolve a weighting
function with the raw data. A simplistic way of understanding this idea of
convolution is to think of it as a sliding multiplication and integral. Take a
weighting function h(x) that typically has some simple finite shape, for a particular
point on the profile center the weighting function over that point, multiply it by
the profile and integrate the resulting function. The result is a new value for a
modified profile. Repeat this procedure for each point in the original profile.
We denote the weighting function by h(x):
h = h(x)
The waviness is then a "weighting" or convolution of the texture profile:
Digital Filters and Fourier Transform Methods
This section details the traditional method for specifying digital filters. Usually
specified is the waviness weighting function as a function of distance:
Intro to Fourier ideas.
How to "think" in the Fourier domain
Usually desired, however, is the Fourier transform of the weighting function (in
terms of wavelength) derived from the weighting function as follows:
The advantage of this form is that the filter can be expressed as a simple
multiplication in the Fourier domain:
This is a standard result for convolution. It is useful to know is the frequency
response of the filter, which is just the magnitude of the Fourier transform of the
weighting function, |H(λ)|.
Discussion of convolution for filter response...
When the filter is phase-correct and is designed to give 50% transmission at the
cutoff frequency, there is a complementary relationship between roughness and
waviness:
This is also simply expressed in the Fourier domain:
Or defining the roughness filter in itself,
If the filter is not phase-correct or does not have 50% transmission at the cutoff,
then there are two related but independent filters for the roughness and for the
waviness.
Frequency Response
It Is easy to calculate the frequency response of a filter in the Fourier domain. The
attenuation of a sine wave by a filter H(λ) is simply IH(λ)I.
Digital Equivalent of Analog 2RC Filter
Fourier Transform Analysis
Adigital approximation of the analog 2RC filter can be constructed from the
differential equations describing the analog electrical circuit. . . . The Fourier
transform of the 2RC filter is:
Note the imaginary term in the above transform. This term produces the
wavelength-dependent phase shift in the roughness profile compared to the
primary profile.
The waviness has no standard definition with 2RC filtering, but a reasonable one
which complements Eq. (7.4.1) is a filter with the opposite frequency response
and the same phase lag:
H(X) = ... ?? need to calculate (7.4.2)
These have both real and imaginary parts because the filter is not phase correct.
The signal is phase shifted by an amount which depends on wavelength. Note that
the filter may be easily modified to yield a (nonstandard) 50% transmission at the
cutoff by removing the factor of 3 everywhere it appears in front of λc.
Frequency Response
The frequency response of the 2RC filter may be found by taking the magnitude of
the Fourier transform which defines the filter. The result is
This is the equation for the frequency response plotted earlier without proof. We
see that the frequency response at the cutoff is
(This result was already assumed in our conversion from RC to λc. We took this
circular approach in order to have more useful intermediate results- in the
physical domain rather than in the electrical domain.)
Phase Lag in the Frequency Response
The phase shift of the 2RC filter may also be calculated from its Fourier transform.
In general, the phase lag as a function of the wavelength of the profile is
Or for the 2RC filter, converting the phase lag angle to a fraction of a cycle,
Below is the relative phase lag as a function of the frequency of the original
sinusoidal profile. On this chart a lag of 0 means no lag at all. A lag of 0.5 means
the output is exactly out of phase with the input.
Right at the cutoff frequency the phase lag is 60? or one sixth of a full cycle. At
the longest wavelengths the phase lag reaches 180? the output of the filter is
precisely out of phase with the input. For the shortest wavelengths, the phase lag
becomes negligible. A real surface is a complicated mixture of many frequencies
added together. The phase lag of each component of the surface will depend on
its frequency as shown above. The sum, therefore, will have a complicated phase
lag behavior.
PICTURE: 2 superimposed wavelengths with different phase lags
Because the phase lag is significant near and above the cutoff wavelength,
undesirable effects can occur with spikes and other sharp features. In the Fourier
(frequency) domain steep transitions are a mixture of several wavelengths. The
sharp feature, after it goes through the filter will be "smeared out" in the direction
of filtering because of the variable phase lag of the components which make up
the feature. The most commonly seen failing is the behavior of the filter around a
sharp spike or a deep valley in an otherwise fairly smooth surface.
PICTURE of roughness of a spiked valley
The roughness "pushes up" on one side of a deep valley in the surface. The one-sided-ness is
due to the phase lag of the filter. In this case data was collected from right to left and the
filter responds to the valley only on the left.
Because the 2RC filter has a phase lag that increases with wavelength, the waviness, if
defined as the texture minus the roughness, has a lag and an asymmetry relative to the raw
trace of the surface.
Comments ...
Perfect steps are unlikely in surface finish measurement (or they should be), but it
is instructive to examine what a step looks like after 2RC filtering.
PICTURE of roughness of a step
Comments . .
Weighting Function
The 2RC filter may be implemented digitally using the following approximate
weighting function:
For 75% transmission at the cutoff frequency, A = 3.64.
Phase-Correct 2RC Filter
Background
The phase-correct 2RC filter is a digital filter that matches the frequency response
of the 2RC filter but has no phase lag. It retains the same 75% transmission at the
cutoff and has the very same frequency response curve. Like any phase-correct
filter it can not be implemented easily with analog electronics (despite its
relationship to the analog 2RC filter).
Its purpose is to approximate the behavior of the 2RC filter so that roughness
parameters can be compared with the older industry standard, but to do away
with the disadvantages that result from phase lags so that roughness profiles can
be examined with greater confidence. This filter is sometimes referred to as "the"
phase correct filter or the "PC" filter, but this name is more often given to the
Gaussian filter, so confusion can obviously arise. It is best to use the full name of
either phase correct filter.
Weighting Function
The phase-correct 2RC filter is a filter which has the same frequency response as
the 2RC filter but is phase-correct. Mathematically, this amounts to replacing the
Fourier transform of the 2RC filter by its magnitude;
The corresponding waviness filter is???.
Frequency Response
Gaussian Filter
Background
The Gaussian filter is designed to more precisely separate the roughness from the
waviness. Its frequency response has a steeper slope near the cutoff than the 2RC
frequency response, meaning that wavelengths near the cutoff (above or below)
are more sharply distinguished as either waviness or roughness.
Weighting Function
The weighting function for the Gaussian filter is as follows:
This is a Gaussian bell-shaped curve which gives the filter its name;
The width of the bell determines the cutoff of the filter. The width is in turn
determined by the α' and λc values. the parameter α' is defined so as to give 50%
transmission of a sine wave with wavelength equal to the cutoff.
The time and Fourier domain versions of the weighting function are:
GET RID OF THIS:
The Gaussian filter is defined to have 50% transmission at the cutoff wavelength.
This specification is what determined the value of α':
Frequency Response
The frequency response of the Gaussian filter is as shown:
The "push up" around a valley is less with the Gaussian filter than with
the 2RC and is symmetric. These are advantages of the phase-correct
filter approach.
Triangle Filter
Weighting Function
The weighting function for a triangle filter is defined in terms of the base halfwidth, B, of the unit-area triangle, as follows:
The main significance of the triangle filter is its simplicity. Sometimes it is used as
a computationally faster approximation of the Gaussian filter. The triangle filter is
also the basis for each pass of the two-pass Rk filter.
...
Frequency Response
The frequency response of the triangle filter is:
The frequency response of the triangle filter is close to that of the Gaussian filter,
except for "wiggles" at higher frequency. These are the result of the sharp changes
in the shape at x=0 and x=B.
Rk Filter
Background
The Rk filter is a special filter that is suitable for plateaued surfaces. It is designed
to reduce the overshoot that occurs in the roughness on either side of a sharp
valley.
Rk Filter
The Rk filter defined by German standard DIN 4774 is two passes of the above
triangle filter. (The DIN standard uses a slightly different definition for B, twice
the B used here). Because of the specialized processing between passes, there is
no way to combine the passes into a single Fourier transform.
Filter Procedure
There is a multistep procedure involved in the Rk filter. The first step is to
perform an ordinary triangle filter on the texture profile to get a first-pass
waviness profile. Next use this waviness as a truncation line: any part of the
primary profile which projects below the waviness is truncated to the first pass
waviness value. The truncated primary profile is next filtered a second time, again
with a triangle filter. The result is the Rk waviness. Subtracting from the original
texture gives the Rk roughness.
As shown in the highlighted areas of the first figure above, the Rk filter has less
"push up" in the final roughness, compared to a standard, one-pass roughness
filter. The waviness follows the plateaus and is less affected by the deep valleys
between.
When several valleys are close together, even the Rk filter will suffer from push-up
on either side of the group.
Alternatives to Rk Filtering
Recent research efforts have looked for alternatives to the Rk filter approach.
Several different algorithms have been proposed that find and truncate individual
valleys. There are multiple options for how to define what is a deep valley and
how to do the truncation. .
Short Wavelength Roughness Filtering
So far we have considered the high-pass roughness filter that separates the high
frequency (short wavelength) roughness components of texture from the long
wavelength waviness components of texture. At very high frequencies the
measurement made by a real instrument will be limited by the mechanics and
electronics and sampling rate of the instrument. However, the very newest
instruments can be designed with measurement loops that perform better than
necessary. In this case it is desirable to mathematically filter noise or very fine
features that are not of interest.
PICTURE: mechanical lower limit
Discussion: wavelength measurable by a given stylus radius. .
Choosing Filters and Cutoffs
When a part is manufactured from a blueprint the specification for surface finish
includes a cutoff for calculating the roughness, even if it is the (too often used)
default value of 0.030 in. However, when no blueprint is available, some guideline
is needed for how to choose the cutoff Also, the more savvy product designer may
want a means for choosing what cutoff value to specify. The tables in this section
give suggested values for the cutoff to use for different surface conditions.
First of all, there are five different standard cutoff lengths. These are listed in the
following table.
Table of Cutoffs and Cutoff Ratios
λc
λc:λs
diamond tip radius
0.003 in (0.08 mm)
30
?/φοντ> 0.00002 ιν
0.01 in (0.25 mm)
100
?/φοντ> 0.0001 ιν
0.03 in (0.8 mm)
300
?/φοντ> 0.0001 ιν
0.1 in (2.5 mm)
300
?/φοντ> 0.0004 ιν
0.3 in (8.0 mm)
300
?/φοντ> 0.004 ιν
In this table, and throughout this document, we use inch units primarily and
metric units secondarily. It is important to note, however, that surface finish
standards (including the ANSI standard) specify the values in metric units. The inch
values are only approximate equivalents. These are the standard cutoff and
sample lengths; there is rarely a reason to choose a nonstandard length except for
specialized periodic surfaces. Now we address the question of how to choose a
cutoff.
First, for periodic surfaces the sample length should be long enough to include a
reasonable number of periods of the profile waveform. The following table
suggests how to choose the sample length based on the 5m value of the primary
profile. The cutoff is chosen to give at least two periods of the surface in each
sample length.
Selecting cutoff for periodic surface
X
For:
<
Sm
0.0005 in
0.0016 in
0.005 in
0.016 in
0.050 in
?/φοντ>
Ψ
0.0016 in
0.005 in
0.016 in
0.050 in
0.160 in
Choose:
λc
0.003 in
0.01 in
0.03 in
0.1 in
0.3 in
For non-periodic surfaces, choose the sample length based on the expected value
of Ra or adjust the cutoff until the measured value of Ra fits within the bounds of
the table. (If the measurement is too high for one row and too low for the next,
choose the higher cutoff value to retain all relevant frequency contents.)
Selecting cutoff for random surfaces
X
<
For:
Ra
0.8 µin
4.0 µin
80 µin
400 µin
?/φοντ>
0.8 µin
4.0 µin
80 µin
400 µin
Ψ
Choose:
λc
0.003 in
0.01 in
0.03 in
0.1 in
0.3 in
Waviness Filtering
So far we have discussed "roughness filters"- filters for separating roughness from
waviness. At longer wavelengths the same concepts apply for separating waviness
from form error.
Surface Metrology Guide - Profile Parameters
Surface Profile Parameters
Parameter
Name
Standards
Related
Height Parameters
Ra
Roughness Average (Ra)
1,2,3,4
Pa, Wa
Rq
Root Mean Square (RMS) Roughness
1,3,4
Pq, Wq
Rt
Maximum Height of the Profile
1,3
Pt, Wt
Rv, Rm
Maximum Profile Valley Depth
1,3,4
Pv, Wv
Rp
Maximum Profile Peak Height
1,3,4
Pp, Wp
Rpm
Average Maximum Profile Peak
Height
1
Rz
Average Maximum Height of the
Profile
1,3
Pz, Wz, Rtm
Rmax
Maximum Roughness Depth
1
Ry, Rymax, Rti,Rz
Rc
Mean Height of Profile Irregularities
3,4
Pc, Wc
Rz(iso)
Ten Point Height
4
Ry
Maximum Height of the Profile
4
Wt, W
Waviness Height
1,2,3
Rt,Pt
Spacing Parameters
S
Mean Spacing of Local Peaks of the
Profile
4
Sm, RSm
Mean Spacing of Profile Irregularities
1,3,4
PSm, WSm
D
Profile Peak Density
4
Sm
Pc
Peak Count (Peak Density)
1
HSC
Hight Spot Count
λa
Average Wavelength of the Profile
4
λq
Root Mean Square (RMS) Wavelength
of the Profile
4
Hybrid Parameters
∆a
Average Absolute Slope
1,3
P∆a, W∆a
∆q
Root Mean Square (RMS) Slope
1,3
P∆q, W∆q
Lo
Developed Profile Length
4
lr
lr
Profile Length Ratio
4
Lo
ADF and BAC Parameters
Rsk,Sk
Skewness
1,3,4
Psk, Wsk
Rku
Kurtosis
1,3
Pku, Wku
tp, Rmr(c)
Profile Bearing Length Ratio
(Material Ratio of the Profile)
1,3,4
Pmr(c), Wmr(c),
Pmr, Rmr, Wmr
Htp, Rδc
Profile Section Height Difference
1,3
H
Swedish Height
Rk
Core Roughness Depth
5
Rpk
Reduced Peak Height
5
Rpk*
Rvk
Reduced Valley Depth
5
Rvk*
Mr1
Material Portion
5
Rmr(c), tp
Mr2
Material Portion
5
Rmr(c), tp
Vo
"Oil-Retention" Volume
Htp, Rt
Rpq, Rvq,
Rmq
Material Probability Curve
Parameters
Notes:
1: ASME B46.1-1995
2: ASME B46.1-1985
3: ISO 4287-1997
4: ISO 4287/1-1984
5: ISO 13565-1996
Roughness Amplitude Parameters
Ra - Average Roughness
Also known as Arithmetic Average (AA), Center Line Average (CLA), Arithmetical Mean
Deviation of the Profile.
The average roughness is the area between the roughness profile and its mean line, or
the integral of the absolute value of the roughness profile height over the evaluation
length:
When evaluated from digital data, the integral is normally approximated by a
trapezoidal rule:
Graphically, the average roughness is the area (shown below) between the roughness
profile and its center line divided by the evaluation length (normally five sample lengths
with each sample length equal to one cutoff):
The average roughness, Ra, is an integral of the absolute value of the roughness profile. It Is
the shaded area divided by the evaluation length, L. Ra is the most commonly used roughness
parameter.
The average roughness is by far the most commonly used parameter in surface finish
measurement. The earliest analog roughness measuring instruments measured only Ra
by drawing a stylus continuously back and forth over a surface and integrating (finding
the average) electronically. It is fairly easy to take the absolute value of a signal and to
integrate a signal using only analog electronics. That is the main reason Ra has such a
long history
It is a common joke in surface finish circles that "RA" stands for regular army, and "Ra" is
the chemical symbol for Radium; only "Ra" is the average roughness of a surface. This
emphasizes that the a is a subscript. Older names for Ra are CLA and AA meaning center
line average and area average..
An older means of specifying a range for Ra is RHR. This is a symbol on a drawing
specifying a minimum and maximum value for Ra.
Older drawings may have used this notation to express an allowable range for Ra. This
notation is now obsolete.
For example, the second symbol above means that Ra may fall between 10 µin and 20
µin.
Ra is Not the End of the Story
Ra does not tell the whole story about a surface. For example, here are three surfaces
that all have the same Ra, but you need no more than your eyes to know that they are
quite different surfaces. In some applications they will perform very differently as well.
These three surfaces all have the same Ra, even though the eye immediately
distinguishes their different general shapes.
These three surfaces differ in the shape of the profile - the first has sharp peaks, the
second deep valleys, and the third has neither. Even if two profiles have similar shapes,
they may have a different spacing between features. The following three surfaces also
all have the same Ra.
If we want to distinguish between surfaces that differ in shape or spacing, we need to
calculate other parameters for a surface that measure peaks and valleys and profile
shape and spacing. The more complicated the shape of the surface we want and the
more critical the function of the surface, the more sophisticated we need to be in
measuring parameters beyond Ra.
Rq - Root-Mean-Square Roughness
The root-mean-square (rms) average roughness of a surface is calculated from another
integral of the roughness profile:
The digital equivalent normally used is:
For a pure sine wave of any wavelength and amplitude Rq is proportional to Ra; it's
about 1.11 times larger. Older instruments made use of this approximation by
calculating Rq with analog electronics (which is easier than calculating with analog
electronics) and then multiplying by 1.11 to report Rq. However, real profiles are not
simple sine waves, and the approximation often fails miserably. Modern instruments
either digitize the profile or do not report Rq. There is never any reason to make the
approximation that is proportional to Ra.
Rq has now been almost completely superseded by Ra In metal machining specifications.
Rq still has value in optical applications where it is more directly related to the optical
quality of a surface.
Rt, Rp, and Rv
The peak roughness Rp is the height of the highest peak in the roughness profile over
the evaluation length (p1 below). Similarly, Rv is the depth of the deepest valley in the
roughness profile over the evaluation length (v1). The total roughness, Rt, is the sum of
these two, or the vertical distance from the deepest valley to the highest peak.
These three extreme parameters will succeed in finding unusual conditions: a sharp
spike or burr on the surface that would be detrimental to a seal for example, or a crack
or scratch that might be indicative of poor material or poor processing.
Rtm, Rpm and Rvm
These three parameters are mean parameters, meaning they are averages of the sample
lengths. For example, define the maximum height for the i-th sample length as Rpi.
Then Rpm is:
Similarly,
and
where Rvi is the depth of the deepest valley in the i-th sample length and Rti is the sum
of Rvi and Rpi:
These three parameters have some of the same advantages as Rt, Rp, and Rv for finding
extremes in the roughness, but they are not so sensitive to single unusual features.
Rymax (or Rmax) - Maximum Roughness Height Within a Sample Length
Ry and Rmax are other names for Rti. Rmax is the older American name. Ry is the newer
ISO and American name. For a standard five cutoff trace there are five different values
of Ry. Ry is the maximum peak to lowest valley vertical distance within a single sample
length.
what's it good for...
Rymax(ISO) - Maximum Ry
Rymax is an ISO parameter that is the maximum of the individual or Rmax (i.e. Rti)
values.
serves a purpose similar to Rt, but it finds extremes from peak to valley that are nearer
to each other horizontally.
Rz(DIN)
Rz(DIN), i.e. Rz according to the German DIN standard, is just another name for Rtm in
the American nomenclature. (over five cutoffs)
What's its origin & what's it good for.
Rz(ISO) - Ten Point Average Roughness
Rz(ISO) is a parameter that averages the height of the five highest peaks plus the depth
of the five deepest valleys over the evaluation length.
R3zi - Third Highest Peak to Third Lowest Valley Height
The parameter R3zi is the height from the third highest peak to the third lowest valley
within one sample length.
R3z - Average Third Highest Peak to Third Lowest VaJicy Height
R3z is the average of the R3zi values:
R3z has much the same purpose as Rz except that less extreme peaks and valleys are
being measured.
R3zmax - Maximum Third Highest Peak to Third Lowest Valley Height
R3zmax is the maximum of the individual R3zi values:
R3z and R3zmax are not defined in national standards, but they have found their way
into many high-end instruments. They originated in Germany as a Daimler-Benz
standard.
Roughness Spacing Parameters
Pc - Peak Count
Peak count is a number giving the number of peaks per length of trace in a profile. For
the purpose of calculating Pc a "peak" is defined relative to an upper and lower
threshold. Usually this is a single number, the "peak count threshold", the distance from
a lower threshold up to an upper threshold, centered on the mean line. A peak must
cross above the upper threshold and below the lower threshold in order to be counted.
Peak count is the number of peaks in the evaluation length divided by the evaluation
length. (Or to be picky, by the distance from the beginning of the first peak to the end
of the last peak). Pc is thus reported as [peaks/in] or [peaks/cm].
Some instruments allow the thresholds to be centered on a height that differs from the
mean line. This is nonstandard but may be convenient. For example) a pair of thresholds
that counts low peaks accompanied by deeper valleys may be appropriate for plateaued
surfaces.
[What's it good for]
The value obtained for Pc depends quite heavily on the peak count threshold for most
surfaces. The figure below shows peak count versus threshold for a ground surface and a
turned surface as representative samples. For the ground surface the parameter shows
no stability. For the turned surface there is a bit of flattening out at a threshold of
about 40 µin, but even for this surface Pc shows a wide variation with threshold.
HSC - High Spot Count
High spot count, HSC, is similar to peak count except that a peak is defined relative to
only one threshold. High spot count is the number of peaks per inch (or cm) that cross
above a certain threshold. A "peak" must cross above the threshold and then back below
it.
High spot count is commonly specified for surfaces that must be painted. A surface
which has protrusions above the paint will obviously give and undesirable finish.
Sm - Mean Spacing
Sm is the mean spacing between peaks, now with a peak defined relative to the mean
line. A peak must cross above the mean line and then back below it.
If the width of each peak is denoted as Si (above), then the mean spacing is the average
width of a peak over the evaluation length:
Sm is usually reported in µin or µm.
λa - Average Wavelength
The average wavelength of the surface is defined as follows:
This parameter is analogous to Sm in that it measures the mean distance between
features, but it is a mean that is weighted by the amplitude of the individual
wavelengths, whereas Sm will find the predominant wavelength.
λq - RMS Average Wavelength
λpc - Peak Count Wavelength
The above formula leaves in the reciprocal units of λpc. Therefore the value must
ordinarily be converted from [in] to [λin] or from [cm] to [λm].
K - Randomness Factor ??? What is this?
Roughness Hybrid Parameters
∆a - Average Absolute Slope
This parameter is the average of the absolute value of the slope of the roughness profile
over the evaluation length:
It is not so straightforward to evaluate this parameter for digital data. Numerical
differentiation is a difficult problem in any application. Some instrument manufacturers
have applied advanced formulas to approximate dz/dx digitally, but the simplest
approach is to apply a simple difference formula to points with a specified spacing L/N:
If this approach is used, the value of LIN must be specified since it greatly influences
the result of the approximation. Ordinarily LIN will be quite a bit larger than the raw
data spacing from the instrument.
[What1s it good for..]
∆q - RMS Average Slope
Lo - Actual Profile Length
One way to describe how a real profile differs from a flat line is to determine how long
the real profile is compared to the horizontal evaluation length. Imagine the profile as a
loose string that can be stretched out to its full length.
FIGURE
The 2-D length of a profile comes from the following equation:
As for ∆a and ∆q, the answer in a digital evaluation depends on the spacing of the points
we choose to approximate dr/dx:
Lr - Profile Length Ratio
The profile length ratio, Lr, is the profile length normalized by the evaluation length:
The profile length ratio is a more useful measure of surface shape than Lo since it does
not depend on the measurement length.
The larger the value of Lr, the sharper or crisper the surface profile appears and the
larger the true surface area of the surface is. In some applications, particularly in
coating, where good adhesion is needed, it may be desirable to have a large value of Lr,
i.e. a large contact surface area.
For most surfaces Lr is only slightly larger than one and is difficult to determine
accurately.
Statistical Analysis
The Amplitude Distribution Function
The amplitude distribution function (ADF) is a probability function that gives the
probability that a profile of the surface has a certain height, z, at any position x.
Ordinarily the ADF is computed for the roughness profile, although the texture or even
primary profiles might be used in specialized applications.
The ADF has a characteristic bell shape like many probability distributions. The ADF tells
"how much" of the profile lies at a particular height, in a histogram sense. It is the
probability that a point on the profile at a randomly selected x value lies at a height
within a small neighborhood of a particular value z:
The Bearing Ratio Curve
The Bearing Ratio Curve is related to the ADF, it is the corresponding cumulative
probability distribution and sees much greater use in surface finish. The bearing ratio
curve is the integral (from the top down) of the ADF.
We postpone further discussion of the bearing ratio curve until a later section, after we
have considered other statistical techniques that work with a profile directly or are
related to the shape of the ADF.
Other names for the bearing ratio curve are the bearing area curve (this is becoming
obsolete with the increase in topographical methods), the material ratio curve, or the
Abbott-Firestone curve.
Statistical Parameters
Rq - Root-Mean-Square Roughness
The root-mean square average roughness, Rq, was defined earlier. We note at this
point, though that is the variance of the amplitude distribution function. In this sense it
is a statistical parameter that measures the width of the ADF: the wider the ADF, the
larger the value of~, and the rougher the surface.
Rsk - Skewness
Skewness is another parameter that describes the shape of the ADF. Skewness is a
simple measure of the asymmetry of the ADF, or, equivalently, it measures the
symmetry of the variation of a profile about its mean line.
or
Surfaces with a positive skewness, such as turned surfaces have fairly high spikes that
protrude above a flatter average. Surfaces with negative skewness, such as porous
surfaces have fairly deep valleys in a smoother plateau. More random (e.g. ground)
surfaces have a skew near zero:
The skewness parameter correlates with load carrying capability, porosity, and other
characteristics of surfaces produced by processes other than conventional machining. A
value of Rsk greater than about 1.5 in magnitude (positive or negative) indicates that
the surface does not have a simple shape and a simple parameter such as Ra is probably
not adequate to characterize the quality of the surface. For example, as drawn above,
each surface has about the same ~ and Rt, but the surfaces are quite different.
Note that skewness is non-dimensional. Often the skewness is denoted as "Sk" instead of
Rsk.
Surfaces with a large positive skewness can cause large measurement errors when
measured with skidded instruments, particularly if there is a large spacing between the
spikes of the surface.
Rku - Kurtosis
Kurtosis is the last ADF shape parameter considered. Kurtosis relates to the uniformity
of the ADF or, equivalently, to the spikiness of the profile.
or
PICTURES OF KURTOSIS
A reader familiar with statistics will recognize that Rq, Rsk, and Rku are related to
moments of the ADF probability distribution.
The zeroth moment (average) of the roughness is zero by definition. [NOT TRUE]
is the square root of the second moment (variance). Rsk is the third moment and ~ is
the fourth moment of the ADF probability distribution. In statistics, a probability
distribution can be constructed from all its moments. The more moments are known,
the more precisely the shape of the distribution is known.
Bearing Ratio Analysis
Background
Abbott-Firestone Curve
Bearing Area Curve
Physical Significance of the Bearing Ratio Curve
The bearing ratio curve mathematically is the integral of the amplitude distribution
function. It is a cumulative probability distribution. Ordinarily, the integral is performed
from the highest peak downward, so each point on the bearing ratio curve has the
physical significance of showing what linear fraction of a profile lies above a certain
height (compared to the ADF which tells how much of a surface lies at a given height).
Comments about shape, plateau, peaks, valleys.
Mathematics of the Bearing Ratio Curve
Mathematically the bearing ratio curve may be calculated from the ADF
...
or calculated directly from a profile:
...
Simple Bearing Ratio Parameters
tp - Bearing Ratio
The symbol tp has two meanings. First, it is used generically as the abscissa of the
bearing ratio curve. It is just a percent bearing ratio. Second, tp as a parameter refers
to the bearing ratio at a specified height. The most common way of specifying the
height is to move over a certain percentage (the reference percent) on the bearing ratio
curve and then to move down a certain depth (the slice depth). The bearing ratio at the
resulting point is "tp". The purpose of the reference percent is to eliminate spurious high
peaks from consideration; these will wear off in early part use. The slice depth then
corresponds to an allowable roughness or to a reasonable amount of wear.
Another common way of choosing the height level for tp is as a distance up or down
from the mean line of the roughness profile.
[tpa vs. tpi, unfiltered, filtered]
Htp - Bearing Height
The parameter tp is the bearing ratio at only one point. If we want to measure the
roughness of the surface from the bearing ratio curve, it become appropriate to look at
two points on the curve and look at the height difference between them. The bearing
height is the height between two points on the bearing ratio curve at specified values of
tp, tp1 and tp2 These specified values will depend on the application.
H - Swedish Height
The Swedish height parameter, H, is just Htp with specific values for tp1, and tp2,
namely 5% and 90%. H thus has a purpose similar to Rt, but is not as strongly influenced
by occasional high peaks or deep valleys.
Waviness Profile Parameters
So far we have considered parameters derived from the roughness profile. This is by far
the most common type of parameter measured. However, in some applications we may
be concerned with surface texture deviations with longer wavelengths. Statistical
parameters of the waviness profile may be evaluated just as they are for the roughness
profile.
One major problem with evaluating waviness parameters is that a longer trace length is
needed in order to have statistically significant results. There is no standard for how
long is long enough or how to break the waviness into separate sample lengths as we do
for roughness. Thus the following parameters do not have such a rigorous connection to
sample length and filter cutoff. Usually they are evaluated for one sample length equal
to the longest trace possible on a particular part with a particular instrument.
Wt - Total Waviness Height
Like Rt, Wt is the height from the lowest valley to the highest peak of the waviness
profile.
[Discussion . . ]
Before digital instruments and phase-correct filtering, there was no way to compute the
waviness cleanly. It was common in such a case to compute Wt by an approximation:
The worst deviation of the roughness plus the worst deviation of the waviness is
approximately equal to the worst deviation of the texture or total profile. This
approximation should be unnecessary with modern instruments.
Wa - Average Waviness
Another parameter used to report waviness is the arithmetic absolute average,
analogous to the ubiquitous Ra.
or
Advanced Statistical and Bearing Ratio
Analysis
Rk Parameters
There is a significant amount of information encapsulated in the shape of the bearing
ratio curve for a surface. Recent efforts in surface finish have tried to summarize that
shape information in a few parameters. The Rk parameters are a simple approach where
the knee-shaped BAC is approximated by a set of straight lines.
Rk Construction
The Rk construction is designed to divide the bearing ratio curve into three sections:
the small peaks above the main plateaus, the plateaus themselves, and the deep valleys
between plateaus.
The first step is to slide a "window" across the bearing ratio curve looking for the
minimum secant slope. The window is 40% tp wide. As the window slides across the
curve it intersects two points on the curve. The goal is to find the position where the
slope between the two points is minimized, or since the window has constant width,
where the height Htp between the two points is minimized. Following are shown three
steps in the process.
Once the window with minimum secant slope is found, a fairly complicated construction
begins. In the figure below we have found the minimum slope window and the points A
and B where the window intersects the bearing ratio curve. Next draw a line through
these two points to find the intercepts at 0% and 100%, points C and D. The vertical
height between C and D is the first parameter, Rk. Draw a horizontal line across from C
to the bearing ratio curve, point E. Find the area below the bearing ratio curve and
above the line CE, shown shaded in the upper part of the figure. Next, compute Rpk as
the height of triangle CEG which has the same area as the shaded area. For the valleys
draw a horizontal line from D over to point F on the curve. Compute the area of the air
space below line DF and above the bearing ratio curve (shown shaded in the lower part
of the figure). Next compute the height, Rvk, of triangle DFH which has the same area
as the shaded region.
Rk
The parameter Rk is the vertical height between the left and right intercepts of the line through the ends of the minimum Htp 40% window.
Rk correlates with the depth of the working part of the surface, the flat part of the
bearing area curve. After the initial running in period (i.e. after the peaks represented
by Rpk are worn down), this part of the surface carries the load and most closely
contacts the mating surface. Sometimes this part of the surface is called the "core
roughness" or the "kernel" (hence the k subscript).
Rpk
Rpk is an estimate of the small peaks above the main plateau of the surface. These
peaks will typically be worn off (or down) during the run-in period for a part. Generally,
it would be desired to have a fairly small Rpk.
Rvk
Rvk is an estimate of the depth of valleys which will retain lubricant in a funtioning
part.
MR1
MR1 is the fraction of the surface which consists of small peaks above the main plateau.
MR2
MR2 is the fraction of the surface which will carry load during the practical lifetime of
the part. Alternatively, 100%-MR2 is the fraction of the surface that consists of deeper
valleys that will retain lubricant.
A1
The "area" of the peak portion of the bearing ratio curve is denoted by A1. It is related
to Rpk and MR1:
A2
The "area" of the valleys in the Rk construction is denoted by A2. It is related to Rvk and
MR2:
A2 is also called Vo, the oil retention "volume" of the surface.
Gaussian Probability Scale
The Gaussian probability scale linearizes the cumulative
Gaussian distribution. The slope of the line is Rq.
Gaussian Probability Parameters
.
Surface Metrology Guide - Advanced Analysis
Advanced Statistical and Frequency
Analysis
Power Spectral Density Function
The power spectral density function is [PUT THIS IN TERMS OF WAVELENGTH]
(10.1.1)
In practice the Fourier transform is done by FFT, so the frequency, f; corresponds
to a
Autocorrelation
Autocovariance
...
The autocovariance is, mathematically; a convolution of the profile with itself:
(10.2.1)
In discrete form, for a finite profile, taking into to consideration that there are
fewer and fewer overlapping points as the shift distance increases, the
autocorrelation function may be calculated as
(10.2.2)
The autocorrelation function may be calculated more efficiently by taking the
Fourier transform of the power spectral density function:
Autocorrelation
The autocorrelation function is simply a normalized version of the autocorrelation
function. It is the autocorrelation function normalized to be one at ∆x = 0.
(8.4.1)
We have noted above that the mean square roughness, Rq2, is equal to the zero
shift value of the autocovariance.
The autocorrelation function ranges from 1, meaning perfect correlation to 1,
meaning perfect correlation with the inverted, shifted profile. The autocorrelation
function is independent of the profile amplitude. Therefore it is more useful than
the autocovariance in comparing the shape of two different profiles.
Correlation Length and Correlation Wavelength
A simple parameter calculated from the autocorrelation function is the correlation
length, ∆x0, the largest shift distance ∆x with a particular ACF value. In other
words, the correlation length is the shift length needed for the correlation
between two points to always fall below a certain value. Typical values used to
define the correlation length are ACF lIe = 36.8% or ACF = 10%.
For periodic surfaces, one might choose ACF = 0% and look for the first zero
crossing Another approach is to define λw, the correlation wavelength, the
wavelength of the dominant periodic component in the profile. This value
corresponds to the shift distance, ∆x> 0, where the ACF is maximized.
Autocorrelation and Surface Shape
Mathematical Nomenclature
English Symbols
C
capacitance in an electrical circuit
i
refers to the i-th sample length in an evaluation length
j
imaginary number; square root of-I
Surface Metrology Guide - Advanced Analysis
M
the number of sample lengths in an evaluation length (almost
always 5)
n refers to the n-th individual point in a digitized trace
N
the number of digitized points in a profile
r the roughness profile height
R
Roughness. When subscripted refers to a roughness height
parameter.
R
resistance in an electrical circuit
V voltage
w the waviness profile height
W
Waviness. When subscripted refers to a waviness height
parameter.
x
coordinate in the direction of travel of a stylus of other
measuring transducer.
y
coordinate
z "height' of a surface at a particular (x,y) or traced profile height
Greek Symbols
λ wavelength
λc
cutoff wavelength
References
Hu Amstutz, Surface Texture: The Parameters, Sheffield Measurement Division.
Michael Brock, "Fourier Analysis of Surface Roughness," Bruel & Kjaer Instruments,
Technical Review, No. 3, 1983.
Bill Grant and Mark Malburg, Cummins Engine Company, Personal Communications,
1992.
ISO Standard 1879, "Instruments for the Measurement of Surface Roughness by the
Profile Method - Vocabulary," 1981.
ISO Standard 4287/1, "Surface Roughness - Terminology - Part 1: Surface and Its
Parameters," 1984.
ISO Standard 4287/2, "Surface Roughness Terminology - Part 2: Measurement of
Surface Roughness Parameters," 1984.
Leigh Mummery, Surface Texture Analysis - The Handbook, Hommelwerke, 1990.
T.V. Vorburger and 3. Raja, "Surface Finish Tutorial", NJSTIR 89-4088.
.
Surface Metrology Guide - Standards
Surface Metrology Standards
ISO Standards
US Standards
Other Related Standards
Obtaining Standards
ISO Standards
ISO Technical Committee 213 (TC 213) is responsible for establishing standards for
Geometrical Product Specifications (GPS), including surface texture. The
committee has its own web site at www.ds.dk/isotc213. Some of the information
given below was compiled from this site.
Current ISO Standards
ISO 4288:1996; Geometrical product specifications (GPS) - Surface texture:
Profile method - Rules and procedures for the assessment of surface texture
Replaces ISO 4288:1985
ISO 12085:1996; Geometrical Product Specifications (GPS) - Surface texture:
Profile method - Motif parameters
Profile method - Nominal characteristics of contact stylus instruments
Replaces ISO 1880:1979 and ISO 3274:1975
Profile method - Metrological characteristics of phase correct filters
ISO 13565-1:1996; Geometrical Product Specifications (GPS) - Surface
texture: Profile method; Surfaces having stratified functional properties Part 1: Filtering and general measurement conditions
ISO 13565-2:1996; Geometrical Product Specifications (GPS) - Surface
texture: Profile method; Surfaces having stratified functional properties Part 2: Height Characterization using the linear material ratio curve
Profile method - Terms, definitions and surface texture parameters
Replaces ISO 4287-1:1984
ISO 5436:1985 Calibration specimens - Stylus instruments - Types, calibration
and use of specimens
Watch for revisions and expansion of this standard
ISO 1302:1994; Technical Drawings - Method of indicating surface texture.
Watch for revisions
ISO/TR 14638:1995 Geometrical product specification (GPS) -- Masterplan
This is an ISO Technical Report (TR) not an ISO Standard
Standards under Preparation
ISO DIS 5436-1; Geometrical product specifications (GPS) - Surface texture:
Profile method; Measurement standards - Part 1: Material measures
ISO CD 5436-2; Geometrical Product Specifications (GPS) - Surface texture:
Profile method - Calibration - Part 2: Soft gauges
ISO CD 1302; Geometrical Product Specifications (GPS) - Indication of Surface
texture
ISO DIS 12179; Geometrical product specifications (GPS) - Surface texture:
Profile method - Calibration of contact (stylus) instruments
ISO FDIS 8785; Geometrical product specifications (GPS) - Surface
imperfections - Terms, definitions and parameters
ISO/DIS 13565-3; Geometrical Product Specifications (GPS) - Surface texture:
Profile method stratified functional properties - Part 3: Height
characterization using the material probability curve
ISO/DIS 10479; Surface waviness - Vocabulary
Withdrawn ISO Standards
ISO 1880:1979; Instruments for the measurement of surface roughness by the
profile method - Contact (stylus) instruments of progressive profile
transformation - Profile recording instruments
Replaced by ISO 3274:1996 by 1996-12-01.
ISO 2632-1:1985; Roughness comparison Specimens - Part 1: Turned, ground,
bored, milled, shaped and planed
No replacement. Withdrawn by 1997-03-27.
ISO 2632-2:1985; Roughness comparison Specimens - Part 2: Spark-eroded,
shot-blasted and grit-blasted, and polished
No replacement. Withdrawn by 1997-03-27.
ISO 3274:1975; Instruments for the measurement of surface roughness by the
profile method - Contact (stylus) instruments of consecutive profile
transformation - Contact profile meter, system M
ISO 4287-1:1984; Surface roughness - Terminology - Part 1: Surface and its
parameters
ISO 4287/2:1984; Surface roughness - Terminology - Part 2: Measurement of
surface roughness parameters
No replacement.
ISO 4288:1985; Rules and procedures for the measurement of surface
roughness using stylus instruments
ASME Standards
The ASME B46 committee (Classification and Designation of Surface Qualities) is
responsible for establishing American standards on surface texture measurement.
The committee meet twice a year (in spring and fall). Contact current ASME B46
secretary for meeting schedules and other B46 businesses.
Current Standards
ASME B46.1-1995; Surface Texture (Surface Roughness, Waviness, and Lay).
Revision of ANSI/ASME B46.1-1995
Terms Related to Surface Texture
Classification of Instruments for Surface Texture Measurement
Terminology and Measurement Procedures for Profiling, Contact,
Skidless Instruments
Measurement Procedures for Contact, Skidded Instruments
Measurement Techniques for Area Profiling
Measurement Techniques for Area Averaging
Filtering of Surface Profiles
Specification and Procedures for Precision Reference Specimens
Specification and Procedures for Roughness Comparison Specimens
ASME Y14.36M-1996; Surface Texture Symbols.
Standards under Preparation
Fractal analysis
Nanometer surface texture & step height measurements by stylus profiling
instruments
Functional correlation
Computation surface metrology
standard data file format
algorithm verification
etc. etc.
3D surface metrology
Other Related Standards
(ASTM, ISO 172 on power spectral density function)
Obtaining Standards Documents
American National Standards Institute (ANSI) and NSSN
The American Society of Mechanical Engineers (345 E. 47th Street, New York,
NY 10017; Tel: 1-800-THE-ASME)
Your favourite engineering libraries
Other commercial document handlers
Information Handling Services (IHS)
Document Center
Custom Standards Services, Inc.
.

Surfaces and Profiles

Transcription

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