The Wind Tunnel Model Surface

[Gauge for Measuring Roughness ————— — I "i^—— I

T. V. Vorburger, D. E. Gilsinn, E. C. Teague,

C. H. W. Giauque, F. E. Scire, and L. X. Cao*

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Manufacturing Engineering

Gaithersburg, MD 20899

June 1987

I

‘Permanent Address: Department of Aircraft Manufacturing Engineering,

H

' v*e*u o*

U.S. DEPARTMENT OF COMMERCE

t NATIONAL BUREAU OF STANDARDS

Northwestern Polytechnical University, Xian, China

l~ QC — A

_ _ 100

• U56

87-3586

1987

.Research L. /urination Center

National bureau of Standards

Gaithersburg, Maryland 20899

NBSIR 87-3586

THE WIND TUNNEL MODEL SURFACE

GAUGE FOR MEASURING ROUGHNESS

T. V. Vorburger, D. E. Gilsinn, E. C. Teague,

C. H. W. Giauque, F. E. Scire, and L. X. Cao*

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Manufacturing Engineering

Gaithersburg, MD 20899

June 1987

‘Permanent Address: Department of Aircraft Manufacturing Engineering,

Northwestern Polytechnical University, Xian, China

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Abstract

This report covers research performed in the optical inspection of surface

roughness by members of the Center for Manufacturing Engineering under contracts

L-4718B and L-20078B with the NASA Langley Research Center. The project has

proceeded along two lines: first, research into a quantitative understanding of

light scattering from metal surfaces and into the appropriate models to describe

the surfaces themselves, and second, the development of a practical instrument

for the measurement of rms roughness of high performance wind tunnel models with

smooth finishes. The research has been discussed in previous articles and is

only summarized here. This report is concerned primarily with the latter

subject. We have developed a practical technique for the optical estimation of

rms roughness based on three things: a commercially available, optical

roughness gauge, a special nosepiece that allows for rapid alignment of the

gauge on curved surfaces, and a series of comparator studies that correlate the

results for obtained by the gauge with rms roughness (R ) measurements of

surfaces by stylus techniques. is an optical scattering parameter that is

proportional to the variance of the light scattering angular distribution about

its mean angle. We have proposed upper limit criteria for the value of that

should be expected on a properly finished model surface having rms roughness

less than 0.2 pm. We have estimated that valid measurements of may be taken

within an angle of 60° from the leading edge of the wind-tunnel model wing that

we tested and have shown from stylus measurements that the roughness increases

dramatically around the leading edge.

Key Words: aircraft, finish, light scattering, model, optical roughness,

optical scattering, rms roughness, roughness, stylus, surface,

transonic, wind tunnel

TABLE OF CONTENTS

Page

1 . Introduction 1

2. Description and Use of the Model Surface Gauge 3

3. Experimental Tests of the Model Surface Gauge 11

4. Limitations of the Present Instrument 38

5. Related Work 39

6. Acknowledgments 43

7. References 44

Appendix A 46
.
1 . Introduction

In the fall of 1980, NASA and NBS initiated a project, with partial funding

from NASA under contracts L-4718B and L-20078B, to address any potential new

problems that might be imposed on the surface finish requirements for models to

be used in the National Transonic Facility, a high-pressure, cryogenic wind

tunnel under development at the time and since completed. At the largest

Reynolds numbers that the National Transonic Facility would achieve, admissible

roughness heights for the surfaces of models fell below the surface finishes

currently specified for models. These higher demands for surface finishes of

the models arose because surface roughness influences skin friction, shock wave

location, and boundary layer separation location. Generally the aim in

fabricating a model's surface is to make it smooth enough that it does not

produce a measurable aerodynamic effect. Estimated roughness heights at which

surface irregularities can have an aerodynamic effect at typical Reynolds

numbers in the NTF are 0.25 micrometers (10 microinches) or higher [1].

The objectives of the joint NASA/NBS project were therefore: (1) to

evaluate the performance of stylus instruments for measuring the topography of

NTF model surfaces both for monitoring during fabrication and as an absolute

measurement of topography, (2) to measure and characterize the true 3D

topography of NTF model surfaces so that their characteristics could be related

back to that of sand grain surfaces historically used to obtain data on surface

roughness versus drag, and (3) to develop a prototype light scattering

instrument that would allow for rapid assessment of the surface finish of a model surface.

Work to accomplish the first objective has consisted of comparing research

grade and shop grade stylus measurements of the surface finish of three test

specimens fabricated by NASA [1]. We concluded from this study that the shop

grade instruments can damage the surfaces of models and that their use for

monitoring fabrication procedures can lead to surface finishes, in critical

areas of the leading edges of wings, that are substantially out of range.

To accomplish the second objective, NBS has developed a 3D stylus

instrument [2]. This instrument enables one to obtain quantitative images of

surface topography with a lateral resolution of less than 1 micrometer and

vertical resolutions of less than 1 nm. A research grade stylus transducer is

incorporated into the instrument so the stylus forces are usually 20 mg or less.

This experimental capability has been used to measure the 3D surface

1
microtopography of NTF model components and metal surfaces prepared with the

same processes used to finish model surfaces. While this characterization work

is continuing, some data for model surfaces has been described in earlier work

[ 1 , 2 ].

Based on discussions with NASA personnel concerning the third objective,

the measurement technique developed should: (1) be capable of detecting and

quantifying surface topography variations for surface roughnesses less than

about 0.25 micrometers, (2) be usable during model fabrication on surfaces that

have radii of curvature 2.5 mm or larger, (3) provide characterizations of the

surface topography which are sufficient to give feedback to a fabricator for

optimizing model surfaces, and (4) provide characterizations such that surfaces

produced by different processes can be compared and qualified in a consistent

manner

.

The model surface gauge (MSG) described in this report is a step towards

satisfying the third objective. The recommendations concerning its use that are given in this report address the first three of the criteria for an instrument

to assess the finish of a model surface. In addition, the MSG is easy to use and align and is therefore capable of rapidly sampling the surface roughness in

a number of places on the models. Other technical papers [3~8] describing

experimental and theoretical outputs of this joint NASA/NBS project contain

adequate information for the development of an instrument that could meet the

fourth criterion. Development of a practical shop instrument capable of

discriminating between surfaces produced by different processes was beyond the

scope of this project.

During the course of this project, several research questions have arisen

which are the subject of ongoing work on measurement techniques and their

applicability to aerodynamic surfaces. First, in interpreting and generalizing

the classical work of Nikuradse [9], what properties of the surface topography

influence the air flow pattern across a surface and what are the admissible

values for these as a function of Reynolds number? A closely related issue

concerns the statistical characterization of irregularity heights and

irregularity spacings that are most applicable. Furthermore, the modeling of

the three-dimensional aspects of light scattering from surfaces and its detailed

relationship to the surface topography have only been treated in a preliminary

way within the scope of this project and should be studied in more depth. Early

results on this work were recently reported [8].

2
Section 2 gives a description of the MSG design and its operating

principles. Section 3 describes the experimental tests to relate the optical

roughness values to the standard rms roughness values measured by a stylus

instrument and the tests to determine the conditions for proper operation of the

instrument. Section 4 outlines precautions about using the MSG and about the

data in Section 3, and Section 5 gives some more details about related work

described earlier in this Section.

2. Description and Use of the Model Surface Gauge

The MSG inspects surface roughness by measuring the angular distribution of

light scattered from the surface. It consists of a commercial Rodenstock RM 400

instrument* modified with a special delrin nosepiece. The purpose of the

nosepiece is to allow the gauge to be gently rested on the surface of the model

without damaging it and in such a way that valid readings may be taken of the

angular distribution from the curved surface.

A schematic diagram of the optical system is shown in Fig. 1 [10]. The

source consists of a light emitting diode (LED) that produces radiation at a near infrared wavelength of 800 nm. This radiation passes first through a collimating lens, then through one side of a special measuring lens, that

focuses and redirects the radiation so that it illuminates the surface to be

measured at a slight angle but very close to the optical axis. The radiation

scattered by the surface then passes through the other side of the measuring

lens and is redirected to a linear photodiode array which measures a line sample

of the scattering light beam to obtain an angular distribution of light

intensity.

If the surface is smooth, the pattern of scattered light falling on the

diode array is nearly the same as the circular pattern of the incident beam

leaving the collimating lens. If the surface is rough, the scattered radiation

pattern is broadened. When the pattern of marks (lay) left on the surface by

the finishing process is unidirectional, the scattered radiation pattern is

elongated along the roughness direction. All of the NASA specimens were

* Certain commercial equipment are identified in this report to specify

adequately the experimental procedure. In no case does such identification

imply recommendation or endorsement by the National Bureau of Standards, nor

does it imply that the equipment identified is necessarily the best available

for the purpose.

3
IR LED

Collimating

Lens

Measuring

Lens

Surface

jy— Diode Array

Light Scattering

Pattern

Figure 1 Schematic diagram of the optical system of the MSG (taken from

Reference 10).
finished by unidirectional hand lapping and hence yield elongated scattering

patterns. Figure 1 shows the MSG with the proper rotational alignment for

sensing the unidirectional surface roughness since the long axis of the array is

parallel to the elongated scattering pattern.

Important parameters of the optical system are the angle of incidence of

the light (a), the angular resolution and angular range (3) of the detected

scattering pattern, the illumination spot size y', and the axial distance of the

surface from the measuring lens. The instrument supplied to NASA has an angle

of incidence of about 8.4° [10]. The angular range of the detector is ±15°

about the center. It is determined by the length of the diode array and the

focal length of the measuring lens. The axial position of the surface is not a critical factor because the system has been designed to be insensitive to

misalignment in the axial direction [10]. The tolerance in axial positioning is

±2 mm.The gauge outputs a light scattering parameter called S^ that serves as a measure of surface roughness condition. The unitless parameter is

proportional to the variance of the light scattering distribution about the mean

(M) of the data. Figure 2 shows a typical bell-shaped, light-scattering

distribution as measured by the gauge. The distribution is composed of 20 diode

readings identified as i = 1,2, •••,20 with intensity values I . The mean

value M of the distribution with respect to the center of the array is then

given by

20

M = (1/1 ) l I. • (i - 10.5), (1)

S i-11

where I is the sum of the 20 intensity values of the array and the center of

the 20-diode array is halfway between the tenth and eleventh diodes (i = 10.5).

The light scatter parameter is then given by

2°

S = (k/I ) I I. (i - 10.5 - M) , (2)

S 1-11

where k is a normalizing factor that yields an value of 100 if all of the

intensity values 1^ are equal.

5
Figure 2 Typical light scattering distribution as measured and recorded by the

MSG. The abscissa spans an angle of about ±15°. The total intensity

I and S„ values are also shown as part of the printed record. The

mean value M is not printed, but is displayed on the instrument

controller. The vertical line shown here is the ordinate axis.

6
In general, the value of increases as the roughness of the surface

increases. As shown in our other experimental and theoretical studies, the

shape of the angular distribution is a complex function of roughness

irregularity heights, height distributions, and spacings. All these properties

cannot be boiled down to a single parameter. However, for a given type of

surface, the one parameter may be used to establish relative roughness

heights. Therefore, we use the value as a comparative estimator of the root

mean square roughness R . In addition to S^, the system also outputs the values

of M and I

Two calibration checks should be performed before using the MSG. The first

is a procedure for nulling the dark current of each detector in the array.

Normally this is accomplished by holding a special light absorbing cell over the

nosepiece of the detector head and following the manufacturer's instructions for

the nulling procedure. However, the special nosepiece to be described does not

adapt to the light absorbing cell, and it is sufficient to perform the

manufacturer's nulling procedure in a dark room. Second, a check should be made of the gauge response for a smooth surface.

To accomplish this, a small mirror or smooth glass plate may be held against the

nosepiece. The angular distribution and S„ reading are then recorded and

compared with results from the manufacturer's setup procedure. After this, the

MSG is ready to use. For a flat surface the gauge may be easily aligned to yield an appropriate

S^ reading. This can be shown by referring to Fig. 3 and considering the three

angular misalignment errors that can occur. If the gauge is misaligned by

rotation about the x-axis, (Fig. 3a) the misalignment can be sensed and

corrected by rotating the gauge so that M = 0. If rotation around the y-axis is

the problem, the scattering pattern will move off the axis of the array (Fig.

3b) and will result in a value of total intensity I that is less than the

maximum. Therefore, the gauge orientation around the y-axis can be manually

corrected to yield a maximum value for I. Finally, if the gauge is misoriented

by rotation around the z-axis, the radiation pattern falling on the diode array

will appear to be narrower than it actually is (Fig. 3c). Hence, the gauge can

be properly oriented by looking for a maximum reading as it is rotated about

the z-axis.

The nosepiece has been designed for manual operation on the curved surfaces

of aerodynamic models. A photograph of the nosepiece is shown in Fig. 4, and a

7
a. Pitch:

Peak Moves

t

b. Yaw:

I Decreases

Figure 3 Details concerning the

optical alignment errors

and the resulting changes

in the light scattering

pattern falling on the

diode array: (a) changes

due to rotation of the

surface about the x-axis

(pitch); (b) changes due

to rotation about the yaxis (yaw); (c) changes

due to the rotation about

the z-axis (roll).

8
-igure 4 Photograph of the nosepiece mounted on the sensor head. The

controller panel is shown below.

9
set of machine drawings is given as Appendix A. The nosepiece permits the

operator to hold the gauge against the part so that it is constrained with good

axial alignment and with close rotational alignment about the x and y axes (Fig.

3). The operator then rotates the gauge about the z-axis so that proper

azimuthal orientation is achieved as indicated by the maximum value for S. T . As

shown in Appendix A, the nosepiece contains a precision bearing that allows easy

rotation. When the MSG is used to measure gently curving surfaces such as those

on the top surface of a model airplane wing, the nosepiece contacts the surface

at the three spherical points of support. On the other hand, when the MSG is

used to measure highly curved surfaces near the leading edge of the wing, the

v-groove of the nosepiece contacts the wing.

The recommended procedure for inspecting the roughness at a position on the

model is to rest the nosepiece on the surface, contacting it by means of the

three feet or the v-groove. Then, while holding the nosepiece steady, the gauge

head should be rotated about its axis to produce a maximum S^ reading. This

ensures that the elongated angular distribution from the surface is well aligned

with the diode array. As discussed before, the elongated angular distribution

comes from the unidirectional roughness lay pattern formed by the hand lapping

finishing process along the direction of flow. That means that the MSG can also

be used to determine the lay direction.

As the gauge is rotated, the maximum S reading and the total signal

intensity (I) are then noted. The gauge should then be rotated approximately

180° until a second maximum is found. and its accompanying intensity

value I are again noted. The final reading is the one corresponding to the

larger of the two I values. In accordance with considerations to be described

in Sec. 3, this reading should be less than 50 for an acceptable surface. If

the S^ reading is between 50 and 72, the surface roughness is marginal, and if

the S^ reading is greater than 72, the surface roughness is likely unacceptable

assuming that an acceptable wind tunnel model should have rms roughness less

than 0.20 ym (8 yin).

From our preliminary testing on the prototype instrument, it appears that

valid readings may be taken on nearly all areas of the aerodynamic model wing

except the most highly curved positions on the leading edge. There are two

signal criteria from the gauge that indicate that it is being used on a proper

location. First, the value should give a clear maximum as the gauge is

rotated through the angular position that intercepts the radiation pattern

10
caused by the unidirectional roughness marks. This position is easy to spot by

eye and the adjustment is easy to perform after some experience with the gauge

has been gained. Second, the total signal intensity I should be 50 or greater.

This represents about 5 % of the total intensity measured for a highly reflecting

specular surface. The actual value depends on the LED intensity and the factory

settings for sensitivity and varies from one unit to the next. The second

criterion should ensure that the x and y angular alignment of the gauge with the

surface is good enough so that a significant portion of the optical angular

distribution is falling upon the diode array.

The surface roughness is a critical factor on the leading edges of model

wings due to aerodynamic considerations . However, these areas are also more

difficult to finish as well as to measure because of the high surface curvature.

Therefore, it is important to know how close to the leading edge the gauge may

be used. From our studies to be described in Sec. 3, we have developed the

criterion that the gauge may be used to within about a 60° angle of the leading

edge on both the upper and lower wing surfaces. Figure 5 shows a cross section

of the leading edge. The angular direction normal to this edge is taken to be

equal to 0° and various angular positions with respect to this origin are also

shown. The numerical angular positions are equal to the slope angle of the

surface with respect to its vertical slope angle at the leading edge. Hence the

+80° position is located at the top of the wing's curved surface where the

surface is nearly horizontal and the -80° position is at the bottom.

3. Experimental Tests of the Model Surface Gauge

The MSG was tested on 35 stainless steel surfaces with hand lapped finishes

typical of high performance wind tunnel models. These surfaces included 11 flat

specimens of different stainless steel materials having varying degrees of

finish and 24 positions on a rear wing of a Pathfinder model. Table I describes

the specimens and the wing positions, and Fig. 6 depicts the wing positions.

The positions W-1 , 2, and 3 are gently curving positions on the top surface of

the wing. W-7, 8 and 9 are positions of increasing curvature near the leading

edge. W-4 and 6 represent sets of positions around the leading edge of the wing

at its wide end near the fuselage and at its tip respectively. At each of the

W-4 and 6 locations, nine readings were made at various angles with respect to

the 0° position at the leading edge itself. All of these surfaces were tested
80°

- 80°

Figure 5 Figure showing the angular positions around the leading edge of the

wing.

12
TABLE I Descriptions of the individual flat specimens and the positions on the wing that

were measured for roughness using both a stylus instrument and the optical MSG.

The wing was manufactured from Nitronic 40 stainless steel.

Specimen Nominal Surface Finish Type of

(pm) Stainless Steel

1 Nitronic 40 (N40)

3 0.2 N40

5 0.2 AF-1 410

6 0.4 AF-1410

7 0.2 1 3-8

8 0.4 13-8

10 0.4 347

12 0.2 N40

13 0.4 N40

14 0.1 N40

15 0.2 347

Wing Position Description

1, 2, 3 Topside

4(-80°), 4(-60°), 4(-40°) Around the leading edge of the wide end

4(-20°), 4(0), 4(20°) of the wing.

4(40°), 4(60°), 4(80°)

6(-80°), 6(-60°), 6(-40°) Around the leading edge of the narrow

6(-20°), 6(0), 6(20°) end (outer tip) of the wing.

6(40°), 6(60°), 6(80°)

7 , 8 , 9 Topside, approaching the leading edge.

13
Figure 6 Photograph depicting the various positions on the wing (W-1 to W-9)

that were measured. There was no W~5 position.

14
optically for S

N

with the MSG and mechanically for rms roughness with a stylus

instrument

The stylus instrument is a Talysurf 6 model that contains an LVDT (linear

variable differential transformer) transducer that gives a direct readout of the

surface height under the stylus probe. As the stylus traverses the surface, its

vertical motion is converted into a time varying electrical signal that

accurately represents the surface peaks and valleys within the range and

resolution limits of the instrument. The horizontal resolution is limited by

the stylus tip width which was measured to be -5 pm. The long wavelength

sensitivity is determined in a standard way by the high pass electrical

filtering of the instrument [11] and specified in terms of a long wavelength

cutoff. The cutoff for our measurements was 0.25 mm and the total evaluation

length was 1.25 mm or a distance of five cutoff lengths. The vertical

resolution was limited by the rms vertical noise of the instrument, and this was measured to be 0.01 pm by traversing an extremely smooth glass surface whose

actual roughness was smaller than the instrumental noise. The vertical range

was about 600 pm.

For the flat specimens and the flatter positions on the wing, stylus traces

were taken perpendicular to the lay of machining marks. However, for the more

curved positions on the wing, particularly including positions 4, 6, and 9,

traces were taken parallel to the leading edge to avoid introducing surface

curvature effects into the roughness measurements.

Each location was measured for roughness average and rms roughness R , two quantities defined in many of the national and international standards [11].

As shown in Fig. 7, R is the average deviation of the roughness profile from

a the mean line and R is the root mean square deviation. Table II shows the

q

results for these parameters. Each R^ and R^ value given there is an average

derived from profiles measured at either 5 or 9 positions, as shown in column 2.

Two sets of values are shown in Table III, representing values measured

for two different MSG heads. One head, described before, produced a 1 .8 mm illumination spot size and an angular detection range of ±15° about the central

angle. The other had a 0.3 mm illumination spot size and an angular range of

approximately ±12°. The second gauge head was tested for comparison purposes

because it was reckoned that the smaller spot size would render this gauge less

sensitive to surface curvature. However, results taken with the 0.3 mm head are

also expected to be more variable than that of the 1 .8 mm head because the

15
Average Deviation of Profile

y(x) from the mean Line

Total Shaded Area /

L

JL f

L |y(x)|dx = JL E

L I o N

• Rq = rms Deviation . . . =V ± E y, 2

N

Figure 7 Schematic diagram showing the definitions of R and R as obtained

from surface profiles. ^

16
TABLE II

Results for roughness average Ra and rms roughness R measured with a stylus

instrument with 0.25 mm cutoff.

3

Column 2 shows the dumber of different

positions (5 or 9) used for the stylus measurements. The uncertainties

represent statistical uncertainties of 1 standard deviation over the 5 or 9

positions

Specimen or Number of

R ( urn

)

R ( urn

)

Wing Position Stylus Positions a q

Specimen1 9 0.221 _+ 0.01 6 0.284 ± 0.020

3 9 0.121 ± 0.006 0.156 ± 0.008

5 9 0.083 ± 0.006 0.112 + 0.012

6 9 0.29 ± 0.03 0.38 ± 0.04

7 9 0.106 ± 0.005 0.138 + 0.008

8 9 0.21 4 ± 0.011 0.280 + 0.016

10 9 0.27 3 ± 0.019 0.355 ± 0.025

12 9 0.172 + 0.009 0.220 ± 0.013

13 9 0.188 + 0.014 0.244 ± 0.019

14 9 0.044 ± 0.002 0.055 + 0.003

15 9 0.130 + 0.009 0.166 + 0.012

Wing: 1 9 0.055 ± 0.005 0.071 + 0.010

2 9 0.057 + 0.006 0.077 + 0.019

3 9 0.087 ± 0.006 0.111 + 0.010

7 9 0.055 + 0.005 0.073 4- 0.012

8 9 0.063 + 0.005 0.081 ± 0.008

9 9 0.069 ± 0.012 0.095 + 0.028

4 (80°) 5 0.056 + 0.002 0.072 + 0.003

4 (60°) 5 0.102 ± 0.023 0.15 ± 0.06

4 (40°) 5 0.167 + 0.017 0.223 ± 0.024

4 (20°) 5 0.64 ± 0.20 0.86 ± 0.22

4 (0°) 5 0.47 ± 0.09 0.65 ± 0.10

4 (-20°) 5 0.36 ± 0.04 0.49 ± 0.08

4 (-40°) 5 0.21 + 0.03 0.26 ± 0.04

4 (-60°) 5 0.109 ± 0.014 0.141 + 0.021

4 (-80°) 5 0.071 + 0.007 0.091 ±_ 0.010

6 (80°) 5 0.127 ± 0.014 0.165 + 0.017

6 (60°) 5 0.224 + 0.021 0.290 + 0.027

6 (40°) 5 0.31 ± 0.05 0.40 + 0.07

6 (20°) 5 0.37 ± 0.04 0.47 + 0.07

6 (0°) 5 0.51 ± 0.21 0.66 + 0.26

6 (-20°) 5 0.46 + 0.10 0.59 ± 0.14

6 (-40°) 5 0.30 ± 0.1 1 0.38 ± 0.14

6 (-60°) 5 0.156 + 0.01 4 0.198 ± 0.020

6 (-80°) 5 0.13 + 0.03 0.17 + 0.05

17
TABLE III

S values taken with two different probes having spot sizes of - 1.8 and ~0.3 mm. The uncertainties represent statistical uncertainties of one standard deviation.

In some cases, no uncertainty is given, either because only one reading was taken or because two readings were taken and they were identical. The total

number of observations and the number of different observers for each reading

are also shown. Several of the readings were questionable (?) due to their

proximity to the leading edge.

Specimen 1.8 mm Probe 0.3 mm Probe

or Wing Position S

N #Readings

,

//Observers

S

N //Readings

,

//Observers

Specimen: 1 86.0 ± 2.2 4, 4 90.1 ± 2.7 2 , 2

3 77.9 + 1 .5 4, 4 83.4 ± 0.9 • 2 , 2

5 45.3 ± 1 .0 4, 4 47.7 ± 0.1 2 , 2

6 88.5 + 2.2 4, 4 92.4 + 0.1 2 , 2

7 73.0 ± 1 . 4 4, 4 75.4 ± 4.1 2 , 2

8 84.6 ± 2.0 4, 4 89.4 ± 5.7 2 , 2

10 87.8 + 1.3 4, 4 91 .8 + 0.8 2 , 2

12 83.5 + 3.0 3, 2 87.8 ± 4.5 3, 1 13 87.0 ± 1 .7 4, 4 89.5 + 3.7 2 , 2

1 4 39.3 ± 2.0 4, 4 41 .7 + 0 . 6 2 , 2

15 72.1 + 1.4 4, 4 74.0 + 0.4 2 , 2

Wing: 1 25.9 ± 1 .7 4, 4 27.3 2 , 2

2 20.7 ± 1 .0 4, 4 25.2 + 2.4 2 , 2

3 34.1 ± 2.1 4, 4 33.5 ± 2.3 2 , 2

7 23.4 ± 0 .

6

4, 2 26.2 ± 0.5 3, 1 8 22.7 ± 0.8 4, 2 23.0 + 0.9 3, 1 9 21 .8 ± 1 .7 3, 1 23.

1

+ 0.6 3, 1

4(80°

)

27.0 ± 0.8 3, 2 27.1 ± 1.6 2 , 1 4(60°

)

42.7 ± 3.2 3, 2 37.8 + 3.3 4, 2

4(40°) 7 85.2 1 , 1 64.4 1 , 1 4(20°) 7 89.8 1

, 1 7 62.2 + 0.9 2 , 2

4(0°) 7 85.7 1

, 1 7 71 .0 + 4.5 2 , 2

4

(

20 ° ) 7 89.3 1 , 1 7 82.6 + 6.0 3, 1 4

( -40°

)

7 91 .0 1

, 1 72.7 ± 1 .5 3, 2

4

(

60 °

)

48.2 ± 1 .7 3, 2 52.4 1 , 1 4(-80°

)

29.1 + 0.7 3, 1 33.2 ± 1 .9 2 , 1 6 ( 80 °

)

56.3 ± 0.4 2 , 2 56 . 6 + 2.6 2 , 1 6(60°

)

80.9 ± 2.1 2 , 2 7 86.8 1 , 1 6(40°

)

— -- 82.3 ± 1 .5 2 , 1 6 ( 20 °) -- — 7 75.6 ± 6.9 2 , 1 6 ( 0 °

)

-- -- 7 78.2 1 , 1 6 (

20 °

)

-- — 7 79.0 1 , 1 6

( -40°

)

— -- 7 77.5 + 4.0 2, 1 6 (- 60 °

)

73.4 ± 4.4 2, 2 7 83.5 1 , 1 6 (

80 °

)

51 .3 + 6.4 2, 2 53.8 + 1 .2 2, 1 Reference Mirror 5.1 + C . 1 2, 2 5.8 ± C . 1 2, 2

18
smaller spot is probing a smaller statistical sample of the surface peaks and

valleys. The total number of readings that went into each of the values and the

number of different observers are also shown in adjacent columns to the values

themselves

A principal objective for testing the MSG was to show the correlation

between the S. T results and the R results. Accordingly, the R values have been

N q q

plotted versus the values taken with the 1.8 mm head (termed S^O.8)) in Fig.

8, and a functional correlation has been developed between them.

Two observations constrained the form of the function that we fitted for R

q vs S . First, the curve has an asymptote at = 100. An value of 100

corresponds to a flat angular distribution having uniform scattering intensity

at all angles. For a random surface finish, the angular distribution is a bell

shaped curve having its maximum in the specular direction. The distribution

generally becomes broader as the roughness increases, but it should approach a flat distribution only as the value of R^ becomes very large. Hence, the

asymptote at S = 100.

rJ Second, the spreading of the optical beam in the gauge is such that the

value of equals 5 when the rms roughness R^ is essentially equal to zero.

This is the situation that occurs when the MSG is tested with smooth optical

surfaces. Hence, the function R (S^) should pass through the point (5,0).

In view of these constraints, the following formula for R was chosen:

Q

R

q

(um)

b( V5)

a(S

N"

5) + 95 ( 1 00-S ) N

( 3 )

having the parameters a and b. These were fitted to the data by a linear least

squares method. The resulting best fit values for a and b, rounded to three

significant figures, were

a = 0.00248 ± 0.00063 um , (4)

b = 1.43 ± 1 .03 um

where the uncertainties in the fitted parameters represent estimates of one

standard deviation for each parameter. The fitted curve is the lower one in

Fig. 8.

19
Rq

(

um

)

Rq vs. SN C 1 . 8 ) - NflSR Surfaces

SN (1.8)

Figure 8 R values as measured with a stylus instrument vs. the S„ values

obtained from the MSG with 1.8 mm spot size. The lower curve is the

best fit to the data points represented by Eqs. 3 and 4. The upper

curve is the 95 percent upper confidence limit.

20
For the results in Fig. 8, we calculated a coefficient of determination r [12,13]. This statistic is similar to the correlation coefficient and is a standard approach for expressing how well the variation in the R^ data is

accounted for by the fitted curve. For the nonlinear model of Eq. (3), the

2

formula for r is given by

2 r

R . R . qi qi

(5)

where R . is the set of 25 R values, R is the mean of these data and R . is

qi q q qi

2

the set of R^ values predicted by the fitted curve. The calculated value for r was 0.81 representing a fairly good correlation between the vs. R data and

the fitted curve, considering that the data include points taken on four

different materials and with widely differing surface curvatures.

This empirical model of Eqs. 3 and 4 can be rewritten by combining terms to

yield the following, more conventional form:

R (mm) = -0.0275 + 0.00248SrT + 1 . 43/( 1 00-Sj , (6)

q N N

which represents the same function as Eqs. 3 and 4. We particularly note that

the three constants are not independent. The leading constant is related to the

other two by the constraint that R =0 when S. T = 5.

q N

The adequacy of this model was further evaluated by comparing it with one having three arbitrary constants where the aforementioned constraint is relaxed.

That is, where

!

R - a' + b'S + c ' / ( 1 00-S ) . (7)

C4 INI JM

Once again, a linear least squares technique was used to find the best values of

a’, b’ and c

? yielding a result

R

q

= 0.0346 + 5.52 x lo"

4 S

N

+ 2.92/ ( 1 00-S

N

) . (8)

We then tested the significance of adding the third parameter to the model by

calculating the F-statistic [14], a method for comparing the two models (3),

21
(4), and (8). First, we calculated the sum of the squares of the deviations

between the data points and the fitted curve for both mathematical models, and

these quantities were divided by the number of degrees of freedom for each.

Then the ratio (F) between these quantities was calculated.

F =

25

22 l (R .-R

i = 1 Q 1 <3 l2

25 : : 23 l (R .-R

>1 qi qi3

1 . 41 , (9)

where R^^ is the set of R values predicted by the two parameter model;

^ is

the set of R^ values predicted by the three parameter model, and 22 and 23 are

the number of degrees of freedom for each model. The above value of 1.41 falls

well within the ninety percent confidence limits of 0.49 and 2.04 for the

F-statistic obtained from a modified version of the OMNITAB statistical software

package [15]. This result implies that the simpler two parameter model is

statistically reasonable and that there is little significance to adding the

third parameter.

As a result of the foregoing analysis, we conclude that the data from

the MSG together with the reworked two parameter model given by Eq. 6 are

appropriate for estimating the rms roughness of hand lapped stainless steel

surfaces. We now discuss the criteria that should correspond to the surface

roughness acceptability criterion that R^ be less than 0.2 ym (8 yin). Given a particular measurement of at some position, how confident can we be that the

R value there is less than 0.2 ym?

Q

To provide an answer to this question, we require not only the best

estimate of R as a function of S M obtained with Eq. 6, but also the uncertainty

q N

estimate, ±AR^. This quantity varies slightly over the range of the data but is

approximately ±0.075 ym and represents a 90$ confidence interval. For an S. T value of 50.4, the expected value for R^ is 0.126 urn from Eq. (6), the estimated

AR is 0.074 ym, and the 90$ confidence range is from 0.052 ym to 0.200 ym.

Since we would expect 5$ of the R values to fall below this range and 5$ above,

that implies that for a measured value of 50.4, the corresponding value of R^

would be expected to be smaller than 0.200 ym 95$ of the time. Hence, the

criterion of 50 for an acceptable surface discussed in Sec. 2. The criterion of

72 for a marginal surface is the value of S^ that corresponds to a best estimate

22
for R of 0.20 pm obtained from Eq. 6. Figure 8 shows the two curves from which

the criteria were calculated.

The above arguments are derived from statistical considerations only and do

not take into account potential systematic errors that might be caused by (1)

systematic variations in the stylus measurements of roughness themselves, (2) a breakdown of the chosen model for certain types of surfaces, or (3) invalid

readings. These eventualities could cause errors that add to the estimated

confidence intervals. Indeed, these eventualities could affect not only the

correlation between stylus measurements and the MSG results but also the

correlation between roughness measurements taken with different stylus

instruments. For example, roughness values measured by a direct profiling

instrument, such as ours, could differ from those measured with shop-type

instruments, and these differences could vary depending on the surface

curvature, the levelling conditions, and the instrument cutoff. However, the

above potential sources of error are not expected to be problematical for our experiments or for subsequent use. We discuss these three sources individually.

Systematic errors in the roughness measurements could be caused first by

error in the calibration of the vertical scale of the instrument. This

possibility was investigated by measuring sinusoidal roughness standards with

well known R values of 0.3, 1.0 and 3*0 pm. The errors between the measured

d. and accepted R values for these standards were 2.1$, 0.9$ and 0.5$,

cL respectively. Therefore, this source of error is not expected to be

significant

A more important source of variation is the arbitrariness of measurement

conditions for stylus instruments. Roughness is not an intrinsic property of a surface, and the results of measurements of rms roughness depend on the

conditions under which the measurements were taken, the most important of these

being the stylus width that usually limits the high frequency, short wavelength

response of the instrument and the electronic cut off that limits the long

wavelength response. Furthermore, measurements of rms roughness are much more

sensitive to the long wavelength cut off than the short wavelength limit,

because in general longer wavelengths have larger amplitudes [16].

In our measurements we used a stylus with a tip width of ~5 ym. Therefore

the horizontal resolution of the measurements was approximately 5 ym. The long

wavelength cutoff for our measurements was 0.25 mm, a value listed among the set

of preferred values in the ANSI/ASME Standard B46. 1-1985 [11] but shorter than

23
the most commonly used, standard value of 0.8 mm. The shorter cutoff was chosen

for two reasons. First, surface curvature is a significant factor in some of

the positions on the wing that we measured. The surface curvature, when

superimposed on the profile of the roughness structure to be measured, can significantly increase the measured values of rms roughness. Therefore, a cutoff value of 0.25 mm masks the curvature effects and emphasizes the finer

roughness structures better than one of 0.8 mm. Second, although the upper

wavelength limit on the MSG changes with roughness height and is difficult to

characterize, it tends to be quite short. That is, the optical gauge is

sensitive to surface roughness wavelengths on the order of 100 pm or less rather

than those near 1 mm. Therefore, the 0.25 mm cutoff of the stylus instrument is

better matched to the spatial bandwidth of the MSG than the more standard 0.8 mm cutoff.

An example of the variability of roughness measurements with experimental

conditions is shown in Fig. 9, where the results as measured by two

procedures are compared. Along the vertical axis are plotted the R results of

measurements on nine NASA specimens using a Talystep instrument with a 0.1 ym

stylus width, a 2 mm trace length, and an electrical signal that did not undergo

high pass filtering. The bandwidth of measured wavelengths extends to

approximately the 2 mm trace length, and this value might be taken as roughly

the effective cutoff length of the profiles. Along the horizontal axis are plotted the R results for the same surfaces using the Talysurf 6 instrument

with the 5 ym stylus tip, 1.25 mm trace, and 0.25 ym cutoff. The results taken

with the longer cutoff are about 20$ larger than those taken with the shorter

cutoff, but the correlation between the two sets of data is very high. The

coefficient of determination for a straight line fit through the data of Fig. 9

is 0.996.

We would prefer to correlate the optical data with roughness parameters

that are closely linked to the functional characteristic of aerodynamic drag,

but, as discussed in the introduction, much work remains to be done before

proper roughness characterizations for aerodynamic drag will be known. Instead,

we estimated a maximum specification for rms roughness of 0.2 ym for models in

the NTF under extreme flow conditions [3] based on the concept of the admissible

roughness for an aerodynamically smooth surface [9, 17] and on assumptions about

the relationship between admissible roughness and rms [ 3 ]. Likewise, our selection of a 0.25 mm electrical cutoff for use in roughness measurements

24
.5

Figure 9 R values as measured with a Talystep plotted vs R values as measured with a Talysurf 6.

25
results from an estimation of the appropriate upper limit of the width of the

roughness features found on these surfaces. Figure 9 implies that a scaling

factor will result if the SM values are compared with R values measured with a

N q

cutoff different from 0.25 mm.

In summary then, we have surmised that a roughness spatial bandwidth

ranging from 5 um to about 250 pm is useful for determining aerodynamic drag

effects on hand lapped stainless steel surfaces, and we have correlated the

response of the MSG with the rms roughness measured over that bandwidth. The

estimation of a maximum admissible rms roughness of 0.2 pm when measured with a 250 pm cutoff depends on a number of assumptions and should be verified by

experiment in wind tunnels under extreme flow conditions.

The second potential source of systematic error is a breakdown of the model

represented by Eq. 3. We have tried to minimize this by including in the study

only similar stainless steel surfaces finished by hand lapping. The comparator

approach should be valid when a small class of specimens with similar surface

topographies is the subject for correlation between two measurement techniques.

Other classes of specimens would produce quite different responses in the MSG

even though such specimens had similar R *s to the ones studied here.

Finally, invalid readings can result if the MSG is not properly aligned

on the surface or if the surface curvature is high. Misalignment causes the

scattering pattern to miss the diode array as shown in Fig. 3, resulting in a low total intensity value I and perhaps an unstable value of S^ . Surface

curvature along the same direction as the long axis of the diode array leads to

an increase in the apparent value of S^ over that which would be measured on a flat surface of equal roughness. Both problems may be avoided by staying away

from the asymmetric, highly curved sections near the leading edges of the wing.

Unfortunately, the leading edges are the critical places, where roughness can most affect drag, and hence where roughness measurement is important.

We have made empirical studies concerning the question of how close to the

leading edge valid readings may be taken. We did this by taking polar maps

of at several positions very close to the leading edge of the wing. As shown

in Fig. 10, the MSG was held vertically in its stand and set down upon the wing

so that the V-groove of the nosepiece cradled the curved surface. The wing

itself was mounted in a gimbel so that it could be rotated about its leading

edge. That way the angle 9 of the gauge with respect to the leading edge could

be varied and measured. Then Sxr and I were measured as a function of the

26
Figure 10 Schematic diagram showing alignment of the MSG for a reading at an angle 0 of about 60° topside near the leading edge of the wing.

27
azimuthal angle <J>. Altogether vs <J> was measured in areas 4 and 6 (see Fig.

6) at nine angular positions each at the leading edge: with the wing held

vertically (0 = 0°), at four positions on the top side (0 = 20°, 40°, 60° and

80°), and at four positions on the bottom (0 = -20°, -40°, -60° and 80°). The

+80° and -80° positions were located near the top and bottom of the wing,

respectively (see Fig. 5). The 0.3 mm probe was initially used for these

measurements because its small spot was thought to be preferable to the other.

Subsequent measurement near the leading edge showed the 1 .8 mm probe to give

more stable readings, so polar maps were then gathered with it.

The map for the 60° location in the W-4 area around the front edge of the

wing is shown in Fig. 11. Its shape may be explained by referring to Fig. 12a,

a schematic picture of the topside near the front edge of the wing itself. The

direction of the lapping marks that constitute the roughness pattern of the

surface and the direction of the highest curvature are shown along with the

approximate position of the measured area at an angle of 60° topside. The

scattering pattern from this part of the surface is shown schematically in the

center of Fig. 12b. It is broadened from top to bottom by geometrical

scattering from the curve of the surface and in the NE-SW direction by

diffraction from the surface roughness. By contrast, the left hand pattern of

Fig. 12b schematically shows the scattering pattern if the surface has

unidirectional roughness but no curvature, and the right hand side of Fig. 12b

shows the pattern for surface curvature with no roughness. These infrared

patterns have been inferred from observations of visible patterns obtained by

scattering a He-Ne laser beam from the surface. The orientation of the diode

array in the detector for an optimum roughness reading is depicted as well in

Fig. 12b. This orientation has the diode array aligned parallel to the

scattering pattern. It can be seen that the length of the pattern, and hence

the reading, at this orientation is only slightly increased by the surface

curvature, since the direction of maximum curvature and the direction of maximum

roughness are approximately 34° apart.

Figure 11 shows the polar map produced when the gauge is rotated. The

direction of optimum alignment is indicated by the arrow L in Fig. 11 and the

corresponding orientation of the diode array in Fig. 12b. Since the geometry is

fairly symmetric, the polar map has maxima in the -40° and +150° directions

clearly indicating the lay of the surface. The total intensity (I) is likewise

28
Sn

-40

270°

.3 Figure

3

Diagram of SM

vs. the azimuthal angle 4> measured in area M at an angle 8 of 60° topside with respect to the leading edge. The 1.8 mm

probe was used. Vector L shows the direction of the lapping marks.

Vector V shows the direction of the leading edge.

29
Diode

Array

No

Roughness

Figure 12 (a) Schematic diagram of the leading edge of a model wing showing

the direction of the lapping marks and the direction of highest

curvature around the location of a measured area.

(b) Heuristic diagram of the optical scattering pattern overlaying

the diode array detector rotated for a maximum S reading such

as the one at <j> = 150° in Fig. 11. The two satellite patterns

correspond to cases involving no curvature or no roughness.

30
fairly strong in the two optimum directions indicating good translational

alignment of the pattern on the diode array.

When the illuminated area gets too close to the leading edge, the surface

curvature becomes so large that the symmetry of the vs. <p curve about the

roughness direction is lost and the intensity decreases because of misalignment.

Valid readings of the scattering pattern are no longer possible. Figure 13

shows the pattern taken on the bottom of the wing in area 4 at an angle of

20° from the leading edge. The maximum value of in the polar curve occurs

along the direction of maximum curvature instead of the apparent roughness

direction. In addition, total intensity at all angles is decreased

significantly from that of the 60° topside position. From these and other data, we have established the criterion that the roughness direction must clearly be

identifiable from the reading and that the total intensity (I) must be larger

than 50. With these criteria, we were able to take valid data to within an angle of 60° of the leading edge with the 1.8 mm probe.

In addition to the foregoing studies concerning the accuracy of the gauge,

we also performed roughness studies of the wing itself. On Fig. 14 are plotted

the values of R , measured with the Talysurf 6 stylus instrument, as a function

of position on the wing. Positions 1-3 and 7~9 were taken on the top surface of

the wing whereas positions -80° to +80° were taken around the leading edge at

areas 4 and 6. It is clear from these measurements that the roughness degrades

rapidly as one approaches the leading edge. This phenomenon is understandable

in view of the fact that the model plane is finished by hand lapping. The

gently curved top and bottom surfaces of the wing are easier to work by hand

than the highly curved leading edge and hence have evidently received a more

complete finishing process. Therefore for both areas 4 and 6, the roughness

within about 60° of the leading edge is unacceptable because R^ is greater than

0.2 ym.

This trend for the value to increase around the edge is duplicated by

the data of Fig. 15. Once again the values increase rapidly as the

leading edge is approached. The points from area 4 labeled with "?" were of

uncertain validity in view of the criteria previously discussed. The missing

points from area 6, were either highly questionable or unmeasurable, taken, as they were, around the leading edge at the narrow end of the wing. Nevertheless,

the optical data of Fig. 15 reveal the same trend in roughness near the leading

edge as the stylus data of Fig. 14.

31
20° From Leading Edge

1.8mm Probe

Figure 13 Polar graph of S

N

vs. <j> at a position of 20° underside from the

leading edge, too close for a valid reading. The 1.8 mm probe was used. The maximum value now occurs when the diode array is

aligned to detect the scattering pattern broadened by the edge

curvature

.

32
Rq(pm)

Figure 14

NASA Wing, RMS Roughness Measurements

R measurements vs. position on the wing. The positions are shown in

Frgs. 5 and 6.

33
Position

Figure 15 S„ obtained with the 1.8 mm probe vs. position on the wing. The

values shown with question marks have uncertain validity due to

proximity to the leading edge. Some values around area 6 were not

measured at all due to misalignment difficulties near the leading

edge.

34
The optical data for the two probe sizes are compared in Fig. 16. The

probe with the 0.3 mm spot size has an advantage and a disadvantage with respect

to the 1.8 mm probe. On the one hand, the probe with the smaller spot size

should be less susceptible to having geometrical scattering from the curved

surface affect the roughness scattering results. On the other hand, the smaller

illumination spot averages over a smaller number of surface peaks and valleys.

So the readings from the 0.3 mm probe should have more variability than those

from the 1.8 mm probe. The 0.3 mm probe also seemed to suffer larger

fluctuations in intensity near the leading edge of the wing, and we therefore

reckoned it to be more susceptible than the 1 .8 mm probe to misalignment of the

surface around the y-direction (Fig. 3) due to the asymmetric curvature of the

wing airfoil shape.

The correlation between the two set of readings is excellent for those

samples and those positions where both readings are expected to be valid, based

on the signal intensity and directionality criteria discussed earlier. This

is shown clearly in Fig. 16. The coefficient of determination for these data

with respect to a best fit straight line is 0.995. The points shown as question

marks are those taken where either or both of the probe readings are of

questionable validity according to the intensity and directionality criteria.

Although, the 0.3 mm probe seemed to be susceptible to misalignment it appears

that the 0.3 mm probe was able to take valid readings to within 40° of the

leading edge in wing area 4 according to the intensity and directionality

criterion (see Table III).

Figure 17 shows what happens when the SM readings taken with the 0.3 mm

probe are plotted versus the readings. The correlation between and R^ is

similar to that of Fig. 8 except for the circled points. These were taken only

40° from the leading edge of the wing, and it appears that the readings for

these are biased lower than they should, given the R^ values. The source of

this difficulty is not yet apparent. Our preliminary estimation is that the

0.3 mm probe is more sensitive to misalignment than the 1 .8 mm probe and because

of this, the probe does not accurately sample the angular distribution for

points too close to the leading edges where the surface curvature is changing

rapidly and where some misalignment around the y-axis of Fig. 3 is no doubt

occurring.

35
90

80

70

60

SN (0.3)

50

40

30

20

10

NASA Hand Lapped Specimens

F Flat Specimens

• TopofWing

E Near Leading Edge

? At Leading Edge

S Smooth Specimen s

f

F fF

? F / ?

/

/

/

F /

V

/

:/

F/

/

E/

E /

F/

/

• vE

/

e 4

/

/

/

/

/

/

10 20 30 40 50 60

SN (1.8)

70 80 90

Figure 16 (0.3) vs. S (1.8) for the flat specimens (F) and at various

positions on the wing (coded). Point S was measured for the smooth

reference specimen supplied by the manufacturer. The question marks

are points of uncertain validity near the leading edge. The dashed

line has a 45° slope and passes through the origin and is shown for

reference.

36
Rq

(

um

)

Rq VS. SNC0.3) - NRSR Surfaces

Figure 17 measurements vs. obtained with the 0.3 mm probe.
4. Limitations of the Present Instrument

The present instrument is useful as a working prototype to be tested for

inspecting the roughness of wind tunnel model surfaces. Several features should

be added to turn it into a useful, ergonomic instrument for the model shop.

To make the device more convenient to handle, two modifications should be

made. First, the nosepiece should be fitted with some sort of handle so that it

can be held solidly on the surface while the probe is rotated to find the

optimum readings. Second, the control buttons should be located on the probe

itself rather than the controller or should be implemented with foot switches.

That way, an operator would not have to remove his or her hand from the probe to

record a roughness reading. With the present system, the optimum alignment can

be lost when the operator’s hand moves to take a recording.

The present device is being used as a comparator for roughness. That is,

estimations of the rms roughness R^ are being made based on the high correlation

between R readings measured by stylus and readings measured by the gauge.

It would be preferable to derive rms values directly from the optical

measurements and with a suitable theory, without resorting to the comparator

approach that relies on previous measurements of similar surfaces to provide a calibration. To perform such a task, a proper theory to describe the light

scattering needs to be developed along with an appropriate mathematical

inversion technique to back out the rms roughness from the optical scattering

angular distribution. The light scattering theory and the inversion technique

would be installed as software on a laboratory computer to control the MSG. In

its present state of development, the MSG is controllable by a computer through

an RS-232 interface, and we have installed such a system on the inspection

station of the Automated Manufacturing Research Facility (AMRF) at NBS [18]. We

have also shown that the optical angular scattering pattern may be described

fairly accurately if the topography of the surface is known from profiling

measurements [4]. What is now needed is the appropriate inversion procedure to

extract the rms roughness from the optical scattering pattern itself.

Another limitation is the difficulty of taking valid S^ readings within 60°

of the leading edge of the wing because of the high curvature in those

locations. It should be possible to make measurements right at the leading edge

itself (9 = 0°), because that is a position of symmetry and the hand lapping

marks should be parallel to the surface curvature there. Consequently, the

broadening of the scattering pattern due to roughness effects should be

38
unaffected by the curvature. This is not the case in practice. Inspection of

the leading edge shows that the directionality of the lapping marks varies

considerably due to the workmanship of the finishing process. In some places

the lapping marks are perpendicular to the leading edge. In others the marks

are slanted with respect to the edge but parallel to the lapping marks on the

top of the wing indicating a simple continuation of those marks by the

machinist. In those places, it is not possible to take valid readings since

the curvature effects in the scattering cannot be separated from the roughness

effects. In still others, the marks at the leading edge are continuations of

the lapping marks on the bottom of the wing.

We, therefore, propose a refinement to the hand finishing process. If the

machinist can make sure that the hand lapping strokes at the leading edge are

perpendicular to the edge rather than simple continuations of the strokes on the

top or bottom of the wings, the extra care might enable valid optical roughness

measurements to be made with the MSG at the leading edge itself and might also

lead to a better finished leading edge with improved aerodynamic properties.

!

5. Related Work

We have performed a number of other activities under contract with the NASA

Langley Research Center. These have been thoroughly documented in previous

publications [1-8], but a brief summary of the optical scattering work is given

here as well.

We constructed a research instrument [1 ,5] that measures the light

scattering distribut ions from rough surfaces. Named DALLAS, detector array for

. laser light angular scattering, it has the capabilities for varying the angle of

incidence of laser light on the specimen and for collecting nearly the entire

I

hemisphere of scattered radiation. We have used this instrument to characterize

the light scattered from the surfaces of NASA hand lapped, stainless steel

specimens and to test theories of optical scattering from rough surfaces.

Our initial experiments involved the measurement of the same surfaces with

both the stylus technique and the DALLAS instrument. The key question in this

work was whether or not the optical theory was capable of generating a quantitatively accurate description of the angular distribution of scattered

light using knowledge of the surface topography obtained from surface profiles.

The surface profiles were measured with the stylus technique, then digitized,

and stored on a computer disk. A straightforward, but appropriate scattering

L

39
theory, using a phase integral approach, was applied to the profile data to

yield a theoretical angular scattering distribution that could be compared to

the one measured by DALLAS [5]. The technique was first applied to a set of

ground specimens. The surface profiling data were taken at a lateral resolution

of about 1 .5 pm and the agreement between the theoretical and experimental

angular distribut ions was moderately good [5]. Subsequently, we have measured

nine hand lapped NASA specimens and improved the lateral resolution of the

surface profile. The agreement between theory and experiment is quite good. A

complete article based on this research will be published subsequently, but one

typical result is shown in Fig. 18. Our preliminary estimation is that the

small degree of disagreement between theory and data is due to lateral ' resolution limits of the surface profiles, but we require more analysis to

confirm this.

From this work we can say that if one knows the surface topography,

represented by the surface profiles, one can quantitatively describe the optical

angular scattering distribution for moderately rough surfaces of the types

studied with R^'s up to about 0.3 pm. This is a strong indication that the

optical phase screen theory that we used is valid in the range of roughnesses

exemplified by the NASA specimens.

The next step is to invert the scattering data to obtain accurate values of

geometrical surface parameters such as the roughness height or average roughness

spacing. The first experiments along these lines were performed for a set of

six sinusoidal surfaces with differing amplitudes and spatial wavelengths [7,8],

The experimental scattering distributions consisting of sharply peaked,

diffraction patterns, obtained with DALLAS operating in a special high

resolution mode, were compared with theoretical calculations that relied on two

variable parameters, the amplitude of the surface sine wave (which could be

directly related to its R value) and the wavelength D. The values of the

a. parameters that yielded the best fits between the data and the theory are shown

in the right hand columns of Table IV. The agreement between these and the

parameters measured by stylus shown in the middle columns is excellent. The

parenthesis around the 800 pm value indicates that this surface was a special

case. The diffraction peaks in the angular distribution were so closely spaced

that they could not be individually resolved by the detector. This produced an ambiguity and a tradeoff between the best adjusted values of amplitude and

wavelength. However, when a wavelength value of 800 pm was assumed in the

40
INTENSITY

• • NRSR S.S. Spec. #3; Incidence Rng 1 e=-54Data measured with DRLLHS Theoretical Rngular Distrbtion,

DEGREES

Figure 18 Angular scattering distribution obtained from flat NASA specimen #3

using the DALLAS system. The angle of incidence was -54°. Also

shown is the theoretical distribution generated from topographic data

measured by a stylus instrument.

Ml
TABLE IV

Comparison of stylus and optical measurements of sinusoidal roughness

parameters. Uncertainties in the stylus results represent estimates of both

random and systematic errors. Uncertainties in the optical results represent

estimates of random errors only. For the R = 1pm, D = 800pm, surface the value

of D = 800pm was assumed and the corresponding best value of R was calculated.

Si

Nominal

Surface

((R ,D) (pm)

)

a

Parameters Measured

by Stylus

Parameters Deduced from

Optical Technique

R (pm) D (pm) R (pm) D (pm)

Brass (1 , 40) 1 .02 + 0.02 40.1 + 0.4 1 .016 + 0.002 39.89 ± 0.03

Brass (1 , 100) 1 .02 ± 0.02 100.2 + 0.4 1 .006 ± 0.003 99.6 ± 0.2

Brass (1 , 800) 1 .01 ± 0.02 800 + 1 1 1 .003 + 0.014 (800)

Nickel (1 , 100) 1 .03 + 0.02 100.2 ± 0.4 1 .01 1 + 0.002 100.2 ± 0.3

Nickel (0.3, 100) 0.31 ± 0.02 100.2 + 0.4 0.313 ± 0.004 100.8 ± 0.7

Nickel (3, 100) 2.98 + 0.04 100.1 + 0.4 2.99 ± 0.05 99.3 *• 1 .3

42
fitting calculation, the best value of R was in very good agreement with the

3. results from stylus data.

The close agreement between the optically derived parameters and the

stylus results depended on two factors: the validity of the optical scattering

theory and the validity of the sinusoidal model of the surface profiles.

The next step in our research will be to develop a suitable statistical

model that incorporates appropriate roughness parameters for random surface

profiles typical of the NASA hand lapped specimens. Then the combination of

this statisical surface model, the optical scattering theory (which so far has

proved out to be valid), and mathematical inversion techniques will lead to the

measurement of surface roughness parameters from first principles without

resorting to comparator approaches.

A promising surface model, developed by Beckmann and Spizzichino [19],

uses the rms roughness and the autocorrelation length as parameters. We plan to

test whether this two parameter model will adequately characterize the surface

statistics of the specimens and then attempt to determine the rms roughness and

autocorrelation length from the optical scattering data obtained from DALLAS.

If successful, the models and inversion techniques could then be

incorporated into the software of a controller for the MSG, an instrument whose

hardware is better suited than DALLAS to on line measurement in manufacturing.

Such an instrument will be an important breakthrough for the inspection of

surfaces roughness not only for wind tunnel models but other types of

manufactured components as well.

6 . Acknowledgments

The work described here was largely supported by NASA Contracts L-4618B

and L-20078B. Part of the supporting research was supported by the NBS Office

of Nondestructive Evaluation and the Navy Materiel and Air and Sea Systems

Commands. V. S. Gagne and S. A. Swearingen expertly assisted in the preparation

of the manuscript. We also thank J. Zimmerman and E. P. Whitenton for their

careful reviewing of the manuscript.

43
7. References

[1] E. C. Teague, T. V. Vorburger, F. E. Scire, S. M Baker, S. W. Jensen, C.

Trahan, and B. B. Gloss, "Evaluation of Methods for Characterizing Surface

Topography of Models for High Reynolds Number Wind-Tunnels", in AIAA 12th

Aerodynamic Testing Conference , Pub. CP-822 (American Institute of

Aeronautics and Astronautics, New York, 1982) pp. 246-251.

[2] E. C. Teague, F. E. Scire, S. M. Baker, and S. W. Jensen, "ThreeDimensional Stylus Prof i lometry , " Wear 83, 1-12 (1982).

[3] T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W.

Giauque, and E. C. Teague, "Surface Roughness Studies for Wing Tunnel

Models Used in High Reynolds Number Testing", J. Aircraft 23, 56-61

(1986).

[4] D. E. Gilsinn, T. V. Vorburger, F. E. Scire, E. C. Teague, and M.J. McLay,

"Surface Texture Characterization ’by Angular Distribution of Scattered

Light," in Review of Progress in Quantitative Nondestructive Evaluation , Vol. 4B, D. 0. Thompson and D. E. Chimenti , eds. (Plenum, New York 1985)

pp 779-788.

[5] T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, and D. E.

Gilsinn, "Surface Roughness Studies with DALLAS-Detector Array for Laser

Light Angular Scattering", J. Res. NBS 89, 3“ 1 6 (1984).

[6] D. E. Gilsinn, T. V. Vorburger, E. C. Teague, M. J. McLay, C. Giauque, and

F. E. Scire, "Surface Roughness Metrology by Angular Distributions of

Scattered Light", Measurement and Effects of Surface Defects and Quality

of Polish , SPIE Vol. ~52~5 "(1985) pp 2-15.

[7] T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W.

Giauque, and E. C. Teague, "Optical Measurement of the Roughness of

Sinusoidal Surfaces", Wear 109 , 15-27 (1986).

[8] D. Gilsinn, T. Vorburger, L. X. Cao, C. Giauque, F. Scire, and E. C.

Teague, "Optical Roughness Measurement of Industrial Surfaces", in Optical

Techniques for Industrial Inspection , SPIE Vol. 665 (1986) pp. 8-16.

[9] N. Schlichting, Boundary Layer Theory , 7th edition, translated by J.

Kestin (McGraw Hill, New York, 1979).

[10] R. Brodmann, 0. Gerstorfer, and G. Thurn, "Optical Roughness Measuring

Instrument for Fine-Machined Surface", Opt. Eng. 24, 408-413 (1985).

[11] ANSI/ASME B46. 1-1985 , Surface Texture (Surface Roughness, Waviness and

Lay) (American' Society of Mechanical Engineers, New York).

[12] D. V. Huntsberger and P. Billingsley, Elements of Statistical Inference , Third Ed. (Allyn and Bacon, Boston, 1973), p. 227.

44
[13] N. R. Draper and H. Smith, Applied Regression Analysis (John Wiley and

Sons, New York, 1960).

[14] See for example, P. R. Bevington, Data Reduction and Error Analysis for

the Physical Sciences (McGraw-Hill, New York, 1969), p. 196.

[15] S. T. Peavy, R. N. Varner, and D. Hogben, Source Listing of OMNITAB II

Program, NBS Special Publication 339 (U. S. Dept, of Commerce, Washington,

DC, 1970).

[16] R. S. Sayles in Rough Surfaces , T. R. Thomas, ed., (Longman, London, 1982)

Chapter 5.

[17] L. W. McKinney, "Overview of National Transonic Facility Model Technology

Program", in Cryogenic Wind Tunnel Models, Design and Fabrication , C.P.

Young, Jr. and B.B. Gloss, eds.. NASA CP 2262, pp. 1-9.

[18] Navy Manufacturing Technology Program Report, (Naval Material Command

Industrial Resources Detachment, Philadelphia) August, 1985, p. 6.

[19] P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves

from Rough Surfaces (Pergamon, Oxford, 1963)

45

L
APPENDIX A

Shop drawings on the most recent MSG nosepiece fabricated at NBS . The design is

still evolving so a few of these dimensions may be slightly different from those

of previous manifestations. We use a precision bearing to allow z-rotation but

also to minimize the degree of wobble about the x- and y-axes (see Fig. 3).

46

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N. S

NBS-1 14A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See/nstructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 87-3586

2. Performing Organ. Report No. 3. Publ ication Date July 1987

4. TITLE AND SUBTITLE

THE WIND TUNNEL MODEL SURFACE GAUGE FOR MEASURING ROUGHNESS

5. AUTHOR(S)

T.V. Vorburger, D.E. Gilsinn, E.C. Teague, C.H.W. Giauque, F.E. Scire, and L.X. Cao

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No. L4718B and L20078B

8 . Type of Report & Period Covered

Final

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

NASA Langley Research Center

Hampton, VA 23665

10.

SUPPLEMENTARY NOTES

~| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most si gnificant information. If document includes a si gni fi cant

bi bl iography or literature survey, mention it here)

This report covers research performed in the optical inspection of surface roughness by

members of the Center for Manufacturing Engineering under contracts L-4718B and L-20078B

with the NASA Langley Research Center. The project has proceeded along two lines: first

research into a quantitative understanding of light scattering from metal surfaces and

into the appropriate models to describe the surfaces themselves, and second, the develop

ment of a practical instrument for the measurement of rms roughness of high performance

wind tunnel models with smooth finishes. The research has been discussed in previous

articles and is only summarized here. This report is concerned primarily with the latte: - subject. We have developed a practical technique for the optical estimation of rms roughness based on three things: a commercially available, optical roughness gauge, a special

nosepiece that allows for rapid alignment of the gauge on curved surfaces, and a series

of comparator studies that correlate the results for obtained by the gauge with rms roughness (R ) measurements of surfaces by stylus techniques. is an optical scattering paramete? that is proportional to the variance of the light scattering angular distr

bution about its mean angle. We have proposed upper limit criteria for the value of S that should be expected on a properly finished model surface having rms roughness less

than 0.2ym. We have estimated that valid measurements of may be taken within an angle

of 60° from the leading edge of the wind tunnel model wing that we tested and have shown

from stylus measurements that the roughness increases dramatically around the leading edie

N

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) aircraft, finish, light scattering, model, optical roughness, optical scattering,

rms roughness, roughness, stylus, surface, transonic, wind tunnel

13. AVAILABILITY

iX~~l Unlimited

| 1 For Official Distribution. Do Not Release to NTIS

H Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

3] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

56

15. Price

$13.95

USCOMM-OC 6043-P80