- Email: [email protected]
Range expansion and automation of a classical profilometer
Range Expansion and Automation of a Classical Profilometer M. Chuard, J. Mignot, Laboratoire de Biologic Cutanee, Faculte de Medecine, Besancon, France Ph. Nardin, D. Rondot, Institut Universitaire de Technologic, Belfort, France
and by using a method which makes the numerical signal given by the stylus independent of the precision of the stepper motor.
Abstract A classical profilometer is modified in order to allow the measurement of a series of samples without any operator intervention. The extension needs the use of a stepper motor displacing the samples or the stylus in a vertical plane. One advantage of this technique is to extend the vertical range of a classical apparatus independently of the precision of the motor.
The Measurement System The principle of the measurement system is given in Figure 1. The different elements are: • A classical profilometer (Talysurf5M, Talysurf 10, or Perthometer C5D). • A V I C T O R S1 or I B M / A T microcomputer (with floppy or hard disk). The signal given by the p r o f i l o m e t e r is digitized over 12 bits (4096 values). • Two lateral stepper motors (minimum step of 1 # m ) to facilitate the displacement of the sample beneath the stylus which is fixed in the horizontal plane. • A vertical stepper motor (step of 1 # m) which gives the vertical displacement of the sample relative to the detector, or of the detector relative to the sample (Figure 1). This setup which keeps the stylus fixed in the horizontal direction has been chosen by a great number of authors over the last twenty years.~3 Other authors used the normal traverse mechanism of the stylus but only traversed the sample in the Y direction. 4.5 The method used here defines every point of a surface by its x, y, z coordinates. It is possible to retrieve this point later by the use of a relocation deviceY
Keywords: Automatic Profilometer , Rough Surface, Wide-range System, Shape Defect.
Introduction A large number of manufacturers have to control and measure the surface microtopography of the products they produce. In all cases, this control requires the presence of an operator to adjust the position of each sample under the profilometer. An interesting addition to the capabilities of a classical profilometer would be automation, which would allow the determination of the cust o m a r y roughness parameters over a series of samples without the aid of an operator. The solution proposed here allows for the development of a widerange profilometer, without any change in the classical system of detection. This is achieved by simply using a vertical stepper motor giving vertical displacements of the sample under the profilometer
223
Journal of Manufacturing Systems Volume 61 No. 3
~Cnal°g'DigitIIal
t
onvertor
IVictor$1
~ 1 ~
"lo'ne'o'f'Ver'tica'l'6isnl'ac'e'~lent'/ll/ll~ ................................
OI~Sk
Computer
4005 H
Zone of Horizontal Displacement (Measurement Zone)
I
(+5v)
4095-c~ I
I
2048
/
(Ov)
Figure 1 Principle of the Measurement System
Figure 2 Zones of the Numerical Signal
Using the system of the two stepper motors, classical parameters were deduced from profile or surface analysis, and this has been described in previous papers, s.*
0 and 4095 (12 bits). This range is separated into three zones: F r o m zero to a. (a is a numerical value which varies with the amplification and the type of profilometer used. This zone forms the disconnected lower part, in which every point of measurement should be translated by a displacement of the measurement system (or by displacement of the sample) to the second zone. The first zone should offer a linear part of variation of the signal (i) as a function of vertical displacement: i a z. F r o m a to 4095 - a. This zone is the chosen useful range in which the signal continues to obey the linear law: i a z. F r o m 4095 - a to 4095. This zone constitutes the disconnected high part in which every point of measurement should be translated by displacement into the preceding zone. In the two extreme ranges, the horizontal displacement of the sample is stopped in order to allow the vertical displacement of the profilometer (or the sample) to bring the reading into the useful range again (Figure 3). This vertical displacement is operated by the use of a stepper motor (step size of 1 # m . The precision of the translation table does not affect the precision of the measurement. Therefore, the connection of the numerical values of the signal given before and after vertical d i s p l a c e m e n t of the measurement system does not require knowledge of the exact vertical position of this system. An example of the numerical connection of the signal is given in Figure 4 where the sample is a ball, 2.78 mm in diameter. In this example, each change in the vertical position of the sample is represented by the vertical
Transformation In manufactured stylus systems (and often in the most sophisticated ones, such as Talysurf 6 from Taylor Hobson), the best choice of a signal amplification system is an automatic one. However, when the amplification chosen by the operator is too high (this value is controlled in the first part of the detector displacement), the electrical signal moves out of its linear range. The value of the amplification is automatically decreased to a lower value. This type of system becomes unsatisfactory in the case of surfaces which have a large error of form and a low roughness, since after elimination of the error of form, the small variations of roughness can be analyzed only with a low magnification. The system proposed here has the capability of analyzing such surfaces at high magnification as well as the capability of measuring several samples without any human intervention.
Measurement Zones The principle of numerical signal zones (Figure 2), is based on the conversion of the vertical scale by using a mechanical procedure based on the use of a vertical stepper motor. The stepper motor displacement error does not disturb the precision of the measurement signal. The analog signal given by the profilometer is digitized by an analog/digital converter. The electronic signal varying between -5 and +5 volts is converted into a numerical value between
224
Journal o f Manufacturing Systems Volume 6/No. 3
The horizontal length of each rectangular form shown in Figure 4 depends on the local slope of the sample. It also gives the m a x i m u m travel length which can be described with a classical apparatus. The length is a function of the magnification chosen. Such an example is characteristic of the increased capacity of the apparatus, since for the amplification used in Figure 4 (x 1000), the vertical range of a classical profilometer is limited to 60/~ m. The only limitation of the new system is that of the value of the angle of the tip of the stylus (90 °) which limits the measurements of the local slope to values less than 45 ° . The numerical connection of the signal after each vertical displacement shown in Figure 4 is obtained by a software method. The principle is described in Figure 3. Assume that the actual point of m e a s u r e m e n t corresponds to the (i ÷ 1)'* vertical displacement and that the abscissa of this point is xi.,. If the height Z , , falls into the upper range ( Z , , > 4095 - t~), then a vertical displacement is carried out which brings the measurement point from the third zone into the second zone. The real height of this point with respect to a fixed reference is given by (Figure 3):
Signal Given After the I + 1 rH Vertical Movement A
4o9s
I
Signal Given After k~X~\ ~ \ \ \ \ \ \ \ \ \ \ \ ~ \ ' ~ " the ITM Vertical i 4095 " a _ ..//"! Movement
:
I
,4o95
" ~ilIJlIIIIIIIIIIilIA
4 0 9 5 - (x
ll,/
I////I////1 0
l
i"
( / / / ~ I + 1 r. ~r Vertical Movement
! "
,0
Offset i + 1
Offset I
Figure 3 Reference and Vertical Displacements
z~., ,,i = z~. i + offseta
when offset~ is the s u m of all the precedent i displacements. The exact value z~. ,,,o~ is that given by the analog/digital converter after the vertical displacement i+ 1, to which is added a new offset representing the last displacement, i.e.,: z,,.t = z N + offsets., g M +offseti ---- g N ÷
offset ~.,
offsets., = z M - z N + offset~ The first value of the offset~__ t = -zo is the opposite of the first measured value. The origin of the vertical reference is therefore fixed at the height of the first point. When the signal given by the profilometer reaches the upper limit (4095 - a) or the lower one (a), the vertical stepping m o t o r displaces the sample so t h a t the n u m e r i c a l signal reaches a value approaching the middle of the scale (2048). However, it is not necessary to k n o w the position of the vertical stepping m o t o r , since the exact height of the measuring point is given by the
Figure 4 Vertical Displacements and Numerical Connection
linear displacement of a rectangular form. The length of the base of each rectangular form translates the length which can be described by a classical system not provided with the present automatic vertical displacement. The height of each rectangular form is represented digitally by the range 0 - 4095 quantization levels with the magnification used, i.e., the value of the vertical scale of a classical apparatus.
225
Journal of Manufacturing Systems Volume 6/No. 3
values listed in T a b l e 1 give the limits of the use of the new system, taking into a c c o u n t the required a c c u r a c y i n d e p e n d e n t l y o f the s t e p p e r m o t o r precision.
p r o f i l o m e t e r as a numerical value before the vertical displacement. In software, one has to establish the numerical relationship between the value given after the vertical displacement a n d before this displacement. The a c c u r a c y of this numerical relationship is based on the following a s s u m p t i o n : D u r i n g the vertical d i s p l a c e m e n t (where the sample is fixed in the h o r i z o n t a l plane), the tip of the p r o f i l o m e t e r has the same point of c o n t a c t with the surface. Such an a s s u m p t i o n is studied in detail in the section, Validity of the System. By such a numerical c o n t i n u i t y , an error can occur, d e p e n d i n g on the precision of the a n a l o g / digital converter. T h e r e f o r e , at each c o n n e c t i o n a m a x i m u m error of one q u a n t i z a t i o n level is possible. Such a c o n t i n u i t y error is a f u n c t i o n of the magnification used a n d of the classical a p p a r a t u s . The
Table l Numerical Connection Error for a Talysurf 5 R System
Magnification
x200
Numerical connection error (#m)
0.309 0.122
Vertical range of a classical s~cstem (#m)
250
x500 xl000 x5000 x20000
100
0.06
0.01
0.0036
50
10
2.5
The a l g o r i t h m of calculation of the " e x a c t " value of the signal is described as follows:
BEGIN {wide range profilometer} CASE Z OF 0..a : BEGIN Zm:=Z;
1F d m THEN B : - 4095- a ELSE B : = 2048; WHILE Z > B D O BEGIN make a÷i move on Z; wait for mechanical stabilization; read Z ; END OFFSET : = OFFSET + Zrn - Z ; d m : = TRUE; END; a..4095 - t~ : {no move} 4095 - c~..4095 : BEGIN Zm:=Z I F d m THEN
B : = 2048 B : = c~ ;
ELSE WHILE B > Z DO BEGIN make a-I move on Z; wait for mechanical stabilization ; rea......~dZ ; END OFFSET : = OFFSET ÷ Z m - Z ; d m : - FALSE ; END :~ND
226
Journal of Manufacturing Systems Volume 6/No. 3
in its highest and lowest positions, and if t~,, t~2 are respectively the angles between the stylus arm and the horizontal axis in the two preceding extreme positions, and B~, Bs are the contact points between the d i a m o n d tip and the sample surface, then the height difference between B t and B2 can be written
Validity of the System The purpose of this system is to permit the measurement of small surface roughnesses when the errors of form of the sample are important. In this case, the low values of the roughness parameters (such as Ra or Rt) require the use of a high magnification. When using high magnification, three sources of errors are possible: • Thermal effects which produce dilatation of the elements of the measurement system. • Vibrations of the stepper motors. • Displacement of the tip of the stylus during the vertical displacement of the sample (or profilometer). The first cause is also present in all the m e a s u r e m e n t systems of roughness and is not unique to this system. Likewise, the second is present in all the systems which use stepper motors. Such eventualities are eliminated by pausing after each displacement of the motor, the length of this pause depending on the type and on the inertia of the motor. The third cause is specific to the system proposed here and its effect should be analyzed in detail. During the vertical displacement of the sample (or of the profilometer), the tip of the diamond stylus can be displaced over the sample surface represented in Figure 5 by the line B, Bs. The local slope of the sample is tan/3. If A, and A s are the positions of the pivot point when the assembly which supports the transducer is
as:
z, - z s - 1 tan/3 (cosa, - cosa 2) xj - x s = I (cosoq - coset,)
(1)
when 1 is the length of the stylus arm. The vertical displacement of the measurement system from A, to A 2 is given by: H~
l ( a , + a s ) 1+ 1 t a n / 3 ( a , - a s )
T
(2)
In the classical stylus instrument system, the magnification can reach 200,000. For a mean amplification of 20,000, a variation in the numerical signal of one digit corresponds to 0.0036/~ m. In this case (which is not the most favorable case), the vertical displacement H is given by: H < 2048 x 0.0036 - 7.3#m
(3)
where the value 2048 corresponds to the numerical range described during the vertical displacement of the stylus and the value of a: tan a <
7.3 - 1.8.10 .4 radian (the length 40,000 of the detector arm 1 is 4 cm).
(4)
If the slope is/3 - 45 ° (very improbable value): z, - z 2 = 1 tan/3 (cos~t, - cosa2) < 1 tan/3 (coscq-1) max (z, - z2) # 1 tan/3 ( - ~ - ) The bigger difference is given by:
A 1
max (z, - zs) --- 1.7 10"~ ~tm ~
mm
q
.
.
.
.
.
.
.
The horizontal displacement of the d i a m o n d tip has a value of the same order of magnitude:
2
H X,-X I
I
I
I
H2
I
H1
~
,h
O"
-
Z l - z2 tan/3
~Z,-Z~
Therefore, this source of error is negligible. This example shows that the error due to the displacement of the profilometer tip during the vertical displacement of the sample (1.7 104 # m for a 20,000 magnification) is less than the numerical connection error (3.6 l0 -~ # m) given in Table 1.
-
0
Figure 5 Displacement of the Diamond
2-
Detector
227
Journal of Manufacturing Systems Volume 6/No. 3
Figures 6 and 7 show examples of a profile detected with the wide-range system. A classical apparatus using the same magnification (x 1000) allows analysis of only a small part of this profile for which Rt " 300 /~m. Thus, the present system provides the possibility of measuring the statistical properties of such a profile though the error of form, as a Wt parameter is equal to several millimeters. Figure 6 shows the general profile detected over a pulverizer ball (g = 4 mm) obtained by turning. Each vertical displacement of the sample under the diamond tip of the profilometer is indicated by a vertical line. The basis width of each rectangular form represents the m a x i m u m length which can be detected by a classical apparatus using the magnification of 1000. The points a and b represent the most important defects of the profile. These are greatly enlarged in the insets.
v
°
Figure 7 Profile Obtained by the Wide-range System
the surface in the vicinity of the rotation axis of the ball (profile (c) middle region) and points for which the rotation speed is higher (profile (c) extreme regions). Profiles (d) and (e), respectively, give the aspect of the surface obtained along the direction of turning (d) and perpendicular to the turning direction (e). The vertical steps shown in profile (e) are evidence for "fish scale" on the surface. This aspect of "fish scale" is clearly visible in the image obtained (Figure 8) by scanning electron microscopy.
A u t o m a t i o n of a Profilometer The automation of a profilometer is based on these two principles: I. The best system to detect the distance between a sample and the tip of the profilometer is the tip of the profilometer itself. 2. The use of a profilometer to analyze a series of samples without h u m a n intervention requires a specimen holder. The form and dimensions of this device depend on that of the samples. The example in Figure 9 shows the practical realization of a specimen holder permitting the treatment of a series of eight samples of length less than 30 mm (several profiles can be detected over each sample). In this montage, the principle of
Figure 6 Profile Obtained by the Wide-range System
The enlarged views also permit inspection of the numerical connection of the signal at each vertical displacement of the sample. The connection errors are negligible on this scale. Figure 7 represents successively: • The general view of the profile over a total length of 2.4 mm (a); • The mean profile obtained by low pass numerical filtering (b); • The resultant profile (c) obtained by high pass filtering shows differences in the topography of
228
Journal o f Manuf~zcturing Systems Volume 6 No. 3
8a Magnified x 360
8b Magnified x 24 Figure 8
View of the Pulverizer Ball
by Scanning Electron Microscope
acquisition of successive profiles is obtained by displacement of the y motor. The progression from one sample to the next one is realized by the use of the vertical motor in order to avoid any contact between the tip of the profilometer and a sample during the fast translation of the sample. The magnitude of the vertical displacement of the motor is fixed by the user in connection with the difference in depth between the samples. The horizontal translation between two neighboring samples is obtained by the y motor whose displacement determines the maximum number of samples which can be treated. In Figure 9, the y motor has about 250 mm of play.
Automatic Treatment of Data In order to allow the automatic acquisition of data and its treatment, the operator must, at the beginning of the operations, define the following parameters. Definition of the Specimen Holder. The specimen holder is defined by the number of samples which can be obtained and by the positions and
Figure 9
Specimen Holder
229
Journal o f Manufacturing .~vsterns Volume 6 No. 3
distance between successive samples. In order to obtain the exact location of each profile, the following parameters must be defined: • The starting point of measurement. • The direction and length of any profile, defined by a vector D ( Dxi, Dyi). • The distance between two neighboring profiles, defined by a vector X (Xxi, Yyi). An example of the movements described by the profilometer in respect to the samples (or by the samples in respect to the profilometer) is given in Figure 10, a simple case of parallel profiles.
sample currently being analyzed. According to the choice of the operator at the beginning of the stage, numerous treatments can be made, and these have been developed in a previous study, s
Concluding Remarks C o n v e n t i o n a l a p p a r a t u s e s for r o u g h n e s s measurement have several defects. They are not modular and do not allow any expansion of their capacity. They need accurate positioning of the sample before any measurement which demands a complex manual operation. They use an electrical filtering which is not always the best value for the given sample. They only analyze profiles and not surfaces. And, finally, they require the presence of an operator if more than one sample is to be analyzed. The system proposed here eliminates or attenuates these defects with the development of several devices around a microcomputer, while retaining a classical profilometer as the detector. This widerange profilometer allows the m e a s u r e m e n t of roughness and undulation under an area independent of the 3-D form of this surface (norms NFE-05-015 and NFE-05-017). If the mean form of the surface is located inside a reasonable range of magnitude, it is not necessary to know this mean form to measure the roughness.
Figure 10 Principle of the Specimen Holder
Definition of Data Acquisition. The parameters required include: • The vector step between two neighboring points of a profile. • The magnification (if the magnification chosen by the operator is too high, the vertical motor starts the wide-range system). • The number and the names of samples. The definition of all these parameters permits us to obtain the number of profiles in the directions chosen and on the chosen samples. The possibility of vertical displacement of the sample described in the section on the Transformation of a Classical Apparatus into a Wide-range System, allows the treatment of the successive profiles even if the difference in depth between two successive samples has a high value (several mm), and even if the roughness has numerous variations through the different samples. For example, with this system, it is possible to measure the roughness and waviness over surfaces as different as ball bearings, gear teeth, and welding. Numerical Treatment. The treatment of the data is made after all data is recorded. If an accident occurs during the data acquisition (e.g., a power cut), the system is automatically restarted on the
Acknowledgement The authors would like to thank Ms. J.E. Carrey-Wood for help with the translation, Mr. J. Bielle for his comments and remarks, and particularly Dr. Th. Vorburger (Micro and Optical Metrology Group of the National Bureau of Standards, Gaithersburg, Maryland) for revievAng the manuscript and m a k i n g n u m e r o u s suggestions. The authors also thank the I N S E R M (Institut National de la Sante et de la Recherche Medicale) for its financial support through contract #838029.
References 1. J. Peklenik. "Investigation of the Surface Topology". Annals o f the CIRP, Volume XV, 1967, pp. 381-385. 2. B. Snaith, M.J. Edmonds, S.D. Robert. "Use o f a Profilometer for a Surface Mapping", Precision Engineering, Volume 141, 1981, pp. 87-90. 3. E.C. Teague, F.E. Scire, S.M. Baker, S.W. Jensen. "ThreeDimensional Stylus Profilomet ry", WEA R, Volume 83. 1982, pp. l - 12.
230
Journal of Manufacturing Systems Volume 6/No, 3
7. J.B.P. Williamson, R.T. Hunt. =Relocation Profilometry", Journal
4. J.B.P. Williamson. "Topography of Solid Surfaces*, Proceedingsof
of Scientific Instruments. Volume 21. No. I, 1968. pp. 749-752.
NASA Symposium on Interdisciplinary Approaches to Friction and Wear, San Antonio, TX, Nov. 28-30, 1967.
8. M. Chuard, A.C. Roudot, J. Mignot. "On the Use of a Modular System for Microtopographical Surface Measurement", WEAR, Volume 97, 1984, pp. 257-274. 9. D. Mairey, J.M. Sprauel, M. Chuard, J. Mignot. "Study of Residual Stresses Induced During Simulated .Wear Mechanism", Journal of Tribology, Volume 107, 1985, pp. 195-199.
5. R.S. Sayles, T.R. Thomas. "Mapping a Small Area of a Surface", Journal of Scientific Instruments, No. 10, 1976, pp. 855-861. 6. M.J. Edmonds, A.M. Jones, P.W. O'Callaghan, S.D. Robert. "A Three-Dimensional Relocation Profilometer State", WEA R, Volume 43, 1977, pp. 329-340.
Author(s) Biography M. Chuard received a Masters degree in Mathematics in 1982 and a Thesis (3rd cycle) in 1985 from the University of Besancon, France. Ph. Nardin received a Masters degree in Mathematics in 1979 and graduated from the Engineering School of Mechanics in 1980 from the University of Besancon, France. D. Rondot received a Masters degree in Physics in 1970 and a Thesis (Doctorates Sciences) in Material Sciences in 1977. He is a Professor at the Institute of Technology in Belfort, France. J. Mignot received a Masters degree in Physics in 1968 and a Thesis (Doctorates Sciences) in 1975 in Physics. He is a Professor at the University of Besancon, France.
231
and by using a method which makes the numerical signal given by the stylus independent of the precision of the stepper motor.
Abstract A classical profilometer is modified in order to allow the measurement of a series of samples without any operator intervention. The extension needs the use of a stepper motor displacing the samples or the stylus in a vertical plane. One advantage of this technique is to extend the vertical range of a classical apparatus independently of the precision of the motor.
The Measurement System The principle of the measurement system is given in Figure 1. The different elements are: • A classical profilometer (Talysurf5M, Talysurf 10, or Perthometer C5D). • A V I C T O R S1 or I B M / A T microcomputer (with floppy or hard disk). The signal given by the p r o f i l o m e t e r is digitized over 12 bits (4096 values). • Two lateral stepper motors (minimum step of 1 # m ) to facilitate the displacement of the sample beneath the stylus which is fixed in the horizontal plane. • A vertical stepper motor (step of 1 # m) which gives the vertical displacement of the sample relative to the detector, or of the detector relative to the sample (Figure 1). This setup which keeps the stylus fixed in the horizontal direction has been chosen by a great number of authors over the last twenty years.~3 Other authors used the normal traverse mechanism of the stylus but only traversed the sample in the Y direction. 4.5 The method used here defines every point of a surface by its x, y, z coordinates. It is possible to retrieve this point later by the use of a relocation deviceY
Keywords: Automatic Profilometer , Rough Surface, Wide-range System, Shape Defect.
Introduction A large number of manufacturers have to control and measure the surface microtopography of the products they produce. In all cases, this control requires the presence of an operator to adjust the position of each sample under the profilometer. An interesting addition to the capabilities of a classical profilometer would be automation, which would allow the determination of the cust o m a r y roughness parameters over a series of samples without the aid of an operator. The solution proposed here allows for the development of a widerange profilometer, without any change in the classical system of detection. This is achieved by simply using a vertical stepper motor giving vertical displacements of the sample under the profilometer
223
Journal of Manufacturing Systems Volume 61 No. 3
~Cnal°g'DigitIIal
t
onvertor
IVictor$1
~ 1 ~
"lo'ne'o'f'Ver'tica'l'6isnl'ac'e'~lent'/ll/ll~ ................................
OI~Sk
Computer
4005 H
Zone of Horizontal Displacement (Measurement Zone)
I
(+5v)
4095-c~ I
I
2048
/
(Ov)
Figure 1 Principle of the Measurement System
Figure 2 Zones of the Numerical Signal
Using the system of the two stepper motors, classical parameters were deduced from profile or surface analysis, and this has been described in previous papers, s.*
0 and 4095 (12 bits). This range is separated into three zones: F r o m zero to a. (a is a numerical value which varies with the amplification and the type of profilometer used. This zone forms the disconnected lower part, in which every point of measurement should be translated by a displacement of the measurement system (or by displacement of the sample) to the second zone. The first zone should offer a linear part of variation of the signal (i) as a function of vertical displacement: i a z. F r o m a to 4095 - a. This zone is the chosen useful range in which the signal continues to obey the linear law: i a z. F r o m 4095 - a to 4095. This zone constitutes the disconnected high part in which every point of measurement should be translated by displacement into the preceding zone. In the two extreme ranges, the horizontal displacement of the sample is stopped in order to allow the vertical displacement of the profilometer (or the sample) to bring the reading into the useful range again (Figure 3). This vertical displacement is operated by the use of a stepper motor (step size of 1 # m . The precision of the translation table does not affect the precision of the measurement. Therefore, the connection of the numerical values of the signal given before and after vertical d i s p l a c e m e n t of the measurement system does not require knowledge of the exact vertical position of this system. An example of the numerical connection of the signal is given in Figure 4 where the sample is a ball, 2.78 mm in diameter. In this example, each change in the vertical position of the sample is represented by the vertical
Transformation In manufactured stylus systems (and often in the most sophisticated ones, such as Talysurf 6 from Taylor Hobson), the best choice of a signal amplification system is an automatic one. However, when the amplification chosen by the operator is too high (this value is controlled in the first part of the detector displacement), the electrical signal moves out of its linear range. The value of the amplification is automatically decreased to a lower value. This type of system becomes unsatisfactory in the case of surfaces which have a large error of form and a low roughness, since after elimination of the error of form, the small variations of roughness can be analyzed only with a low magnification. The system proposed here has the capability of analyzing such surfaces at high magnification as well as the capability of measuring several samples without any human intervention.
Measurement Zones The principle of numerical signal zones (Figure 2), is based on the conversion of the vertical scale by using a mechanical procedure based on the use of a vertical stepper motor. The stepper motor displacement error does not disturb the precision of the measurement signal. The analog signal given by the profilometer is digitized by an analog/digital converter. The electronic signal varying between -5 and +5 volts is converted into a numerical value between
224
Journal o f Manufacturing Systems Volume 6/No. 3
The horizontal length of each rectangular form shown in Figure 4 depends on the local slope of the sample. It also gives the m a x i m u m travel length which can be described with a classical apparatus. The length is a function of the magnification chosen. Such an example is characteristic of the increased capacity of the apparatus, since for the amplification used in Figure 4 (x 1000), the vertical range of a classical profilometer is limited to 60/~ m. The only limitation of the new system is that of the value of the angle of the tip of the stylus (90 °) which limits the measurements of the local slope to values less than 45 ° . The numerical connection of the signal after each vertical displacement shown in Figure 4 is obtained by a software method. The principle is described in Figure 3. Assume that the actual point of m e a s u r e m e n t corresponds to the (i ÷ 1)'* vertical displacement and that the abscissa of this point is xi.,. If the height Z , , falls into the upper range ( Z , , > 4095 - t~), then a vertical displacement is carried out which brings the measurement point from the third zone into the second zone. The real height of this point with respect to a fixed reference is given by (Figure 3):
Signal Given After the I + 1 rH Vertical Movement A
4o9s
I
Signal Given After k~X~\ ~ \ \ \ \ \ \ \ \ \ \ \ ~ \ ' ~ " the ITM Vertical i 4095 " a _ ..//"! Movement
:
I
,4o95
" ~ilIJlIIIIIIIIIIilIA
4 0 9 5 - (x
ll,/
I////I////1 0
l
i"
( / / / ~ I + 1 r. ~r Vertical Movement
! "
,0
Offset i + 1
Offset I
Figure 3 Reference and Vertical Displacements
z~., ,,i = z~. i + offseta
when offset~ is the s u m of all the precedent i displacements. The exact value z~. ,,,o~ is that given by the analog/digital converter after the vertical displacement i+ 1, to which is added a new offset representing the last displacement, i.e.,: z,,.t = z N + offsets., g M +offseti ---- g N ÷
offset ~.,
offsets., = z M - z N + offset~ The first value of the offset~__ t = -zo is the opposite of the first measured value. The origin of the vertical reference is therefore fixed at the height of the first point. When the signal given by the profilometer reaches the upper limit (4095 - a) or the lower one (a), the vertical stepping m o t o r displaces the sample so t h a t the n u m e r i c a l signal reaches a value approaching the middle of the scale (2048). However, it is not necessary to k n o w the position of the vertical stepping m o t o r , since the exact height of the measuring point is given by the
Figure 4 Vertical Displacements and Numerical Connection
linear displacement of a rectangular form. The length of the base of each rectangular form translates the length which can be described by a classical system not provided with the present automatic vertical displacement. The height of each rectangular form is represented digitally by the range 0 - 4095 quantization levels with the magnification used, i.e., the value of the vertical scale of a classical apparatus.
225
Journal of Manufacturing Systems Volume 6/No. 3
values listed in T a b l e 1 give the limits of the use of the new system, taking into a c c o u n t the required a c c u r a c y i n d e p e n d e n t l y o f the s t e p p e r m o t o r precision.
p r o f i l o m e t e r as a numerical value before the vertical displacement. In software, one has to establish the numerical relationship between the value given after the vertical displacement a n d before this displacement. The a c c u r a c y of this numerical relationship is based on the following a s s u m p t i o n : D u r i n g the vertical d i s p l a c e m e n t (where the sample is fixed in the h o r i z o n t a l plane), the tip of the p r o f i l o m e t e r has the same point of c o n t a c t with the surface. Such an a s s u m p t i o n is studied in detail in the section, Validity of the System. By such a numerical c o n t i n u i t y , an error can occur, d e p e n d i n g on the precision of the a n a l o g / digital converter. T h e r e f o r e , at each c o n n e c t i o n a m a x i m u m error of one q u a n t i z a t i o n level is possible. Such a c o n t i n u i t y error is a f u n c t i o n of the magnification used a n d of the classical a p p a r a t u s . The
Table l Numerical Connection Error for a Talysurf 5 R System
Magnification
x200
Numerical connection error (#m)
0.309 0.122
Vertical range of a classical s~cstem (#m)
250
x500 xl000 x5000 x20000
100
0.06
0.01
0.0036
50
10
2.5
The a l g o r i t h m of calculation of the " e x a c t " value of the signal is described as follows:
BEGIN {wide range profilometer} CASE Z OF 0..a : BEGIN Zm:=Z;
1F d m THEN B : - 4095- a ELSE B : = 2048; WHILE Z > B D O BEGIN make a÷i move on Z; wait for mechanical stabilization; read Z ; END OFFSET : = OFFSET + Zrn - Z ; d m : = TRUE; END; a..4095 - t~ : {no move} 4095 - c~..4095 : BEGIN Zm:=Z I F d m THEN
B : = 2048 B : = c~ ;
ELSE WHILE B > Z DO BEGIN make a-I move on Z; wait for mechanical stabilization ; rea......~dZ ; END OFFSET : = OFFSET ÷ Z m - Z ; d m : - FALSE ; END :~ND
226
Journal of Manufacturing Systems Volume 6/No. 3
in its highest and lowest positions, and if t~,, t~2 are respectively the angles between the stylus arm and the horizontal axis in the two preceding extreme positions, and B~, Bs are the contact points between the d i a m o n d tip and the sample surface, then the height difference between B t and B2 can be written
Validity of the System The purpose of this system is to permit the measurement of small surface roughnesses when the errors of form of the sample are important. In this case, the low values of the roughness parameters (such as Ra or Rt) require the use of a high magnification. When using high magnification, three sources of errors are possible: • Thermal effects which produce dilatation of the elements of the measurement system. • Vibrations of the stepper motors. • Displacement of the tip of the stylus during the vertical displacement of the sample (or profilometer). The first cause is also present in all the m e a s u r e m e n t systems of roughness and is not unique to this system. Likewise, the second is present in all the systems which use stepper motors. Such eventualities are eliminated by pausing after each displacement of the motor, the length of this pause depending on the type and on the inertia of the motor. The third cause is specific to the system proposed here and its effect should be analyzed in detail. During the vertical displacement of the sample (or of the profilometer), the tip of the diamond stylus can be displaced over the sample surface represented in Figure 5 by the line B, Bs. The local slope of the sample is tan/3. If A, and A s are the positions of the pivot point when the assembly which supports the transducer is
as:
z, - z s - 1 tan/3 (cosa, - cosa 2) xj - x s = I (cosoq - coset,)
(1)
when 1 is the length of the stylus arm. The vertical displacement of the measurement system from A, to A 2 is given by: H~
l ( a , + a s ) 1+ 1 t a n / 3 ( a , - a s )
T
(2)
In the classical stylus instrument system, the magnification can reach 200,000. For a mean amplification of 20,000, a variation in the numerical signal of one digit corresponds to 0.0036/~ m. In this case (which is not the most favorable case), the vertical displacement H is given by: H < 2048 x 0.0036 - 7.3#m
(3)
where the value 2048 corresponds to the numerical range described during the vertical displacement of the stylus and the value of a: tan a <
7.3 - 1.8.10 .4 radian (the length 40,000 of the detector arm 1 is 4 cm).
(4)
If the slope is/3 - 45 ° (very improbable value): z, - z 2 = 1 tan/3 (cos~t, - cosa2) < 1 tan/3 (coscq-1) max (z, - z2) # 1 tan/3 ( - ~ - ) The bigger difference is given by:
A 1
max (z, - zs) --- 1.7 10"~ ~tm ~
mm
q
.
.
.
.
.
.
.
The horizontal displacement of the d i a m o n d tip has a value of the same order of magnitude:
2
H X,-X I
I
I
I
H2
I
H1
~
,h
O"
-
Z l - z2 tan/3
~Z,-Z~
Therefore, this source of error is negligible. This example shows that the error due to the displacement of the profilometer tip during the vertical displacement of the sample (1.7 104 # m for a 20,000 magnification) is less than the numerical connection error (3.6 l0 -~ # m) given in Table 1.
-
0
Figure 5 Displacement of the Diamond
2-
Detector
227
Journal of Manufacturing Systems Volume 6/No. 3
Figures 6 and 7 show examples of a profile detected with the wide-range system. A classical apparatus using the same magnification (x 1000) allows analysis of only a small part of this profile for which Rt " 300 /~m. Thus, the present system provides the possibility of measuring the statistical properties of such a profile though the error of form, as a Wt parameter is equal to several millimeters. Figure 6 shows the general profile detected over a pulverizer ball (g = 4 mm) obtained by turning. Each vertical displacement of the sample under the diamond tip of the profilometer is indicated by a vertical line. The basis width of each rectangular form represents the m a x i m u m length which can be detected by a classical apparatus using the magnification of 1000. The points a and b represent the most important defects of the profile. These are greatly enlarged in the insets.
v
°
Figure 7 Profile Obtained by the Wide-range System
the surface in the vicinity of the rotation axis of the ball (profile (c) middle region) and points for which the rotation speed is higher (profile (c) extreme regions). Profiles (d) and (e), respectively, give the aspect of the surface obtained along the direction of turning (d) and perpendicular to the turning direction (e). The vertical steps shown in profile (e) are evidence for "fish scale" on the surface. This aspect of "fish scale" is clearly visible in the image obtained (Figure 8) by scanning electron microscopy.
A u t o m a t i o n of a Profilometer The automation of a profilometer is based on these two principles: I. The best system to detect the distance between a sample and the tip of the profilometer is the tip of the profilometer itself. 2. The use of a profilometer to analyze a series of samples without h u m a n intervention requires a specimen holder. The form and dimensions of this device depend on that of the samples. The example in Figure 9 shows the practical realization of a specimen holder permitting the treatment of a series of eight samples of length less than 30 mm (several profiles can be detected over each sample). In this montage, the principle of
Figure 6 Profile Obtained by the Wide-range System
The enlarged views also permit inspection of the numerical connection of the signal at each vertical displacement of the sample. The connection errors are negligible on this scale. Figure 7 represents successively: • The general view of the profile over a total length of 2.4 mm (a); • The mean profile obtained by low pass numerical filtering (b); • The resultant profile (c) obtained by high pass filtering shows differences in the topography of
228
Journal o f Manuf~zcturing Systems Volume 6 No. 3
8a Magnified x 360
8b Magnified x 24 Figure 8
View of the Pulverizer Ball
by Scanning Electron Microscope
acquisition of successive profiles is obtained by displacement of the y motor. The progression from one sample to the next one is realized by the use of the vertical motor in order to avoid any contact between the tip of the profilometer and a sample during the fast translation of the sample. The magnitude of the vertical displacement of the motor is fixed by the user in connection with the difference in depth between the samples. The horizontal translation between two neighboring samples is obtained by the y motor whose displacement determines the maximum number of samples which can be treated. In Figure 9, the y motor has about 250 mm of play.
Automatic Treatment of Data In order to allow the automatic acquisition of data and its treatment, the operator must, at the beginning of the operations, define the following parameters. Definition of the Specimen Holder. The specimen holder is defined by the number of samples which can be obtained and by the positions and
Figure 9
Specimen Holder
229
Journal o f Manufacturing .~vsterns Volume 6 No. 3
distance between successive samples. In order to obtain the exact location of each profile, the following parameters must be defined: • The starting point of measurement. • The direction and length of any profile, defined by a vector D ( Dxi, Dyi). • The distance between two neighboring profiles, defined by a vector X (Xxi, Yyi). An example of the movements described by the profilometer in respect to the samples (or by the samples in respect to the profilometer) is given in Figure 10, a simple case of parallel profiles.
sample currently being analyzed. According to the choice of the operator at the beginning of the stage, numerous treatments can be made, and these have been developed in a previous study, s
Concluding Remarks C o n v e n t i o n a l a p p a r a t u s e s for r o u g h n e s s measurement have several defects. They are not modular and do not allow any expansion of their capacity. They need accurate positioning of the sample before any measurement which demands a complex manual operation. They use an electrical filtering which is not always the best value for the given sample. They only analyze profiles and not surfaces. And, finally, they require the presence of an operator if more than one sample is to be analyzed. The system proposed here eliminates or attenuates these defects with the development of several devices around a microcomputer, while retaining a classical profilometer as the detector. This widerange profilometer allows the m e a s u r e m e n t of roughness and undulation under an area independent of the 3-D form of this surface (norms NFE-05-015 and NFE-05-017). If the mean form of the surface is located inside a reasonable range of magnitude, it is not necessary to know this mean form to measure the roughness.
Figure 10 Principle of the Specimen Holder
Definition of Data Acquisition. The parameters required include: • The vector step between two neighboring points of a profile. • The magnification (if the magnification chosen by the operator is too high, the vertical motor starts the wide-range system). • The number and the names of samples. The definition of all these parameters permits us to obtain the number of profiles in the directions chosen and on the chosen samples. The possibility of vertical displacement of the sample described in the section on the Transformation of a Classical Apparatus into a Wide-range System, allows the treatment of the successive profiles even if the difference in depth between two successive samples has a high value (several mm), and even if the roughness has numerous variations through the different samples. For example, with this system, it is possible to measure the roughness and waviness over surfaces as different as ball bearings, gear teeth, and welding. Numerical Treatment. The treatment of the data is made after all data is recorded. If an accident occurs during the data acquisition (e.g., a power cut), the system is automatically restarted on the
Acknowledgement The authors would like to thank Ms. J.E. Carrey-Wood for help with the translation, Mr. J. Bielle for his comments and remarks, and particularly Dr. Th. Vorburger (Micro and Optical Metrology Group of the National Bureau of Standards, Gaithersburg, Maryland) for revievAng the manuscript and m a k i n g n u m e r o u s suggestions. The authors also thank the I N S E R M (Institut National de la Sante et de la Recherche Medicale) for its financial support through contract #838029.
References 1. J. Peklenik. "Investigation of the Surface Topology". Annals o f the CIRP, Volume XV, 1967, pp. 381-385. 2. B. Snaith, M.J. Edmonds, S.D. Robert. "Use o f a Profilometer for a Surface Mapping", Precision Engineering, Volume 141, 1981, pp. 87-90. 3. E.C. Teague, F.E. Scire, S.M. Baker, S.W. Jensen. "ThreeDimensional Stylus Profilomet ry", WEA R, Volume 83. 1982, pp. l - 12.
230
Journal of Manufacturing Systems Volume 6/No, 3
7. J.B.P. Williamson, R.T. Hunt. =Relocation Profilometry", Journal
4. J.B.P. Williamson. "Topography of Solid Surfaces*, Proceedingsof
of Scientific Instruments. Volume 21. No. I, 1968. pp. 749-752.
NASA Symposium on Interdisciplinary Approaches to Friction and Wear, San Antonio, TX, Nov. 28-30, 1967.
8. M. Chuard, A.C. Roudot, J. Mignot. "On the Use of a Modular System for Microtopographical Surface Measurement", WEAR, Volume 97, 1984, pp. 257-274. 9. D. Mairey, J.M. Sprauel, M. Chuard, J. Mignot. "Study of Residual Stresses Induced During Simulated .Wear Mechanism", Journal of Tribology, Volume 107, 1985, pp. 195-199.
5. R.S. Sayles, T.R. Thomas. "Mapping a Small Area of a Surface", Journal of Scientific Instruments, No. 10, 1976, pp. 855-861. 6. M.J. Edmonds, A.M. Jones, P.W. O'Callaghan, S.D. Robert. "A Three-Dimensional Relocation Profilometer State", WEA R, Volume 43, 1977, pp. 329-340.
Author(s) Biography M. Chuard received a Masters degree in Mathematics in 1982 and a Thesis (3rd cycle) in 1985 from the University of Besancon, France. Ph. Nardin received a Masters degree in Mathematics in 1979 and graduated from the Engineering School of Mechanics in 1980 from the University of Besancon, France. D. Rondot received a Masters degree in Physics in 1970 and a Thesis (Doctorates Sciences) in Material Sciences in 1977. He is a Professor at the Institute of Technology in Belfort, France. J. Mignot received a Masters degree in Physics in 1968 and a Thesis (Doctorates Sciences) in 1975 in Physics. He is a Professor at the University of Besancon, France.
231