6.new approach

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International Journal of Mechanical and Production

Engineering Research and Development (IJMPERD)ISSN 2249-6890

Vol. 3, Issue 1, Mar 2013, 41-52

TJPRC Pvt. Ltd.

A NEW APPROACH IN MEASURING OF THE ROUGHNESS FOR SURFACE

CONSTITUTED WITH MACHINING PROCESS BY MATERIAL REMOVAL

MITE TOMOV1, MIKOLAJ KUZINOVSKI1 & PAVEL KOVAC2

1Ss. Cyril and Methodius University in Skopje, Faculty of Mechanical Engineering, Skopje, Karpos II. BB., Macedonia

2University of Novi Sad, Faculty of Technical Sciences, Serbia

ABSTRACT

This paper suggests a new approach to measuring surface roughness facilitated by the introduction of a new

parameter, called parameter of statistic equality of sampling lengths. The procedure for obtaining the primary profile, the

roughness profile and the waviness profile is presented as a set of recommendations of several ISO standards. In addition,

the paper suggests the expansion of the presented measuring procedure by direct inclusion of the new parameter. Another

novelty is that the proposed algorithm now allows the inclusion of feedback which thus far has not been the case in

roughness measuring. The newly proposed parameter was been verified using etalons and real surfaces, representing

several machining process by material removal.

KEYWORDS: Parameter of Statistical Equality of Sampling Lengths, Surface Roughness, Roughness Profile, Waviness

Profile, Primary Profile

INTRODUCTION (THE NEED FOR INTRODUCING A NEW APPROACH)

The modern production processes and technologies as well as the nanotechnology development contributed

towards surface roughness becoming a dominant factor for the successful functioning of the products. The genesis of the

surface metrology discipline, as well as the expected directions for future development are presented systematically and in

detail in (Jiang et al, 2007; Jiang et al, 2007b), where one of the conclusions regarding the future development of surface

metrology considers the shift from profile to aerial characterization, from stochastic to structural surfaces and from simple

shapes to complex freeform geometries.

However, the core objective of surface metrology is to enable full control over surface constitution and provide an

understanding of the functionally significant surface characteristics.

Todays achievements regarding the product surface roughness prediction models, at least for conventional

machining, are based on a planar projection of the geometry of the tool (regardless whether it is with defined geometry or

not) onto the surface of the workpiece (Stanisaw et al, 2009; Edward & ukasz, 2012). Hence the conclusion that

investigations regarding the roughness profile and the roughness parameters will continue to remain current, but the

emphasis will shift towards ways to determine them more accurately. This paper looks at providing the conditions for more

accurate determination of the roughness profile and the roughness parameters.

In order to ensure comparability and replicability of the results (the parameters values), the procedures for

measuring and obtaining the primary profile, the roughness profile and the waviness profile are implemented in accordance

with the recommendations contained in several international (ISO) standards, where the basic and necessary standards

include: ISO 4287:1997; ISO 4288:1996; ISO 3274:1996; ISO 11562:1996 and ISO 16610 standard series. Based on these


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42 Mite Tomov, Mikolaj Kuzinovski &Pavel Kovac

standards and the recommendations contained therein, one can establish a measuring procedure for obtaining the primary

profile, the roughness profile and the waviness profile, by using contact skidless instruments, shown of Figure 1.

m

0

5

10

15

20

0 0.5 1 1.5 2 2 .5 3 3.5 4 mm

Nominal form (removed)

ISO3274:1996

ISO4287:1997

6

m

-2

-1

0

1

2

0 0.5 1 1.5 2 2.5 3 3.5 mm

Application of the profil filter s

ISO4287:1997;

ISO3274:1996;

ISO11562:1996;

ISO16610series.

Noise

7

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0 0.5 1 1.5 2 2.5 3 3.5 4

Waviness profile

Application of the profil filter f

ISO4287:1997;

ISO3274:1996;

ISO11562:1996;

ISO16610series.

11

Traced profile

ISO

3274:1996

4

IS

O4288:1996

IS

O3274:1996

3

Real surface

Surface profile

x

z

y

ISO4287:1997

1

2

m

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5 4 mm

Total profile

ISO3274:1996

5

m

-2

-1

0

1

0 0 .5 1 1 .5 2 2 .5 3 3 .5 4 m m

Primary profile

ISO3274:1996

Mean line for theprimary profile

8

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2 2.5 3 3.5 4

ISO4287:1997;

ISO3274:1996;

ISO11562:1996;

ISO16610series.

Application of the profil filter c

9

Roughness paremeterRa, Rq, Rt, Rp, Rv..

12

m

-2

-1

0

1

0 0.5 1 1.5 2 2 .5 3 3.5 mm

Mean line for theroughness profile

ISO4287:1997

Roughness profile

10

Measurement process

an

dother.

Figure 1: Procedure for Obtaining the Primary Profile, the Roughness Profile and the Waviness Profile

The focal point of the presented procedure are the referent mean lines, which are a basis for obtaining the primary

profile (step 6 and 7), the roughness profile (step 9 and 10) and the waviness profile (step 11), as well as for calculating the


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A New Approach in Measuring of the Roughness for Surface 43Constituted with Machining Process by Material Removal

corresponding parameters (P, R and W). The presented procedure employs multiple methods to determine the referent

mean lines, such as the least squares method, c profile filter and f profile filter.

Today there are several types ofc profile filters; however the standard Gaussian filter is mostly used. (Raja et al,

2002) analyze several profile filters (2RC, Gaussian, Rk, Spline, Robust spline, Gaussian regression, Zero-order Gaussian

regression, Second-order Gaussian regression, Robust Gaussian regression, Morphological and Wavelet-based filters) used

to measure surface roughness, pointing out its metrological characteristics, advantages and disadvantages. New filters

introduced by the ISO/TS 16610 standard series include: Gaussian filters (ISO 16610-21:2011), Gaussian regression filters

(ISO/TS 16610-31:2010), Spline filters (ISO/TS 16610-32:2009; ISO/TS 16610-22:2006), Spline wavelets (ISO/TS

16610-29:2006), Disk and horizontal line-segment filters (ISO/TS 16610-41:2006), Scale space techniques (ISO/TS

16610-49:2006) and Motif filters (under preparation). In order to remove the disadvantages (distortions at the ends of the

filter mean line obtained using the standard Gaussian filter) ISO/TS 16610-28:2010 recommends several ways to increase

the length of the primary profile length. Also ISO 13565-1:1996 recommends a special method of filtering of profiles with

deep valleys.

In order to obtain the roughness profile (separate it from the primary profile) the metrologist should choose one of

the above mentioned profile filters in step 9 of the procedure presented in Figure 1. A logical question at this point would

be: Which profile filter to select? The primary objective that the profile filters need to fulfill is to have the determined

mean line pass through the center of the irregularities comprising the profile through which the mean line passes.(Raja et

al, 2002,) in their research show that the disadvantages of the mean line determined with some profile filters are

accentuated in specific cases and directly depend to the shape of the total profile, i.e. the primary profile.

oday, the operator assesses the state (shape and character) of the primary profile qualitatively (high level of

waviness, low level of waviness, significant or insignificant end distortions etc.). This qualitative assessment of the

primary profile is based on the experience and the conviction of the operator that can lead to an inappropriate selection of a

profile filter type. But also, it is impossible to describe the state (shape and character) of the primary profile if used

measuring device which does not allow the graphical display of the primary profile (such as most of portabilnite devices).

Hence, the authors of this paper conclude that the qualitative assessment of the total or the primary profile should

be replaced with a parameter that will provide information about the irregularities on the total or the primary profile around

the mean line. To corroborate this way of thinking we note the a-priori accepted practice whereby the profiles obtained

from the surface are considered as stationary and ergodic random functions. According (John & Irwin, 1965), a stationary

function is any function that has the same statistical characteristics along its length, and a function is ergodic if the

temporal and statistical mean values between the stationary statistical ensembles (parts) are equal.

Therefore, the introduction of the new parameter will help link the state of the profiles obtained from topography

with the methodology for obtaining the parameter values, Figure 1, irrespective of whether they are parameters of the

primary profile, the waviness or the roughness profile, with an ultimate view to determining these parameters as accurately

as possible.

A NEW PARAMETER FOR THE STATISTICAL EQUALITY OF SAMPLING LENGTHS

To determine, whether a function is stationary and ergodic, or not, needs is the comparing the mean value

(statistical and temporal) for a certain part of the function (with exactly known size), with other parts of the same size.

From here, in further research will be used only methodology for determination, without to accept the condition of the


4/12


analyzed profile is stationary and ergodic function. If mentioned methodology is applied to the profile obtained by

measuring the surface topography and represented with discrete values in a reference system of coordinates, then the mean

value of a segment of the profile needs to have an approximately equal value to the values of other segments along the

profile.

The segments (parts) whose basic statistical characteristics will be compared to each other, are considered to

equal the sampling length rl , an already standardized value in ISO 4287:1997, with the use of the basic distribution

measures, i.e. mean arithmetic value, variation (dispersion) and the standard deviation.

For the purposes of deriving the mathematical formulation of the new parameter we will consider two theoretic

cases of scattering the irregularities around the mean line.

First case: The points used to represent the primary profile within the sampling lengths have different mean

values and approximately equal standard deviations, Figure 2.

Second case: The points used to represent the primary profile within the sampling lengths have approximately

equal mean values, and different standard deviations, Figure 3.

Primary profile

Sampling

length

x

zApproximately equal

standard deviations

Mean value of

primary profile

Different

mean value

Standard deviation of

primary profile

Evaluation length = 5 x Sampling length

Figure 2: First Case: Different Mean Values and Approximately Equal Standard Deviations

In practice, the real profiles obtained by measuring the real topography of surfaces usually exhibit irregularity

deviations which are a combination of the profiles from the first and the second case.

The primary profiles on Figure 2 and Figure 3 are presented on a Cartesian right oriented reference system where

the horizontal longitudinal axis is marked with x, while the vertical axis is the z-axis. The points used to represent the

primary profile with its evaluation length and the sampling lengths, as parts of the primary profile, shall be considered as a

sample, since they are a part (sample) of the points that can be used to represent the entire surface topography. The points

used to represent the entire surface topography shall be considered to be the population. Hence, the standard deviation for

n data points shall be marked with s , while the mean value for n data points shall be marked with z .

For graphical presentation of the standard deviations sizes of Figure 2 and 3 adopted is normal (Gaussian)

distribution, although there is a possibility where the distribution of irregularities, within the sampling lengths, is not

normal (be have another form).

In the first case the standard deviation determined for the primary profile shall be greater than the standard

deviations of the individual sampling lengths as a result of the scattering of the mean values of the sampling lengths around

the mean line (mean value) of the primary profile. The lower the scatter of the mean values of the sampling lengths, the


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lower the standard deviation for the primary profile will be, and it will converge to the standard deviation values of the

sampling lengths.

x

z

Mean value of

primary profileApproximately equal

mean value

Different standard

deviationsPrimary profile

Evaluation length = 5 x Sampling length

Sampling

length

Figure 3: Second Case: Approximately Equal Mean Values, and Different Standard Deviations

In order to describe this interdependence mathematically, we introduce the coefficient sK , which we propose to

calculate as follows:

2

2

p

ss

sK = (1)

where s is the standard deviation calculated as the mean value of the individual standard deviations within the

sampling length, while ps is the standard deviation calculated for the primary profile, i.e.:

5

25

24

23

22

212 sssss

s

++++

= (2)

...., 21 ss are standard deviations calculated within the sampling lengths. Equation 2 applies when the total profile

contains five sampling lengths, while if there are n sampling lengths2

s will be calculated as follows:

n

ssss n

222

212 ........+++= (3)

The standard deviations ...., 222

1 ss and2

ps , for n data points will be calculated as (ISO 13565-1:1996; Karl 1999;

Taylor & Cihon 2004):

( )2

1

2

1

1

=

=

n

ii zz

ns (4)

where z is the mean value of the points iz used to represent the profile, and if there are n points, it is calculated

as follows:

==

n

iiz

nz

1

1(5)


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Also, as can be seen from Equation 4, for determining the standard deviations adopted is to use a mathematical

formulation that is adequate for normal (Gaussian) distribution. This prerequisite is necessary, because, if adopted to check

the shape of the distribution of irregularities and the use appropriate mathematical formulation with accordance to the

determined form (type) of the distribution, the inevitable situation where will to compare the mean values obtained from

different mathematical formulations, which absolutely is not justified.

The value of the coefficient sK

will converge to one if the mean values of the sampling length data points are

equal or approximately equal with the mean value of the primary profile, provided that the sampling length data points

have equal or approximately equal standard deviations. The value of the coefficient sK

will converge to zero if the mean

values of the data points in the sampling lengths are significantly different from the mean value of the primary profile.

For the second case we propose to introduce a coefficient smK

which will be calculated as follows:

2

max

2min

2max

s

ssKsm

= (6)

where maxs is the value of the maximal standard deviation calculated within the sampling lengths, while mins is the

value of the minimal standard deviation calculated within the sampling lengths. The value of the coefficient smK will

converge to zero if there are no differences between the values of the standard deviations determined within the sampling

lengths. If the value of smK converges to one, then that means that there are large differences between the values of the

standard deviations determined within the sampling lengths.

The fact that real primary profiles are a combination of the two previously described elementary cases, suggests

that the expression of the scattering of the irregularities around the mean line, presented using points in a reference system,

requires the interdependence of the coefficients sK and smK .

Basically, the coefficient smK complements sK on two grounds. The introduction of smK removes the condition

that the values of the standard deviations within a given sampling length are approximately equal to each other. Secondly,

the value s is a mean value, which means that if the value of any standard deviation within a sampling length deviates

significantly from the others, its real impact will be reduced due to the averaging. It is also worth emphasizing that the

values that the coefficients sK and smK may have are inversely proportional, which means that for a primary profile where

the irregularities are evenly accumulated around the mean value (mean line), sK gets a value that converges to one, while

smK gets a value that converges to zero, and vice versa. As a consequence of the above, we propose to introduce a new

non-dimensional parameter called parameter of statistic equality of sampling lengths, denoted by SE, which will be

calculates as:

s

sm

K

KSE= (7)

In case of a primary profile where the irregularities are evenly accumulated around the mean value (mean line),

or, in other words, the data points within the sampling lengths have approximately equal statistic characteristics with each

other as well as with the primary profile, then the parameter SEwill have the following value:


7/12


-4

-3

-2

-1

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3 3.5 4

Gaussian mean linePrimary profile

Ks=0.99; Ksm=0.05;SE=0.05;

mm

m

-8

-6

-4

-2

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks= 0.96 Ksm= 0.19 SE=0,20

mm

m

01

0

s

sm

K

K( will go to zero)

In the opposite case:

0

1

s

sm

K

K

( will go to infinity)

The correlations describe above suggest that the parameter of statistic equality of sampling lengths SE is an

increasing parameter in the case of increasing scattering of the data points around the mean line.

VERIFICATION OF THE SE PARAMETER

The research regarding the verification of the SE parameter have been made using primary profiles obtained by

measuring etalon surfaces representing: turning (two surfaces with Ra=1.6 and 3.2 m), face milling (two surfaces with

Ra=1.6 and 3.2m), circular grinding (two surfaces with Ra=0.4 and 0.8m), polishing (two surfaces with Ra=0.1 and

0.2m), lapping (two surfaces with Ra=0.05 and 0.1m), super finish (two surfaces with Ra=0.025 and 0.05m), and a real

surface obtained with honing.

The real surface is obtained with the following conditions: material EN-GJL-250 (DIN EN 1561),n (rotation of

honing head)=60 rpm; f (feed of honing head)=40 double motion /min; four honing stones: C150/1I9V60 (grain size 150).

The value of the Ra parameter for etalon surfaces was used here solely to distinguish between different profiles from the

same cutting process.

The shapes of the primary profiles, as well as the calculated values for sK , smK and SEare shown on Figures 4,

5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. These Figures also show the Gaussian filter mean lines determined for the respective

primary profiles using Matlab (R2009b).

The weight function for the Gaussian filter is the mathematical formulation provided in ISO 11562:1996 and ISO

16610-21:2011. The surfaces were measured using a stylus measuring system MarSurf XR20, according to the procedure

shown in Figure 1. The nominal form was removed from the total profile using the least squares method.

Figure 4: Primary Profile, Gaussian Mean Line and Value

of the SE Parameter for the Etalon Surface Representative

of Turning, with Ra = 1.6 m.

Figure 5. Primary Profile, Gaussian Mean Line and Value of

the SE Parameter for the Etalon Surface Representative of

Turning, with Ra = 3,2m


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-5

-4-3

-2

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2


Ks=0.99 Ksm=0.46 SE=0.47

mm

m

-8

-6-4

-2

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.99; Ksm=0.17; SE=0.18;

mm

m

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.96 Ksm=0.39 SE=0.41

mm

m

-4

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.92; Ksm=0.48; SE=0.53;

mm

m

-1.6

-1.4

-1.2

-1

-0.8-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.41; Ksm=0.65; SE=1.59;

mm

m

DetailA

Detail

B

-2

-1.5

-1

-0.5

0

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.97; Ksm=0.41; SE=0.42;

mm

m

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.2 0.4 0.6 0.8 1 1.2


Ks=0.87; Ksm=0.60; SE=0.69;

mm

m

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.97; Ksm=0.41; SE=0.42;

mm

m



of Face Milling, with Ra = 1.6m

Figure 7: Primary Profile, Gaussian Mean Line and Valueof the SE Parameter for the Etalon Surface Representative

of Face Milling, with Ra = 3.2m



of Circular Grinding, with Ra = 0.4 m



of Circular Grinding, with Ra = 0.8 m



of Polishing, with Ra = 0.1 m



of Polishing, with Ra = 0.2 m

Figure 12 : Primary Profile, Gaussian Mean Line and Value


of Lapping with Ra = 0.05 m



of Lapping with Ra = 0.1 m


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-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.2 0.4 0.6 0.8 1 1.2

Gaussian mean line

Primary profile

Ks=0.59 Ksm=0.93 SE=1.58

mm

m

DetailC

DetailD

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1 1.2

Gaussian mean line Primary profile

Ks=0.84 Ksm=0.67 SE=0.80

mm

m

-1 2

-1 0

-8

-6

-4

-2

0

2

0 0.5 1 1.5 2 2.5 3 3.5 4


Ks=0.96; Ksm=0.97; SE=1.01;

mm

m

Detail E

Figure 16 : Primary Profile, Gaussian Mean Line and Value of the SE Parameter for the Real Surface Obtained

with Honing

The disadvantages of the Gaussian mean lines can be seen on the shapes shown on Figures 10, 14 and 16. Figure

10 (detail A and detail B), and Figure 14 (detail C and detail D) show notable distortions at the ends of the filter mean

lines, while Figure 16 shows that the filter mean line withdraws from the middle of the primary profile due to the deep

valleys, which is especially accentuated on Detail E. For the other profiles, the form of the filter mean line has no

disadvantages and passes through the middle of the irregularities.

An analysis of the calculated values of the SEparameter will show that its value increases in the event of an

increased scattering of the irregularities around the mean line. For the considered primary profiles where the mean lines

have disadvantages, the value of SE is greater than one or close to one. Hence, the authors think that one is the key value

of the SE parameter from the point of view of software filtration using a standard Gaussian filter.

For primary profiles where the value of SE is less than one, one should not expect any disadvantages of the mean

line determined using the Gaussian filter.

The example shown on figure 16 is characteristic. There the application of the filtering procedure prescribed in

ISO 13565-1:1996 is justified due to the deep valleys of the primary profile. To recognize such primary profiles the authors

propose the use of the value of the sK coefficient as an additional criteria.

Figure 14 : Primary Profile, Gaussian Mean Line and Valueof the SE Parameter for the Etalon Surface Representative

of Super Finish with Ra = 0.025 m

Figure 15 : Primary Profile, Gaussian Mean Line and Valueof the SE Parameter for the Etalon Surface Representative

of Super Finish with Ra = 0.05 m


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IMPLEMENTATION OF SE IN THE PROCEDURES FOR MEASURING SURFACE ROUGHNESS

Based on the value of the SE parameter, this paper proposes to expand the current procedure for obtaining the

primary profile, the roughness profile and the waviness profile, shown on Figure 1, with the algorithm shown on Figure

17.

The proposed algorithm includes feedback which facilitate the establishment of an additional verification of the

previously implemented steps as well as a mechanism for eliminating the possibility of errors by the metrologist.

For example, the SE parameter can have a larger value if the reference system used for the measurements is

inappropriately setup, which is especially accentuated in the case of cylindrical objects with small diameters, or in cases

where the nominal shape has been inappropriately removed.

The part of the algorithm shown on Figure 17, marked with dotted lines was introduced to the procedure to

facilitate the continuity to some follow-up investigations, primarily in the area of software filtering, since, according to the

established development framework, the investigations related to the ISO 16610 standard series have not been completed

by the working group, and also the part of newly introduced standards from the ISO 16610 series, until the time of these

investigations, have not been additionally confirmed.

Application of other profile filter (not

standard Gaussian) from ISO 16610-series

Whetherfilter mean

line hasdisadvantages

Roughness profile, step 10

Application of standard

Gaussian profile filter c

Calculation ofSE and Ks

No

Yes

Ks > 0. 9Application of the filtering procedure

ISO 13565-1:1996

Whether step

2 and 3 are correctrealized

Repetition of the measurement

procedure starting from step 2

Whether step6 is correct

realized

Repetition of the measurement

procedure starting from step 6

Application of one of the recommendationsgiven in ISO / TS 16610-28:2010

No

Yes

No

Ye s

Ye s

No

No

Ye s

Roughness profile, step 10

SE 1

Figure 17: Algorithm for Augmenting Step 9 of the Measuring Procedure Shown on Figure 1


11/12


CONCLUSIONS

- These investigations propose a new approach to the determination of surface roughness, where the choice of the

most appropriate profile filter directly depends on the shape of the primary profile. This paper proposes that the shape of

the primary profile should be determined quantitatively, instead of qualitatively (as the current practice), using the new

parameter of statistic equality of sampling lengths SE.

-The new SEparameter has been proven as a successful attempt to qualitatively determine the status of primary

profiles. The value of one was shown to be a significant value from the point of view of filtration using a Gaussian filter.

For primary profiles where the value ofSE is less than one, one should not expect any disadvantages of the mean line

determined using the standard Gaussian filter and vice versa.

- The proposed algorithm to expand the procedure for obtaining the primary profile, the roughness profile and the

waviness profile suggests a new approach to investigating surface topography, facilitated by the use of feedback loops,

which establishes an additional verification of the previously implemented steps as a mechanism to eliminate the

possibility of errors.

REFERENCES

1. Jiang, X., Scott, P. J., Whitehouse, D. J. & Blunt, L. (2007). Paradigm shifts in surface metrology. Part I.

Historical philosophy. Proc. R. Soc. A 2007 463, 20492070. (doi:10.1098/rspa.2007.1873)

2. Jiang, X., Scott, P. J., Whitehouse, D. J. & Blunt, L. (2007). Paradigm shifts in surface metrology. Part II. The

current shift. Proc. R. Soc. A 463, 20712099. (doi:10.1098/rspa.2007.1873)

3. Stanisaw A., Edward M., Franci .(2009).A model of surface roughness constitution in the metal cutting process

applying tools with defined stereometry. Journal of Mechanical Engineering 55(2009)1, 45-54. UDC 621.91

4. Edward M., ukasz N. (2012).Analysis and verification of surface roughness constitution model after machining

process.Procedia Engineering 39 (2012), 395-404

5. ISO 4287:1997; Geometrical Product Specifications (GPS) - Surface texture: Profile method - Terms, definitions

and surface texture parameters.

6. ISO 4288:1996; Geometrical product specifications (GPS) - Surface texture: Profile method - Rules and

procedures for the assessment of surface texture.

7. ISO 3274:1996; Geometrical Product Specifications (GPS) - Surface texture: Profile method - Nominal

characteristics of contact stylus instruments

8. ISO 11562:1996; Geometrical Product Specifications (GPS) - Surface texture: Profile method - Metrological

characteristics of phase correct filters

9. Raja J., Muralikrishnan B., Fu. Shengyu (2002). Recent advances in separation of roughness, waviness and form.

Elsevier, Precision Engineering. Journal of the International Societies for Precision Engineering and

Nanotechnology. 26 (2002), 222-235

10. ISO 16610-21:2011; Geometrical product specifications (GPS)-Filtration:Linear profile filters: Gaussian filters

11. ISO/TS 16610-31:2010; Geometrical product specifications (GPS)-Filtration: Robust profile filters: Gaussian

regression filters


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12. ISO/TS 16610-32:2009; Geometrical product specifications (GPS)-Filtration:Robust profile filters: Spline filters

13. ISO/TS 16610-22:2006; Geometrical product specifications (GPS)-Filtration:Linear profile filters: Spline filters

14. ISO/TS 16610-29:2006; Geometrical product specifications (GPS)-Filtration: Linear profile filters: Spline

wavelets

15. ISO/TS 16610-41:2006; Geometrical product specifications (GPS)-Filtration: Morphological profile filters: Disk

and horizontal line-segment filters

16. ISO/TS 16610-49:2006; Geometrical product specifications (GPS)-Filtration: Morphological profile filters: Scale

space techniques

17. ISO/TS 16610-28:2010; Geometrical product specifications (GPS) - Filtration - Part 28: Profile filters: End effects

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6.new approach

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