5th International DAAAM Baltic Conference
“INDUSTRIAL ENGINEERING – ADDING INNOVATION CAPACITY OF LABOUR
FORCE
AND ENTREPRENEURS”
20–22 April 2006, Tallinn, Estonia
THREE-DIMENSIONAL ROUGHNESS ANALYSES FOR
AIR COMPRESSOR CYLINDERS
Rudzitis, J., Torims, T., Konrads, G., Shperbergs, J.
 – slope module; S – surface area; V –
volume of irregularities.
We have obtained equations for mathematical expectation for mentioned parameters
in the way similar to presented below for
some parameters.
Abstract: The present surface roughness
research is based on machine parts surface
cross section profile analysis. But in
practical applications machine parts
surface roughness behaves as a 3D object.
Therefore it is necessary to create a new
theoretical and practical basis for machine
parts surface assessment as a 3D quantity.
This paper contents investigation of 3D
surface parameters, characterizing height
and spacing of surface roughness
irregularities, description of the 3D
measurement system and air compressor
cylinders surface analysis.
It is found that Air Compressor Cylinders
surface roughness can be presented by
mean arithmetic deviation of surface and
mean spacing between peaks in two
perpendicular directions of surface.
These parameters are relatively convenient
for measurement using standard equipment
and are easily reproduced in manufacturing practice.
1.1.Mean arithmetic deviation of surface
Major parameter of surface roughness
describing height properties of surface, is
the average roughness.
Ra 
1
h( x, y) dxdy ,
A 

where h(x, y) – deviation of surface from
least squares mean surface; A – size of an
investigation area . If to designate
g  h( x, y) , mathematical expectations Ra
for surface and profile are identical, as
ERa 

1
dxdy gf ( g )dg ,
A 

0
where f(g) – density function of absolute of
the deviation of the surface from mean
surface. We obtained
Key words: 3D surface roughness,
parameters, Cylinders of Air Compressor.
ERa 
1. THEORETICAL RELATIONS FOR
3D ROUGHNESS ASSESSMENT
2

.
1.2.Relative bearing area
A relative bearing area at level u we
shall understand the ratio of the total
platforms of cut of surface at level u
form least squares mean surface over
nominal area A considered:
Let normal homogeneous random field h(x,
y) describes rough surface. On the basis of
its continuity we can specify commonly
used roughness parameters:
Ra – mean arithmetic deviation of surface;
u – relative bearing area; Nv – density of
summits; Hm – average peak height; kx,
ky – mean summits curvature along “X”
and “Y” axes; kv – full summits curvature;
u 
1
 (h, u )dzdy ,
A 

where  (h, u) – variable depending on
surface height and level u measured from
mean plane, as follows:
163
E u  
1
u
E (h, u )dxdy  1     ,
A 
 

where  ( x) 
x
1
2
e
t 2
2
dt
For a detailed study a measuring system
has been elaborated which consist of a twocoordinate table. A counter and a connecting block integrating this system with a
computer into a common mathematical
software circuit.
Such a system ensures 3D recording of
roughness and surface micromap in terms
of isoline tops and the numeric values of
tops and steps as well as shape parameters
of asperities.
– function of

Laplace.
1.3.Other parameters
Mathematical expectations for
parameters [Rudzitis J., 1992]:
EN v   c
other
2
E 2 m1 ;
3 3
1
1
Ek v   Ek x  E k y   2E 2 n1 01  c 2 
2
2

E h  
 




3. DESCRIPTION OF THE
MEASUREMENT SYSTEM

En1 0  1  c 2 ;
2
2 2 2
ES   1 
 E n1 01  c 2 ;
2
2
1  2
E V  
e
  1     ,
2

For verification of theoretical equations the
three-dimensional measurement system has
been used.
The 3D system is composed of following
three parts:
– The mechanical structure including two
step motors, a support with setting and
adjusting screws with an inductive sensor,
stage (X-Y), gearbox, column stand;
– The electronic part including a
transducer, a frequency filter, a digitization
and amplification circuitry. This unit
receives the output signal from the sensor
and transforms it into a form necessary to
the computer to receive it, as well as
controls the step motors.
– The computer which is used to control all
operating
procedures,
to
calculate
parameters and to display drawings and
results into the memory of PC.
The system is capable of dealing separately
with roughness, waviness, summary
surface and also showing them by means of
graphical images.
For this purpose, the user, in a dialogue
mode, sets the filter size Fx and Fy along x
and y-axes. Then the surface roughness rij
at point hij is determined as difference
between the height measured at this point
and the mean height of the nearest ij
points:

where c – surface anisotropy ratio; m1 –
profile peak density and n1 – profile zerocrossing density in x direction respectively;
 – surface texture parameter;  – root
mean square deviation of a surface,  –
normalized surface section level, () –
function of the Laplace.
2. METHODS OF EXPERIMENTAL
MICRO-TOPOGRAPHIC
REGULARITIES DETERMINATION
Surface roughness parameters can be
obtained by sectional methods. For a
general
profile
anisotropic
surface
determination five sections are sufficient
with a definite orientation from x axis. ,
n(0), m are determined by section  = 0
and n(0) and m are determined by  = 45;
90 and m by  = 30 and 135 (n(0) and m
are the numbers of zeroes and maxims for
a unit of route length). Microtopographical parameters can by calculated
on the basis of the initial parameters drawn
from the sections. Directional anisotropy
rough surfaces contain their man
information across three sections with the
angles 0, 30 and 60 to x axis. Isotropic
surfaces contain all their information in
one randomly orientated section.
Fx Fy
rij  hij 
164
hij

i 1 j 1
Fx  Fy
material, metal, plastic, wooden etc. items
and machine parts), in medicine it cold be
dermatological investigations, in biology,
for example, plant surface investigations,
in criminology – dactiloscopy and other
fields.
4. BORE SURFACE ANALYSIS
Specimens of air compressor cylinder
surface were tested by above-mentioned
system. Total scanned area is square
3.23.2 mm for all specimens. Tests were
managed and test data processed by system
software, developed in the Riga Technical
University. Results are placed in Table 1.
6. REFERENCES
Rudzitis J. Surface Roughness Topography
Investigations. Proceedings of the VIII.
Internationales Oberflächen Colloquium,
1992, February 3-5, Chemnitz. TU
Chemnitz, 1992.
4.1. Parameter values
Specimen
No
1
2
3
4
5
Surface roughness parameters
Ra,
Nv, Km, Kx, Ky, 10,
m 1/m2 1/m 1/m 1/m %
0.22 90.62 0.84 1.65 0.03 51
0.36 103.20 0.67 1.32 0.02 62
0.65 100.00 2.49 4.87 0.11 34
0.28 112.50 1.68 3.31 0.05 38
0.38 121.88 1.28 2.51 0.05 58
7. CORRESPONDING AUTHOR
Janis Rudzitis, Prof., Dr.habil.Sc.ing.
Riga Technical University, Institute of
Mechanical Engineering
Address: 1 kalku Street, Riga, PDP, LV1658, Latvia
Phone: +371 9425510; Fax: +371 7089701
E-mail: arai@ latent.lv
Table 1. Test results.
4.2. Graphical presentation of test
results
Fig. 1. View of measured surface.
5. CONCLUSION
The difference between proposed 3D
system and current profile analysis is based
firstly on use of another datum – plane
instead of line and secondly on another set
of parameters, describing area features of
asperities. The system can be used in any
field where machine parts quality is an
important issue. In industry it is surface
microgeometry investigation (composite
165
166