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Once the prototypes were manufactured, effective rough-
ness was measured with a Taylor–Hobson form Taylsurf
series 2 profile rugosimeter. In order to evaluate surface
roughness, seven positions depending on the angel has been
selected on the cylindrical surface of the manufactured
parts as Fig. 4 shows. Afterwards, the Ra parameter was
determined as the average value of the seven roughness
measurements carried out along the Y-axis, in the positions
shown in Fig. 4. An evaluation length of 4.8mm (6mm ×
0.8mm) was used, and a nominally 2m stylus tip was
used in conjunction with a 0.8 Gaussian cut-off filter and a
bandwidth ratio of 300:1 to evaluate the Ra parameter.Fig. 4. Positions in which the measurements were performed (semi-circle
of radius = 20mm).
A stylus speed of 0.5mm/s was used in conjunction with
a 0.8mN static stylus force and the stylus cone angle used
was 90◦.
Fig. 5 shows the rugosimeter used in the experiments. The
uncertainty of the rugosimeter is given, from the certificate
of calibration of the manufacturer, by ± (0.004m + 2%)
Ra. Therefore, it is clear that it has no sense to use, for finalexpression of the roughness values, as many digits as Table 2
shows.
Nevertheless, for intermediate calculations, it is very use-
ful to have as many digits as possible because of round er-
rors and hence, we have used five digits for intermediate
calculations and for developing the roughness models. For
final expression of the roughness values, only one signifi-
cant digit will be used.
The roughness parameter which was selected as a tech-
nological response variable, defined in accordance with the
UNE-EN-ISO 4287:1999 norm, was that of the arithmetic
average roughness of the evaluated roughness profile (Ra),
as is shown in Eq. (1). This definition is set out in Eq. (1),
where Z(y) is the profile values of the roughness profile and
lr is the evaluation length.
This roughness parameter is the one which has had the
widest diffusion and which is generally most widely used,
as practically all types of measuring equipment have this
implemented in its configuration. For these reasons, it will
be this one which is studied in this current work.
3. Design of the experiment
The design of experiments technique is a powerful work
tool, which permits us to carry out the modelling and anal-
ysis of the influence of determined process variables over
Table 1
Factors and levels selected
Level Ad (mm) Rd (mm) fz (mm/z) Vc (m/min)
Minimum 0.1 0.1 0.02 150
Maximum 0.3 0.3 0.06 250other specified variables, which are usually called response
variables. This response variable is an unknown function of
the former design variables, which are also known as design
factors.
Although there are various types of DOE that can be con-
sidered, we are going to use factorial design in this work as
it permits us to experiment with all combinations of vari-
ables and levels.
As mentioned earlier, and in accordance with the bibli-
ography consulted, as well as drawing from personal expe-
rience, the design factors selected for this study were: ax-
ial depth of cut (Ad), Y-axis radial depth of cut (Rd), feed
per tooth (mm/z) (fz), and cutting speed (Vc). Before us-
ing the DOE cutting conditions (finishing stages) the part
have been rough machined and heat treated. After wards,
a semi-finished machining is performed leaving an uniform
stock thickness which is removed using the experiment cut-
ting conditions.
So, the design which was finally chosen was a first fac-
torial design 24 with four central points, which allow us to
check if there is curvature in the first-order model, conse-