**1. Analisi del contesto interno in una prospettiva evolutiva**

**1.5 Livello di attuazione e sviluppo del lavoro agile nella fase emergenziale e post-emergenziale**

One of the reasons to apply beam integrators for laser cladding, is to attain a more homogeneous temperature distribution over the width of the tracks. It is sufficient to homogenise the laser beam in the lateral direction only.

The developed line integrator, which is shown schematically in figure 4.3, con-sists of three parts. All will be discussed in the order in which the laser radia-tion travels through the system.

1. Telescopic system consisting of two spherical mirrors

The laser beam must be parallel when arriving at the faceted mirror.

This is achieved by using a spherical convex mirror and a spherical
concave mirror respectively. The system can be adjusted to CO_{2} laser
sources with a different beam divergence by changing the distance
be-tween these two mirrors.

The second function of the telescopic system is the enlargement of the
beam diameter. Firstly, higher laser powers can be utilised, because this
reduces the power density on the mirrors. Secondly, the segmented
*mir-Fig. 4.3 Schematic lay-out of the line integrator.*

ror is filled by a larger beam. Hence, more small beamlets can be made which results in a better homogeneity in the line shape.

2. Cylindrical mirror

The parallel beam is focused in the meridional plane by means of a cy-lindrical mirror. The curvature of this mirror and the distance to the workpiece determine the spot length in the traverse direction.

3. Segmented mirror

The final function, i.e. “integration” in the sagital plane is achieved by means of a segmented mirror. This mirror consists of eight segments positioned in mutually different angles. The laser beam is split into sev-eral beamlets by this mirror and recombined by overlap in the focal plane. A proper choice of the angles under which the segments are po-sitioned, assures that a spot with a laterally homogeneous energy dis-tribution is attained. The principle of beam integration by means of a segmented mirror is illustrated in figure 4.4.

The optical system was designed with the computer programme OPDESIGN.

This software allows the analysis of optical systems and was developed by Beckmann [1991]. Based on the configuration of an optical system (curvature of optical elements, distance between elements, angle of incidence, wavelength of radiation, etc.) the programme calculates the path of a number of rays through the entire system. The beam shape at the exit of the optical system can be studied in the desired plane of reference.

The cylindrical mirror and the segmented mirror manipulate the beam in differ-ent planes. Hence, the spot length and width are decoupled. The goal of the op-timisation of the optical system with OPDESIGN is the achievement of a line fo-cus in the sagital plane which position agrees with the focal point in the meridi-onal plane. The line focus has the desired shape, if the aberrations in the

*sagi-Fig. 4.4 Principle of beam integration by means of a segmented*
*mirror. The parallel laser beam is split into beamlets by the *
*seg-ments and recombined in the focal plane.*

tal plane form a line with the centre on the optical axis. The length of the line approximates the segment width. The analysis with OPDESIGN has resulted in the optical system which is shown in table 4.1, figure 4.5 and 4.6.

*Tab. 4.1 Parameters of the developed line integrator (surface 1: convex spherical*
*mirror; surface 2: concave spherical mirror; surface 3: concave cylindrical mirror;*

*surface 4: segmented mirror with 8 segments).*

Surface radius [dm]

distance to next surface [dm]

tan(tilt of surface)

1 1.86209 -2.16388 -0.22170

2 6.16595 2.00000 0.18534

3 -12.5000 -> toric surface meridional curvature and radius -0.24008 3 infinite -> toric surface sagittal curvature and radius

3 -2.30000

4 - x - 3.65016 0.27732

segment no. lower height [dm] tangent of segment angle 0

1 2 3

0.00000 0.07500 0.14999 0.22497

0.00556 0.01669 0.02781 0.03892

*Fig. 4.5 Dimensions [mm] of the line integrator in the meridional plane.*

The shape of the manipulated laser beam in the focal region can be seen in fig-ure 4.7 and table 4.2. The beam converges in front of the focal point for both the meridional and the sagital directions. The focal point for the sagital direc-tion is posidirec-tioned 10 mm in front of the focal point of the meridional plane.

The dimensions of the line spot are sensitive to a variation in distance to the
workpiece (figure 4.8 and table 4.2). Hence, it is possible to adjust the power
density in the line spot. The smallest line spot has an area of 0.3 x 9.1 mm^{2},
whereas the area at a distance of 10 mm from the meridional focal point
amounts to 1.1 x 7.8 mm^{2}.

*Fig. 4.6 Path of the rays in the line integrator.*

*Fig. 4.7 Shape of the line source around the focal point.*

The results presented so far proceed from calculations based on ray tracing.

Apparently, the energy distribution over the line width should be homogeneous.

This suggestion has been verified by calculating the energy distribution in the
focal plane (figure 4.9). The calculations were performed under the assumption
of a Gaussian laser beam. That intensity profile is a worst case situation. Figure
4.9 shows that the attained energy distribution is rather uniform indeed
be-tween the sagital focal point and about 10 mm behind it. In the focal point the
*Tab. 4.2 Dimensions of the line in the focal region. The focal plane off-set is *
*rela-tive to the focal point in the meridional plane.*

**focal plane**

*Fig. 4.8 Course of the length of the line shape in the traverse direction*
*around the focal point in the meridional plane.*

two peaks in the energy distribution are less than 10% higher than the average value. At larger distances from the focal point the edge of the line source be-comes less well defined.

The calculated laterally homogeneous energy distribution could be confirmed by measurements. The measured distribution is shown in figure 4.10. The peaks that can be noticed are interference patterns. The occurrence of these peaks can be prevented by the intentional introduction of small errors in the segmented mirror. Especially small changes of the angles under which the segments are positioned, are effective [Beckmann, 1995].

The temperature distribution that is achieved with the obtained line spot is shown in figure 4.11. These temperature distributions were calculated with the

*Fig. 4.9 Energy distribution along the line source in the sagital plane*
*around in the focal point in the sagital plane (figures on different scale!).*

*Fig. 4.10 Measured energy distribution in the line spot.*

numerical method described in chapter 3. The calculations were performed for
three different line dimensions that all have a homogeneous energy distribution
in the lateral direction: 0.3 x 9.1 mm^{2} (smallest area), 0.6 x 8.3 mm^{2} (average)
and 1.1 x 7.8 mm^{2} (largest area). The distribution in the other direction was
as-sumed to be Gaussian. As can be seen, the attained temperature distribution
over the line width is quite constant for all three line shapes. The temperature
on the surface can be varied with a factor two by only changing the distance
between integrator and workpiece.

The maximum temperatures that are attained according to figure 4.11 are quite low. Depending on the applied line configuration they vary between 1148 and 2421 °C. This is due to the low absorption of laser energy in the base material with this line integrator. When applying the laser system’s maximum output power of 1800 W, surprisingly only 8 % of the supplied laser energy is effec-tively coupled into the irradiated material. Due to this low energy efficiency no melt pool could be formed. Therefore, this line integrator could not be used for laser cladding in the author’s laboratory. The experiments on laser cladding with preplaced powder and powder injection that are discussed in the following chapters are therefore performed with ordinary optics.

*Fig. 4.11 Temperature distributions for three different line shapes. Left: *
*tem-perature contours on surface; Right: temtem-perature distribution along line width;*

*Material: C45; Absorbed laser power: 150 W; Feed rate: 5 mm/s.*