BCA86

Very often beam diameter is represented as diameter of 1/e²=0.135 times of total power when Gaussian beam profile (TEM00) is discussed. This diameter contains 86 % of all highest laser power (Steen, 1991; Siegman, 1997). Beam cross-section area (BCA86) means that cross-section area of laser beam where beam hits sample top surface and cross-section area contains 86 % of the beam power. Figure 39.6 shows definition of BCA86. Appendix 7 illustrates beam profiles, cross-sections and beam caustics measured with beam profile analyser. Table 39.7 shows how BCA86 is calculated.

BCA

BCA ICA Laser beam

Table 39.5 Calculation of BCA.

Test ID Laser power, W

Focal plane position, mm

Radius of beam, µm

Radius of beam, mm

Area of

beam, mm² BCA, mm² 1 139 3.0 258.0 0.2580 0.2091 0.2091 2 145 2.0 175.0 0.1750 0.0962 0.0962 3 139 1.0 124.0 0.1240 0.0483 0.0483 4 142 0.0 68.7 0.0687 0.0148 0.0148 5 140 -1.0 72.8 0.0728 0.0167 0.0167 6 264 3.4 252.0 0.2520 0.1995 0.1995 7 266 2.4 194.0 0.1940 0.1182 0.1182 8 264 1.4 133.0 0.1330 0.0556 0.0556 9 266 0.4 81.2 0.0812 0.0207 0.0207 10 268 -0.6 74.0 0.0740 0.0172 0.0172 11 384 3.5 251.0 0.2510 0.1979 0.1979 12 387 2.5 180.0 0.1800 0.1018 0.1018 13 384 1.5 121.0 0.1210 0.0460 0.0460 14 384 0.5 69.5 0.0695 0.0152 0.0152 15 386 -0.5 74.8 0.0748 0.0176 0.0176 16 494 3.8 248.0 0.2480 0.1932 0.1932 17 494 2.8 180.0 0.1800 0.1018 0.1018 18 494 1.8 118.0 0.1180 0.0437 0.0437 19 503 0.8 68.8 0.0688 0.0149 0.0149 20 503 -0.2 79.3 0.0793 0.0198 0.0198 Table 39.6 Example of definition of BCA86.

Laser power, W 139

Focal plane position, mm 3

Definition of BC86A

BCA86

Table 39.7 Calculation of BCA86.

Beam cross-section area of highest intensity BCAImax and beam cross-section area of lowest intensity BCAImin are defined in table 39.8.

Appendix 7 illustrates beam profiles, cross-sections and beam caustics measured with beam profile analyser. Table 39.9 shows how BCAImax and BCAImin are defined.

39.7 PImax and PImin

Highest intensity of BCAImax is called PImax and lowest intensity in BCAImin is determined to be PImin. These values can be defined as table 39.10 shows.

39.8 Pmax and Pmin

Laser power in BCAImax and BCAImin was decided to use to describe PImax and PImin in BCAImax and BCAImin. Pmax is calculated as equation 39.1 shows.

BCA ax

PI

P_max _max _Im (39.1)

where Pmax laser power in BCAImax, W.

Table 39.8 Example of definition of BCAImax and BCAImin. Laser

power, W 139 503

Focal plane position,

mm

3 -0.2

Definition of BCAImax

and BCAImin

Pmin is determined according to equation 39.2.

BCA in

PI

P_min _min _Im (39.2)

where Pmin laser power in BCAImin, W.

Pmax and Pmin are calculated as equation 39.1 and 39.2 shows in table 39.11.

39.9 Fluence

As different pulse lengths were used, pulse energy was determined first, as equation 39.3 shows.

pulse laser pulse t

E P (39.3)

where Epulse pulse energy, J Plaser laser power, W tpulse pulse length, s.

PImin

PImax

PI_min PI_max

7.55 MW/cm²

BCA_Imin BCA_Imax

BCA_Imin BCA_Imax

When pulse energy is divided by BCA, fluence can be calculated as equation 39.4 shows.

Table 39.11 Definition of Pmax and Pmin.

Appendix 9 shows calculation of fluence values used in this study.

40 I-O parameters used in analysis of interaction of laser beam and paper material 40.1 Maximum spectral intensity

Spectrometer is used to analyse intensity of radiation emitted by laser beam and paper material interaction over wavelength range of 194-652 nm. Unit of intensity is expressed as Au (arbitrary unit). Appendix 10 shows an example of spectrometer measurement.

Maximum spectral intensity was determined to be the highest value of intensity of emitted radiation during measurement over whole wavelength range.

As each laser power, focal plane position and pulse length parameter combination was repeated four times (see appendix 6), so there were also four different spectrometer measurements. Average of four repeats was calculated for further analyses for this thesis.

It was noticed by Piili (Piili, 2009) that this maximum spectral intensity peak appears always in wavelength of 588-589 nm. This study was carried out with copy paper. This is in range of yellow light, so it refers to maximum spectral intensity appearing in the range of yellow light. This

intensity peak is also detected with different laser processes, for example in studies of laser additive manufacturing of ceramic materials (Taimisto et al., 2011) and laser additive manufacturing of metallic materials (Lehti et al., 2011). So this refers to the fact that appearance of peak intensity in range of wavelength 588-589 nm is not related to material or to laser process.

40.2 Maximum temperature

Pyrometer is used to analyse interaction temperature during laser beam and paper material interaction. Pyrometer is capable of measuring temperatures above 488°C. Appendix 11 shows example of pyrometer measurements.

Maximum temperature was defined to be highest temperature during measurement.

Each laser power, focal plane position and pulse length parameter combination was repeated four times (see appendix 6), so there was as well four different pyrometer measurements. Average of four repeats was determined for further analyses for this thesis.

40.3 Hole area

Table 37.2 shows all radius measurements done in this thesis for all samples and figure 37.1 illustrates how hole radius was defined from macrographs. Radius of hole was measured from top and bottom side of each sample. Hole area was calculated from radius measurement as equation 40.1 shows.

AH = π rH2 (40.1)

where AH hole area, mm² rH radius of hole, mm.

41 Variables created to analyse interaction of laser beam and paper material 41.1 HAZ

It was decided to determine in this thesis the area of heat impact of laser treatment for dried kraft pulp, since it describes quality of laser beam and paper material interaction and gives numerical value of quality. Hole area expresses the area of laser treatment but it is not describing quality at all.

The heat-affected zone (HAZ) is usually determined in manufacturing technology as the area of base material, either a metal or a thermoplastic, which has had its microstructure and properties altered by thermal processing like welding or heat intensive cutting.

When macrographs were analysed it was noticed that there is clear area of black debris recognisable by its colour around every hole referring to thermal impact of laser beam and paper material interaction. Table 41.1 shows examples of these areas of black debris.

Radius of this so called heat impact zone was measured for top and bottom side of each sample, as table 37.2 and figure 37.2 represents (see table 41.2). This heat impact zone which also consists of area of hole itself is expressed as HIZ. Area of heat impact zone was calculated from radius measurement as equation 41.1 shows.

Table 41.1 Examples of areas of black debris in laser treated dried kraft pulp (top side).

Laser power, W 139 266 503

Focal plane

position, mm 3.0 2.4 -0.2

Pulse length, ms 40 40 10

Macrograph

Area of black debris

AHIZ = π rHIZ2

(41.1)

where AHIZ area of HIZ, mm² rHIZ radius of HIZ, mm.

Area of hole AH and area of heat impact zone AHIZ were calculated as equations 40.1 and 41.1 shows. Table 41.2 shows these values with macrographs.

Table 41.2 Example of definition of AH and AHIZ in laser treated dried kraft pulp (top side).

Laser power, W

139 266 503

Focal plane position, mm

3.0 2.4 -0.2

Pulse length, ms

40 40 10

Definition of AH and AHIZ

Ainner

A_outer

A_H A_HIZ

A_inner

A_outer

A_H

A_HIZ

A_inner A_outer

A_H A_HIZ

Area of HAZ AHAZ in this thesis was defined as equation 41.2 shows.

AHAZ = AHIZ – AH (41.2)

To be able to get such HAZ value which is independent of hole area, AHAZ was divided by hole area and multiplied with 100 %. Unit of HAZ is percent (%). Equation 41.3 shows this calculation.

%

100



H HAZ

A HAZ A

(41.3) where HAZ heat affected zone in paper material, %

AH hole area, mm².

Figure 41.1 shows difference of small HAZ and large HAZ.

As figure 41.1 shows, small HAZ value refers to fact that area of heat impact zone around hole is small and respectively large HAZ refers to large area of heat impact zone around hole.

41.2 ΔHAZ

It was also decided to create value of ΔHAZ to be second parameter to describe quality of result of laser beam and paper material interaction. ΔHAZ in this thesis is describing difference between HAZ in top side of material and bottom side of material as equation 41.4 illustrates.

Figure 41.1. Diagram of small and large HAZ values and their effect on hole formed during laser beam and dried kraft pulp interaction.

ΔHAZ = HAZtop - HAZbottom (41.4) where ΔHAZ difference between HAZ in top side of material and bottom side of

material, %

HAZtop HAZ in top side of material, % HAZbottom HAZ in bottom side of material, %.

Figure 41.2 illustrates difference between large and small ΔHAZ value.

Figure 41.2 shows that ΔHAZ values close to zero relate to small area of heat impact zone in top and bottom side of pulp. When ΔHAZ values smaller than zero are considered, they relates to large area of heat impact zone in bottom side of material. Accordingly, ΔHAZ values larger than zero refer to large area of heat impact zone on top of material.

41.3 Conicality

Conicality was determined to be third value to describe quality of result of laser treatment, namely conical characteristics of holes. Figure 41.3 shows diagram of conicality.

Conicality was calculated as relation between hole area in top side of sample and hole area in bottom side expressed as percentage (see equation 41.5).

%

100



HB H

A

Conicality A (41.5)

where Conicality conicality, %

AHB hole area in bottom side, mm².

Figure 41.2. Diagram of small and large ΔHAZ values and their effect on hole formed during laser beam and dried kraft pulp interaction.

Figure 41.3 illustrates difference between large and small conicality value.

Figure 41.3 illustrates that when value of conicality is near 100 %, shape of hole in dried pulp is cylinder with straight walls. If concicality is much larger than 100 %, shape of hole is V-shaped cone and correspondingly if conicality is much lower than 100 % shape of hole is A-shaped cone.

Figure 41.3. Diagram of small and large conicality values and their effect on hole formed during laser beam and dried kraft pulp interaction.

41.4 BHR100

Beam-hole-ratio BHR100 was calculated for BCA which has 100% of all laser power for the purpose being able to define ratio between BCA and hole area produced during interaction of laser beam. BHR100 is determined as equation 41.6 illustrates.

% 100

100 

AH

BHR BCA (41.6)

where BHR100 beam-hole-ratio for BCA, %.

Figure 41.4 illustrates difference between large and small BHR100 value.

Figure 41.4 illustrates that when BHR100 is close to zero the hole area formed is much bigger than BCA. As BHR100 approaches 100 %, the hole area is equal to BCA.

41.5 BHR86

Beam-hole-ratio BHR86 was defined similarly as BHR100 but instead of BCA the value used was BCA86. BCA86 is a beam cross-section area which has 86% of all laser power. BHR86 is calculated as equation 41.7 illustrates.

Figure 41.4. Diagram of small and large BHR100 values and their effect on the hole formed during laser beam and dried kraft pulp interaction.

% 86 100

86 

AH

BHR BCA (41.7)

where BHR86 beam-hole-ratio for BCA86, %.

Figure 41.4 shows also difference between large and small BHR86 value.

41.6 BIR

When empiric data was analysed, it was concluded that value to define ratio of beam cross-section area (BCA) of highest intensity BCAImax to beam cross-section area of lowest intensity BCAImin

should be created. This value is called BIR (Beam-Intensity-Ratio). Equation 41.8 shows how BIR-value is then calculated.

% 100

Im

Im 



in ax

BCA

BIR BCA (41.8)

where BIR beam intensity ratio, %.

Figure 41.5 shows difference between large and small BIR value.

Figure 41.5. Diagram of small and large BIR values.

Figure 41.5 represents that if BIR approaches zero BCAImax is remarkably smaller than BCAImin. When BIR increases, BCAImax also increases i.e. it approaches BCAImin.

42 Effect analyses of I-I, I-O and PI-O parameters

To be able to analyse interaction between laser beam and paper material (see figure 34.1) and to understand effect of I-I, I-O and PI-O parameters to the whole process, concept of effect analyses was created for this thesis. Term effect analyses means analyses group of:

- DP/IP (direct proportionality/inverse proportionality) analysis,

- this analysis is introduced to examine direct/inverse proportionality of input and output parameters of interaction of laser beam and paper material.

- correlation analysis

- this analysis was carried out to determine best correlations of input and output parameters between each other i.e. which parameters have significant effect on each other.

- dependence analysis.

- this analysis was executed to understand dependence and its characteristics of input and output parameters of interaction.

Diagram of these analyses created for this thesis are shown in figure 42.1 and it is executed for all tested parameters in this thesis.

Based on figure 34.1, an analysis system of I-I parameters to I-O parameters and PI-O parameters was developed for this thesis to be able to carry out effect analyses (see figure 42.1).

Analysing the effect of every parameter to each other was done by grouping table 42.1 into smaller groups of:

- I-I, I-O and PI-O parameters and - I-O and PI-O parameters.

Figure 42.1. Diagram of effect analyses.

Table 42.1 Analysis system for effect analyses of I-I, I-O and PI-O parameters.

I-I parameter

I-O parameters PI-O parameters

I-O parameters Maximum spectral

42.1 Analysis system of I-I, I-O and PI-O parameters

First part of effect analyses concentrates to evaluation of I-I parameters to I-O and PI-O parameters.

This is shown in table 42.2.

Table 42.2 Analysis system to analyse I-I, I-O and PI-O parameters.

I-O parameters PI-O parameters Maximum

HAZ ΔHAZ Conicality

I-I

As can be seen from table 42.2, it was decided to use fluence as I-I parameter, since it is a combination of all three I-I parameters, laser power, pulse length and focal plane position, as equation 39.4 shows. Maximum spectral intensity and maximum temperature were chosen as I-O parameters, because they are clear, definable and natural variables to describe data collected by spectrometer and pyrometer during interaction of laser beam and paper material. Hole area, HAZ, ΔHAZ and conicality for their part were determined to be PI-O parameters since they describe most effectively properties of result of interaction of laser beam and paper material.

Effect analyses of I-I, I-O and PI-O parameters was divided to subgroup analysis of average laser power, pulse length and average focal plane position.

This way all I-I parameters are included to parameters analysis. So detailed analysis system for effect analyses is described in table 42.3.

Table 42.3 Detailed analysis system of I-I, I-O and PI-O parameters.

I-O parameters PI-O parameters Maximum

42.2 Analysis system of I-O parameters and PI-O parameters

It was decided to evaluate also I-O and PI-O parameters. Table 42.4 illustrates set-up of this analysis.

Table 42.4 Analysis system of I-O and PI-O parameters.

I-O parameters PI-O parameters Maximum

This analysis system was also determined to be divided into analysis of subgroups of average laser power, pulse length and average focal plane position. Detailed analysis system to study effect of I-O and PI-O parameters is described in table 42.5.

Table 42.5 Detailed analysis system to analyse I-O and PI-O parameters.

I-O parameter PI-O parameter

42.3 DP/IP analysis of I-I, I-O and PI-O parameters

DP/IP (direct proportionality/inverse proportionality) analysis was introduced to be able to understand direct/inverse proportionality of input and output parameters of interaction of laser beam and paper material.

As linear trend line was fitted to parameters data points, an equation of linear dependence for each parameter combinations was defined. This equation was determined by Excel spreadsheet program and an option of linear line fitting and corresponding equation was chosen. General equation of linear line is shown in equation 42.1.

y = kx + b (42.1)

Equation 42.1 can be written also as function as equation 42.2 presents.

f(x) = kx + b (42.2)

As x is set to be zero x = 0, point where fitted linear line crosses y-axis, namely f(0), can be defined as equation 42.3 illustrates.

f(0) = b (42.3)

Direct/inverse proportionality can be defined, when these f(0) values are calculated to each parameter combinations shown in tables 42.3 and 42.5 and they are compared to each other.

Appendix 12 shows an example of this calculation and DP/IP analysis.

Table 42.6 shows the system of marking direct/inverse proportionality.

Table 42.6 Marking of direct/inverse proportionality.

Proportionality Sign Direct proportionality  Inverse proportionality  No proportionality * 42.4 Correlation analysis of I-I, I-O and PI-O parameters

Correlation analysis was carried out to be able to define which input and output parameters coming from DP/IP analysis have the best correlation between each other i.e. which parameters have significant effect on each other.

Correlations were defined by Excel spreadsheet program by fitting linear trend line to parameter data points shown in table 42.1. When fitting trend lines an option of linear line fitting and R² value representing correlation was chosen.

Correlation determination was carried out to each parameter combinations shown in tables 42.3 and 42.5. Correlations were compared and evaluated with a system shown in table 42.7.

Table 42.7 Correlations and their descriptions.

Correlation R², - Description R² < 0.10 Very poor, insignificant 0.10 < R² < 0.30 Poor 0.30 < R² < 0.45 Rather poor 0.45 < R² < 0.55 Adequate 0.55 < R² < 0.70 Satisfactory 0.70 < R² < 0.90 Good

R² > 0.90 Significant

From all correlations the ones reaching the level of adequate, satisfactory, good and significant (R²

> 0.45) were chosen for further analysis. All correlation values higher than 0.70 represented in tables 42.3 and 42.4 are also taken into account in next analysis of dependence because of their high correlation value.

42.5 Dependence analysis of I-I, I-O and PI-O parameters

Dependence analysis was executed for parameters resulting from correlation analysis to be able to understand the dependence of input and output parameters of interaction of laser beam and paper material and its characteristics.

As linear trend line was fitted to parameters data points shown in tables 42.3 and 42.4, also corresponding equation was determined. It can also be written as function as equation 42.1 illustrates. When this function is derivated, f´(x) can be defined as equation 42.4 represents.

f´(x) = k (42.4)

Derivate tells how function changes as x changes and it can be used to describe whether a function is increasing or decreasing. Table 42.8 shows the how increasing or decreasing characteristics of function is defined.

Table 42.8 Definition of increasing and decreasing characteristics of function Definiton Description

f´(x) > 0 Strictly increasing f´(x) < 0 Strictly decreasing f´(x) = 0 Constant

When these f´(x) values are calculated for each parameter combinations shown in tables 42.3 and 42.5, dependence can be defined. Appendix 13 shows example of this calculation and dependence analysis.

As table 42.8 shows increasing and decreasing characteristics of f´(x) is defined by value of zero.

However, it was noticed during experiments, that definition of exact value of zero is very difficult especially with experimental data. This is why an approximate value of 0.001 was used instead of exact value of zero. Table 42.9 shows the system used for marking of increasing/decreasing characteristics of functions used in this thesis.

Table 42.9 Definition of increasing/decreasing behaviour of functions to be able to define dependence between input and output parameters.

Definition Description Sign f´(x) > 0.001 Increasing  f´(x) < -0.001 Decreasing  -0.001 < f´(x) < 0.001 Constant 

Ranking in dependence analysis is executed by evaluating if one parameter correlation has same increasing/decreasing behaviour inside series. If this behaviour is changing, it is concluded that there is no dependence and this parameter combination is not analysed further. But if parameter combination inside series has same increasing/decreasing behaviour, it will be included for discussion analysis. Table 42.10 shows principle of this ranking.

42.6 Diagram of effect analyses of I-I, I-O and PI-O parameters

Finally, ranking factors of effect analysis can be added to figure 42.1 and completed diagram of these analyses is illustrated in figure 42.2.

Figure 42.2. Diagram of effect analyses with ranking factors.

43 Effect analysis of BHR100 and BHR86

To be able to analyse interaction between laser beam and paper material (see figure 34.1) and to understand effect of input-output parameters to the whole process, BHR100 and BHR86 were analysed.

Effect analyses of BHR100 and BHR86 consisted only of correlation analysis. DP/IP analysis and dependence analysis cannot be executed since the dependence between I-I parameters and BHR100 and BHR86 obeys natural logarithm function and zero point of natural logarithmic function is undefined. Also zero point of first derivate is undefined. Fluence was determined to be used as I-I

Effect analyses of BHR100 and BHR86 consisted only of correlation analysis. DP/IP analysis and dependence analysis cannot be executed since the dependence between I-I parameters and BHR100 and BHR86 obeys natural logarithm function and zero point of natural logarithmic function is undefined. Also zero point of first derivate is undefined. Fluence was determined to be used as I-I

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