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SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
L. Wilke
H. Potente
J. Schnieders
Institut für Kunststofftechnik Paderborn, University of Paderborn (Germany)
ABSTRACT The laser transmission welding of thermoplastics has become increasingly important since it was introduced into industrial series production 15 years ago. The respective influences of laser intensity, warming up time and both the joining pressure and the joining displacement on the quality of the weld have generally been established through experimental studies. In order to be able to predict the temperature, the melt shift profiles and the residual melt layer thickness in the welding zone, calculations were performed on the basis of a simplified mathematical-physical model, employing finite element analysis. The quasi-simultaneous and simultaneous laser welding process was simulated, including the heating and cooling phase, using temperature-dependent data. The convective cooling and emissivity at the surface of the adherends was taken into consideration. The intensity distribution, pressure and warming up time have to be specified as the influencing parameters for the computation. Pressure-regulated welds with time as the termination criterion were simulated, since these are the type of welds generally employed in practice. The simulation results have been continuously adapted for the experimental determination of the melt layer thickness with different process parameters. This paper presents the influence of the process parameters on the heat-affected zone, taking the example of a PA 6.
IIW-Thesaurus keywords: Comparisons; Computation; Finite element analysis; Laser welding; Mathematical models; Plastics; Process conditions; Process parameters; Thermoplastics.
INTRODUCTION As developments in the field of joining plastics over the past few years have shown, the laser transmission welding of thermoplastics is gaining increasing importance. Laser technology is set to open up a range of applications in future, not all of which can be forecast at present. This will provide joining technicians with a welcome alternative to the welding processes that are already available today. Sample applications for laser
Doc. IIW-1815-07 (ex-doc. XVI-857-06) recommended for publication by Commission XVI “Polymer joining and adhesive technology”. Welding in the World, Vol. 52, n° 1/2, 2008
welding include multi-color rear vehicle lights in PMMA/ABS, opaque swirl pots welded into black fuel tanks, housings for electronic components and vehicle fittings in PC/ABS. In laser transmission welding, a laser-transparent and a laser-absorbent semi-finished product are pressed together under a defined joining pressure, thus ensuring that the adherends come into contact with each other. The laser beam passes through the transparent part virtually unimpeded and is converted into heat as it is absorbed by the absorbent semi-finished product. The adherend that is transparent to the laser beam heats up through thermal conduction, and the adherends weld together. A characteristic feature of laser transmission welding is that the heating and joining phases take place simultaneously.
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
A number of process variants have been developed on the basis of the laser transmission welding process. Mention should be made here of contour and simultaneous welding, mask welding and quasi-simultaneous welding (Figure 1). In contour welding, the laser beam is moved along the weld relatively slowly (v = 0.1 to 500 mm/s). The weld is only heated up on a partial basis, i.e. only part of the weld is melted, and there is no melting displacement. Mask welding is based on the selective irradiation of the joining surface through a type of mask. This is primarily suited to very small joining surfaces.
57
The principle behind quasi-simultaneous welding differs from that of simultaneous welding by the type of heat application. In quasi-simultaneous welding, the beam is conveyed over the weld by a system of tilting mirrors at a relatively high speed (v = 100 to 10 000 mm/s) at frequencies of up to f = 80 Hz, while, with simultaneous welding, the joining surface is heated by a matrix of laser diodes over the full length of the weld. Both methods lead to virtually homogeneous heating of the entire weld. A characteristic melting displacement versus time curve thus results for both methods, which can be divided up into four phases (Figure 2).
Figure 1 – Variants of laser transmission welding
Phase Phase Phase Phase
1: 2: 3: 4:
Non-steady-state without any increase in melting displacement. Non-steady-state with an increase in melting displacement. Steady-state (constant melting rate). Cooling.
Figure 2 – Schematic joining displacement curve for the principles of quasi-simultaneous and simultaneous laser welding
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SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
This curve is a function of the process and material parameters, with the steady-state phase (Phase 3) assuming particular importance, since an equilibrium state develops between the energy introduced and the energy eliminated via the weld bead in this phase. By conducting temperature measurements, it proved possible to establish that the temperature during the welding process tends towards a stationary end value once the steady-state melting rate has been attained [1]. As was confirmed by further investigations, the strength only reaches its maximum value (or a level just short of this value) once the steady-state phase has been reached. It then only increases slightly after the steadystate phase has commenced. The level of the weld strength, by contrast, is conditioned by the resultant residual melt layer thickness and the welding temperature (as in vibration welding) [2, 3].
.
Φ = Ix = 0 ⋅ Keff ⋅ (e
– Keff . x
)
(5)
where
Keff is the material-dependent absorption constant, Ix = 0 is the radiator intensity distribution in the joining plane and x the direction of the laser radiation over the depth of the adherend (cf. Figure 3). The heat loss due to radiation and convection on the side surfaces of the adherends (only in the y-direction) is made up of the convective component and the radiation component and is described by the following relationship: α c ⋅σ ∂Τ – = (T – T0) + 12 ⋅ (T 4 – T04) (6) ∂ y x = const. λ λ
( )
where
c12 is the radiation exchange number, α is the coefficient of heat transfer,
THEORETICAL PRINCIPLES The temperature field can be calculated on the basis of the general differential equation of thermal conduction. The general differential equation of thermal conduction describes the non-steady-state temperature field, with the absorption of the laser radiation being taken into account as an internal heat source: . → ∂Τ ρ.c. + (∇v )T = Δ (λ . T) + Φ (1) ∂t
(
)
Assuming that no energy exchange occurs over the length of the component (z-axis), the differential equation for heat conduction can be simplified to a twodimensional heating and cooling problem. Assuming an identical mean constant thermal conductivity for both adherends, the following is obtained: . ∂Τ ∂Τ ∂Τ ∂2Τ ∂2Τ Φ (2) + vx + vy =a. + + ∂t ∂x ∂y ∂ x2 ∂ y2 ρ.c where
(
)
vx, and vy are the velocity components of the melt flow, a is the effective temperature conductivity, and . Φ is the heat source term distribution. The heat source term that is introduced is obtained in the x direction (assuming the system of coordinates shown in Figure 3) from the intensity gradients in the absorbing part: . ∂ Ι (x, y, z) (3) Φ= ∂x
⎪
⎪
The values established show that the axially-symmetrical intensity distribution takes the form: I(x = 0) = T ⋅ a ⋅ (e – br2) (4) where the laser-transparency is taken into account via factor T, a and b are beam-specific values, and r is the beam radius. Assuming validity of the Lambert-Beer law, which describes an exponential reduction in intensity in the direction of the depth of the absorbing part, the heat source term works out at [4, 5, 6]:
λ is the thermal conductivity, and σ is the Stefan Boltzmann constant.
PERFORMING THE SIMULATION CALCULATION The complex nature of the temperature development in the joining plane with a temperature profile that varies as a function of time and place, as is the case with the melting displacement that occurs during laser transmission welding, makes it clear that an analytically closed solution can no longer be implemented. The temperature development is thus calculated on the basis of a reduced two-dimensional and coupled temperature/ mechanical model using the ABAQUS 6.5 FEA program (Figure 3). The target parameters are the flow and temperature profile as a function of the boundary conditions and the weld parameters. The calculations are performed for specified material properties, joining pressure, laser action time, overall welding time, scanning frequency and also scanning velocity. The model that has been developed describes the entire joining process, including cooling, and covers the process variants of contour welding, simultaneous welding and quasi-simultaneous welding.
Mechanical calculation Stresses and strains are generated in the part as a function of time and temperature on account of the mechanical and thermal stresses that act during the welding process. These can be established with the aid of the thermoelasticity and plasticity theory [6]. This works on the basis of elastic-plastic material deformation, with the overall strain εall made up of an elastic component εel, a thermal component εth and a plastic component εpl. When the load is removed, the plastic component remains: el
th
pl
εall = εij + εij + εij
(7)
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
59
Figure 3 – Two-dimensional model for strain and temperature calculation where el
εij =
where
1+ν ν σij – σkkδij E E
(8)
x1 and z1 are constants.
th ij
ε = αΔTδij
( )
3 σv ε = α σ0 2 pl ij
(9) n–1
Sij E
(10)
and
Position x’ corresponds to the actual position of the joining plane, i.e. this shifts as follows as the melting displacement increases: x’ = x – ν ⋅ t
whereby Sij = σij –
ω is the angular velocity and
where
1 σkkδij 3
(11)
ν is the melting velocity and
x is the original coordinate in the fixed coordinate system.
c
σv = 3 Sij Sij 2
(12)
where εpl is the plastic strain to Ramberg-Osgood, Sij is the stress deviator, and σv is the Mises reference stress. Depending on the parameters selected, the stresses that build up in the part can affect the joining displacement versus time curve as a function of the temperature.
One necessary input for calculating the heat source term is the laser intensity Ix = 0 that reaches the joining plane. This is determined experimentally for the motionless laser beam (vscan = 0 m/s). To do this, the laser intensity behind the transparent adherend is measured with a perforated plate and a photodiode. Over the y-axis and in the direction in which the laser beam moves (zdirection), this corresponds to a Gaussian intensity distribution (Figure 5). At point x’, y, z = 0, a time-dependent input intensity as shown in Figure 6 is obtained.
Thermal calculation / Energy application To depict the dynamic time and place-dependent energy input for the process variants of contour welding and quasi-simultaneous welding, a dynamic calculation is performed for the point at which the energy is introduced. Figure 4 shows this in a schematic diagram. The trajectory of the moved laser beam is implemented in the model through the following movement vector: x’ x1 ⋅ (1 – cos (ω1t) + νscan ⋅ t) y = 0 (13) z z1 ⋅ sin (ω2t)
() (
(14)
)
Figure 4 – Schematic visualization of the scanning curve
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SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
Figure 5 – Laser beam distribution as a function of the beam diameter behind the transparent joining partner (P = 250 W)
(P = 250 W, f = 25,47 Hz, v = 2 m/s)
Figure 6 – Time dependent intensity in the joining surface The calculation of the energy input into the absorbing adherend was performed in the x-direction in accordance with the Lambert-Beer law [cf. Eq. (5)]. The order of magnitude of Keff is established by aligning the simulation results to the experimentally-determined melt layer thicknesses for different parameter settings. The absorption constant Keff is a function of the wavelength, the radiation introduced, the plastic and the additives. It is temperature-dependent for the semi-crystalline material and falls as the temperature rises, as a function of the material density [7, 8]. Use was made of an average value for Keff, however, for the calculations listed here.
Comparative calculation of simultaneous and quasi-simultaneous welding While there are no problems in calculating the temperature by means of FEA up to the start of Phase 2 (cf.
Figure 2), in the case of the process variant of quasisimultaneous welding with melting displacement, an enormous computing and time outlay is required for a coupled temperature-mechanical calculation with a simultaneously-moving laser, and convergence problems are encountered at times. To ensure that the temperature development can still be calculated with simultaneous melting, it is necessary to derive a conversion factor, which describes the transposition of the mean temperature conditions prevailing during the simultaneous welding process to the quasi-simultaneous welding process. The basic idea behind this approach is that identical, mean temperatures are obtained for a scanning laser beam (quasi-simultaneous welding) and a motionless laser beam (simultaneous welding), if the laser power of the motionless laser beam is set at a correspondingly lower level than that of the scanning beam. To simplify
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
61
a) Gaussian laser beam distribution
b) Equivalent laser beam
Figure 7 – Transformation from the Gaussian laser beam distribution to an equivalent laser beam the derivation of the conversion factor, it is possible to transform the Gaussian intensity distribution [Figure 7 a)] in the direction of the scanning movement (z-coordinate) into a laser beam of an equivalent length deq [Figure 7 b)]. The equivalent laser length deq can be calculated from the laser power of the equivalent beam and a subsequent comparison with the Gaussian laser power: The laser power corresponds to the volume integral of the intensity curve. This is calculated as follows for a Gaussian intensity distribution [7]: R
PGauss =
2π
兰 兰 I0 (r) ⋅ r ⋅ dϕ ⋅ dr = 0
0
R
2 ⋅ π ⋅ 兰r ⋅ a ⋅ e – b ⋅ r 2 ⋅ dr = π ⋅ 0
a ⋅ (1 – e – b ⋅ R 2) b
(15)
where
ϕ is the angle coordinate in the polar coordinate system, and R is the laser radius. The following is obtained for R r ∞: PGauss = π ⋅
a b
(16)
The total laser power of the equivalent laser beam Peq [Figure 7 b)] is obtained from the product of the Gaussian end surface AGauss(y-coordinate) and the equivalent laser beam length deq in the direction of movement of the beam: y a ⋅ cπ ⋅ erf (cb ⋅ y) Peq = AGauss ⋅ deq = 兰 I (y) ⋅ d y ⋅ deq = ⋅ deq cb –y (17)
(
)
for y r ∞, the following applies: a ⋅ cπ Peq = ⋅ deq cb
(
power Peq and the heating time per scan Δterw by multiplying the energy introduced per scan (the product of the laser power Peq and the heating time per scan Δterw by the number of scans N. The energy input over time for the equivalent laser beam is shown on a schematic diagram in Figure 8. E1 = N ⋅ Peq ⋅ Δterw
(20)
The number of times the laser sweeps over the surface that is to be scanned will depend on the scan length l, or the length of the part, and the overall heating time t. The number of scans N is thus: ν N = t ⋅ ƒ = t ⋅ scan (21) l The heating time per scan Δterw is obtained from the scan velocity vscan and the equivalent laser beam length deq through the following equation: d Δterw = eq (22) νscan Eq. (23) is then obtained for the energy input of the equivalent laser beam with Eq. (19), (20), (21) and (22): cπ P ⋅ cπ E1 = ƒ ⋅ Peq ⋅t or E1 = eq ⋅t (23) νscan ⋅ cb l ⋅ cb where
f is the number of scans per second, Peq is the laser power,
)
(18)
By equating the laser power of the equivalent laser beam and the Gaussian laser beam [Eq. (22), Eq. (24)], the equivalent laser length deq is obtained. cπ deq = (19) cb The energy input from the scanning laser E1 can now be calculated from the number of scans N, the laser
Figure 8 – Energy input for a transformed laser beam
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SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
vscan is the scanning velocity,
face of the transparent material, the following expression is obtained for the intensity distribution in the transparent adherend:
l is the scanning length and b is an intensity distribution factor.
I(x < 0) = (1 – R) ⋅ a ⋅ e
The energy input over time t of the motionless laser beam is worked out from the product of the overall action time t and the laser power P2. This should correspond to the energy input of the scanning laser beam at precisely the time when the laser power P2 is equal to the laser power Peq divided by a factor W (Figure 9). The energy input for the motionless laser E2 is then: P E2 = P2 ⋅ t = eq ⋅ t (24) W with the equivalent laser power Peq and the conversion factor W, which makes allowance for the scanning velocity and the scanning length. Assuming that the input energy components E1 and E2 are equally high, the following is obtained from Eq. (23) and Eq. (24): Peq P ⋅ cπ ⋅ t = eq ⋅t (25) W l ⋅ cb The conversion factor W being sought is then obtained through a reduction: l ⋅ cb ν ⋅ cb W= or W = scan (26) cπ ƒ ⋅ cπ
Allowing for the absorption by the transparent adherend The comparison of calculated and measured residual melt layer thicknesses shows that the residual melt layer thicknesses calculated for the absorbing adherend are too small. This is because the laser-transparent adherend frequently displays slight absorption and is thus heated during the welding process. The absorption coefficient for the transparent adherend is derived from the correlation between the absorption A, the reflectance R and the transmittance T:
A+R+T=1
(27)
where the individual parameters are all expressed in terms of the irradiated radiant flux at wave number λ. Assuming that all the reflection takes place at the sur-
( – Ktr ⋅ (x + Δx))
(28)
where Δx is the part height of the transparent adherend, and
Ktr is the absorption coefficient in the transparent adherend. If there is assumed to be an exponential reduction in the laser power according to the Lambert-Beer law in the transparent adherend, in the same way as in the absorbing adherend, the following is obtained for the intensity in the joining plane (x = 0): I(x = 0) = I(x = – Δx) ⋅ e
(– Ktr ⋅(x + Δx))
(29)
Eq. (30) then applies for the absorption coefficient in the transparent adherend in the joining plane, i.e. at the point x = 0: 1 T Ktr = – ln ⋅ (30) 1 – R Δx
(
)
Calculation results / Discussion of the influence of the process parameters The following results relate to FEA calculations for the material polyamide 6 (Durethan B30S). The material has a melting point of 222 oC. While the transparent material (s = 6 mm) has a transmittance of 0.15, the absorbing adherend was filled with 0.1 % by weight carbon black and thus has a mean absorption coefficient of Keff = 3 mm– 1. The calculations were performed by varying the parameters of scan length and joining pressure. Figure 10 shows the temperature development for quasisimultaneous welding (at the scanning velocity) for three different scanning velocities in the centre of the weld (x’ = 0; y = 0; z = 0). The scanning length was adapted in such a way that the scanning frequency was the same for all three calculations. The individual heating times and the subsequent cooling of the weld can be seen for the individual beam passes. This process is repeated with the specified frequency f. As is evident, a doubling of the scanning velocity leads to a halving of the time for which the temperature acts, thereby reducing the
Figure 9 – Energy input for the moving equivalent laser and motionless laser
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
63
Figure 10 – Temperature development as a function of time for a moving laser beam and three different scanning velocities (P = 250 W, f = 12,36 Hz) energy input. The temperature differential per scan falls as the scan velocity increases, i.e. when the scan velocity is increased, it is not the melting velocity that is reduced but only the maximum temperature differential between two laser passes, i.e. more uniform heating is achieved. As per Eq. (28), a given laser-beam focus setting (represented by the factor cb) will always produce the same energy input per unit of time if W is kept constant, i.e. the same mean energy input will be obtained for identical scan lengths. This makes it clear that, when the scan velocity is doubled, the scan also needs to be doubled in order to obtain the same temperature increase. This correlation is confirmed by comparing the calculated temperature development for identical W factors (Figure 11). As the calculations show, it is not possible to increase the melting velocity for a given scan length or component size by increasing the scanning velocity. In simultaneous welding, it is possible to achieve the same energy input as for quasi-simultaneous welding if the laser intensity of the laser diodes is reduced pre-
cisely by a factor of 1/W compared with that of the scanning laser. This correlation is confirmed by the calculated mean temperatures for the scanning and motionless laser and two different power distributions (Figure 12). After the material has exceeded the melt temperature (Tk = 222 oC) it starts to flow. As has already been explained, a characteristic joining displacement versus time curve develops (Figure 13). It is clear that a constant melting velocity (v = Δx/Δt) is calculated in Phase III (cf. Figure 2). Once the steady-state melting velocity has been attained, the temperature and residual melt layer thickness also tend towards a maximum value. The simulation calculations additionally show that the maximum temperature does not occur in the joining plane but in the absorbing material. The melt layer thickness in the transparent part is thus generally thinner than in the absorbent part, and the squeeze flow starts in the absorbing part to begin with and only later spreads to the transparent material (Figure 14). The laser absorp-
Figure 11 – Temperature development as a function of time for different scanning frequencies and three different conversion factors W [moving laser beam (P = 250 W)]
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SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
(x’, y, z = 0; v = 0,5m/s; f = 6,36 Hz; W = const.)
Figure 12 – Temperature development as a function of time for a moving and motionless laser beam and different laser powers
Figure 13 – Calculated joining displacement-time-curves for different joining pressures (simultaneous)
(Material PA6, 0.1 wt-% carbon black, P = 250 W; Keff = 3 mm-1, pressure 1 MPa, scanning speed 8 m/s, f = 94,1 Hz; Itr = 1 %)
Figure 14 – Calculated temperature and remaining melt layer thickness as a function of heating time
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
65
Figure 15 – Calculated remaining melt layer thickness as a function of joining pressures p and intensity I
tion in the transparent part causes a gradual shift in the location of the maximum temperature towards the transparent adherend as the welding time increases. At higher pressures, the melt layer thickness in the absorbent adherend falls to a greater extent than in the transparent adherend. The joining pressure thus has a major influence on the temperature and residual melt layer thickness in the joining seam (Figure 15). Since the weld strength is a function of the temperature, the time for which the temperature acts and the residual melt layer thickness in the joining seam, it can be assumed that identical temperatures and the resultant residual melt layer thicknesses lead to identical strengths. Data published to date on the parameter dependence of weld strength in simultaneous and quasisimultaneous welding tallies with the calculation results and shows that poorer welding results are achieved with an increasing joining pressure, although these differ to a lesser extent for different intensities as the joining pressure increases. The strengths in the simultaneous and quasi-simultaneous welding process ought also to be identical for identical W factors.
CONCLUSION This article presents a simplified model for calculating the flow and temperature in laser transmission welding. The model was compiled on the basis of finite element analysis (FEA) and permits the comprehensive simulation of the process variants of contour welding, quasisimultaneous welding and simultaneous welding. The model makes allowance for both the influence of the mechanical and thermal loading on the residual melt layer thickness and the temperature profiles in the joining seam. As the calculations show, both the temperature and the residual melt layer thickness fall considerably as the joining pressure increases.
The theoretical derivation and comparison of simulation calculations revealed the influence of the scanning frequency and scanning velocity on the temperature development in the joining plane. It was shown that, for a given laser intensity distribution, a comparable mean welding temperature is obtained if the scanning velocity is in the same ratio to the scanning frequency. It is also possible to use the derived factor to compare the simultaneous welding process with quasi-simultaneous welding. For a given power distribution, scanning velocity and scanning frequency, conclusions can be drawn regarding an equivalent temperature development for simultaneous welding. For purposes of verifying these results, temperature and strength measurements are currently being conducted with comparable line energies and W factors. The formulations implemented in the model and the degrees of freedom in respect of the choice of materials to be joined and the welding parameters employed mean that there is scope for optimizing the model. This is now to be done on the basis of experimental data. The experimental data is being obtained from investigations employing high-speed microfocus radioscopy, tracking the flow processes of the tracer particles embedded in the plastic matrix. Just how far the results of the model calculations presented are also correct in quantitative terms is currently being looked into.
NOMENCLATURE A
absorption [%]: absorbed radiant flux expressed in terms of the irradiated radiant flux
AGauss
area of the one-dimensional Gauss distribution [m2]
a
coefficient of the Gauss function [W/m2]
b
coefficient of the Gauss function [m-1]
c
specific heat [Jg-1K-1]
c12
radiation exchange number [ ]
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deq E f I Itr K Keff Ktr
equivalent laser beam length [m] elastic modulus [N/m2] frequency [Hz] intensity [W/m2] intensity in the transparent material [W/m2] constant of absorption [m-1] absorption coefficient [ms-1] absorption constant in the transparent material [m-1] l scanning length N number of scans [ ] P total power of the laser beam [W] pF joining pressure [MPa] R max. beam radius, spectral reflectance [%]: reflected radiant flux expressed in term of the irradiated radiant flux r radius coordinate [m] s thickness of the absorbent part [m] t welding time [s] tE heating time [s] T transmittance [%]: transmitted radiant flux expressed in terms of the irradiated radiant flux T0 ambient temperature [oC] = 20 oC TK crystalline melting temperature [oC] W conversion factor [ ] vscan scanning velocity [m/s] v, vx, vy velocity [m/s] vs scanning velocity [m/s] Δx height of the transparent part [m] x’,x, y, z, y0 coordinate [mm] α heat transfer coefficient [Wm-2K-1] δij Kronecker symbol [ ] ε, εij elongation [%] εP, εE emissivity of the plastic and environment [ ]
SIMULATION OF QUASI-SIMULTANEOUS AND SIMULTANEOUS LASER WELDING
λ ρ v σ σ0, σv
heat conduction [WK-1m-1] density [kg/m3] Poisson number [ ] Boltzmann constant [W/(m2K4)] yield and Mises stress [N/m2]
REFERENCES [1] Welli T.: Untersuchungen zur Prozessführung beim quasisimultanenKunststoff-Laserschweißen, Diplomarbeit, Fachhochschule Soest, Hella KgaA Hueck & Co, 2005. [2] Ehrenstein G., Vetter J.: Bioaxiales Vibrationsschweißen und Qualitätssicherung, Erlanger Kunststofftage 1999, 26/27.10 1999, pp. 59-75. [3] Potente H., Wilke L., Fiegler G.: Fügen von Kunststoffen am Institut für Kunststofftechnik, KTP-Jubiläumstagung 2324.02 2005, Shaker Verlag, Aachen, 2005. [4] Potente H., Fiegler G., Becker F., Korte J.: Comparative investigations into quasi-simultaneous welding on the basis of the materials PEEK and PC, 60th Annual Technical Conference (ANTEC), Society of Plastics Engineers, San Francisco 5-9 May 2002. [5] Grewell D., Benatar A.: Modelling heat flow for a moving heat source to describe scan micro-laser welding, 60th Annual Technical Conference (ANTEC), Society of Plastics Engineers, San Francisco 5-9 May 2002. [6] Brocks W., Klinbeil D., Olschewski J.: Forschungsbereicht 175, BAM, Berlin, 1990. [7] Becker F.: Einsatz des Laserdurchstrahlschweißens zum Fügen von Thermoplasten, Dissertation Universität Paderborn, Shaker Verlag, Aachen, 2003. [8] Potente H., Becker F.: A step towards understanding the heating phase of laser transmission welding in polymers, Polymer Engineering and Science, 2002, Vol. 42, No. 2.
