5 CONTROL OF LASER BASED MACHINING OF POLYMERS

5 CONTROL OF LASER BASED

MACHINING OF POLYMERS

The diffusion of innovative working process is needed to achieve sustainable production technology. In many case high energy-density techniques have been proved to be valid alternatives to conventional process (especially in case of engraving, welding and surface treatment). These techniques provide at the same time a high resolution of the process and a reduction in energy consumption since the action is localized in a very restricted area.

Laser Beam Machining (LBM) is one of those contactless technologies that is getting wide acceptance in the field of production. The use of laser technologies leads anyhow to the introduction of a different type of uncertainties in the production processes respect to the mechanical removal techniques described in the previous chapters. Since almost every industrial laser interacts with the workpiece by intense and localized heat transfer mechanisms, the first step towards process control starts with the development of models able to predict temperature distribution.

If scientific contributes are available in literature in case of modelling LBM of metals, only few efforts are devoted to the laser treating of plastic materials. This chapter represents then a first step for an approach on the monitoring of LBM of polymers. Theoretical relations will be proposed to describe the thermal interaction between laser radiation and plastic material (depending on process parameters) and compared to those available for metals.

NOMENCLATURE

abs absorption coefficient

Cp specific heat J / kg K

k thermal conductivity W / m K

P power of laser beam W

I specific thermal power of the laser radiation W/m2

Q intensity of line heat source J/m

r cylindrical coordinate m

ref reflection coefficient

s distance traveled in the time unit mm

t time s

t* radiation incidence duration s tr transmission coefficient

T(z) temperature in the z direction K

Tg glass transition temperature K

To initial temperature of the powder bed K

V scanning speed mm/s

z coordinate in the direction of the laser beam mm α thermal diffusivity (= k / ρ Cp) m2 / s

Ø spot diameter of laser beam µm

ρ density kg/m3

5.1 INTRODUCTION

One of the main problems concerning with the application of laser technology is the optimal parameters selection. For a given kind of material it corresponds to define thermophysical properties like density, specific heat, thermal conductivity, melting temperature and vaporization point. The main technological parameters to control in a laser process are:

1. laser wavelength; 2. pulse duration; 3. pulse repetition rate; 4. beam average power; 5. beam spot diameter; 6. beam scanning speed.

Models can be then important to understand how the various process variables (parameters) affect the physical phenomena in order to select appropriate values before processing and to provide guidelines for optimization of the process both on technological and energetic point of view.

Laser processing of metals is mainly carried out with high power laser sources (from 500W up to 10kW) emitting in the near IR (Nd-YAG 1064nm) or far IR (CO2

10.64µm). These types of sources work in continuous wave (CW-lasers) or in pulsed regime (ranging between 1ms to 1µs); only few industrial machines are able to use ns-duration pulses by means of the so called Q-switching technique. The

use of high power industrial laser is motivated by the high productivity required in case of cutting or welding and is directly related to the chemical structure of metals. As a matter of fact, models proposed to describe the thermal distribution during these processes is aimed at understanding which values of process parameters should be used to melt the material at predetermined boundary conditions. Models are mainly time independent since the low process speeds (around 1 to 10 m/min in case of cutting and welding) allow a theoretical steady thermal balance in an infinitesimal control volume of material.

5.2 LASER BEAM MACHINING OF POLYMERS

As far as the kind of laser sources is concerned, most organic materials are highly absorptive at CO2 laser wavelength of 10.6µm, and transparent at the most

common semiconductor (0.8µm) and Nd-YAG (1.06µm) ones. All organic polymers also show an intense absorption in the ultraviolet region (excimer laser wavelengths of about 0.19-0.35µm) [3,4,5].

Figure 1 – Dependence of material removal mechanism on laser wavelength. Photons emitted in the infrared induce molecular and lattice vibrations (“Inverse Bremsstrahlung” phenomenon) which can be detected by an increase in temperature of the work piece. Consequently, material processing with CO2 lasers

has generally a thermal nature (also reported in figure 1). Technical polymers present different behaviours at these frequencies, depending on the type of material and the molecular mass. Some authors [6] subdivide polymers into three groups according to the dominant phenomenon which generates the material removal:

− Most thermoplastics are laser machined by a “melt shearing” process: the material is melt by the laser beam which brings about this physical change disentangling the monomer chains of the bulk plastic. The small molten pool is blown away by the gas jet.

− Polymethylmethacrylate (PMMA) and polyacetals are laser machined by “vaporization” which can actually be considered a pure sublimation process. − All thermosets (e.g. phenolic or epoxy resins), and vulcanized rubbers, are

laser machined by “chemical degradation”. The energy of the beam acts to break the chemical bonds by disrupting the integrity of the material.

All organic polymers also show an intense absorption in the ultraviolet region (UV). Photons emitted at these short wavelengths are characterized by an extremely high energy which makes it possible to use an energy transfer mechanism called “photochemical ablation” (also reported in figure 1): since the photon energy is

ABLATION _{THERMAL PROCESS}

greater than the material specific dissociation energy, molecular components are cracked, carrying out smooth surfaces and clean edges eliminating heat affection to the workpiece [4]. Due to the extremely short pulse duration which characterize UV-lasers the impact of high energy photons on the surface induce a local sublimation of the material. Vapours ejected at hundreds of MPa from the micro-cavity are instantaneously ionized by the beam and brought to plasma temperature (over 10000K). The plasma plume has intermittent switching in the order of 1 ps or maximum of 10ns and for this reason cannot induce thermal transfer to the workpiece; this phenomenon called “cold ablation” is mostly frequent in case of plastic materials since the photons energy is equivalent to the debinding energy of the major part of chemical bonds which constitute organic materials.

Figure 2 - Dependence of material removal mechanism on pulse duration. A second important distinction which influences the removal mechanism is represented by the interaction time between laser and material. In figure 2 the difference between industrial laser and experimental lasers is introduced considering the actual state of art.

CW

µs

ns

ps

fs

Industrial lasers

Experimental

Time 1s 100µs 10ps Power 1W 1kW 1MW 100MW 1 J 0.1 J 10 mJ 1 m J

CW Pulsed Q-switched Mode-locking

HAZ CFRP La ser b eam P la sma plum e Vap orized particles

POLYMER

CW

µs

ns

ps

fs

Industrial lasers

Experimental

Time 1s 100µs 10ps Power 1W 1kW 1MW 100MW 1 J 0.1 J 10 mJ 1 m J

CW Pulsed Q-switched Mode-locking

HAZ CFRP La ser b eam P la sma plum e Vap orized particles

POLYMER

It can be noted also that CW lasers and pulsed laser (less that 10ns) induce thermal transfer to the workpiece and a large Heat Affected Zone (HAZ) which represents a boundary zone characterized by chemical degradation of the polymer (change of colour, density reduction, burning). As previously described, ultra short pulses (less than 10 ns) hinder a heat transfer due to the extremely reduced interaction time. With modern laser sources it is possible to obtain ns or ps pulses up to 1064nm. Due to the gaseous nature of the active mean CO2 lasers cannot

emit pulses shorter than µs regime.

As a matter of fact CW or pulsed (ms or µs duration) CO2 lasers represent the

common choice for the machining of plastic materials especially if high speeds of fabrication are required in addition to smoothness of the surface and accuracy in cutting. UV lasers represent a valid alternative for micro-maching (very small removal rates) when HAZ has to be avoided.

5.3 MODELLING OF HEAT TRANSFER: STEADY CASE

LBM of polymers is characterised by a deep interaction between heat, mass and momentum transfer along with chemical transitions and variations of the mechanical and thermophysical materials properties. According to the optimisation method outlined in figure 3, models can be used to preliminarily estimate the process parameters testing range, so simple phenomenological models are required.

Figure - 3 Concept of multi-objective optimisation method.

It is then assumed that LBM of polymers is dominated by heat transfer and the proposed models are based on the following hypotheses.

Optimisation of polymers LBM Optimisation criteria

Energy & environment

Modelling Descriptive ~ Qualitative Experimental 1D ~ 2D ~ 3D ~ Numerical HE UR IS T IC AN AL IT IC AL Process selection

Process variables Productivity Resolution Mechanical properties

Process characterisation Material characterisation

Optimal technological parameters Optimal model parameters

Cost

DOE

Optimisation of polymers LBM Optimisation criteria

Energy & environment

Modelling Descriptive ~ Qualitative Experimental 1D ~ 2D ~ 3D ~ Numerical HE UR IS T IC AN AL IT IC AL Process selection

Process variables Productivity Resolution Mechanical properties

Process characterisation Material characterisation

Optimal technological parameters Optimal model parameters

Cost

A complete thermal model should include the terms shown in Figure 2, but convection and radiation at the boundary are negligible because of the low exchange surface and temperatures.

• The material removal is observed mostly when the radiating energy is acting [7].

• The variations of the thermo-physical material properties, particularly of the thermal conductivity and of the specific heat, are averaged in the observed temperature range.

• The material is considered continuous and homogenous with isotropic thermal conductivity.

• Local phenomena related to chemical reactions that could vary density and consistence of the material are neglected.

The mathematical description involves the solution of the heat conduction equation (Fourier equation) in steady or unsteady case. A good model should reproduce the thermal history within the polymer treated layer after the radiation incidence starts. There are several analytical solutions that can be useful for the calculation of the transient temperature and of the heat transfer of objects irradiated by a power input [2].

Figure 4 - Main energy terms in LBM.

When the laser spot hits the powder, the surface interaction with the radiant energy can be described by the coefficients representing the fraction of absorbed abs, reflected ref, and transmitted energy tr (figure 4). It can be then defined that:

abs + ref + tr = 1 (1).

Radiant flux

Laser beam

z

x

y

Radiant flux

Laser beam

z

x

y

The three coefficients depend on the polymer used. For nylon, the absorption coefficient, abs, is sensibly higher than 0.9. As mentioned before, the penetration of the melting or vaporizing temperature front into the material determines the depth and width of the treated zone. However this thermal problem, even if conceptually simple, has not a simple solution for the following reasons:

- the intrinsic complexity of the phenomenon and its mathematical modelling (three-dimensional thermal conduction with convective surface heat dissipation);

- the difficulties in the characterisation of the material from a thermo-physical point of view (thermal conductivity, specific heat capacity and thermal diffusivity);

- the difficulties in a correct modelling of the material from a chemical point of view (polymerisation temperature, energy released during the polymerisation process caused by the breakage of chemical links, melting, etc.).

Assuming negligible every heat exchange due to convection and radiation due to the very small emitting surface (equivalent to the laser spot area) it is possible to derive the general Fourier equation starting from the thermal balance on an infinitesimal control volume:

(1). This expression can be significantly simplified by the following hypotheses derived from the characteristics of the LBM:

1. heat is absorbed only on polymer surface and no internal source of heat can be noted after laser radiation (q’’’ is equal to zero);

2. homogeneous and isotropic material (heat conduction is uniform into the workpiece);

3. for a straightforward heat transfer model, phase changes and latent heat are not included;

4. deriving from assumption 3, no mass flow can be observed; 5. polymer characteristics (k , ρ ,Cp) are temperature-independent.

The first study on thermal distribution during welding operation was carried out by Rosenthal [1, 2,3]. This model assumes the laser beam as a moving heat source of different geometries (point source, line source, plane source) at constant speed v. (2) If the scanning speed is assumed to be constant, imposing

(3)

It is possible to derive the Fourier equation for an inertial system which includes the laser source, moving at constant v (see figure 5).

t

T

k

q

T

∂

∂

=

+

∇

α

1

''

'

vt

x

−

=

ξ

t

T

z

T

y

T

x

T

∂

∂

=

∂

∂

+

∂

∂

+

∂

∂

α

1

Figure 5 – Fixed system and “source system” moving at constant speed v.

(4)

If the workpiece dimensions can be retained infinite compared to the ones of the thermal flux, the temperature distribution results time independent for an observer hat is moving at the same speed of the laser source. The derivation of temperature respect to time is then equal to zero and equation 3 can be simplified as follows:

(5) In case of cutting processes the laser beam acting on the surface can be represented as a plane heat source (like in figure 6) and the Rosenthal equation which describes the isotropic heat conduction can be solved using the following boundary conditions: (6)

z

z

v

x,

y

ξ

y

O

O’

ξ

ξ

ξ

ξ

ξ

∂

∂

−

∂

∂

=

∂

∂

∂

∂

=

∂

∂

)

,

,

,

(

)

,

,

,

(

)

,

,

,

(

)

,

,

,

(

)

,

,

,

(

t

z

y

T

v

t

t

z

y

T

t

t

z

y

x

T

t

z

y

T

x

t

z

y

x

T

ξ

α

ξ

∂

∂

−

=

∂

∂

+

∂

∂

+

∂

∂

v

T

z

T

y

T

T

0

=

∂

∂

=

∂

∂

z

T

y

T

''

lim

0

lim

q

T

k

T

=

∂

∂

−

=

∂

∂

ξ

ξ

Figure 6 – Propagation of the cutting front.

Figure 7 - Moving plane source of heat: a model for cutting.

Since isotherms in front of the plane source are represented by parallel planes, it can be stated that there is no conduction along y and z directions. From these boundary conditions equation 5 becomes:

(7)

ξ

α

ξ

∂

∂

−

=

∂

∂

T

v

T

x

y

z

LASER

Cutting front

v

v

x

y

z

q’

ξ

and its solution is easily given by:

for and

for (8).

In case of welding a distinction has to be introduced depending on the technique adopted in the production processes. Laser technology allows joint of different geometries depending on the power density adopted, as reported in figure 8.

Figure 8 – Joint geometryin adimensional unit (depth to width ratio) versus power density [3].

The process of conduction welding is characterized by the use of low power density and the joint has normally a half-sphere shape. The beam is represented by a point heat source (like in figure 9) and the Rosenthal equation which describes the isotropic heat conduction in the semi-infinite space defined by z<0, can be solved using the following boundary conditions:

(9) being ξ α

ρ

ξ

e

v

C

q

T

v

T

(

,

)

=

+

''

ξ

≥

0

v

C

q

T

v

T

_ρ

ξ

,

)

''

(

=

+

ξ

<

0

0

lim

0

lim

=

∂

∂

=

∂

∂

y

T

T

ξ

r

Q

T

k

r

=

∂

∂

−

2

lim

π

0

lim

=

∂

∂

_z

T

_y

_z

r

=

ξ

+

+

.

Figure 9 – Moving point source of heat: a model for conduction welding. In this case isotherms are represented by half spheres having centre point in the heat source. The solution reported in [1] and [2] is given by:

(10)

Deep penetration welding (called also keyhole welding), the laser beam acting on the surface is represented as a line heat source (like in figure 8). In this case isotherms are represented by concentric cylinders whose axis is the axis of the moving laser beam. As a result conduction happens only along x and y direction. The Rosenthal equation which describes the isotropic heat conduction in the semi-infinite space defined by z<0 (the whole material thickness), can be solved using the following boundary conditions:

(11) being

Equation 5 then becomes (12)

z z

v

x,

y

ξ

y

O

Q

r

π

2

)

,

(

_e

_e

kr

Q

Ti

v

r

T

=

+

0

=

∂

∂

z

T

0

lim

0

lim

=

∂

∂

=

∂

∂

y

T

T

ξ

ξ

α

ξ

∂

∂

−

=

∂

∂

+

∂

∂

v

T

y

T

T

Q

r

T

rhk

∂

=

∂

−

2

π

lim

_y

r

=

ξ

+

Figure 10 – Moving line source of heat: a model for keyhole welding [4]. The solution expressed in [1] and [2] is given by:

(13) where K0 is a Bessel function of the second type and zero order.

As a result, the Rosenthal solution describes the thermal distribution seen from a system which has the same speed of the laser source. Apart from the initial transient needed to reach a constant speed the model describes a steady solution of the problem and as a direct consequence the solutions (8), (10) and (13) are time independent. It is possible to generalize the three cases assuming that

)

,

,

(

_y

_z

e

T

T

ϕ

ξ

+

=

⎥⎦

⎤

⎢⎣

⎡

=

−

α

π

2

2

_K

vr

e

kh

Q

T

T

z

h

W

Keyhole

Q=P

(1- ref)

h

LASER BEAM

Melted pool

r

x,ξ

y

is a general solution where φ(ξ,y,z) satisfies equation 5 with predetermined boundary conditions [4].

5.4 MODELLING OF HEAT TRANSFER: UNSTEADY CASE

The afore mentioned models adopted for metal processing have proved to produce only rough approximated results for laser application on polymers and are definitely not conservative. This is mainly due to the relevant difference in the chemical structure of most polymer materials respect to metallic ones. The different polymers adopted in the technical field are characterized by a very wide range of variation in chemical properties: generally they offer low thermal conductivity (around 0.1-0.2 W/m K), extremely low thermal diffusivity (around 6-7.10-8 m2/s), specific heat (around 2-3 kJ/kgK) and density. For this reason only small amounts of input energy are required to activate the removal process on the polymer surface and scanning speed much higher than in case of metals are sustainable. Furthermore the use of high speed rate for the laser source makes the analysis of the transient conditions very important during the machining of polymers.

The process modelling in unsteady condition has been then performed in various forms (from one to three dimensions) by most authors dealing with polymers [5] [6]. The heat transfer in a plane perpendicular to the laser axis is normally neglected and the heat transfer, dominated by conduction, is only studied in the laser beam direction (z in figure 4). The phenomenon is governed by the following one-dimensional heat conduction equation which derives from (2):

2 2 p T(z, t) k T(z, t) t c z ∂ _{= ⋅}∂ ∂ ρ ⋅ ∂ (15) with the following boundary conditions

z 0

T

-k

q''

0 t t*

z

∂

=

≤ ≤

∂

&

( )

q'' [W/m2_{] is the specific thermal power of the laser radiation determined by P/(Ø}._s),

being P and Ø the power and the spot diameter of laser beam, s the distance travelled by the laser in the unit of time at scanning speed V, To the initial

temperature of the polymer and t* the radiation incidence duration that can be estimated by

t* = (Ø / V) (17)

The temperature rise during the radiation incidence can be expressed analytically for a rectangular surface circumscribing the laser spot as

( )

q ''

t

z

q ''

z

T(z, t) T

2

exp

z erfc

k

4 t

k

₂

_t

⎡

⎤

⎛

⎞

α

⎛

⎞

_⎢

_⎥

=

+

⋅

_⎜

_⎟

⎜

_⎜

−

⎟

_⎟

−

⋅ ⋅

⎢

⎥

π

α

⎝

⎠

_⎝

_⎠

_⎣

α

_⎦

&

&

internal friction generated by IR photons energy and liquid and vapour phases generation is dominated by polymer chemistry. The zone interested by laser radiation in the polymer material is determined by the penetration of the thermal front included inside the envelope of the Tg. Equation (18) can be used to estimate

the maximum penetration only along z which is retained to be the preferential conductive direction. As a particular case, from equation (5) it is possible to estimate the history of the maximum temperature, which occurs on the surface (z=0) o

2q ''

t

T(0, t) T

k

α

−

=

⋅

π

This value must be then compared with the polymer melting or degradation temperature, depending on the type of process which has to be carried out.

Figure 11 – Instantaneous line source of heat generating semicylindrical isotherms.

The moving point heat source model is the more commonly used in the literature, as in [5] [6], but it seems not suitable for high conductive polymers (k>0.4W/mK), because the thermal conduction in the lateral direction is not negligible with respect to the model preferential direction z. In addition, it is not suitable for high scanning speeds (in the order of 2-3m/s) because it is very sensitive to the selection of the radiation incidence duration (t* in the previous model).

x

y

z

x

y

z

To overcome the mentioned limitations, a different time dependent conduction model in which heat is generated instantaneously by a line heat source of intensity Q [J/m] is here proposed, as shown in figure 11.

Assuming that conduction happens on a semi-infinite solid, representing the workpiece, the switching of a linear source, whose axis belongs to the polymer surface, generates semicylindrical isotherms as described in the draft in figure 11. Therefore this model gives an evaluation of conduction not only along z but also along y axis. Since conduction in this case is governed by a radial flow of heat, the model can be retained a 1.5-dimensional model [17] along the cylindrical coordinate r with respect to the ideal axis. As a direct result of the isotherms shape conduction along y should be the double of conduction along z.

The temperature increase around the line heat source can be expressed by

2 o Q r T(r, t) T exp 4 kt 4 t ⎡ ⎤ − = ⎢− ⎥ π _⎢⎣ α _⎥⎦ (20).

This model shows a direct connection between Q and the energy density (ED), expressed in [J/mm2], defined as

ED P

V Ø =

⋅ (21).

ED is a parameter commonly used in literature (e.g. [5] [6]) to include laser main variables and express them from an energetic point of view.

5.5 CONLCUSIONS

Starting from state-of-the-art considerations it was shown that IR laser processing has a thermal nature, especially if continuous wave sources or long-pulse sources are used. It was shown also that thermal models conventionally adopted for metal processing (cutting or welding) make use of the Rosenthal solution. In this case considering a source of heat moving at constant speed it was possible to derive formulas for determining the temperature distribution in steady conditions.

This approximation doesn’t fit to the case of polymers for the afore mentioned differences in the chemical structures which allowed the use of much higher beam speeds. For this reason models of unsteady conduction have been proposed aimed at considering the thermal distribution depending on the irradiation time in addition to the preferential conduction axes.

The conventional model of the moving heat source (represented by a constant heat flow boundary condition) has revealed some drawbacks especially for those polymers whose high conductivity hinders to use the hypotheses of uniaxial flow. Furthermore the use of high scanning speeds conventionally adopted for polymers machining makes it difficult to determine the irradiation time parameter.

The second unsteady model proposed considers the switching of an instantaneous line heat source and leads to a preliminary approximation of lateral conduction using the semicylindrical shaped isotherms which characterize the radial flow. Laser parameters like average power P scanning speed v and spot diameter can be used to express the effects on the polymer material from energetic perspective

using the energy density notation. It will be shown in the next chapter regarding technical laser application on polymers that the control of energy density will be retained as a key-factor for a better understanding and monitoring of IR laser processing of plastic materials.

5.6 REFERENCES

[1] H. S. Carslaw, J. C. Jaeger, 1967, Conduction of heat in solids 2nd edition, Oxford University Press.

[2] Bejan A., 1993, Heat Transfer, J. Wiley & Sons.

[3] Capello E., 2003, Le lavorazioni industriali mediante laser di potenza, Libreria CLUP.

[4] Mackwood A.P., Crafer R.C, 2005, Thermal modelling of laser welding and related proceses: a literature review, Optics and Laser technology 37: 99-115. [5] Berzins M., Childs T.H.C., Ryder G.R., 1996, The selective laser sintering of

polycarbonate, Annals of the CIRP, 45/1:187–190.

[6] Childs T.H.C., Berzins M., Ryder G.R., Tontowi A.E., 1999, Selective laser sintering of an amorphous polymer: simulations and experiments. Proc. IMechE, Part B: J. Engineering Manufacture, 213:333-349.