# Production and Processing of a Spherical Polybutylene Terephthalate Powder for Laser Sintering
## 3 Results and Discussion
### Powder classification  
In order to produce a sufficient amount of powder for laser sintering trials, 9 kg PEG flakes were dry blended with 6 kg PBT granules, and extruded using the process parameters from Trial 7, as discussed in the previous section. After removal of the PEG matrix phase, approximately 1.5 kg fibrous mass was extracted. This translates to a conversion efficiency of 75%, going from PBT granulate to PBT powder. The particle size distribution for the as-extruded PBT powder is shown in Figure 5. The distribution is rather broad, and contains a considerable amount of fine particles. Of the total volume, 67% falls within the 10-100 \(\upmu\)m range, which is 10% more than measured during initial trials. As shown by [PERSON] [18] and [PERSON] et al. [29], who studied the performance of two thermoplastic elastomers with different shapes and size distributions, the reduction of fine particles can improve flowability and lead to a higher packing density. The part properties can be improved in this way. Figure 4: (**a**) Percentage of total particle volume with a size that lies in the range of 10–100 \(\upmu\)m in dependence of nozzle selection and extruder rotational speed; (**b**) Amount of PBT that comes out of the extruder in fibrous state, relative to total PBT blend content. Figure 3: Particle size (D\({}_{10}\), D\({}_{50}\), D\({}_{90}\)) in dependence of nozzle selection and extruder rotational speed. Colored regions indicate optimal size region (green), suboptimal size regions (yellow), and undesired size regions (red). To reduce the amount of fine particles in the distribution, the powder was led through a settling tank that was specifically designed and constructed for this purpose. The functional principle is based on Stokes' law, which equates the frictional force between a fluid and a spherical particle to the fluid's viscosity and flow velocity, and the density and size of said particle. The terminal settling speed of a particle can then be determined by balancing the gravitational force on a particle against the frictional force as given by Stokes' law and the buoyancy, and solving for velocity:  
\[\
u_{\infty}=\frac{\left(\rho_{\mathrm{p}}-\rho_{\mathrm{f}}\right)}{18\mu} \mathrm{g}\mathrm{D}^{2}, \tag{1}\]  
with \(\rho_{\mathrm{p}}\) and \(\rho_{\mathrm{f}}\) the densities of particle and fluid respectively, \(\mu\) the fluid viscosity, g the gravitational constant, and D the diameter of the particle. For particles with a size of 10 \(\mu\)m, the terminal settling speed was calculated according to (1) to be 0.02 mm/s. The density of the particles was assumed to be equal to the material density of 1.31 g/cm\({}^{3}\). The density and dynamic viscosity of water at room temperature were taken from literature [30] and set at 1.0 g/cm\({}^{3}\) and 0.89 mPa.s, respectively. The flow rate in the settling tank depends on its geometry. A schematic representation of the settling tank is shown in Figure 6a. The tank has a total volume of 148 liters and is fitted with ten plates inclined at an angle of 60\({}^{\circ}\). The flow rate Q to remove particles with a certain maximum terminal settling velocity for a settling tank with this geometry is given by:  
\[\mathrm{Q}=\
u_{\infty}\mathrm{NA}\cos\alpha, \tag{2}\]  
with N and A the number of plates and their respective area, and \(\alpha\) the inclination angle of the plates. To remove particles smaller than 10 \(\mu\)m, i.e., to prevent them from settling at the bottom of the tank, the terminal settling speed from (1) is plugged into (2). It then follows that a flow rate of 1.4 L/min should be set. To verify that this is the correct flow rate, the particle size in the effluent was measured by dynamic light scattering.