# Capabilities and Limitations of Using Desktop 3-D Printers in the Laser Sintering Process
## Materials and Methods
### Powder Flowability  
Two methods were used to assess the flowability of the powder: quasi-static (Hausner Ratio, HR) and dynamic (Revolution Powder Analyze). These methods describe the behavior of the powder in the process conditions very well. The ratio of the tap and bulk density provides a statement on the flowability of powders, and is called the \"Hausner Ratio (HR)\" [16]. A practical equation widely used to evaluate flow properties can \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Machine**} & \multirow{2}{*}{**Material**} & **Mixing Ratio** & **Layer** & **Laser Power** & **Temperature on** & **Temperature** & **Scanning Speed** \\  & & **(Used: Virgin)** & **Thickness** & **[W]** & **Print Surface** & **in Removing** & **(Hitching)** \\  & & **[mm]** & **[m]** & **[\({}^{\circ}\)C]** & **Chamber** [\({}^{\circ}\)C] & **[mm/s]** \\ \hline Formiga & & & & & & \\ P110 & PA2200 & 50:50 & 0.1 & 21 & 167 & 148 & 2500 \\ Lisa & PA12 Smooth & 70:30 & 0.1 & Laser power ratio-1 & 170 & n/a & n/a \\ S1 & PA12 Black & 30:70 & 0.1 & 5 & 170 & 140 & 650 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Laser Sintering Process Parameters Used to Produce Parts According to Each Machine. be given by the following equation, which calculates powder volume changes in a graduated cylinder after a certain period of taps [17]:  
\[HR=\frac{\rho_{n}}{\rho_{0}}=\frac{V_{o}}{V_{n}} \tag{1}\]  
where \(n\) is the number of taps provided to the sample, \(\rho_{n}\) and \(\rho_{0}\) are the tapped and loose bulk density, and \(V_{0}\) and \(V_{n}\) are the loose and tapped volume, respectively. The determination of the bulk and the tapped density is described by norms: ISO 3953 and ASTM D7481. The test was performed using the tap density tester ETD-1020 (Electrolab, Mumbai, India). Compaction of the powder in a measuring cylinder with a volume of 100 mL took place under its weight by cyclical tapping--a constant value of \(14\pm 2\) mm with a frequency of 5 Hz. Loosely filled powder up to the level of 50 mL was precompacted after 500 taps. In the next cycle, tapping was continued, 750 and 1250 times, until the indicated volume difference was less than 2% of the previous measurement. This procedure was repeated three times for each powder (each done with a new powder sample). One of the dynamic methods of quantitative evaluation of powder flowability is the so-called Revolution Powder Analysis (RPA) [8]. This measurement corresponds approximately to the loading by the LS application tools (roller or blade). In this method, the drum with an inner diameter of 84 mm and a width of 20 mm rotates around its axis at an angular velocity ranging from 2 to 60 rpm. The transparent sidewalls allow the observation of the powder behavior inside, which can be captured by the image vision system [18]. This method allows for the measurement of the first avalanche angle (AA), flowing angle (\(\alpha_{\mathrm{f}}\)) and dynamic cohesive index (\(\sigma_{\mathrm{f}}\)). The avalanche angle describes the angle at which the powder reaches the highest potential energy (the highest point) in the drum just before the loss of stability--visible as an avalanche [8]. The avalanche behavior of a powder sample can be used as a good predictor of powder flowability for powders that are not too cohesive [19]. The first avalanche angle is measured by image analysis at a low rotational speed, and the flowing angle is measured at a variable rotational speed. In general, a low value of these factors corresponds to a good flowability [20,21]. In this test, one rotating speed (1 rpm speed) was used for the first avalanche angle, and 9 different rotating speeds between 2 and 60 rpm were used, both at an increasing and decreasing angular velocity, for the flowing angle. A total of 25 images were taken for each rotation speed, separated by 1.0 s. Based on the recorded images, the average position of the powder/air interface and the fluctuations around this value were tracked.