# Evaluation of the Circularity of Recycled PLA Filaments for 3D Printers
## 8 MCI Calculation  
The objective of this study is to find the approximate MCI of a 3D printed part for educational use (parts to explain mechanical assemblies to students) with this mixture of virgin PLA and recycled PLA, using approximate data required for its calculation, already explained in the methodology at the product level of the MCI. It is not intended to produce a report like that which would be obtained through the MCI process via the Ellen MacArthur Foundation. This study only aims to calculate the MCI of the product, without considering complementary indicators or analysis of components and materials. The following considerations have been made:  
* The average mass of the part is 73 g, then \(M=73\) g.
* A part is only made of PLA plastic, 70% of which is recycled and 30% is virgin material ([8,9] recommend using 20-40% virgin PLA so as not to alter the quality of the pieces obtained). Therefore, the fraction of the F\({}_{r}\) feedstock that comes from recycled material is \(F_{r}=0.7\). This makes \(V=M\cdot(1-F_{r})=21.9\) g.
* It is considered that the fraction of the product that can be recycled \(C_{r}\) is 99% (1% is removed because of defects due to blows and similar actions that can make a piece detach part of material). Therefore, the amount of unrecoverable waste from a piece is \(W_{o}=M\cdot(1-C_{r})=0.73\) g.  
* The efficiency of the \(E_{c}\) recycling process has been estimated at 95%. Thus, the waste from the recycling process is \(W_{r}=M\cdot C_{r}(1-E_{c})=3.61\) g.
* A 2% loss has been assumed in the process of creating the filaments formed by recycled PLA and virgin PLA. This is an estimated value, due that some PLA waste is burnt and some granulates are drop off. That is, the efficiency of the process of creating recycled raw material \(E_{f}\) is 98%. Therefore, \(W_{f}=M\cdot F_{r}(1-E_{f})/E_{f}=3.61\) g.
* As for the utility \(X\), due to the difficulty of measuring the utility (lifetime or functional units) of the 3D parts with respect to others of equal measures, it has been chosen to consider the utility \(X=1\). That is, the lifetime of the part and its functional units are the same as those of parts of the same dimensions manufactured with other printers and similar materials. If the printer's MCI were to be measured, the number of parts printed per year could be used as the functional unit. We assume that we can print 4000 units/year. Therefore, we get \(U=U_{av}=4000\). Therefore, \(X=U/U_{av}=1\). Both the efficiencies and the percentage of recycled material (\(R_{c}\)) are very high because it is a highly recyclable material (PLA). Almost 100% of the final product is used that is observed in an experimental way. Since the final product is made only of PLA, it can be converted back into PLA filaments for new parts. Even shavings and chips can be converted to PLA filaments. However, considering efficiencies of 100% and material losses of 0% seems utopian and ideal. Therefore, these small losses have been considered in the recycling process. This means that the actual result of the MCI will surely be better than the one obtained in this first study carried out in a conservative way. With \(W_{o}\), \(W_{c}\), and \(W_{f}\), you get \(W\) (the waste mass of the system), used together with \(W_{c}\), \(W_{f}\), \(V\) and \(M\) to calculate the LFI (Linear Flow Index). With the utility \(X\) (assumed to be equal to the unit) and the LFI, MCI* is calculated. As the LFI can be negative, the MCI will be the maximum between 0 and MCI*. As shown in Table 1, using the formulas explained in the methodology at the product level of MCI, the score obtained was an MCI of 0.84 (out of 1). On the other hand, as the production of parts using these filaments is not yet in operation, 70% has been taken as the percentage of PLA recycled in the filaments. In order not to affect the quality of the pieces, it is recommended to use a \(F_{r}\) between 60% and 80% [9].