*2.4. Costing Model for Additive Manufactured Parts via Fused Filament Fabrication*

In the present study, the calculation of the costs for manufacturing a part utilizing AM technologies is performed as indicated in Equation (3):

$$\mathbf{C}\_{\text{AM}} = \mathbf{C}\_{\text{E}} + \mathbf{C}\_{\text{L}} + \mathbf{C}\_{\text{MAT1}} \tag{3}$$

where:


In this costing model, again, CE and CL are function of the processing time required, and CMAT is function of the material weight utilized.

#### *2.5. Costing Model for Parts in Stock*

In the present study, the calculation of the costs generated for a stocked part is make as indicated in Equation (4):

$$\text{Cs} = \text{C}\_{\text{MAN}} + \text{C}\_{\text{TRA}} + \text{C}\_{\text{H}} + \text{C}\_{\text{MGT}} \tag{4}$$

where:


In this costing model, CMAN, CTRA, CH and CMGT are function of the processing time required, of the material weight and of the physical dimensions of the part. For this reason, Cs can be expressed as shown in Equation (5):

$$\begin{array}{c} \text{Cs} = \left(K\_{\text{MAN}}^{t} \cdot t\_{\text{MAN}} + K\_{\text{MAN}}^{m} \cdot \mathbf{m} + K\_{\text{MAN}}^{v} \cdot v\right) + \left(K\_{\text{TRA}}^{t} \cdot t\_{\text{TRA}} + K\_{\text{TRA}}^{m} \cdot \mathbf{m} + K\_{\text{TRA}}^{v} \cdot v\right) \\ \quad + \left(K\_{H}^{t} \cdot t\_{H} + K\_{H}^{m} \cdot \mathbf{m} + K\_{H}^{v} \cdot v\right) + \left(K\_{\text{MGT}}^{t} \cdot t\_{\text{MGT}} + K\_{\text{MGT}}^{m} \cdot \mathbf{m} + K\_{\text{MGT}}^{v} \cdot v\right) \end{array} \tag{5}$$

where:


This cost modelling framework is interesting for global companies as it enables a comparison of different manufacturing and inventory costs incurred in different locations, as far as the labor costs, the land costs and the logistic chains are quantified; as well as the processing times required, material weight and physical dimensions of the parts.

If a designer can reduce the mass and the manufacturing processing times of a product, without modifying any of the rest of factors, the variation of Cs for a single part in the stock can be calculated as shown in Equation (6):

$$
\Delta \mathbf{C} \mathbf{s} = \left( K\_{MAN}^t \cdot \Delta t\_{MAN} + K\_{MAN}^m \cdot \Delta \mathbf{m} + K\_{TRA}^m \cdot \Delta \mathbf{m} + K\_H^m \cdot \Delta \mathbf{m} + K\_{MGT}^m \cdot \Delta \mathbf{m} \right), \tag{6}
$$

where:

$$
\Delta t\_{MAN} = t\_{MAN}^{\text{Conventional process}} + t\_{MAN}^{\text{DfAM process}},\tag{7}
$$

$$
\Delta \mathbf{m} = m^{\text{Conventional product}} + m^{\text{D}fAM\text{ product}},\tag{8}
$$

Or, grouping the terms of Equation (7), as shown in Equation (10):

$$
\Delta \text{Cs} = \left( K\_{MAN}^t \cdot \Delta t\_{MAN} + K\_{MAN}^m \cdot \Delta \text{m} \right) + \left( K\_{TRA}^m + K\_H^m + K\_{MGT}^m \right) \cdot \Delta \text{m} \tag{9}
$$

Which, in the aggregation of all the changes in Cs for all the parts in the stock, can be calculated as expressed in Equation (11):

$$
\sum\_{i=1}^{i=n} \Delta \mathbf{C} \mathbf{s}\_i = \sum\_{i=1}^{i=n} \Delta \mathbf{C}\_{MANi} + \sum\_{i=1}^{i=n} (K\_{TRA}^m + K\_H^m + K\_{MGT}^m) \cdot \Delta \mathbf{m}\_i. \tag{10}
$$

Or, in terms of the TIMC, as expressed in Equation (12):

$$\mathbf{C} \sum\_{i=1}^{i=n} \, \Delta \mathbf{C} \mathbf{s}\_i = (TIM \mathbf{C}\_n^{\text{Conv. proc.}} \cdot \delta) + (K\_{TRA}^m + K\_H^m + K\_{MGT}^m) \cdot \mathbf{m}\_{total\ a}^{\text{Conv. proc.}} \cdot \gamma \,. \tag{11}$$

where:


#### **3. Results**

The product object of the case study in the present work is a real case articulated in the fluid handling industry. To be consistent in the analysis and following to the product segmentation undertaken in Section 2.1, it has been chosen a relatively common product (weighting less than 1 kg), demanded on a relatively low number of orders (less than 42 orders) and in relatively short series (less than 2400 units per order in average). The product is redesigned, and the costs are assessed in the conventional manufacturing process and in an AM technology (FFF) both for the original part design and for its redesign. The reduction in the manufacturing costs are then used to infer the reduction of overall inventory costs that could be achieved through the introduction of AM.

#### *3.1. Case Study (Spare Part for Fluid Handling): Product Definition*

#### 3.1.1. Product Specifications

The overall product is a flow regulation system for fluids (an automatic valve), which contain many different parts. A pneumatic piston acts on the actuator (green) which is connected to the membrane (black) by means of a metal insert in form of a pin. The support (red) is responsible for aligning the actuator with the membrane so that it can restrict the flow and separate the pneumatic system from the hydraulic system. Finally, the body of the valve (dark gray) is responsible for the conduction of the fluid (see Figure 4). The system is fixed with stainless steel screws that go through all the parts until reaching the pneumatic piston.

In this case, the part to be studied is the support of the automatic valve. The need is to manufacture 2000 units of supports to fully supply the customer.

The technical specifications of the support require the use of materials with good mechanical and thermal properties. For this reason, technical polyamide (PA666) also used in the automotive industry, is the material selected for manufacturing the part. It is a strong, ductile and easy to print material. The filament for the present study (*Novamid® ID1070*), was supplied by *Nexeo Solutions*, suppliers of the material used.

**Figure 4.** Automatic valve section, in red the part to be redesigned and assessed (support).

#### 3.1.2. Original Product Costs (Molding)

The case study for this inventory part starts with the costs assessment considering that this part was originally designed to be manufactured by injection molding technologies. All the economic treatment is handled in Euros as the company in the case study has its headquarters in the Barcelona region (Spain).

As it can be seen in Table 4, the cost analysis reaches a minimum total cost per part of 1.71 €, in the case of a total production volume of 275,940 parts per year over a 10 years' production period. In the case of manufacturing only the 2000 units to supply the demand in the considered order, the total cost per part is of 21.61 €.

**Table 4.** Injection molding costs assessment for the original product at a maximum production rates and at an order level of 2000 units.


#### 3.1.3. Original Product Costs (AM)

As a starting point approximation, the 3D printing costs of the case study part (support) are analyzed without carrying out any type of structural redesign. The printer used for the present study is an FFF machine from the manufacturer "BCN3D" (Sigma model) that has the impact on the cost of the part accounted in Table 5. With this calculation method, the total cost per part when manufactured via AM technologies is of 40.06 € with independency of the number of units to be manufactured.


**Table 5.** Additive manufacturing (AM) costs assessment for the original product.

The operation data presented in Table 5 has been calculated with the BCN3D CURA software, including the number of parts per platform in the present case-2-, and the platform build time—143 h. CURA also calculates the amount of material used in the construction, given a determined level of infill; which in the present case accounts for 862 g per part.

The relevant printing parameters utilized by the BCN3D CURA software (Version 2.0, BCN3DTechnologies, Barcelona, Spain) to calculate the cited output, which will be needed for the cost calculations are the following:


BCN3D CURA software graphical interface is capable of representing the parts in 3D located in the construction platform as they will be obtained once the parts manufacturing is completed. For the manufacturing of the case study part, it is chosen to place the parts laying on its bigger flat surface. The BCN3D CURA graphical simulation is shown in Figure 5.

**Figure 5.** BCN3D CURA software platform simulation the case study part (support) in the original design model.
