# Design and Multi-Objective Optimization of Fiber-Reinforced Polymer Composite Flywheel Rotors
## 3 Modeling
### Costs
#### 3.2.2 Manufacturing Costs  
In general, manufacturing costs are subdivided into operating costs and conversion costs. Operating costs occur during the operation of the machine. Hence, they are determined by the process time multiplied by the sum of the MHR and the labor costs. Conversion costs are incurred through cleaning, replacing of tools or other processes necessary to prepare a machine for the next task. Conversion costs are calculated by multiplying the conversion time by the sum of the MHR and the conversion costs per time \(c_{\text{conv}}\). The MHR is part of the calculation for conversion costs because the machine cannot be used for other tasks during conversion. \(c_{\text{conv}}\) may represent labor cost or another MHR when a robot performs the conversion. Since a conversion generally happens for each rim, the conversion costs are multiplied by the number of rims \(N_{\text{rim}}\). Equation (5) shows a generic formula for the manufacturing costs. \[C_{\text{manu,generic}}=t_{\text{process}}(MHR+c_{\text{ labor}})+N_{\text{rim}}t_{\text{conv}}(MHR+c_{\text{conv}}). \tag{5}\]  
The required time for the filament winding process is determined by the volume of the rim, the cross-sectional area of a fiber strand and the speed of the fibers. It should be noted that the speed of the fibers is not directly configured but the rotational speed of the mandrel. As the rim grows larger during the winding process, the fiber speed also increases. For the calculation of the process time it is sufficient to calculate the average fiber speed. The filament winding process time can be written as follows  
\[t_{\text{winding}}=\frac{\sum_{j=1}^{N_{\text{rim}}}\pi h\left(r_{j+1}^{2}-r_{ j}^{2}\right)}{N_{\text{receels}^{\text{$\mathcal{V}$ fibers}}}A_{\text{woving}}}. \tag{6}\]  
The labor cost is assumed to be 35 CAD/h. According to [21], the conversion time for the preliminary work and the cleaning process for a four-axis filament winding machine is 80 min. Finally, the costs for filament winding must be divided by the number of spindles for mandrel rotation and the number of filament winding machines, respectively. The curing time is depended on many factors such as the oven power, the rim temperature caused by the chemical reaction of the resin systems and the heat capacity of the rims. These factors are rather complex, and hence, the curing time is considered a design variable. Since an oven may be able to cure several rims at the same time, the manufacturing costs per rotor must be divided by the oven capacity. On the other hand, rotors may consist of more than one rim. Hence the manufacturing costs must be multiplied by the rim number. Thus, the cost of curing can be written as  
\[C_{\text{curing}}=\left(t_{\text{curing}}(MHR_{\text{oven}}+c_{\text{ labor}})+t_{\text{conv,curing}}(MHR+c_{\text{conv,curing}})\right)\frac{N_{\text{rim}}}{C_{ \text{oven}}}. \tag{7}\]  
According to [21], the conversion time for the oven is 25 min. In the present study, only press fitting by tapered rim surfaces was considered. To create tapered surfaces between adjacent rims, the rims must be machined. The first rim does not need a tapered surface, whereas the following rims need a tapered surface only on the outside diameter (mandrels areprovided with the appropriate geometry to shape the rim surface on the inside diameter). Assuming a constant speed of the tool \(v_{\rm turning}\) with the tool width \(d_{\rm tool}\), the process time can be expressed as  
\[t_{\rm turning}=\sum_{j=2}^{N_{\rm trim}}\frac{4\pi hr_{j}}{v_{\rm turning} \times d_{\rm tool}} \tag{8}\]  
The process costs result in  
\[C_{\rm turning}=\frac{t_{\rm turning}(MHR+c_{\rm labor})+N_{\rm rim}t_{\rm conv,turning}\big{(}MHR+c_{\rm conv,turning}\big{)}}{N_{\rm machines}} \tag{9}\]  
The conversion time for the press is assumed to be 10 min. Similar to the curing time, the time for press fit assembly is also considered a design variable. According to [21], this time and the conversion time are 15 min each.