Simultaneous optimization of topology and process parameters for laser-powder bed fusion additive manufacturing

Abstract

Additive manufacturing (AM) technology is used in sectors such as automotive and aerospace, due to its advantages in producing complex and lightweight structures. However, it is necessary to reduce the total manufacturing costs for AM technology to become widespread. The topology optimization (TO) studies in the literature typically optimize only the design without taking into account the manufacturing phase or sequentially optimize the topology first and then the process parameters. On the other hand, simultaneous optimization of topology together with process parameters provides more efficient and less costly solutions. This paper describes a strategy for simultaneous optimization of topology along with process parameters of the laser-powder bed fusion (L-PBF) process. The topology, laser power, scanning speed, energy density, and yield strength are controlled by integrating the overall process–property–structure–performance relationship of the L-PBF process into the optimization. The proposed simultaneous optimization method aims to minimize the total cost function including material, manufacturing, and energy costs. Moreover, the constraint functions of the optimization include the volume fraction, the strength of the structure, and the energy density calculated according to the process parameters. The proposed method is successfully applied to three different design problems as cantilever beam, MBB beam, and L bracket, respectively. The results of different TO methods including conventional TO (compliance minimization), structural TO (similar to stress-constrained TO), and sequential process parameters and topology optimization are compared with the results of the proposed method. It is found that the proposed method provided the minimum cost results, and the obtained designs met the structural requirements.

Appendix

Artificial densities determine the optimum material distribution/optimum design, so, it affects the amount of material and the material cost. If the value of artificial densities increases the objective function (total cost) will increase as well as compliance constraint will relax. There is a conflict between the increasing objective function and relaxing compliance constraint and an optimization can be performed using the conflict. This mentioned optimization is formulated given in Eq. (20). The optimization formulation does not include the volume constraint and the optimization is performed for the cantilever beam design.

$$\begin{gathered} {\text{Find}}\;\;\;\;\;\;\;\left[ {{\varvec{\rho}},\user2{ P},{\varvec{V}}} \right] = \left[ {\rho_{1} ,..,\rho_{N} , P_{1} ,..,P_{N} , V_{1} ,..,V_{N} } \right] \hfill \\ {\text{Minimize}}\;\ Cost \left( {{\varvec{\rho}},\user2{ P}, {\varvec{V}}} \right) \hfill \\ {\text{Subject}}\;{\text{to}}\;K\left( {\varvec{\rho}} \right)u = f \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;C\left( {\varvec{\rho}} \right) - c_{0}^{max} \left( {{\varvec{\rho}},{\varvec{P}},{\varvec{V}}} \right) \le 0 \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;ED_{min} \le ED_{i} \left( {{\varvec{P}}, {\varvec{V}}} \right) \le ED_{max} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0 \le \rho_{i} \le 1 \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P_{min} \le P_{i} \le P_{max} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;V_{min} \le V_{i} \le V_{max} \hfill \\ \end{gathered}$$

(20)

Optimization results are given in Fig. 12. It is shown that laser power and scanning speed of each element converged to upper bounds (Fig. 12a, b). Due to the convergence to upper bounds, yield strength and ED values of each element are constant (see Fig. 12c,d).

Fig. 12

Optimization results: a power distribution, b speed distribution, c yield strength distribution and d) ED distribution

After the optimization, the average of artificial densities converged to 0.56. Moreover, production and cost information are listed in Table 9. According to the results, the material cost is higher than the solution with volume constraint, as expected. On the other hand, production cost and therefore total cost is lower than the original SiPPTO solution. The yield strength of the element increases with increasing scanning speed and the compliance constraint relaxes at higher scanning speed. However, yield strength is inversely proportional to laser power. It is expected that laser power decrease and scanning speed increase at the regions that should have higher yield strength. In these results, both the decrease of the total cost and the increase of the yield strength with the increasing scanning speed is meaningful. However, it is unexpected that laser power converged the upper bound. Because, while decreasing the total cost with increasing laser power, the yield strength of the structure decreases. The increasing rate of the material cost is less than the increasing rate of the production cost. According to the results, it is concluded that while rising the material cost, production cost decreases radically with increasing artificial density, and therefore process parameters converge to the upper bound with the optimization formulation without the volume constraint. Therefore, it is suggested that the volume constraint function should be used in SiPPTO method.

Table 9 Production and cost information of cantilever beam designed without volume constraint