Evaluation of Structural Design Enhancement and Sensitivity of Automatic Ocean Salt Collector According to Design of Experiments

2.1 Calculation of Design Load Conditions

Fig. 2 shows the initial design of the electric AOSC developed to automate the collection of salt in ocean salt farms and enhance ocean salt collection safety as well as production per unit of salt collection crystallizing pond area.

As shown in Fig. 2, a salt collector part and towing part were designed and applied to the AOSC to automate ocean salt collection, and a drive and power part for transferring electric driving power and a rail frame part for transferring the collected salt were installed. To safely support the load generated during operation and mounting of the AOSC’s functional components, a collector frame, rail frame, and main frame were applied. Table 1 summarizes principal information on the AOSC.

In terms of the main design load conditions for reviewing the AOSC’s structural safety, considering the harshest operating conditions that may arise during salt collection, a maximum loading case, braking case, and operating case under the maximum loading case were selected. Table 2 summarizes the design load conditions for each load case.

As shown in Table 2, the design loads generated in the AOSC for each load case were combined to configure the design load conditions. In the loading case (LC1), the weight of each functional product was applied considering the center of gravity and mounting position. To reflect the entire AOSC’s weight, an inertial load was applied considering gravity acceleration, and the maximum salt collecting capacity was applied as distribution pressure on the top of the rail frame in the center of the AOSC. In the operating case (LC2), along with the loading case, the maximum towing capacity and acceleration measured through the operation of prototype equipment manufactured with the initial design were applied in the transport direction. In the braking case (LC3), to consider a sudden braking case along with the loading case, driving acceleration was applied in the opposite direction of the transport direction. Gravity load was applied for the acceleration of LC2 and LC3 so that the gravitational influence of acceleration acted on the entire structure.

2.2 FEM-based Structural Analysis

To conduct an FEM-based strength performance evaluation of the AOSC's initial structural design, an FEM (Fig. 3) was generated considering the main structure (main frame, rail frame, and collector frame) and bracket part that can apply the weight and design load of the functional products.

As shown in Fig. 3, the thicknesses of the main frame part, rail frame part, collector frame part, and bracket part are 2.5 mm, 1.5–4.0 mm, 1.5 mm, and 4.0 mm, respectively, which were applied in the initial design stage through empirical design. The elements used in the FEM consisted of a shell element for the main structure of the main frame part, rail frame part, collector frame part, and bracket part, and lumped mass elements for the weight of each functional product. Rigid links were used for the connection of each structural member and application part of the functional weight and design load, and the driving direction constraints of the rigid links were defined considering the operating mode. Table 3 summarizes the model information used in the FEM, and material properties of the austenitic stainless steel (SUS304L). The design conditions defined in Table 2 were applied for the load condition used in the structural analysis and for the boundary condition; all degrees of freedom were constrained except the rotation direction of the driving direction for each wheel of the wheel part.

Abaqus/Implicit (Simulia, 2018), a general-purpose finite element analysis program, was used to conduct the structural analysis, and the stress and deformation of the major structural parts were calculated for each design load condition. Table 4 summarizes the structural analysis results of the AOSC’s initial design stage, and Fig. 4 shows the overall stress and strain distribution results for the braking case (LC3).

As shown in Table 4, under all design load cases, the stress values of the main frame part and the rail frame part failed to satisfy the material’s allowable yield stress. Furthermore, the braking case (LC3) showed the harshest results of all design cases. In all design load cases, the maximum stress occurred in the main frame part, and as shown in Fig. 4, the maximum stress was distributed in the center of the main frame part. The maximum stress occurred locally at the upper center of the main frame and bracket joint, which is likely because the design thickness of the main frame was 2.5 mm in a thin plate, and a gentle shape change design was not applied in the bracket joint. Accordingly, the structural analysis results of the initial design stage demonstrate that design improvements are required to secure the strength and safety of the AOSC’s structural design.

3.1 DOE Theory

OAD detects the main effects and interactions between factors for experiments with a large number of factors and excludes information on high-order interaction and interaction between low-influence factors, thereby reducing the number of experiments through an OAT. The OAT has two, three, four, five, and mixed levels, with two and three levels typically used. This study applied OAT with three levels, as in the following equation (Park, 2012).

where m is an integer of 2 or more, 3^m is the experiment size, and (3^m − 1)/2 is the number of rows in the OAT.

As shown in Fig. 5, the BBD method has a feature by which corner points are not used in the experimental space. This technique is also referred to as spherical, rotational, or approximate rotational quadratic design (Box and Behnken, 1960).

As shown in Fig. 5, BBD uses polyhedral edge center points, excluding center points and corner points in the entire experimental space, thus allowing economical DOE. BBD is advantageous for calculating quadratic regression equations and exploring optimal conditions when the factors are quantitative and have three levels. In terms of the number of independent variables k, BBD can easily generate orthogonal blocks with a small number of experimental points, through which a quadratic regression equation can be obtained.

CCD adds center points and axial points to 2^k factor experiments and detects the curved change in the amount of responses caused by changes in the level of variables (Park, 2012). In CCD, the number of center points becomes at least one, and the number of axial points becomes 2k. If the number of center points is n_o, then the number of CCD experiments n can be defined by the following equation.

As in Eq. (2), in the case of k > 2, the DOE method can be performed with significantly fewer experiments than factorial design, and it is highly advantageous if the experimental cost is high. Moreover, rather than performing DOE again when the regression model estimation must be changed, CCD can perform sequential experiments that add new data points to the center and axis.

3.2 Comparison of Best Design Cases and Structural Design Sensitivity According to DOE Characteristics

To conduct the AOSC structural design effect evaluation according to the DOE characteristics, the thickness of the main structural members was set to three levels of the design factors, and the maximum stress and weight for each design load case shown in Tables 2 and 4 were set as the output response. The upper and lower limits of the design factors were set considering the range within which the AOSC can be manufactured. Table 5 and Fig. 6 show the configuration of AOSC design factors.

The configured design factors and three-level design factor range in Table 5 and Fig. 6 were applied. An experimental matrix with 81 runs was configured for OAD, 41 runs for BBD, and 43 runs for CCD. Tables 6–8 show the results of the response functions calculated via finite element analysis according to changes in design factors in the experimental matrices configured through each DOE technique.

From the results summarized in Tables 6–8, combinations of design factors for which the maximum stress under all design load cases was calculated at the allowable yield stress of 182.8 MPa or less were explored, among which the combination with the lowest weight increase rate was selected as the best design case. Table 9 shows the best design plan selected for each DOE technique.

As shown in Table 9, the best design case in all DOE methods satisfied the allowable yield stress at a level in which the maximum stress was similar for all design load cases compared to the initial design, although there was a variation in weight. Among the DOE methods for the structural design of the AOSC considered in this study, the CCD method exhibited a weight increase rate of 43.4%, which was superior to the OAD and BBD methods, while the BBD method showed the highest increase rate of 55.2%. In terms of the change in thickness of the main member, the main frame (DF-#1) thickness design factor tended to increase to the upper limit of 6.0 mm for all DOE techniques, while the remaining design factors showed variations of 1.0 mm or less. Considering the weight increase rate and the number of experiments of DOE, which represents the numerical calculation cost, CCD was shown to be the most efficient method for deriving improvement cases for the AOSC’s structural design. Fig. 7 shows the overall stress and deformation distribution results of the enhanced best design case calculated from CCD for LC3.

As shown in the results of Fig. 4 and Fig. 7, the maximum stress value was improved by 39% in the best design case compared to the initial design, the location of maximum stress moved from the main frame to the center bracket, and the maximum deformation was improved by 81%. The cause of the movement of the maximum stress location is attributed to the main frame member’s thickness increasing more than that of the bracket. Moreover, the overall structural safety improved as the maximum stress location moved from the main frame (main structural member) to the bracket (local member). A quantitative main effect analysis of the design factors for each response function was conducted according to the DOE method using the experimental matrix of OAD, BBD, and CCD, the results of which are shown in Table 10. The main effect is an indicator of the observed response function’s average change according to the change in the level of the design factor, i.e., the sensitivity. As such, the greater the effect calculated for each design factor, the higher the importance for the response function of that design factor.

As shown in Table 10, in all DOE methods, the effect of the main frame (DF-#1) was greatest on the maximum stress of the weight and design load cases, and the strength of the collector frame (DF-#4) showed the lowest main effect. The principal effect on weight was nearly identical in all DOE methods, while that on the strength of DF-#1 in BBD was higher than in the other DOE methods. Accordingly, an exploration of design enhancement cases applying various DOE techniques was performed. The results indicated that the most effective exploration method was to apply CCD to enhance the strength performance of the AOSC’s structural design, and that the main frame (DF-#1) was the most important structural member to consider in design.

3.3 Review of DOE Suitability Through Approximate Modeling

Because approximate models are typically generated from DOE, by quantitatively examining the accuracy of the generated approximate model, the overall suitability of the DOE method considering the number of experiments, the level of design variables, and DOE method selection, can be verified (Lee and Song, 2013). To verify the suitability of the sensitivity analysis results of major structural members and the exploration of AOSC improvement cases using various DOE techniques applied in Section 3.2, approximate modeling using RSM was conducted for each DOE technique, and the RSM design space exploration accuracy generated from each DOE technique was examined. The least-squares method can be used to define the RSM, a quadratic polynomial regression model, as follows (Song and Lee, 2010).

From the n experimental points calculated using the DOE techniques (OAD, BBD, and CCD), if matrix Z expressed by k basic variables and the real response vector g is given, then the relationship between g and Z can be expressed as follows.

To minimize the random error vector e and estimate the unknown RSM approximation coefficient vector A_R, a least squares function is applied as follows.

Applying the approximation coefficient calculated from Eq. (5), the quadratic regression approximate model is expressed as follows.

An RSM approximate model of Eq. (6) is generated for each response function using the results of the DOE techniques (OAD, BBD, and CCD). Fig. 8 shows the response surface results of DF-#1 and DF-#5 (design factors with high main effect), and for LC3 (the braking case maximum stress response function) using the CDD method among the RSM approximate model results.

As shown in Fig. 8, the RSM, a quadratic regression approximate model, effectively approximates the nonlinear design space of von-Mises stress, the LC3 response function.

The accuracy of the approximate model calculated from each DOE method is determined by R² as shown in Eq. (7).

where t_i is the actual value, y_i is the predicted value estimated from the approximate model, and t̄_i is the average of the actual values. When R² is 1.0, the predicted value estimated from the approximate model exactly matches the actual value in the entire design space. Table 11 shows the accuracy analysis results of the RSM generated by the response function using each DOE technique.

As shown in Table 11, the accuracy of the approximated RSM was very high for each response function. The accuracy of the approximate model of weight was 1.0, which signifies no difference with the actual value for all DOE techniques. In terms of the accuracy of the approximate model for the response function under each design load case, an error of less than 3% of the actual value was observed, and the difference between DOE methods was found to be very small. Therefore, this study found that the overall DOE implementation method used to analyze the sensitivity of major structural members and explore enhanced design cases of the AOSC’s structure was reasonable, which includes the number of experiments, levels of design variables, and DOE method selection.