積層製造（ AM）的最新進展使直接數字製造成為可能，從而可以製造比傳統製造工藝更高效，更快速的複雜形狀，例如超材料，漸變密度結構和復雜的幾何形狀。彈簧是許多設備/機器的重要組成部分，從小的錶到大的輪船或飛機。有限的研究人員在中底使用螺旋彈簧來提高機械性能，例如能量吸收，壓碎行為和強度重量比。在本研究中最初設計了六個漸變密度彈簧（ GDS）和一個均勻密度彈簧（ UDS）通過實驗和數值方法進行比較，從能量吸收、剛度和受力方面找出最佳螺旋彈簧。根據最初的研究結果，依腳的受力分佈數據選擇了兩個優化的螺旋彈簧，並針對中底進行了重新設計。此外，在中底研究中，設計並比較了三種漸變且密度均勻的螺旋彈簧中底，並根據腳的受力分佈數據檢查了其受力。為了比較，將所有樣品的總質量，邊界框和總高度保持恆定。所有樣品都是通過名為 Multijet Fusion（ MJF）的高速積層製造技術製造的。結果表明不同的形狀其導線直徑、線圈直徑和彈簧間距會明顯影響螺旋彈簧的性能，因此，可以通過針對特定應用來改變它們以控制剛度和變形量。還揭示了通過 GDS 可以獲得非線性力-位移行為及剛度隨著重量和最大應力而減少。在比較彈簧時得出的結論是， GDS 的承受力比 UDS 高 7 倍。此外，與 UDS 中底相比， GDS 中底的承壓能力高 6 倍，永久材料設定值更低。經實驗後，UDS 中底發現的變形高於 GDS（ 24％）的變形（ 45％）。 GDS 中底也與市售的波浪狀彈簧之中底進行了比較，結果表明，儘管基於波浪彈簧的中底重量增加了兩倍，但 GDS 中底在柔韌性和受力方面具有更高的機械性能。最後結論是， GDS 和優化彈簧參數可以提高彈簧和中底的機械性能，例如承載力，柔韌性和穩定性，並具有更高的強度重量比

Recent advances in additive manufacturing (AM) have made it possible for direct digital manufacturing to fabricate intricate shapes such as metamaterials, graded density structure, and complex geometries that are more efficient and faster over the traditional manufacturing processes.
The spring is a vital component of many equipment/machines ranging from as small as a watch to as big as a ship or airplane. A limited number of researchers have used helical springs in the midsole to increase mechanical properties such as energy absorption, crushing behavior, and strength-to-weight ratio. In this study, initially, six graded density springs (GDS) and one uniform density spring(UDS) were designed for comparative investigation through experimental and numerical methods to identify the optimal helical spring in terms of energy absorption, stiffness, and force bearing capacity. Based on the initial study results, the two optimized helical springs were selected and redesigned for the midsoles according to the force distribution data of feet.
Additionally, in the midsole study, three midsoles of graded and uniform density helical springs were designed and compared to examine the force bearing capacity according to feet force distribution data. For comparison purposes, the total mass, bounding box, and the total height of all samples was kept constant. All the samples were fabricated by high-speed additive manufacturing technology named Multijet Fusion (MJF). Results have shown that the variable shape, wire diameter, coil diameter, and pitch of the spring affect the properties of helical springs significantly, therefore, the stiffness and deformation can be controlled by varying them for a particular application. It has also been revealed that the non-linear force-displacement behavior and stiffness along with a reduction in weight and maximum stresses can be obtained by GDS. In the comparison of springs, it has concluded that GDS exhibits 7 fold higher force bearing capacity over the UDS. Furthermore, it was found that GDS midsole has 6 fold higher force bearing capacity, and has a lower permanent material setting when compared to UDS midsole. Moreover, a higher (45%) distortion was found in UDS midsole over the GDS (24%) distortion after the experimental.work. A GDS midsole has also been compared to the commercially available wave spring-based midsole and it was revealed that despite the 2 fold higher weight of the wave spring-based midsole, GDS midsoles have higher mechanical properties in terms of flexibility and force bearing capacity.
Finally, it has been concluded that the GDS and optimally defining the spring parameters can enhance the spring and midsole mechanical properties such as force bearing capacity, flexibility, and stability with a higher strength-to-weight ratio.

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