# Experimental Study on the Behavior of Polyurethane Springs for Compression Members
## 4 Experimental Results and Discussion
### Type 1 Specim Size Control
When the singularity for the 25% and 40% strains is considered, the overall trend demonstrates that the specimen length and the maximum force were proportional. This proportionality indicates that regardless of the stiffness of the specimen, the maximum force applied to the specimen can be adjusted according to the size of the specimen. Additionally, the maximum force and size of the specimen exhibited a positive linear relationship under the same stiffness and the size conditions of the designed specimens. The maximum force and strain of the specimens with the same size and compressive stiffness were linearly proportional. The maximum force increased with the maximum strain (see Figure 8), and as mentioned above, the size of the specimen and the maximum force also increased proportionally. In addition, as can be seen in Table 3, which lists a summary of the results of the linear regression analysis of the relationship between maximum force and maximum strain, the R\({}^{2}\) was almost 1, and it can be statistically inferred that the two variables had a linear relationship. Here, slope (a) means the slope of the linear regression equation, and Const. (b) means the y-intercept of the regression equation. Moreover, the slopes of the regression equations for 60L-72D-0P, 70L-77D-0P, and 80L-82D-0P demonstrated close values of 6.6998, 7.2369, and 6.9310, respectively. The slopes for 90L-88D-0P and 100L-92D-0P are 11.683 and 11.592, respectively, which are close. Accordingly, when cases for similar slopes are grouped, and the average slopes of three cases with a relatively small size and a relatively large size are compared, the case with a  
Figure 7: Relationship between length and maximum force. (**a**) Type 1-25%; (**b**) Type 1-30%; (**c**) Type 1-35%; (**d**) Type 1-40%. large size exhibits a gradient about 1.67 times larger. This indicates that even at the same compressive stiffness, the larger the size of the specimen, the higher the compressive force that can be accommodated at the same strain level. It was found that the difference in capacity reacted sensitively to the specimen size. At the point where strain is not zero in the unloading curve of one cycle, the first strain, known as the unloading strain (\(\epsilon_{UL}\)), occurs, at which point the compressive force becomes zero. In addition, the unloading strain is restored immediately. This restored strain is defined as the recovered strain (\(\epsilon_{RC}\)), and the remaining strain, excluding the immediately restored strain, is defined as the residual strain (\(\epsilon_{RD}\)). The unloading strain, recover strain, and residual strain covered in this study are expressed as the average values for each cycle. Figure 9 presents a schematic drawing of the three strains defined above and the polyurethane rubber spring. The unloading strain increased or decreased as the size of the specimen changed without any tendency, under other maximum strain conditions (see Figure 10a), except for the 40% maximum strain condition. However, the increase and decrease were small and occurred at a relatively constant level regardless of the change in the specimen size  
Figure 8: Relationship between maximum strain and maximum force. Figure 9: Schematic drawing of hysteretic behavior. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Slop (a)** & **Const. (b)** & \(\mathbf{R}^{2}\) \\ \hline
60L-72D-0P & 6.6998 & 29.097 & 0.9757 \\
70L-77D-0P & 7.2365 & 40.341 & 0.9299 \\
80L-82D-0P & 6.9310 & 30.900 & 0.96  
under the same maximum strain condition. The unloading strains of 3.87%, 4.83%, and 4.98% occurred on average under maximum 25%, 30%, 35%, and 40% strain conditions, respectively. Additionally, the size of the specimen remained constant, but when the maximum strain was varied, the unloading strain tended to increase with the maximum strain. Therefore, the unloading strain of the polyurethane rubber spring with the same compressive stiffness was generated at a constant level regardless of the size and in proportion to the maximum force.