## 3 Results and Discussion  
### Stress Relaxation Model for the Compression of Machine-Harvested Seed Cotton  
Machine-harvested seed cotton is a common agricultural fiber material, and for the rheological properties of agricultural fiber material, scholars often use the Maxwell and Burgers models. Many studies have also shown that the Maxwell model can better describe the stress relaxation of agricultural materials. Therefore, in this study, the Maxwell model was chosen to characterize the stress relaxation properties of machine-harvested cotton  
Figure 2: The experiment procedures. (**a**) mechanized harvesting; (**b**) machine-harvested seed cotton sampling; (**c**) rehydration (adding impurities) treatment machine-harvested seed cotton samples; (**d**) processed samples; (**e**) feeding quality control; (**f**) guarantee of initial density; (**g**) machine-harvested seed cotton compresses and strain remains 300 s; (**h**) machine-harvested seed cotton molding. by comparing the obtained stress relaxation curves with common viscoelastic models. Although the Maxwell model can describe the stress relaxation process of machine-harvested cotton, the more Maxwell cells, the closer it is to the actual stress relaxation process of the material; it will introduce many variables, which is not conducive to the further solution of the model. And the stress rapid decay time \(T_{1}\) is the time required for the stress to decrease to 1/e of the initial stress. The generalized Maxwell has multiple stress relaxation times that are equal to the time required for each Maxwell element to decrease to 1/e of their respective initial stresses. More importantly, due to the special nature of the Maxwell cells (which consists of a spring and a viscous pot), the initial stress on it does not eventually decay to zero, but to a stable value, which we call the equilibrium stress (or modulus). The stress relaxation of machine-harvested seed cotton with 6% moisture content, 12% trash content and 300 kg/m\({}^{3}\) compression density were used as an example, and the stress variation curve of machine-harvested seed cotton with time is plotted when its strain remains 300 s. Using Origin 2017 to fit the regression to it using the Maxwell model and generalized Maxwell model, we can obtain the expression of stress relaxation characteristics of machine-harvested seed cotton, which can be used in 2 Maxwell cells and 1 equivalent spring parallel five-element model [23], as shown in Figure 3a, and the expression is shown in Equation (3). \[E(t)=E_{1}e^{-t/T_{\text{S1}}}+E_{2}e^{-t/T_{\text{S2}}}+E_{e}, \tag{3}\]  
where  
\(T_{\text{S1}}=\eta_{1}/E_{1}\); \(T_{\text{S2}}=\eta_{2}/E_{2}\). \(T_{\text{S1}}\), \(T_{\text{S2}}=\) the rapid decay time of the stress, the slow decay time of the stress (s)  
\(E_{1}\), \(E_{2}=\) the modulus of elasticity for the first Maxwell model, the modulus of elasticity for the second Maxwell model (MPa)  
\(E_{e}=\) the equilibrium elastic modulus (MPa)  
\(\eta_{1}\), \(\eta_{2}=\) the coefficients of viscosity for the first Maxwell model, the coefficients of viscosity for the second Maxwell model (MPa-s). The compression process of machine-harvested seed cotton is divided into two stages. The first stage is the compression, where with increasing compression displacement the compression density of machine-harvested seed cotton increases continuously; the second stage is the stress relaxation stage, in which the stress change in this stage also has two stages. In the initial of stress relaxation, stress decays rapidly to 1/e of the initial, which occurs within 10 s of stress relaxation; after that the stress decreases slowly and its value tends to a constant value. The proper equation is shown in Equation (4). \[E(t)=0.0706e^{-t/4.9377}+0.0368e^{-t/98.8569}+0.2005, \tag{4}\]  
Figure 3: Stress relaxation model and fitting curve. (**a**) five-element Maxwell mode; (**b**) stress relaxation of machine-harvested cotton fitting curve.