Analysis of forming properties based on pellet feed forming constitutive model

Abstract: In the feed industry, through crushing, mixing and conditioning, feedstuffs are pelleted by mechanical equipment to obtain pellet products. In this compression process, the feed material particles are overlapped and staggered with each other, and the granular system is changed from the loose state into the curing bond with squeeze flow and the gap flow occurs synchronously. The mechanism for the pelleting process appears to be a regular relationship of stress and strain and other mechanical properties. Therefore, it is necessary to learn the stress-strain relationship and rheology properties of the feedstuffs during the compression process, and it is of theoretical significance to analyze the forming rules of granules and optimize the pelleting process and equipment. In this paper, based on characteristics and nonlinear properties of wheat as a feedstuff, a nonlinear visco-elasto-plastic constitutive model for characterization of rheological properties was constructed. Based on the experiment, and establishment and verification of the numerical model, the rheological properties such as viscoelasticity and plasticity of the feedstuff were analyzed by the model coefficients, and the influence of material properties and processing parameters on the rheological properties is studied. Also, the relationship between the rheological coefficients of the materials and the quality of the pellet is learned, which provides a new methodology for the study on the compression process of pellet feed. According to the process of pelleting, the factors in compression trials were selected including moisture, particle size (i.e., mesh size) and forming temperature, compression load. During the initial stage of the compression process, air between the particles was extruded by pressure and relative positions of particles are rearranged under the action of the inertial force. With the process progressing, the gap gradually decreases to infinitely small and the relative positions of the particles cease to change significantly, after which the deformation of the material can be considered as caused by its own viscoelastic properties, and therefore the compression process is divided into inertial deformation stage and visco-elasto-plastic compression stage for better description. According to the theory of rheology, the feedstuffs properties exhibited during the compression process are summarized as elastic-plastic, viscous and particle-wall friction, and represented by the strain hardening spring element, Newton viscous dashpot element, and Coulomb friction element, respectively. The elastic modulus shows the flexibility of the elastic element or the difficulty of compression. It turns out that the larger the coefficient, the more difficult the deformation and the stronger the stiffness of the material, which can stand for the strength and deformation properties. The improvement of the plastic strain showed by combined plastic exponent, which is coupled by plastic modulus and strain hardening exponent, indicates that the deformation can be maintained after the removal of the compressive stress, which has a special meaning on the quality control of the pellet feed. The viscous coefficient is mainly characterized by the ability of the particles to be bonded in the process of pelleting, thus reflecting the capacity of the formed pellet to stay stable under external force without significant damage in the current state. Meantime, the frictional loss factor can reflect the characteristics of energy dissipation, which mainly includes the friction and adhesion between the particles or the particles and the die wall. The compression stage was divided into 5 even ranges in order to study the various material properties along with the process. The numerical results of the constitutive model of wheat were obtained under 15% material moisture content, 2.0 mm mesh size, 80 ℃ forming temperature and 3 kN compression load, which showed that the determination coefficients (R2) in all stress ranges were beyond 0.99 and the mean relative error values were 3.883%, 1.798%, 2.992%, 1.496%, and 6.721% in the ranges of 1-5, respectively. The comparative curve showed a good fit between the actual test value and model value; besides, the χ2 examination showed that the χ2 values of the data in each range were much smaller than the standard values in the degree of freedom of 130 and the significance of 0.001. Based on the above criteria, this constitutive model possesses a good performance that can be used to characterize the rheological properties of wheat. The constitutive model coefficients and the rheological properties of the feedstuff were characterized by regular changes, which showed obvious stress function: The elastic modulus increased with the increase of stress, indicating the deformation performance of the material was gradually weakened and the overall compressibility of the material decreased step by step to reach the end of forming, and the stiffness increased significantly. The increases of combined plastic exponent showed that the plastic deformation of the material increased gradually with a sudden downside in the last range. The absolute value of the viscosity coefficient increased gradually, which means that the bonding force among the material particles is enhanced with the progress of the forming, and the connection between the particles is strengthened therewith. For the influence of various forming factors, results were showed as follows: The increase in forming temperature can improve the elastic modulus, which means a better compression deformation capacity; with preferable softening, and bonding effect on the compressibility, higher moisture content can improve the combined plastic exponent and viscosity coefficient at the same time; the decrease of the particle size increases the absolute value of the viscosity coefficient, indicating its significant positive effect on the particle bonding force. The correlation relations between the pellet quality index and the constitutive model coefficients show that the pellet density, the pellet forming ratio and the pellet hardness were correlated with the viscous coefficient, plastic modulus, and elastic modulus respectively (P<0.001), which owned the highest correlation coefficients that were all above 0.80, illustrating the close relationship between pellet product quality and feedstuff rheological properties. The nonlinear visco-elasto-plastic constitutive model constructed in this paper can provide a new methodology and perspective for the research of the process of feed pelleting, and provide theoretical basis for analyzing the particle forming characteristics, and product quality from the view of material rheology, which give contribution to the efficient and low-cost pellet production and the improvement of product quality.