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Comparison of various modeling methods for analysis of powder compaction in roller press Roman T. Dec a , Antonios Zavaliangos b, * , John C. Cunningham b a K.R. Komarek Briquetting Research Inc., Anniston, AL 36207, USA b Department of Materials Engineering, Drexel University, Philadelphia, PA 19104-2875, USA Abstract Recently used models relating basic properties of the feed material, roller press design and its operating parameters are reviewed. In particular, we discuss the rolling theory for granular solids proposed by J.R. Johanson in the 1960s, later trials utilizing slab method and newly developed final element models. These methods are compared in terms of efficiency and accuracy of predicting the course of basic process variables like nip angle, pressure distribution in roll nip region, neutral angle, roll torque and roll force. The finite element method offers the most versatile approach because it incorporates adequate information about powder behavior, geometry and frictional conditions. This enables to perform realistic computer experiments minimizing costs, time and resources needed for process and equipment optimization. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Roll compaction; Modeling methods; Finite element model 1. Introduction The conceptual simplicity and low operating cost make roll pressing a very popular pressure agglomeration method. It is used for a large number of materials in mining, mineral, metallurgical, chemical, food and pharmaceutical industries. There can be a number of reasons for particle size enlarge- ment, the most important are to improve material storage, handling, feeding, dosing or mixing characteristics. In ther- mal operations, it can also improve efficiency of melting, drying or burning. A roll compaction operation is successful when it produ- ces compacts with uniform, desired mechanical (or other) properties at a specified production rate and unit cost. It dependsonproper matchingofthepropertiesofpowdertobe processed with the design and operating parameters of the roller press. The main feed material properties to be considered are the stress–strain relationship and friction coefficient as a function of powder density (or stress state). Important design factors will be: feed system design, roll diameter and roll surface geometry. The main operating parameters to be set are: the roll speed, roll gap, roll torque, roll force, feeder and deaerating device conditions. Current industrial compacting and briquetting practice is largely based on trial-and-error techniques. While it is possible to achieve the optimum process performance using such an approach, it results in an increase of operating cost and time, especially with higher value materials and more demanding quality requirements. An alternative approach is to use mathematical modeling to provide necessary information for proper equipment and process design. In spite of its apparent simplicity, powder compaction in a roller press exhibits some behaviors and interactions that are poorly understood from an analytical view. Mathematical models that will allow realistic numer- ical simulation of powder compaction and appropriate visualization of these results can permit the process engineer to gain a better understanding through the process, leading to its better design and control. The purpose of this paper is to review the existing models and compare them in terms of efficiency and accuracy of predicting the course of basic process variables. Only three models developed through the last few decades and thought to be best suited for predicting mechanical behavior of granular materials during roll compaction are considered. 0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S0032-5910(02)00203-6 * Corresponding author. Tel.: +1-215-895-2078; fax: +1-215-895- 6760. E-mail address: azavalia@coe.drexel.edu (A. Zavaliangos). Powder Technology 130 (2003) 265–271 2. Models of compaction process in the roller press 2.1. Model proposed by J.R. Johanson Developed in mid-1960s, it was the first complex model allowing to predict behavior of the material undergoing continuous shear deformation between the rolls. The mate- rial is assumed to be isotropic, frictional, cohesive and com- pressible and to obey the effective yield function (Jenike– Shield [1]). Pressure distribution above the nip region was determined based onthe continuousplane-straindeformation and assum- ingtheslipalongtherollsurface.Thefollowinginputdataare needed: effective angle of internal friction and angle of wall friction. Both can be determined using a Jenike shear tester. In the nip region, a very simplified material model was applied. It was assumed that there is no slip between the material and the roll surface and all material trapped between the rolls at the position of nip angle must be compressed into a strip with the width equal to the roll gap. As a result, pressure in the nip region is described by the pressure–density relationship obtained from the experi- ment using punch-die system. Two equations are considered to determine the nip angle, as it is illustrated in Fig. 1. First one, represented by solid line, describes pressure gradient for the x direction, assum- ing that slip occurs along the roll surface. When slip does not take place between compacted material and the rolls, pressure gradient is given by the second equation shown by the dashed line in Fig. 1. Based on the examinations presented in Ref. [2], it is indicated that the intersection of the two curves gives the angle of nip, a. The actual pressure gradient above the a is given by solid line, and from a to the rolls center axis by the dashed line. This model can be very useful to determine the angle of nip for gravity fed roller presses. It gives a good agreement with experimental data when applied to the cases where smooth rollers with large diameter (over 500 mm) are used. Discrepancies are much higher when cavities are cut into the roller working surface and, as a result of simplifying assumption, roller diameter is reduced by the mean depth of those cavities. In the case of predicting the values of basic operating parameters like roll force and roll torque, the agreements are reasonably good for granular materials showing high coef- ficient of friction against the roller surface and mid and high values of compressibility constant, K. Discrepancies between computed and measured values are bigger (some- times over 50%) when higher compaction pressures (over 100 MPa) are applied and materials are very compressible (low K value). In spite of its limitations, it should be pointed out that it has been the first model allowing engineers to analyze the correlation between basic process variables and properties of the granular material. It also emphasizes that a lack of understanding compaction mechanism can result in a proc- ess and equipment design which will not produce a product with the required characteristics. Considering the simplifications made while modeling powder behavior in the nip region were responsible for discrepancies with the real system, a modeling technique known as a slab method was evaluated. 2.2. Analysis of nip region based on ‘‘slab method’’ This method of modeling was widely used to predict pressure distribution and roll separating force in metal rolling process. Similarly to the Johanson model, plane sections are assumed to remain plane as they pass through the rolls. It was first applied to analyze metal powder rolling by Katashinskii [3]. However, yield criterion for fully dense metal was used in those initial studies. In the analysis presented below, the concept of yield criterion for metal powders proposed by Kuhn and Downey [4] was employed in order to develop the material model. Deformation zone under the rolls was divided into trapezoidal slabs as seen in Fig. 2 [5]. The force balance on the slab results in the equilibrium equation for the x direction and is expressed as: Behr x T Bx t 2eptana x C0 s f T?0 e1T In Eq. (1) the frictional stress is expressed as: s f ? YeqT : for lepTpzYeqTe2T s f ? lepTp : for lepTp 95%) porous metal. The friction for the roll/material was assumed to follow the Coulomb friction law with a constant frictional coef- ficient. The effect of the feed system was represented by a constant feed stress applied to the mesh in the rolling di- rection at the inflow boundary. To address the severe mesh distortion observed in the initial implicit Lagrangian simulations, the arbitrary Lagran- Fig. 5. The roll pressure vs. rolling angle as function of feed stress for powder/roll friction coefficient of 0.50. Fig. 6. The roll pressure vs. rolling angle as function of feed stress and coefficient of friction. R.T. Dec et al. / Powder Technology 130 (2003) 265–271 269 gian–Eulerian (ALE) analysis features with adaptive mesh- ing were employed with the explicit version of the ABA- QUS finite element code. The mass and densities of the roll and material mesh were optimized to minimize inertial effects for this quasi-static deformation problem and to minimize computational time. Eulerian inflow and outflow boundaries were used. The simulation was conducted until steady state conditions were reached based on the constant values of the roll force and roll torque. The simulations were conducted to evaluate the effect of the frictional coefficient at the roll/powder interface and the feed stress on basic process variables: roll force, roll torque, nip angle and neutral angle. The nip angle was defined as a value of the rolling angle in which the linear velocity of the roll surface is equal to the velocity of contacting material (no slip), the neutral angle as the angle in which the frictional shear stress at the roll surface reverses direction. These values along with the relative density of compact at the exit are presented in Table 1. The roll pressure profiles as a function of feed stress and coefficient of friction are shown in Figs. 5 and 6, respec- tively. The shear stress profiles as a function of feed stress and coefficient of friction are shown in Fig. 7. The results indicate reveals the anticipated two regions of slip in the feed zone and sticking in the nip region. The nip angle is approximately 8.5j and 12j for coefficients of friction of 0.35 and 0.50, respectively. The feed stress had a significant effect on the maximum roll pressure generated. Increasing the coefficient of friction for a given feed stress likewise increased the maximum roll pressure. In all con- ditions, the maximum roll pressure is observed 0.5j to 1.1j before the centerline between the rolls. The roll force and roll torque increased as expected with increasing feed stress and frictional coefficient. Likewise, the exit relative density also increases with the increase of frictional coefficient and the feed stress. The contour plot of velocity in the rolling direction for the simulation in which the feed stress is 0.21 MPa and the Fig. 7. The shear stress at the roll surface vs. rolling angle as function of feed stress and coefficient of friction. Fig. 8. Velocity in the rolling direction (v1) in mm/s for example simulation (feed stress=0.21 MPa and coefficient of friction at roll/powder=0.50). The roll is rotating with a linear velocity of C050 mm/s at the surface. Note the nonhomogeneous velocity especially in the feed zone. R.T. Dec et al. / Powder Technology 130 (2003) 265–271270 coefficient of friction at the roll is 0.50, which is shown in Fig. 8, reveal a nonhomogeneous velocity field especially in the feed zone. Additional refinement of the finite element model is necessary before final experimental verification of the results. For example, material stress at the roll entry should be considered as a function of time and position to better represent influence of the feed screw system. Also, improve- ment in the material model and treatment of the friction phenomena should add to better agreement with the real physical system [13]. 3. Summary and conclusions Presented work demonstrates the historical development of the models describing compaction process in the roller press. As it was shown, final element-based analysis has several advantages over the modeling methods used in the past. By utilizing the commercially available software, models can be adjusted, to generate improved solutions through a process of hypothesis, numerical testing and reformulation. Prediction of relative densities, material flow, deformation energy, shear stress (roll torque), pressure distribution (roll force), position of nip angle and neutral angle, failure of the compact during release, etc. can all be made with these models. All of these important consider- ations can be taken one step further by including model of the feeding process and forming tool geometry (cavities in the roll surface). It leads to realistic analysis of the com- paction process and with appropriate visualization of the results to a better design and control. This is particularly important with manufacturing of engineered agglomerated products with specific properties (pharmaceutical, chemical, ceramic or semi-conductor industries). The biggest challenges with the implementation of the FEM modeling are arising not from the computational problems, but from preparation of the adequate input data. There is a need for better, more accurate material models, which realistically represent the behavior of the powder through the wide range of densities during compaction. Using the appropriate friction model, describing phenom- ena on the material/forming tool interface is of great importance as well, because all the processing energy is transmitted throughout the roll-material contact. Another need is to move into three-dimensional modeling and to incorporate models of material behavior in the feeding devices. References [1] A.W. Jenike, R.T. Shield, On the plastic flow of coulomb solids beyond original failure, Journal of Applied Mechanics 26, Trans. ASME 81, Series E (1959) 599–602. [2] J.R. Johanson, A rolling theory for granular solids, ASME, Journal of Applied Mechanics 32 (ser. E, No. 4) (1965) 842–848. [3] V.P. Katashinskii, Analytical determination of specific pressure during the rollingof metalpowders(in Russian),Soviet PowderMetalCeram. 10 (6) (1986) 765–772. [4] H.A. Kuhn, C.L. Downey, Deformation characteristics and plasticity theory of sintered powder materials, International Journal of Powder Metallurgy 7 (1) (1971) 15–25. [5] R.T. Dec, Study of compaction process in roll press, Proceedings, Institute for Briquetting and Agglomeration 22 (1991) 207–218. [6] R.T. Dec, R.K. Komarek, Roll press design for powder and bulk solids, Proc. 15th Powder and Bulk Solids Conference, June, 1990, pp. 125–136. [7] V.P. Katashinskii, M.B. Stern, Stress–strain state of powder being rolled in the densification zone: I. Mathematical model of rolling in the densification zone, Poroshkovaya Metallurgiya 11 (251) (1983) 17–21. [8] V.P. Katashinskii, M.B. Stern, Stress–strain state of powder being rolled in the densification zone: II. Distribution of density, longitudi- nal stain and contact stresses in the densification zone, Poroshkovaya Metallurgiya 12 (252) (1983) 9–13. [9] S. Shima, M. Yamada, Compaction of metal powder by rolling, Pow- der Metallurgy 27 (1) (1984) 39–44. [10] PM Modet Modelling Group, Comparison of computer models rep- resenting powder compaction process, Powder Metallurgy 42 (4) (1999) 301–311. [11] ABAQUS Version 5.8, Reference Manuals, Hibbitt, Karlsson and Sorensen, Pawtucket, R.I., 1999. [12] P.T. Wang, M.E. Karabin, Evolution of porosity during thin plate rolling of powder-based porous aluminum, Powder Technology 78 (1994) 67–76. [13] J. Cunningham, PhD Thesis, Drexel University, Philadelphia, PA, USA (in press). R.T. Dec et al. / Powder Technology 130 (2003) 265–271 271