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Comparison of various modeling methods for analysis of powdercompaction in roller pressRoman T. Deca, Antonios Zavaliangosb,*, John C. CunninghambaK.R. Komarek Briquetting Research Inc., Anniston, AL 36207, USAbDepartment of Materials Engineering, Drexel University, Philadelphia, PA 19104-2875, USAAbstractRecently used models relating basic properties of the feed material, roller press design and its operating parameters are reviewed. Inparticular, we discuss the rolling theory for granular solids proposed by J.R. Johanson in the 1960s, later trials utilizing slab method andnewly developed final element models. These methods are compared in terms of efficiency and accuracy of predicting the course of basicprocess 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 forprocess and equipment optimization.D 2002 Elsevier Science B.V. All rights reserved.Keywords: Roll compaction; Modeling methods; Finite element model1. IntroductionThe conceptual simplicity and low operating cost makeroll 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. Itdepends onproper matchingofthepropertiesofpowdertobeprocessed with the design and operating parameters of theroller press.The main feed material properties to be considered arethe stressstrain relationship and friction coefficient as afunction of powder density (or stress state). Importantdesign factors will be: feed system design, roll diameterand roll surface geometry. The main operating parameters tobe set are: the roll speed, roll gap, roll torque, roll force,feeder and deaerating device conditions.Current industrial compacting and briquetting practice islargely based on trial-and-error techniques. While it ispossible to achieve the optimum process performance usingsuch an approach, it results in an increase of operating costand time, especially with higher value materials and moredemanding quality requirements.An alternative approach is to use mathematical modelingto provide necessary information for proper equipment andprocess design. In spite of its apparent simplicity, powdercompaction in a roller press exhibits some behaviors andinteractions that are poorly understood from an analyticalview. Mathematical models that will allow realistic numer-ical simulation of powder compaction and appropriatevisualization of these results can permit the process engineerto gain a better understanding through the process, leadingto its better design and control.The purpose of this paper is to review the existing modelsand compare them in terms of efficiency and accuracy ofpredicting the course of basic process variables. Only threemodels developed through the last few decades and thoughtto be best suited for predicting mechanical behavior ofgranular 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 (A. Zavaliangos)./locate/powtecPowder Technology 130 (2003) 2652712. Models of compaction process in the roller press2.1. Model proposed by J.R. JohansonDeveloped in mid-1960s, it was the first complex modelallowing to predict behavior of the material undergoingcontinuous 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 (JenikeShield 1).Pressure distribution above the nip region was determinedbased on the continuousplane-straindeformation and assum-ingtheslipalongtherollsurface.Thefollowinginputdataareneeded: effective angle of internal friction and angle of wallfriction. Both can be determined using a Jenike shear tester.In the nip region, a very simplified material model wasapplied. It was assumed that there is no slip between thematerial and the roll surface and all material trappedbetween the rolls at the position of nip angle must becompressed into a strip with the width equal to the rollgap. As a result, pressure in the nip region is described bythe pressuredensity 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 solidline, describes pressure gradient for the x direction, assum-ing that slip occurs along the roll surface. When slip doesnot take place between compacted material and the rolls,pressure gradient is given by the second equation shown bythe dashed line in Fig. 1. Based on the examinationspresented in Ref. 2, it is indicated that the intersection ofthe two curves gives the angle of nip, a. The actual pressuregradient above the a is given by solid line, and from a to therolls center axis by the dashed line.This model can be very useful to determine the angle ofnip for gravity fed roller presses. It gives a good agreementwith experimental data when applied to the cases wheresmooth rollers with large diameter (over 500 mm) are used.Discrepancies are much higher when cavities are cut into theroller working surface and, as a result of simplifyingassumption, roller diameter is reduced by the mean depthof those cavities.In the case of predicting the values of basic operatingparameters like roll force and roll torque, the agreements arereasonably good for granular materials showing high coef-ficient of friction against the roller surface and mid and highvalues of compressibility constant, K. Discrepanciesbetween computed and measured values are bigger (some-times over 50%) when higher compaction pressures (over100 MPa) are applied and materials are very compressible(low K value).In spite of its limitations, it should be pointed out that ithas been the first model allowing engineers to analyze thecorrelation between basic process variables and propertiesof the granular material. It also emphasizes that a lack ofunderstanding compaction mechanism can result in a proc-ess and equipment design which will not produce a productwith the required characteristics.Considering the simplifications made while modelingpowder behavior in the nip region were responsible fordiscrepancies with the real system, a modeling techniqueknown as a slab method was evaluated.2.2. Analysis of nip region based on slab methodThis method of modeling was widely used to predictpressure distribution and roll separating force in metalrolling process. Similarly to the Johanson model, planesections are assumed to remain plane as they pass throughthe rolls. It was first applied to analyze metal powder rollingby Katashinskii 3. However, yield criterion for fully densemetal was used in those initial studies.In the analysis presented below, the concept of yieldcriterion for metal powders proposed by Kuhn and Downey4 was employed in order to develop the material model.Deformation zone under the rolls was divided intotrapezoidal slabs as seen in Fig. 2 5. The force balanceon the slab results in the equilibrium equation for the xdirection and is expressed as:BhrxBx 2ptanax? sf 01In Eq. (1) the frictional stress is expressed as:sf Yq :for lppzYq2sf lpp :for lpp 95%) porous metal.The friction for the roll/material was assumed to followthe Coulomb friction law with a constant frictional coef-ficient. The effect of the feed system was represented by aconstant feed stress applied to the mesh in the rolling di-rection at the inflow boundary.To address the severe mesh distortion observed in theinitial 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) 265271269gianEulerian (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 rolland material mesh were optimized to minimize inertialeffects for this quasi-static deformation problem and tominimize computational time. Eulerian inflow and outflowboundaries were used. The simulation was conducted untilsteady state conditions were reached based on the constantvalues of the roll force and roll torque.The simulations were conducted to evaluate the effect ofthe frictional coefficient at the roll/powder interface and thefeed stress on basic process variables: roll force, roll torque,nip angle and neutral angle. The nip angle was defined as avalue of the rolling angle in which the linear velocity of theroll surface is equal to the velocity of contacting material(no slip), the neutral angle as the angle in which thefrictional shear stress at the roll surface reverses direction.These values along with the relative density of compact atthe exit are presented in Table 1.The roll pressure profiles as a function of feed stress andcoefficient of friction are shown in Figs. 5 and 6, respec-tively. The shear stress profiles as a function of feed stressand coefficient of friction are shown in Fig. 7.The results indicate reveals the anticipated two regions ofslip in the feed zone and sticking in the nip region. The nipangle is approximately 8.5j and 12j for coefficients offriction of 0.35 and 0.50, respectively. The feed stress had asignificant effect on the maximum roll pressure generated.Increasing the coefficient of friction for a given feed stresslikewise increased the maximum roll pressure. In all con-ditions, the maximum roll pressure is observed 0.5j to 1.1jbefore the centerline between the rolls. The roll force androll torque increased as expected with increasing feed stressand frictional coefficient. Likewise, the exit relative densityalso increases with the increase of frictional coefficient andthe feed stress.The contour plot of velocity in the rolling direction forthe simulation in which the feed stress is 0.21 MPa and theFig. 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 isrotating with a linear velocity of ?50 mm/s at the surface. Note the nonhomogeneous velocity especially in the feed zone.R.T. Dec et al. / Powder Technology 130 (2003) 265271270coefficient of friction at the roll is 0.50, which is shown inFig. 8, reveal a nonhomogeneous velocity field especially inthe feed zone.Additional refinement of the finite element model isnecessary before final experimental verification of theresults. For example, material stress at the roll entry shouldbe considered as a function of time and position to betterrepresent influence of the feed screw system. Also, improve-ment in the material model and treatment of the frictionphenomena should add to better agreement with the realphysical system 13.3. Summary and conclusionsPresented work demonstrates the historical developmentof the models describing compaction process in the rollerpress. As it was shown, final element-based analysis hasseveral advantages over the modeling methods used in thepast. By utilizing the commercially available software,models can be adjusted, to generate improved solutionsthrough a process of hypothesis, numerical testing andreformulation. Prediction of relative densities, material flow,deformation energy, shear stress (roll torque), pressuredistribution (roll force), position of nip angle and neutralangle, failure of the compact during release, etc. can all bemade with these models. All of these important consider-ations can be taken one step further by including model ofthe feeding process and forming tool geometry (cavities inthe roll surface). It leads to realistic analysis of the com-paction process and with appropriate visualization of theresults to a better design and control. This is particularlyimportant with manufacturing of engineered agglomeratedproducts with specific properties (pharmaceutical, chemical,ceramic or semi-conductor industries).The biggest challenges with the implementation of theFEM modeling are arising not from the computationalproblems, 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 powderthrough the wide range of densities during compaction.Using the appropriate friction model, describing phenom-ena on the material/forming tool interface is of greatimportance as well, because all the processing energy istransmitted throughout the roll-material contact. Anotherneed is to move into three-dimensional modeling and toincorporate models of material behavior in the feedingdevices.References1 A.W. Jenike, R.T. Shield, On the plastic flow of coulomb solidsbeyond original failure, Journal of Applied Mechanics 26, Trans.ASME 81, Series E (1959) 599602.2 J.R. Johanson, A rolling theory for granular solids, ASME, Journal ofApplied Mechanics 32 (ser. E, No. 4) (1965) 842848.3 V.P. Katashinskii, Analytical determination of specific pressure duringthe rollingof metalp