Chuan-Yu Wu

Rebound behaviour of spheres for plastic impacts

Abstract This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity Vi to the yield velocity Vy which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Youngs Modulus E* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(Vi/Vy)/(E*/Y)]−1/2.

The flow of powder into simple and stepped dies

An experimental study of die filling into constrained cavities of simple and complex geometries is presented. A model shoe system for the study of powder flow in air and vacuum has been developed. Transparent dies and shoes have been used, which allow the flow and rearrangement of the powder to be observed using a high-speed video system. Both qualitative and quantitative estimations of the influence of powder characteristics and shoe kinematics on the die filling process have been made. Measurements of filling rate and filling ratio for various shoe and die geometries are presented. The influence of airflow is revealed by comparison of experiments conducted in air and in vacuum. Possible positive and negative contributions of the entrained air during die filling have been addressed. Results are presented in the context of the Beverloo equation, which was originally developed to characterize hopper flow. The concept of a critical velocity is introduced, below which complete filling of a standard die is achieved. This provides a measure of the flowability of a powder and can be used to gauge the influence of airflow and pressure on the filling process.

A theoretical model for the contact of elastoplastic bodies

Abstract The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. Formulae describing the force-displacement relationship for static contact problems and the coefficient of restitution for dynamic impact problems are derived. The present model can be considered as a modification of Johnsons model by using a more detailed pressure distribution function which is based on finite element analysis (PEA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, finite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coefficients. Good agreements between the model predictions and the FEA results are found.

Experimental and numerical study of die filling, powder transfer and die compaction

Abstract Experimental and numerical studies are presented of the behaviour of a Distaloy AE powder during filling and transfer (i.e. the parallel movement of punches from their filling position to their starting position prior to compaction). Discrete element simulations provide information about the density distribution in a die after filling and how this is modified during transfer. The transfer process creates a depression in the top of the powder. The discrete element computations explain this behaviour in terms of the circulation patterns generated in the powder as a result of the transfer process. The profile of the powder in the die and the density distribution after transfer provide the initial conditions for a finite element simulation of the compaction process. These computations employed a Drucker–Prager–Cap model, which was implemented in the finite element code ABAQUS/Explicit, using a user material subroutine. A sensitivity study is presented which evaluates how the density distribution and depression created during filling and transfer influence the green bodys final density distribution.

A semi-analytical model for oblique impacts of elastoplastic spheres

Results of finite-element analysis (FEA) of oblique impacts of elastic and elastic, perfectly plastic spheres with an elastic flat substrate are presented. The FEA results are in excellent agreement with published data available in the literature. A simple model is proposed to predict rebound kinematics of the spheres during oblique impacts. In this model, the oblique impacts are classified into two regimes: (i) persistent sliding impact, in which sliding occurs throughout the impact, the effect of tangential (elastic or plastic) deformation is insignificant and the model reproduces the well-established theoretical solutions based on rigid body dynamics for predicting the rebound kinematics and (ii) non-persistent sliding impact, in which sliding does not occur throughout the impact duration and the rebound kinematics depends upon both Poissons ratio and the normal coefficient of restitution (i.e. the yield stress of the materials). For non-persistent sliding impacts, the variation of impulse ratio with impact angle is approximated using an empirical equation with four parameters. These parameters are sensitive to the values of Poissons ratio and the normal coefficient of restitution, but can be obtained by fitting numerical data. Consequently, a complete set of solutions is obtained for the rebound kinematics, including the tangential coefficient of restitution, the rebound velocity at the contact patch and the rebound rotational speed of the sphere during oblique impacts. The accuracy and robustness of this model is demonstrated by comparisons with FEA results and data published in the literature. The model is capable of predicting complete rebound behaviour of spheres for both elastic and elastoplastic oblique impacts.

Flow behaviour of powders during die filling

Abstract In this paper, the powder behaviour during die filling is discussed. Initially, methods used to test powder flow properties are reviewed and a novel method based on the measurement of critical shoe velocity is emphasised. It is shown that this method not only can be used to characterise the flow of powders, but it can also be used to assist process design in powder metallurgy and similar operations. The powder behaviour during die filling is then discussed in two successive stages: the flow of powder from a shoe and the packing of powder inside a die. Previous studies are reviewed and typical behaviour of powder during die filling is summarised. Finally, segregation during die filling is also discussed and further studies on die filling are suggested.

Coefficients of restitution for elastoplastic oblique impacts

The paper presents results of a finite element analysis of both elastic and elastoplastic oblique impacts of a sphere with a target wall using the DYNA3D code. For elastic oblique impacts, the results are in complete agreement with previous publications. For elastoplastic oblique impacts, the rebound kinematics depend on the normal coefficient of restitution, which is conventionally assumed to be a function of the normal impact velocity irrespective of the impact angle. The results of the finite element simulations of elastoplastic impacts demonstrate that this is not the case.

The effect of lubrication on density distributions of roller compacted ribbons

Roller compaction is a continuous dry granulation process for producing free flowing granules in order to increase the bulk density and uniformity of pharmaceutical formulations. It is a complicated process due to the diversity of powder blends and processing parameters involved. The properties of the produced ribbon are dominated by a number of factors, such as the powder properties, friction, roll speed, roll gap, feeding mechanisms and feeding speed, which consequently determine the properties of the granules (size distribution, density and flow behaviour). It is hence important to understand the influence of these factors on the ribbon properties. In this study, an instrumented roller press developed at the University of Birmingham is used to investigate the effect of lubrication on the density distribution of the ribbons. Three different cases are considered: (1) no lubrication, (2) lubricated press, in which the side cheek plates of the roller press are lubricated, and (3) lubricated powder, for which a lubricant is mixed into the powder. In addition, how the powders are fed into the entry region of the roller press and its influence on ribbon properties are also investigated. It is found that the method of feeding the powder into the roller press plays a crucial role in determining the homogeneity of the ribbon density. For the roller press used in this study, a drag angle (i.e., the angle formed when the powder is dragged into the roller press) is introduced to characterise the powder flow pattern in the feeding hopper. It is shown that a sharper drag angle results in a more heterogeneous ribbon. In addition, the average ribbon density depends upon the peak pressure and nip angle. The higher the peak pressure and nip angle are, the higher the average ribbon density is. Furthermore, the densification behaviour of the powder during roller compaction is compared to that during die compaction. It has been shown that the densification behaviour during these two processes is similar if the ribbons and the tablets have the same thickness.

Predicting the Tensile Strength of Compacted Multi-Component Mixtures of Pharmaceutical Powders

PurposePharmaceutical tablets are generally produced by compacting a mixture of several ingredients, including active drugs and excipients. It is of practical importance if the properties of such tablets can be predicted on the basis of the ones for constituent components. The purpose of this work is to develop a theoretical model which can predict the tensile strength of compacted multi-component pharmaceutical mixtures.MethodsThe model was derived on the basis of the Ryshkewitch‐Duckworth equation that was originally proposed for porous materials. The required input parameters for the model are the relative density or solid fraction (ratio of the volume of solid materials to the total volume of the tablets) of the multi-component tablets and parameters associated with the constituent single-component powders, which are readily accessible. The tensile strength of tablets made of various powder blends at different relative density was also measured using diametrical compression.ResultsIt has been shown that the tensile strength of the multi-component powder compacts is primarily a function of the solid fraction. Excellent agreement between prediction and experimental data for tablets of binary, ternary and four-component blends of some widely used pharmaceutical excipients was obtained.ConclusionIt has been demonstrated that the proposed model can well predict the tensile strength of multi-component pharmaceutical tablets. Thus, the model will be a useful design tool for formulation engineers in the pharmaceutical industry.

Roller compaction of moist pharmaceutical powders

The compression behaviour of powders during roller compaction is dominated by a number of factors, such as process conditions (roll speed, roll gap, feeding mechanisms and feeding speed) and powder properties (particle size, shape, moisture content). The moisture content affects the powder properties, such as the flowability and cohesion, but it is not clear how the moisture content will influence the powder compression behaviour during roller compaction. In this study, the effect of moisture contents on roller compaction behaviour of microcrystalline cellulose (MCC, Avicel PH102) was investigated experimentally. MCC samples of different moisture contents were prepared by mixing as-received MCC powder with different amount of water that was sprayed onto the powder bed being agitated in a rotary mixer. The flowability of these samples were evaluated in terms of the poured angle of repose and flow functions. The moist powders were then compacted using the instrumented roller compactor developed at the University of Birmingham. The flow and compression behaviour during roller compaction and the properties of produced ribbons were examined. It has been found that, as the moisture content increases, the flowability of moist MCC powders decreases and the powder becomes more cohesive. As a consequence of non-uniform flow of powder into the compaction zone induced by the friction between powder and side cheek plates, all produced ribbons have a higher density in the middle and lower densities at the edges. For the ribbons made of powders with high moisture contents, different hydration states across the ribbon width were also identified from SEM images. Moreover, it was interesting to find that these ribbons were split into two halves. This is attributed to the reduction in the mechanical strength of moist powder compacts with high moisture contents produced at high compression pressures.