A revised method of determining lateral-pressure and external-friction coefficients for powder pressing

There are basic parameters of granular and loose fibrous materials used in pressing: the lateral pressure coefficient ~, which is equal to the ratio of the pressure on the side of the die to the axial pressure, and the external friction coefficient f on the side surface, These parameters are needed to design tools in which powdered materials are pressed (milling and briquetting presses, tableting machines, and so on). Experiments have been made [1-4] to determine the lateral pressure and external friction by reference to the elastic strain in the wall of the pressing chamber and the strain in a special elastic element, which are recorded by strain gauges. For example, in [1] the combination ~.fwas determined from the measured external forces on displacement of the charge in a pressing chamber for a given distribution of the axial pressing force along the charge. In that method, it is fairly difficult to determine the distribution of the axial load and consequently of the lateral load along the material, and additional research is needed to determine the external friction coefficient. In [4], experiments were done on the distribution of the lateral pressure Px along a column of pressed powder, and estimates were made of ~ andf. Figure 1 shows the working scheme. The cylindrical die 3 containing plungers 6 and 1 was mounted on the elastic component 4. The free space between the plungers was filled with the powder. At the outer surface of the die in the powder zone, there were strain gauges 2 used to estimate the deformation of the wall due to the lateral pressure. The external friction was estimated with the strain gauges 5 cemented to the elastic element 4. During the pressing, the speed of the powder in contact with the upper plunger 1 is equal to that of the plunger itself; the speed of the powder at the lower plunger 6 is zero (neglecting axial deformation), The displacement of" the powder with respect to the inner surface of the die produces a frictional force, under which the die moves downwards and deforms the elastic element. Consequently, the displacements or velocities of the die and elastic element are identical. The displacement of the powder in the vertical direction during pressing ranges from maximal (at the upper plunger) to zero (at the lower one), so at a certain height, the speeds of the powder and die will be equal, so the frictional force in that zone will be zero. Below that zone, the frictional force changes direction and resists the displacement of the plunger 6 and the deformation of the elastic element 2. Figure 1 shows the variation in the relative velocity of the plunger 6 and powder. The residual frictional force is recorded by the strain gauges 5 in the elastic element 4 (if the external friction coefficient is constant over the height of the powder and one knows the distribution of the lateral pressure Px) and is given by