Modeling of simultaneous deposition of powder in three parallel-oriented cylindrical dies

Die filling is a critical unit operation that is far from being sufficiently understood. No models or methods published can be used to study or simulate the feed shoe filling process or pressure (mass) increase for real-world problems involving a large number of 3-D particles of various shapes and sizes. In order to further understanding of the die-filling process, models were developed and verified to simulate the pressure ratio increase for the entire filling process by using the second-generation pressure deposition tester (PDT-II). The results indicated that the entire pressure increase profile could be divided into 10 stages, and all the stages could be simulated by a rate equation, based on the data collected and the physics of the filling process. Based on the powder deposition characteristics, the overall rate equation for all 10 stages is: dPp/dτ = αPpF(τ) + β, where Pp is prorated pressure at normalized time τ, and F(τ), α, and β are location-specific forcing function and constants. Furthermore, for stage 1 with the largest amount of powder deposited, the rate equation is dPp/dτ = αPp/(ebτ - 1). The average, maximum, and minimum values of the root-mean-square error (RMSE) for a total of 17 locations in the vicinity of the center (r ≤ 4 mm) of the center die are 0.13, 0.19, and 0.11, respectively. The average, maximum, and minimum values of the average relative difference (ARD) for a total of 17 locations in the vicinity of the center (r ≤ 4 mm) of the center die are 0.07, 0.09, and 0.06, respectively.