(中南大學(xué) 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院，長(zhǎng)沙 410083)
摘 要: 根據(jù)高速壓制工藝過程的特點(diǎn)，底部和側(cè)面邊界采用反彈與反射的混合格式，頂部通過改變分布函數(shù)構(gòu)造能模擬動(dòng)態(tài)壓制過程的邊界格式。利用粉體的初始密度和壓制最大理想密度建立一個(gè)動(dòng)態(tài)的松弛函數(shù)來代替格子Boltzmann方法的固定松弛時(shí)間。對(duì)圓柱體及單級(jí)臺(tái)階的圓柱體模具的高速壓制成形過程進(jìn)行二維數(shù)值模擬，直觀顯示壓制過程中粉末的流動(dòng)以及應(yīng)力波的形成與傳播過程。模擬結(jié)果表明：模具形狀對(duì)應(yīng)力波的波形有較大影響；壓制完成后，圓柱體壓坯最大密度差為12 mg/cm3，密度分布均勻且左右對(duì)稱，壓坯頂部和底部密度較中間部分密度稍大，與實(shí)驗(yàn)結(jié)果基本相似；圓柱體壓坯中存在密度較低的橫向窄帶區(qū)域，揭示成形坯有可能形成分層或斷裂。
關(guān)鍵字: 高速壓制；格子Boltzmann方法；松弛函數(shù)；應(yīng)力波
（School of Mathematics and Statistics, Central South University, Changsha 410083, China）
Abstract:According to the characteristics of high velocity compaction process, the rebound and reflection mixed boundary condition was used on the bottom and sides of the mould. By changing distribution function, a kind of boundary condition which can simulate the dynamic process was proposed. A relaxation function was established according to the powder flow characteristic using initial and maximum density. Two-dimensional numerical simulations were given to cylinder mould and single step cylinder mould. The dynamic evolution process of powders and the stress wave transformation process were presented. The results indicate that the shape of the mould has a great influence on the wave pattern of stress. The density of green compact is uniformly and symmetrically distributed, and the greatest density difference is 12 mg/cm3. The top and bottom parts have slight higher density than the middle part. These results are consistent with the experimental results. A narrow low density band is found in the green compact which reveals that there may exist density stratification.
Key words: high velocity compaction; lattice Boltzmann method; relaxation function; stress wave
