粉末压制功与不完全Γ函数的关系

来源期刊：中南大学学报(自然科学版)1983年第2期

论文作者：黄培云

文章页码：1 - 7

关键词：粉末压制； 函数值； 压制压力； 粉末体； 应变； 总功； 电子计算机； 致密金属； 压制方程； 压制过程

摘    要：本文导出了粉体从应变为0(ε=0)到应变无穷大(ε=∞)时的压制总功: α_总=MW(1/d_o-1/d_m)Γ(m+1) 式中,M是粉末压制模量,W是粉末的重量,d_o是粉末的原始密度,d_m是致密金属的理论密度,Γ(m+1)是m+1的Γ函数, Γ(m+1)=∫₀ ∞e^-εε^mdε ε是压制应变, ε=ln(d_m-d_o)d/(d_m-d)d_o d是压坯密度,m是非线性指数。 还导出了应变从ε₁到ε₂时实际的粉末压制功, α=∫_ε1^ε₂e^-εε^mdε 式中,∫_ε1^ε₂e^-εε^mdε是m+1的不完全Γ函数,其函数值可由电子计算机近似求得。 文中列表给出了钨粉压制功的计算实例。

Abstract: The total work of compaction of powders, from zero strain(ε= 0) to in-finite strain (ε= ∞), is derived in this paper to be: a_total= Mw (1/d₀-1/d_m) Γ(m + 1) where M is the modulus of compaction of powder, w is the weight of powder,d₀ is the initial density of powder, d_m is the theoretical density of densemetal, m is the index of non-linearity and Γ(m + 1) is the gamma functionof (m + 1). Γ(m + 1) = ∫₀^∞ e^-8ε^mdε where ε is the strain of compaction, ε=ln((d_m-d₀)d)/((d_m-d)d₀) and d is the green density of powder compact. The actual work of compaction of powders from ε₁ to ε₂ is derived to be: a = Mw (1/d₀-1/d_m)∫ε₁ε² e^-εε^mdε where ∫_ε1^ε₂e^-εε^mdεis the incomplete gamma function of (m + 1), the numer-ical value of which can be evaluated by computers. Examples of calculations for the work of compaction on tungsten powderare given and tabulated.