细长压杆失稳理论对一级台阶凸模的设计指导  

Guidance of slender compressive bar stability-losing theory to one-step male die

作　　者：董冠文 李宗义 朱七二 

机构地区：[1]甘肃机电职业技术学院,甘肃天水741001

出　　处：《锻压装备与制造技术》2015年第3期120-122,共3页China Metalforming Equipment & Manufacturing Technology

基　　金：甘肃机电职业技术学院2013年教学研究项目(JY1406)

摘　　要：分析了一级台阶凸模在冲裁过程中的受力特点,结合细长压杆失稳理论,将台阶凸模刃口长度部分视为弹性杆,其余部分视为刚性杆,建立了弹性和刚性的混合杆系的力学模型。通过分析该模型,取得了一个关于临界载荷的特征根方程。该特征根方程是含有正切三角函数的超越方程,同时含有两个未知数,无法求出其显式解析解,所以对该超越方程引进适当的无量纲量,用反三角函数求解,并计算了其初值和一阶导数,这样,问题就转化为一阶常微分方程的初值问题。进而采用4阶经典Rung-Kutta法,计算了弹性和刚性的混合杆系的力学模型的数值解,给出了随一级台阶凸模的弹性长度与刚性长度之比的大范围变化的载荷参数的关系曲线。为同类结构冷冲模设计提供了参考。The mechanical characteristics of one-step male die during blanking process have heen considered. Combining witb the slender compressive bar stability-losing theory, the stepped convex die cutting edge length has heen regarded as elastic rod while the remaining part has been considered as a rigid rod, the mechanical model of mixed linkage about the elastic and rigid has been established. A critical load characteristic root equations has been obtained by analysis of ttle model. The characteristic root equation is a transcendental equation containing the tangenl trigonometric function and two unknowns, which cannot find out the explicit analytical solution. So the appropriate dimensionless quantity has been introduced to solve the inverse trigonometric function. The initial value and firs! derivative have been calculated. Thus in this way, the problem has been transformed into initial value problems of the first order ordinary differential equation. Then the classical 4 order Rung-Kutta method has been adopted to calculate the value of numerical mechanics model of mixed rod elasticity and rigidity. Tbe relation curve of loading parameters of large range with one step length of convex die elastic and rigid length ratio has been given. It provides reference for blanking punch with this kind of structure type.

关 键 词：模具设计 一级台阶凸模 细长压杆失稳理论 4阶经典Rung-Kutta法 弹性和刚性混合杆系 无量纲载荷参数 

分 类 号：TG386[金属学及工艺—金属压力加工]