外锥内直孔件开式冷挤压成形理论建模研究

Theoretical modeling of open-die cold extrusion of conical workpiece with straight hole

运用流体动力学和塑性变形理论,给出了外锥内直孔件开式冷挤压变形过程非稳态速度场的瞬时流函数方程,并由流函数方程建立了非稳态动可容速度场,分析了影响速度场变化的主要因素。分析了速度间断面的形式和表达式,并以此为积分边界,以间断速度、应变速率为积分函数,采用高斯五点数值积分求得应变功率、速度间断功率和摩擦功率,从而得到上限功率。利用上限原理,得到了挤压功率、挤压力的理论模型。通过模型优化和编程计算,得到了挤压功率和挤压力理论数值,与有限元模拟结果对比,误差小于10%,验证了外锥内直孔件开式冷挤压理论模型建立的可行性和正确性,可用于此类件的工艺制定和设备选取。

Based on the theory of hydrodynamics and plastic deformation,the instantaneous flow function equation of the unsteady velocity field in open-die cold extrusion of conical workpiece with straight hole was given,and the unsteady kinematically admissible velocity field was built by the flow function equation,the main factors influencing the velocity field were analyzed. The form and expression of the velocity discontinuity were analyzed and taken as the integral boundary,and the intermittent velocity and strain rate were taken as integral functions,so the upper limit power was obtained by using Gaussian five-point numerical integration to obtain the strain power,speed discontinuous power and friction power. Using upper bound method,the theoretical models of the power of the extrusion and the extrusion pressure were obtained. By using model optimization and programming calculation,the theoretical values of the power of extrusion and the extrusion pressure were obtained,and compared with the results of finite element simulation,the error was less than 10%. So the feasibility and correctness of the theoretical model of open-die cold extrusion of conical workpiece with straight hole was verified,which could be used for the process determination and equipment selection in this kind of workpiece.