AN UPPER BOUND SOLUTION FOR THE FORCE OF COMBINED BACKWARD-FORWARD EXTRUSION

A rigid-triangle velocity field for combined backward-forwardextrusion based on the experiments and the slip-line field isproposed in this paper.The flow separation point in the ri-gid-triangle velocity field is defined in accordance with theslip-line theory.A formula of minimum upper bound solutionfor the punch pressure of the combined extrusion is derived.The values from this formula are compared with those from theslip-line solution and with experimental results.The formulaof upper bound solution can be used in practice.     

A MODEL FOR SIMULATION OF FRICTION PHENOMENON BETWEEN DIES AND WORKPIECE

Based on the interaction of asperities and upperbound approach a mathematical model for simulation of friction phenomenon between dies and workpiece is proposed.Optimizing the mathematical model with respect to several variables it is found that in addition to adhering, tearing, ploughing, etc., asperities workpiece can move wave-like along the surface layer and under certain circumstances they may disappear. If the asperities wavily move along the surface layer the friction coefficient depends on the geometry of asperities. However,the bonding strength of asperities has no significant influence on friction coefficient. The depth of the plastic deformation layer is related to the geometry of asperities, too.The soundness of the prerequisite of the proposed model and some analytical results were verified by experiments.     

A model for simulation of friction phenomenon between dies and workpiece

Based on the interaction of asperities and upperbound approach a mathematical model for simulation of friction phenomenon between dies and workpiece is proposed. Optimizing the mathematical model with respect to several variables it is found that in addition to adhering, tearing, ploughing, etc., asperities workpiece can move wave-like along the surface layer and under certain circumstances they may disappear. If the asperities wavily move along the surface layer the friction coefficient depends on the geometry of asperities. However, the bonding strength of asperities has no significant influence on friction coefficient. The depth of the plastic deformation layer is related to the geometry of asperities, too. The soundness of the prerequisite of the proposed model and some analytical results were verified by experiments.Department of Materials Engineering, Northwestern Polytechnical UniversityThis is a project of the cooperative program between the Department of Materials Engineering of Northwestern Polytechnical University of the People's Republic of China and the Institute for Metal Forming at Lehigh University of the United States of America.     

ANALYSIS OF SURFACE CRACK ON FORWARD EXTRUDING BAR DURING AXISYMMETRIC CUP-BAR COMBINED EXTRUSION PROCESS

In this paper,the kinematically admissible velocity field with surface crack on forwardextruding bar is put forward during the axisymmetric cup-bar combined extrusion process,in accordance with the results of model experiments.On the basis of velocity field,the necessary condition for surface crack formation onthe forward extruding bar is derived,with the help of upper bound theorem and theminimum energy principle.Meanwhile,the relationships between surface crack formationand combination of reduction in area for the part of forward and backward extursions(εb,εf),relative residual thickness of billet(T/R_0),frictional factor(m)or relativeland length of ram and chamber(l_b/R_0,l_f/R_0)are calculated during the extrusion process.Therefore,whether the surface crack on forward exturding bar occurs can be predictedbefore extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusionprocess.The analytical results agree very well with experimental results of aluminium alloyLY12 (ASTM2024)an     

模具与工件之间摩擦过程的一个模型*

本文中以刚性微凸体与可变形微凸体的相互作用模拟金属压力加工过程中模具与工件之间的摩擦过程,并用上限法分析所提出的模型.将数学模型进行多变量最优化处理后发现,金属压力加工过程中,除了可能发生工件上的微凸体与模具上的微凸体相互粘结、撕裂和犁沟等现象外,工件上的微凸体可能沿工件表面波浪式前进,形成塑性波,也可能被辗平而消失.在形成塑性波的条件下,摩擦系数与微凸体几何形状有关.但微凸体的连结强度对摩擦系数影响不大.微凸体的几何形状对工件表面下的塑性变形层的深度有显著的影响.实验结果证实了本文所提出的模型的前提的正确性以及部分理论分析结果.     

Analysis of surface crack on forward extruding bar during axisymmetric cup-bar combined extrusion process

In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.On the basis of velocity field, the necessary condition for surface crack formation on the forward extruding bar is derived, with the help of upper bound theorem and the minimum energy principle. Meanwhile, the relationships between surface crack formation and combination of reduction in area for the part of forward and backward extursions (ε_b,ε_f) relative residual thickness of billet (T/R₀),frictional factor (m) or relative land length of ram and chamber (l_b|R₀,l_f|R₀) are calculated during the extrusion process. Therefore, whether the surface crack on forward exturding bar occurs can be predicted before extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusion process.The analytical results agree very well with experimental results of aluminium alloy LY12 (ASTM 2024) and LC4 (ASTM 7075).     

复合挤压力的上限解

本文根据实验和滑移线场拟定复合挤压时的速度不连续刚性三角形,由此得出复合挤压时凸模单位压力的最小上限解的解析式,将此式解值和实测值进行比较,表明上限值可供实际使用.