Bearing region plays an important role in controlling material flow and its optimal design could lead to high quality extruded products. On the other hand, too much of bearing causes the process load to increase. Thus, there must be an optimum point where the bearing lands and the extrusion pressure are just the right values. Determining the proper bearing length is often performed using trial and error methods in the extrusion industry and numerical analysis. The aim of this study is to optimize the bearing length in forward extrusion dies using upper bound method for non-axisymmetric sections. A generalized kinematically admissible velocity field is employed to obtain uniform velocity at the exit surface of the die. Dead metal zone and bearing region define the geometry of the deformation zone. The multi-objective optimization using response surface methodology was applied to optimize the relative extrusion pressure and the deviation of the mean value for the velocity at die exit. Using this method, the proper bearing length is determined. Optimization of bearing land is performed for extrusion of rectangular and L-shaped profiles. The proposed analytical method was verified by physical modelling experiments and numerical simulations. A unique answer for the bearing design could be obtained using the suggested method in a few seconds opposing to numerical method which required many timely and costly trials. This method would be useful for die designers to get the appropriate bearing land and at the same time not to increase the process load excessively.

轴承区域在控制物料流中起着重要作用，其最佳设计可以生产出高质量的挤压产品。另一方面，过多的轴承会导致过程负荷增加。因此，必须有一个最佳点，在该点上轴承着陆和挤出压力恰好是正确的值。在挤压行业和数值分析中，通常使用反复试验的方法来确定合适的轴承长度。这项研究的目的是使用上限方法对非轴对称截面的前向挤压模具的轴承长度进行优化。采用广义的运动学上允许的速度场来获得模具出口表面的均匀速度。死区和轴承区定义了变形区的几何形状。应用了使用响应曲面方法的多目标优化来优化相对挤压压力和模具出口速度平均值的偏差。使用这种方法，可以确定合适的轴承长度。为挤压矩形和L形型材进行了优化的轴承座。通过物理建模实验和数值模拟验证了所提出的分析方法。相对于需要大量及时而昂贵的试验的数值方法，使用建议的方法可以在几秒钟内获得轴承设计的唯一答案。这种方法对于模具设计人员获得适当的轴承座并且同时不会过度增加工艺负荷将很有用。