This paper, on the basis of error modelling, proved the optimal pocket machining sequences of a simply end supported pocketed beam using mathematic induction method. The optimal pocket machining sequence with the minimum pocket floor height error is the machining from both ends to the middle and the optimal sequence is not unique because of the symmetric supports about the central plane; meanwhile, the optimal pocket machining sequence with the minimum wall position error is the machining from the fixed end to the free end and the optimal machining sequence is unique. A beam of Al7075 (744 mm in length, 172 mm in width, and 100 in thickness ) with 9 pockets was used to demonstrate the optimal sequences. One of the optimal sequence with minimum floor height error was used in pocketing (roughing), and the maximum distortion was 0.693 mm in the middle and the maximum floor height error appeared on both sides rather than the middle, which were 0.477 mm and 0.388 mm, and part growth produced maximum wall position error was 0.719 mm. On the same part, further demonstrated the optimal sequence with minimum wall position error in finishing (with 1 mm dimension in stock for all surfaces) and the wall position errors were fully removed. The pocketed beam machining is a typical and representative case and the results and conclusion can be extended to pocketed plate/board machining and even surfacing.

本文在误差建模的基础上，采用数学归纳法证明了简单端部支撑袋装梁的最佳袋装加工顺序。具有最小袋底高度误差的最佳腔加工顺序是从两端到中间的加工，并且由于围绕中心平面的对称支撑，最佳顺序不是唯一的。同时，壁位置误差最小的最佳型腔加工顺序是从固定端到自由端的加工，并且最佳加工顺序是唯一的。使用带有9个凹坑的Al7075（长度744 mm，宽度172 mm，厚度100）光束来演示最佳顺序。装袋（粗加工）时使用地板高度误差最小的最佳顺序之一，最大变形为0。中间693毫米，最大的地板高度误差出现在两侧，而不是中间，分别为0.477毫米和0.388毫米，零件生长产生的最大壁位置误差为0.719毫米。在同一部分上，进一步展示了在精加工中具有最小壁位置误差（所有表面的库存尺寸均为1 mm）的最佳顺序，并且壁位置误差被完全消除。袋装横梁加工是一个典型的典型案例，其结果和结论可以扩展到袋装板/板加工甚至堆焊。进一步证明了在精加工中具有最小壁位置误差的最佳顺序（所有表面的库存尺寸均为1 mm），并且壁位置误差被完全消除。袋装横梁加工是一个典型的典型案例，其结果和结论可以扩展到袋装板/板加工甚至堆焊。进一步证明了在精加工中具有最小壁位置误差的最佳顺序（所有表面的库存尺寸均为1 mm），并且壁位置误差被完全消除。袋装横梁加工是一个典型的典型案例，其结果和结论可以扩展到袋装板/板加工甚至堆焊。