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摘要:
为了保证待加工型面加工余量的均匀性及其相对于基准之间的位置关系，提出一种同时基于基准约束与余量约束的配准算法。所提算法在配准模型中增加基准约束与余量约束，建立在基准约束与余量约束下的配准模型，引入局部坐标系进行配准计算，并将计算结果反算至全局坐标系中。通过引入局部坐标系进行配准计算的算法，降低了测量点变换过程中测量点的运动自由度，从而降低了计算过程中变量的维度，提高了计算效率，保证了计算结果满足基准面约束与余量约束。所提算法在典型的飞机零件“襟翼滑轨”的简化模型上进行了应用验证，相关结果表明：在平面基准约束与余量约束下的配准算法，计算时间为仅在余量约束下配准算法计算时间的33.6%，配准后基准面上测量点的最大偏差小于0.04 mm，待加工面上余量的波动小于0.03 mm，适用于该类零件的自适应精加工过程。
Abstract:This paper presents a registration algorithm based on datum constraints and allowance constraints, which allows the surface to be machined with a uniform allowance and to maintain accurate position relations. First, a local coordinate system was introduced to compute the registration results. Then a conversion method would be employed to solve the corresponding results in the global coordinate system. The introduction of the local coordinate system reduced the degree of freedom of the point set during registration, thus decreasing the number of dimensions and improving the computational efficiency while the algorithm was solved. The results can satisfy both the datum constraints and the allowance constraints. The algorithm was applied on a simplified model of a typical aircraft part “flap track”. The computational results showed that the computing time used by this method was only 33.6 percent of that used by the registration method with the allowance constraints alone, the maximal error for measure points was less than 0.04 mm, and the fluctuating of the allowance was less than 0.03 mm. Therefore, the method is suitable for finishing the surface of similar aircraft parts adaptively.
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图 2 基于基准约束下的变换矩阵与平移矢量求解流程
Figure 2. Process of solving transformation matrix and translation vector based on datum constraints
图 3 面向基准约束的配准模型求解流程
Figure 3. Process of solving registration model based ondatum constraints
图 6 在基准平面约束下的配准结果
Figure 6. Registration result of method based on constraint of a plane
图 7 在基准平面约束下配准后偏差曲线
Figure 7. Deviations of different points after applying registration method based on constraint of a plane
图 8 在基准平面与基准圆柱面约束下的配准结果
Figure 8. Registration result of method based on constraint of a plane and a cylinder
图 9 在基准平面约束与基准孔约束配准后偏差曲线
Figure 9. Deviations of different points after applying registration method based on constraint of a plane and a cylinder
图 10 余量约束下配准结果
Figure 10. Registration result of method based on allowance constraints
图 11 仅余量约束下配准后偏差曲线
Figure 11. Deviations of different points after applying registration method based on allowance constraints
表 1 不同方法配准结果比较
Table 1. Comparison of different registration method
方法 基准平面最大偏差/mm 基准孔最大偏差/mm 待加工面最小偏差/mm 待加工面最大偏差/mm 偏差值波动量/mm 计算时间/s 方法 1 0.038436 1.337247 0.241043 0.263811 0.022768 0.146 方法 2 0.033438 0.054354 0.186074 0.219661 0.033587 0.254 方法 3 0.149557 1.320907 0.213938 0.247241 0.033303 0.434 
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