In large assemblies, the perpendicularity of a bolting hole has remarkable effects on the fatigue life and fluid dynamic configuration. While the Computer Aided Design (CAD) model of complexly curved workpieces is hardly satisfied because of manufacturing errors, it is very necessary to measure the normal direction in robotic drilling. One advisable approach is to arrange four laser displacement sensors at the vertices of a rhombus whose center aims at the drilling position. The influencing factors of the measurement precision are firstly discussed in this study, and a novel method to optimize the arrangement size of the displacement sensors for higher precision is introduced. The measurement error for the normal direction consists of the principle error and instrumental error, caused by inconstant curvature of the surfaces and distance measuring errors of instruments, respectively. When the displacement sensors are arranged closer to each other, the principle error will be decreased, whereas the instrumental error will be increased. After the curvature feature of the surface is obtained with the introduced method, the graph of the measurement precision and the arrangement size is plotted. Then, the graph can contribute to developing an optimized design of arrangement size for higher precision. Finally, an example of the curvature obtainment and the arrangement optimization is given. The experimental results show that the optimized design has achieved a higher precision of ± 0.17° for αY and ± 0.26° for αX, whereas the precision of another design is about ± 0.21° for αY and ± 0.29° for αX. The proposed optimization method will bring greater benefit for complexly curved surfaces in practical products and it offers a chance to optimize the arrangement during design phase with little costs.

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