For an X–Y stage’s six-degrees-of-freedom (6-DOF), displacement measurement system using multi-interferometers, this paper builds the geometric error’s transfer model first, and then analyses the sensitivity of the measurement error to the geometric error. On this basis, a method of a geometric error tolerance design for the accuracy of a measurement system is proposed using an improved genetic algorithm (GA) with minimal weighted and multi-source error bounds. For the high correlation of transfer coefficients in the propagation process of various errors, using GA’s global optimal searching capability in the entire motion range of each stage, this method overcomes the shortcoming that conservative results are usually produced when an equivalent effect method is used. Therefore, this method acquires a more objective result of the tolerance design of a geometric error for the X–Y stage measurement system accuracy.
ChoBRKimYJKimblerDL. (2000) An integrated joint optimization procedure for robust and tolerance design. International Journal of Production Research38(10): 2309–2325.
2.
FontaineBLHauschildJDusaM. (2003) Study of the influence of substrate topography on the focusing performance of advanced lithography scanners. Proceedings of the SPIE5040: 570–581.
3.
GaoZYHuJCZhuY. (2012) A new 6-degree-of-freedom measurement method of X–Y stages based on redundant information. Precision Engineering (under review).
4.
HanSKYongJC (2000) The kinematic error bound analysis of the Stewart platform. Journal of Robotic Systems17: 63–73.
5.
HollandJH (1975) Adaptation in Natural and Artificial Systems. Cambridge, MA: MIT Press.
6.
HomaifarALaiSHYQiX (1994) Constrained optimization via genetic algorithms. Simulation62: 242–254.
7.
HuangTWhitehouseDJChetwyndDG (2002) A unified error model for tolerance design, assembly and error compensation of 3-DOF parallel kinematic machines with parallelogram struts. Annals of CIRP51: 299–303.
8.
JeangA (1999) Optimal tolerance design by response surface methodology. International Journal of Production Research37(14): 3275–3288.
9.
LiXYChenWYHanXG (2011) Accuracy analysis and synthesis of 3-RPS parallel machine based on orthogonal design. Journal of Beijing University of Aeronautics and Astronautics37: 979–984.
10.
LuQZhangYL (2002) Accuracy synthesis of a hexapod machine tool based on Monte-Carlo method. China Mechanical Engineering13: 464–467.
11.
RoutBKMittalRK (2006) Tolerance design of roblt parameters using Taguchi method. Mechanical Systems and Signal Processing20: 1832–1852.
12.
RoutBKMittalRK (2007) Tolerance design of manipulator parameters using design of experiment approach. Structural and Multidisciplinary Optimization34: 445–462.
13.
RoutBKMittalRK (2008) Optimal manipulator parameter tolerance selection using evolutionary optimization technique. Engineering Applications of Artificial Intelligence21: 509–524.
14.
RudolphG (1994) Convergence analysis of canonical genetic algorithm. IEEE Transactions on Neural Networks5: 96–101.
15.
TakacM (1993) Self-calibration in one dimension. Proceedings of the SPIE 13th Annual BACUS Symposium on Photomask Technology and Management, Santa Clara, CA, pp. 80–86.
16.
WuCCChenZTangGR (1997) Comonent tolerance design for minimum quality loss and manufacturing cost. Computers in Industry35: 223–232.
17.
YeJ (1996) Errors in high-precision mask making and metrology. PhD dissertation, Stanford University, Stanford, CA.
18.
YooSKimSW (2004) Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages. International Journal of Machine Tools & Manufacture44: 767–774.
19.
ZhaoYJZhaoXHGeWM (2004) An algorithm for the accuracy synthesis of a 6-SPS parallel manipulator. Mechanical Science and Technology23: 392–395.
