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Cartesian coordinate system rotating surface geometric error of the mathematical model

Discrete sampling error so that the center section of the square to the axis of the distance L D, (J = 1,2, ..., n), then: where:: {. , B,}, A = {X. , Y0, 0}, S = {g, k, f}. Therefore, the axis straightness error is: = max {2Df (J = I, 2, ..., n) (19) 3.3 strike a coaxial error cause actual measured element of the discrete sampling of the square center section 0 (a, b, z) the distance to the axis of ? D: (J: 1,2, ..., Ⅳ), then the least squares evaluation method of the coaxial error is: indistinct = max {2D,} (J = 1,2,[link widoczny dla zalogowanych], ...,[link widoczny dla zalogowanych], .7,[link widoczny dla zalogowanych], 『) (20) 3.4 radial circular bound of the actual elements of the measured error of the first set. , A sample cross section of the samples Q (, Y, z) to the distance between the reference axis L, D, measurement of the radial l70 7, 2002 full moon bounce error: f = max {max {D \{D \OZ axis intercept: d | = a 0gx | + ky | + z | the End Circular Run error: dil: a 0gx | J + k | J + z | J is the most ritZ. By the end evaluation method for the whole run error:: (max {d} a min {d, / ~ / g + k +1 (, = 1,2, ..., M; J = 1,2, ..., Ⅳ) (24) 3.8 degree of error in the assessment of cylindrical cylindrical error, the use of least squares the circle center to strike a similar approach to obtain least squares linear axis, will be detailed in another chapter. f: (max { d,} for a min {d / (,: 1,2, ...,) (22) 4 3.6 Precision Analysis of radial runout error of all the practical elements of the first test set -, a sample section and the reference axis, J the intersection is A 』(』, Y 』, z』), the sampling points Q \error is: f = max {D \to the axis, J family of parallel planes each plane in the OZ axis intercept: in a Cartesian coordinate system the mathematical form and position error measurement model, the nonlinear expressions at the point of (n, b, R) field near the point ‰ (n., b., R.) at the Taylor expansion, and take the first order approximation by linear expressions, the theory of the existence of \select a different article. (n.,[link widoczny dla zalogowanych], b., R.) points were calculated, the deviation is 10 a /, m, can be ignored. from Table 1 lists the data processing results can be seen, the model results good agreement with the simulation results. Table 1 Comparison of units: / * m5 Conclusion (1) This paper is a fundamental solution to the sample case of rectangular coordinates, the rotation error of measurement of the surface geometric center of the circle and square the axis of the Least Squares The strike issues. established for Cartesian coordinates, the origin of coordinates can be arbitrarily selected,[link widoczny dla zalogowanych], not between each discrete sampling points required for the equal angle case, the geometric error evaluation of the least squares model. (2) simulation to prove the model and its development with the Matlab language data processing software has good reliability and practicability. (3) In this article the mathematical model based on the direct use of unconstrained optimization algorithm, can be obtained meet the minimum reference conditions and reference center axis, and then meet the minimum conditions for access to the form and position errors, in order to provide dispute arbitration basis. (4) The mathematical model is established for the coordinate measuring machine can also be used for other smart meter measurement part of the form and position errors. References [1] Zhang Yu. aided precision test [M]. Shenyang: Northeastern University Press, 1993. [2] Lisa Lau. one for roundness error and the optimization algorithm [J] . Scientific Instrument, 1998,19 (4) :430-433. [3] Hou Yu. coordinate measuring machine form error evaluation of the theory and method [J]. Scientific Instrument, 1996, I7 (6): 618 - 621. [4] Hou Yu. Cylindrical Coordinate Measuring Machine Evaluation of a practical algorithm [J]. Aerospace Metrology and Measurement, 1994,13 (6) :16-19. [5] Guo Junjie. A calculation using coordinates A universal algorithm for cylindrical and Eigenvector orientation method of least squares [J]. Scientific Instrument, 1998,19 (4) :434-437.

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