Rearching On Roundness Error Evaluating Algorithm Based On Mesh Searching

Roundness error is one of common form errors of machine parts. It refers to the variation quantity of the measuring circle contour to its ideal circle. In this area, the main methods of evaluating the roundness error include the minimum zone circle (MZC), least square circle (LSC), minimum circumscribed circle (MCC) and maximum inscribed circle (MIC). These methods are to seek the center which radius range value of two concentric circles is minimum.According to the definition of roundness error and evaluating criterion, a new algorithm is to be studied, and simulation and experiment to solve roundness error will be carried out in detail in this dissertation. The mathematical models and typical algorithms for evaluating roundness error are studied, and the criterion for evaluating roundness error are discussed, and iteration method and simplex method to solve the roundness error are analyzed. The mathematical models of iteration method and simplex method are presented on the rotary surfaces in the rectangular coordinates whose center may be set on random. Also, the corresponding software of processing data is programmed and their calculation precision is examined by tests. The substance of the iteration method and simplex method for evaluating roundness error are grasped.In view of the definition of roundness error and the criterion for evaluating roundness error, the rectangular coordinate mesh searching algorithm, rectangular coordinate transformation, polar mesh searching algorithm and polar coordinate transformation algorithm are presented. The principle and step of using those algorithms for solving the roundness error are described in detail. There is no restriction for well-distributed sampling points and there is no need to satisfy the'minimum error'or'deviation'hypothesis if those algorithms are used to evaluate the roundness error. The precision of evaluating roundness error can be realized by repeating only the point-to-point distance formula using those algorithms. The relation of precision degree and mesh point number is discussed, and the rule of mesh division is obtained. The results of the experiment indicate that precision degree is correlative with mesh point number. The more the point is, the higher the precision degree is. The precision evaluating can realize by 400-1200 mesh points. The data system on C++ Builder is designed and applied to the new algorithm in the experiment. The processing results of the new algorithm, iteration method and simplex method are contrasted and analyzed. The results of the emulation and experiment indicate that the roundness error can be evaluated effectually and accurately using mesh searching algorithm.The mesh searching algorithm and coordinate transformation algorithms in this dissertation can be applied in the CMM and other intelligent instrument as a kind of applying algorithm to evaluate the form and position errors for after improve further.