Optimum Dataset Size and Search Space for Minimum Zone Roundness Evaluation by Genetic Algorithm

Abstract

Roundness is one of the most common features in machining. The minimum zone tolerance (MZT) approach provides the minimum roundness error, i.e. the minimum distance between the two concentric reference circles containing the acquired profile; more accurate form error estimation results in less false part rejections. MZT is still an open problem and is approached here by a Genetic Algorithm. Only few authors have addressed the definition of the search space center and size and its relationship with the dataset size, which greatly influence the inspection time for the profile measurement and the convergence speed of the roundness estimation algorithm for a given target accuracy. Experimental tests on certified roundness profiles, using the profile centroid as the search space center, have shown that the search space size is related to the number of dataset points and an optimum exists, which provides a computation time reduction up to an order of magnitude.

Minimal Exhaustive Search Heuristics (MESH) of point clouds for form tolerances: The minimum zone roundness

“…The algorithm accuracy A* by equation 18is as low as 2% and the maximum is 60%. A* conservatively does not exploit all the available range up to 100% because the mesh spacing reduces from ε to ε M by equation (25) to design a square mesh with N circ cross points on each side.…”

“…In this section, it will be shown that the MESH algorithm is incumbent with respect to the GAs in [25] and in [20].The search space of the minimum zone center by the GA in [25] is restricted to an arbitrary (large) search space centered on the centroid. The centroid in turn is farther from the minimum zone center (about 50 times with respect to MESH), because the cloud datapoints generated by the NPL certified software are not equiangular.…”

“…The second approach is based on the minimization of the E MZ as a function of C MZ ( Figure 2) and considers primarily the location of the center of the concentric circle pairs (center-based [25]. The authors developed a cross-validation method to assess the kind of manufacturing signature [26] on the roundness profile in order to detect critical points such as peaks and valleys [27].…”

“…Optimization techniques such as genetic algorithms were developed to minimize the computation time in the roundness error evaluation. A fast genetic algorithm, with convergence speed greater than 0.1 µm per 30 generations as the selected stop condition, was developed and for large signature-based samples in [20] and for non-manufacturing signature specific in [25] with validation by certified software. [25] discussed the statistical distribution of the GA error as a function of the cloud datapoints size and of the search space size because by NPL Chebyshev best-fit circle certified software the minimum zone center is known (for example, it is fixed in (0,0)).…”

“…A fast genetic algorithm, with convergence speed greater than 0.1 µm per 30 generations as the selected stop condition, was developed and for large signature-based samples in [20] and for non-manufacturing signature specific in [25] with validation by certified software. [25] discussed the statistical distribution of the GA error as a function of the cloud datapoints size and of the search space size because by NPL Chebyshev best-fit circle certified software the minimum zone center is known (for example, it is fixed in (0,0)). Also, the deviations on the roundness profile are equally distributed in the range of the difference of radii between inner and outer minimum zone circles, so results are more general and not manufacturing signature specific.…”