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The cross-sectional method is undoubtedly the most widely used method of measuring cylindricity. The method consists of measurements of roundness profiles in several cross-sections of the cylindrical surface. Usually, the distance between subsequent cross-sections is equal. The number of cross-sections used depends on the required accuracy of the assessment of the cylindricity deviation. If one wants to get only rough estimation of the cylindricity deviation, then the measurement can be made in a few cross-sections only. However, if the required measurement accuracy is high, measurements should be carried out in a large number of cross-sections. The consequence of taking the measurements in a large number of sections is significant extension of the measurement time. In this work, an adaptive method of measuring cylindricity is proposed, the purpose of which is to ensure the required measurement accuracy while reducing the necessary number of cross-sections in which roundness profile measurements should be conducted. The proposed strategy is iterative and it is based on carrying out measurements in the cross-sections of the measured part. The proposed method implies two criteria: the correlation coefficient and the predicted values of the form deviations in the non-measured areas of the measured part. The paper presents the fundamentals of the method and the selected results of its practical verification. The experimental results show the ability of the new method to measure the form deviations of cylindrical parts. [ABSTRACT FROM AUTHOR]

Measurements of form deviations of 3D elements can be conducted with various strategies. Such strategies differ in a number and distribution of sampling points located on an investigated surface. The low number of sampling points can bring about the situation that some surface irregularities cannot be detected by a measuring system. An application of higher density of sampling points, in turn, results in significant lengthening of measurement time, which is undesirable. This is why the authors propose to develop a novel adaptive measurement strategy. Proposed adaptive strategy consists of two stages: a preliminary measurement and additional measurements. During the preliminary measurement, an investigated area is scanned along a preselected trajectory. If the measurement results show that there is a significant change in sensor readings in a certain fragment of an investigated surface, then we conduct additional measurements in the area where the large change in sensor readings occurred. The paper presents the state-of-the-art on contemporary measurement strategies of 3D elements and fundamentals of the adaptive strategy proposed by the authors. [ABSTRACT FROM AUTHOR]

The form, waviness and roughness components of a measured profile are separated by means of digital filters. The aim of analysis was to develop an algorithm for one-dimensional filtering of profiles using approximation by means of B-splines. The theory of B-spline functions introduced by Schoenberg and extended by Unser et al. was used. Unlike the spline filter proposed by Krystek, which is described in ISO standards, the algorithm does not take into account the bending energy of a filtered profile in the functional whose minimization is the principle of the filter. Appropriate smoothness of a filtered profile is achieved by selecting an appropriate distance between nodes of the spline function. In this paper, we determine the Fourier transforms of the filter impulse response at different impulse positions, with respect to the nodes. We show that the filter cutoff length is equal to half of the node-to-node distance. The inclination of the filter frequency characteristic in the transition band can be adjusted by selecting an appropriate degree of the B-spline function. The paper includes examples of separation of 2D roughness, as well as separation of form and waviness of roundness profiles. [ABSTRACT FROM AUTHOR]

At the Kielce University of Technology, a concept of the accurate measurement of sphericity deviations of machine parts has been developed. The concept is based upon the measurement of roundness profiles in many clearly defined cross-sections of the workpiece. Measurements are performed with the use of a typical radius change measuring instrument equipped with a device for accurate positioning of the ball. This paper focuses on the statistical analysis of the differences between measurement results of spherical parts obtained by the new and traditional method. The differences were analyzed by applying preselected statistical parameters and diagrams. Results of the analysis revealed that that the new method may contribute to a much more reliable measurement of form deviations of spherical parts. [ABSTRACT FROM AUTHOR]