Papers by Author: Michael Paul Krystek

Abstract: Least squares association of geometrical features plays an important role in geometrical product specification and verification. Most existing algorithms for the least squares association today usually do not give the covariance matrix associated with the parameters of the respective geometrical feature. The reason is that the complexity of these algorithms can be very high, because partial differential quotients are needed. If the necessary partial difference quotients are calculated by hand and subsequently coded into an algorithm, there is a high risk to introduce unwillingly errors. This paper shows how the least squares algorithm can automatically be generated solely from the equation specifying the distance function of the measured points from the geometrical feature.

Abstract: According to the Guide to the Expression of Uncertainty in Measurement (GUM), all measurement results must have a stated uncertainty associated to them. But in most cases of roundness measurement either no uncertainty value is given, or the calculation is not based on the model of the respective association criterion for the geometrical feature, because no suitable measurement uncertainty calculation procedure does exist. For the case of roundness measurement in coordinate metrology, this paper will suggest algorithms for the calculation of the measurement uncertainty of the roundness deviation based on the two mainly used association criteria LSC and MZC. The calculation of the sensitivity coefficients for the uncertainty calculation can be done by automatic differentiation, in order to avoid introducing additional errors by the traditional difference quotient approximations. The proposed methods are exact and need as input data only the measured co-ordinates of the data points and their associated uncertainties.

Abstract: The helix is a complex geometrical element. During the process of a dynamical measurement of the helical deviations, many factors, including the machine and the environment, lead to measurement errors. Although ISO as well as national standards stipulate the tolerances and assessment methods for helical deviations, these standards contribute little to the uncertainty calculations concerning such measurements. According to the Guide to the Expression of Uncertainty in Measurement (GUM), all measurement results must have a stated uncertainty associated to them. But in most cases of helical deviation measurements, no uncertainty value is given, simply because no measurement uncertainty calculation procedure exists. For the case of helical deviation measurements on a Computer Numeric Control (CNC) polar coordinate machine, this paper analyses in detail all kinds of factors contributing to the measurement uncertainty, and gives the calculation procedure of the measurement uncertainty of helical deviation. As an example, the calculation of the measurement uncertainty of the helical deviations of a worm is presented.

Abstract: Bayesian statistics provides a powerful tool for the analysis of data. The methods are flexible enough to permit a realistic modelling of complex measurements. Prior information about the experiment, as well as knowledge from other sources can be used in a natural way. All relevant quantities concerning the measurement, as e. g. the expected values and their associated uncertainties are obtained from probability density functions. Bayesian data analysis strictly follows the rules of probability theory, thus ensuring that the procedure is free of inconsistencies and is in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM).

Abstract: The uncertainty of dimensional measurements is influenced by numerous different sources, such as the properties of the instrument used, the environmental conditions, the interaction between sensor and surface, and the object properties themselves. In our contribution we focus on the influence of form deviations and surface topography. This influence will be demonstrated by some characteristic examples of micro-component measurements and by the analysis of simulated 2D-data.

Abstract: For functional properties such as gliding, sealing, assembling, adhering etc. the outer layer of the surface is the functional related surface. For the functional assessment of the surface this outer layer should be used as the reference for any functional characteristic. With the existing mean line system for the assessment of roughness and waviness, the standardized characteristics do not follow this logic. However there are valid historical reasons for the acceptance of the shortcomings of the mean line system. They are e.g. the alignment of the profile, the removal of form, the assumption of a sinusoidal structure of the waviness on the surface, and the distortion of the surface by the application of the mean line filtering process. To overcome these shortcomings morphological operations have been used to establish a new developed envelope system. In order to define new parameters to characterize and specify functional properties of surfaces, a common datum is necessary. The presented method for the alignment of datums is consistent with the algorithms used to establish datums and datum systems for workpieces, where the datum is established by the location of a tangent geometrical element such as a line, plane, cylinder etc. The orientation is usually derived by the application of the minimum zone algorithm. The benefit of the assessment of the functional properties of surfaces with morphological operations will be presented for two examples.

Abstract: The reliable determination of periodic micro structures on open surfaces as they exist on involute tooth flanks gain of increasing importance. They allow conclusions from the waviness of the gear surface to the wear and running noise in gears. With the aim of determining traceable wave structures, a method has been developed at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig by which it is possible to model, realise and, especially, reliably evaluate wave-shaped structures on the flank surfaces of involute cylindrical gears.

Abstract: Linear filters are widely used for smoothing measurement data in dimensional metrology and surface texture analysis. In the past, the use of linear filters was mainly limited to Gaussian or even 2RC filters. Recent advances in spline filter theory have paved the way for the development of more flexible and powerful linear filters. This paper deals with the general characteristics of these filters.