Thomas Gendera, Prof. Dr.-Ing. Georg Kampmann, Ingobert Schmadel, Prof. Dr.-Ing. Milan Horemuz, Nick Turicek
A scientific discovery has been made of a new natural constant derived from a novel mathematical process developed for 30+ years, Numerical Balancing. Balancing uses equation symmetry logic (not a model) to determine reality with absolute geometrical and numerical accuracy through an Inner Reference / True Value. This removes measurement/numerical uncertainty in all calculations. Balancing applies across disciplines and dimensions; this paper will focus on 3D metrology applications.
Current/traditional data analysis methods require subjective, biased data manipulation (e.g. strategies for alignment, filtering, fitting, etc.). This means a given data set can produce various results. Fundamental flaws of these methods are not maintaining raw data fidelity, ability to handle any data type without bias (homogeneous, heterogeneous, mixed), and lack of a True Value. A True Value is needed to determine the accuracy of a calculation process (e.g. we know 2+2 = 3.7 is off by 0.3 because we know the true value is 4). The combination of aforementioned issued causes current measurement results to have numerical uncertainty.
Numerical Balancing is an autonomous process to evaluate raw data in a neutral numerical coordinate system before model application. The advantage being, all the previously necessary, subjective strategies are obsolete with only one possible result per data set. Numerical Balancing finds the Inner Reference for every data set, determining its accuracy with certainty. All data is utilized (absolute fidelity) – the consistent data (balance range) is automatically determined per data set and separated from numerical leverages (outside balance range).
These are selected metrology applications:
Evaluating standard geometries like spheres. After measuring spheres, Numerical Balancing determines the balance range accuracy versus numerical leverages in the measurement point cloud. This independently evaluates probe/sensor accuracy. Knowledge about the position and amplitude of numerical leverages can be used to diagnose the root cause such as noise, bad readings or physical defects in a probe.
Evaluating machine capability/accuracy using Numerical Balancing in combination with a traceable, climate invariant 3-dimensional reference body. First, spheres are evaluated individually to determine probing/sensor accuracy. Once the sensor passes the accuracy check, the sphere centers are used in a balanced 12-parameter transformation to give volumetric accuracy and main geometric parameters (scaling/positioning and squareness). This is the first and only true 3-dimensional and numerically certain tool for accurate 3D machine capability testing.
Evaluating discrete point clouds to make alignment-free comparisons of nominal vs measured using automated measurement systems. As a foundation, individual features are evaluated with numerical balancing, giving a balance range accuracy, numerical leverage information, location and feature parameters. Lastly, all features are used in a transformation based on Numerical Balancing that minimizes the maximum deviation in 3D. One overall achieved balance range value in combination within the autonomous identification of numerical leverages gives actionable results. This eliminates the need for secondary systems for correlations, precision fixturing for alignment and false positive / false negative results caused by measurement uncertainty.
There are many future developments (e.g. autonomous object recognition) for Numerical Balancing in metrology, which will also be mentioned in the full paper.
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