A Unified Theory for 3D Gear and Thread Metrology

We propose a unified theory for the metrological treatment of helical machine elements such as cylindrical and conical gears, worms, and screw threads. The main idea is to introduce a universal 3D geometry model for threaded components that provides for distinct parameterization using a unique set o...

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Published inApplied sciences Vol. 11; no. 16; p. 7611
Main Authors Stein, Martin, Keller, Frank, Przyklenk, Anita
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2021
Subjects
areal measurements
Constraint modelling
coordinate metrology
Evaluation
gear metrology
helical machine elements
holistic evaluation
Kinematics
Manufacturing
Parameterization
Parameters
Screw threads
Standardization
Technology assessment
thread metrology
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Abstract We propose a unified theory for the metrological treatment of helical machine elements such as cylindrical and conical gears, worms, and screw threads. The main idea is to introduce a universal 3D geometry model for threaded components that provides for distinct parameterization using a unique set of geometry parameters and that offers and a functional description of the transverse profile. Using modern 3D coordinate measuring technology, a holistic evaluation algorithm yields the actual geometry as the result of a high dimensional best-fit procedure and form deviations as corresponding residuals. All determinants and evaluation parameters can then be calculated from the set of actual geometry parameters. By applying certain constraints to the model to be fitted, the novel method can be reduced to the established 2D methods and hence meets demands for the comparison of the two procedures. The results of the novel approach have proven to be very stable and they enable the evaluation of areal measurements with no loss of information.
AbstractList We propose a unified theory for the metrological treatment of helical machine elements such as cylindrical and conical gears, worms, and screw threads. The main idea is to introduce a universal 3D geometry model for threaded components that provides for distinct parameterization using a unique set of geometry parameters and that offers and a functional description of the transverse profile. Using modern 3D coordinate measuring technology, a holistic evaluation algorithm yields the actual geometry as the result of a high dimensional best-fit procedure and form deviations as corresponding residuals. All determinants and evaluation parameters can then be calculated from the set of actual geometry parameters. By applying certain constraints to the model to be fitted, the novel method can be reduced to the established 2D methods and hence meets demands for the comparison of the two procedures. The results of the novel approach have proven to be very stable and they enable the evaluation of areal measurements with no loss of information.
Author Stein, Martin
Keller, Frank
Przyklenk, Anita
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10.1016/j.measurement.2018.10.088
10.1007/s10010-019-00369-y
10.1017/CBO9780511547126
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SubjectTerms areal measurements
Constraint modelling
coordinate metrology
Evaluation
gear metrology
helical machine elements
holistic evaluation
Kinematics
Manufacturing
Parameterization
Parameters
Screw threads
Standardization
Technology assessment
thread metrology
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Title A Unified Theory for 3D Gear and Thread Metrology
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