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The choice of reference circles when analysis the roundness of parts for ball bearings
https://doi.org/10.32446/0368-1025it.2022-2-14-21
Abstract
The scientific rationale for the choice of reference circles in the analysis of the roundness of rolling bearing parts is presented. The selection criteria were: physical interpretability, minimum roundness, reliability and performance of the calculation algorithm. The measurement of the inner and outer surfaces of the rings and balls of a single-row radial bearing was carried out on a roundness testers and a coordinate measuring machine. The values of roundness are calculated using four reference circles: least squares, minimum zone, minimum circumscribed, maximum inscribed. It was found that the calculation along the minimum zone circle provides the minimum value of roundness. Statistical Monte-Carlo modeling was carried out to assess the distribution of roundness in a batch of bearings. For this, a technique has been developed that allows, on the basis of harmonic analysis, to identify the distribution parameters of the amplitudes and initial phases of the harmonics of the profi le of parts, and then to simulate the distribution in the batch into account the correlation. The results of statistical modeling have confi rmed that the minimum zone circle has the minimum value of roundness in terms of the arithmetic mean and standard deviation. A numerical algorithm for minimizing the functional in the form of the widt hof the minimum zone was applied to calculate the center of the minimum zone circle. In the area of performance of the objective function, there is one local minimum. The algorithm has proven to be reliable and effi cient. Taking into account all the criteria, it is recommended to use the minimum zone circle for the analysis of the roundness of the rings and balls of rolling bearings.
About the Authors
О. V. Zakharov
Yuri Gagarin State Technical University of Saratov; Perm State Agro-Technological University named after Academician D. N. Pryanishnikov
Russian Federation
Russian Federation
Оleg V. Zakharov
Saratov
K. G. Pugin
Perm National Research Polytechnic University; Perm State Agro-Technological University named after Academician D. N. Pryanishnikov
Russian Federation
Russian Federation
Konstantin G. Pugin
Perm
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Review
For citations:
Zakharov О.V., Pugin K.G. The choice of reference circles when analysis the roundness of parts for ball bearings. Izmeritel`naya Tekhnika. 2022;(2):14-21. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-2-14-21
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