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The paper presents the research results of relationship between surface roughness reduction index KRa and three input parameters: burnishing speed Vn, feed fn and burnishing force Fn., and all combinations of levels of yields N measured for 48 points of experiment. The experiment was repeated 3 times. In order to select the model describing the results of tests, the stepping approximation analysis was performed. It relayed at incorporated into the model in following steps approximation elements function, giving the biggest decrease of the sum of squared deviations. The first approximation was based on the ternary monomial of the powers from 0 to 3 for each input value. This approximation aim was to show, that the index of surface roughness reduction does not depend on the burnishing speed in the made in the area of research. The reduced input parameters to two, i.e. fn and Fn. The plan of the experiment was brought to N = 12 and M = 12. The best approximation of test results obtained in the case of Laurent polynomial with stepping selection of elements. The biggest contribution to the decrease in the sum of squared deviations was element 𝑓𝑓𝑛𝑛 −1 ∙ 𝐹𝐹𝑛𝑛 3 , and then fn 2. The article shows that in the range fn {0.6:1.2} there was not information on the successful model and the lack of influence of f and Fn on the results of the experiment. It is postulated to retry the experiment for the feed f <0.6.
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