The tasks of increasing the accuracy of determining shread as a determining phenomenon in the development of technology and in ensuring quality indicators in the conditions of operating rolling mills remain relevant. One of the directions for solving this class of problems is the creation of models based on the processing of experimental data for the conditions of a certain process. The main advantages of such "local" models are to take into account the most significant factors of the process or phenomenon and the possibility of using the most suitable type of model for the existing conditions. To build such models, approximation of experimental data is used. Assessment of the accuracy of known approximation methods for the expansion phenomenon during the rolling of oval rolls in round calibers has both practical and scientific significance. The purpose of the study is to estimate the accuracy of methods for approximating experimental data on the spread of oval workpiece in round passes. Experimental data were obtained from the graphical dependences of O.P. Chekmarev for rolls with a diameter of 250 mm depending on the elongation coefficient and the diameter of the round rolled, which were changed at five levels. The objectives of the study were to obtain expansion models in the form of regression equations by three different approximation methods using the same data set. The study also solves the problem of choosing the most acceptable, from the known, approximation method for the specified conditions. It was found that in terms of the standard error of determining the response function in the form of an spread coefficient, the least accuracy is provided by the use of multiple linear regression. The average level of accuracy is provided by approximation with fixed average values of other factors, and the highest accuracy was obtained for a design of experiment with changing factors at three levels. All used approximation methods provide sufficiently adequate models of the spread phenomenon. That is, depending on the needs and conditions of application, it is possible to use any of the considered methods. But the use of the planned experiment method with changing factors at three levels allows you to determine and take into account second-order effects and interaction of factors. The use of the approximation method with fixed average values of individual factors allows us to analyze the influence of each factor on the response function, but does not take into account the effects of the corner elements of the factor space. The examples given of the application of known methods of approximation of experimental data clearly demonstrate the features of these methods, the level of accuracy, which allows us to recommend their use for building models of other phenomena or processes.

Метою дослідження є оцінка точності методів апроксимації експериментальних даних щодо розширення овальних розкатів у круглих калібрах. В якості вихідних експериментальних даних використано абсолютне розширення овальних розкатів в круглих калібрах за графічними залежностями О.П. Чекмарьова. Розглянуто апроксимацію коефіцієнту розширення в залежності від коефіцієнту видовження та розмірів круглого розкату для валків діаметром 250 мм з використанням трьох різних методів апроксимації для одного й того ж набору вихідних даних. Встановлено, що найменшу точність забезпечує множинна лінійна регресія, середній рівень точності отримано для апроксимації з фіксованими середніми значеннями окремих факторів, а найбільш високу точність отримано з обробки даних планованого експерименту.