10.14489/td.2020.07.pp.042-047

2020, 07 July

DOI: 10.14489/td.2020.07.pp.042-047

Timofeev B. P., Dang N. T., Tran M. H.
THE CALCULATION OF BACKLASH IN THE GEARS BY USING THE MONTE CARLO METHOD
(pp. 42-47)

Abstract. This paper is devoted to ensuring normal lateral clearance during the normalization of manufacturing errors of gear wheels and non-gear transmission elements. The task is complicated by the fact that GOST 1643–81 sets tolerances and maximum deviations relative to the working axles of the gears. The methods of calculating the lateral clearance of spur gears are considered. As the influencing factors on the lateral clearance, the thermal expansion of the link materials, the deviation of the interaxial distance of the wheels, the deviation of the engagement pitch, the radial run-out of the gear crowns, the error in the direction of the tooth, the parallelism and skew of the axles of the wheels are taken into account. The transmission accuracy parameters are read randomly. The results of calculation by the minimum-maximum method and the probabilistic method are compared. As a probabilistic calculation method, the Monte Carlo method is adopted. The input calculation parameters are taken equal to the maximum allowable values from GOST 1643–81, the parameters of the kinematic error of the wheels for calculation by the probabilistic method are considered distributed according to the equally probable and normal distribution laws.

Keywords: lateral clearance, min-max method, Monte Carlo method, histogram, random variable, distribution of quantities.

+ - About the Authors Click to collapse

B. P. Timofeev, N. T. Dang, M. H. Tran (Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University), St. Petersburg, Russia) E-mail: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра. , Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра. , Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.

+ - References Click to collapse

1. Basic norms of interchangeability. Cylindrical gears. Tolerances. Ru Standard No. GOST 1643–81. Moscow: Izdatel'stvo standartov. [in Russian language]
2. Kutsokon' V. A. (1980). Accuracy of kinematic instrument circuits. Leningrad: Mashinostroenie. [in Russian language]
3. Naumov V. A., Markova L. V. (2012). Statistical methods of hydrology in the Mathcad environment, pp. 2016 – 224. Moscow: Izdatel'stvo RGAU–MSKhA im. K. A. Timiryazeva. [in Russian language]
4. Dundin N. I. (1985). Improving the accuracy of gears and gears of navigation devices. Leningrad. [in Russian language]

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