ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 62 / September, 2019

DOI 10.17586/0021-3454-2018-61-2-118-122

UDC 621.833.15


M. V. Abramchuk
ITMO University, Department of Mechatronics; senior lecturer

Read the full article 

Abstract. The methods for calculating the accuracy of the involute cylindrical gear train (the dead course of the transmission) are considered. Expressions from standards GOST 21098-82 and GOST 1643-81 are analyzed, formulas for calculating the dead run of the gear transmission by the maximum method (in which all parameters take the maximum values) are derived. A formula is given for transferring the magnitude of the dead travel of the transmission from micrometers to angular minutes. Calculation of the dead run of the gear transmission by a probabilistic method (the Monte Carlo method) is performed. An algorithm for calculating the dead path is presented.
Keywords: cogwheels, gears, accuracy, GOST 1643-81, ISO 1328, GOST 21098-82, Monte Carlo method, dead run, lateral clearance

  1. ISO 1328-1:1995, Cylindrical gears – ISO system of accuracy. Part 1. Definitions and allowable values of deviations relevant to corresponding flanks of gear teeth.
  2. ISO 1328-2:1997, Cylindrical gears – ISO system of accuracy. Part 2. Definitions and allowable values of deviations relevant to radial composite deviations and runout information.
  3. ISO 1328-1:2013, Cylindrical gears – ISO system of flank tolerance classification. Part 1. Definitions and allowable values of deviations relevant to flanks of gear teeth.
  4. Timofeev B.P., Shalobaev E.V.Vestnik mashinostroeniya (Bulletin of Mechanical Engineering), 1990, no. 12, pp. 34–36.(in Russ.)
  5. Metodicheskie ukazaniya po vnedreniyu GOST 1643 "Peredachi zubchatye tsilindricheskie. Dopuski"(Methodical Instructions on Introduction of GOST 1643 "Cylindrical Tooth Gearings. Admissions"), Moscow, 1975, 110 р. (in Russ.)
  6. Yakushev A.I., Vorontsov L.N., Fedotov N.M. Vzaimozamenyaemost' (Interchangeability), Moscow, 1987, 352 р. (in Russ.)
  7. Abramchuk M.V. Journal of Instrument Engineering, 2016, no. 8(59), pp.619–624.(in Russ.)
  8. Sobol' I.M. Metod Monte-Karlo (Monte Carlo Method), Moscow, 1978, 64 р. (in Russ.)
  9. Golenko D.I. Modelirovanie i statisticheskiy analiz psevdosluchaynykh chisel na elektronnykh vychislitel'nykh mashinakh (Modeling and the Statistical Analysis of Pseudorandom Numbers on Electronic Computers), Moscow, 1965, 228 р. (in Russ.)
  10. Dundin N.I. Povyshenie tochnosti zubchatykh koles i peredach navigatsionnykh priborov(Increase in Accuracy of Cogwheels and Transfers of Navigation Devices), Candidate’s thesis,Leningrad, 1985, 323 р. (in Russ.)
  11. Abramchuk M.V. Sovershenstvovanie raschetov parametrov tochnosti zubchatykh koles, zubchatykh peredach i mnogozvennykh zubchatykh mekhanizmov (Improvement of Calculations of Precision Gears, Gears and Gear Multi-Link Mechanisms), Candidate’s thesis, St. Petersburg, 2014. (in Russ.)