Synthesis and design of hyperboloid gear drives: Methodology and aspects

  • 1 Graduate School of Engineering Science, Faculty of Engineering Science, Akita University, Japan
  • 2 Department Mechatronics, Institute of Mechanics, Bulgarian Academy of Sciences, Bulgaria,


The high current requirements for the characteristics determining the accuracy, reliability and efficient manufacturing of modern machines, apparatus and devices applicable in various fields of industry and transport in a big extend dictate the applied scientific methodology to the technological synthesis, design and production of gears. In the processes of synthesis and design of the different types of gear transmissions, the designer faces an extremely complex set of questions to solve, which together define the desired optimal construction.
In this case, an optimal design means a gear transmission that is capable of delivering preliminary defined kinematic and / or strength requirements at minimum design, production and operation costs (including the repair costs during their exploitation). This work presents a review of the methodology, developed by the authors, oriented towards the synthesis and design of spatial gear mechanisms (hyperboloid gear drives), realizing rotations transformation between crossed shafts. The main principles, on which the construction of adequate software programs are based for the synthesis of treated transmissions, are presented.



  1. Abadjiev, V. Gearing Theory and Technical Applications of Hyperboloid Mechanisms, Sc. D. Thesis, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, 2007, 309p (In Bulgarian).
  2. Goldfarb, V. Aspects of Gears and Reduction Drives Automated Design. Gearing and Transmissions, Izhevsk, Assoc. Engineers, 1991, No 1, 20-24 (in Russian).
  3. Bulgarian Standard 17108 (CT na CIV 5744 - 86). Cylindrical Involute Gears with Externally Meshing. Standardization Strength Calculation of the Gear’s Teeth, G-15, 1999, Sofia, p. 124, (in Bulgarian).
  4. Gear Engineering Standard. Bending, Stresses in Bevel Gear Teeth. Gleason Works, Rochester, N.Y., Copyright 1955, 1960, 1965, 28 p
  5. Anchev, A., K. Minkov, D. Petrova, Og. Kumchev. Synthesis and Analysis of Bevel Gears with Spiral Teeth, Publishing House of the Bulgarian Academy of Sciences, Sofia, 1980, p. 160
  6. Giznbrug, E., N. Golovanov, N. Firun, N. Hlebskiy. Gears Handbook of Mechanical Engineering. Leningrad, 1980, 416 p., (in Russian).
  7. Dudley, D., J. Sprengers, D. Schroder, H. Yamashina. Gear Motor Handbook, Springer – Verlag, Berlin Heidelberg, 1995, 607 p.
  8. Radzevich, St. Dudley's Handbook of Practical Gear Design and Manufacture, Second Edition, CRC Press, Taylor &Francis Group, 2012, 862 p.
  9. Abadjiev, V. On the Synthesis and Analysis of Spiroid Gears. Ph. D. Thesis, 1984, Sofia, 158 p. (in Bulgarian).
  10. Abadjiev, V., D. Petrova. Aided Design of Hyperboloid Gears with High Gear Ratios. Theoretical and Applied Mechanics, Vol. 4, Publishing House of the Bulgarian Academy of Sciences, Sofia, 1984, pp. 24-30.
  11. Abadjiev, V., D. Petorva. Primary Synthesis of Helicon Gear Drives. Mashinostroene, Vol. 11, Sofia, 1995, pp. 225-227.
  12. Minkov, K. Synthesis and Analysis of Semi-Conjugated Conic and Hypoid Gears. Sc. D. Thesis, LITMO, Leningrad, 1971, p. 170
  13. Minkov, K. Mechanical and Mathematical Modeling of Hyperbolic Gears. Sc. D. Thesis, Sofia, 1986, 330 p. (in Bulgarian).
  14. Abadjiev, V. Mathematical modelling for synthesis of spatial gears, Journal of Process Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part E, Vol 216, (2002)¸ pp. 31-46
  15. Abadjiev, V., D. Petrova. On the Synthesis and Computer Design of Spiroid Gears: A Review of the Bulgarian Approach. Journal of Theoretical and Applied Mechanic, Vol.33, No 3, Sofia, 2003, pp. 3-30.
  16. Abadjiev V., E. Abadjieva, D. Petrova. Synthesis of Hyperboloid Gear Sets Based on the Pitch Point Approach. Journal Mechanism and Machine Theory, Vol. 55, Pergamon, USA, 2012, pp. 51-66,
  17. Abadjieva, E., V. Abadjiev, H. Kawazaki, T. Mouri. On the Synthesis of Hyperboloid Gears and Technical Application, Proceedings of the ASME 2013 International Power Transmission and Gearing Conference, Portland, Oregon, USA on August 4-7, 2013 (published on CD)
  18. Georgiev, A., V. Goldfarb, S. Manshin, S. Ezerskaya. Spiroid Gear Drives with Cylindrical Worms. Calculation of Geometry. Recommendation. Gostandart of the USSR, VNIITMASH, Moscow, 1977, 86 p.
  19. Nelson, W. Spiroid Gearing. Part 1 – Basic Design Practices. Mashine Design, 16 Febr. 1961, pp. 136-144.
  20. Abadjieva, E., V. Abadjiev. Software Assurance of the Synthesis and Design of Hyperboloid Gear Drives, International Scientific Journal “Industry 4.0”, Published by Scientific Technical Union of Mechanical Engineering “Industry 4.0”, Year I, Issue 2 , 2017, Bulgaria, p. 92- 95

Article full text

Download PDF