Skip to main content
SpringerLink
Log in

Structural optimization methods of nonlinear static analysis with contact and its application to design lightweight gear box of automatic transmission of vehicles

  • INDUSTRIAL APPLICATION
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper, we consider lightweight design methods for gear box of automatic transmission of vehicles with contact constraints. Lightweight design is a fundamental requirement for protecting the environment and improving fuel economy. In addition, durability is another important requirement for safe driving. However, in the design of automatic transmissions, these two requirements are usually in a trade-off relationship and engineers spend a long design study time. This paper deals with design approaches using structural optimization method to design lightweight structures and to minimize stress with contact constraints. Stress with contact constraints is solved using the finite element method. Three different structural optimization methods, topometry, topography and freeform optimization, are applied for the design of a lightweight gear box of an automatic transmission. The optimization results show that the optimization methods successfully found the lightweight gear box design and can be used at the early stage of the design process of automatic transmissions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Allaire G, Jouve F, Toader AM (2002) A level-set method for shape optimization. C R Math 334(12):1125–1130

    Article  MathSciNet  MATH  Google Scholar 

  • Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393

    Article  MathSciNet  MATH  Google Scholar 

  • Azegami H, Kaizu S, Shimoda M, Katamine E (1997) Irregularity of shape optimization problems and an improvement technique. Comput Aided Optim Des Struct 5:309–326

    Google Scholar 

  • Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224

    Article  MathSciNet  MATH  Google Scholar 

  • Bennett JA, Botkin ME (1985) Structural shape optimization with geometric description and adaptive mesh refinement. AIAA J 23(3):458–464

    Article  Google Scholar 

  • Canfield RA (1990) High quality approximations of eigenvalues in structural optimization of trusses. AIAA J 28(6):1116–1122

    Article  Google Scholar 

  • DOT Design Optimization Tools User’s Manual, Version 5.0 (1999) Vanderplaats Research & Development, Inc., Colorado Springs, CO

  • Gambling M, Wang S (2013) The development of TruPly, an efficient composite optimization tool for Simulia Abaqus. In: Proceedings of 10th world congress of structural and multidisciplinary optimization, Orlando, Florida, USA, 19-24 May, 5151

  • Herskovits J, Leontiev A, Dias G, Santos G (2000) Contact shape optimization: a bilevel programming approach. Struct Multidisc Optim 20(3):214–222

    Article  Google Scholar 

  • Ide T, Otomori M, Leiva JP, Watson BC (2014a) Structural optimization methods and techniques to design light and efficient automatic transmission with low radiated noise. Struct Multidisc Optim 50(6):1137–1150

    Article  Google Scholar 

  • Ide T, Otomori M, Leiva JP, Watson BC (2014b) An efficient approach to reduce radiated noise of automatic transmission of vehicles using topometry optimization. Adv Comput Sci Eng 13(2):107–131

    Google Scholar 

  • Imam MH (1982) Three-dimensional shape optimization. Int J Numer Methods Eng 18(5):661–673

    Article  MATH  Google Scholar 

  • Kikuchi N, Chung KY, Torigaki T, Taylor JE (1986) Adaptive finite element methods for shape optimization of linearly elastic structures. Comput Methods Appl Mech Eng 57(1):67–89

    Article  MathSciNet  MATH  Google Scholar 

  • Kitajima H, Ide T, Leiva JP, Watson BC (2010) Structural optimization with contact constraints applied to design automatic transmission of vehicles. SAE Technical Paper 2014-01-0407

  • Leiva JP (2003) Methods for generation perturbation vectors for topography optimization for structures. In: Proceedings of 5th world congress of structural and multidisciplinary optimization. Lido di Jesolo-Venice, Italy, 19-23 May, A070

  • Leiva JP (2004) Topometry optimization: a new capability to perform element by element sizing optimization of structures. In: Proceedings of 10th AIAA/ISSMO symposium on multidisciplinary analysis and optimization Albany, New York, USA, 30 August-1 September, 2004-4595

  • Leiva JP (2010) Freeform optimization: a new capability to perform grid by grid shape optimization of structures. In: Proceedings of 6th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kyoto, Japan, 22-25 June, J-13

  • Leiva JP (2011) Structural optimization methods and techniques to design efficient car bodies. In: Proceedings of international automotive body congress 2011, Troy, Michigan, USA, 9-10 November

  • Schmit LA (1960) Structural design by systematic synthesis. In: Proceedings of 2nd conference on electronic computation ASCE, New York, USA, 8-9 September

  • Schmit LA, Farshi B (1974) Some approximation concepts for structural synthesis. AIAA J 12(5):692–699

    Article  Google Scholar 

  • Schmit LA, Miura H (1976) Approximation concepts for efficient structural synthesis, NASA CR-2552, March 1

  • Sigmund O, Maute K (2013) Topology optimization approach. Struct Multidisc Optim 48(6):1031–1055

    Article  MathSciNet  Google Scholar 

  • Taylor JE, Bendsøe MP (1984) An interpretation for min-max structural design problems including a method for relaxing constraints. Int J Solids Struct 20(4):301–314

    Article  MathSciNet  MATH  Google Scholar 

  • Vanderplaats GN (1979) Approximation concepts for numerical airfoil optimization. NASA Technical paper 1370

  • Vanderplaats GN (2000) Very large scale optimization. In: 8th AIAA/USAF/NASA/ISSMO Symposium at Multidisciplinary Analysis and Optimization, Long Beach, CA September 6-8

  • Vanderplaats GN (2004) Saving energy through design optimization. SAE Technical paper 2003-01-1331

  • Vanderplaats GN (2007) Numerical optimization techniques for engineering design: with applications. Vanderplaats Research & Development, Inc., Colorado

    MATH  Google Scholar 

  • Vanderplaats GN (2011) Multidiscipline design optimization. Vanderplaats Research & Development, Inc., Colorado Springs

    Google Scholar 

  • Vanderplaats GN, Salajegheh E (1989) New approximation method for stress constraints in structural synthesis. AIAA J 27(3):352– 358

    Article  Google Scholar 

  • Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246

    Article  MathSciNet  MATH  Google Scholar 

  • Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199(45–48):2876–2891

    Article  MathSciNet  MATH  Google Scholar 

  • Yi SI, Lee HA, Park GJ (2010) Optimization of a structure with contact conditions using equivalent loads. J Mech Sci Technol 25(3):773–782

    Article  Google Scholar 

  • Zienkiewicz OC, Campbell JS (1973) Shape optimization and sequential linear programming. In: Optimum structural design - theory and applications. Wiley, pp 109–126

Download references

Author information

Authors and Affiliations

  1. AISIN AW Co., LTD. Fujii-cho, Takane 10, Anjo, Aichi, 444-1192, Japan

    Takanori Ide & Masaki Otomori

  2. AW ENGINEERING CO.,LTD. Sakurai-cho, Kitaawarashimo 48-8, Anjo, Aichi, 444-1154, Japan

    Hiroyuki Kitajima

  3. Vanderplaats Research & Development, Inc., 41700 Gardenbrook, Suite 115, Novi, MI, 48375, USA

    Juan Pablo Leiva & Brian C. Watson

Authors
  1. Takanori Ide
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroyuki Kitajima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masaki Otomori
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juan Pablo Leiva
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Brian C. Watson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takanori Ide.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ide, T., Kitajima, H., Otomori, M. et al. Structural optimization methods of nonlinear static analysis with contact and its application to design lightweight gear box of automatic transmission of vehicles. Struct Multidisc Optim 53, 1383–1394 (2016). https://doi.org/10.1007/s00158-015-1369-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-015-1369-y

Keywords

Search

Navigation