Development of codes for motion analysis of multibody systems based on the null space matrix method of differential equation type

• Project/Area Number: 18K04033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 20010:Mechanics and mechatronics-related
• Research Institution: Aichi Institute of Technology
• Principal Investigator: KAMIYA KEISKE 愛知工業大学, 工学部, 教授 (50242821)
• Co-Investigator(Kenkyū-buntansha): 井上 剛志 名古屋大学, 工学研究科, 教授 (70273258)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: マルチボディシステム / 運動解析 / 零空間行列 / 拘束力 / 摩擦 / 拘束力解析 / 摩擦力

Outline of Final Research Achievements

This study has developed an analysis method that has ability to analyze, with high efficiency and precision, motion of multibody systems which have redundant constraints and/or singular configurations and which are subjected to forces depending on the constraint forces such as friction. The key points for this are efficient elimination of constraint forces appeared in the equations of motion and efficient computation of constraint forces. In the developed method, this contradictory problems are solved by obtaining the null space matrix for the constraint Jacobian from differential equations with use of LU decomposition with modified threshold complete pivoting and by developing an algorithm that yields constraint forces necessary for analysis.

Academic Significance and Societal Importance of the Research Achievements

一般に機械は，ジョイントで結合されたいくつかの部品から成っており，各部品は結合先の部品に対して相対運動を行う．このように，複数の部品（物体）がジョイントで結合されてできたシステムをマルチボディシステムという．マルチボディシステムの運動解析を効率よくかつ高精度に行うことは，機械の動特性を考慮した設計・開発にとって極めて重要な課題である．本研究で開発した方法は，これまでに開発されている方法や商用ソフトウェアでは解析が困難な拘束条件をもつシステムに対しても適用可能で，計算効率も高い．本研究で開発した解析法を用いることで，設計・開発の効率化，機械の高性能化につながると期待される．

Research Products

• [Journal Article] Analysis of constraint forces in multibody systems based on the null space matrix method of differential equation type (2020)
  • Author(s): 神谷恵輔
  • Journal Title: Transactions of the JSME (in Japanese) Volume: 86 Issue: 887 Pages: 19-00419-19-00419
  • DOI: 10.1299/transjsme.19-00419
  • NAID: 130007879930
  • ISSN: 2187-9761
  • Peer Reviewed / Open Access
• [Journal Article] Improvement of the nullspace matrix method of differential equation type for motion analysis of multibody systems (2018)
  • Author(s): KAMIYA Keisuke
  • Journal Title: Transactions of the JSME (in Japanese) Volume: 84 Issue: 868 Pages: 18-00288-18-00288
  • DOI: 10.1299/transjsme.18-00288
  • NAID: 130007550631
  • ISSN: 2187-9761
  • Peer Reviewed / Open Access
• [Presentation] 摩擦力が作用するマルチボディシステムの微分方程式型零空間行列法に基づく運動解析 (2020)
  • Author(s): 神谷恵輔
  • Organizer: 日本機械学会 Dynamics and Design Conference 2020
• [Presentation] ANALYSIS OF CONSTRAINT FORCES IN MULTIBODY SYSTEMS BASED ON THE DIFFERENTIAL NULL SPACE MATRIX METHOD (2019)
  • Author(s): Keisuke Kamiya
  • Organizer: ASME 2019 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
  • Int'l Joint Research
• [Presentation] 微分方程式型零空間行列法に基づくマルチボディシステムの拘束力解析 (2019)
  • Author(s): 神谷恵輔
  • Organizer: 日本機械学会 Dynamics and Design Conference 2019
• [Presentation] 零空間行列法に基づく拘束力の効率的計算法（拘束が冗長な場合） (2019)
  • Author(s): 神谷恵輔
  • Organizer: 日本機械学会東海支部TOKAI ENGINEERING COMPLEX 2019(TEC19)第68期総会・講演会
• [Presentation] IMPROVED DIFFERENTIAL NULLSPACE MATRIX METHOD FOR THE DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS (2018)
  • Author(s): Keisuke Kamiya
  • Organizer: ASME 2018 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
  • Int'l Joint Research