대한기계학회논문집A (Transactions of the Korean Society of Mechanical Engineers A)

  • 제40권12호
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  • Pages.1077-1085
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  • 2016
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  • 1226-4873(pISSN)
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  • 2288-5226(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
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외부하중을 받는 선형 롤러베어링의 LM 블록 변형을 고려한 변위 모델링

Modeling of Displacement of Linear Roller Bearing Subjected to External Forces Considering LM Block Deformation

  • 권선웅 (금오공과대학교 기계시스템공학과) ;
  • 통반칸 (금오공과대학교 기계시스템공학과) ;
  • 홍성욱 (금오공과대학교 기계시스템공학과)
  • Kwon, Sun-Woong (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology) ;
  • Tong, Van-Canh (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology) ;
  • Hong, Seong-Wook (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology)
  • 투고 : 2016.08.30
  • 심사 : 2016.09.12
  • 발행 : 2016.12.01
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초록

선형 롤러베어링은 하중이 크고 정밀성이 요구되는 이송장치를 지지하기 위해 광범위하게 사용되는 기계요소이다. 본 논문에서는 외력을 받는 선형 롤러베어링의 변위를 계산하기 위한 새로운 모델링 방법을 제시하였다. 먼저 LM 블록을 강체로 가정하여 롤러와 LM 블록의 지배방정식을 유도하였고 Newton-Raphson법을 이용해 계산하였다. 롤러와 레이스 사이의 접촉하중은 롤러의 형상을 고려하여 슬라이싱 기법을 이용하여 계산하였다. 강체 LM 블록 모델에 의해 계산된 접촉하중을 활용하여 LM 블록의 구조적 변형을 유한요소 모델로부터 계산하였다. 최종적인 변위는 강체 LM 블록을 가정한 모델로부터 계산된 변위와 LM 블록 구조해석 결과를 조합하여 도출하였다. 제안된 방법에 의한 결과와 베어링 제작 업체 프로그램 결과와의 비교를 통해 제안된 방법을 검증하였다.

Linear roller bearing (LRB) is an important mechanical element that is widely used in precise positioning systems that are subjected to large loads. This paper presents a new model for estimating the displacement of an LRB subjected to external forces. For this purpose, assuming that the linear motion block (LM block) is rigid, the equilibrium conditions for the LRB were obtained by solving the equilibrium equations of the rollers and the rigid LM block using the iterative Newton-Raphson method. The contact loads between the rollers and raceways were determined considering the profiled rollers. Then, the structural deformations of the LM block, subjected to the contact loads from the rigid LM block model, were computed using a finite element model for the LM block. The displacements of the LRB were then determined by superposition of the rigid LM block displacements on the induced displacements due to the structural deformations of the LM block. The proposed method was verified through comparison with a program by the bearing manufacturer.

키워드

참고문헌

  1. Jastrzebski, D., Pawelko, P. and Szwengier, G., 2012, "Modeling the Effect of Geometric Errors on the Static Characteristics of Guide Rail Systems," Advances in Manufacturing Science and Technology, Vol. 36, No. 2, pp. 31-41.
  2. Zou, H. T. and Wang, B. L., 2015, "Investigation of the Contact Stiffness Variation of Linear Rolling Guides due to the Effects of Friction and Wear During Operation," Tribology International, Vol. 92, pp. 472-484. https://doi.org/10.1016/j.triboint.2015.07.005
  3. Shaw, D. and Su, W.L., 2011, "Study of Stiffness of a Linear Guideway by FEA and Experiment," Structural Longevity, Vol. 5, No. 3, pp. 129-138.
  4. Pawelko, P., Berczynski, S. and Grzadziel, Z., 2014, "Modeling Roller Guides with Preload," Archives of Civil and Mechanical Engineering, Vol. 14, No. 4, pp. 691-699. https://doi.org/10.1016/j.acme.2013.12.002
  5. Sun, W., Kong, X., Wang, B. and Li, X., 2015, "Statics Modeling and Analysis of Linear Rolling Guideway Considering Rolling Balls Contact," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 299, No. 1, pp. 168-179.
  6. Tao, W., Zhong, Y., Feng, H. and Wang, Y., 2013, "Model for Wear Prediction of Roller Linear Guides," Wear, Vol. 305, No. 1, pp. 260-266. https://doi.org/10.1016/j.wear.2013.01.047
  7. Rahmani, M. and Bleicher, F., 2016, "Experimental and Analytical Investigations on Normal and Angular Stiffness of Linear Guides in Manufacturing Systems," Procedia CIRP, Vol. 41, pp. 795-800.
  8. Ohta, H. and Tanaka, K., 2009, "Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail," Journal of Tribology, Vol. 132, No. 1, pp. 011102.
  9. Lee, H., Oh, M.S., Park, C.H. and Lee, C.H., 1998, "Study on the Preload Characteristics of Linear Motion Ball Bearing," Proceedings of the 1998 KSPE Conference, pp. 857-860.
  10. Kim, H.Y., Jeong, J.K., Won, J.J. and Jeong, J.I., 2012, "A Computational Modeling Reflecting Static and Dynamic Characteristics of LM Bearings for Machine Tools," Journal of the Korean Society for Precision Engineering, Vol. 29, No. 10, pp. 1062-1069. https://doi.org/10.7736/KSPE.2012.29.10.1062
  11. Oh, K.J., Kim, G.H., Park, C.H. and Chung, S.C., 2016, "Formulation of Friction Forces in LM Ball Guides," Trans. Korean Soc. Mech. Eng. A, Vol. 40, No. 2, pp. 199-206. https://doi.org/10.3795/KSME-A.2016.40.2.199
  12. Choi, J.C., Yoo, J.H., Yi, Y.S., Kim, Y.Y. and Lee, D.J., 2005, "Vibration Analysis and its Application of a Linear Motion Guide Supported by Rolling Ball Bearings," Trans. Korean Soc. Mech. Eng. A, Vol. 29, No. 7, pp. 955-963. https://doi.org/10.3795/KSME-A.2005.29.7.955
  13. Hartnett, M.J., Robinson, C.J. and Tharp, E.B., 1984, "Roller Bearing with Specially Constructed Rollers," U.S. Patent, No. 4,456,313.
  14. Harris, T.A. and Katzalas, M.N., 2006, "Rolling Bearing Analysis," CRC Taylor & Francis, Vol. 2, pp. 13.
  15. Lundberg, G., 1961, "Elastic Contact Between Two Semi-infinite Bodies," Forschung auf den Gebiete des Ingenieurwesen, Vol. 10, No. 5, pp. 201-211.
  16. ISO/TS 16281:2008, 2008 "Rolling Bearings-methods for Calculating the Modified Reference Rating Life for Universally Loaded Bearings," International Organization for Standardization.
  17. INA, 2012, "Monorail Guidance Systems - Linear Recirculating Roller Bearing and Guideway Assemblies Linear Recirculating Ball Bearing and Guideway Assemblies Linear Guidance Systems with Linear Recirculating Ball Bearing Units Accessories"
  18. Schaeffler Technologies, BEARINX(R)-online Linear System Calculation, (https://bearinx-online.ina.de/), 2015.

피인용 문헌

  1. Five-degrees-of-freedom model for static analysis of linear roller bearing subjected to external loading pp.2041-2983, 2019, https://doi.org/10.1177/0954406218792573