Mô Hình Tải – Giải Nén Trong Liên Kết Giữa Các Bề Mặt Thô Fractal

Yuan Yuan1, Kuo Xu1, Ke Zhao1
1School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, China

Tóm tắt

Bài báo này trình bày một mô hình đàn hồi – nhựa trong quá trình tải và giải nén giữa các bề mặt thô fractal ba chiều. Trong quá trình tải, các tính chất cơ học của một asperity đơn lẻ tuân theo lý thuyết Hertz. Trong quá trình giải nén, các mối quan hệ tải – vùng tiếp xúc của một asperity đơn lẻ được xác định bằng mô hình EK. Các hàm phân phối kích thước cắt cho các cấp độ khác nhau của asperities được suy diễn. Và diện tích tiếp xúc thực tổng thể cũng như tổng tải trọng tiếp xúc được thu được trong suốt quá trình tải – giải nén. Kết quả cho thấy khi bề mặt thô đang trong trạng thái biến dạng đàn hồi, các mối quan hệ tải – vùng trong quá trình tải và giải nén là giống nhau. Khi bề mặt thô đang trong trạng thái biến dạng không đàn hồi, diện tích tiếp xúc thực tổng thể trong quá trình giải nén lớn hơn trong quá trình tải. Một thí nghiệm được thiết kế để xác minh tính hợp lệ của mô hình hiện tại.

Từ khóa

#mô hình tải – giải nén #bề mặt thô fractal #biến dạng đàn hồi #biến dạng không đàn hồi #diện tích tiếp xúc thực

Tài liệu tham khảo

Greenwood, J. A., & Williamson, J. B. P. (1966). Contact of nominally flat surfaces. Proceedings of the Royal Society of London A,295, 300–319. Greenwood, J. A., & Tripp, J. H. (1967). The elastic contact of rough spheres. Journal of applied mechanics ASME,34, 153–159. Qiu, D., Peng, L., Yi, P., et al. (2017). A micro contact model for electrical contact resistance prediction between roughness surface and carbon fiber paper. International Journal of Mechanical Sciences,124, 37–47. Yang, X., & Jackson, R. L. (2017). Statistical models of nearly complete elastic rough surface contact-comparison with numerical solutions. Tribology International,105, 274–291. Weike, Y., Jianmin, L., Yue, D., et al. (2018). Statistical contact model of rough surfaces: The role of surface tension. International Journal of Solids and Structures,138, 217–223. Huifang, X., & Yunyun, S. (2019). On the normal contact stiffness and contact resonance frequency of rough surface contact based on asperity micro-contact statistical models. European Journal of Mechanics/A Solids,75, 450–460. Chang, W. R., Etsion, I., & Bogy, D. B. (1987). An elastic-plastic model for the contact of rough surfaces. Journal of Tribology, Transactions of the ASME,109, 257–263. Zhao, Y. W., David, M. M., et al. (2000). An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow. Journal of Tribology, Transactions of the ASME,122, 86–93. Kogut, L., & Etsion, I. (2002). Elastic-plastic contact analysis of a sphere and a rigid flat. Journal of Applied Mechanics, Transactions of the ASME,69, 657–662. Lin, L. P., & Lin, J. F. (2005). An elastoplastic microasperity contact model for metallic materials. Journal of Tribology, Transactions of the ASME,127, 666–672. Etsion, I., Kligerman, Y., & Kadin, Y. (2005). Unloading of an elastic-plastic loaded spherical contact. International Journal of Solids and Structures,42, 3716–3729. Kadin, Y., Kligerman, Y., & Etsion, I. (2006). Unloading an elastic-plastic contact of rough surfaces. Journal of the Mechanics and Physics of Solids,54, 2652–2674. Song, H., Vakis, A. I., et al. (2017). Statistical model of rough surface contact accounting for size-dependent plasticity and asperity interaction. Journal of the Mechanics and Physics of Solids,106, 1–14. Sayles, R. S., & Thomas, T. R. (1978). Surface topography as a nonstationary random process. Nature,271, 431–434. Majumdar, A., & Bhushan, B. (1990). Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces. Journal of Tribology, Transactions of the ASME,112, 205–216. Majumdar, A., & Bhushan, B. (1991). Fractal model of elastic-plastic contact between rough surfaces. Journal of Tribology, Transactions of the ASME,113, 1–11. Yan, W., & Komvopoulos, K. (1998). Contact analysis of elastic-plastic fractal surfaces. Journal of Applied Physics,84, 3617–3624. Runqiong, W., Lida, Z., & Chunxia, Z. (2017). Research on fractal model of normal contact stiffness for mechanical joint considering asperity interaction. International Journal of Mechanical Sciences,134, 357–369. Jialan, L., Chi, M., Shilong, W., et al. (2019). Contact stiffness of spindle-tool holder based on fractal theory and multi-scale contact mechanics model. Mechanical Systems and Signal Processing,119, 363–379. Yao, L., Yashun, W., Xun, C., et al. (2018). A spherical conformal contact model considering frictional and microscopic factors based on fractal theory. Chaos, Solitons & Fractals,111, 96–107. Guan, D., Jing, L., Junjie, G., et al. (2018). Normal contact analysis for spherical pump based on fractal theory. Tribology International,124, 117–123. Yin, X., & Komvopoulos, K. (2010). An adhesive wear model of fractal surfaces in normal contact. International Journal of Solids and Structures,47, 912–921. Wenjun, G., Yunxia, C., Mengwei, L., et al. (2019). Adhesion-fatigue dual mode wear model for fractal surfaces in AISI 1045 cylinder-plane contact pairs. Wear,430–431, 327–339. Liou, J. L., & Lin, J. F. (2010). A modified fractal microcontact model developed for asperity heights with variable morphology parameters. Wear,268, 133–144. Miao, X., & Huang, X. (2014). A complete contact model of a fractal rough surface. Wear,309, 146–151. Morag, Y., & Etsion, I. (2007). Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces. Wear,262, 624–629. Yuan, Y., Cheng, Y., et al. (2017). A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces. Applied Surface Science,425, 1138–1157. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. San Francisco, CA: Freeman. Mandelbrot, B. B. (1977). Fractals: form, chance and dimension. San Francisco: Freeman. Johnson, K. L. (1987). Contact Mechanics. Cambridge: Cambridge University Press. Shuming, G., Changhe, L., Yanbin, Z., et al. (2018). Analysis of volume ratio of castor/soybean oil mixture on minimum quantity lubrication grinding performance and microstructure evaluation by fractal dimension. Industrial Crops and Products,111, 494–505. Lixin, S. (2002). On the fractal characterization of turning surfaces. Journal of Agricultural Mechanization Research,3, 66–68. Haiwang, T., Jun, Z., Hao, L., et al. (2018). Study on topography of surface milled with ball-end cutter based on fractal theory. Tool Engineering,52, 29–32. Contreras-Ruiz, J. C., Martínez-Gallegos, M. S., & Ordoñez-Regil, E. (2016). Surface fractal dimension of composites TiO2-hydrotalcite. Materials Characterization,121, 17–22. Yanrong, L., & Runqiu, H. (2015). Relationship between joint roughness coefficient and fractal dimension of rock fracture surfaces. International Journal of Rock Mechanics and Mining Sciences,75, 15–22. Miru, K., Sang, M. L., Deug, W. L., et al. (2017). Tribological effects of a rough surface bearing using an average flow analysis with a contact model of asperities. International Journal of Precision Engineering and Manufacturing,18, 99–107. Yong, Y. C., & Tae, W. C. (2011). Development of algorithm for 3D mixed elasto-hydrodynamic lubrication analysis. International Journal of Precision Engineering and Manufacturing,12, 1065–1070.