Fractal Model of Normal Contact Stiffness between Two Spheres of Joint Interfaces with Simulation


  • Jingfang SHEN
  • Sha XU
  • Wenwei LIU
  • Jiajun YANG



The contact stiffness of joint surface plays a significant role in the overall static and dynamic characteristics of mechanical systems. When considering joint interfaces with two rough surfaces, the traditional model based on Hertz contact theory between a sphere and a plane is difficult to use, especially for increasingly complex engineering surfaces. In order to overcome the weakness, here we propose a new contact stiffness model in view of the influence of domain extension factor between two rough surfaces. We study the deformation mechanism and the critical contact parameters. Subsequently, we analyze evolution of the elastic-plastic contact involving three distinct stages ranged from complete elastic through elastic-plastic to fully plastic deformation. Our fractal model is more universal than the traditional model based on some strict assumptions which simplify the contact of two rough surfaces to a rough surface and a rigid plane. In fact, the traditional model could be regarded as a special case in our new model. Simulations show that non-dimensional normal contact stiffness increases with dimensionless contact total load under the mechanism of elastic-plastic transition when the fractal dimension is between 1.1 to 1.5. The results indicate that contact stiffness of our fractal model is appropriate and the theoretical contact stiffness is consistent with the experiment data.