A Contact Model of Rough Surface for Metal Static Seals Considering Substrate Deformation

Metal static seal consists of two rough surfaces contacting to form a sealing interface. Therefore, the rough surface contact model is the basis for analyzing the leakage characteristics of metal static seals. In order to improve the calculation accuracy of the contact model, a new rough surface elastoplastic contact model is proposed based on the assumption of the continuity of the asperity. A contact analysis was performed on a single asperity containing a substrate. Assuming that the substrate was in elastic deformation, the deformation of asperity and substrate were studied separately. The relation between real deformation of asperity and contact force can be obtained by GW contact model. When calculate the deformation of the substrate, according to the basic assumption of elasticity, it can be considered that the deformation of the substrate was distributed in the cube space whose length was the diameter of the asperity. Therefore, the deformation of the substrate is equal to the deformation of the cube subjected to contact force. The strain of the elastic cube is the ratio of the deformation to the diameter of the asperity, and the average contact pressure of the substrate is the product of the strain and the elastic modulus. Furthermore, the average contact pressure is multiplied by the bottom area of the asperity to obtain the contact force of substrate. According to the force balance equation, the contact force on asperity was same as the contact force on substrate. The deformation of the substrate and the functional relation between the real deformation of asperity and the compression was obtained. Referring to the modeling method of ZMC contact model, the template function which was continuous and derivable on the boundary was used to obtain the contact equation of the asperity in the elastic-plastic stage, and based on the continuity assumption, the elastic and plastic deformation stages of the asperity were connected. Furthermore, assuming that the high of asperities on the rough surface obey gaussian distribution, and the surface density of the asperities on the rough surface was calculated based on the distribution characteristics of the asperities on the rough surface, then the product of the surface density and the nominal contact area of the rough surface was the number of asperities on the rough surface. The contact force of the rough surface was the sum of the contact force of asperities in the elastic stage, the contact force of the asperities in elastic-plastic stage and the contact force in the plastic stage. Based on the above stress analysis and the distribution characteristics of the asperities on the rough surface, a contact model of rough surface considering the deformation of the substrate was established. The analysis based on this model showed that the influence of the deformation of the substrate on the contact characteristics of the contact surface became more significant with the increase of the normal load. The effectiveness of the model were verified by comparing the model with ZMC contact model and KE contact model. Applying the autocorrelation function method to generate point cloud data of rough surfaces with different lateral resolutions, the effects of lateral resolution and nominal contact area on the average contact pressure were analyzed. It showed that the average contact pressure was inversely proportional to the lateral resolution. A stable average contact pressure value can be calculated under the condition that the resolution was less than 1 μm. The nominal contact area had no effect on the average contact pressure under the condition that the value of the nominal contact area was greater than 600 μm×600 μm.