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Material deformation due to nanoindentation is well known. However, the deformation of a material, indentation cavity, and piled-up region drastically increases and nanohardness significantly decreases if the nanoindentation is performed in such a way that the deformation of one nanoindentation affects the others. This situation arises in various materials when they are subjected to tribological application such as pantograph assembly in electric trains and contact between the electrical power supply plug and pins. This situation has been addressed in this study and the quantitative reduction in nanohardness has been evaluated in detail. In this work, the nanoindentation was performed on the laser powder bed fusion (LPBF) CuCrZr alloy specimen under a load condition of 4500$\mu$N. This test was conducted at 100 points with an array of $10\times 10$ at a 1$\mu$m pitch value. Two significant findings were identified in this work. First, the indentation impression was smaller and the corresponding nanohardness and contact stiffness values were higher in the first column of 10 nanoindentations and the first row of 10 nanoindentations. The remaining 80 nanoindentations displayed contrasting behavior compared to the initial 20 nanoindentations due to the prior deformation of nearer regions. Nanohardness value decreased parabolically from the low deformation to the high deformation region. This finding was validated by increasing the pitch to 15$\mu$m under the 4500$\mu$N load conditions. The piled-up region around the impression of indentation changed from a semi-circular shape at a 15$\mu$m pitch value to a cone shape at a 1$\mu$m pitch value. These findings will be beneficial for industries during the design of materials and will help reduce material failures resulting from tribological activities.

Machine joint surface has an important impact on the performance of mechanical systems. Based on fractal theory, joint surface is assumed to be the contact between absolute smooth surface and rough surface. Through the analysis of the contact process, the contact mechanics model, the contact stiffness model and the three-dimensional surface micro-contact model are studied. To obtain fractal characteristic, the factors and laws affecting the contact characteristics are indicated through digital simulation. The concept of micro-convex body hierarchy is proposed. The critical values are related to the scale of micro-convex bodies and affected by the property parameters of the material. It is proved that the critical point is smooth and continuous, the parameter characteristics of the critical point are determined and the error between prediction and practice is reduced. In the integral calculation of the model, the experimental constants are also established to facilitate the calculation. The results show that the contact process of rough surface is consistent with the actual contact. It makes up the deficiency of KE model by considering the interaction between micro-convex bodies.

Lateral loading and interfacial slip of multi-asperity (i.e., rough) elastic contacts are studied for micro-slip contact conditions. The Mindlin micro-slip model for smooth surfaces is generalized to rough surface contacts using the Greenwood–Williamson (GW) approach, and the general relations of lateral contact force and related stiffness are obtained. The method extends previous approaches by incorporating micro-slip, allowing application to rough surfaces and providing simple expressions for experimental analysis by use of the Greenwood–Williams roughness parameters. As applications, the numerical results of micro-slip contacts on rough surfaces for Gaussian and exponential asperity height distributions, respectively, are obtained based on the general relations of the extended model, and are compared and discussed for low load cases.

The surface roughness induced by geometric irregularities (asperities) has substantial influence on the contact stiffness, which further affects the working performance and service life of mechanical equipment. In this study, an elastic–plastic contact law between a sinusoidal asperity and a rigid smooth flat is first studied, which is then applied on a statistical model to simulate the contact behavior of a pair of 18CrMo4 steel surfaces to investigate the influences of morphology parameters on the contact stiffness. The analysis shows that smaller shape ratios $\xi$ and larger wavelengths $\lambda$ induce larger normal contact stiffness $K_n$ for surfaces with identical roughness, wherein the roughness is defined by the mean value of asperity heights $R_a$ and the standard deviation of asperity heights $R_q$. The normal contact stiffness increases as $R_a$ decreases under the same loading conditions, while the normal contact stiffness increases as $R_q$ decreases for surfaces with a fixed $R_a$. Besides, the normal pressure and normal contact stiffness derived from the proposed contact model are validated. The results demonstrate the potential of the proposed model in contact design due to its ability of establishing the relations between the normal contact stiffness and surface morphology parameters.

The contact properties of an interface are crucial to the performance of equipment, and it is necessary to study the contact damping and contact stiffness, especially in the case of mixed lubrication. A calculation model for contact damping and contact stiffness considering lubrication was proposed on the basis of the KE contact model and mixed elastohydrodynamic lubrication theory. Both the damping and the stiffness were composed of the oil film portion and the asperity contact portion. Since the damping and the stiffness of oil film mainly depended on the film thickness and the pressure, which can be obtained with the mixed lubrication model, another crucial point was to figure out the contribution of asperity contact. Ignoring the effect of the tangential deformation, the stiffness and the load determined with the normal deformation of the asperity were obtained. Then, the contact damping and the contact stiffness considering lubrication could be derived. Finally, the model was applied to the study of contact damping and stiffness of the involute spur gear.

We research the rolling guideway of NC machine tool based on the contact theory of contact mechanics. The solution formula of contact stiffness for the contact surface is established, and the theoretical model of contact stiffness is obtained. Then the contact stiffness of contact surface for rolling guideway is analyzed and calculated. The model of rolling guideway for contact surface is established based on the finite element analysis software. The loading and solution are then conducted to obtain the processed results and stress nephogram. Finally, the processed results are compared with the theoretical calculation results, which verify that this model is feasible. This research lays the foundation for further research on the contact surface of rolling guideway.