# Estimation and Adjustment of Interface Stiffnesses for Machine-Tool
## 1 Introduction
Similarly, the elastic interaction force is facilitated through the application of the Hertz theory. The domain extension factor is also applied in order to facilitate microcontact size distribution. By combining these three theories, an enhanced translational contact stiffness model and the first rotational contact stiffness model are established. The dynamic model for the ultra-precision machine-tool is also arranged by joining both the transfer matrix method for multibody systems and fractal theory. After observation, the joint between the column and lathe bed is more sensitive due to the maximum vibration displacement of the two joint surfaces, which rise up to 1.74% and 2.90%, respectively, when the preload of both joints is decreased by 15%. In conclusion, when the preload is decreased, the interfacial joint will vibrate more strongly [7]. [PERSON] et al. (2017) incorporated the influence of the surface roughness interaction onto the fractal contact stiffness model, especially for mechanical joints. The surface deformation is assessed based on the elastic theory. Hertz contact theory and fractal theory are both applied to obtain further derivation concerning the relationship between surface stiffness, normal load, and contact area. A fractal model is then used to observe the effect of the contact surface roughness, acquiring fractal smoothness. After taking the derivative of the total load, the normal contact stiffness of the mechanical joint is formed, and the fractal parameters are investigated with the intention to enhance the joints' rigidity. As the fractal dimension D rises, the fractal surface roughness inclines, resulting in escalation of both the joint stiffness and the effect of contact surface roughness, which also enhances the effect of the normal contact stiffness. The developed model is also able to represent the real load-stiffness relationship [8]. [PERSON] and [PERSON] (2020) introduced a new approach called the cutter mark cross (CMC) method in order to make the real contact area become uniformly distributed and to also enhance the contact stiffness. The waviness condition required to make the real contact area become uniformly distributed is determined based on the plastic deformation, enabling one to control the distribution of real contact area. An experiment was then conducted as the verification, discovering the influence of the contact stiffness on the distribution of real contact area. This method is effective in improving both horizontal and vertical contact stiffness up to grinding finished quality. The stiffness in the outer perimeter is also bigger than in the centre [9]. [PERSON] et al. (2018) observed the effect of preload on bolted joints on the natural frequencies, and its correlation to contact stiffness, proposing a new estimation procedure for the contact stiffness of bolted joints. Research shows that the rise of the preload on the surface with bolted joints also increases the first six modes of natural frequencies. The first natural frequency increased with the increasing of number of loading due to work-hardening from numerous loading-unloading cycles. A thin layer element acting as the surface contact stiffness is used in the FEM simulation, exhibiting similar a result to when the stiffness of the thin layer elements is changed. After examining the differences of the natural frequency in both experiments and FE, the quantitative regularity of bolted joints' contact stiffness is determined. The relation between contact stiffness and bolt preload is assessed while also incorporating the significance of each natural frequency. After verification with experimental data, the error of the all-natural frequency estimation is less than 3%, while the error related to contact stiffness estimation is less than 5% [10]. [PERSON] et al. (2021) introduced a prospective non-linear modelling of bolted joint interface by enhancing the Iwan micro-slip model, which is also used in a quasi-static experiment to classify the micro-slip model parameters.