# Estimation and Adjustment of Interface Stiffnesses for Machine-Tool
## 1 Introduction
The annularly shared spatial dispersion along the bolted joint contact surface influence the development of a new density function of the critical sliding force. The collaboration between the new critical sliding force density function, the Iwan micro-slip model, and the residual shear stiffness on the interface during macro-slip and separation are used to establish an enhanced micro-slip model. The developed micro-slip model is incorporated, along with the macro-slip model, replicating the tensile and compressive stiffness of the bolted joint and surface friction, thus obtaining the non-linear model of the bolted connection. A procedure to determine the specification of the micro-slip model is then established by further investigation of the hysteresis loops produced from the quasi-static shear analysis on the bolted join interface. It is observed that when there is no macro-slip, the Iwan model discharged the most energy, followed by the improved micro-slip model, which then ended with the macro-slip model, which does not discharge energy. The reverse characteristic could be observed when macro-slip occurs, corresponding to the equivalent stiffness when there is no macro-slip. The contact pressure dispersion has no important influence on the characteristic of the micro-slip hysteresis, therefore it could be viewed as constant [11]. [PERSON] et al. (2014) came up with a new procedure to forecast the contact stiffness and friction damping coefficient of bolted joints using an analytical method. Due to an unrealistic calculation period for a sticking/sliding contact surface, a torsional contact model over the bolted joint was proposed. The calculation algorithm is then arranged, firstly by solving the linear problem for the contact stress distribution. The torsional deformation is then obtained and analysed via the finite element method. The more complicated non-linear contact problems are then solved, one at a time, by linearly incorporating the FEM result. In the proposed method, the essential factors are: structural dimensions, bolt clamping force, material properties, and friction coefficient between the bolted joint [12]. [PERSON] et al. (2020) investigated the analysis procedure for statistical contact pressure and stiffness distribution occurring between the shaft and bearing, as subject to the size distribution of the T&F (tolerance and fit) specification. The pressure distribution is analysed based on the T&F specification by a probability density function and convolution, while the contact pressure and stiffness occurring on the mating surface are analysed based on the interference. The illustration is made based on a 50 mm roller bearing on a \(\mathcal{O}\)50H6/k5 transition fitting. Analysis showed clearance fit is highly possible, with a 0.5 \(\upmu\)m gap expected, indicating contact stiffness loss, not as initially intended. In order to solve this condition, two methods applied: tighten the tolerance of the inner ring bearing, or increase the dimensional deviation of the shaft diameter. By tightening the inner ring bearing tolerance, the probability of interference through fabrication cost increases. Similarly, by increasing the dimensional deviation of the shaft diameter, the interference increases, while precision grade and fabrication cost are kept steady [13]. [PERSON] et al. (2014) suggested a procedure developed to predict the stiffness and stress distribution of a spindle-holder taper joint when it is subjected to clamping and centrifugal force. The conventional 7/24 taper joint of the BT50 spindle-holder is utilized to forecast the von-Mises stress on the contact surface of the model developed by FEM. The study shows that the von-Mises stress of the model is distributed non-linearly due to the holder's clamping force. The end of the holder experienced a lot of stress when subjected to high speed of centrifugal force. Various clamping forces are applied, as well as stiffness, in both axial and radial directions, along with observed hysteresis cycles.