# Estimation and Adjustment of Interface Stiffnesses for Machine-Tool
## 1 Introduction
Finally, the contact characteristics could be estimated. The suggested model is beneficial in determining the characteristics of the spindle-holder taper joint when subjected to various force circumstances during the machining process [14]. [PERSON] et al. (2015) suggested utilizing an ultrasonic vibration for measuring the contact stiffness and pressure distribution occurring on a spindle-holder joint. The ultrasonic reflection coefficient resulting from ultrasonic transducer scanning on the taper joint leads to the estimation of the nominal contact area. Afterwards, the stiffness distribution and global radial stiffness are calculated. The ultrasonic reflection is then converted into contact pressure by a developed calibration curve. Finally, the influence of angle fitting error and clamping force were investigated and rooted to the developed ultrasonic method. As the characteristic developed based on a 7/24 taper joint, a commonly used BT 40 taper joint was studied. The clamping force increased as the contact area, contact pressure and contact stiffness rose. To the contrary, the angle fitting error rose with the decreasing of contact area, influencing both pressure and stiffness at the big end of the taper joint, which increased rapidly compared to the small end of the taper joint. During this period, the global radial stiffness firstly increased, followed by decrease. The global radial stiffness is better paired with a larger angle fitting error that is still in a permissible range (+0'' to +26''). Angle fit error greater than +36'' is also not suitable for a practical application of a taper joint due to the small contact pressure occurring on the small end [15]. Since the rigidity of the ground footing interface is related to various factors, it is not easy to solve. With different stacking and moving positions of the subsystems, the stiffness of each footing along each direction will always be altered. Based on the previous studies, the methods used to estimate and adjust the interface stiffness of a machine-tool are highly complicated and impractical for industrial application. Therefore, a simple estimation and adjustment method for interface stiffness is necessary. A more suitable method to ensure that the appropriate rigidity can be properly adjusted should be developed, and, finally, the relevant interface stiffness should be identified. Therefore, it is necessary to constantly try to estimate and adjust the interface stiffness for obtaining the best dynamic characteristics of the whole machine-tool. Therefore, estimation and adjustment of the interface contact stiffness of a three-axis machine-tool are investigated in this study. The contact model for each different contact interface is established firstly, and the initial value of the estimated stiffness on each different contact interface is calculated by the static analysis and deformation formula in the mechanics of material. The interface that has a great impact on the natural frequency variation of the whole machine-tool is determined through the comparisons between FMA and EMA results, subsequently, as each different contact interface of the initially estimated stiffnesses is prescribed on the interfaces. Finally, the adjusted method proposed in this study is applied for the stiffness adjustment on the main object interface, i.e., footing interface in this study. The error of the natural frequencies of the whole machine-tool between FMA and EMA is less than 5% after being completely adjusted, which indicates that the proposed method for footing interface stiffness adjustment is feasible and practical.