# Estimation and Adjustment of Interface Stiffnesses for Machine-Tool
## 1 Introduction  
For many years, the abnormal vibration of the machine-tool structure has been a concern of the industry and an undesired phenomenon during machining processes, which are often due to improper design of the structure. When an improperly designed machine-tool structure is fabricated, stresses will usually be concentrated on some parts or locations, which result in insufficient structural stiffness and strength, and it can often only be utilized under worse cutting conditions. Since the structural components are often widely joined in the form of bolted connection, and the contact interface has different degrees of friction, tensile and compressive stresses, the local rigidity and damping of the contact interface are discontinuous and have a complex nonlinear dynamic response. Therefore, the modal parameters relating to contact interface of the bolted connection have great significance for the dynamic research of the machine-tool structure. Usually, the machining vibrations will be transmitted to the ground by machine-tool parts. The vibration transmitted reversely back from the ground and the interference vibration of the motor-driver may be regarded as the main sources of the vibration of thewhole machine-tool. Hence, the vibration of the machine tool must be suppressed to reduce the dynamic error during machining processes. Among them, the bending or torsion vibration usually represents the most common vibration mode of the whole machine-tool, and the dynamic characteristics of the bending or torsion vibration are largely affected by the rigidity of the foundation interface. Therefore, the correct structural design and rigidity identification are very important. [PERSON] et al. (2015) came up with a new procedure to adjust the machine-tool support based on its contact stiffness, without the usage of anchor bolts. The idea is to adjust the three-support placement on a rectangular base so that the first natural frequency of the machine-tool is elevated, making the overall stiffness higher, but still preventing the machine-tool from rolling over. For starters, a small-medium sized machine-tool model is designed, and the bulk stiffness on the base is calculated. The main protocol is to choose an appropriate placement for the first two supports based on the bulk stiffness previously calculated. Usually, the first two supports are placed in either the left or the right side, while the remaining will be placed across the two, with size proportional to the preload. Through FEA, this method is proven to improve the support stiffness up to the stiffness when four-support is used ([PERSON] et al., 2013). [PERSON] et al. (2013) broadened the scope of the contact stiffness configuration suggested by [PERSON] et al., aimed at defining the contact stiffness in both normal and tangential directions of the surface of machine-tool support. The contact stiffness is mainly acquired as the result of multiplying the unit contact stiffness with the real contact area. After thoroughly analyzing the concrete's contact stiffness and the interactions with various metals, such as S50C, S5400, and FC250, [PERSON] et al. concluded that the stiffness on the contact area between the machine-tool support and floor is measurable. They found that concrete is the main source of contact stiffness between metal and concrete surfaces, wherein unit contact stiffness is less than 0.1 of metals ([PERSON] et al., 2018). [PERSON] and [PERSON] (2018) established a procedure to assess the floor stiffness based on the model developed for machine-tool support subject to the preload on the contact surface due to difficulty to duplicate the existing floor to measure support stiffness. After establishing the preload-stiffness relationship for the model on the floor, the natural frequency is calculated in terms of translational vibration in the vertical direction, disregarding the insignificant effect of bulk stiffness. The preload-stiffness relationship is acquired from the calculation on the model with various weight.