## 1 Introduction
Unfortunately, many of the methods discussed in the literature are supported only by simulations and are not verified by experimental research, especially if they concern large workpieces. Many of the fixture optimization methods rely on simulations of the workpiece deformations and vibrations or simulations of the milling process, which is why some of them are based on modeling the milling process dynamics along with the physics of elements of the machine-tool-workpiece system [6]. Methods that take into account the dynamic properties of the tool and/or workpiece (for example, in order to tune the Finite Element Method (FEM) model or to determine the dominant frequencies of normal vibration) require the identification of these properties through experimental or operational modal analysis [23]. Because the number of sensors used in experiments is always limited, in some applications, there occurs the problem of how to determine the properties of the model for every point of the machined workpiece without performing a large number of modal tests. One proposed solution to this issue is to interpolate normal modes or modal shapes for positions between the points where they have been identified. Such methods are used, for example, in civil engineering to detect structural damage [24; 25] or to optimize the location of sensors used for modal tests in order to minimize errors of modal shape reconstruction and increase the resolution of the FEM mesh [26]. The literature review unveils that there are various developments in preventing geometrical errors (deformations) of the clamped large-size workpieces, but the vibration reduction problem is of less interest. Although a lot of progress has been made in terms of fixture design optimization, proposed methods still have some important limits preventing its wider applications [27]. From this perspective, fixture optimization techniques should be a promising area of research because there is usually no need to modify machine tools nor to involve numerous, sophisticated, and expensive measurement and control equipment. However, the latter does not concern active fixtures or active workpiece support devices. The problem of searching for optimal conditions for mounting large-sized workpieces on the machine table, while simultaneously ensuring the necessary repeatability of tightening the clamping screws, has been of interest to the authors in recent years. For this purpose, the following was proposed:  
* Estimation of the minimum work of cutting forces in the direction of the cut layer width, using only the experimentally determined frequency response function (FRF) of the workpiece [28];
* Application of the experimentally determined FRF of the workpiece and simulated plots of nominal cutting forces [29]. In both cases, however, the impact of dynamic changes in the geometry of the cut layer was omitted, which significantly simplified the considerations. As shown earlier in [30], only computational model simulations of the entire large-size machining process, including the flexible workpiece, the cutting tool, and the dynamics of the cutting process, taking into account the complex vibration state, are reasonable means leading to an effective solution in order to search for the best implementation conditions. However, the previously developed method of Experimentally Aided Operational Virtual Prototyping (EAOVP) has now been significantly improved. And so the following is ascertained:  
* To create a modal model of the workpiece, frequency response functions (FRFs) were determined at excitations in the vicinity of all accelerometers installed along the machined surface. * The influence of spindle speed on the dynamic properties of the rotating tool was taken into account. The above results in the fact that, unlike a non-rotating system (mainly characterized by double natural frequency and decoupled modes in two mutually perpendicular planes), now we observe two different frequencies and the corresponding coupled modes of natural vibrations.