# Measurement of Static Stiffness after Motion on a Three-Axis CNC Milling Table
## 1 Introduction
This, however, offers only limited information, because stiffness values are different at different positions of the spindle with respect to the table. A progressive method of measuring the stiffness of milling machines is the measurement in which the load is applied to a machine and measured by \"ball bar\", the so-called LDBB (Loaded Double Ball Bar) [17; 18; 19]. The principle lies in that a ball bar is attached between the spindle and the table, subjected to a force applied to the ball bar by means of a pneumatic cylinder, while measurement of deformation of the table against the spindle is done simultaneously therewith. The measurement is carried out in motion along the specified trajectory. Thus, it is possible to simultaneously determine the positioning accuracy and the stiffness of the workspace. The published results of measuring the stiffness of the milling spindle against the table showed very low values in this case (in the order of 10 N/\(\upmu\)m). The experimental results presented in this paper indicate a possible explanation for low stiffness. Recently, progressive methods of measuring machine stiffness have been introduced based on camera measurement of 3D optical distortions of points in space [20; 21]. This system is used, for example, to determine the technical condition of the forming machine and the tool. Early identification of wear or incorrect adjustment greatly reduces additional maintenance and operating costs. An advantage is that the measurement can also be carried out during machine in operation. High-speed cameras thus also make dynamic analysis possible. There are many compensating techniques for improving the behavior of the required machining properties of a CNC (Computer Numerical Control) machine, such as [22; 23]. Nevertheless, these compensatory techniques, however perfect, cannot replace the essential requirements for the required static stiffness and its diagnostics. The static stiffness of the entire system of the locomotive mechanism will always be the basic requirement for the overall accuracy of the product, which depends on it to the greatest degree. The motivation of the authors of this paper was not only an improvement of the classic method of static stiffness measurement. Classic measurement focuses primarily on development fostering environment. The main motivation of the authors was to use the stiffness measurement to achieve greater precision in defining the machine condition. Many error conditions of machines are accompanied by a change in stiffness. For example, wear and tear of the guide will not only result in increased noise and vibration, but also in a changed stiffness of the machine frame. Similarly, it also applies to wear of spindle bearings [24]. By measuring stiffness, incorrect assembly operations may also be revealed. For example, misalignment of the bearing preload. A deviation from guide parallelism allowance is manifested by a change in stiffness, too. It is therefore appropriate to develop modified, new compensation and measurement methods for the above ways of determining the stiffness of machines in practice [25]. One of the probable reasons why the stiffness measurement in practice is little used is the absence of compact portable equipment with the appropriate products on the market. This situation should be improved in the future. Progressive compensation methods may significantly contribute to the overall suitable characteristics (e.g., by compensation for vibrations [26], by predicting deviations from the exact path [27] and by subsequent controlled alignment, or calibration [28; 29; 30; 31]) but all the experts agree on the need to achieve the highest static stiffness of the base frame and the slide mechanisms of manufacturing machines. As experience shows, the machine stiffness characteristics are of a complex nature. Therefore, the commonly used simplified view of static stiffness of machines in their designing process is not sufficient. These reasons have been the main motive for research in this field.