# Measurement of Static Stiffness after Motion on a Three-Axis CNC Milling Table
## 1 Introduction  
The overall working accuracy of the machine tool mechanics is determined in particular by the precision of positioning of its slides, static stiffness, dynamic stiffness, thermal stability and geometric accuracy of components. Typical sources of working inaccuracy are kinematic deviations, thermo-mechanical deviations, static and dynamic forces [1], the manner of motion control and the control software [2]. The issue of TCP (Tool Center Point) dynamics is addressed by [3]. In addition, working precision is also given by the appropriate choice of technological conditions and required work performance [4]. After a period in operation, the accuracy starts to change, the possible causes being that of wear and tear of the contact surfaces, which can be successfully diagnosed with different diagnostic methods [5]. Vibrodiagnostics also contributes to addressing the issue of application of technical diagnostics tools in verifying the technical condition, which affects the resulting accuracy [6]. A true position of the moving part of the machine with respect to its base even under static load application is influenced by three basic drive nonlinearities. These are friction, backlash and pliability [7]. Many papers [8; 9; 10; 11; 12] state the temperature factor as the major influence on the TCP position. The stiffness experiments show that in addition to temperature, the delimitation of clearance or themanifestation of the stiffness in the guides, the bearings and the ball screw also play their respective roles in the accuracy of the machine tool. The temperature influence during machining is very difficult to simulate with a mathematical model. The machine is practically never thermally stabilized. Thermal expansions vary over a range of many hours and are largely dependent on the work program. This is the main unpredictable factor. Properly executed simulation identifies imperfection within the machine's design. This way, erroneous TCP specification can be minimized by design adjustments [13]. The design arrangement of the mechanics of a node has a significant influence on the behavior of the motion system and it merits further scrutiny [14]. It is generally assumed that the working precision and performance of a machine tool depends to a large extent on the static stiffness of the machine in the workspace. Practical experience confirms this fact. Drawing on this basis, many papers are concerned with calculating stiffness by the method of finite elements [15; 16]. The classic static stiffness measurement is performed on the stationary machine most often at the point where the tool is clamped against the workpiece clamping point. The loader is gradually applied to and then retracted from the working space in the direction of the main machine axes. The deformation at a given location in the direction of load is measured by the dial micrometer indicator. Based on measured values, stiffness is determined in the given location. At the same time, deformations are measured outside the load area. This determines a degree to which deformations change stiffness brought about by individual machine components. Such measurement is of great importance in prototype tests. Based on the measurement of the degree to which stiffness is changed, the shortcomings in the machine design are revealed. Some parts need to be reinforced to increase their respective stiffness. Thus, an acceptable machine stiffness is achieved. Typically, such measurements are rarely performed with the machine in operation. The stiffness measurement depends on appropriate loaders and in many cases, the experimenter is struggling with inadequate access to the place of measurement. Even so, the load is usually applied to the middle of the work area. At prototype tests, the table is loaded against the spindle. The stiffness measurement is not standardized. Stiffness information is generally given only from a single load location. Only load directions vary.