# Experimental Study of the Volumetric Error Effect on the Resulting Working Accuracy--Roundness
## 1 Introduction  
The increase of the production accuracy of machine tools is a continuous process with the involvement of all manufacturers. Production accuracy is a machine feature that is also an indicator of competitiveness; its continuous improvement is also required by the machine users themselves. The percentage of quasi-static errors and the resulting accuracy of the three-axis machine tool was described in 2000 by [PERSON] [1]. Here, the percentage was 60-70%. Subsequently, [PERSON] expanded this hypothesis in his 2010 publication [2] with up to 80% for five-axis machine tools. The increase in the proportion of quasi-static errors is caused by the kinematic pair of rotary axes of five-axis machines. There are two options to ensure high geometric accuracy. The time-consuming and more expensive option uses a mechanically adjusted machine, i.e., no software compensation. This option is offered by machine manufacturers, especially for their special machines, which are supplied to industries with extremely high requirements for long-term dimensional stability. Another option is the use of softwarecompensation, eliminating the basic sources of machine tool errors. These sources include geometric, thermal, dynamic and tool wear errors. [3]. Quasi-static errors are defined as errors in the relative position of the tool centre point (TCP) and the workpiece; these change slowly over time. They are directly related to the structure of the machine tool itself and can be divided into geometric, kinematic and thermal errors. There are several ways of achieving the goal of increasing production accuracy or assessing machine accuracy. These include the use of commercially available software compensations for CNC machine tools, supplemented by new, more effective methodical procedures for measurement and evaluation and the deployment of new measurement technologies. The robustness of a compensation method, with respect to the human factor, is presented in reference [4]. In reference [5], the effect of volumetric compensation on the improvement of the geometric accuracy of a small machining centre, by up to 60%, is presented. The increase of the volumetric accuracy of a five-axis machining centre using a reconfigurable artefact is presented in [6]. The use of tracking interferometers to assess 2D geometric errors influenced by temperature change is described in [7]. The utilisation of manufacturing accuracy data for rotational error assessment is presented in [8], linear axis compensation procedures in publications [9; 10], the use of the Ballbar for machine tool error assessment and compensation in [11], a comprehensive assessment of measurement methods, overexertion and their effects on large machines in [12] and the use of on-machine tool measurement in [13]. When assessing the effects of machine geometric errors on a future workpiece, it is necessary to consider all effects that increase measurement uncertainty and those that minimise these uncertainties. Another group is the development of new mathematical models that describe the geometry of the machine, which specifies the position of the TCP [8]. Publication [14] describes the principle of weighted multilateration and its influence on the positioning of a point in the machine's working space, including its application to the small machining centre presented in [15]. The data obtained from the measurement can then be used as compensation values sent for further processing of the CNC program from the CAM. A compensation algorithm for reducing geometric errors by changing the CNC program is published in [16]. These are mostly designed for basic measuring devices that are commonly available on the market and have already been established in the field of machine inspection and diagnostics. The same is true of temperature models of machine tools and their compensations [17], where the thermo-elastic behaviour of machine tool structures and their influence on TCP is described in [18]. This area also includes temperature measurements of machine tools [19].