# Spindle Error Movements and Their Measurement
### Synchronous and Asynchronous Error Movements  
Total error movement is a combination of all radial error movements of the spindle. Its value is the worst case possible, giving a preliminary estimate of the accuracy of the machine tool. The total error movement consists of asynchronous and synchronous error movements. It is important to distinguish between them because their causes are different. Synchronous movement errors are related to the spindle's speed (angular position). This means that their value is the same at a certain angular position in every rotation. The chart (Figure 6) shows \"lobes\" that repeat with each revolution. In machining, a synchronous error movement causes, for example, irregularities in milled holes or turned external surfaces. The item will be made with the same number of \"lobes\" as shown in the diagram of synchronous movement error. The phenomenon of \"lobes\" in the synchronous error diagram is described in [9]. Figure 6: Sample graphs of synchronous error. Asynchronous error movements are not related to the rotational speed (angular position) of the spindle. They are characterized by \"blurring\" in polar diagrams and affect the quality of the treated surface. Although their sources may be well-defined and repeatable, they are not speed-synchronized, i.e., their frequency is not a multiple of the rotation frequency. An excellent example to understand the importance of synchronous and asynchronous errors is shown in Figure 7[10]. Figure 7a shows the path drawn by the head on a perfect disk rotating without error movements. In Figure 7b, the rotating disk has only synchronous error movement. You can see that the path is not circular but has zero thickness despite multiple revolutions. In Figure 8b, asynchronous error movement has been added. With each turn, the head leaves a slightly different trace. This increases the thickness of the path. As can be seen from Figure 8, the asynchronous error is not a random error but is an error that repeats for every non-complete multiple of the spindle's rotation. In general, most movement errors in spindles on ball bearings are usually asynchronous errors. It should be noticed that the problem of error separation is a very important part of the research on spindle error movements, which has been described in detail in many scientific publications [11; 12; 13; 14; 15; 16; 17; 18]. The three most common types of spindles used in precision machining are spindles mounted on rolling, aerostatic, or hydrostatic elements. In spindles mounted on rolling elements, the value of synchronous error movement is usually less than 100 nm but the asynchronous error is usually much larger (100-1000 nm). The value of the total error movement is also significantly influenced by a level of pre-stress error less  
Figure 8: Radial errors in the spindle movement (measurement of multiple revolutions): (**a**) synchronous and (**b**) asynchronous. Figure 7: Graphical representation of synchronous and asynchronous errors [10]: (**a**) perfect disc rotating (without error movements); (**b**) disk with only synchronous error movement; and (**c**) real disc rotating (synchronous and asynchronous errors). than the bearings [19]. In high-quality aero or hydrodynamic spindles, the asynchronous error is less than 5 nm and the synchronous error is 25 nm [20]. Based on the measurements and the analysis performed, one can, for example:  
* determine the condition of the bearings, the expected surface quality due to the obtained result of synchronous and asynchronous errors, improper machine levelling, and improper preload of the machine;
* conclude at what rotational speeds the spindle will be susceptible to resonant vibrations (this information is especially important from the operators' point of view); and
* receive information on how the spindle will behave with sudden changes in speed, whether it results in deterioration of the workpiece geometry or not.