## 4 Methodology
### Design of Experiments  
In the test, the parameters of tool tumble and radial feed were varied. The radial feed influences the distance the tool plunges into the workpiece, and therefore has a direct influence on tooth thickness, which is a central parameter for gears. The tool tumble describes the axial inclination of the milling tool and leads to unwanted deviations of the profile line. With large tumble values, the profile line deviates more strongly from its nominal curve, since the skewing of the tool produces wavy tooth flanks. A full-factorial experimental design is used so that data is recorded for each combination of radial feed and tool tumble settings. Four equidistant steps are used to vary the tumble between 0 \(\upmu\)m and 21 \(\upmu\)m. Measuring the tumble with a dial gauge only allows the setting of a tumble value close to 0 \(\upmu\)m. This setting of minimum tumble will be referred to as tumble class 0 \(\upmu\)m in the following. For each tumble step, the radial feed is varied in five steps between \(-0.02\) mm and \(+0.02\) mm in randomized order, with each parameter set being repeated ten times. A total of 200 components were manufactured with 20 different combinations of tumble and radial feed settings. The structure-borne sound signals are recorded at a sampling frequency of 3.125 MHz, which, according to the sampling theorem, allows frequencies up to 1.5625 MHz to be investigated.  
By varying the radial feed and the tool tumble, the relationship between the process parameters, the emitted structure-borne sound, and the component quality of the manufactured gears are investigated. The question to be answered is whether structure-borne sound measurements offer the potential to predict the two process parameters tool tumble and radial feed directly in the process. In the next step, it is to be investigated whether structure-borne sound signals, in addition to the process parameters, also allow direct conclusions to be drawn about the component quality. The quality variables used here as examples to characterize the component quality of gears are the median-profile total deviation over all teeth (see DIN ISO 1328-1 [33]) and the offset of the single flank rolling test (STFT), which is defined as the overall transmission error (OTE) in the further discus  
Figure 6: Classification data pipeline.  
sion. Both values refer to the left tooth flanks. The median profile total deviation over all teeth was chosen since it is one of the most characteristic parameters for describing gears. The OTE, on the other hand, was chosen since it can be calculated from the deviation of rotation measured in the STFT (Figure 7 in blue) during one revolution of the microgear (13 teeth), which represents a functional test of gears. If a sine function is fitted into this data (red curve), the deviation of the axis around which this sine oscillates (green) from the axis without rotation deviation describes the OTE.  
With increased tooth thickness, the master gear and the tested microgear are engaged earlier in the STFT, resulting in a large rotational-angle deviation and a larger OTE. For the later classification of the geometry data, five classes of the OTE and four classes of the total profile deviation are defined in an equidistant discretization. Classes are then assigned to the value-continuous quality data.