# Image-Based Analysis of Plate Separation and Clearance Distribution in Wet Clutches
## 2 Materials and Methods  
### Test Set-Up and Image-Based Measurement Methodology  
The investigations were conducted using the LK-4 drag torque test rig (see Figure 11 of Appendix A). Detailed information about its design and function principle can be found in Ref. [9]. To measure the axial movements of the plates, the test set-up and methodology proposed in Ref. [27] were used. The plates' movements were determined from image series of rotating clutch plates using image processing algorithms. The image series were recorded during the test runs. Figure 2: Clearance distribution scenarios: (**a**) clutch pack in end position showing set total clearance \(h_{\text{tot}}\); (**b**) clutch plates equidistantly distributed showing nominal clearance \(h_{\text{nom}}\); (**c**) clutch plates non-uniformly distributed during operation showing actual clearances \(h_{i}(t)\). Note: Clearances are visualized disproportionately for illustrative purposes; FP, friction plate; SP, separator plate. An SLR camera with a macro lens (see Figure 3a) was used to capture the image series. An LED spotlight was added to achieve short exposure times and brighten the surfaces. Optical access to the clutch plates was achieved through an inspection window in the housing and slot-shaped openings in the outer carrier (see Figure 3b). To maintain a clear view of the plates even during intense oil feed, the oil was displaced from the measuring zone using compressed air (see flat-jet nozzle in Figure 3b). Locally applying compressed air does not influence the movements of the plates or drag torque [27]. The test set-up and the components used are detailed in Ref. [27]. Figure 4a displays the investigated clutch system. The clutch pack consists of five outer plates (O1 to O5) and four inner plates (I1 to I4). The movements of the plates are axially limited by the closing cover and spacer ring. Figure 4b shows the clutch plates in the radial view. Figure 4c shows a detailed view of the measurement zone and also provides the numbering of the gaps. The measurement methodology is detailed in Ref. [27] and briefly summarized hereinafter. Initially, all edges are detected, after which the plates are identified in each image. The edges are then assigned to the identified plates. The geometric center of each edge pair represents the plate position relative to a reference edge. The movements of the plates are reconstructed using the determined plate positions and image acquisition times. The clearances are then calculated based on the positions and thickness of the plates. The image  
Figure 4: Mounting of the clutch pack: (**a**) sectional view; (**b**) radial view; (**c**) detailed view of the measurement zone and numbering of the gaps \(i\)[27]. Figure 3: Test set-up for creating the image series: (**a**) LK-4 drag torque test rig in front view with installed camera and LED spotlight; (**b**) view of clutch plates and installed flat-jet nozzle [27]. processing was implemented in Python (version 3.9.7), utilizing the OpenCV open-source software and library (version 4.5.1) [28] for image processing and the Matplotlib library (version 3.5.1) [29] for result visualization. Figure 5 shows--analogous to Figure 4 (c)--an image of the clutch plates during operation and the plate detection results. Fully detected edge pairs are highlighted in red, while edges marked in yellow indicate that only one plate edge was detected. The edge of the stationary spacer ring is marked in blue and is used as zero line for the positions. The LK-4 drag torque test rig was originally designed as a non-shiftable clutch test rig. Therefore, for this study, a pneumatic actuation unit was integrated to investigate the separation behavior after disengaging the clutch. Figure 6 of Appendix A shows the pneumatic actuation unit graphically. Actuation was performed from the left through openings in the closing cover (see Figure 4a, pneumatic actuation unit not shown). The actuation unit allows the clutch pack to be pushed towards the spacer ring into the end position.