preloaded bearing pairs tend to be more compliant in general, and gapping occurs at load points lower than  with equivalent bearing pairs under hard preload. Sometimes, snubbers are added to limit the stroke in the  gapping range by adding a mechanical end-stop. The snubber effect can also be seen in Figure 3.  Modelling and Simulation Approach  In general, ball bearings have nonlinear load-deflection characteristics, with substantial asymmetries and  possibly additional dynamic effects, e.g. due to snubbers, in the soft preloaded case. Therefore, predicting  their dynamic behavior may be rather challenging. This has been the main reason to create a computerbased model for the investigation. The widely used software package MATLAB®/Simulink® was selected  for modelling and simulation . At this stage of the research, the dynamic model only takes the axial degree  of freedom of the bearings into account. In this context, a numerical solver integrates the equations of  motion for the bearing system and generates results in the time domain. The load-deflection characteristics  of the bearings are modelled on the basis of the bearing geometry, mounting and preload configuration as  well as material parameters, referring to established bearing analysis, see for instance in [5]. Under quasistatic assumptions, they are pre-computed by an iterative numerical solver (based on the same algorithm  as used in the ball bearing software tool CABARET [6]) before running a dynamic simulation, and they form  the “backbone” of the model. Furthermore, other relevant phenomena, e.g. gapping and snubber contact,  have been added to the dynamic model.  As part of the modelling and simulation process (see overall structure in Figure 4), the user can input any  time-domain profile for housing acceleration (base excitation), equivalent to a shaker test. Alternatively, a  force profile may be applied on the shaft, simulating a static tension/compression test. On this basis, the  dynamic behavior of the individual bodies is computed, including the bearing loads. A separate postprocessing module has been developed to extract additional values of interest like contact stresses or  gapping distances.  Figure 4. Overall structure of the modelling and simulation approach  Experimental Test Set-up  In order to correlate the model results with real experimental data, a vibration test program has been carried  out. Three different bearing cartridges have been used as test units. In fact, the same test articles had been  used before in a related investigation led by ESTL [1]. All of them comprise two bearings preloaded in a  back-to-back configuration. Their design is shown in Figure 5. On the top of the shaft, a dummy mass of  1.25 kg has been attached, with the option of increasing the total mass by an additional 0.625 kg. For the  soft preloaded bearing cartridges, a set of Belleville washers (conical disc springs) at the bottom end of the  shaft pushes on the inner ring of the lower bearing. The inner ring has a clearance fit, i.e. is allowed to slide  along the shaft. Moreover, a snubber is added at the top of the bearing assembly. When touching a shoulder  NASA/CP—2018-219887 86