## 7 Results of Simulation  
### The Impact of Heat Source Modeling  
The simulation tests consisted in registering the temperature course at selected points (Figure 4). Figure 5 shows two examples of the temperature course for the variants of the heat source V1 and V6, for the bearing rotational speed of 6000 rpm. The most important conclusions from these runs are:  
* temperatures on the outer and inner raceways reach the values of 80-92 \({}^{\circ}\)C and differ by approx. 11 \({}^{\circ}\)C
* temperatures in the places of contact of the balls with raceways differ from the temperatures on the outer and inner rings by approx. 1-2 \({}^{\circ}\)C
* the time to reach the steady state is about 1 h Similar simulations were carried out to evaluate the modeling of heat sources for variants V2-V5. The summary of the results is presented in Figure 6. The results in Figure 6 allow for the following conclusions:
* the temperature on the outer and inner rings does not significantly depend on the method of modeling heat sources, represented by variants V1-V6
* the temperature difference on the outer and inner rings also does not depend on the arrangement of the heat sources and amounts to approx. 11 \({}^{\circ}\)C
* for the temperatures at the point of contact of the balls with the raceways, an increase in temperatures on the outer and inner rings is observed as the area to which heat sources are assigned decreases (surfaces to which heat sources are assigned meet  
Figure 4: Temperature measurement places: (**a**) on the rings Tor, Tir, (**b**) in the places of contact Tpor, Tpir. Figure 5: Exemplary time courses of temperatures: (**a**) V1 variant, (**b**) V6 variant: Tir—inner and Tor —outer ring, Tpir, Tpor—points of contact of the ball and raceways; speed = 6000 rpm. the condition V1 > V2 > V3, similarly to V4 > V5 > V6). However, the temperature differences at the points of contact of the balls with the raceways are at the level of 7-8 \({}^{\circ}\)C.  
On the basis of the simulation tests carried out, a recommendation can be made to model the heat sources in the bearing in the simplest variant, i.e., assigning heat sources only to the entire raceway surfaces, without assigning it to the surface of balls. In order to estimate the influence of the bearing rotational speed on its temperatures, simulation tests were carried out for the V1 variant. The results of these tests are extremely important for the modeling of heat sources in the bearing, as the viscous resistance significantly depends on the temperature (the viscous resistance depends on the viscosity of the lubricant, which significantly changes with temperature). The tests were carried out in the speed range of 1000-9000 rpm, and as part of the preliminary tests, the temperatures in the bearing were estimated for which viscous resistances were then determined, and then, as part of the main tests, the influence of speed on temperatures was estimated. During the research, the forced convection coefficients were also corrected (5), respectively to the rotational speed. Figure 7 shows the test results in the form of the temperature dependence on raceways on the rotational speed of the bearing. The conclusions from the simulation tests carried out are quite obvious, the increase in speed significantly influences the temperature increase on both rings and at the points of contact of the ball with the raceways. Figure 6: Collective presentation of the results: (**a**) temperature on the outer (Tor) and inner (Tir) rings, (**b**) temperature at the point of contact of the ball with raceways Tpir, Tpor. Figure 7: Influence of the rotational speed on the temperatures on the outer (Tor) and inner (Tir) raceways and at the points of contact (Tpir, Tpor). It is a non-linear relationship, and in the speed range of 1000-9000 rpm the temperatures increase from approx. 27 \({}^{\circ}\)C to approx.