PSI - Issue 12

T. Novi et al. / Procedia Structural Integrity 12 (2018) 145–164 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Most of the parameters for Yovanovich’s correlations depend on material properties, and surface and heat treat ments, and are, therefore, fixed parameters. The same thing cannot be said for the pressure between the contacting components that mostly depends on the pressure of the actuation oil, so the instantaneous locking percentage. The value of TCC varies due to the many di ff erent pressure conditions evaluated as each contact depends on pressure in a di ff erent way. For instance, there is a direct dependency on pressure between two discs, whereas between the discs and casing, this value depends on the torque transmitted which depends on the friction torque and so ultimately on the actuation oil pressure. The situation is the same for bearings, gears and all the other components. All of these factors were taking into consideration when applying the boundary conditions to the model.

4. Reasults and discussion

4.1. Steady state

The first analysis done is the case of steady-state. When steady-state conditions are reached, the amount of heat entering the object exactly equals the one exiting; therefore, no energy is used to raise the object’s temperature. These conditions are an asymptotic value, meaning that they are reached only in a very large time scale. However, for this kind of di ff erential, these conditions never occur since the loading conditions change continuously. A steady state analysis is important because it shows for each of the various conditions what the hottest parts in the whole di ff erential are and how the radial and axial distribution of temperature on the disc surfaces stabilize over time. The first case analysed is where no heat flux is generated by the clutch, so as if it were an open di ff erential run for many hours. From this analysis, it can be seen how heat fluxes deriving from bearings, seals and gears influence the thermal behaviour of di ff erentials. Seal temperatures tend to be very high, because standard rubber is considered due to the absence of data on seal material while, in reality, these are designed for sliding contacts and are, therefore, very resistant to heat. This kind of analysis is important since the clutch internal to the di ff erential cannot be actuated for many hours, for instance during a drive along a motorway. Therefore, a steady-state analysis is fundamental to study how heat is dissipated in such conditions, without the contribution of the heat generated by the disc pack. It can be seen that fluxes due to bearings and seals are important as they raise the initial temperature of the system by 15 ◦ C to an initial temperature of approximately 40 ◦ C . A slightly higher temperature can be seen in the area where gear contact occurs. The temperature of the casing was measured during experimental testing of the di ff erential without actuation, and was found to be approximately 40 ◦ C , which validates this model. In figure 4, the steady-state analysis is shown. At this point, the steady-state analysis results of conditions with pressure in the piston chamber, so when working as a locking di ff erential, can be analysed. The analysis is run for pressure values p of 1; 4; 8; 12; 16; 20bar and for each pressure value, the relative rotational velocities of the discs ∆ ω of 0 . 5; 1; 1 . 5; 2; 2 . 5; 3 rad s are considered. Therefore, a total of 36 load cases are considered. It should be noted that any time one of these values changes, not only do the heat fluxes a ff ected by these parameters change, but also other values of the model such as TCC . The same considerations are made for the case in which the relative velocity between the discs is kept fixed and the variable parameter is the pressure in the piston chamber. The most important results of this research are obtained considering unsteady-state conditions. Therefore, the results obtained from the simulation can now be focused on. Many di ff erent kinds of simulations are run to properly study the phenomenon. The main goal is to obtain the temperature distribution of the friction surfaces of the disc pack in both the radial and axial direction after a certain amount of time of a certain load being applied. The amount of time for which the load is applied and after which the disc pack temperature distribution is analysed considered in this paper is the most critical in terms of di ff erential actuation in terms of continuous actuation time. This time lapse has been measured from experimental tests (telemetry data) and corresponds to 10 s . Therefore, the results shown are instantaneous conditions of the di ff erential after 10 s of continuous loading starting from standard conditions. With these results the local temperature for each contact surface can be known, so the e ff ective friction torque generated can also be found with other appropriate models (which include other phenomena other than heat). The reason why instantaneous conditions have been evaluated rather than the trend in time of the temperatures, is that the SAD works 4.2. Unsteady-state analysis