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The PbM presented in the previous section 4.1 has to be implemented for the planetary transmission of the aircraft’s IDG taking into account all the features that may affect the metal-metal contact phenomena. The journal geometry and bearing supports influence the deformations and therefore the film thickness is affected. A long groove affects the pressure distribution and cavitation phenomena. Thus, the actual lubricated surface and bearing geometry with the corresponding boundary conditions have to be implemented to take these effects into account.

The hydrodynamic bearing and planetary gear of the planetary transmission installed in the IDG are made of steel BS 080M40. Both bearing surfaces are manufactured in a lathe machine. The replica of the planetary transmission tested in the rig uses the same lubricant as the IDG, Mobil Jet Oil II [132].

The relative inlet lubricant pressure is assumed to be 1.3 bar; whereas the outlet pressure is considered atmospheric. Both boundary conditions are represented in the PbM as shown in Figure 17. The groove is a critical feature of the hydrodynamic bearing, it is assumed that the inlet oil pressure is constant along the groove and equal to the inlet lubricant pressure. It should be noted that, as opposed to common hydrodynamic bearings, in a planetary transmission the lubricant is supplied from the journal.

Figure 17 Hydrodynamic bearing 3D model of the IDG – lubricant pressure boundary conditions

The inlet lubricant temperature is considered an input that can be modified, as previously mentioned, the lubricant temperature along the lubricated surface is assumed equal to the inlet lubricant temperature.

The bearing consists in a hollow shaft, as shown in Figure 17, rather than a solid shaft as commonly occurs in a hydrodynamic bearing. Therefore, the deformations will differ from those of a solid shaft and the deformations of the lubricated surface are obtained based on a FEA model of the solid instead of calculating the deformation analytically. The deformation of the hydrodynamic bearing is also affected by how the hydrodynamic bearing is fixed to the support. The exterior surface, as shown in Figure 18 is tightly fixed to the carrier shaft and can zero displacement is assumed by the PbM. The lubricated surface where the Reynolds equation is computed is also shown in Figure 18.

Figure 18 Hydrodynamic bearing 3D model of the IDG – lubricated (green) and fixed (blue) surfaces

The mesh should be optimized, only half of the bearing is meshed due to its symmetry. The fluid dynamics phenomena are more critical than the solid deformations and a finer mesh is required in the lubricated surface. A triangular mesh is used in the lubricant surface, optimized to obtain an even finer mesh near the boundaries and in the high pressure region. The solid domain consist in a regular tetrahedral mesh. The mesh discretization is fixed for every simulation. The main parameters of the mesh are shown in Table 4.

Table 4 Hydrodynamic journal bearing of the IDG - mesh properties, fluid and solid domains

Mesh parameter Solid domain Fluid domain

Number of elements 55148 12119

Minimum element quality 0.006592 0.3366

Average element quality 0.6354 0.9791

Maximum growth rate 5.248 5.808

Average growth rate 2.04 1.152

The main dimensions of the hydrodynamic bearing are given in Table 5. The surface properties, required for the asperity component, are shown in Table 6. And the mechanical properties of the materials are shown in Table 7 as well. Table 5 Geometrical properties of the hydrodynamic bearing of the IDG

Parameters Value

Length (mm) 48.34

Diameter (mm) 24.22

Clearance (mm) 0.1018

Table 6 Lubricated surface properties of the hydrodynamic bearing of the IDG

Parameters Value

Density of asperities n (m-2_{) 10}11

Average asperity radius βa (m) 10 ∙ 10−6

Table 7 Mechanical properties of the hydrodynamic bearing of the IDG

Parameters Value

Young’s module (GPa) 209

Shaft Poisson’s ratio 0.33

Dry friction coefficient 0.2

The lubricant, Mobil Jet Oil II [132], is commonly used in aviation. And it is used in the aircraft and in the test rig as well. The main lubricant properties are shown in Table 8.

Table 8 Properties of the lubricant Mobil Jet Oil II [132]

Parameters Value

Kinematic viscosity (cSt) at 40o_{C 27.6}

Kinematic viscosity (cSt) at 100o_{C 5.1}

Oil density (kg/m3_{) 1003,5}

A critical aspect that affect the hydrodynamic phenomena is the lubricant viscosity. As shown in the previous section, the viscosity is a function of pressure and temperature. The PbM proposed in this thesis uses Eq. [19] to calculate the dynamic viscosity as a function of the pressure. And the temperture effect is considered decoupled, as shown in Eq. [20].

As previously mentioned, the pressure significantly varies along the lubricated surface; thus, the viscosity is calculated along the surface as a function of the hydrodynamic pressure (see subsection 4.1.5 for more details). However, the lubricant temperature along the lubricated surface is assumed equal to the inlet lubricant temperature.

The relation temperature effect on the dynamic viscosity for the hydrodynamic bearing of the planetary transmission is shown in Eq. [38]. The parameters 𝜂0,𝐼𝐷𝐺,𝑇0, and 𝛽𝐼𝐷𝐺 have to be obtained based on experimental results. As shown

in Table 8, the viscosity of the Mobil Jet Oil II at 40 and 100 ºC is known. Thus, both parameters can be obtained, as shown Table 9. Where the dynamic viscosity 𝜂0,𝐼𝐷𝐺 is obtained in Pa.s as a function of 𝑇𝑖𝑛𝑙𝑒𝑡, which is introduced in

Kelvin.

𝜂_{0,𝐼𝐷𝐺} (𝑇_{𝑖𝑛𝑙𝑒𝑡}) = 𝜂_{0,𝐼𝐷𝐺,𝑇0}𝑒−𝛽𝐼𝐷𝐺 𝑇𝑖𝑛𝑙𝑒𝑡 _[38]

Table 9 Viscosity-temperature model parameters for Mobil Jet Oil II

Parameter Value Units

𝜼_{𝟎,𝑰𝑫𝑮,𝑻𝟎} 189.5224 1/K