# Static Characteristics of a Tilting Five-Pad Journal Bearing with an Asymmetric Geometry

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{pads}. In the same case, the pad can also tilt in the axial direction.

## 2. Bearing Modeling

_{b}and O

_{j}are the center of the bearing and the shaft, respectively. Only the displacement of point P in the radial direction $\eta $ is considered for the pivot flexibility, while the tangential displacement is neglected. The pad tilts about the line contact with angle $\theta $ (see Figure 1). So, the vector of the DOF of the system is:

_{s}and y

_{s}are the shaft center position and ${\theta}_{k}$ and ${\eta}_{k}$ represent the tilt angle and the radial movement of the k-th pad, respectively.

_{p}of the center of each control volume with dimensions $\Delta X$ and $\Delta Z$ is a function of the temperatures of the four edges of the control volume ${T}_{N},\hspace{0.17em}{T}_{E},\hspace{0.17em}{T}_{S},\hspace{0.17em}{T}_{W}$ and the previous value of the iteration for temperature T

_{p}

_{0}:

_{C}, S

_{P}and the intensity of the viscous heating S are obtained by:

_{T}, as shown in Figure 2.

_{outlet}is the average oil film temperature at the pad trailing edge and is achieved by taking into account the heat flux at the trailing edge:

**u**owing to thermal and mechanical stresses considering an isotropic material is given by:

^{2}·K) is applied on the pad surfaces contacting lubricating oil at supply temperature (T

_{supply}= 40 °C and q

_{air}= 20 W/(m

^{2}·K)) in order to evaluate the distribution of the pad temperature. The constant convection coefficient q = 50 W/(m

^{2}·K) was also used in some previous publications [11,29,31,32]. Actually, this value is not uniform at the pad peripheries and it changes with the conditions of the oil flow around the pad [19]. For the estimation of the pad deformation, the Dirichlet boundary condition with null displacement is assumed for the upper surface of the pad face

**F2**(see Figure 3), corresponding to the pivot part. The boundary conditions used in the model of the pad are listed in Table 3.

## 3. Test Rig and Bearing under Test

## 4. Results and Discussion

#### 4.1. Clearance Profile

_{p}sides with respect to the number of pads installed in the bearing.

#### 4.2. Eccentricity Measurement

_{equilibrium}, y

_{equilibrium}) is the equilibrium position of the journal center and C

_{b}is the bearing clearance.

#### 4.3. Temperature Distribution

#### 4.4. Pressure Distribution

## 5. Conclusions

- (1)
- The clearance profile of TPJBs has a polygon shape with the number of sides equal to the number of pads. The measured clearance profile of the test bearing is a strange pentagon, while the nominal one shows a regular pentagonal profile. As the bearing becomes hotter, the shaft, pads and bearing will expand, resulting in a reduction of the clearance profile.
- (2)
- It is more evident that when rotational speed increases, the equilibrium and shaft position will move up. When speed is low, the measured eccentricity deviates slightly from the bearing vertical centerline. The largest eccentricity corresponding to a maximum load of 9 kN and shaft speed of 10 Hz is about 70 µm.
- (3)
- The experiments show that the eccentricity is almost inversely proportional to the rotational speed. Additionally, most of the eccentricity ratios of all tests either touch or coincide with each other when the Sommerfeld number ranges from 0.1 to 0.5.
- (4)
- The measured data show that the pad temperature increases with an increase in the applied static load in which the temperature of pad #1 is always higher than that of pad #2, by nearly 1–1.5 °C. Additionally, it can be stated that the rotational speed has a considerable effect on the pad temperature.
- (5)
- As a function of load direction, on the one hand, the TEHD model underestimates the film temperature for pads #1, #4 and #5. On the other hand, the numerical results show a good agreement with measurement data for pad #2 and pad #3. The code predicts that the pad temperature grows circumferentially on the middle plane from the leading edge to the trailing edge, about 4 °C for pads #1 and #4, and more or less 6 °C for other three pads in the tested bearing.
- (6)
- The effect of the asymmetric geometry on the oil film pressure distribution is not negligible. Owing to the identical geometry of pads in the nominal bearing, the oil film pressure with a maximum value of nearly 30 bar is distributed mostly on the loaded pads.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 11.**Measured clearance profiles at different pad temperatures and the predicted nominal clearance profile.

**Figure 15.**Predicted oil film temperatures along the center line of the loaded pad and measured pad temperatures. Positions A and B present the leading and trailing edge of the loaded pad, respectively.

**Figure 16.**The measured temperature of each pad vs. static load (

**left**) and rotational speed (

**right**) in the test bearing.

**Figure 17.**Measured and predicted temperature of pad #1 and pad #4 vs. static load (

**left**) and rotational speed (

**right**) in the test bearing.

**Figure 18.**Predicted temperature distribution on all pads as a function of shaft speed (

**upper**) and applied static load (

**lower**) in the test bearing.

**Figure 19.**Predicted temperature distribution on pad #1 as a function of shaft speed (

**upper**) and applied static load (

**lower**) in the test bearing.

**Figure 20.**Average predicted temperature distribution of pad #2 is higher than (

**left**) or nearly equal to (

**right**) that of pad #1.

**Figure 21.**Predicted pressure distribution with LOP configuration on each pad of nominal bearing vs. tested bearing.

Item | Value |
---|---|

Viscosity [$\mu $] | 0.03969 Pa.s |

Density [$\rho $] | 861 kg/m^{3} |

Specific heat [c_{p}] | 1.9766 kJ/(kg/°K) |

Thermal expansion coefficient [${\alpha}_{v}$] | 7.34 × 10^{−4} C^{−1} |

Viscosity index [$\kappa $] | 96.552 |

Thermal conductivity [k_{OIL}] | 0.214 W/(m·K) |

Parameter | Babbitt | Steel | |
---|---|---|---|

Young’s modulus [GPa] | $E$ | 40 | 206 |

Poisson’s ratio | $\nu $ | 0.3 | 0.3 |

Thermal expansion coefficient [1/K] | $\alpha $ | 12 × 10^{−6} | 24 × 10^{−6} |

Heat conductivity [W/(m·K)] | $k$ | 26 | 54 |

Face | Boundary Condition Type |
---|---|

Pad lateral and bottom surfaces | Convection with oil @ T supply (q _{oil} = 50 W/(m^{2}·K)) |

Coating lateral surfaces (Babbitt layer) | Convection with oil @ T supply (q _{oil} = 50 W/(m^{2}·K)) |

Fixed surface (F2) | Null displacement |

Leading edge (F8) | Supplied temperature of 40 °C |

Active surface | Given pressure and temperature distribution |

**Table 4.**Pad thickness, bearing assembly clearance and preload factor of the bearing under test [30].

Pad | Pad Thickness [mm] | Assembly Clearance [mm] | Preload Factor |
---|---|---|---|

Nominal | 16.000 | 0.070 | 0.44 |

Pad #1 | 15.994 | 0.066 | 0.47 |

Pad #2 | 16.015 | 0.045 | 0.64 |

Pad #3 | 15.999 | 0.061 | 0.52 |

Pad #4 | 15.981 | 0.078 | 0.37 |

Pad #5 | 16.018 | 0.042 | 0.66 |

Sensor | Model/Type | Sensitivity |
---|---|---|

Proximity | CEMB T-NC/8-API | 7.78 mV/µm |

Load cell | HBM U3 20kN | 2.0 mV/V |

Temperature | Pt100 | 15 °C/V |

Pressure | MEAS M513KPG41-00005-0 | 51.71 bar/V |

Item | Value |
---|---|

Shaft diameter [mm] | 100 |

Bearing length [mm] | 70 |

Housing radius [mm] | 66 |

Pad outer radius [mm] | 59.6 |

Nominal assembled clearance [mm] | 0.070 |

Nominal pad thickness [mm] | 16 |

Angular amplitude of pads [°] | 60 |

Lubricant oil | ISO-VG46 |

Oil inlet temperature [°C] | 40 |

Pad mass [kg] | 0.540 |

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**MDPI and ACS Style**

Dang, P.V.; Chatterton, S.; Pennacchi, P.
Static Characteristics of a Tilting Five-Pad Journal Bearing with an Asymmetric Geometry. *Actuators* **2020**, *9*, 89.
https://doi.org/10.3390/act9030089

**AMA Style**

Dang PV, Chatterton S, Pennacchi P.
Static Characteristics of a Tilting Five-Pad Journal Bearing with an Asymmetric Geometry. *Actuators*. 2020; 9(3):89.
https://doi.org/10.3390/act9030089

**Chicago/Turabian Style**

Dang, Phuoc Vinh, Steven Chatterton, and Paolo Pennacchi.
2020. "Static Characteristics of a Tilting Five-Pad Journal Bearing with an Asymmetric Geometry" *Actuators* 9, no. 3: 89.
https://doi.org/10.3390/act9030089