*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

**Figure 10.** *Pressure evolution for different radial load N = 11,000 rpm.*

#### **Figure 11.**

*Evolution of the fluid flow velocity according the angular position for different radial load N = 11,000 rpm (Re = 3622.64 turbulent regime).*

per cent for textured bearing and estimated at 29 per cent for non-textured bearing (**Figure 12**).

The friction torque along the circumference of the textured bearing is illustrated

*Friction torque in the median plane for different radial load N = 11,000 rpm (Re = 3622.64 turbulent regime).*

**Figure 14** shows the pressure distribution along the bearing circumference, for four shaft rotation speeds (11,000 rpm, 14,000 rpm 17,000 rpm and 21,000 rpm).

Pa = 0.08 MPa. The radial load is 10,000 N. This rotational speed gives respectively

in **Figure 13**. The important values are noted for a radial load of 9000 N, the maximum value of the friction torque is of the order of 17.93 N.m for a textured bearing, and is the order of 10.83 N.m for non-textured bearing. These maximum values are noted in the angular positions at 180° and 195°. The increase in the radial load from 2000 N to 9000 N leads to an increase in the friction torque of 21 per cent

and 29 per cent respectively for a textured and non-textured bearing.

The supply conditions used for this numerical analysis are Ta = 40°C and

**7.3 Effect of the shaft rotation speed**

*Velocity evolution for different radial load N = 11,000 rpm.*

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured…*

*DOI: http://dx.doi.org/10.5772/intechopen.94235*

*7.3.1 Pressure*

**35**

**Figure 12.**

**Figure 13.**

#### *7.2.3 Friction torque*

The fluid friction torque or "viscous" friction is a particular friction force, which is associated with the movement of an object in a fluid (air, water, etc.). It is at the origin of energy losses by friction for the object moving in the fluid. The friction torque is calculated by integrating the shear stresses at the surface of the shaft or of the bushing, the shear stresses in the fluid are given by derivation the fluid velocity in the radial and tangential direction. Therefore, there is an empirical relationship between the flow velocity of the fluid and the friction torque, for this we obtain the same distribution for the fluid flow velocity and the friction torque along the median plane of the hydrodynamic bearing.

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured… DOI: http://dx.doi.org/10.5772/intechopen.94235*

**Figure 12.** *Velocity evolution for different radial load N = 11,000 rpm.*

#### **Figure 13.**

per cent for textured bearing and estimated at 29 per cent for non-textured bearing

*Evolution of the fluid flow velocity according the angular position for different radial load N = 11,000 rpm*

The fluid friction torque or "viscous" friction is a particular friction force, which is associated with the movement of an object in a fluid (air, water, etc.). It is at the origin of energy losses by friction for the object moving in the fluid. The friction torque is calculated by integrating the shear stresses at the surface of the shaft or of the bushing, the shear stresses in the fluid are given by derivation the fluid velocity in the radial and tangential direction. Therefore, there is an empirical relationship between the flow velocity of the fluid and the friction torque, for this we obtain the same distribution for the fluid flow velocity and the friction torque along the

(**Figure 12**).

**34**

**Figure 11.**

**Figure 10.**

*Pressure evolution for different radial load N = 11,000 rpm.*

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

*7.2.3 Friction torque*

*(Re = 3622.64 turbulent regime).*

median plane of the hydrodynamic bearing.

*Friction torque in the median plane for different radial load N = 11,000 rpm (Re = 3622.64 turbulent regime).*

The friction torque along the circumference of the textured bearing is illustrated in **Figure 13**. The important values are noted for a radial load of 9000 N, the maximum value of the friction torque is of the order of 17.93 N.m for a textured bearing, and is the order of 10.83 N.m for non-textured bearing. These maximum values are noted in the angular positions at 180° and 195°. The increase in the radial load from 2000 N to 9000 N leads to an increase in the friction torque of 21 per cent and 29 per cent respectively for a textured and non-textured bearing.

#### **7.3 Effect of the shaft rotation speed**

#### *7.3.1 Pressure*

**Figure 14** shows the pressure distribution along the bearing circumference, for four shaft rotation speeds (11,000 rpm, 14,000 rpm 17,000 rpm and 21,000 rpm). The supply conditions used for this numerical analysis are Ta = 40°C and Pa = 0.08 MPa. The radial load is 10,000 N. This rotational speed gives respectively

**Figure 14.**

#### **Figure 15.**

*Circumferential pressure according the angular coordinate of the non- textured and textured bearing W = 10 KN, N = 14,000 rpm (Re = 5187.6 turbulent regime).*

a Reynolds number of Re = 3622.64, Re = 4687.53, Re = 5187.6 and Re = 6752.54, which indicates that the regime is turbulent.

The curve clearly shows that the maximum pressure is positioned at angular coordinates from 140° to 160°, while at angular positions between 170° and 200°, the pressure is lower than the supply pressure, which indicates the existence of the rupture zone of the oil film. It can also be said that increasing the rotational speed causes a slight decrease in pressure, this decrease being estimated at 24 per cent. The significant pressure is recorded for a very high rotation speed, which is of the order of 21,000 rpm.

21,000 rpm (Re = 6752.54), on the other hand it is less important for a rotational speed of 11,000 rpm (Re = 3622.64). The significant value of the fluid flow velocity is noted for a textured plain bearing which is the order of 89.56 m/s. On the other hand, for a non-textured plain bearing, the maximum value of the fluid flow

*Fluid flow velocity evolution according angular position angular for different rotational speed W = 10 KN*

For the different of the fluid flow velocity (**Figure 18**), has the same variation for the case of plain bearing without texture and a textured plain bearing. This speed takes a maximum value at the angular coordinate of 200° of the bearing. The difference between the fluid flow velocity for a non-textured and textured plain

For the evolution of the friction torque as a function of the angular coordinates of the non-textured and textured plain bearing by varying the rotational speed of

velocity is only of the order of 56.37 m/s.

*7.3.3 Friction torque*

**37**

**Figure 16.**

**Figure 17.**

*(turbulent regime).*

bearing is of the order of 38 per cent (**Figure 19**).

*Distribution circumferential of the pressure for differents rotational velocity.*

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured…*

*DOI: http://dx.doi.org/10.5772/intechopen.94235*

**Figure 15** shows the pressure distribution as a function of the angular position for a textured and non-textured bearing for a radial load of 10,000 N and a rotation speed of 14,000 rpm. The curve clearly shows that the pressure distribution along the median plane of the bearing is different in the case of a non-textured bearing and a bearing with a textured surface; the difference is estimated at 8.5 per cent (**Figure 16**).

#### *7.3.2 Fluid flow velocity*

**Figure 17** illustrates the variation of flow velocity in the circumferential direction of the plain bearing, to a feed temperature of 40°C and feed pressure of 0.08 MPa. The shaft rotational speed varies from 11,000 rpm to 21,000 rpm (Turbulent regime) and a radial load of 10,000 N. The curve shows that the rotational speed leads to an increase in the fluid flow velocity. The increase reached 39 per cent. The flow velocity is significant for a bearing which rotates at a speed of

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured… DOI: http://dx.doi.org/10.5772/intechopen.94235*

**Figure 16.** *Distribution circumferential of the pressure for differents rotational velocity.*

#### **Figure 17.**

a Reynolds number of Re = 3622.64, Re = 4687.53, Re = 5187.6 and Re = 6752.54,

*Circumferential pressure according the angular coordinate of the non- textured and textured bearing W = 10*

*Circumferential pressure for different rotational velocity W = 10 KN (turbulent regime).*

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

dinates from 140° to 160°, while at angular positions between 170° and 200°, the pressure is lower than the supply pressure, which indicates the existence of the rupture zone of the oil film. It can also be said that increasing the rotational speed causes a slight decrease in pressure, this decrease being estimated at 24 per cent. The significant pressure is recorded for a very high rotation speed, which is of the order of 21,000 rpm. **Figure 15** shows the pressure distribution as a function of the angular position for a textured and non-textured bearing for a radial load of 10,000 N and a rotation speed of 14,000 rpm. The curve clearly shows that the pressure distribution along the median plane of the bearing is different in the case of a non-textured bearing and a bearing with

a textured surface; the difference is estimated at 8.5 per cent (**Figure 16**).

The curve clearly shows that the maximum pressure is positioned at angular coor-

**Figure 17** illustrates the variation of flow velocity in the circumferential direc-

tion of the plain bearing, to a feed temperature of 40°C and feed pressure of 0.08 MPa. The shaft rotational speed varies from 11,000 rpm to 21,000 rpm (Turbulent regime) and a radial load of 10,000 N. The curve shows that the rotational speed leads to an increase in the fluid flow velocity. The increase reached 39 per cent. The flow velocity is significant for a bearing which rotates at a speed of

which indicates that the regime is turbulent.

*KN, N = 14,000 rpm (Re = 5187.6 turbulent regime).*

*7.3.2 Fluid flow velocity*

**36**

**Figure 14.**

**Figure 15.**

*Fluid flow velocity evolution according angular position angular for different rotational speed W = 10 KN (turbulent regime).*

21,000 rpm (Re = 6752.54), on the other hand it is less important for a rotational speed of 11,000 rpm (Re = 3622.64). The significant value of the fluid flow velocity is noted for a textured plain bearing which is the order of 89.56 m/s. On the other hand, for a non-textured plain bearing, the maximum value of the fluid flow velocity is only of the order of 56.37 m/s.

For the different of the fluid flow velocity (**Figure 18**), has the same variation for the case of plain bearing without texture and a textured plain bearing. This speed takes a maximum value at the angular coordinate of 200° of the bearing. The difference between the fluid flow velocity for a non-textured and textured plain bearing is of the order of 38 per cent (**Figure 19**).

#### *7.3.3 Friction torque*

For the evolution of the friction torque as a function of the angular coordinates of the non-textured and textured plain bearing by varying the rotational speed of

**Figure 18.**

*Fluid flow velocity according angular position of the non-textured and textured bearing W = 10 KN, N = 14,000 rpm (Re = 5187.6 turbulent regime).*

the shaft from 11,000 to 21,000 rpm and for a radial load of 10,000 N, is presented in **Figure 20**. The increasing the rotational speed causes a slight increase in the friction torque, this increase is of the order of 2 per cent. The important values are obtained for a rotational speed of 21,000 rpm; the maximum value of the friction torque is also positioned at the angular coordinate of 200°. The significant value of the friction torque for a non-textured plain bearing is of the order of 16 N.m, on the

*Friction torque in the median plane of the non-textured and textured bearing W = 10 KN, N = 14,000 tr/min*

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured…*

*DOI: http://dx.doi.org/10.5772/intechopen.94235*

**Figure 21** illustrates the variation of friction torque along the circumferential non-textured and textured plain bearing. The evolution of the friction torque along the angular bearing position has the same shape for the two cases studied, the

This numerical study presents the evolution of the fluid flow for turbulent regime in hydrodynamic plain bearings with a non-textured and textured surface, in order to improve the hydrodynamic lubrication and tribological performance of plain bearing, using the finite volume method, such as pressure, friction torque and

The results obtained for the textured plain bearing were compared to the non-

1.The pressure distribution according to the angular position for the textured and non-textured plain bearing for the radial load of 10,000 N and the speed of rotation of 14,000 rpm has the same appearance for the two cases studied;

2.The rupture zones of the oil film are observed in several angular positions at 190° and 300° for a plain bearing with textured surface, on the other hand for a plain bearing without texture, the rupture zone is positioned only in the angular position at 190°. This rupture of the oil film is due to the drop in

3.The evolution of the friction torque, along the angular position, has the same distribution for the non-textured and the textured plain bearing, the

textured plain bearing, the main conclusions drawn from this study are:

other hand for a textured plain bearing is 26 N.m.

the difference is estimated at 8.5%.

pressure below the supply pressure.

difference is estimated at 38%.

**8. Conclusions**

**Figure 21.**

*(Re = 5187.6 turbulent regime).*

fluid flow velocity.

**39**

difference is estimated at 38 per cent at the 200° level.

**Figure 19.**

*Distribution circumferential of the fluid flow velocity for differents rotational velocity.*

**Figure 20.** *Friction torque in median plane for different rotational speed W = 10 KN (turbulent regime).*

*Turbulent Flow Fluid in the Hydrodynamic Plain Bearing to a Non-Textured… DOI: http://dx.doi.org/10.5772/intechopen.94235*

#### **Figure 21.**

**Figure 18.**

**Figure 19.**

**Figure 20.**

**38**

*N = 14,000 rpm (Re = 5187.6 turbulent regime).*

*Fluid flow velocity according angular position of the non-textured and textured bearing W = 10 KN,*

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

*Distribution circumferential of the fluid flow velocity for differents rotational velocity.*

*Friction torque in median plane for different rotational speed W = 10 KN (turbulent regime).*

*Friction torque in the median plane of the non-textured and textured bearing W = 10 KN, N = 14,000 tr/min (Re = 5187.6 turbulent regime).*

the shaft from 11,000 to 21,000 rpm and for a radial load of 10,000 N, is presented in **Figure 20**. The increasing the rotational speed causes a slight increase in the friction torque, this increase is of the order of 2 per cent. The important values are obtained for a rotational speed of 21,000 rpm; the maximum value of the friction torque is also positioned at the angular coordinate of 200°. The significant value of the friction torque for a non-textured plain bearing is of the order of 16 N.m, on the other hand for a textured plain bearing is 26 N.m.

**Figure 21** illustrates the variation of friction torque along the circumferential non-textured and textured plain bearing. The evolution of the friction torque along the angular bearing position has the same shape for the two cases studied, the difference is estimated at 38 per cent at the 200° level.
