3. Results and analysis

In the present study, the lubrication model of the multi-layer porous bearing under polar coordinate system was established. The combined effects of the roughness, surface Darcy flow and porous structure on the lubrication performance have been studied. The following data given as: <sup>w</sup><sup>i</sup> = 8 or 10%, Dc <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>4</sup> � <sup>5</sup> � <sup>10</sup>�<sup>4</sup> m, T<sup>i</sup> = 0.002 m, η = 0.02 Pa � s.

#### 3.1. Effect of surface Darcy flow on lubrication property

Figure 3 shows the effect of the surface Darcy flow on the hydrodynamic pressure. The pressure distributions with surface Darcy and without surface Darcy flow are shown in Figure 3(a) and (b), respectively. The effect of surface Darcy flow on pressure distribution under different speeds are shown in Figure 3(c) and (d). As can be seen from Figure 3, the

relationship between pore structure and fluid pressure drop is often represented by Kozeny– Carman equation. Supposing that the porous bearing material is composed of tiny spherical particles with an average diameter of Dc, the permeability of the bearing can be described as

In the present study, the lubrication model of the multi-layer porous bearing under polar coordinate system was established. The combined effects of the roughness, surface Darcy flow and porous structure on the lubrication performance have been studied. The following data

Figure 3 shows the effect of the surface Darcy flow on the hydrodynamic pressure. The pressure distributions with surface Darcy and without surface Darcy flow are shown in Figure 3(a) and (b), respectively. The effect of surface Darcy flow on pressure distribution under different speeds are shown in Figure 3(c) and (d). As can be seen from Figure 3, the

cwi 3

180 1 � <sup>w</sup><sup>i</sup> ð Þ<sup>2</sup> (6)

<sup>r</sup>¼<sup>a</sup> <sup>¼</sup> <sup>0</sup>; p<sup>θ</sup>¼<sup>0</sup> <sup>¼</sup> <sup>p</sup><sup>θ</sup>¼2<sup>π</sup> (7)

m, T<sup>i</sup> = 0.002 m, η = 0.02 Pa � s.

ki <sup>¼</sup> <sup>D</sup><sup>2</sup>

where w<sup>i</sup> is the porosity of surface and substrate layers of the porous bearing.

pj

The boundary condition shown as.

116 Lubrication - Tribology, Lubricants and Additives

Figure 2. Film thickness.

3. Results and analysis

where a is the outer radius of the disc bearing.

given as: <sup>w</sup><sup>i</sup> = 8 or 10%, Dc <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>4</sup> � <sup>5</sup> � <sup>10</sup>�<sup>4</sup>

3.1. Effect of surface Darcy flow on lubrication property

Figure 3. Effect of surface flow on pressure and its amplification in varied speeds. (a) Pressure with no surface flow (b) Pressure with surface flow (c) Pressure distribution (d) The pressure amplification.

pressure also presents a sine form, similarly to the film thickness distribution. The maximum pressure occurs at the center of the porous circle surface, and the minimum occurs at the outer circle. In addition, the oil film pressure increases with the increase of speed, and the pressure is higher if take the rough surface Darcy flow into consideration in every instantaneous speed. As shown in Figure 3(d), the pressure amplification increases with the increase of speed along the radius direction. And it is more obvious that the effect of the surface Darcy flow on the pressure amplification with the increase of speed. The maximum pressure amplifications in three speeds are 1.92 104 , 3.84 104 , 5.78 104 Pa, respectively.

Figure 4 illustrates the variation of the load capacity and friction coefficient with the speeds. It is observed that the surface Darcy flow has obvious significance to the lubrication property. The property turns better when considering the surface flow. And its effect becomes obvious with the increase of speed. For example, when the speed is 1500 r/min, the load capacity caused by surface Darcy flow increases by 11.64%. Moreover, the lubrication property of single

porosities of the bearing are constant. On the one hand, when the total porosities of the bearing are larger, lubricant between the contact surfaces is more likely to seepage into the porous matrix. So that the oil film lubrication performance is poor. On the other hand, when the total porosities of the bearing are constant, the lower surface porosity can prevent the oil leaking into the porous matrix. Therefore the oil will be kept in the contact surfaces and the lubrication

Lubrication and Friction of Porous Oil Bearing Materials http://dx.doi.org/10.5772/intechopen.72620 119

The Fe-C-Cu-based multi-layer bearing materials were prepared by powder metallurgy method. The wax-based lubricant as a densification agent was added into the surface layer to Increase the density. And an appropriate amount of TiH2 as a pore-forming agent was added into the bottom layer to increase the oil content properly. The porosities were measured by drainage method. And the porosity of the bottom layer was about 20%, the porosity of surface layer changed within 10–20%. Note that the multi-layer bearing becomes monolayer when the

The tribological properties of the porous samples were tested on a face-to-face contact tribometer under oil lubrication condition. The initial load is 50 N for 10 min as run-in period. And then the load will be added 50 N every 10 min. And the total test time is 30 min. When the experiment tested with sufficient oil supply, the oil bearing materials can work in hydrodynamic lubrication state under the proper speeds and loads. This lubrication state is consistent with the numerical simulation. When the load exceeds a certain limit, the friction coefficient rises sharply. The test machine has a slight noise and vibration, which shows that the oil film cracks. And scratches and adhesion maybe existed in the friction surface. The limit load of the

The results of the friction test are shown in Figure 6. As shown in Figure 6, the friction coefficients of the multi-layer samples are significantly lower than that of the single layer sample (when the surface porosity is 20%) under the fluid lubrication condition. When the surface porosity is 10%, the friction coefficient of the multilayer material is the smallest. And the friction coefficients gradually increased when the surface porosities changed from 10–20%. The multi-layer materials with dense surface layers have better lubrication property than the single layer materials. The reason is that the dense surface can prevent the oil flow into the

Figure 6. Friction coefficients of samples in variational load under fluid lubrication condition.

performance will be improved.

porosities of the two layers are equal.

oil film rupture is the load capacity of the oil film.

Figure 4. Effect of surface Darcy flow on the friction coefficient in different speeds. (a) Carrying capacity (b) Friction coefficient. Note: 1 denote monolayer material ignored Darcy flow; 2 denote multi-layer material ignored Darcy flow; 3 denote multi-layer material included Darcy flow.

and double layer oil bearings is improved with the increase of velocity. And the property of the multi-layer bearing is better than that of the single layer. In the single layer oil bearing, the oil driven by the hydrodynamic pressure penetrates into the porous medium easily, which weaken the oil thickness and the lubrication property. In the multi-layer oil bearing, the dense surface could prevent the fluid seepage into the porous bearing. Therefore, a thicker lubricant film can be formed between the friction pairs. And the multi-layer bearing with dense surface has better property than that of the single layer bearing.

#### 3.2. The experimental verification

Figure 5 shows the variation of the dimensionless load capacity and friction coefficient with the aperture for different porosities of the two layers. It is observed that negatively increasing values of the dimensionless load capacity increase the aperture of the two layers, whereas positively increasing values of the friction coefficient increase the aperture of the two layers. Thus raising the aperture of the two layers has a negative effect on the lubrication performance. Moreover, the lower surface porosity is beneficial to improve the lubrication performance when the total

Figure 5. Effect of pore structure on oil slick bear capacity and friction coefficient.

porosities of the bearing are constant. On the one hand, when the total porosities of the bearing are larger, lubricant between the contact surfaces is more likely to seepage into the porous matrix. So that the oil film lubrication performance is poor. On the other hand, when the total porosities of the bearing are constant, the lower surface porosity can prevent the oil leaking into the porous matrix. Therefore the oil will be kept in the contact surfaces and the lubrication performance will be improved.

The Fe-C-Cu-based multi-layer bearing materials were prepared by powder metallurgy method. The wax-based lubricant as a densification agent was added into the surface layer to Increase the density. And an appropriate amount of TiH2 as a pore-forming agent was added into the bottom layer to increase the oil content properly. The porosities were measured by drainage method. And the porosity of the bottom layer was about 20%, the porosity of surface layer changed within 10–20%. Note that the multi-layer bearing becomes monolayer when the porosities of the two layers are equal.

The tribological properties of the porous samples were tested on a face-to-face contact tribometer under oil lubrication condition. The initial load is 50 N for 10 min as run-in period. And then the load will be added 50 N every 10 min. And the total test time is 30 min. When the experiment tested with sufficient oil supply, the oil bearing materials can work in hydrodynamic lubrication state under the proper speeds and loads. This lubrication state is consistent with the numerical simulation. When the load exceeds a certain limit, the friction coefficient rises sharply. The test machine has a slight noise and vibration, which shows that the oil film cracks. And scratches and adhesion maybe existed in the friction surface. The limit load of the oil film rupture is the load capacity of the oil film.

and double layer oil bearings is improved with the increase of velocity. And the property of the multi-layer bearing is better than that of the single layer. In the single layer oil bearing, the oil driven by the hydrodynamic pressure penetrates into the porous medium easily, which weaken the oil thickness and the lubrication property. In the multi-layer oil bearing, the dense surface could prevent the fluid seepage into the porous bearing. Therefore, a thicker lubricant film can be formed between the friction pairs. And the multi-layer bearing with dense surface

Figure 4. Effect of surface Darcy flow on the friction coefficient in different speeds. (a) Carrying capacity (b) Friction coefficient. Note: 1 denote monolayer material ignored Darcy flow; 2 denote multi-layer material ignored Darcy flow; 3

Figure 5 shows the variation of the dimensionless load capacity and friction coefficient with the aperture for different porosities of the two layers. It is observed that negatively increasing values of the dimensionless load capacity increase the aperture of the two layers, whereas positively increasing values of the friction coefficient increase the aperture of the two layers. Thus raising the aperture of the two layers has a negative effect on the lubrication performance. Moreover, the lower surface porosity is beneficial to improve the lubrication performance when the total

has better property than that of the single layer bearing.

Figure 5. Effect of pore structure on oil slick bear capacity and friction coefficient.

3.2. The experimental verification

denote multi-layer material included Darcy flow.

118 Lubrication - Tribology, Lubricants and Additives

The results of the friction test are shown in Figure 6. As shown in Figure 6, the friction coefficients of the multi-layer samples are significantly lower than that of the single layer sample (when the surface porosity is 20%) under the fluid lubrication condition. When the surface porosity is 10%, the friction coefficient of the multilayer material is the smallest. And the friction coefficients gradually increased when the surface porosities changed from 10–20%. The multi-layer materials with dense surface layers have better lubrication property than the single layer materials. The reason is that the dense surface can prevent the oil flow into the

Figure 6. Friction coefficients of samples in variational load under fluid lubrication condition.

porous material, which could ensure a thicker oil film. When the surface layer has a higher porosity, the lubricant is not easy to exist between the friction pairs. So the lubricant is not sufficient. And the lubrication property is poor. In summary, when design the composite sintered material under the condition of fluid lubrication, the low surface porosity can effectively improve the material lubricating property. These experimental results are consistent with the results of the numerical simulation.

[2] Zhang GT, Yin YG, Xue L, Zhu GQ, Tian M. Effects of surface roughness and porous structure on the hydrodynamic lubrication of multi-layer oil bearing. Industrial Lubrica-

Lubrication and Friction of Porous Oil Bearing Materials http://dx.doi.org/10.5772/intechopen.72620 121

[3] Carmeron A, Morgan VT. Critical conditions for hydrodynamic lubrication of porous metal bearings. Proceedings of the Institution of Mechanical Engineers. 1962;176:761-770

[4] Zhang G, Yin Y, Liu Z, et al. Lubrication property of multi-layer sintering material under hydrodynamic lubrication. Acta Materiae Compositae Sinica. 2016;33:2807-2814

[5] Lin JR, Hwang CC. Lubrication of short porous journal bearings — Use of the Brinkman-

[6] Rao PS, Agarwal S. Effect of surface roughness on the hydrodynamic lubrication of porous inclined slider bearing considering slip velocity and squeeze velocity with couple stress fluids. International Journal of Engineering Science and Technology. 2014;6:45-64

[7] Chritensen H. Stochastic models for hydrodynamic lubrication of rough surfaces. The

[8] Prakash J, Tiwari K. Lubrication of a porous bearing with surface corrugations. Journal of

[9] Andharia PI, Gupta GL, Deheri GM. Effect of surface roughness on hydrodynamic

[10] Meurisse MH, Morales G. Reynolds equation, apparent slip, and viscous friction in a

[11] Usha R, Naire SA. Thin film on a porous substrate: A two-sided model, dynamics and

[12] Naduvinamani NB, Patil SB. Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings. Computers and Struc-

[13] Rao TVVLN, Rani AMA, Nagarajan T, Hashim FM. Analysis of journal bearing with double-layer porous lubricant film: Influence of surface porous layer configuration. Tri-

Proceedings of the Institution of Mechanical Engineers. 1969;185:1013-1026

lubrication of slider bearings. Tribology Transactions. 2001;44:291-297

three-layered fluid film, engineering. Tribology. 2001;222:369-380

stability. Chemical Engineering Science. 2013;89:72-88

tion and Tribology. 2017;69:455-463

extended Darcy model. Wear. 1993;161:93-104

Lubrication Technology. 1982;104:127-134

tures. 2009;87:1287-1295

bology Transactions. 2013;56:841-847
