Thermohydrodynamic (THD) Analysis of Journal Bearing Operating with Bio-based Nanolubricants


The objective of current research is to study the adiabatic solutions of a plain journal bearing operating with bio-based lubricants containing nanoparticles. Estimation of pressure and temperature fields has been accomplished by simultaneous numerical solutions of the modified Reynolds equation and the adiabatic energy equation. These equations have been solved by adopting the finite difference method with suitable iterative scheme. The analysis has been carried out taking into account the heating effects and non-Newtonian rheology of bio-based nanolubricant following the power law model. The results have been investigated for temperature and pressure fields and the static performance parameters for a broad range of eccentricity ratio ε and different power law index values. The calculated results present that the involvement of nanoparticles in bio-based lubricant significantly enhances the pressure, load carrying capacity and friction force. Moreover, the influence of thermal effects on performance parameters is seen to be maximum at higher values of power law index.

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\(U\) :

Tangential velocity of the journal, m s−1

\(\omega\) :

Angular velocity of the journal (\(\omega\) = U/R), rad s−1

\(N\) :

Rotational speed, rpm

h :

Film thickness, m

e :

Eccentricity, m

\(O_{\text{b}}\) :

Bearing centre

\(O_{\text{J}}\) :

Journal centre

\(h_{\min }\) :

Minimum fluid film thickness, m

\(\mu\) :

Apparent viscosity, Pa s

\(\mu_{0}\) :

Reference viscosity of the lubricant, Pa s

\(\mu_{\text{nf}}\) :

Viscosity of nanolubricant, Pa s

x, y, z :

Bearing coordinates, x measures along circumferential direction, y measures along the radial direction, z measures along the axial direction, m

\(\theta\) :

Angular coordinate, rad

R :

Journal radius, m

D :

Journal diameter, m

L :

Bearing length, m

c :

Radial clearance, m

\(\theta_{\text{c}}\) :

Cavitation angle, rad

\(\varphi\) :

Nanoparticle volume fraction, %

\(\varphi_{\text{m}}\) :

Maximum particle packing fraction, %


Intrinsic viscosity

n :

Power law index

\(\varepsilon\) :

Eccentricity ratio

\(\rho\) :

Density of oil, kg m−3

\(\rho_{\text{p}}\) :

Density of nanoparticles, kg m−3

\(\rho_{0}\) :

Density of base oil, kg m−3

\(\rho_{\text{nf}}\) :

Density of nanolubricant, kg m−3

\(C_{\text{pp}} ,C_{{{\text{p}}0}} , C_{\text{pnf}}\) :

Specific heat of nanoparticles, base oil and nanolubricant, (J Kg−1 °C)

\(\beta\) :

Thermoviscosity coefficient, C−1

\(u,v\) :

Oil velocity components in x and y directions, m s−1

\(q_{x} ,q_{y}\) :

Discharge in x and y directions, m3 s−1

\(\phi\) :

Attitude angle, degree

\(p\) :

Lubricant film pressure, N m−2

\(\lambda\) :

Aspect ratio

\(W\) :

Load carrying capacity, N

\(Q_{\text{S}}\) :

Total lubricant side leakage, m3 s−1

\(W_{\theta}\) :

Tangential component of load carrying capacity, N

\(W_{\text{r}}\) :

Radial component of load carrying capacity, N

\(C_{\text{f}}\) :

Coefficient of friction

\(f\) :

Friction force, N

\(\dot{\gamma }\) :

Shear strain rate, s−1

\(D_{e}\) :

Dissipation number


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Correspondence to H. C. Garg.

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Non-dimensional Parameters

$$ \theta = \frac{x}{R} $$
$$ \bar{p} = p\frac{{c^{2}}}{{\mu_{0} \omega R^{2} }}$$
$$\bar{W}_{\theta } = W_{\theta} \frac{{c^{2} }}{{\mu_{0} \omega R^{3} L}}$$
$$\bar{W}_{r} = W_{r} \frac{{c^{2} }}{{\mu_{0} \omega R^{3} L}} $$
$$\bar{W} = W \frac{{c^{2} }}{{\mu_{0} \omega R^{3} L}} $$
$$ \bar{y} = \frac{y}{L}$$
$$ \lambda = \frac{L}{D} $$
$$ \bar{C}_{f} =C_{f} \frac{{ R}}{c} $$
$$ \bar{\mu } = \frac{\mu }{{\mu_{0} }}$$
$$ \bar{z} = \frac{z}{h} $$
$$ \varepsilon = \frac{e}{c} $$
$$ \bar{h} = \frac{h}{c}$$
$$\bar{Q}_{s} = Q_{s} \frac{L}{{\omega R^{3} c}} $$
$$ \bar{f} = f\frac{c}{{\mu_{0} \omega R^{2} L}} $$
$$ \bar{m} = \left[ {1 - \frac{\varphi }{{\varphi_{m} }}} \right]^{{ - \left[ \eta \right]\varphi_{m} }} \left( {\frac{U}{c}} \right)^{n - 1}$$
$$ \bar{c} = \frac{c}{R} $$
$$\bar{T} = \beta \left( {T - T_{0} } \right) $$
$$ \bar{q}_{x} = q_{x}\frac{{1 }}{Uc} $$
$$ \bar{q}_{y} = q_{y}\frac{{2\lambda }}{Uc}$$

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Dhanola, A., Garg, H.C. Thermohydrodynamic (THD) Analysis of Journal Bearing Operating with Bio-based Nanolubricants. Arab J Sci Eng (2020).

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  • Journal bearing
  • Thermohydrodynamic
  • Non-Newtonian lubricant
  • Bio-based nanolubricant
  • Performance characteristics