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A Variable Viscosity Technique for the Analysis of Static and Dynamic Performance Parameters of Three-Lobe Fluid Film Bearing Operating with TiO2-Based Nanolubricant

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Manufacturing Engineering

Part of the book series: Lecture Notes on Multidisciplinary Industrial Engineering ((LNMUINEN))

Abstract

Static and dynamic performance parameters of three-lobe fluid film bearing, operating with TiO2-based non-Newtonian lubricant, are obtained. The Krieger–Dougherty model of effective is used to obtain the viscosity of nanolubricant for a fixed concentration of nanoparticle dispersed in base lubricant. Reynolds equation is modified to incorporate couple stress effect, and then, finite difference method (FDM) is used to solve it to obtain different performance parameter. For varying concentration of nanoparticle in base lubricant, direct and cross-coupled dynamic coefficients (stiffness and damping) are obtained. Results show that flow coefficient and load carrying capacity increases, whereas friction variable decreases, but it does not disturb the stability of three-lobe fluid film bearing working with TiO2-based non-Newtonian lubricant. Dynamic coefficients and attitude angle do not vary with the concentration of solid nanoparticle for a fixed couple stress parameters.

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Abbreviations

C :

Radial clearance in meter

\(C_{m}\) :

Film thickness for a cantered shaft in meter

\(\begin{aligned} & C_{xx} ,C_{xz} , \\ & C_{zx} ,C_{zz} \\ \end{aligned}\) :

Damping coefficients in Ns/m

\(\begin{aligned} & \bar{C}_{xx} ,\bar{C}_{xz} , \\ & \bar{C}_{zx} ,\bar{C}_{zz} \\ \end{aligned}\) :

Damping coefficients in non-dimensional form \(\bar{C}_{xx} = C_{xx} \left( {\omega C/W} \right)\)

e :

Eccentricity in meter

\(\varepsilon\) :

Eccentricity ratio \(\varepsilon = e/C\)

\(e_{1} ,e_{2} ,e_{3}\) :

Eccentricity for each lobe in meter

h :

Oil-film thickness in meter

\(\bar{h}\) :

Film thickness non-dimensional form \(\bar{h} = h/C\)

\(\begin{aligned} & K_{xx} ,K_{xz} , \\ & K_{zx} ,K_{zz} \\ \end{aligned}\) :

Stiffness coefficients in N/m

\(\begin{aligned} & \bar{K}_{xx} ,\bar{K}_{xz} , \\ & \bar{K}_{zx} ,\bar{K}_{zz} \\ \end{aligned}\) :

Stiffness coefficients in non-dimensional form \(\bar{K}_{xx} = K_{xx} \left( {C/W} \right)\)

L :

Bearing length in m

\(D_{d}\) :

Depth of pressure dam in meter

\(\bar{D}_{d}\) :

Depth of non-dimensional pressure dam \(\bar{D}_{d} = D/C\)

\(D_{w}\) :

Width of pressure dam meter

\(\bar{D}_{w}\) :

Width of non-dimensional pressure dam \(\bar{D}_{w} = D_{w} /L\)

\(R_{d}\) :

Depth of relief track meter

\(\bar{R}_{d}\) :

Depth of non-dimensional relief track \(\bar{R}_{d} = R_{d} /C\)

\(R_{w}\) :

Width of relief track in meter

\(\bar{R}_{w}\) :

Depth of non-dimensional relief track \(\bar{R}_{w} = R_{w} /L\)

m :

Rotor mass per bearing in kg

\(\omega\) :

Journal angular velocity in rad/s

\(\bar{M}\) :

Mass parameter \(\bar{M} = mC\omega^{2} /W\)

N :

Journal speed in rps

D :

Journal diameter in meter

p :

Pressure \(\left( {p = W/LD} \right)\) in N/m2

\(\bar{p}\) :

Film pressure non-dimensional form \(\bar{p} = pC^{2} /6\mu UR\)

R :

Radius of bearing in meter

U :

Sliding speed in m/s

\(\bar{\mu }\) :

Effective viscosity

\(\psi\) :

Attitude angle in radian

\(\phi\) :

Volume fraction of solid additive

S :

Sommerfeld number \(S = \mu N/p\left( {R/C} \right)^{2}\)

\(\bar{f}\) :

Friction variable in non-dimensional form \(\bar{f} = f\left( {R/C} \right)\)

\(\mu_{nf}\) :

Nanolubricant viscosity

\(\mu_{bf}\) :

Base lubricant viscosity

W :

Load capacity in N

\(\bar{W}\) :

Load capacity in non-dimensional form \(\bar{W} = WC^{2} /6\mu UR^{2} L\)

\(\bar{p}_{1} ,\bar{p}_{2}\) :

Perturbed pressure

\(\delta\) :

Ellipticity ratio \(\delta = d/C\)

d :

Distance between lobe center and center of entire bearing geometry in meter

t :

Time (s)

\(\tau\) :

Time in non-dimensional form \(\tau = \omega_{p} t\)

\(\omega_{p}\) :

Whirling velocity in rad/s

\(\bar{\omega }_{j}\) :

Speed parameter

\(W_{x}\) :

Resultant load in vertical direction in N

\(W_{z}\) :

Resultant load in horizontal direction in N

\(\theta_{s}\) :

Groove starting angle

\(\theta_{e}\) :

Groove end angle

\(\theta_{r}\) :

Film cavitation angle

\(\bar{Q}\) :

Flow coefficient

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India

    Ashutosh Kumar & Sashindra Kumar Kakoty

Authors
  1. Ashutosh Kumar
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  2. Sashindra Kumar Kakoty
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Correspondence to Ashutosh Kumar .

Editor information

Editors and Affiliations

  1. Department of Industrial and Production Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

    Vishal S. Sharma

  2. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Uday S. Dixit

  3. Department of Industrial and Manufacturing Engineering, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Mexico

    Noe Alba-Baena

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Kumar, A., Kakoty, S.K. (2019). A Variable Viscosity Technique for the Analysis of Static and Dynamic Performance Parameters of Three-Lobe Fluid Film Bearing Operating with TiO2-Based Nanolubricant. In: Sharma, V., Dixit, U., Alba-Baena, N. (eds) Manufacturing Engineering. Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-6287-3_1

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  • DOI: https://doi.org/10.1007/978-981-13-6287-3_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-6286-6

  • Online ISBN: 978-981-13-6287-3

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