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Squeeze Film Bearing Characteristics for Synovial Joint Applications

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Biomaterials in Orthopaedics and Bone Regeneration

Part of the book series: Materials Horizons: From Nature to Nanomaterials ((MHFNN))

Abstract

Squeeze film lubrication in surfaces approaching each other with a normal velocity plays an important role in synovial joints. The objective of this study is to analyze the squeeze film load capacity characteristics of layered parallel plate and partial journal bearing lubricated by couple stress fluids employing one-dimensional analysis. The non-dimensional squeeze film pressure is derived solving one-dimensional modified Reynolds equation using squeeze film boundary conditions. The couple stress fluids are examined on the basis of Stokes micro-continuum theory which takes into account of lubricant properties with additives. Fluid flow in the porous region is analyzed using the Brinkman model. Parallel plate and partial journal bearing lubricated with couple stress fluids are evaluated for porous surface double adsorbent layer, porous–surface adsorbent layer, and surface–surface adsorbent layer. The non-dimensional squeeze film load capacity increases with (i) decline in porous layer permeability, (ii) surface to core layer dynamic viscosity ratio enhancement, and (iii) increase in couple stress effects. The porous–surface adsorbent layers with couple stress fluid film core layer improve the squeeze film bearing characteristics for synovial joint applications.

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Abbreviations

B :

Width of parallel plate, m

C :

Partial journal bearing radial clearance, m

h, H:

Film thickness, m; \( H = h/h_{o} \) for parallel plate; \( H = h/C \) for partial journal bearing

h o :

Reference film thickness, m

k1, K1:

Permeability of porous layer in region I, m2; \( K_{1} = k_{1} /h_{0}^{2} \) for parallel plate; \( K_{1} = k_{1} /C^{2} \) for partial journal bearing

L :

Length of parallel plate; length of partial journal bearing, m

p :

Pressure distribution, N/m2; \( P = ph_{0}^{3} /\mu L^{2} \left( { - \text{d}h/\text{d}t} \right) \) for parallel plate, \( P = pC^{2} /\mu R^{2} \left( {\text{d}\varepsilon /\text{d}t} \right) \) for partial journal bearing

q, Q:

Flow rate (volume) per unit length, m2/s; \( Q = q/L\left( { - \text{d}h/\text{d}t} \right) \) for parallel plate; \( Q = q/RC\left( {\text{d}\varepsilon /\text{d}t} \right) \) for partial journal bearing

R :

Journal radius, m

ui, Ui:

Fluid velocity in surface (or porous) layer region I, couple stress fluid film region II, surface layer region III, respectively, m/s; \( U_{i} = u_{i} /\left[ {\left( {L/h_{o} } \right)\left( { - \text{d}h/\text{d}t} \right)} \right] \) along x direction in parallel plate; \( U_{i} = u_{i} /\left[ {R\left( {\text{d}\varepsilon /\text{d}t} \right)} \right] \) along θ direction in partial journal bearing, i  = 1, 2, 3

uj, Uj:

Fluid velocity at the interface of surface (or porous) layer region I and couple stress fluid film region II, couple stress fluid film region II and surface layer region III, respectively, m/s; \( U_{j} = u_{j} /\left[ {\left( {L/h_{o} } \right)\left( { - \text{d}h/\text{d}t} \right)} \right] \) along x direction in parallel plate; \( U_{j} = u_{j} /\left[ {R\left( {\text{d}\varepsilon /\text{d}t} \right)} \right] \) along θ direction in partial journal bearing, j = 12, 23

w, W:

Static load, N; \( W = wh_{0}^{3} /\mu L^{3} B\left( { - \text{d}h/\text{d}t} \right) \) for parallel plate; \( W = wC^{2} /\mu R^{3} L\left( {\text{d}\varepsilon /\text{d}t} \right) \) for partial journal bearing

x, X:

X direction coordinate, m; \( X = x/L \) for parallel plate; \( \theta = x/R \) for partial journal bearing

y, Y:

Y direction coordinate, m; \( Y = y/h_{o} \) for parallel plate; \( Y = y/C \) for partial journal bearing

δi, Δi:

Thickness of surface (or porous) layer region I, couple stress fluid film region II, surface layer region III, respectively, m; \( {\Delta }_{i} = \delta_{i} /h_{o} \) for parallel plate, \( {\Delta }_{i} = \delta_{i} /C \) for partial journal bearing; i  = 1, 2, 3

ε :

Partial journal bearing eccentricity ratio

µ :

Core layer (base fluid) viscosity, Ns/m2 ; \( \mu = \mu_{2} \)

µ i :

Dynamic viscosity of surface (or porous) layer region I, couple stress fluid film region II, surface layer region III, respectively, Ns/m2; i  = 1, 2 ,3

β i :

Dynamic viscosity ratio of surface (or porous) layer region I to core layer, dynamic viscosity ratio of surface layer region III to core layer, respectively; \( \beta_{i} = \mu_{i} /\mu \); i = 1, 3

η :

Couple stress material constant, kgm/s

λ :

Couple stress parameter; \( \lambda = \left( {\sqrt {\eta /\mu } } \right)/h_{o} \) for parallel plate, \( \lambda = \left( {\sqrt {\eta /\mu } } \right)/C \) for partial journal bearing

θ :

Angle measured from the center position in partial journal bearing

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Authors and Affiliations

  1. Department of Mechanical Engineering, SRM Institute of Science and Technology, Kattankulathur, 603203, India

    T. V. V. L. N. Rao

  2. Department of Mechanical Engineering, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Malaysia

    Ahmad Majdi Abdul Rani

  3. Centre for Biomaterials, Cellular and Molecular Theranostics (CBCMT), Vellore Institute of Technology, Vellore, India

    Geetha Manivasagam

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  1. T. V. V. L. N. Rao
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  2. Ahmad Majdi Abdul Rani
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  3. Geetha Manivasagam
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Corresponding author

Correspondence to T. V. V. L. N. Rao .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Beant College of Engineering and Technology, Gurdaspur, Punjab, India

    Preetkanwal Singh Bains

  2. Department of Mechanical Engineering, Beant College of Engineering and Technology, Gurdaspur, Punjab, India

    Sarabjeet Singh Sidhu

  3. Department of Tissue Engineering and Applied Cell Sciences, School of Medicine, Nervous System Stem Cells Research Center, Semnan University of Medical Sciences, Semnan, Iran

    Marjan Bahraminasab

  4. School of Mechanical Engineering, Lovely Professional University, Jalandhar, Punjab, India

    Chander Prakash

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Rao, T.V.V.L.N., Rani, A.M.A., Manivasagam, G. (2019). Squeeze Film Bearing Characteristics for Synovial Joint Applications. In: Bains, P., Sidhu, S., Bahraminasab, M., Prakash, C. (eds) Biomaterials in Orthopaedics and Bone Regeneration . Materials Horizons: From Nature to Nanomaterials. Springer, Singapore. https://doi.org/10.1007/978-981-13-9977-0_5

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