Abstract
A theoretical analysis for static characteristics of a conical hydrostatic journal bearing for a multirecess constant flow valve compensated under micropolar lubrication has been carried out in this work. The numerical solution of the modified Reynolds equation for the conical bearing has been done using Finite Element Method (FEM) using necessary boundary conditions. The various static characteristics have been presented to analyze the performance of bearing at zero speed.
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Abbreviations
- \( a_{b} \) :
-
Axial bearing land width, m
- \( c \) :
-
Radial clearance, m
- \( D_{m} \) :
-
Mean journal diameter of conical shaft, m
- \( F \) :
-
Fluid film reaction, N
- \( F_{x} , F_{z} \) :
-
Fluid film reaction component, N
- \( h \) :
-
Fluid film thickness, m
- \( l, l_{ m} \) :
-
Bearing characteristic
- \( L \) :
-
Bearing length, m
- \( p_{s} \) :
-
Supply pressure, Pa
- \( Q \) :
-
Lubricant flow, m3/s
- \( R_{j} \) :
-
Journal radius, m
- \( r \) :
-
Radial coordinate
- \( X_{j} , X_{z} \) :
-
Journal center coordinate
- \( \gamma \) :
-
Semi cone angle
- \( \alpha \) :
-
Circumferential coordinate
- \( \beta \) :
-
Axial co-ordinate
- \( \mu \) :
-
Dynamic viscosity, Pa-s
- \( \lambda \) :
-
Aspect ratio (L/Dm)
- \( \theta \) :
-
Inter-recess angle
- \( \varphi \) :
-
Attitude angle, deg
- \( \varOmega \) :
-
Speed parameter
- \( \varepsilon \) :
-
Eccentricity ratio (e/c)
- \( \phi \) :
-
Micro polar function
- \( \bar{F}_{r} \) :
-
\( ({\text{F}}/p_{s} ) \)
- \( \bar{F}_{x} ,\bar{F}_{z} \) :
-
\( \left( {F_{x} ,F_{z} /p_{s } r_{j}^{2} } \right) \)
- \( \bar{h}_{\text{mim}} \) :
-
Minimum fluid film thickness
- \( \bar{p}_{ \hbox{max} } \) :
-
Maximum fluid film pressure
- \( N \) :
-
Coupling number
- \( N_{i} ,\,N_{j} \) :
-
Shape function
- \( \bar{P}_{j} \) :
-
\( ({\text{p/}}p_{s} )R_{j}^{2} \)
- \( \bar{Q} \) :
-
\( {\text{Q}}(\mu /c^{3} {\text{p}}_{\text{s}} ) \)
- \( \dot{\bar{X}}_{j} ,\dot{\bar{Z}}_{j} \) :
-
\( (X_{j} \times Y_{j) } /R_{j} \)
- \( \bar{Q}_{c} \) :
-
Constant flow valve restrictor design parameter
- \( \left[ {\bar{F}_{ij} } \right] \) :
-
Assembled fluidity matrix
- \( \left\{ {\bar{p}} \right\} \) :
-
Nodal pressure vector
- \( \left\{ {\bar{Q}} \right\}^{e} \) :
-
Nodal flow vector
- \( \{ \bar{R}_{{H_{j} }} \}^{e} \) :
-
Column vector due to hydrodynamic terms
- \( \left\{ {\bar{R}_{{x_{j} }} } \right\}^{e} , \{ \bar{R}_{{z_{j} }} \}^{e} \) :
-
Nodal vectors due to journal center velocities
References
T.J. Prabhu, N. Ganesan, Characteristics of conical hydrostatic bearings under rotation. Wear 73, 95–122 (1981)
K. Srinivasan, B.S. Prabhu, Steady state characteristics of conical hybrid bearings. Wear 89, 57–67 (1983)
W. Kalita, C.M. Rodkiewicz, J.S. Kennedy, On the laminar flow characteristics of conical bearings. Part 1—Analytical approach. J. Tribol. 108, 53–58 (1986)
M.F. Khalil, S.Z. Kassab, A.S. Ismail, Performance of externally pressurized conical thrust bearing under laminar and turbulent flow conditions. Wear 166, 147–154 (1993)
M.F. Khalil, S.Z. Kassab, A.S. Ismail, Effect of inertia forces on the performance of externally pressurized conical thrust bearing under turbulent flow conditions. Wear 166, 155–161 (1993)
P. Chandra, P. Sinha, S. Saxena, Effect of lubricant inertia in externally pressurized conical bearings with temperature dependent viscosity. Acta. Mech. 106, 157–171 (1994)
A.E. Yousif, S.M. Nacy, The lubrication of conical journal bearings with bi-phase (liquid–solid) lubricants. Wear 172, 23–28 (1994)
P. Sinha, P. Chandra, S.S. Bhartiya, Analysis of a non-constant gap externally pressurized conical bearing with temperature and pressure dependent viscosity. J. Eng. Tribol. (IMechE) 214, 699–710 (2000)
M.C. Jeng, Y.K. Yang, Comparison of thermal effects on the conical- cylindrical bearing with 2-D and 3-D energy equations. Tribol. Trans. 45, 67–75 (2002)
Y.K. Yang, M.C. Jeng, Thermo hydrodynamic analysis of the misaligned conical cylindrical bearing with non-Newtonian lubricants. Tribol. Trans. 46, 161–169 (2003)
G. Hong, L. Xinmin, C. Shaoqi, Theoretical and experimental study on dynamic coefficients and stability for a hydrostatic/hydrodynamic conical bearing. J. Tribol. 131, 041701–041707 (2009)
S. Verma, V. Kumar, K.D. Gupta, Analysis of multirecess hydrostatic journal bearing operating with micropolar lubricant. J. Tribol. 131(2), 021103 (2009)
S.C. Sharma, V.M. Phalle, S.C. Jain, Performance analysis of a multi-recess capillary compensated conical hydrostatic journal bearing. Tribol. Int. 44, 617–626 (2011)
S.C. Sharma, V.M. Phalle, S.C. Jain, Influence of wear on performance of a multi-recess conical hybrid journal bearing compensated with orifice restrictor. Tribol. Int. 44, 1754–1764 (2011)
S.C. Sharma, A.K. Rajput, Influence of micro polar lubrication on the performance of 4 pocket capillary compensated conical hybrid journal bearing. Adv. Tribol. 898252, 1–18 (2012)
A.K. Rajput, S.C. Sharma, Analysis of externally pressurized multirecess conical hybrid journal bearing system using micropolar lubricant. J. Eng. Tribol., IMechE 227(9), 943–968 (2013)
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Rana, N.K., Gautam, S.S. & Verma, S. Static Characteristics of Conical Hydrostatic Journal Bearing Under Micropolar Lubrication. J. Inst. Eng. India Ser. C 95, 375–381 (2014). https://doi.org/10.1007/s40032-014-0148-7
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DOI: https://doi.org/10.1007/s40032-014-0148-7