Performance of hydrostatic circular thrust pad bearing operating with Rabinowitsch fluid model

The entire load in human body is supported by the hip joint bearing. In the present work, elastohydrodynamic lubrication analysis of metal and metal hip implant is performed by using Newtonian lubricant. The Reynolds equation coupled with stress equilibrium equation has been used to get the pressure and performance characteristics of hip joint bearing. The governing Reynolds equation is nonlinear and cannot be solved by using close form solution methods. The finite element method and Newton‐Raphson method are used to obtain solution of the present equation. It has been observed that numerical convergence is much faster with NR method. From the results, it is observed that FEM with modified Newton‐Raphson method has the capability to compute accurate results for realistic modelling.

show abstract

“…A schematic diagram of hip bearing is shown in Figure . The governing Reynolds equation in the clearance space of MOM implant is written as

\frac{\partial}{\partial ϕ} ((), h^{3} \frac{\partial p}{\partial ϕ}) + sin θ \frac{\partial}{\partial θ} ((), h^{3} sin θ \frac{\partial p}{\partial θ}) = 6 η R_{1}^{2} italicsinθ \times true[- ω_{x} (sin φ sin θ \frac{\partial h}{\partial θ} + cos φ cos θ \frac{\partial h}{\partial θ}) + ω_{y} (cos ϕ sin θ \frac{\partial h}{\partial θ} - sin ϕ cos θ \frac{\partial h}{\partial ϕ}) + ω_{z} sin θ \frac{\partial h}{\partial ϕ}] + 12 η R_{1}^{2} {sin}^{2} θ \frac{\partial h}{\partial t},

where φ and θ are spherical coordinates and

{\overset{true¯}{ω}}_{x, y, z}

represent the angular velocities of x , y , and z direction of motions.…”

Section: Discussionmentioning

confidence: 99%

A finite element simulation of MOM (metal‐on‐metal) hip implant

Chaturvedi

Bharti

Yadav

et al. 2019

Lubrication Science

View full text Add to dashboard Cite

show abstract

“…The governing Reynolds equation in a non-dimensional form for the non-Newtonian lubricant in the clearance space of a two-lobe bearing in Figure 1(b) is written as follows 16,17,19–22 where the non-dimensional parameters are p¯=pps, h¯=hCr, u¯=RωPa(RC)2, α=xR, β=yR, τ=ωt.…”

Section: Discussionmentioning

confidence: 99%

Section: The Side Leakage Of the Flow Is Negligiblementioning

confidence: 99%

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

Yadav

Rajput

Ram

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part J:

Self Cite

View full text Add to dashboard Cite

In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non-linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincaré maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system.

show abstract

“…Singh, Gupta and Kapur [34][35][36] investigated the effects of non-Newtonian pseudoplastic lubricants on the various performances of squeeze film, hydrodynamic sliders bearings. Sharma and Yadav [37] presented the analysis of hydrostatic circular thrust pad bearing. In light of this discussion, it is observed that surface roughness and non-Newtonian lubricants are important considerations for analysis of hydrostatic thrust bearings, and none of the researchers has analysed the combined effects of surface roughness, inertia and non-Newtonian lubricants on hydrostatic thrust bearings using cubic stress fluid model: one of the experimentally verified fluid model.…”

Section: Introductionmentioning

confidence: 99%

Effect of Surface Roughness on Steady Performance of Hydrostatic Thrust Bearings: Rabinowitsch Fluid Model

Singh¹

2019

Preprint

View full text Add to dashboard Cite

Purpose of the present theoretical investigation is to analyze the effects of surface roughness on the steady-state performance of stepped circular hydrostatic thrust bearings lubricated with non-Newtonian Rabinowitsch type fluids. Results for film pressure and load-carrying capacity have been plotted and analyzed on the basis of numerical results. To take the effects of surface roughness into account, Christensen theory of rough surface has been adopted. The expression for pressure gradient has been derived by means of the energy integral approach. This approach avoids the derivation of Reynolds’ equation. The numerical results for film pressure and load capacity have been obtained using Mathematica. It was observed that in comparison with smooth surfaces, dimensionless film pressure and load capacity is lower for longitudinal roughness and higher for circular roughness patterns with and the variations are significant. Load carrying capacity decreases with the increase of longitudinal roughness and, increases with the increase of circular roughness. Further, the effects of surface roughness and non-Newtonian lubricants are significant for larger values of inertia parameter. Because of the closeness of results to the experimental values, this study will be helpful in the design of circular hydrostatic thrust bearings.

show abstract

Performance of hydrostatic circular thrust pad bearing operating with Rabinowitsch fluid model

Cited by 15 publications

References 43 publications

A finite element simulation of MOM (metal‐on‐metal) hip implant

A finite element simulation of MOM (metal‐on‐metal) hip implant

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

Effect of Surface Roughness on Steady Performance of Hydrostatic Thrust Bearings: Rabinowitsch Fluid Model

Contact Info

Product

Resources

About