Jaw-Ren Lin

Derivation of dynamic couple-stress Reynold's equation of sliding-squeezing surfaces and numerical solution of plane inclined slider bearings

Abstract Deriving a general dynamic Reynold’s equation of sliding-squeezing surfaces with non-Newtonian fluids is necessary for the assessment of dynamic characteristics of a lubricating system. Taking into account the transient squeezing-action effect and considering the effects of couple stresses resulting from the lubricant blended with various additives, the non-Newtonian dynamic Reynold’s equation applicable to the general film shape is derived by using the Stokes micro-continuum theory. As an application, the numerical analysis of a two-dimensional plane inclined slider bearing is illustrated. Based upon the small perturbation technique, two Reynold’s-type equations responsible for both the steady performance and the perturbed characteristics are obtained. The steady and perturbed pressures are then numerically calculated by using the conjugate gradient method. From the results obtained, the effects of couple stresses provide an improvment on both the steady-state performance and the dynamic stiffness and damping characteristics especially for the bearing with a higher value of aspect ratio.

Linear stability analysis of long journal bearings: couple stress fluid model

Purpose – The purpose of the present study is to provide the dynamic characteristics of long journal bearings lubricated with couple stress fluids.Design/methodology/approach – Based upon the micro‐continuum theory generated by Stokes, the dynamic Reynolds‐type equation governing the film pressure is derived to account for the couple stress effects resulting from the non‐Newtonian behavior of complex fluids. By applying the linear stability theory to the non‐linear equations of motion the journal rotor, the equilibrium positions and dynamic characteristics of the system are evaluated.Findings – As compared to the classical Newtonian model, the effects of couple stresses signify enhanced stiffness and damping coefficients (including KXX, KXY , BXX and BXY) at moderate values of the steady eccentricity ratio. Totally, as the rotor center operates at an eccentricity ratio about es≤0.71, long bearings lubricated with couple stress fluids under small disturbance results in a higher stability threshold speed th...

Effects of couple stresses and convective inertia forces in parallel circular squeeze‐film plates

A theoretical study of the combined effects of non‐Newtonian couple stresses and fluid inertia forces on the squeeze‐film behaviors for parallel circular plates is presented in this paper. Based upon the micro‐continuum theory, the Stokes constitutive equations are used to account for the couple stress effects resulting from the lubricant blended with various additives. The convective inertia forces included in the momentum equation are approximated by the mean value averaged across the fluid film thickness. Numerical solutions for the squeezing film characteristics are presented for various values of couple stress parameter and Reynolds number. Comparing with the classical Newtonian non‐inertia flow, the combined effects of couple stresses and convective inertia forces result in a larger load‐carrying capacity and therefore, increase the response time of the squeezing film plates.

Effects of Non-Newtonian Rheology on Curved Circular Squeeze Films: the Rabinowitsch Fluid Model

On the ground of the non-Newtonian Rabinowitsch fluid model, the study of Newtonian squeeze film problems of curved circular plates [P. R. K. Murti, Trans. ASME 97, 650 (1975)] is extended in this paper. According to the results, higher load capacities and longer approaching times are obtained for the curved plates lubricated with dilatant fluids, but the pseudoplastic lubricants result in reversed trends. The influences of non-Newtonian dilatant and pseudoplastic properties on the squeeze film characteristics are further emphasized for curved circular plates operating under a smaller minimum film height and a larger curved shape parameter. Numerical results of the non-Newtonian load capacity are also provided for specific values of the curved shape parameter, the nonlinear parameter, and the minimum film height.

Effects of fluid inertia forces in ferrofluid lubricated circular stepped squeeze films – Shliomis model

Purpose This paper aims to study the inertia squeeze film characteristics between ferrofluid-lubricated circular stepped disks. Owing to the development of modern machine systems, the application of ferrofluids has received great attention. Because the circular disks are a special situation of circular stepped squeeze films, a further study of fluid inertia force effects on the ferrofluid-lubricated circular stepped squeezing mechanism is motivated. Design/methodology/approach On the basis of the ferrohydrodynamic flow model of Shliomis incorporating the momentum integral method, the effects of fluid inertia forces in ferrofluid-lubricated circular stepped squeeze films in the presence of external magnetic fields are investigated in this study. Analytical solutions of squeeze film performances are derived. Findings The fluid inertia force effects provide an increased load capacity and a longer squeeze film time for the ferrofluid-lubricated circular stepped squeeze film, especially for a larger value of the inertia parameter, the Langevin parameter and the volume concentration and a smaller value of the radius ratio and the step height ratio. Originality/value For engineering applications, numerical tables for squeeze film loads of circular stepped disks are also provided in this paper.

MAGNETO-HYDRODYNAMIC NON-NEWTONIAN CURVED CIRCULAR SQUEEZE FILMS

The squeeze film performances between curved circular plates lubricated with an electrically conducting non-Newtonian fluid in the presence of external magnetic fields are investigated in this paper. Based upon the magneto-hydrodynamic flow theory together with the Stokes microcontinuum theory, the magneto-hydrodynamic non-Newtonian Reynolds equation is derived and applied to predict the curved circular squeeze film behaviors. Comparing with the hydrodynamic Newtonian case, the squeeze film characteristics for curved circular plates are improved by the use of an electrically conducting non-Newtonian fluid in the presence of external magnetic fields. Numerical values of the load capacity and the approaching time are provided in Tables for engineering applications.

Lubrication Performances of Short Journal Bearings Operating with Non-Newtonian Ferrofluids

The lubrication performances of short journal bearings operating with non-Newtonian ferrofluids have been investigated in the present study. Based upon the ferrofluid model of Shliomis and the micro-continuum theory of Stokes, a two-dimensional modified Reynolds equation is derived by taking into account the effects of rotation of ferromagnetic particles and the effects of non-Newtonian properties. As an application, the short-bearing approximation is illustrated. Comparing with the conventional non-ferrofluid case, the short journal bearings with ferrofluids in the presence of magnetic fields result in a higher load capacity. Comparing with the Newtonian ferrofluid case, the non-Newtonian effects of couple stresses provide an enhancement in the load capacity, as well as a reduction in the friction parameter. The inclusion of non-Newtonian couple stresses signifies an improvement in performance characteristics of ferrofluid journal bearings.

The effects of non-Newtonian rheology in the dynamic coefficients of wide slider bearings with a secant-shaped film profile

Purpose – The purpose of this paper is to investigate the effects of non-Newtonian rheology on the dynamic characteristics of a secant-shaped couple-stress lubricated slider bearing. Design/methodology/approach – By applying the linear dynamic theory to the film force equation, a closed-form solution of the stiffness and damping coefficients is obtained for the secant-shaped bearing taking into account the non-Newtonian effects of Stokes couple stress fluids. Findings – Comparing with the secant-shaped Newtonian-lubricant bearing, the effects of non-Newtonian couple stresses provide an apparent improvement in the dynamic stiffness and damping characteristics, especially for the secant-shaped slider bearing operating at lower squeezing-film heights and with larger non-Newtonian couple stress parameters. Originality/value – Comparing with those of the inclined plane-shaped non-Newtonian slider bearings, better dynamic stiffness and damping performances are provided for the secant-shaped non-Newtonian slider...

Effects of non‐Newtonian Rabinowitsch fluids in wide parallel rectangular squeeze‐film plates

Purpose – In the present paper, the authors aim to analyze the non‐Newtonian effects of Rabinowitsch fluids on the squeeze film performances between wide parallel rectangular plates.Design/methodology/approach – Based on the cubic‐stress equation model, a nonlinear squeeze‐film Reynolds‐type equation has been derived. By using a small perturbation method, a closed‐form solution of the squeeze film characteristics is derived for the parallel plates considering the non‐Newtonian effects of cubic stresses.Findings – Comparing with the Newtonian‐lubricant parallel plates, the effects of non‐Newtonian cubic‐stress flow rheology provide significant influences upon the squeeze film characteristics.Originality/value – It is shown that the non‐Newtonian pseudoplastic behavior reduces the load capacity and the response time; however, the effects of non‐Newtonian dilatant lubricant provide an increase in the load‐carrying capacity and therefore lengthen the response time of parallel squeeze‐film plates.

The surface roughness effects of transverse patterns on the Hopf bifurcation behaviors of short journal bearings

Purpose – On the ground of the Hopf bifurcation theory derived by Hassard et al., the purpose of this paper is to investigate the weakly nonlinear dynamics of transverse rough‐surface short journal bearings.Design/methodology/approach – By application of the stochastic model of rough surfaces, developed by Christensen and Tonder, the roughness effects of transverse surface patterns on the bifurcation behaviors close to the Hopf bifurcation point are investigated.Findings – It is found that the dynamic behavior of transverse rough‐surface short journal bearings can display Hopf bifurcation phenomena. Comparing with the case of isotropic rough‐surface bearing by Lin, under the same parameters, the effects of transverse surface roughness provide a reduced sub‐critical Hopf bifurcation region as well as an increased super‐critical Hopf bifurcation region. In addition, the effects of transverse surface roughness result in a lower stability‐threshold critical speed for both the sub‐critical bifurcation profile ...