24th International Colloquium Tribology - January 2024 129 Effect of Slip on Piezo-Viscous-Polar Lubricated Multirecessed Hybrid Journal Bearing Vishal Singh 1* , Arvind K. Rajput 2 1, 2 Mechanical Engineering Department, IIT, Jammu, J&K, India -181221 * Corresponding author: vishal.singh@iitjammu.ac.in 1. Introduction In recent years, multirecessed hybrid journal bearing (MHJB) have gain significant attention of researchers to improve the performance of rotary machineries attributed to their inherited advantages, viz., higher load carrying capacity, enhanced stiffness and damping characteristics and rotational accuracy. Nowadays, researchers use coating material on journal or bearing surfaces to improve their tribological properties. Consequently, shear stresses at the solid-liquid interface may results in velocity slip at interface [1-3]. The slip at interface may significantly affect the pressure field and thereby characteristics of the bearing system. Furthermore, the characteristics of a fluid film journal bearing primarily depend on the performance of the lubricant. To achieve a better lubricating performance, several form of long chain polymer additives particles are blended into the oil. The blending of long chain polymer additives particles in oil results in the polar effect due to couple stresses and lubricant no longer behaves as a Newtonian lubricant [4,5]. Further higher pressure may induce the piezo viscosity in the oil. Thus, the nature of the lubricant becomes piezo-viscous polar (PVP) lubricant and may exhibit piezo-viscous behaviour at higher pressures [6, 7]. The present work examines the cumulative effect of velocity-slip and piezo-viscous-polar lubrication on the characteristics of MHJB system. Four different cases of velocity-slip are studied, i.e., (i) no velocity-slip at journal or bearing surfaces, (ii) velocity-slip at journal surface, (iii) velocity-slip at bearing surface and (iv) velocity-slip at both (journal and bearing) surfaces. A modified form of the Reynolds equation governing the flow of the PVP lubricant is numerically solved using FE analysis. The simulated results indicate that velocity-slip at journal and bearing surfaces substantially affect the characteristics of MHJB system. Further, the use of PVP lubricant instead of Newtonian lubricant offers better performance of MHJB system i.e, PVP lubricant may compensate the performance loss caused by slip effect. 2. Analysis The schematic diagram of MHJB operating with PVP lubricant is depicted in Figure 1. The flow of PVP lubricant in the clearance space of MHJB governed by modified form of Reynolds equations which can be expressed as [1, 7, 8]: (1) Here, the behaviour of piezo-polar-slip function ( ) is governed by the piezo-viscous coefficient ( ), couple-stress parameter ( ) and velocity-slip coefficient ( ). Figure 1: Schematic of PVP fluid lubricated MHJB system The oil film thickness ( ) in MHJB can be computed from the following expression [9] (2) Where and are the journal centre coordinates. For computation of unknown pressure field, the oil film domain is discretised using four noded isoparametric quadrilateral element. Incorporating the Galerkin’s orthogonality technique of FE analysis, the governing equation (1) can be converted to matrix form as: (3) In MHJB, the load carrying capacity can be computed from the following expressions [9]: (4) The resultant load carrying capacity in radial direction yields as [9]: (5) The rotordynamic coefficients ( , ) yield as [9]: (6) Where, = Generalised force ; (Journal centre displacement); (Journal centre velocity) 3. Validation of model Based on FE formulation, a computer code is devel-oped in MATLAB. For validation of developed code, the computed results have been compared with the published studies. It may be observed from Figure 2 that the computed results are in close agreement with published results of Lv et al. [2]. The minor deviation between computed results and published results is attributed to difference in solution methodology and mesh size. 130 24th International Colloquium Tribology - January 2024 Effect of Slip on Piezo-Viscous-Polar Lubricated Multirecessed Hybrid Journal Bearing Figure 2: Variation of oil film pressure ( ) against circumferential angle (θ) for validation of velocity slip 4. Results and discussion For the performance analysis of MHJB, the geometric and operating parameters are judiciously chosen from literature. Thereafter, the performance characteristics of MHJB against load ( ) are computed. The variation of minimum oil fil thickness ( ) versus load ( ) is presented in Figure 3. It can be noticed from Figure 3 that for Newtonian and PVP lubricant, the consideration of velocity slip causes severe reduction (0.65-32.01%) in the values of ( ) as compared to ideal no-slip condition. Velocity slip on both (journal and bearing) surfaces causes maximum reduction in the values of ( ) in the range of 1.62-32.01% as compared to ideal no-slip condition. It may be due to reduction in relative velocity in MHJB system. Furthermore, the use of PVP lubricant offers higher values of ( ) in the range of 0.89-35.28% than that of Newtonian lubricant attributed to synergistic effect of piezo-viscosity and couple-stresses for various cases of velocity slip. Figure 3: Variation of versus The variation of rotordynamic coefficient ( ) against load ( ) is depicted in Figure 4. It can be observed that the consideration of velocity slip causes substantial drop in the values of ( ) in the range of 31.64-55.86% as compared to ideal no-slip condition. Likewise to trends of (), velocity slip on both surfaces (journal and bearing) causes maximum drop in the value of ( ) in the range of 52.44-55.86% as compared to ideal no-slip condition. Furthermore, the use of PVP lubricant instead Newtonian lubricant offers higher values of ( ) in the range of 53.75-60.43% of as compared to Newtonian lubricant. The other performance characteristics are not presented here due to space constraints. Figure 4: Variation of ( ) versus 5. Conclusions The present work examine the performance CFV compensated of MHJB system considering the influence of velocity slip and PVP lubrication. The computed results reveal that the consideration of velocity causes degradation in the performance of MHJB, viz. , , , and as compared to ideal no-slip condition. Moreover, PVP lubricant offers higher values of , , , and which may compensate performance degradation attributed to velocity slip at journal and bearing surfaces. References [1] Shukla J. B., Kumar S., Chandra P. Generalized reynolds equation with slip at bearing surfaces: Multiple-layer lubrication theory. Wear 1980; 60: 253-68. [2] Lv F., Rao Z., Ta N., Jiao C. 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