Dynamic Performance Characteristics of Misaligned Hybrid Journal Bearing Using Micropolar Lubricant

Transcription

1 Dynamic Performance Characteristics of Misaligned Hybrid Journal Bearing Using Micropolar Lubricant 1 Preeti, 2 Sanjeev 1 M.Tech Research Scholar, C.B.S Group of Institutions, Jhajjar, Haryana 2 Assistant Professor, Mechanical Engg., C.B.S Group of Institutions, Jhajjar, Haryana ABSTRACT The hybrid bearings are designed to take maximum advantage of hydrostatic and hydrodynamic effect and offer some very attractive features such as zero start up wear, good bearing film stiffness at zero speed and high load capacity at higher speeds. An analytical study concerning the effect of misalignment on the hole-entry hybrid journal bearing with double row of twelve holes in each row (symmetric configuration) operating with micropolar has been presented. The modified Reynold s equation governing the lubricant flow field in the clearance space of the journal bearing has been solved to find the performance characteristics like pressure distribution, minimum fluid film thickness, direct stiffness coefficients, cross stiffness coefficients, direct damping coefficients, cross damping coefficients, critical mass and threshold speed of a capillary compensated hybrid journal bearing. Static and dynamic performance characteristics are presented for the different representative values of the journal misalignment and micropolar parameters for hybrid mode of operation of the bearing. The study suggests that the journal misalignment significantly affects the performance of the hole-entry journal bearing and for a more accurate prediction of the bearing performance, it must be considered in the analysis. Keywords: Friction, Hydrodynamic Journal bearing, Machine, Materials, Wear. 1. INTRODUCTION A bearing is a machine element which supports the part of the shaft is known as a journal. It permits a relative motion between the contact surfaces of the members, while carrying the loads. Bearing do not only support the journal, it also absorbs the vibrations of the journal and keeps the journal in equilibrium position by the application of lubricant. Oil film work as spring and damper system during running and stationary conditions. Due to the relative motion between the two contact surfaces, a certain amount of power is wasted in overcoming frictional resistance and if the rubbing surfaces are in direct contact, there will be rapid wear. In order to reduce frictional resistance and wear and in some cases the heat generated, a layer of fluid known as lubricant may be provided. The lubricant used to separate the journal and the bearing is usually a mineral oil refined from petroleum, but vegetable oils, silicon oils, greases etc. may be used. The simplest bearings are bearing surfaces, cut or formed in a part, with varying degrees of control over the form, size, roughness and location of the surface. Other bearings are separate devices installed into a machine or machine part. The most sophisticated bearings for the most demanding applications are very precise devices; their manufacture requires some of the highest standards of current technology. The use of bearings is in vogue for centuries, but the recent developments in science and technology demands critical designs of bearings with high precision and optimum performance even in the most adverse working conditions. The rapid developments in the fields of rocketry and missile technology, cryogenics, aeronautics and space engineering, nuclear engineering, electronics, computer sciences and technologies, biomedical engineering and a lot more fields in science and technology make the aspects of designing bearings 42

2 more and more challenging and innovative. Moreover, the mode, time and place of operations demand exploration of new materials, lubricants and even lubrication theories and technologies. All heavy industrial turbo machines use fluid film bearings of any type to support the shaft weight and control motions caused by unbalance forces. The two primary advances of fluid film bearings over rolling element bearings are their superior ability to absorb energy to damp and important in many types of rotating machines where the fluid film bearings are often the primary source of the energy absorption needed to control vibrations. Dynamic analysis of hybrid hydrodynamic bearings is important because the shaft bears many unbalance forces, aerodynamic forces, and external excitations from seals and couplings. 2. LITERATURE REVIEW In this chapter, a detailed review of literature relating to the research work carried out in the field of hole-entry hybrid journal bearings using different type of fluids / lubricant like Newtonian and micropolar is presented and also detailed review of literature relating to the misalignment in hydrostatic and hydrodynamic bearings. In this chapter literature review divided in two section:- Literature review for micropolar fluids Literature review for misalignment 2.1 Literature Review for Micropolar Fluids Lot of work has been done using micropolar lubrication on hydrodynamic Bearing, to determine the effect on various bearing parameters, viz. Eringen A. Cemal (1966) derived the Equations of motion, constitutive equations and boundary conditions for a class of fluids named micropolar fluids. These fluids respond to micro-rotational motions and spin inertia and therefore can support couple stress and distributed body couples. Thermo dynamical restrictions are studied in detail and field equations are obtained for the density, velocity vector and micro-rotation vector. The system is solved for a channel flow exhibiting certain interesting phenomena. Balram M. (1975) analysis the micropolar squeezes films and derived Expressions for calculating the pressure, the load-carrying capacity of the squeeze film and film thickness-time relationship. Numerical results computed from these expressions reveal that fluid microstructure improves the squeeze film action and increases the loadcarrying capacity of the squeeze film, while the load-carrying capacity reduces rapidly with an increase in fluid substructure. Zaheeruddin Kh. et al. (1978) studied the characteristics of one dimensional journal bearing shows that the load capacity increases and the coefficient of friction decreases as the parameter, which characterizes the microstructure of the base oil due to the presence of additives, increases. The time of approach increases as the parameter increases. Zaheeruddin Kh. et al. (1981) observed that load carrying capacity increase with increase of micropolar effect and load carrying capacity decrease with increase porosity of porous spherical bearing. Singh Chandan et al. (1982) described the three-dimensional Reynold s equation for micropolar fluids are derived. The balance equations for micropolar fluids are simplified by using traditional lubrication assumptions and order-of-magnitude analysis. The simplified equations are solved to yield expressions for the velocity distribution and the micro rotation velocities. Sharma Satish C. et al. (1995) compare the performance of a six pocket capillary compensated hydrostatic/hybrid flexible journal bearing to that of a similar four-pocket journal bearing. The comparison is based on theoretical computed results. The finite-element has been used to obtain simultaneous solutions of the three dimensional elasticity equations and Reynold s equation. It is observed that the six-pocket journal bearing may be more efficient from a stability point of view as compared to a similar four-pocket journal system. Yong Tian et.al (1995) determined the dynamic properties of hybrid bearing. He found that oil whirl occurs so it becomes important to evolutes the stiffness and damping coefficient for hybrid operating bearing in order to predict their stability and threshold speed. 43

3 Sharma Satish C. et al. (1995) studied the hole-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynold s equation for micropolar lubricant is solved using finite element method along with equation of lubricant flow through hole-entry restrictors as a constraint together with appropriate boundary conditions. It has been observed that a hole-entry hybrid journal bearing operating with micropolar lubricant shows an increase in the value of minimum fluid film thickness and a reduction in the value of coefficient of friction as compared to a corresponding similar hole-entry hybrid journal bearing operating with Newtonian lubricant. B.Chetti (2011) studied the dynamic characteristics of four-lope journal bearing. He found that the critical mass increase while the whirl ratio for the four-lope journal bearing decreases with an increase of the parameter coupling number. He also found the stability of the four-lope journal bearing is improved by using a micropolar compared to a Newtonian fluid. Rajaeskar Nicodemus et.al (2012) studied the performance characteristics of micropolar lubricant membrane compensated worn hybrid journal bearing. They used the Dufrane s abrasive wear model. Their result suggest that the effect of wear on the bearing surface and bearing performance. Suresh Verma et.al (2013) studied the performance characteristics of the flexible multi-recessed hydrostatic journal bearing system with constant flow valve and capillary restrictors. They found their result indicate that the micropolar parameter of the lubricant effect the performance of the flexible multi-recessed hydrostatic journal bearing system quiet significantly. Mohamed Nabhani et.al (2014) studied the inertia effect on inclined slider bearing lubricant by a couple stress fluid.they compared their result with non-inertia Newtonian lubricant, the couple effect of fluid inertia forces and non Newtonian couple stress provide a significant improvement in slider a bearing load capacity. 2.2 Literature review for misalignment Mokhtar et al. (1985) studied that minimum film thickness and friction force decrease due to misalignment in journal bearing. He found that minimum film thickness decrease with misalignment Jain et al. (1990) studied the effect of journal misalignment on static and dynamic performance characteristics of a hole-entry hybrid journal bearing. They reported that the misalignment causes severe reduction in minimum fluid film thickness of a hole-entry hybrid journal bearing San Andres (1993) studied the hydrostatic journal bearing operating in turbulent regime including journal misalignment effects. He found that misalignment reduce the load carrying capacity and fluid film thickness and increase the lubricant flow rate and produce misalignment moment. Sathish et al. (2000) studied the combined effect of journal misalignment and surface roughness on the performance of hybrid journal bearing system. Their study indicated that surface roughness compensate the decrease in minimum film thickness caused by shaft misalignment. Das et al. (2001) studied the performance of steady state misaligned journal bearing with micro-polar fluid. They noted that under misalignment condition, micro-polar fluids exhibit better performance than Newtonian fluids. Buyer and fillon (2002) conducted an experimental study of misaligned plain journal bearing and they noted that misalignment has significant role when the rotational speed or load is low. Balupari and Raj Shekhar (2004) plotted the graph between stiffness and dumping characteristics with respect to the bearing characteristic number in journal bearing with Newtonian fluids. Rahmatabadi and Rashidi (2006) studied the effect of bearing mounting angle on the performance of gaslubricated non circular general bearing reported that mount angel has a significant effect on the performance of two lobe journal bearing. Satish C.Sharma (2008) observed that journal misalignment reduced the value of nominal minimum fluid film thickness whereas the effect of surface roughness is to partially Compensate this loss for both symmetric and asymmetric configuration irrespective of the type of compensating device used Orifice/capillary/constant flow value misalignment is to reduce the value of the bearing dynamic coefficient and surface roughness increase these value. 44

4 Satish C.Sharma (2008) studied the non-recessed hybrid flexible bearing with different restrictor. By their calculation he found that for a non-recessed hybrid journal bearing system operating at a specific external load, proper selection of parameters such as type of restrictor, capillary, slot, constant flow valve, orifice and type of bearing configuration (symmetric/asymmetric) improved bearing performance. Yung Kung Yang et.al (2008) studied the thermo hydrodynamic analysis of misalignment conical cylindrical bearing with non Newtonian lubricant. He found that normal load carrying capacity and the value of maximum temperature at the film exit are more higher value of power-law exponent and the verifies that the maximum temperature at the film exit for a conical cylindrical bearing, it does not for a slider bearing. Sharana Basavaraja and Sathish Jain (2009) studied the misaligned roughened two lobe hole entry hybrid journal bearing.they noted that when offset factor is greater than one than the roughness on the bearing is found to minimize the effect of bearing misalignment on the value of minimum film thickness. Basavaraja et al. (2010) studied the performance of a misaligned non recessed bearing lubricated with electrorheological [ER] fluid. They reported that the reduction in bearing performance characteristics due to misalignment can be partially compensated by increasing the electric field of the ER fluid. Boulam Chetti (2011) studied static and dynamic characteristic of hydrodynamic four lobe journal bearing with the couple stress lubricant. He compared the performance characteristics of four lobe bearing to the other bearing with Newtonian fluid. Dhawan Rohit and Verma Suresh (2013) studied the micropolar lubrication in non circular hybrid journal bearings. They noted that an increase in micropolar parameters does not have significant effect on the reduction of bearing flow. 3. PROBLEM FORMULATION The existing literature reveals that the available studies in the area of performance characteristics of hydrostatic, hydrodynamic and hybrid journal bearing using different type of fluids / lubricant like Newtonian and micropolar. Some literatures are available related to misalignment of hydrostatic and hydrodynamic bearings. The present work is based on dynamic performance characteristics of misaligned hybrid journal bearing. 3.1 Problem Formulation The geometric configuration of hole-entry hybrid journal bearing shown in fig. (3.1). the journal is assumed to rotate with uniform angular velocity about its equilibrium position. The hybrid form of journal bearings is designed to support the load at high speed. The problem is being formulated as follows: In present work double row hole-entry HJB with 12 holes per row is used. Fig. 3.1 The geometric configuration of hole-entry hybrid journal bearing 45

5 4. SOLUTION PROCEDURE The mathematical model developed in the previous chapter is used to compute the performance characteristics of hole-entry hybrid journal bearing system considering micropolar effects of lubricant. 4.1 Input Data File for Analysis of Hole-Entry Hybrid Journal Bearing Various data of the input data file for hole-entry HSJB to be implemented on the computer code are as follows, Total number of nodes in solution domain = 60 (0 to 59) No of elements in solution domain = 48 [(0) to (47)] No. of hole in single row = 12 Total no. of hole in double row = 24 (1,3,6,8,11,13,16 56,58) No. of Nodes per element = 4 No of fixed Elements = 24 (Outer Elements) No of fixed nodes = 24 No of sampling points for integration = 2 No of dimension of problem = 2D Nodes on secondary edge = 5 (0, 1, 2, 3, 4) Elements on secondary edge = 4 (44, 45, 46, 47) Fig. 4.1 Discretized Hole-entry hybrid journal bearing Fig. 4.2 Four noded quadrilateral isoparametric element Fig. 4.2 shows the four noded quadrilateral isoparametric element. 5. RESULT AND DISCUSSION 5.1 Influence on Circumferential Pressure Flow ( ) Figure 5.1 shows the variation of maximum pressure ( ) with restrictor design parameter. In case of Newtonian lubricant, it has been observed that increases with increase in restrictor design parameter ( aximum reduction for in Newtonian lubricant is found to be 24 % at. In case of aligned condition, the curve for in micropolar lubricant lies below the curve of Newtonian lubricant. It means micropolar effect decreases with restrictor design parameter ( for all 46

6 value of micropolar parameters in aligned condition. It is noted that is greater in misalignment as compared to aligned condition for both value of micropolar parameters. The maximum reduction in direct stiffness coefficient due to misalignment and micropolar lubricant ( is found to be 73 % at Fig. 5.1: Fluid film pressure ( ) profile 5.2 Influence on Minimum Fluid Film Thickness ( ) Figure 5.2 shows the variation of minimum film thickness with the restrictor design parameter. It is found that misalignment parameter reduces the minimum fluid film thickness ( ) for a bearing operating with either micropolar or Newtonian lubricant. It is because of the reduced clearance between the journal and the bearing. The value of is greater for micropolar lubricant as compared to the Newtonian lubricant, therefore it may be observed from the figure 5.2 that influence of micropolar effect of lubricant is to increase the value of marginally for a bearing operating under aligned/ misaligned conditions. A maximum decrease in is observed at in both Newtonian as well as micropolar lubricant at constant external load = 0.5.) Fig. 5.2: Minimum fluid film thickness ( ) profile 5.3 Influence on Direct Stiffness Coefficient ( ) Figure 5.3 shows the variation of direct stiffness coefficient ( with restrictor design parameter. In case of Newtonian lubricant, it has been observed that direct stiffness coefficient ( increases with increase of restrictor design parameter is upto 0.1 thereafter it decreases. Due to the misalignment, the maximum increment of direct stiffness coefficient ( in Newtonian lubricant is found to be 32 % at. In aligned condition, the curve for direct stiffness coefficient ( lies above the curve of Newtonian lubricant when restrictor design parameter is less than 0.2. It means micropolar effect decreases the direct with restrictor design parameter ( for all value of micropolar parameters in aligned condition when restrictor design parameter is less than 0.2. But in case of misalignment stiffness coefficient ( is lower than aligned condition for both value of micropolar parameters. In case of micropolar lubricant, the maximum reduction in direct stiffness coefficient ( due to misalignment ) and micropolar parameters ( is found to be 17 % at restrictor design parameter. 6 1 Fig. 5.3 Direct stiffness coefficient ( ) vs restrictor design parameter ) 47

7 5.4 Influence on Cross Stiffness Coefficient ( ) Figure 5.4 shows the variation of cross stiffness coefficient ( with restrictor design parameter. In case of Newtonian lubricant, it is observed that cross stiffness coefficient ( decreases with increase in restrictor design parameter ( Due to the misalignment, the maximum reduction in cross stiffness coefficient ( in Newtonian lubricant is found to be 66 % at.the curve for cross stiffness coefficient in micropolar lubricant lies above the curve of Newtonian lubricant in aligned condition. It means micropolar effect increases cross stiffness coefficient with restrictor design parameter ( for all value of micropolar parameters in aligned condition. It is found that is less in misalignment as compared to aligned condition for all value of micropolar parameters. The maximum increment in cross stiffness coefficient due to misalignment ) and maximum coupling number ( in micropolar lubricant is observed to be 9.8% at Fig. 5.4 Cross stiffness coefficient vs restrictor design parameter ) 5.5 Influence on Direct Stiffness Coefficient ( ) Figure 5.5 shows the variation of direct stiffness coefficient ( with restrictor design parameter In case of Newtonian lubricant, it is observed that direct stiffness coefficient ( increases with increase in restrictor design parameter ( upto 0.1 thereafter it decreases. The maximum increment in direct stiffness coefficient ( due to the misalignment is observed to be 26 % at. The curve for direct stiffness coefficient ( in micropolar lubricant lies above the curve of Newtonian lubricant in aligned condition when restrictor design parameter is less than It means micropolar effect increases the direct with restrictor design parameter ( for both value of micropolar parameters in aligned condition when But in case of misalignment stiffness coefficient ( is lower than aligned condition for all value of micropolar parameters. The maximum reduction in direct stiffness coefficient ( due to misalignment and micropolar parameters ( in micropolar lubricant is observed to be 20 % at Fig. 5.5 Direct stiffness coefficient ( ) vs restrictor design parameter ) 48

8 5.6 Influence on direct damping coefficient Figure 5.6 shows the variation of direct damping coefficient ( with restrictor design parameter. In case of Newtonian lubricant, it is observed that direct damping coefficient ( decreases with increase of restrictor design parameter (. Due to the misalignment, the maximum increment of direct damping coefficient ( is found to be 31% at. In aligned condition, the curve for direct damping coefficient in micropolar lubricant lies above the curve of Newtonian lubricant. It means micropolar effect increases direct damping coefficient with restrictor design parameter ( restrictor design parameter ( for all value of micropolar parameters. For micropolar lubricant, it is noted that the value of direct damping coefficient is less in misalignment as compared to aligned condition. The maximum reduction in direct damping coefficient due to misalignment and micropolar parameters is found to be 4% at Fig. 5.6 Direct damping coefficient vs restrictor design parameter ) 5.7 Influence on Cross Damping Coefficient (. Figure 5.7 shows the variation of cross damping coefficient ( with restrictor design parameter. The curve for cross damping coefficient in Newtonian lubricant lies in negative direction but in micropolar lubricant the curve lies in positive direction It means that the micropolar parameters ( = 10) provide stability to the bearing. In case of Newtonian lubricant, the magnitude of the cross coupled damping coefficient increase in positive direction with misalignment parameter (. It means the misalignment in Newtonian lubricant favours the stability of bearing. For micropolar lubricant cross damping coefficient decreases with increase in restrictor design parameter with misalignment. When restrictor design parameter is equal then cross damping coefficients is greater in Newtonian lubricant as compared to micropolar lubricant in misalignment. Result shows that the curve corresponding misalignment and micropolar parameters lies in negative direction. It means misalignment leads the bearing towards instability in micropolar lubricant Fig. 5.7 Cross damping coefficient ( vs restrictor design parameter ) 5.8 Influence on Direct Damping Coefficient ( ) Figure 5.8 shows the variation of direct damping coefficient ( with restrictor design parameter. In case of Newtonian lubricant, it is observed that direct damping coefficient ( decreases with increase of restrictor design parameter (. Due to the misalignment, the maximum increment of direct damping coefficient ( in Newtonian lubricant is observed to be 86 % at. The curve for in micropolar lubricant lies above the curve of Newtonian lubricant in aligned condition. It means micropolar effect increase direct damping coefficient restrictor design parameter ( for all value of micropolar parameters in aligned condition. It has been observed that is more in 49

9 misalignment as compared to aligned condition for all value of micropolar parameters. The maximum increment in due to misalignment and micropolar parameters is found to be 20% at Fig. 5.8 Direct damping coefficient ( vs restrictor design parameter ) 5.9 Influence on Critical Mass ( ) Figure 5.9 shows the variation of critical mass with restrictor design parameter. For the case of Newtonian lubricant, it observed that critical mass increases with increase of restrictor design parameter is less than 0.1 thereafter it decreases. Due to the misalignment, the maximum increment of critical mass is found to be 23 % at. The curve for critical mass in micropolar lubricant lies above the curve of Newtonian lubricant in aligned condition for restrictor design parameter It means micropolar effect decreases critical mass with restrictor design parameter for all value of micropolar parameters in aligned condition for. But in case of misalignment critical mass is lower than aligned condition for all value of micropolar parameters. The maximum percentage reduction in critical mass ( due to misalignment and micropolar lubricant in lubricant is found to be 14 % at Fig. 5.9 Critical mass ( ) vs restrictor design parameter ) 5.10 Influence on Threshold Speed ( ) Figure 5.10 shows the variation of threshold speed ( ) with restrictor design parameter. For case of Newtonian lubricant, it is observed that threshold speed ( ) increases with increase of restrictor design parameter 0.1 thereafter it decreases. Due to the misalignment, the maximum increment of threshold speed ( ) in Newtonian lubricant is found to be 73 % at The curve for threshold speed ( in micropolar lubricant lies above the curve of Newtonian lubricant in aligned condition. It means micropolar effect increases threshold speed ( with restrictor design parameter for all value of micropolar parameters in aligned condition. The maximum reduction in threshold speed ( ) due to misalignment and micropolar parameter is found to be 7 % at. 50

10 Fig Threshold speed ( ) vs restrictor design parameter ) CONCLUSIONS An analytical study concerning the misalignment effect on capillary compensated hole-entry hybrid journal bearing with double row of twelve holes in each row (symmetric configuration) operating with micropolar lubricant has been presented in this dissertation work. Based on the numerically simulated results the static and dynamic characteristics such as pressure distribution, minimum fluid film thickness, stiffness coefficients, damping coefficients, critical mass and threshold speed have been evaluated for various values of micropolar and misalignment parameters. The following conclusion can be drawn from the results presented in this study:- In the case of Newtonian lubricant, the maximum pressure ( is observed to be increased for both aligned and misaligned conditions with restrictor design parameter (, whereas for micropolar lubricant maximum pressure ( increases with the increase in value of restrictor design parameter ( ) upto 0.1 thereafter it decreases slightly. Minimum fluid film thickness ( is observed to be decreased in misaligned condition for both the cases i.e Newtonian and micropolar lubricants as compared to aligned condition with increase of restrictor design parameter ( ). In case of Newtonian lubricant with aligned condition, direct stiffness coefficient ( increases with increase in the value of restrictor design parameter ( ) up to 0.1, thereafter it decreases. For the case of micropolar lubricant with misalignment it decreases with increase of restrictor design parameter ( ). The value of cross stiffness coefficients ( is found to be increased for Newtonian lubricant as the misalignment is introduced. While its value for micropolar lubricant with misalignment condition is found to be decreased as compared to Newtonian lubricant with aligned journal. In case of Newtonian lubricant, the direct damping coefficient ( increases for misaligned condition as compared to aligned condition but in case of micropolar lubricant, it decreases for misalignment as compared to aligned condition. In case of misalignment, the value of cross damping coefficients ( lies in positive region for both micropolar and Newtonian lubricant, whereas in aligned condition it is observed to be negative. For Newtonian lubricant with aligned condition, the value critical mass ( increases with increase in restrictor design parameter ( ) up to 0.1, thereafter it sharply decreases.as the misalignment is introduced increase with the increase the value of up to 0.15, thereafter it has negligible variation with restrictor design parameter ( ). For micropolar lubricant, the critical mass is lower in misaligned condition as compared to aligned condition at restrictor design parameter ( = 0.1). For Newtonian lubricant, threshold speed is observed to be increased with misaligned condition as compared to aligned condition. The maximum increase in threshold is 73% at restrictor design parameter ( = 0.3). In the case of micropolar lubricant, threshold speed decreases with the presence of misalignment as compared to the aligned condition and the maximum reduction is observed to be 7% at restrictor design parameter ( 51

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