Performance of vertical herringbone grooved hydrodynamic journal bearings

PERFORMANCE OF VERTICAL HERRINGBONE GROOVED HYDRODYNAMIC JOURNAL BEARINGS CARREN CLIEF RONDONUWU (B Eng (Hons) University of Technology Sydney, Australia) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 ACKNOWLEDGEMENTS I thank and praise God who through His grace and providence has given me the opportunity, energy and wisdom to complete this research work I would like to give a special gratitude to my supervisor, Assoc Prof Dr S.H Winoto who has entrusted me with this challenging research project and provided me with academic guidance, motivation, constant supervision, and corrections both in the learning process and in the technical writing I would also like to thank the technical officers in the Fluid Mechanics Laboratory, especially Mr Yap Chin Seng, Ms Iris Chew Boey, Ms Lee Cheng Fong, and Mr Tan Kim Wah for their continuous support and professionalism that have greatly helped me especially in the experimental work I would like to thank the people who are personally close to me: my parents, my sister, family members, and girlfriend, for their ceaseless prayer, encouragement and moral as well as material support during my research study I am also deeply grateful to the National University of Singapore who has given me the opportunity to pursue a Master of Engineering degree with full scholarship I would also extend my gratitude to everyone else who have helped me and contributed to the completion of this thesis project i TABLE OF CONTENTS Pages ACKNOWLEDGEMENTS i TU UT TABLE OF CONTENTS ii TU UT SUMMARY iv TU UT NOMENCLATURE .vi TU UT LIST OF FIGURES .ix TU UT LIST OF TABLES xiii TU UT Chapter INTRODUCTION TU UT 1.1 background and motivation 1.2 Objectives and scope 1.3 Thesis organization .5 TU UT TU UT TU UT T Chapter LITERATURE REVIEW .6 U U 2.1 2.2 2.3 2.4 U U U U THEORETICAL BACKGROUND NUMERICAL STUDIES ON HYDRODYNAMIC JOURNAL BEARING EXPERIMENTAL WORKS ON HYDRODYNAMIC JOURNAL BEARING TECHNOLOGICAL APPLICATIONS AND INVENTIONS U U U U Chapter EXPERIMENTAL WORK 11 U U 3.1 EXPERIMENTAL SETUP 11 3.1.1 Components and Parts 11 3.1.2 Assembly 15 3.1.3 Specimen Shafts 17 3.1.4 Drive System 19 3.1.5 Lubricant Supply System 19 3.1.6 Leakage Collection 20 3.1.7 Data Acquisition System 20 3.1.7.1 Pressure Reading 20 3.1.7.2 Temperature Reading 21 3.2 EXPERIMENTAL PROCEDURE .21 3.2.1 Pressure Measurement 23 3.2.2 Temperature Measurement 24 3.2.3 Leakage Measurement 24 3.2.4 Changing Specimen Shaft 24 3.2.5 Changing Specimen Sleeve 25 3.2.6 Changing Rotational Speed 26 U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U ii Chapter NUMERICAL WORK 28 U U 4.1 INTRODUCTION TO FLUENT 28 4.2 GEOMETRY BUILDING AND MESH GENERATION 29 4.3 BOUNDARY CONDITIONS AND PHYSICAL MODELING 30 4.4 SOLVER METHODS AND SOLUTIONS CONTROL .32 4.5 GRID INDEPENDENCE 35 4.6 ITERATIVE CONVERGENCE 36 U U U U U U U U U U U U Chapter RESULTS AND DISCUSSIONS 37 U U 5.1 EXPERIMENTAL RESULTS 37 5.2 NUMERICAL RESULTS 46 U U U U Chapter CONCLUSIONS AND RECOMMENDATIONS 53 U U 6.1 CONCLUSIONS .53 6.2 RECOMMENDATIONS 55 U U U U REFERENCES 56 U U FIGURES .58 U U APPENDIX A : Engineering Drawings 137 U U APPENDIX B : Roundness Test Results .156 U U APPENDIX C : Motor Specifications 159 U U APPENDIX D : Motor Driver Specifications 161 U U APPENDIX E : DSA 3007 Specifications 162 U U APPENDIX F: FLUENT Segregated Solver with SIMPLE Pressure-Velocity U Coupling Algorithm 163 U iii SUMMARY The significant advantages of fluid bearings over ball bearings have led to increasing use of fluid bearing technology on the latest hard-disk drive spindle motors produced These include low acoustic noise, higher spindle speed, less non repeatable run-out (NRRO), better shock performance, better fatigue performance, and better stiffness and dynamic stability The most commonly used grooved pattern in the journal of such bearings is the herringbone groove type A test rig has been designed and fabricated to investigate the performance of some vertical hydrodynamic journal bearings with herringbone groove patterns on the shafts in terms of side leakage rates and axial pressure distributions, at low and high rotational speeds for one plain journal (Shaft 1) and seven different grooved journals (Shafts to 8) which consist of: Shaft (with symmetrical and discontinuous grooves and 0.25 mm clearance), Shaft (with symmetrical and discontinuous grooves and 0.35 mm clearance), Shafts and (asymmetrical and discontinuous grooves), Shaft (with symmetrical and continuous four grooves), Shaft (with asymmetrical and continuous three grooves), and Shaft (90-degrees groove angle) Computational simulations were performed for these eight herringbone-grooved journal bearings by the use of a computational fluid dynamic software called Fluent at rotational speeds ranging from 203 to 2110 rpm The computational simulations agree with the experimental results and theoretical expectations in terms of axial pressure and side leakage rates Some discrepancies between experimental and computational results are due to the underlying assumptions made in the simulations and the limitation of the experimental test rig The overall experimental results also show that the test rig and experimental setup have successfully achieved the objectives of this project The experimental iv results in terms of pressure profile and leakage rate are as expected and produce useful insights into the performance characteristics of the vertical herringbone grooved journal bearings especially in the pressure distributions and pumping sealing Asymmetrical grooves such as on Shafts and can produce a good pumping sealing as the ratio of LB on LA is increased The increase in radial clearance as for B B B B Shafts and decreases the maximum pressure generated The continuous grooves type as on Shafts and generally produces higher peak pressures than the discontinuous grooves such as on Shafts – Bearing of Shaft can be rotated both ways and produces a relatively high pumping sealing effect v NOMENCLATURE A swept area between shaft and bearing r A surface area vector r Af area of face f ap B momentum-weighted averaging coefficient B the average of the momentum equations ap coefficients for the cells on either ap B B side of face f ⎛ N faces * ⎞ net flow rate into a cell ⎜⎜ = ∑ J f A f ⎟⎟ f ⎝ ⎠ b b1 B groove width B groove distance b2 B B c radial clearance or gap between shaft and bearing D shaft diameter F force r F force vector Ho B ⎛ h+c⎞ film thickness ratio ⎜ = ⎟ h ⎠ ⎝ B h groove depth I identity matrix Jf B mass flux through face f B J*f resulting face flux from p* PB P B a correction added to J*f J’f B B L P LA B LB B PB B B length of a groove set length of upper set of herringbone grooves B length of lower set of herringbone grooves B vi LAB B LJB B B B length of gap between LA and LB B B B B total effective length of journal bearing l circumferential length of journal bearing N rotational speed (rpm) N faces number of faces enclosing cell ng number of grooves (circumferentially) B B nga number of grooves (axially) P fluid pressure B B pc pressure within a cell B B pam ambient pressure p* estimate of pressure field p’ cell pressure correction Re Reynolds number (= πNDc/60ν) R radius of bearing r shaft radius rpm rotations per minute Sϕ source of φ per unit volume t time U tangential speed V cell volume r v velocity vector B B vii Greek Symbols ⎛ b1 groove width ratio ⎜⎜ = ⎝ b1 + b2 α αp B ⎞ ⎟⎟ ⎠ under-relaxation factor for pressure B β groove angle Γϕ diffusion coefficient for φ γ ⎛ L + LB ⎞ groove length ratio ⎜ = A ⎟ L ⎠ ⎝ Λ ⎛ 6µUR ⎞ ⎟ dimensionless bearing number ⎜⎜ = ⎟ p c am ⎝ ⎠ λ length to diameter ratio (= L/D) µ dynamic viscosity of lubricant ν kinematic viscosity of lubricant ρ fluid density ρf density at face f τ stress tensor φ a scalar transport quantity ϕf value of φ convected through face f ω angular velocity viii LIST OF FIGURES Page Fig 1.1 Components of a hard disk drive 58 Fig 1.2 Parts of a spindle motor 58 Fig 1.3 Schematic of a spindle motor construction with fluid bearing 59 Fig 1.4 Examples of common herringbone groove patterns 59 Fig 1.5 Herringbone grooved journal bearing parameters 60 Fig 3.1 Schematic of experimental setup 61 Fig 3.2 Photograph of experimental setup 62 Fig 3.3 Test rig overall dimensions (in mm) 63 Fig 3.4 Assembly view of test rig showing its main parts 64 Fig 3.5 Test rig mounted on metal table 65 Fig 3.6 Belt-pulley connection between the motor shaft and the driving shaft 65 Fig 3.7 Groove-ridge coupling connecting the driving shaft and the specimen shaft 66 Fig 3.8 The specimen shafts tested 66 Fig 3.9 Motor driver 67 Fig 3.10 Motor speed calibration results 67 Fig 3.11 Lubrication supply mechanism 68 Fig 3.12 Flow inlet arrangement 68 Fig 3.13 Leakage collector 69 Fig 3.14 DSA 3007 pressure transducer 69 Fig 3.15 The 11 pressure taps on sleeve 70 Fig 3.16 Calibration results of DSA 3007 pressure transducer 70 Fig 3.17 DC converter 71 Fig 3.18 Temperature taps on sleeve 71 Fig 4.1 Basic program structure of a FLUENT package 72 Fig 4.2 Picture of a Shaft geometry built in GAMBIT 72 Fig 4.3 Picture of a Shaft meshed volume in GAMBIT 73 Fig 4.4 Cell Types 74 Fig 4.5 Boundary elements defined in each journal bearing 75 Fig 4.6 Grid independent test results 75 Fig 4.7 Iteration convergence of Shaft at 203 rpm 76 Fig 5.1 Pressure distributions of Shaft at six rotational speeds 77 Fig 5.2 Leakage rates of Shaft at six rotational speeds 77 Fig 5.3 Pressure variations with time for Shaft at 203 rpm 78 Fig 5.4 Pressure variations with time for Shaft at 451 rpm 78 Fig 5.5 Pressure variations with time for Shaft at 803 rpm 78 Fig 5.6 Pressure variations with time for Shaft at 1185 rpm 79 Fig 5.7 Pressure variations with time for Shaft at 1469 rpm 79 Fig 5.8 Pressure variations with time for Shaft at 2110 rpm 79 Fig 5.9 Temperature variations with time for Shaft at 203 rpm 80 Fig 5.10 Temperature variations with time for Shaft at 451 rpm 80 Fig 5.11 Temperature variations with time for Shaft at 803 rpm 80 Fig 5.12 Temperature variations with time for Shaft at 1185 rpm 81 Fig 5.13 Temperature variations with time for Shaft at 1469 rpm 81 Fig 5.14 Temperature variations with time for Shaft at 2110 rpm 81 Fig 5.15 Pressure distributions of Shaft at six rotational speeds 82 Fig 5.16 Leakage rates of Shaft at six rotational speeds 82 U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U ix APPENDIX A Fig A.33 Part of test rig Fig A.34 Part of test rig 153 APPENDIX A Fig A.35 Part of test rig Fig A.36 Part of test rig 154 APPENDIX A Fig A.37 Part of test rig 155 APPENDIX B : Roundness Test Results Fig B.1 Roundness test results of Shaft Fig B.2 Roundness test results of Shaft Fig B.3 Roundness test results of Shaft 156 APPENDIX B Fig B.4 Roundness test results of Shaft Fig B.5 Roundness test results of Shaft Fig B.6 Roundness test results of Shaft 157 APPENDIX B Fig B.7 Roundness test results of Shaft Fig B.8 Roundness test results of Shaft 158 APPENDIX C : Motor Specifications 159 APPENDIX C 160 APPENDIX D : Motor Driver Specifications 161 APPENDIX E : DSA 3007 Specifications 162 APPENDIX F: FLUENT Segregated Solver with SIMPLE Pressure-Velocity Coupling Algorithm The control-volume-based technique used by FLUENT consists of integrating the governing equations about each control volume, resulting in discrete equations that conserve each quantity on a control-volume basis The integral form for an arbitrary control volume V, considering the steadystate conservation equation for transport of a scalar quantity φ, is described as follows (Fluent Inc., 2003): r r r ∫ ρ ϕ v ⋅ dA = ∫ Γϕ ∇ϕ ⋅ dA + ∫ Sϕ dV V (F.1) where ρ = density r v = velocity vector r A = surface area vector Γϕ = diffusion coefficient for φ ∇ ϕ = gradient of φ Sϕ = source of φ per unit volume Equation F.1 is applied to each control volume, or cell, in the computational domain An example of a two-dimensional cell, a triangular cell, is shown in Fig F.1 163 APPENDIX F c1 A c0 Fig F.1 Two-dimensional control volume Discretization of Equation F.1 on a given cell yields N faces r r ∑ ρ f v f ϕ f ⋅ Af = f N faces ∑ Γϕ (∇ϕ ) n f r ⋅ A f + SϕV (F.2) where N faces = number of faces enclosing cell ϕf = value of φ convected through face f r r ρ f v f ⋅ A f = mass flux through the face r Af = area of face f (∇ϕ )n = magnitude of ∇ϕ normal to face f V = cell volume For a steady-state analysis, the integral forms of the continuity and momentum equations are as follow: r r ∫ ρ v ⋅ dA = rr r r (F.3) r r ∫ ρ v v ⋅ dA = −∫ pI ⋅ dA + ∫τ ⋅ dA + ∫ F dV V (F.4) r where I is the identity matrix, τ is the stress tensor, and F is the force vector 164 APPENDIX F The discretization scheme applied for a scalar transport equation is also used to discretize the momentum equations The x-momentum equation for example can be obtained by setting φ = u: ) a p u = ∑ a nb u nb + ∑ p f A ⋅ i + S (F.5) nb Equation F.3 is integrated over the control volume in Fig F.1 to yield the following discrete equation: N faces ∑J f Af = (F.6) f where Jf is the mass flux through face f, ρvn B B B B Since FLUENT stores both pressure and velocity at cell centers, in order to r proceed, it is necessary to relate the face values of velocity v n , to the stored values of velocity at the cell centers Linear interpolation of cell-centered velocities to the face results in unphysical checker-boarding of pressure To prevent this FLUENT uses a procedure in which the face value of velocity is not averaged linearly; instead, momentum-weighted averaging, using weighting factors based on the ap coefficient B B from Equation F.5 is performed, by which the face flux, Jf, may be written as: B B ) J f = J f + d f ( p c − p c1 ) (F.7) where pc0 and pc1 are the pressures within the two cells on either side of the face, and B B B B ) J f contains the influence of velocities in these cells The term df is a function of a p , B B the average of the momentum equations ap coefficients for the cells on either side of B B face f The use of Equation F.7 in deriving an equation for pressure from the discrete continuity equation (Equation F.6) yields to the pressure-velocity coupling 165 APPENDIX F The SIMPLE algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field If the momentum equation is solved with a guessed pressure field p*, the resulting face flux, J*f, computed from Equation F.7 P PB B ) J ∗ f = J ∗ f + d f ( p ∗ c − p ∗ c1 ) (F.8) does not satisfy the continuity equation Therefore, a correction J’f is added to the face B B flux J*f so that the corrected face flux, Jf P PB B B B J f = J∗f + J'f (F.9) satisfies the continuity equation The SIMPLE algorithm postulates that J’f be written B B as J ' f = d f ( p' c − p ' c1 ) (F.10) where p’ is the cell pressure correction The SIMPLE algorithm substitutes the flux correction equations (Equations F.9 and F.10) into the discrete continuity equation (Equation F.6) to obtain a discrete equation for the pressure correction p’ in the cell: a p p ' = ∑ a nb p ' nb + b (F.11) nb where the source term b is the net flow rate into the cell: b= N faces ∑J * f Af (F.12) f Having solved the pressure-correction equation (Equation F.11), such as by the algebraic multigrid (AMG) method used in FLUENT, the cell pressure and the face flux are corrected using p = p ∗ + α p p' (F.13) J f = J ∗ f + d f ( p ' c − p ' c1 ) (F.14) 166 APPENDIX F where αp is the under-relaxation factor for pressure Because of the nonlinearity of the B B equation set being solved by FLUENT, it is necessary to control the change of φ By under-relaxation factor the change of φ can be controlled and in this case reduced during each iteration The corrected face flux, Jf, satisfies the discrete continuity B B equation identically during each iteration 167 [...]... called herringbone grooves Some examples of common herringbone groove patterns, as also among those used in this project are shown in Fig 1.4 The parameters of the herringbone grooved journal bearing used in this work are shown in Fig 1.5 1.2 OBJECTIVES AND SCOPE The main objectives of this work are: • To design and construct a test rig to assess the performance of vertical herringbone grooved fluid journal. .. the basis for most of the experimental journal bearing and test rig dimensions It is designed to study the effects of changing certain parameters of the herringbone grooved journal bearing on the bearing performance in terms of pressure, temperature, and leakage profiles The scope of this work includes the followings: • Design, fabrication and construction of a test rig for a vertical journal bearing... results regarding the computational estimation of the critical rotational speed in smooth or of negligible roughness and waviness of hydrodynamicaly lubricated journal bearings Recently, Jang and Yoon (2003) provided an analytical method to study the stability of a hydrodynamic HGJB They show that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing... NUMERICAL STUDIES ON HYDRODYNAMIC JOURNAL BEARING Since the exact analytical solutions for herringbone grooved journal bearings (HGJB) are not possible, the majority of published literatures involve the use of numerical or computational methods in predicting a journal bearing performance Raimondi (1961) numerically solved the Reynolds equations pertaining to the finite length journal bearing with a... aging, or degradation of acoustics due to long term running, shipping, and handling In FDB technology, the metal balls as used in the ball bearing technology are replaced with either gas or lubricating oil In a typical FDB hard disk drive motor, the spindle is supported by two hydrodynamic journal bearings and two hydrodynamic thrust bearings The hydrodynamic journal and thrust bearings are formed between... lathe out of mild steel The driving shaft housing is joined to the upper sleeve housing by three pairs of nuts and bolts Grooved Shaft U In the fabrication of the herringbone grooved shafts, plain or blank shafts were initially machined on a precision lathe, and the herringbone grooves were then machined on the shafts using a 5-axis CNC milling machine Aluminum is chosen for the material of the grooved. .. with large number of grooves and small eccentricity ratios The performance of HGJB with small number of grooves was eventually determined by Bonneau and Absi (1994) Hashimoto and Matsumoto (2001) described the optimum design methodology to improve the operating characteristics of hydrodynamic journal bearings and its application to elliptical journal bearing design used in high-speed rotating machinery... bottom of the journal bearing is removed at the end of the second minute d) The motor driver is stopped at the end of the tenth minute e) The oil container is weighed and the increase in weight is determined by subtracting the initial from the final amount of oil leakage at the bottom of the journal bearing for the two minutes period f) If another experiment needs to be conducted, a certain amount of time... distributions of Shaft 7 at six rotational speeds 129 Numerical leakage rates of Shaft 7 at six rotational speeds 129 Numerical pressure contour of Shaft 7 130 Numerical pressure distributions of Shaft 8 at six rotational speeds 131 Numerical leakage rates of Shaft 8 at six rotational speeds 131 Numerical pressure contour of Shaft 8 132 Experimental and Numerical Pressure distributions of. .. procedures of several aspects of the experimental tests This covers the necessary procedures starting from the preparation of the test rig up to actual parameters measurement Numerical simulation procedures from the geometry and mesh generation up to the calculation and post processing using the Fluent and Gambit softwares are presented in Chapter 4 The experimental and numerical results of all the journal bearings ... length of a groove set length of upper set of herringbone grooves B length of lower set of herringbone grooves B vi LAB B LJB B B B length of gap between LA and LB B B B B total effective length of. .. designed and fabricated to investigate the performance of some vertical hydrodynamic journal bearings with herringbone groove patterns on the shafts in terms of side leakage rates and axial pressure... drive motor, the spindle is supported by two hydrodynamic journal bearings and two hydrodynamic thrust bearings The hydrodynamic journal and thrust bearings are formed between a shaft and thrust-plate