LIQUID - LUBRICATED SPIRAL-GROOVE BEARINGS*) BY J. BOOTSMA *) Thesis, Technological University Delft, 19 november 1975. Promotor: Prof. Dr Ir E. A. Muijderman. Philips Res. Repts Suppl. 1975, No. 7.
CONTENTS 1. GENERAL INTRODUCTION 1 1.1. The operation of spiral-groove bearings 1 1.2. A survey of the literature 3 1.3. The aim of the present investigation 5 References 7 2. DIFFERENTIAL EQUATION FOR THE SMOOTHED PRES SURE 9 2.1. Introduction 9 2.2. The Reynolds equation 9 2.3. Derivation of the differential equation for the smoothed pressure, in generalised coordinates 12 2.4. The general differential equation for the smoothed pressure.. 18 2.5. The differential equation for the smoothed pressure under stationary operating conditions 20 2.6. Discussion 21 2.6.1. The derivation of the smoothed-pressure equation.... 21 2.6.2. Finite number of grooves 22 2.6.3. Difference between grooves in the rotating member and grooves in the non-rotating member of the bearing... 24 2.6.4. Half-w whirl 25 References 26 3. SPIRAL-GROOVE BEARINGS IN CONCENTRIC OPERATING CONDITIONS 28 3.1. Introduction 28 3.2. Axial load capacity, axial stiffness, and frictional losses of flat, conical, and spherical bearings 28 3.3. Optimisation 31 3.3.1. Optimisation with respect to load capacity P z and film thickness h r 31 3.3.2. Optimisation with respect to axial stiffness of a bearing without a prescribed P z 32 3.3.3. Optimisation with respect to axial stiffness of a bearing with a prescribed P z 32 3.3.4. Load capacity P z, as h r -> 0, and take-off velocity co t.. 33 3.3.5. Frictional losses 35 3.3.6. Example of a calculation 36
Appendix ЗА 37 Appendix ЗВ 47 References 48 4. THEORY OF SPIRAL-GROOVE JOURNAL BEARINGS... 49 4.1. Introduction 49 4.2. Basic equations 51 4.2.1. Differential equation 51 4.2.2. Boundary conditions 53 4.2.3. Rupture of lubricating film 54 4.2.4. Load capacity 55 4.3. Determination of pressure distribution and load capacity... 56 4.3.1. Perturbation method 57 4.3.2. Numerical method 60 4.3.3. Comparison of the results of the two approximation methods 63 4.4. Stability 66 4.4.1. Stability criterion for unloaded bearings 66 4.4.2. The effect of the free boundary on the stability 67 Appendix 4A 73 Appendix 4B 81 Appendix 4C 85 References 87 5. LOAD CAPACITY, FRICTIONAL LOSSES, AND STABILITY OF SPIRAL-GROOVE JOURNAL BEARINGS 88 5.1. Introduction 88 5.2. Completely herringbone-grooved journal bearing 90 5.2.1. Comparison of load capacity of a completely herringbonegrooved journal bearing and a plain journal bearing.. 90 5.2.2. Optimisation of groove parameters with respect to stiffness 91 5.2.3. Load capacity, frictional losses, and stability as functions of groove and bearing parameters 91 5.2.4. The effect of the width of the bushing on the load capacity of bearings with a free boundary 98 5.2.5. Scheme of calculation 99 5.3. Partially grooved journal bearings 102 5.4. Spiral-groove journal bearings with a dead-end cavity 104 5.5. Spiral-groove journal bearings with net axial flow of lubricant.. 107 5.6. Viscous-screw pump 109 References 112
6. SPHERICAL AND CONICAL SPIRAL-GROOVE BEARINGS.. 113 6.1. Introduction 113 6.2. Theory 113 6.2.1. Differential equation and boundary conditions 113 6.2.2. Perturbation method '. 116 6.2.3. Accuracy of the results 124 6.3. Load capacity, stiffness, and frictional losses of spherical and conical bearings with a completely filled bearing gap 126 6.4. Stability 131 6.5. Comparison of bearing characteristics of spiral-groove spherical conical, and journal bearings 134 6.6. Summary and possible further investigations 136 Appendix 6A 137 Appendix 6B 138 References 142 7. EXPERIMENTS WITH SPIRAL-GROOVE JOURNAL BEAR INGS 143 7.1. Introduction 143 7.2. Test arrangements 143 7.3. Spiral-groove journal bearings with free boundary 145 7.3.1. Shape of interface independent of surface tension and forces of inertia 145 7.3.2. The shape of the free boundary 146 7.3.3. Load capacity and attitude angle 147 7.4. Grooves in the housing or in the shaft 149 7.4.1. Journal bearing with a free boundary 149 7.4.2. Journal bearing with fixed boundary 150 7.5. Stability 151 7.6. Summary 153 8. NO-LEAKAGE CONDITIONS OF SELF-SEALING HERRING BONE JOURNAL BEARINGS 154 8.1. Introduction 154 8.2. Leakage in conditions of concentric operating 154 8.2.1. Experimental results 154 8.2.2. Discussion of experimental results 162 8.3. Leakage in conditions of eccentric operating 169 8.4. Air ingestion 171 8.5. Grease-lubricated herringbone journal bearings 173 8.6. Some theoretical considerations 173
8.6.1. Breakdown of air-to-liquid interface in ungrooved section 174 8.6.2. Leakage starting along plain bearing face 178 8.7. Summary 180 References 181 List of symbols 183