TECHNICAL REPORT Research on Lubricant Leakage in Spiral Groove Bearing T. OGIMOTO T. TAKAHASHI In recent years, bearings for spindle motors have been required for high-speed rotation with high accuracy due to a remarkable improvement of storage capacity and processing speed in digital devices. In order to comply with such requirements, Spiral Groove Bearings (SGB) have been adopted in the spindle motors. Despite the excellent features, SGB has a practical problem of causing leakage of lubricants. Therefore, from the viewpoint of design, the critical issue is to establish certain countermeasures against the leakage. This paper describes the analysis focused on the tapered radial clearance, which is the main cause of the leakage, and shows that it coincides with the experimental results. Key Words: fluid dynamic bearing, radial clearance, lubricant leakage, spiral groove bearing 1. Introduction Recently, storage devices used for information devices have been remarkably improved in the storage capacity and the processing speed. In accordance with this, spindle motors have also been remarkably improved in rotational accuracy and rotational speed (example of HDD: see Fig. 1). Head Disk low NRRO. The use of oil as lubricating fluid also provides strong damping characteristic, bringing impact and vibration resistance characteristics. In spite of such superior characteristics, SGB has a practical problem of frequent leakage of lubricating oil. Thus, how to cope with the leakage has been an important issue for the design of SGB. Especially when SGB is used in HDD spindles, such leakage of lubricating oil directly results in the contamination of the magnetic head and the disc and deterioration of the bearing performance, which may cause a fatal effect to the spindle motor. In view of the above, this report describes both analytical and experimental results concerning the mechanism of lubricating oil leakage in SGB. 2. Mechanism of Lubricating Oil Leakage Fig. 1 HDD Spindle motor Conventionally, rolling bearings have been used for these spindles. However, in accordance with higher rotational speed, it has become difficult for spindles to satisfy such performance as low noise, low non-repeatable run-out (NRRO), high impact resistance, high vibration resistance, and compactness. To satisfy such requirements, a fluid hydrodynamic bearing (FDB), especially a spiral-groove bearing (SGB) using lubricating oil, which is expected to provide higher rotational accuracy, has been increasingly used. SGB is characterized in the pumping action of dynamic grooves that keeps lubricating fluid (lubricating oil) in the bearing clearance so that the perfect fluid lubrication condition (non-contact condition) is maintained without supplying lubricating oil from the outside, thus providing low noise and SGB has the structure which is self-sealed by the pumping action of dynamic grooves during operation. In spite of this self-sealing mechanism, the leakage of lubricating oil has been observed during continuous operation. Movement of lubricating oil due to its thermal expansion, posture change, or external vibration is suppressed by a capillary seal part (a sealing mechanism through the capillary phenomenon and surface tension) that is provided between the radial bearing part and the atmospheric air. Nevertheless, leakage of lubricating oil has not been prevented. The only reason was that a flow of lubricating oil was presumed, which occurred in the inside of the bearing and which was not foreseen in the design stage. 64 Koyo Engineering Journal English Edition No.165E (2004)
Though there are some factors causing the flow of lubricating oil, this report describes the inclination of the radial clearance that has been observed as the most remarkable action. Figure 2 shows the concept of the inclination of the radial clearance. When the radial clearance has an inclination, a radial hydrodynamic bearing loses the symmetry to cause the pressure generated at the clearance of the narrower side to be higher than that generated at the wider side. The difference in the generated pressure causes the flow of lubricating oil. P 3. Analysis model The analysis model of SGB used in this report is shown in Fig. 3. 3R P AgxR 4 / 3R 2 P : Pressure A : Coefficient g : Fluid viscosity x : Rotation angular velocity R : Shaft radius 3R : Bearing radial clearance Fig. 2 Lubricant flow due to tapered radial clearance P The bottom end part of the shaft has a flange, both faces of which form an axial bearing, providing a sandwich type hydrodynamic bearing with both faces having the same specifications. These hydrodynamic grooves also have a herringbone shape. There is a capillary seal part forming tapered clearance expanding from the upper radial bearing to the top end. For the purpose of analyzing the lubricating oil leakage due to the inclination of radial clearance, an analysis model only with a radial hydrodynamic bearing without an axial hydrodynamic bearing should be naturally used. However in this case, in order to convert the force of lubricating oil flow in the numerical analysis directly into the amount of the lubricating oil leakage, a number of assumptions must be made and the quantification in a verification experiment is difficult. Then, the authors noticed that when one end (axial hydrodynamic bearing side) has the sealed structure, then the flow force of the lubricating fluid in the radial hydrodynamic bearing becomes the pressure which generates in the axial direction (the atmospheric pressure for the entire axial bearing part that does not depend on the pressure generated in the axial hydrodynamic bearing), thus the floating amount in the axial direction may change. Specifically, the authors used a simple phenomenon in which higher pressure in the entire axial bearing causes the shaft to move upward by the difference in the projected areas sandwiching the flange, while negative pressure in the entire axial bearing causes the shaft to have a contact with the lower part for the same reason. Figure 4 shows the outline of this phenomenon. Capillary seal part Shaft Flow of lubricating oil Sleeve Upper Radial hydrodynamic grooves (herringbone) Lower Shaft flange Negative pressure Direction of force by difference in projected areas Positive pressure Fig. 4 Lubricant flow and force direction due to differencein projection areas Axial hydrodynamic grooves (herringbone) Thrust plate Fig. 3 Analysis model This SGB is the shaft rotation type in which two upper and lower parts of the rotation axis (shaft) have radial bearing parts, the hydrodynamic grooves of which have symmetric herringbone shape. Thus, by use of this model, a numerical analysis can be easily performed and also reliable verification measurements become possible because the leakage amount of lubricating oil is not measured directly but can be measured as the displacement in the axial direction. Bearing specifications of this model are shown in Table 1. Koyo Engineering Journal English Edition No.165E (2004) 65
Radial Axial Table 1 Specifications of analyzed SGB Shaft diameter: D u3.5mm Groove type Symmetric herringbone Groove depth / clearance 1 Groove angle 20 Bearing width at upper part / D 0.9 Bearing width at lower part / D 0.7 (Average) clearance h Bearing outer diameter 6.0mm Bearing inner diameter 4.0mm Groove type Herringbone Groove depth (same for both faces) 0.006mm Groove angle 14 Number of grooves 20 Clearance 0.014mm 5. Verification Method With regards to the analysis model, the relation between the inclination amount of the radial bearing and the axial displacement amount was measured by an experiment to verify the analysis result. 5. 1 Identification Method of Bearing Clearance Inclination Figure 6 shows the schematic diagram of clearance. The bearing clearance can be obtained by the difference between the measured values of the sleeve inner diameter and the shaft outer diameter. But the inclination is not necessarily linear. Therefore, the bearing clearance at each position obtained by equally dividing the bearing width into seven parts was respectively plotted. The inclination amount was obtained from the least-squares approximation straight line of the data and the clearance in the center of the grooves was used as the average clearance of the bearing. 4. Analysis Method The analysis was performed by using Control Volume Method (Finite Volume Method) 1) frequently used as a fluid analysis system. In the analysis method, one radial hydrodynamic bearing was divided at the center of the herringbone and each divided part was provided with predetermined clearance and clearance inclination. Then, the generated pressure was calculated and the difference in generated pressure was assumed to be the pressure causing the flow in the axial direction. Figure 5 shows an example of the distribution of pressure generated in the radial clearance obtained by Control Volume Method. Fig. 5 Pressure distribution of radial clearance by control volume method Next, the same calculation was performed for an axial hydrodynamic bearing. The balanced clearance considering the weight of a rotation body of the sandwiching axial hydrodynamic bearing was calculated. Based on this balanced clearance, the displacement amount of the rotation body in the axial direction was calculated considering the force by the clearance inclination in a radial hydrodynamic bearing (pressure difference in the projected area). Inclination amount Bearing clearance Average clearance, h Approximation straight line Groove center position Radial bearing part Fig. 6 Schematic diagram of tapered clearance Position measured 5. 2 Verification Sample Table 2 shows the specifications of verification samples using the inclination amount identified by the above-described method as parameters. Upper and lower radial bearing inclination amounts were changed from h/3 to +h/3 with the unit of h/12 and the average clearance was fixed as "h" in order to clarify the effect only by the inclination. The inclination direction along which the clearance increased in the lower direction (shaft flange side) was defined as "+" while an inclination direction along which the clearance increased in the upper direction (capillary seal side) was defined as "." Table 2 Configurations of investigated SGB No. Inclination amount of clearance Upper side Lower side 1~8 h/3~+h/3 0 9 0 0 10~17 0 h/3~+h/3 66 Koyo Engineering Journal English Edition No.165E (2004)
5. 3 Measuring Method of Axial Displacement As the shaft was rotated by an air turbine, the axial displacement amount was defined as the displacement amount of an air turbine from the stoppage point, which was measured by a non-contact displacement apparatus. The total weight of the shaft and the turbine corresponds to the weight of the rotation body in the analysis model. Basically, in order to verify the influence only by the flow of the lubricant, the weight of the rotation body is to be omitted. However, measurement with the rotation body weight of 0 (zero) was practically difficult. Therefore, axial displacement amounts in both positive and negative postures were measured and compared. Figures 7(a) and 7(b) show the measurement method by the driven air turbine and the displacement amount in the axial direction, respectively. Depth of oil level Change of lubricating oil amount Laser displacement gauge (KEYENCE LT-8110) Air spindle Detent Sample measured Capacitance sensor (IWATSU ST-0507) Air turbine Turbine weight : 100 gf Rotational speed: 5 000 min 1 Fig. 8 Measurement of lubricant volume fluctuation in capillary seal area 6. Analysis and Experiment Result Chuck Sample measured (a) Measurement method by driving of air turbine Displacement amount at positive posture Displacement amount at negative posture (b) Displacement amount in axial direction Fig. 7 Measurement method of axial displacement 5. 4 Observation of Leakage of Lubricating Oil Generally, the capillary seal part retains a predetermined amount of lubricating oil. However, when the lubricating oil begins to leak, the amount of this lubricating oil in the capillary seal part increases. And when this amount of lubrication oil exceeds the capacity of the capillary seal part, then oil leaks out in the end. In this observation, the increased amount of the lubricating oil in the capillary seal part was observed as v when the shaft was fixed and the sleeve was rotated by an air spindle with 5 000 min 1 for 30 seconds. The amount of the lubricating oil in the capillary seal part was calculated by using a laser displacement apparatus to measure the depth of the surface level of the lubricating oil. Figure 8 outlines the measurement method of the oil level depth when the shaft was rotating (measuring the change of the lubricating oil amount in the capillary seal part). Figures 9(a) and (b) show the relation between the inclination amount of radial clearance and the amount of axial displacement obtained by the numerical analysis of Control Volume Method, and the result of the verification experiment, respectively. Figures 9(a) and (b) indicate the relation between the inclination of the upper radial clearance and the amount of axial displacement, and the inclination of the lower radial clearance inclination and the amount of axial displacement, respectively. The increased amount of lubricating oil v from the inclination of the radial clearance is also shown above the amount of axial displacement in the figures. Most of the analysis results correspond to the verification experiment results. The amount of axial displacements inverted in symmetry between the positive posture and negative posture at the radial clearance inclination of "0." As a result, the inclination of radial clearance, on which the authors focused as a factor of the lubricating oil leakage, turned out to be the cause that breaks the symmetry of a radial bearing leading to the difference in generated pressure and resulting in the flow of the lubricating oil. Discrepancy between the analysis result and the verification experiment result at the negative clearance inclination ( h/6 or less) almost corresponds to the appearance of the increase of the lubricating oil amount (rising amount). This considered to be caused by the axial hydrodynamic bearing part having negative pressure to involve air into the bearing, resulting in the rise in the lubricating oil level. Thus, it is naturally assumed that the discrepancy of the axial displacement amount is caused between the verification experiment and the analysis result in which such gas-liquid condition cannot be taken into consideration. A larger discrepancy for the negative posture also can be explained by the negative posture that tends to involve air in the bearing than in the case of the positive posture (because air is light and tends to move upward). Koyo Engineering Journal English Edition No.165E (2004) 67
v, ml Axial displacement, lm 1.00 0.60 0.20 0.20 14.0 12.0 10.0 8.0 6.0 4.0 2.0 (experiment value) (experiment value) s The value of the difference in the generated pressure can be obtained by numerical analysis and thus can be easily presumed. Therefore, it was clarified that contrivance in the design and/or the dimensional accuracy limitation in machining could provide fluid hydrodynamic bearings having no leakage of lubricating oil. Reference 1) Suhas V. Patankar: Numerical Heat Transfer and Fluid Flow, hemis phere Publishing Co., (1980). 0.0 h/3 h/4 h/6 h/12 0 h/12 h/6 h/4 h/3 Inclination of radial clearance (a) Upper side v, ml 1.00 0.60 0.20 0.20 14.0 12.0 (experiment value) (experiment value) Axial displacement, lm 10.0 8.0 6.0 4.0 2.0 0.0 h/3 h/4 h/6 h/12 0 h/12 h/6 h/4 h/3 7. Conclusion Inclination of radial clearance (b) Lower side Fig. 9 Relationship between tapered radial clearance and axial displacement With regards to the lubricating oil leakage that may decide the possibility of practical application of the fluid hydrodynamic bearing, this report described, by providing the test with dozens of parameters and various analyses, the inclination of radial clearance that is the most remarkable influence on such leakage and that may cause a fatal defect. Main results in this report are summarized as shown below. a The inclination of clearance breaks the symmetry in the radial hydrodynamic bearing, which causes the difference in the generated pressure and the flow in the lubricating oil, thus causing the leakage of the lubricating oil. T. OGIMOTO * T. TAKAHASHI * * Analysis Engineering Department, Bearing Business Operations Headquarters 68 Koyo Engineering Journal English Edition No.165E (2004)