Bearings for Extreme Special Environments - Part 3 Basic Performance of Ceramic (Silicon Nitride) Bearings

Transcription

1 Bearings for Extreme Special Environments - Part 3 Basic Performance of Ceramic (Silicon Nitride) Bearings H. TAKEBAYASHI * *Bearing Engineering Center, EXSEV Engineering Department Outlines of Koyo EXSEV bearing series (bearings for extreme special environments) have been explained serially from the Koyo Engineering Journal no. 156E. In this edition the basic performance of ceramic (silicon nitride) bearing is shown. That is, static load characteristics, fatigue life, the influence of scratches and flaking and fitting of ceramic bearing are described. Key Words: bearing, special environment, silicon nitride, life, performance 1. Introduction As a result of recent technological progress, the environments and conditions under which rolling bearings (hereafter referred to as bearings) are used are becoming severe and diverse. As a result, many industrial customers want to get bearings that can be used in these special environments or under such severe conditions. To respond to these demands, Koyo has produced bearings that can be used in special environments or under severe conditions. Koyo has named these bearings Koyo EXSEV Bearing for Extreme Special Environment. Beginning with the edition 156E, Koyo has presented a series of articles on bearings for extreme special environments, or Koyo EXSEV bearings. This edition will present ceramic bearings, which occupy a key position within the fields of bearings for special environments. The applicability of all types of ceramic materials for ceramic bearings, for example of silicon nitride (Si 3 N 4 ), zirconium oxide (ZrO 2 ), silicon carbide (SiC), and aluminum oxide (Al 2 O 3 ), was discussed in edition 156E. This edition will focus on silicon nitride, which shows characteristics of being the most superior bearing material amongst various ceramic materials, and will present its basic performance for application to bearings. Specifically, such subjects as static load carrying capacity, rolling contact fatigue life, influences affecting the life of surface scratches and flaking, and fitting will be discussed. 2. Silicon Nitride Materials This section will present the manufacturing process and the characteristics of silicon nitride used for bearings Manufacturing Process Fig. 1 shows the general manufacturing process for silicon nitride. If manufacturing process or conditions are different, such characteristics as density or strength will differ significantly. Therefore, each process including forming, sintering, grinding is controlled strictly in the processing of silicon nitride for bearings. Si3N4 q / Raw material power / Mixing Sintering aid w Drying and granulation e Forming r Dewaxing / / / / / / / / a Raw materials Raw materials are an α-type silicon nitride (Si 3 N 4 ) fine powder, and sintering aids. As sintering aids, aluminum oxide (Al 2 O 3 ) and yttrium oxide (Y 2 O 3 ), etc. are used. s Mixing The raw material powder added with a solvent is mixed in a ball mill. In this process, the silicon nitride powder and sintering aids are mixed into a uniform slurry. d Drying and granulation A binder is added to the slurry, and using a spray drier, the slurry is granulated to ball-shaped uniform particles. f Forming The granulated powder is charged into a molding die and is then molded by die pressing. g Dewaxing Then, the forming body is heated in a dewaxing furnace, and the binder and any other organic materials are removed. h Sintering In order to apply gas pressure thoroughly to the sintered body in the next HIP (Hot Isostatic Pressing) process, sintered body with no pores is produced in this process. j HIP Under high-temperature, and high-pressure gas atmosphere, a dense sintered body without any residual pores is obtained. k Grinding The sintered body obtained from the HIP process is ground to the specified dimension and surface roughness t Sintering y HIP u Grinding Fig. 1 Manufacturing process of silicon nitride i Inspection o KOYO Engineering Journal English Edition No.158E (2001) 53

2 needed for the final product. A diamond wheel is mainly used for grinding. l Inspection Ground surface is checked to see that there are no cracks, pinholes, or any other defect Characteristics Table 1 shows a comparison of the characteristics of silicon nitride and high carbon chromium bearing steel (SUJ2/52100). Silicon nitride has approximately 40% of the density, approximately 1.5 times the Young's modulus, and approximately 25% of the linear expansion coefficient of bearing steel. Moreover, it can be seen that the value of the fracture toughness of silicon nitride is small in comparison to that of high carbon chromium bearing steel, this means silicon nitride is a brittle material. The characteristics of silicon nitride were measured with the following methods. Density : Archimedes' method Hardness : Vickers hardness tester (JIS R1610) Young's modulus : Ultrasonic wave pulse method and Poisson's ratio (JIS R1602) Bending strength : Three point bending test (JIS R1601) Fracture toughness : IF (indentation fracture) method (JIS R1607) Ball crushing load: Method shown in Fig. 2 Table 1 Comparison of characteristics between silicon nitride and high carbon chromium bearing steel (SUJ2) Test material High carbon chromium Silicon nitride bearing steel Density, g/cm Hardness, HV Young's modulus, MPa Poisson's ratio Linear expansion coefficient, 1/; Bending strength, MPa Fracture toughness, MPa m 1/2 7 Approx. 20 Crush load for an 8mm diameter ball, kn Load Fig. 2 Test method of crushing loads Ceramic balls (silicon nitride) 3. Static Load Rating of Ceramic Bearings 1) The allowable load that can be statically loaded on rolling bearings is specified as a basic static load rating. JIS B1519 (1989), specification has defined it as "The static radial load in the center of the contact area between the rolling element and the raceway receiving the maximum load, corresponding to the calculated contact stresses shown as follows: Self-aligning ball bearings : MPa Other radial ball bearings : MPa Radial roller bearings : MPa" This is because, with the amount of permanent deformation of the rolling element and the raceway, under their contact stress, being approximately times the diameter of the rolling element, the normal revolution of the bearings becomes impossible. In other words, in steel bearings, the allowable load can be determined from the amount of permanent deformation of the bearings. In the case of bearings manufactured with brittle materials like silicon nitride, where plastic deformation cannot be expected, the JIS B1519 static load rating specification cannot be applied. It is well known that if a ball is pushed against the flat plate of a brittle material such as silicon nitride, ring cracks called as Hertz cracks will occur around the boundary of the contact area. This is caused by tensile stresses in the radial direction of the contact circle on the surfaces of the contact point. Koyo studied the static load rating of all ceramic bearings from the load at which these cracks appear Static Load Rating of All-Ceramic Bearings In this section, noticing the occurrence of cracks in silicon nitride, the static load rating was studied for an all ceramic bearing, in which silicon nitride is used for the inner and outer rings and balls (This is because if silicon nitride is loaded, cracks appear usually without the occurrence of permanent deformation.). Fig. 3 shows the measuring method of the cracking load. A silicon nitride flat plate and a silicon nitride ball were used as test materials. The cracking load was decided by detecting acoustic emissions while gradually adding a load to the test pieces. Three kinds of balls, 5/32, 5/16 and 3/8, were used in this test. Fig. 4 is a comparison of the measuring results of the cracking load of silicon nitride balls, and the static load rating for conventional steel bearing calculated at the maximum contact stress of MPa. From these results, it can be seen that the allowable loads, using cracking loads of silicon nitride rolling bearings, is considerably larger than static load ratings of steel rolling bearings. In the case of silicon nitride ball being pushed on a silicon nitride flat plate, all cracks occurred in the silicon nitride flat plate. Consequently, it can be seen that an all-ceramic bearing made of silicon nitride can well withstand the same load as the static load rating of a conventional steel bearing, and that there are no problems at all in their practical use in terms of their static load rating. 54 KOYO Engineering Journal English Edition No.158E (2001)

3 Load Table 2 Static load rating of ceramic rolling bearings Load cell Ball Flat plate Load measuring device Filter amplifier AE converter Noise eliminating equipment Filter amplifier Recorder Calculation equipment Bearing View on static load rating Koyo's static load rating All ceramic bearing Cracking load Same as that of steel bearings (SUJ2) Hybrid ceramic bearing Permanent 0.85 times that of Balls : silicon nitride deformation steel bearings (SUJ2) Inner/outer rings : SUJ2 Load, 9.8 N Fig. 3 Measuring method of the cracking loads Cracking load Steel bearing static load rating (load equaling a contact stress of MPa) (Ball diameter d) 2, mm 2 Fig. 4 Comparison of cracking load and static load rating 4. Rolling Fatigue Life of Ceramic Bearings 3) In this section, the life test results for ceramic bearings will be presented. Specifically, life test results for three types of bearings will be discussed; all ceramic bearings, hybrid ceramic bearings, and steel bearings Test Bearings and Test Methods Fig. 5 shows the dimensions of the test bearing and Table 3 shows the configurations of the test bearings. The test bearings are equivalent to 6206 deep-groove ball bearings, and the three types of bearings shown in Table 3 were used. The three types of bearings are all-ceramic bearings NC 6206, hybrid ceramic bearings 3NC 6206, and steel bearings The cage used for the three types of bearings is silver-plated AMS Nine balls with a diameter of 9.525mm are used in each bearing. The three types of bearings were manufactured so that the inner- and outer-ring raceway curvature, the roughness of the inner- and outer-ring raceways and of the balls' surface, the internal clearance of the bearings, and other features were essentially the same Views on the Static Load Rating of Ceramic Bearings Silicon nitride bearings include all-ceramic bearings, which use silicon nitride for inner and outer rings and balls, and hybrid ceramic bearings, in which inner and outer rings are made of bearing steel and balls are made of silicon nitride. Table 2 shows Koyo's views on the static load rating of ceramic bearings 2). At the moment, there are no standards established by ISO or JIS, regarding the static load rating of all-ceramic bearings. Koyo, as mentioned in the previous section, is working on the assumption that the static load rating of all-ceramic bearing will have the same value as that of conventional steel bearing (SUJ2) based on the results of the cracking load of silicon nitride balls. In addition, for a hybrid ceramic bearing, the views on the static load rating of a conventional steel bearing (JIS B1519) can be used, because the inner and outer rings made of conventional bearing steel undergo plastic deformation. As a result, Koyo proposes that the static load rating of a hybrid ceramic bearing is 0.85 times that of a conventional steel bearing. φ 62 Fig. 5 Dimensions of test bearings Outer ring Ball Cage Inner ring KOYO Engineering Journal English Edition No.158E (2001) 55

4 Type Inner and outer ring Material Ball Cage Table 3 Configurations of test bearings All ceramic bearing Hybrid ceramic bearing NC6206 3NC6206 Steel bearing M Silicon nitride AISI M50 AISI M50 Si 3 N 4 Silicon nitride Si 3 N 4 AMS6414 silver plating Silicon nitride Si 3 N 4 AMS6414 silver plating AISI M50 AMS6414 silver plating Fig. 6 shows the test equipment and Table 4 shows the test conditions. For the test, a radial life test apparatus is used. A load is added by using a coil spring, and the lubricating oil temperature is 70;. Four bearings are used at one time, and as shown in Fig. 6 the test bearings are two of these bearings at the outside edges. A failure of test bearings are detected using vibration pick up, and the equipment is designed so that if the vibration value reaches twice that of its starting value, the test equipment will shut down. In addition, the interference between the inner ring of the all-ceramic bearing and the steel shaft is about 14 µm and the circumferential stress of the bore surface of ceramic inner ring becomes about 110 MPa. Vibration pick-up 4. 2 Test Results Fig. 7 shows the life test results of three types bearings, allceramic bearings NC6206, hybrid ceramic bearing 3NC 6206, and steel bearing Two test bearings are used in one test, and the results are plotted on Weibull probability papers using the sudden death method. With a test load of N, the maximum contact stress Pmax occurring in the three types of bearings is as follows: Pmax=4.3 GPa for all-ceramic bearings, Pmax=3.8 GPa for hybrid ceramic bearing, and Pmax=3.3 GPa for steel bearings. From the results in Fig. 7, it can be seen that, although all-ceramic bearings NC 6206 and hybrid ceramic bearings 3NC 6206 have a comparatively higher maximum contact stress than steel ball bearing 6206 under the same load, they have a rolling contact fatigue life equal to or longer than that of steel bearings. Moreover, the damage form of all ceramic bearing and hybrid ceramic bearing due to rolling contact fatigue is identical in form to that of the rolling contact fatigue flaking observed with bearing steel. Consequently, the life of all-ceramic bearings and hybrid ceramic bearings can be detected by the vibration pick up in the same manner as for steel bearings. Using the above results, Koyo proposes that, in terms of the life of all-ceramic bearings and hybrid ceramic bearings, the dynamic load rating is the same value as that of steel bearings, and therefore life prediction can be conducted using the life calculation formula for steel bearings. Coil spring for load Support bearings Test bearings Coupling Fig. 6 Test method Table 4 Test conditions Condition Load, N Number of revolutions, r/m Oil Aero-Shell turbine oil#500 Temperature, ; 70±2 Test bearing NC NC6206 Cumulative fracture probability, % Number of Load, N revolutions, r/m L10 life, h L50 life, h , h Fig. 7 Life test results Weibull slope Influences of Surface Scratch and Ball Flaking on Life 4) With silicon nitride bearings, in cases where a scratch or flaking exist on the rolling surface, there is a concern about a drop in strength, reliability and this will cause catastrophic failure of the bearing within an extremely short time. 56 KOYO Engineering Journal English Edition No.158E (2001)

5 This section will introduce the results of testing the influence of a scratch on the silicon nitride flat plate on bearing life with a thrust-type bearing test equipment, and the influence of ball flaking on all-ceramic bearings life with a radial-type bearing test equipment Results of Thrust-Type Bearing Tests In this section, life tests will be performed using the silicon nitride flat plate with a linear scratch. Fig. 8 shows the linear scratch on the silicon nitride flat plate; they are 40 µm in width, and are produced by pressing a microvickers-diamond indenter into the silicon nitride flat plate, and moving the plate vertically against the device. Fig. 9 shows the test method and Table 5 shows the test conditions. The silicon nitride balls roll on the silicon nitride flat plate just on the linear scratch of the plate without fail. From the load conditions shown in Table 5, the maximum Hertz contact stress between the silicon nitride flat plate and the silicon nitride balls at this time is MPa. The vibrations during the test are measured using a vibration pickup, and the test has been designed so that if the vibration value reaches twice that of its starting value, the test will be automatically stopped. Table 6 shows the test results, and Fig. 10 shows the linear scratch area on the silicon nitride flat plate and the surface appearance of the silicon nitride balls after the test. From the test results in Table 6, it can be seen that even if a linear scratch of width 40 µm are made on the silicon nitride flat plate and life tests conducted, 250 hours running were possible. It can therefore be seen that severe damage originating from a linear scratch does not occur, and also that the vibration does not increase significantly from its starting value. Next, from Fig. 10, it can be seen that wear is occurring on both sides of the linear scratch on the silicon nitride flat plate. This wear can be considered to have occurred and advanced as a result of the silicon nitride balls repeatedly rolling back and forth on the linear scratch during the test. In addition, wear on the surface of the silicon nitride balls thought to have occurred in the same way. Table 6 Test results No. Test duration, h Test result Not completed Not completed Not completed Raceway Silicon nitride flat plate Linear scratch 40 µm 40 µm 5.7 µm Fig. 8 Linear scratch on silicon nitride flat plate Load Inner ring Silicon nitride ball alinear scratch area of silicon nitride flat plate ssurface of silicon nitride ball 11 '46 Fig. 9 Thrust-type test method Table 5 Test conditions Test plate (silicon nitride) Condition Load, N Number of revolutions, r/m Lubricating oil Aero-Shell turbine oil#500 Number of balls 3 Ball diameter 3/8" (=φ 9.525) Maximum contact stress, MPa Fig. 10 Appearance of specimen (test results) From the tests, it has become clear that if rolling life tests are conducted on a silicon nitride flat plate in which a linear scratch is present, severe damage originating from this scratch does not occur in a short period of time, and also that, wear occurs and advances on both sides of the linear scratch and on the surface of the silicon nitride balls Results of Radial-Type Bearing Tests In this section, influence on bearing life exerted by a flaked ball is presented. The test is conducted using all-ceramic bearings with a flaked ball. Fig. 5 (see Section 4. 1) shows the dimensions of the test bearings. The test bearings are equivalent to deep-groove ball bearings 6206, and are all-ceramic bearings. Nine ceramic KOYO Engineering Journal English Edition No.158E (2001) 57

6 balls are used in the bearings, one of which is a flaked ball. Fig. 6 (see Section 4. 1) and Table 4 (see Section 4. 1) show the test equipment and test conditions, respectively. The test is carried out using four bearings, only one of which is the test bearing. An accelerometer is used to measure the vibration during the test, which has been designed so that if the vibration reaches twice its starting level, the test equipment will be automatically stopped. Table 7 shows the test results and Fig. 11 shows the appearance of the flaked area of the silicon nitride ball before and after the test. As shown in Table 7, the test was conducted twice, and both times the flaked areas of the silicon nitride balls are expanded compared with their original appearances. Simultaneously, new flaking appears on the inner- or outerring raceway. However, despite conducting the test using a allceramic bearing including a flaked ball under a high load, a fatal damage such as ball fracture cannot be observed. If the flaked areas on the surface of the silicon nitride balls before and after the test in Fig. 11 are compared, it can be confirmed that the flaked areas on the ceramic ball surface are expanded after the test. Table 7 Test results 6. Fitting of Ceramic Bearings 5) It is necessary to think about two kinds of fitting: Fitting between the inner ring and the shaft; and fitting between the outer ring and the housing. For all-ceramic bearing, in the case of fitting between the silicon nitride inner ring and the steel shaft, the linear expansion coefficient of steel is four to five times greater than that of silicon nitride. Consequently, if temperature rises, the shaft expands, and there is a possibility of the silicon nitride inner ring being failed. Meanwhile, in the case of fitting between the silicon nitride outer ring and the steel housing, with an expansion of the housing an excessive clearance occurs between the outer ring and the housing, and it is possible that this will adversely affect the rotation performance of the bearing. This section will introduce the results of examining the fitting between the silicon nitride inner ring and the steel shaft, which is possibly linked to fatal damage of the bearing. First, using a silicon nitride ring and a steel shaft, the static limit of interference fit for silicon nitride ring damage will be shown, and next, using all-ceramic bearing, the dynamic limit of interference fit for the silicon nitride ring and the steel shaft during operation will be shown. No. 1 2 Starting condition One ball with flaking One ball with flaking Initial testing time, h 13 7 Test results Ball flaking progresses Inner ring flaking occurs Ball flaking progresses Outer ring flaking occurs 6. 1 Static Limit of Interference Fit A silicon nitride ring and a SUS303 steel shaft were used for fitting tests. Table 8 shows the physical properties of the silicon nitride and of the SUS303 used for the shaft. The linear expansion coefficient of SUS303 is approximately five times that of silicon nitride. Fig. 12 shows the dimensions of the silicon nitride ring, and Fig. 13 shows those of the steel shaft. Three types of shaft are used: A solid shaft, a hollow shaft, and a spline shaft. For the spline shaft, the test is designed so that the contact area between this shaft and the bore surface of the silicon nitride ring will be 30% of the surface area. Table 8 Physical properties of ring and shaft Ring Shaft HIP-Si 3 N 4 SUS303 Material Young's modulus, MPa abefore testing safter testing 1mm Poisson's ratio Linear expansion coefficient, 1/; Fig. 11 Flaked portions of silicon nitride balls before and after the test From the above result, it has been seen that if tests are conducted using a flaked silicon nitride ball, the flaked areas on the ball surface is expanded, and there is also a possibility of flaking generation in the inner- and outer-ring raceways. It has however become clear that a serious damage of the bearing (e.g. fracture of the silicon nitride ball) does not occur. In other words, in the case of all-ceramic bearings, it can be speculated that even if flaking occurs on a silicon nitride ball, this does not result in a serious damage of the bearing in a short period of time. 16 φ 38.5 Fig. 12 Dimensions of Si3N4 ring 58 KOYO Engineering Journal English Edition No.158E (2001)

7 Shaft Thermocouples Heater φ 38.5 Solid shaft Ceramic ring 16 Fig. 14 Test method Land (30%) Hollow shaft Number of teeth: 40 Spline shaft Fig. 14 shows the test method. In the test, the silicon nitride ring is fitted to the steel shaft, and this shaft is heated from both ends by heaters. Due to the difference in the linear expansion coefficients, the interference between the two components is produced, and with the rise in temperature the interference increases, finally resulting in the fracture of the silicon nitride ring. Table 9 shows the influence of the shaft types on silicon nitride ring fracture. Fifteen times tests were conducted for each type of shafts. If fracture interference values at a cumulative fracture probability of 50% are compared for the three types of shafts, it can be seen that the interference values of the hollow and spline shafts are approximately 1.3 times greater than that of the solid shaft. Consequently, it can be said that compared with a solid shaft, a hollow or a spline shaft contributes to the relief of the circumferential stress generating in the bore surface of the silicon nitride ring, and makes the fracture interference increase. For the solid shaft, the fracture interference at a cumulative fracture probability of 10% is approximately 50 µm, and the circumferential stress generating in the bore surface of the silicon nitride ring at that time is approximately 400 MPa. φ Fig. 13 Dimensions of steel shaft B10, µm Table 9 Test results B50, µm Minimum value of fracture stress, MPa Weibull Interference coefficient ratio Solid shaft Hollow shaft Spline shaft Dynamic Limit of Interference Fit The test bearings used are all-ceramic bearings NC6206, equivalent to 6206 (see Fig. 5 and Table 3). Fig. 13 (see Section 6. 1) shows the details of the fitting areas of the steel shafts. The shaft material is SUJ2 and three types of shaft are used: A solid shaft; a hollow shaft and a spline shaft. Fig. 6 (see Section 4. 1) shows the test method and Table 4 (see Section 4. 1) shows the test conditions. Four bearings are used for the test, one of which is the test bearing. From the difference between the linear expansion coefficient of silicon nitride and that of bearing steel (SUJ2 : /;), when an all-ceramic bearing is mounted, 10; temperature rise causes the interference to increase by 2.8 µm. If a test is carried out under the conditions shown in Table 4, the shaft temperature becomes 80; and the interference increase is 16.8 µm during the test. Table 10 Test results Interference, µm Solid shaft Hollow shaft Spline shaft n=1 33 (Inner ring fracture) 51 (Inner and outer ring fracture) 53 (Inner and outer ring fracture) 2 33 (Inner ring fracture) 51 (Inner ring fracture) 53 (Inner and outer ring fracture) 3 33 (Inner ring fracture) 51 (Inner and outer ring fracture) 47 (Inner ring fracture) 4 39 (Inner ring fracture) 51 (Inner and outer ring fracture) 48 (Inner and outer ring fracture) 5 38 (Inner ring fracture) 49 (Inner ring fracture) 47 (Inner ring fracture) 6 35 (Inner ring fracture) 43 (No abnormalities) 39 (No abnormalities) 7 34 (Inner ring fracture) 41 (No abnormalities) 39 (No abnormalities) 8 15 (No abnormalities) 41 (No abnormalities) 38 (No abnormalities) 9 31 (No abnormalities) 34 (No abnormalities) 38 (No abnormalities) (No abnormalities) 35 (No abnormalities) 38 (No abnormalities) (No abnormalities) 29 (No abnormalities) 30 (No abnormalities) (No abnormalities) 34 (No abnormalities) 29 (No abnormalities) Table 10 shows the test results for dynamic fitting. Interference tests are conducted using three types of shafts, in other words, interference tests were conducted with three kinds of interference. Life tests are conducted under each type of interference condition in the table, and if there are no failures, the tests are suspended after one hundred hours. Bearing damage occurs in the either form of inner ring fractures or of inner and outer ring fractures. In addition, most bearing failures occur within just one hour after the test starts. It can be considered that a fracture of the inner ring occurs KOYO Engineering Journal English Edition No.158E (2001) 59

8 first and then that of the outer ring occurs. Fig. 15 shows the typical appearance of fracture of the inner ring. The fracture appears in one area. From the test results in Table 10, it can be seen that fracture of the inner ring does not occur within an interference of 31 µm in the solid shaft, of 43 µm in the hollow shaft, and of 39 µm in the spline shaft. It is thus clear that in dynamic fitting tests too, compared to the solid shaft, the hollow and spline shafts can make the interference increase until fractures occur. References 1) T. Fujiwara, H. Takebayashi: Tribologists (Journal of Japanese Society of Tribologists) 33, 4 (1988) 55. 2) H. Takebayashi: Koyo Engineering Journal, 145 (1994) 24. 3) H. Takebayashi: Study of Ceramic Bearing for the Basic Performance and Applications, Takebayashi doctoral dissertation (1998) 31. 4) H. Takebayashi, K. Tanimoto, etc.: The Growth of the Fatigue - Flaking Spot in the Silicon Nitride Raceway Fatigue 90 (1990). 5) H. Takebayashi, K. Kitamura, T. Hattori: Tribologist (Journal of Japanese Society of Tribologists) 44, 1 (1999) 61. Fig. 15 Appearance of silicon nitride inner ring Table 11 is a summary of the interference for the solid and hollow shafts, which do not cause fracture of the inner ring, and the circumferential stress occurring in the bore surface of the silicon nitride inner ring at that time. The spline shaft is omitted because circumferential stress cannot be calculated using the formula in the strength of materials. Looking at Table 11, it can be seen that when an all-ceramic bearing is mounted in a steel shaft and then used, the circumferential stress occurring in the silicon nitride inner ring must be designed to be less than 200 MPa. Table 11 Limit of fitting Interference, µm Circumferential stress, MPa Solid shaft Hollow shaft Spline shaft Conclusion The physical as well as mechanical characteristics of ceramics are very different from those of steels. Consequently, to expand the applications of ceramic bearings, it is very important to grasp their characteristics thoroughly and to understand their merits and demerits as a bearing material. To further understand the basic properties of ceramic bearings, Koyo will continue to vigorously promote further research and development in this field. 60 KOYO Engineering Journal English Edition No.158E (2001)