5 Bearing Preload and Rigidity

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1 Technology>Precision>Innovation outer ring. 2)The contact surface pressure on the raceway surface reaches 4200Mpa or 428kgf/mm2 in either the inner or outer ring raceway. The allowable axial loa for each bearing is foun in the precision bearing tables. 4.5 Bearing life for high spee application For high spee applications, the effects of ball centrifugal forces an gyroscopic moments nees to be inclue. The force an moment equilibrium equations for the bearing inner ring are solve for the bearing axial, raial, an angular e ections. If the bearing has a complement of Z balls, then a system of 4Z+5 equations is solve numerically using the Newton-Raphson metho. For the analysis incluing the etermination of ball friction forces an spees, in aition to the 5 force an moment loa equilibrium equations for the inner ring, the torques acting on the cage in the plane of bearing rotation is balance, an cage spee is etermine. In this case a system of 9Z+6 equations are solve numerically. TPI's HSE high spee type angular contact ball bearings are optimally esigne with their internal con guration to accommoate both low frictional 24 heat or ball skiing effect an high rigiity by using TH-BBAN. 4.6 Life for hybri bearings When calculating the rating life for hybribearings, the same life values can be use as for all-steel bearings. The ceramic balls in hybri bearings are much harer an stiffer than the all-steel bearings. Although this increase level of harness an stiffness creates a higher egree of contact stress between the ceramic ball an the steel raceway, extensive experience an testing shows that in typical machine tool applications, the service life of a hybri bearing is signi cantly longer life than that of an all-steel bearing. The reasons for this are: 1) low ensity minimizes centrifugal an inertial forces; 2) low surface ahesive wear is reuce by the lower af nity to steel; an 3) better surface nish enables the bearing to maximize the effects of the lubricant. References R. Barnsby, T. Harris, E. Ioannies, W. Littmann, T. Loesche, Y. Murakami, W. Neeelman, H. Nixon, an M. Webster, "Life Ratings for Moern Rolling Bearings", ASME Paper 98-TRIB-57 (October 26, 1998). 5 Bearing an 5.1 Stiffness of spinle System rigiity in machine tool applications is extremely important because the magnitue of e ection uner loa etermines machining accuracy. Bearing stiffness is only one factor that in uences system stiffness, others inclue shaft iameter, tool overhang, housing stiffness number, position an type of bearings. For axial stiffness of spinles, bearing stiffness plays an important role of it. Giving preloa to a bearing results in the rolling element an raceway surfaces being uner constant elastic compressive forces at their contact points. This has the effect of making the bearing extremely rigi so that even when loa is applie to the bearing, raial or axial shaft isplacement oes not occur. If high raial rigiity of bearing is neee, cylinrical roller bearings are normally use. In contrast to angular contact ball bearing, they provie more surface contact an gross sliing an are not suitable for very high spee applications. For axial loaing applications, angular contact ball bearings are normally use. Their larger contact angle type provie higher axial rigiity. The stiffness of this type also epens on number an size of balls. Recently, the ceramic material silicon nitrie Si3N4 is use for precision ball bearings. The raial rigiity of this hybri bearings is approximately 15% higher because of the higher Young s moulus. As mentione in 4.5, TPI s HSE type angular contact ball bearings are optimally esigne with their internal con guration to accommoate both low ball skiing effect an high rigiity by using TH-BBAN. 5.2 Bearing preloa The preloa metho is ivie into xe position preloa an constant pressure preloa as shown in Fig The xe position preloa is effective for positioning the two bearings an also for increasing the rigiity. Due to the use of a spring for the constant pressure preloa, the preloaing amount can be kept constant, even when the istance between the two bearings uctuates uner the in uence of operating heat an loa. Fig. 5.1 ing methos for bearings T. A. Harris an M. H. Kotzalas, "Rolling Bearing Analysis: Avance Concepts of Bearing technology", pp.209~258, 5th E., CRC Press, (2007). 18 Precision Rolling Bearings

2 The increase rigiity effect preloaing has on bearings is shown in Fig When the offset inner rings of the two paire angular contact ball bearings are presse together, each inner ring is isplace axially by the amount o an is thus given a preloa, F 0, in the irection. Uner this conition, when external axial loa F a is applie, bearing I will have an increase isplacement by the amount a an bearing II s isplacement will ecrease. At this time the loas applie to bearing I an II are F I an F II, respectively. Uner the conition of no preloa, bearing I will be isplace by the amount b when axial loa F a is applie. Since the amount of isplacement, a, is less than b, it inicates a higher rigiity for a.. When external axial loa F a keeps increasing until b equals to 0, that is, F II =0 or F I =2.83 F 0. Now, bearing II becomes release from preloa while bearing I is loae with 2.83 times of given preloa F 0. This amount of loa is calle the limiting axial loa an it may epen on bearing arrangement an contact angle. Fig. 5.2 Fixe position preloa versus axial isplacement spee, rigiity an heat generation. It is also neee to be aware that the proper preloa uring high spee operation is important. Fig. 5.3 shows the factors may lea to preloa change after installation an uring operation. Among those factors, TPI may provie face sie offset increase ue to interference t between inner an shaft. Please contact TPI for further information. There are four stanar preloas :L(Light preloa), N(Normal preloa), M(Meium preloa), an H(Heavy preloa). These preloa from light to heavy have certain ratio of ynamic basic loa rating C r. Table 5.1 is the preloa comparison table of TPI bearings with other bran bearings for 7014C angular contact ball bearings. It is note that preloa setting methos may be ifferent for other bran bearings. Table 5.9 shows stanar preloa, rigiity,an measure face sie offset in DB an DF arrangement of various series of angular contact ball bearings. To stabilize the measurement of face sie offset, measuring loa is usually axially applie an liste in Table 5.2. As shown in Fig. 5.2, the true face sie offset is -2 0, while the measure face sie offset in DB an DF arrangement as shown in Table 5.9 is compensate with measuring loa. The positive an negative signs are e ne in Appenix IV. Table 5.10 shows stanar preloa an rigiity in DB an DF arrangement of HTA an BS series of angular contact ball bearings. Fig. 5.3 setting stuy ow Table 5.1 preloa comparison table of TPI bearings with other bran bearings for 7014C Bearing stanar preloa Universal combination bearings an matche bearing sets are prouce in four ifferent stanar preloa to meet the varying requirements incluing rotational Bran TPI NTN NSK FAG SKF Remark Light L(0.3) L(0.2) EL(0.3) A(0.3) Mormal N(0.6) N(0.6) L(0.6) L(0.6) B(0.8) Meium M(1.6) M(1.2) M(1.6) M(1.8) C(1.5) Heavey H(3.1) H(3.1) H(3.8) 7014C for instance, 0.3 in ( ) means 0.3% C r 19

Technology>Precision>Innovation Table 5.2 Measuring loa of face sie offset Nominal Outsie Diameter D Over Incl. Measuring loa 10(incl.) 50 24.

3 Technology>Precision>Innovation Table 5.2 Measuring loa of face sie offset Nominal Outsie Diameter D Over Incl. Measuring loa 10(incl.) In the case of DT arrangement, it is necessary to remember that axial e ection a of the combination bearings uner preloa is less that of in DB an DF arrangement. Therefore, this ifference has to be consiere to the value of with reuction of spacer for altering preloa as shown in Table Iniviual ajustment of preloa In case where universal combination bearings or matche bearing sets are use, preloa is etermine at the factory uring prouction. In some cases, however, it may be necessary to optimize the preloa to accommoate operating conitions. It is possible to increase or ecrease preloa by using spacer rings between the bearings. For instance, in DB arrangement, reuce with of outer spacer rings shoul ecrease preloa while reuce with of inner rings shoul increase preloa. In DF arrangement, reuce with of outer spacer rings shoul increase preloa while reuce with of inner rings shoul ecrease preloa as shown in Fig By grining the sie face of the inner or outer spacer the preloa in the bearing set can be change. In these cases, the bearings shoul not be moi e, as this requires special tools, an the bearings coul be amage. Table 5.3 provies information about which of the equalwith spacer ring sie faces must be groun an what effect it will have. Table 5.9 contains the necessary imensional eviation for the overall with of the spacer rings from eviation of measure face sie offsets between two ifferent stanar preloas(positive value). Table 5.3 Necessary spacer ring with reuction change N(Normal preloa)-> L(Light preloa) N(Normal preloa)-> M(Meium preloa) N(Normal preloa)-> H(Heavy preloa) With reuction (positive value) ( L preloa)-(n preloa) (M preloa)-(n preloa) (H preloa)-(n preloa) Effect Decrease preloa Increase preloa Increase preloa Table 5.4 Axial e ection for No. of row in DT arrangement No. of row in DT Axial e ection a 0.63 a 0.48 a 0.40 a However, it is not necessary to etermine axial eflection although it can be calculate once bearing arrangement an contact angle(incluing mixe contact angle) are esignate for applications. As long as the bearing preloa provies suf cient system stiffness, the resulting preloa can be etermine by a factor for its bearing arrangement as shown in Table 5.5. The value of resulting preloa P r is N where can be obtaine in Table 5.9 Table 5.5 Factor P 1 for ifferent bearing arrangements Arrangement Factor P 1 DB 1.00 DBT 1.35 DTTB 1.60 DTBT 2.00 Fig. 5.4 Increase or ecrease preloa by ajusting spacer ring with 5.3 of angular contact ball bearing 20 Increase preloa(db) Increase preloa(df) Decrease preloa(db) Decrease preloa(df) Precision Rolling Bearings Elastic eformation in rolling bearings results in the rings being isplace relative to each other. For angular contact ball bearings, the following formula is use to calculate this relative isplacement in a raial an axial irection: where r :raial isplacement uner pure raial loa, mm

4 a :axial isplacement uner pure axial loa, mm F r : pure raial loa, kgf F a : pure axial loa, kgf i : No. of row Z : No. of balls per row D w : ball pitch iameter, mm : contact angle, egrees In Table 5.9, the (axial) rigiity is e ne as the external axial loa of a bearing set in DB or DF arrangement, which causes a e ection of 1 micron of the bearing rings to each other. Before reaching to limiting axial loa, bearing rigiity can is consistently measure an the result is close to the calculate value uner light an normal preloa. However, for bearings uner meium an heavy preloa, the calculate value becomes oubtable because change of initial an nal contact angles. The above formula for raial an axial isplacements is not vali uner heavy loa an nee more rigorous analytical computer program such as TH- BBAN program to solve it. Raial rigiity varies with contact angle an preloa. In contrast to the axial rigiity, raial rigiity ecreases as contact angle increases an changes markely as a function of the ratio between axial an external loas applie to the bearing. In practical manner, the raial an axial rigiity are etermine as follows. factors with various arrangements, contact angle, an preloa in the formula can be obtaine in Table 5.6 an 5.7. R r = q 1 q2 R a R a = q 1 N/ m Table 5.7 factor for bearings with various Conatct angle arrangement an preloa q 2 15 o o o o Limiting Axial Loa Limiting axial loa is the external axial loa of a preloae bearing pair or set that causes loss of contact between the balls an race in preloa bearings. This effect may lea to balls skiing against the raceways an surface amage. In some machine tools applications, where the working axial loa is preominantly in one irection, limiting axial loa can be increase by using a bearing set with a mixe contact angle. The axially more rigi bearing withstans the work loa an the less rigi one is the reaction element. Table 5.8 is a example to aress the above concept. Compare to the bearing set with same contact angle, the bearing set with a mixe contact angle of 15 an 25 egrees withstans higher 5.9 times of axial preloa loa ( compare to 2.83 times of preloa). Furthermore, it coul be consier that increasing their contact angle by 3~5 egree, bearings withstan their axial loa may have 16 ~32% more limiting axial loa an axial stiffness as well. where, q 1 : rigiity factor for bearing arrangement, please refer to Table 5.6 q 2 : rigiity factor for contact angle an preloa, please refer to Table 5.7 Table 5.6 factor for bearings with various arrangements q 1 Arrangement Raial factor q 1 Axial factor q 1 DB DBT DTBT Table 5.8 Limiting axial loa of bearings with an equal/a mix contact angle an various arrangements Arrangement contact angle 1:bearing withstans axial loa;2:bearing paire to bearing 1 Limiting axial loa Unit, P 1 P 2 P 1 P 2 DB DBT DTBB DTBT

5 Technology>Precision>Innovation Table 5-9(1) an (DB an DF Arrangement) of 70C stanar series Bearing an Face Sie 7000C (2) (-2) (-10) (-19) 7001C (2) (-2) (-10) (-19) 7002C (1) (-3) (-11) (-19) 7003C (1) (-3) (-11) (-19) 7004C (-2) (-6) (-17) (-28) 7005C (-2) (-6) (-17) (-28) 7006C (0) (-5) (-16) (-28) 7007C (-1) (-6) (-19) (-32) 7008C (-1) (-7) (-19) (-31) 7009C (-2) (-8) (-21) (-35) 7010C (-3) (-8) (-21) (-34) 7011C (-5) (-11) (-26) (-42) 7012C (-5) (-11) (-26) (-41) 7013C (-5) (-11) (-26) (-41) 7014C (-7) (-14) (-30) (-48) 7015C (-7) (-14) (-30) (-47) 7016C (-5) (-13) (-32) (-51) 7017C (-5) (-13) (-31) (-50) 7018C (-7) (-16) (-36) (-58) 7019C (-7) (-15) (-36) (-57) 7020C (-6) (-15) (-35) (-56) (70 series C angle:15 nominal contact angle, steel ball) Table 5-9(2) an (DB an DF Arrangement) of 70AD stanar series Bearing an Face Sie 7000AD (0) (-2) (-9) (-16) 7001AD (0) (-2) (-9) (-16) 7002AD (0) (-3) (-9) (-16) 7003AD (0) (-3) (-9) (-16) 7004AD (-2) (-5) (-13) (-21) 7005AD (-2) (-5) (-13) (-21) 7006AD (-1) (-4) (-13) (-22) 7007AD (-2) (-5) (-15) (-24) 7008AD (-2) (-5) (-14) (-24) 7009AD (-2) (-6) (-16) (-26) 7010AD (-2) (-6) (-16) (-26) 7011AD (-4) (-8) (-19) (-31) 7012AD (-4) (-7) (-19) (-30) 7013AD (-4) (-7) (-18) (-30) 7014AD (-5) (-9) (-22) (-35) 7015AD (-5) (-9) (-21) (-34) 7016AD (-4) (-9) (-23) (-37) 7017AD (-4) (-9) (-22) (-37) 7018AD (-5) (-10) (-26) (-42) 7019AD (-5) (-10) (-25) (-41) 7020AD (-5) (-10) (-25) (-41) (70 series AD angle:25 nominal contact angle, steel ball) 22 Precision Rolling Bearings

6 Table 5-9(3) an (DB an DF Arrangement) of 5S-70C stanar series Bearing an Face Sie 5S1-7000C (1) (-3) (-11) (-20) 5S1-7001C (1) (-3) (-11) (-20) 5S1-7002C (0) (-3) (-12) (-20) 5S1-7003C (0) (-4) (-12) (-20) 5S1-7004C (-2) (-7) (-18) (-29) 5S1-7005C (-3) (-7) (-18) (-28) 5S1-7006C (-1) (-6) (-17) (-29) 5S1-7007C (-2) (-7) (-20) (-33) 5S1-7008C (-2) (-8) (-20) (-32) 5S1-7009C (-3) (-9) (-22) (-36) 5S1-7010C (-4) (-9) (-22) (-35) 5S1-7011C (-5) (-12) (-27) (-43) 5S1-7012C (-5) (-12) (-27) (-42) 5S1-7013C (-5) (-12) (-26) (-41) 5S1-7014C (-7) (-15) (-31) (-49) 5S1-7015C (-7) (-15) (-31) (-48) 5S1-7016C (-6) (-14) (-33) (-52) 5S1-7017C (-6) (-14) (-32) (-51) 5S1-7018C (-7) (-17) (-37) (-58) 5S1-7019C (-7) (-17) (-37) (-58) 5S1-7020C (-7) (-16) (-36) (-57) (5S-70 series C angle:15 nominal contact angle, ceramic ball) Table 5-9(4) an (DB an DF Arrangement) of HSECE1 stanar series Bearing an Face Sie HSE000CE (5) (3) (-1) (-5) HSE001CE (5) (3) (-1) (-5) HSE002CE (4) (2) (-3) (-7) HSE003CE (3) (2) (-3) (-7) HSE004CE (2) (0) (-5) (-11) HSE005CE (2) (0) (-5) (-11) HSE006CE (3) (-1) (-8) (-17) HSE007CE (2) (-2) (-11) (-20) HSE008CE (1) (-2) (-11) (-20) HSE009CE (1) (-3) (-10) (-20) HSE010CE (0) (-4) (-12) (-23) HSE011CE (0) (-3) (-12) (-22) HSE012CE (0) (-3) (-12) (-22) HSE013CE (-1) (-5) (-14) (-24) HSE014CE (-1) (-5) (-15) (-27) HSE015CE (-2) (-6) (-16) (-27) HSE016CE (0) (-5) (-16) (-29) HSE017CE (0) (-5) (-16) (-29) HSE018CE (0) (-5) (-16) (-28) HSE019CE (-1) (-7) (-20) (-34) HSE020CE (-1) (-7) (-19) (-33) (HSE series CE1 angle:18 nominal contact angle, steel ball) 23

7 Technology>Precision>Innovation Table 5-9(5) an (DB an DF Arrangement) of 5S-HSECE1 stanar series Bearing an Face Sie 5S1-HSE000CE (4) (2) (-2) (-6) 5S1-HSE001CE (4) (2) (-2) (-6) 5S1-HSE002CE (3) (1) (-3) (-8) 5S1-HSE003CE (3) (1) (-3) (-8) 5S1-HSE004CE (1) (-1) (-6) (-11) 5S1-HSE005CE (1) (-1) (-6) (-11) 5S1-HSE006CE (2) (-2) (-9) (-18) 5S1-HSE007CE (1) (-3) (-11) (-21) 5S1-HSE008CE (0) (-3) (-11) (-21) 5S1-HSE009CE (0) (-3) (-11) (-21) 5S1-HSE010CE (-1) (-4) (-13) (-24) 5S1-HSE011CE (-1) (-4) (-13) (-23) 5S1-HSE012CE (-1) (-4) (-13) (-22) 5S1-HSE013CE (-1) (-5) (-14) (-25) 5S1-HSE014CE (-2) (-6) (-16) (-27) 5S1-HSE015CE (-3) (-6) (-16) (-28) 5S1-HSE016CE (-1) (-6) (-17) (-30) 5S1-HSE017CE (-1) (-6) (-17) (-30) 5S1-HSE018CE (-1) (-6) (-17) (-29) 5S1-HSE019CE (-2) (-7) (-20) (-34) 5S1-HSE020CE (-2) (-7) (-20) (-34) (HSE series CE1 angle:18 nominal contact angle, ceramic ball) Table 5-9(6) an (DB an DF Arrangement) of 72C stanar series Bearing an Face Sie 7200C (2) (-2) (-10) (-19) 7201C (1) (-4) (-14) (-24) 7202C (-1) (-5) (-17) (-28) 7203C (-2) (-7) (-20) (-32) 7204C (-3) (-9) (-23) (-36) 7205C (0) (-6) (-19) (-32) 7206C (-2) (-9) (-24) (-40) 7207C (-5) (-12) (-30) (-48) 7208C (-6) (-14) (-33) (-51) 7209C (-7) (-16) (-35) (-55) 7210C (-7) (-16) (-35) (-55) 7211C (-9) (-18) (-40) (-62) 7212C (-11) (-21) (-45) (-69) 7213C (-12) (-23) (-47) (-72) 7214C (-8) (-20) (-45) (-72) 7215C (-9) (-20) (-45) (-71) 7216C (-10) (-22) (-49) (-78) 7217C (-11) (-24) (-51) (-80) 7218C (-14) (-28) (-59) (-91) 7219C (-16) (-31) (-64) (-98) 7220C (-17) (-33) (-69) (-106) (72 series C angle:15 nominal contact angle, steel ball) 24 Precision Rolling Bearings

8 Table 5-10(1) an (DB an DF Bearing Number Arrangement) of HTA A stanar series Bearing M H HTA010A DB HTA011A DB HTA012A DB HTA013A DB HTA014A DB HTA015A DB HTA016A DB HTA017A DB HTA018A DB HTA019A DB HTA020A DB Table 5-10(2) an (DB an DF Arrangement) of HTA B stanar series Bearing Number Bearing M H HTA010B DB HTA011B DB HTA012B DB HTA013B DB HTA014B DB HTA015B DB HTA016B DB HTA017B DB HTA018B DB HTA019B DB HTA020B DB Table 5-10(3) an (DB an DF Arrangement) of BS stanar series Bearing BS BS BS BS BS Lubrication of Bearings The purpose of bearing lubrication is to prevent irect metal to metal contact between the various rolling an sliing elements. This is accomplishe through the formation of a thin oil(or grease) lm on contact surfaces. Lubrication also helps to reuce friction an wear, issipate friction heat, keep away from ust. In orer to achieve the above avantages an prolong the bearing life, the most effective lubrication metho an lubricant has to be selecte for each iniviual operating conitions. The main spinle of a machine tool usually uses an extremely low volume of lubricant so heat generation from stirring of the lubricant is minimal. Fig. 6.1 summarizes the relationships between oil volume, friction loss, an bearing temperature. The lubrication methos available for bearings in a machine tool inclue grease lubrication, oil mist lubrication, air-oil lubrication, an jet lubrication. Each metho has unique avantages. Therefore, the lubricating system that best suits the lubrication requirements shoul be use. Tables 6.1 an 6.2 summarize the features of various lubrication methos. Fig. 6.1 Oil volume, friction loss an bearing temperature Table 6.1 Different Zone(Fig. 6.1) an its lubrication metho Zone A B C Features With an extremely low volume of oil, partial metal-to-metal contact occurs between the rolling elements an raceway surface, possibly leaing to abnormal wear an bearing seizure. A uniform, uninterrupte oil lm is forme. Friction is minimal an bearing temperature is kept low. Even with a greater oil volume, heat generation an cooling are in balance. Typical lubrication metho Grease lubrication Oil mist lubrication Air-oil lubrication Circulating lubrication 25

Pipe bracket spacing and support of pipelines

Pipe bracket spacing and support of pipelines Pipe an support of pipelines General Pipe support for plastics pipes Plastic pipe systems shoul be installe using supports esigne for use with plastics an shoul then be installe taking care not to amage