Fo New Technology Netwok R copoation Ball and Rolle Beaings @
Technical Data A- Deep Goove Ball Beaings B- Miniatue and Exta Small Beaings B- 29 Angula Contact Ball Beaings B- 41 Self-Aligning Ball Beaings B- 77 Cylindical Rolle Beaings B- 89 Tapeed Rolle Beaings B-131 Spheical Rolle Beaings B-229 Thust Beaings B-26 Locknuts, Lockwashes & Lockplates C- 1 Catalog List & Appendix Table D- 1
Waanty NTN waants, to the oiginal puchase only, that the deliveed poduct which is the subject of this sale (a) will confom to dawings and specifications mutually established in witing as applicable to the contact, and (b) be fee fom defects in mateial o fabication. The duation of this waanty is one yea fom date of delivey. If the buye discoves within this peiod a failue of the poduct to confom to dawings o specifications, o a defect in mateial o fabication, it must pomptly notify NTN in witing. In no event shall such notification be eceived by NTN late than 13 months fom the date of delivey. Within a easonable time afte such notification, NTN will, at its option, (a) coect any failue of the poduct to confom to dawings, specifications o any defect in mateial o wokmanship, with eithe eplacement o epai of the poduct, o (b) efund, in pat o in whole, the puchase pice. Such eplacement and epai, excluding chages fo labo, is at NTN's expense. All waanty sevice will be pefomed at sevice centes designated by NTN. These emedies ae the puchase's exclusive emedies fo beach of waanty. NTN does not waant (a) any poduct, components o pats not manufactued by NTN, (b) defects caused by failue to povide a suitable installation envionment fo the poduct, (c) damage caused by use of the poduct fo puposes othe than those fo which it was designed, (d) damage caused by disastes such as fie, flood, wind, and lightning, (e) damage caused by unauthoized attachments o modification, (f) damage duing shipment, o (g) any othe abuse o misuse by the puchase. THE FOREGOING WARRANTIES ARE IN LIEU OF ALL OTHER WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. In no case shall NTN be liable fo any special, incidental, o consequential damages based upon beach of waanty, beach of contact, negligence, stict tot, o any othe legal theoy,and in no case shall total liability of NTN exceed the puchase pice of the pat upon which such liability is based. Such damages include, but ae not limited to, loss of pofits, loss of savings o evenue, loss of use of the poduct o any associated equipment, cost of capital, cost of any substitute equipment, facilities o sevices, downtime, the claims of thid paties including customes, and injuy to popety. Some states do not allow limits on waanties, o on emedies fo beach in cetain tansactions. In such states, the limits in this paagaph and in paagaph (2) shall apply to the extent allowable unde case law and statutes in such states. Any action fo beach of waanty o any othe legal theoy must be commenced within 1 months following delivey of the goods. Unless modified in a witing signed by both paties, this ageement is undestood to be the complete and exclusive ageement between the paties, supeceding all pio ageements, oal o witten, and all othe communications between the paties elating to the subject matte of this ageement. No employee of NTN o any othe paty is authoized to make any waanty in addition to those made in this ageement. This ageement allocates the isks of poduct failue between NTN and the puchase. This allocation is ecognized by both paties and is eflected in the pice of the goods. The puchase acknowledges that it has ead this ageement, undestands it, and is bound by its tems. NTN Copoation. 21 Although cae has been taken to assue the accuacy of the data compiled in this catalog, NTN does not assume any liability to any company o peson fo eos o omissions.
NTN Ball and Rolle Beaings
TECHNICAL DATA CONTENTS 1. Classification and Chaacteistics of Rolling Beaings A- 1.1 Rolling beaing constuction A- 1.2 Classification of olling beaings A- 1.3 Chaacteistics of olling beaings A-9 2. Beaing Selection A-1 2.1 Beaing selection flow chat A-1 2.2 Type and chaacte is tics A-12 2.3 Selection of beaing aangement A-13 3. Load Rating and Life A-1 3.1 Beaing lifea-1 3.2 Basic ated life and basic dynamic load ating A-1 3.3 Machine applications and equisite life A-16 3.4 Adjusted life ating factoa-16 3. Basic static load atinga-17 3.6 Allowable static equivalent load A-18 4.6 Beaing ated life and load calculation examples A-26. Bounday Dimensions and Beaing Numbe Codes A-28.1 Bounday dimensions A-28.2 Beaing numbes A-29 6. Beaing Toleances A-33 6.1 Dimensional accuacy and unning accuacy A-33 6.2 Chamfe measuements and toleance o allowable values of tapeed hole A-44 6.3 Beaing toleance measuement methods A-46 7. Beaing Fits A-47 7.1 Intefeence A-47 7.2 The necessity of a pope fit A-47 7.3 Fit selection A-47 4. Beaing Load Calculation A-19 4.1 Loads acting on shaftsa-19 4.2 Beaing load distibution A-21 4.3 Mean load A-22 4.4 Equivalent load A-23 4. Allowable axial load fo cylindical olle beaings A-2 8. Beaing Intenal Cleaance and Peload A-6 8.1 Beaing intenal cleaance A-6 8.2 Intenal cleaance selection A-6 8.3 Peload A-64 A-2
9. Allowable Speed A-68 1. Fiction and Tempeatue RiseA-69 1.1 Fiction A-69 1.2 Tempeatue isea-69 11. Lubication A-7 11.1 Lubication of olling beaings A-7 11.2 Lubication methods and chaacteistics A-7 11.3 Gease lubication A-7 11.4 Solid gease (Fo beaings with solid gease) A-74 11. Oil lubication A-74 14. Shaft and Housing DesignA-83 14.1 Fixing of beaings A-83 14.2 Beaing fitting dimensionsa-84 14.3 Shaft and housing accuacy A-8 14.4 Allowable beaing misalignment A-8 1. Beaing Handling A-86 1.1 Beaing stoage A-86 1.2 Installation A-86 1.3 Intenal cleaance adjustment A-88 1.4 Post installation unning testa-9 1. Beaing disassembly A-9 16. Beaing Damage and Coective Measues A-93 12. Extenal beaing sealing devices A-78 13. Beaing MateialsA-81 13.1 Raceway and olling element mateials A-81 13.2 Cage mateialsa-82 17. Technical data A-9 17.1 Deep goove ball beaing adial intenal cleaances and axial intenal cleaances A-9 17.2 Angula contact ball beaing axial load and axial displacement A-9 17.3 Tapeed olle beaing axial load and axial displacement A-97 17.4 Fitting suface pessuea-98 17. Necessay pess fit and pullout foce A-99 A-3
Classification and Chaacteistics of Rolling Beaings 1. Classification and Chaacteistics of Rolling Beaings 1.1 Rolling beaing constuction Most olling beaings consist of ings with aceway (an inne ing and an oute ing), olling elements (eithe balls o olles) and a olling element etaine. The etaine sepaates the olling elements at egula intevals holds them in place within the inne and oute aceways, and allows them to otate feely. See Figs. 1.1-1.8. Rolling elements come in two geneal shapes: ball o olles. Rolles come in fou basic styles: cylindical, needle, tapeed, and spheical. Balls geometically contact the aceway sufaces of the inne and oute ings at "points", while the contact suface of olles is a "line" contact. Theoetically, olling beaings ae so constucted as to allow the olling elements to otate obitally while also otating on thei own axes at the same time. While the olling elements and the beaing ings take any load applied to the beaings (at the contact point between the olling elements and aceway sufaces), the etaine takes no diect load. It only seves to hold the olling units at equal distances fom each othe and pevent them fom falling out. Outeing Inne ing Cage Ball Deep goove ball beaing Fig 1.1 Oute ing Inne ing Cage Rolle Oute ing Inne ing Ball Cage Angula contact ball beaing Fig. 1.2 Oute ing Rolle Cage 1.2 Classification of olling beaings Rolling beaings fall into two main classifications: ball beaings and olle beaings. Ball beaings ae classified accoding to thei beaing ing configuations: deep goove, angula contact and thust types. Rolle beaings on the othe hand ae classified accoding to the shape of the olles: cylindical, needle, tape and spheical. Rolling beaings can be futhe classified accoding to the diection in which the load is applied; adial beaings cay adial loads and thust beaings cay axial loads. Othe classification methods include: 1) numbe of olling ows (single, multiple, o 4-ow), 2) sepaable and non-sepaable, in which eithe the inne ing o the oute ing can be detached, 3) thust beaings which can cay axial loads in only one diection, and double diection thust beaings which can cay loads in both diections. Cylindical olle beaing Fig. 1.3 Oute ing Rolle Cage Inne ing Tapeed olle beaing Fig. 1. Needle olle beaing Fig. 1.4 Oute ing Inne ing Rolle Cage Spheical olle beaing Fig. 1.6 Thee ae also beaings designed fo special applications, such as: ailway ca jounal olle beaings (RCT beaings), ball scew suppot beaings, tuntable beaings, as well as ectilinea motion beaings (linea ball beaings, linea olle beaings and linea flat olle beaings). Ball Inne ing Rolle Inne ing Cage Cage Oute ing Thust ball beaing Fig. 1.7 Oute ing Thust olle beaing Fig. 1.8 A-
Classification and Chaacteistics of Rolling Beaings Single ow deep goove ball beaings Single ow angula contact ball beaings Radial ball beaings Duplex angula contact ball beaings Double ow angula contact ball beaings Fou-point contact ball beaings Ball beaings Self-aligning ball beaings Inset ball beaings Single diection thust ball beaings with flat back face Thust ball beaings High-speed duplex angula contact ball beaings (fo axial loads) Double diection angula contact thust ball beaings Rolling beaings Single ow cylindical olle beaings Double ow cylindical olle beaings Radial olle beaings Needle olle beaings Single ow tapeed olle beaings Double ow tapeed olle beaings Spheical olle beaings Rolle beaings Cylindical olle thust beaings Needle olle thust beaings Thust olle beaings Tapeed olle thust beaings Spheical olle thust beaings A-6
Classification and Chaacteistics of Rolling Beaings Ulta thin wall type ball beaings Tuntable beaings Ball scew suppot beaings Railway ca jounal olle beaings (RCT beaings) Ulta-clean vacuum beaings Special application beaings ;;; ;;;;; ;;;;;; ;;;;;;; ;;;;;;; ;;;;;;; SL-type cylindical olle beaings Rubbe molded beaings Cossed olle thust beaings Cleaance adjusting needle olle beaings Complex beaings Connecting od cage-equipped needle olles Yoke type tack olles Stud type tack olles Special application beaings ae not listed in this catalog. Linea motion beaings Linea motion beaings ae not listed in this catalog Fig. 1.9 Classification of olling beaings A-7
Classification and Chaacteistics of Rolling Beaings Snap ing Width Contact angle Cage Rivet Ball Inne ing aceway Oute ing aceway Beaing boe diamete Oute ing Inne ing Pitch cicle diamete Inne ing side face Shield Beaing outside diamete Oute ing, font face Inne ing, back face Effective load cente Oute ing, back face Inne ing, font face Beaing chamfe Deep goove ball beaing Angula contact ball beaing Contact angle Beaing width Inne ing with ib Oute ing with 2 ibs L-shaped loose ib Standout Tapeed olle Cone font face ib Rolle inscibed cicle diamete Cone back face ib Effective load cente Cup small inside diamete (SID) Cylindical olle Cone, back face Cone, font face Cup, font face Cup, back face Cylindical olle beaing Tapeed olle beaing Tapeed boe of inne ing Lock washe Locknut Sleeve Beaing height Beaing boe diamete Shaft washe Ball Inne ing Beaing outside diamete Spheical olle Oute ing Housing washe Spheical olle beaing Single-diection thust ball beaing Fig. 1.1 Diagam of epesentative beaing pats A-8
Classification and Chaacteistics of Rolling Beaings 1.3 Chaacteistics of olling beaings 1.3.1 Chaacteistics of olling beaings Rolling beaings come in many shapes and vaieties, each with its own distinctive featues. Howeve, when compaed with sliding beaings, olling beaings all have the following advantages: (1) The stating fiction coefficient is lowe and thee is little diffeence between this and the dynamic fiction coefficient is poduced. (2) They ae intenationally standadized, intechangeable and eadily obtainable. (3) They ae easy to lubicate and consume less lubicant. (4) As a geneal ule, one beaing can cay both adial and axial loads at the same time. () May be used in eithe high o low tempeatue applications. (6) Beaing igidity can be impoved by peloading. Constuction, classes, and special featues of olling beaings ae fully descibed in the bounday dimensions and beaing numbeing system section. 1.3.2 Ball beaings and olle beaings Geneally speaking, when compaing ball and olle beaings of the same dimensions, ball beaings exhibit a lowe fictional esistance and lowe face un-out in otation than olle beaings. This makes them moe suitable fo use in applications which equie high speed, high pecision, low toque and low vibation. Convesely, olle beaings have a lage load caying capacity which makes them moe suitable fo applications equiing long life and enduance fo heavy loads and shock loads. 1.3.3 Radial and thust beaings Almost all types of olling beaings can cay both adial and axial loads at the same time. Geneally, beaings with a contact angle of less than 4have a much geate adial load capacity and ae classed as adial beaings; wheeas beaings which have a contact angle ove 4have a geate axial load capacity and ae classed as thust beaings. Thee ae also beaings classed as complex beaings which combine the loading chaacteistics of both adial and thust beaings. 1.3.4 Standad beaings and special beaings Beaings which ae intenationally standadized as to shape and size ae much moe economical to use, as they ae intechangeable and available on a woldwide basis. Howeve, depending on the type of machine they ae to be used in, and the expected application and function, a non-standad o specially designed beaing may be best to use. Beaings that ae adapted to specific applications, and "unit beaings" which ae integated (built-in) into a machine's components, and othe specially designed beaings ae also available. A-9
Beaing Selection 2. Beaing Selection Rolling element beaings ae available in a vaiety of types, configuations, and sizes. When selecting the coect beaing fo you application, it is impotant to conside seveal factos, such as the calculation of vaious angles and cleaances, which will ensue pope fit. A compaison of the pefomance chaacteistics fo each beaing type is shown in Table 2.1. As a geneal guideline, the basic pocedue fo selecting the most appopiate beaing is shown in the following flow chat. 2.1 Beaing selection flow chat Pocedue Confimation items Confim opeating conditions and opeating envionment Function and constuction of components to house beaings Beaing mounting location Beaing load (diection and magnitude) Rotational speed Vibation and shock load Beaing tempeatue (ambient and fiction-geneated) Opeating envionment (potential fo coosion, degee of contamination, extent of lubication) Select beaing type and configuation Dimensional limitations (efe to page inset 28) Beaing load (magnitude, diection, vibation; pesence of shock load) (efe to page inset 19) Rotational speed (efe to page inset 68) Beaing toleances (efe to page inset 33) Rigidity (efe to page inset 64) Allowable misalignment of inne/oute ings (efe to page inset 8) Fiction toque (efe to page inset 69) Beaing aangement (fixed side, floating side) (efe to page inset 13) Installation and disassembly equiements (efe to page inset 86) Beaing availability and cost Select beaing dimensions Design life of components to house beaings (efe to page inset 17) Dynamic/static equivalent load conditions (efe to page inset 23) Safety facto (efe to page inset 17) Allowable speed (efe to page inset 68) Allowable axial load (efe to page inset 17, 2) Allowable space (efe to page inset 28) Select beaing toleances Shaft unout toleances (efe to page inset 33) Rotational speed (efe to page inset 68) Toque fluctuation Selection of beaing type and configuation (1) Dimensional limitations The allowable space fo beaings is typically limited. In most cases, shaft diamete (o the beaing boe diamete) has been detemined accoding to the machine s othe design specifications. Theefoe, a beaing s type and dimensions ae detemined accoding to standad beaing boe diametes. Fo this eason all dimension tables ae oganized accoding to standad boe diametes. Thee is a wide ange of standadized beaing types and dimensions: the ight one fo a paticula application can usually be found in these tables. (2) Beaing load The chaacteistics, magnitude, and diection of loads acting upon a beaing ae extemely vaiable. In geneal, the basic ated loads shown in beaing dimension tables indicate thei load capacity. Howeve, in detemining the appopiate beaing type, consideation must also be given to whethe the acting load is a adial load only o an axial load only, o combined adial and axial load, etc. When ball and olle beaings within the same dimension seies ae consideed, the olle beaings have a lage load capacity and ae also capable of withstanding geate vibation and shock loads. (3) Rotational speed The allowable speed of a beaing will diffe depending upon beaing type, size, toleances, cage type, load, lubicating conditions, and cooling conditions. The allowable speeds listed in the beaing tables fo gease and oil lubication ae fo standad NTN beaings. In geneal, deep goove ball beaings, angula contact ball beaings, and cylindical olle beaings ae most suitable fo high speed applications. (4) Beaing toleances The dimensional accuacy and opeating toleances of beaings ae egulated by ISO and JIS standads. Fo equipment equiing high toleance shaft unout o high speed opeation, etc., beaings with Class toleance o highe ae ecommended. Deep goove ball beaings, angula contact ball beaings, and cylindical olle beaings ae ecommended fo high otational toleances. () Rigidity Elastic defomation occus along the contact sufaces of a beaing s olling elements and aceway sufaces when unde load. With cetain types of equipment it is necessay to educe this defomation as much as A-1
Beaing Selection Select beaing s intenal cleaance Select cage type and mateial Select lubicant, lubication method, sealing method Select any special beaing specifications Confim handling pocedues Mateial and shape of shaft and housing (efe to page inset 83) Fit (efe to page inset 47) Tempeatue diffeential between inne/oute ings (efe to page inset 7) Allowable misalignment of inne/oute ings (efe to page inset 8) Load (magnitude, natue) (efe to page inset 19) Amount of peload (efe to page inset 64) Rotational speed (efe to page inset 68) Rotational speed (efe to page inset 68) Noise level Vibation and shock load Momentay load Lubication type and method (efe to page inset 7) Opeating tempeatue (efe to page inset 7) Rotational speed (efe to page inset 68) Lubication type and method (efe to page inset 7) Sealing method (efe to page inset 78) Maintenance and inspection (efe to page inset 86) Opeating envionment (high/low tempeatue, vacuum, phamaceutical, etc.) Requiement fo high eliability Installation-elated dimensions (efe to page inset 84) Installation and disassembly pocedues (efe to page inset 86) possible. Rolle beaings exhibit less elastic defomation than ball beaings, and theefoe ae ecommended fo such equipment. Futhemoe, in some cases, beaings ae given an initial load (peloaded) to incease thei shafting igidity. This pocedue is commonly applied to deep goove ball beaings, angula contact ball beaings, and tapeed olle beaings. (6) Misalignment of inne and oute ings Shaft flexue, vaiations in shaft o housing accuacy, and fitting eos, etc. esult in a cetain degee of misalignment between the beaing s inne and oute ings. In cases whee the degee of misalignment is likely to be elatively lage, self-aligning ball beaings, spheical olle beaings, o beaing units with selfaligning popeties ae the most appopiate choices. (Refe to Fig. 2.1) (7) Noise and toque levels Rolling beaings ae manufactued and pocessed accoding to high pecision standads, and theefoe geneally poduce only slight amounts of noise and toque. Fo applications equiing paticulaly low-noise o low-toque opeation, deep goove ball beaings and cylindical olle beaings ae most appopiate. (8) Installation and disassembly Some applications equie fequent disassembly and eassembly to enable peiodic inspections and epais. Fo such applications, beaings with sepaable inne/oute ings, such as cylindical olle beaings, needle olle beaings, and tapeed olle beaings ae most appopiate. Incopoation of adapte sleeves simplifies the installation and disassembly of selfaligning ball beaings and spheical olle beaings with tapeed boes. Allowable misalignment angle Self-aligning ball beaing Allowable misalignment angle Spheical olle beaing Fig. 2.1 A-11
Beaing Selection 2.2 Type and chaacte is tics Table 2.1 shows types and chaacteistics of olling beaings. Table 2.1 Types and chaacteistics of olling beaings Beaing types Deep goove ball beaings Angula contact ball beaings Double ow angula contact ball beaings Duplex angula contact ball beaings Selfaligning ball beaings Cylindical olle beaings Singleflange cylindical olle beaings Doubleflange cylindical olle beaings Double ow cylindical olle beaings Chaacteistics Load Caying Capacity Radial load Axial load High speed High otating accuacy Low noise/vibation Low fiction toque High igidity Vibation/shock esistance Allowable misalignment fo inne/oute ings Fo fixed beaings Fo floating beaings Non-sepaable o sepaable Tapeed boe beaings Remaks Refeence page Fo duplex aangement Fo DB and DF aangement Fo DB aangement NU, N NJ, NF NUP, NP, NH type type type B- B-41 B-72 B-41 B-77 B-89 B-89 B-89 B-89 Tapeed olle beaings Multi-ow, 4-ow tapeed olle beaings. Spheical olle beaings Thust ball beaings Double ow angula contact thust ball beaings Spheical olle thust beaings Refeence page Beaing types Chaacteistics Load Caying Capacity Radial load Axial load A-66 A-31 A-67 A-4 A-18 A-79 A-13 A-13 A-79 High speed High otating accuacy Low noise/vibation Low fiction toque High igidity Vibation/shock esistance Allowable misalignment fo inne/oute ings Fo fixed beaings Fo floating beaings Non-sepaable o sepaable Tapeed boe beaings The numbe of stas in dicate the degee to which that beaing type displays that paticula chaacteistic. Not applicable to that beaing type. Indicates dual diection. Indicates single diection axial movement only. Indicates movement at aceway. Indicates movement at mated suface of inne o oute ing. Indicates both inne ing and oute ing ae detachable. Indicates inne ing with tapeed boe is possible. Fo duplex aangement Remaks B-131 B-131 B-229 B-26 B-26 B-26 Refeence page A-12
Beaing Selection 2.3 Selection of beaing aangement Shaft assemblies geneally equie two beaings to suppot and locate the shaft adially and axially, elative to the stationay housing. These two beaings ae called the fixed-side and floating-side beaings. The fixed-side beaing fixes o contols movement of the shaft axially in elation to the housing. The floating-side beaing moves o floats axially in elation to the housing and is theefoe able to elieve stess caused by the expansion and contaction of the shaft due to tempeatue fluctuations, and allow fo misalignment caused by fitting eos. Fixed-side beaings have the capacity to eceive both axial and adial loads, and theefoe a beaing which contols axial movement in both diections should be selected. Floating-side beaings eceive only adial loads, and theefoe beaings which ae mounted to pemit fee axial movement, o beaings with sepaable inne and oute ings ae most desiable. Cylindical olle beaings ae geneally sepaable and allow fo axial displacement along thei aceway sufaces; deep goove ball beaings ae non-sepaable, but can be mounted to allow fo displacement along thei fitting sufaces. In applications with shot distances between beaings, shaft expansion and contaction due to tempeatue fluctuations is slight, theefoe the same type of beaing may be used fo both the fixed-side and floating-side beaing. In such cases it is common to use a set of matching beaings, such as angula contact ball beaings, to guide and suppot the shaft in one axial diection only. Table 2.2 (1) shows epesentative beaing aangements whee the beaing type diffes on the fixed side and floating side. Table 2.2 (2) shows some common beaing aangements whee no distinction is made between the fixed side and floating side. Vetical shaft beaing aangements ae shown in Table 2.2 (3). Table 2.2 (1) Beaing aangement (Fixed and Floating) Fixed Aangement Floating Comment Application 1. Geneal aangement fo small machiney. 2. Fo adial loads, but will also accept axial loads. 3. Peloading by spings o shims on oute ing face. Small pumps, small electic motos, auto-mobile tansmissions, etc. 1. Suitable fo high speed. Widely used. 2. Even with expansion and contaction of shaft, non-fixing side moves smoothly. Medium-sized electic motos, ventilatos, etc. 1. Radial loading plus dual diection axial loading possible. 2. In place of duplex angula contact ball beaings, double-ow angula contact ball beaings ae also used. Womgea speed educes, etc. 1. Heavy loading capable. 2. Shafting igidity inceased by peloading the two back-to-back fixed beaings. 3. Requies high pecision shafts and housings, and minimal fitting Machine tool spindles, etc. 1. Allows fo shaft deflection and fitting eos. 2. By using an adapto on long shafts without scews o shouldes, beaing mounting and dismounting can be facilitated. 3. Not suitable fo axial load applications. Counte shafts fo geneal industial equipment, etc. 1. Widely used in geneal industial machiney with heavy and shock load demands. 2. Allows fo shaft deflection and fitting eos. 3. Accepts adial loads as well as dual diection axial loads. Reduction geas fo genealindustial equipment, etc. 1. Widely used in geneal industial machiney with heavy and shock loading. 2. Radial and dual diectional axial loading. Industial machiney eduction geas. etc. 1. Capable of handling lage adial and axial loads at high otational speeds. 2. Maintains cleaance between the beaing s oute diamete and housing inne diamete to pevent deep goove ball beaings fom eceiving adial loads. Diesel locomotives, etc. A-13
Beaing Selection Table 2.2 (2) Beaing aangement (Placed oppositely) Aangement Comment Application Geneal aangement fo use in small machines. Small electic motos, small eduction geas, etc. 1. This type of back-to-back aangement well suited fo moment loads. 2. Peloading inceases shaft igidity. 3. High speed eliable. Spindles of machine tools, etc. 1. Accepts heavy loading. 2. Suitable if inne and oute ing shink-fit is equied. 3. Cae must be taken that axial cleaance does not become too small duing opeation. Constuction equipment, mining equipment sheaves, agitatos, etc. Back to back 1. Withstands heavy and shock loads. Wide ange application. 2. Shafting igidity inceased by peloading. 3. Back-to-back aangement fo moment loads, and face-to-face aangement to alleviate fitting eos. 4. With face-to-face aangement, inne ing shink-fit is facilitated. Reduction geas, automotive axles, etc. Face to face Table 2.2 (3) Beaing aangement (Vetical shaft) Aangement Comment Application When fixing beaing is a duplex angula contact ball beaing, non-fixing beaing is a cylindical olle beaing. Machine tool spindles, vetical mounted electic motos, etc. 1. Most suitable aangement fo vey heavy axial loads. 2. Depending on the elative alignment of the spheical suface of the olles in the uppe and lowe beaings, shaft deflection and fitting eos can be absobed. 3. Lowe self-aligning spheical olle thust beaing pe-load is possible. Cane cente shafts, etc. A-14
Load Rating and Life 3. Load Rating and Life 3.1 Beaing life Even in beaings opeating unde nomal conditions, the sufaces of the aceway and olling elements ae constantly being subjected to epeated compessive stesses which causes flaking of these sufaces to occu. This flaking is due to mateial fatigue and will eventually cause the beaings to fail. The effective life of a beaing is usually defined in tems of the total numbe of evolutions a beaing can undego befoe flaking of eithe the aceway suface o the olling element sufaces occus. Othe causes of beaing failue ae often attibuted to poblems such as seizing, abasions, cacking, chipping, gnawing, ust, etc. Howeve, these so called "causes" of beaing failue ae usually themselves caused by impope installation, insufficient o impope lubication, faulty sealing o inaccuate beaing selection. Since the above mentioned "causes" of beaing failue can be avoided by taking the pope pecautions, and ae not simply caused by mateial fatigue, they ae consideed sepaately fom the flaking aspect. 3.2 Basic ating life and basic dynamic load ating A goup of seemingly identical beaings when subjected to identical load and opeating conditions will exhibit a wide divesity in thei duability. This "life" dispaity can be accounted fo by the diffeence in the fatigue of the beaing mateial itself. This dispaity is consideed statistically when calculating beaing life, and the basic ating life is defined as follows. The basic ating life is based on a 9% statistical model which is expessed as the total numbe of evolutions 9% of the beaings in an identical goup of beaings subjected to identical opeating conditions will attain o supass befoe flaking due to mateial fatigue occus. Fo beaings opeating at fixed constant speeds, the basic ating life (9% eliability) is expessed in the total numbe of hous of opeation. The basic dynamic load ating is an expession of the load capacity of a beaing based on a constant load which the beaing can sustain fo one million evolutions (the basic life ating). Fo adial beaings this ating applies to pue adial loads, and fo thust beaings it efes to pue axial loads. The basic dynamic load atings given in the beaing tables of this catalog ae fo beaings constucted of NTN standad beaing mateials, using standad manufactuing techniques. Please consult NTN Engineeing fo basic load atings of beaings constucted of special mateials o using special manufactuing techniques. The elationship between the basic ating life, the basic dynamic load ating and the beaing load is given in fomula (3.1). L 1 C p 3.1 P whee, p= 3...Fo ball beaings p= 1/3...Fo olle beaings L1 : Basic ating life 1 6 evolutions C : Basic dynamic ating load, N (C: adial beaings, Ca: thust beaings) P : Equivalent dynamic load, N (P: adial beaings, Pa: thust beaings) The basic ating life can also be expessed in tems of hous of opeation (evolution), and is calculated as shown in fomula (3.2). L1h f h p 3.2 C f h f n 3.3 P f n 33.3 1p 3.4 n whee, L1h : Basic ating life, h fh : Life facto fn : Speed facto n : Rotational speed, / min n /min 6, 4, 3, 2, 1, 1, 8, 6, 4, 3, 2, 1, 1, 8 6 1 1 4 3 2 1 8 6 4 3 2 1 Ball beaings fn.82.9.12.14.16.18 n 8, 6, 4, 3, 2, 1,.2 1,.22.24.26.28.3.3.4..6.7.8.9 1.1 1.2 1.3 1.4.1 1. 1.49 L1h 8, 6, 4, 3, 2, 1, 1, 9 8 7 6 4 3 2.4 6, 4, 4. 3, 4 2, 1, 3. 1, 8, 3 6, 2. 2 1.9 1.8 1.7 1.6 1. 1.4 1.3 1.2 1.1 fh n fn L1h 1..9.9.8.8.7.74 /min 4, 3, 2, 1, 1, 8 6 4 3 2 1 1 8 6 4 3 2 1 1 Rolle beaings.16.12.14.16.18.2.22.24.26.28.3.3.4..6.7.8.9 1. 1.1 1.2 1.3 1.4 1.44 8, 6, 4, 3, 2, 1, 1, 8, 6, 4, 3, 2, 1, 1, 9 8 7 6 4 4.6 4. 4 3. 3 2. 2 1.9 1.8 1.7 1.6 1. 1.4 1.3 1.2 1.1 1..9.9 3.8 2 Fig. 3.1 Beaing life ating scale n.8 fh.76 A-1
Load Rating and Life Fomula (3.2) can also be expessed as shown in fomula (3.). L 1h 16 C p 3. 6 n P The elation ship between Rotational speed n and speed facto fn as well as the elation between the basic ating life L1h and the life facto fn is shown in Fig. 3.1. When seveal beaings ae incopoated in machines o equipment as complete units, all the beaings in the unit ae consideed as a whole when computing beaing life (see fomula 3.6). The total beaing life of the unit is a life ating based on the viable lifetime of the unit befoe even one of the beaings fails due to olling contact fatigue. 1 L 1 1 1 1e 3.6 L 1 e L 2 e whee, e = 1/9...Fo ball beaings e = 9/8...Fo olle beaings L : Total basic ating life of entie unit, h L1 L2 Ln: Basic ating life of individual beaings, 1, 2, n, h When the load conditions vay at egula intevals, the life can be given by fomula (3.7). Lm j Lj -1 3.7 L n e whee, j : Fequency of individual load conditions L j : Life unde individual conditions 3.3 Machine applications and equisite life When selecting a beaing, it is essential that the equisite life of the beaing be established in elation to the opeating conditions. The equisite life of the beaing is usually detemined by the type of machine in which the beaing will be used, and duation of sevice and opeational eliability equiements. A geneal guide to these equisite life citeia is shown in Table 3.1. When detemining beaing size, the fatigue life of the beaing is an impotant facto; howeve, besides beaing life, the stength and igidity of the shaft and housing must also be taken into consideation. 3.4 Adjusted life ating facto The basic beaing life ating (9% eliability facto) can be calculated though the fomulas mentioned ealie in Section.2. Howeve, in some applications a beaing life facto of ove 9% eliability may be equied. To meet these equiements, beaing life can be lengthened by the use of specially impoved beaing mateials o special constuction techniques. Moeove, accoding to elastohydodynamic lubication theoy, it is clea that the beaing opeating conditions (lubication, tempeatue, speed, etc.) all exet an effect on beaing life. All these adjustment factos ae taken into consideation when calculating beaing life, and using the life adjustment facto as pescibed in ISO 281, the adjusted beaing life can be detemined. Lna a1a2a3cp p 3.8 Table 3.1 Machine application and equisite life Sevice classification Machines used fo shot peiods o used only occasionally Shot peiod o intemittent use, but with high eliability equiements Machines not in constant use, but used fo long peiods Life facto and machine application L1h 4 412 123 36 6 Electic hand tools Household appliances Medical appliances Measuing instuments Automobiles Two-wheeled vehicles Fam machiney Office equipment Home ai- conditioning moto Constuction equipment Elevatos Canes Small motos Buses/tucks Dives Woodwoking machines Cane (sheaves) Machine spindles Industial motos Cushes Vibating sceens Main gea dives Rubbe/plastic Calende olls Pinting machines 1 3 h Machines in constant use ove 8 hous a day Rolling mills Escalatos Conveyos Centifuges Railway vehicle axles Ai conditiones Lage motos Compesso pumps Locomotive axles Taction motos Mine hoists Pessed flywheels Papemaking machines Populsion equipment fo maine vessels Wate supply equipment Mine dain pumps/ventilatos Powe geneating equipment 24 hou continuous opeation, non-inteuptable A-16
Load Rating and Life whee, Lna : Adjusted life ating in millions of evolutions (1 6 )(adjusted fo eliability, mateial and opeating conditions) a1 : Reliability adjustment facto a2 : Mateial adjustment facto a3 : Opeating condition adjustment facto 3.4.1 Life adjustment facto fo eliability a1 The values fo the eliability adjustment facto a1 (fo a eliability facto highe than 9%) can be found in Table 3.2. insufficient oil film fomation can be caused, fo example, by the lubicating oil viscosity being too low fo the opeating tempeatue (below 13 mm 2 /s fo ball beaings; below 2 mm 2 /s fo olle beaings); o by exceptionally low otational speed (n/min x dpmm less than 1,). Fo beaings used unde special opeating conditions, please consult NTN Engineeing. As the opeating tempeatue of the beaing inceases, the hadness of the beaing mateial deceases. Thus, the beaing life coespondingly deceases. The opeating tempeatue adjustment values ae shown in Fig. 3.2. Table 3.2 Reliability adjustment facto values a1 Reliability % Ln Reliability facto a1 9 9 96 97 98 99 L1 L L4 L3 L2 L1 1..62.3.44.33.21 Life adjustment value a 1..8.6.4.2 3.4.2 Life adjustment facto fo mateial a2 The life of a beaing is affected by the mateial type and quality as well as the manufactuing pocess. In this egad, the life is adjusted by the use of an a2 facto. The basic dynamic load atings listed in the catalog ae based on NTN's standad mateial and pocess, theefoe, the adjustment facto a2 =1. When special mateials o pocesses ae used the adjustment facto can be lage than 1. NTN beaings can geneally be used up to 12 C. If beaings ae opeated at a highe tempeatue, the beaing must be specially heat teated (stabilized) so that inadmissible dimensional change does not occu due to changes in the mico-stuctue. This special heat teatment might cause the eduction of beaing life because of a hadness change. 3.4.3 Life adjustment facto a3 fo opeating conditions The opeating conditions life adjustment facto a3 is used to adjust fo such conditions as lubication, opeating tempeatue, and othe opeation factos which have an effect on beaing life. Geneally speaking, when lubicating conditions ae satisfactoy, the a3 facto has a value of one; and when lubicating conditions ae exceptionally favoable, and all othe opeating conditions ae nomal, a3 can have a value geate than one. Howeve, when lubicating conditions ae paticulaly unfavoable and the oil film fomation on the contact sufaces of the aceway and olling elements is insufficient, the value of a3 becomes less than one. This 1 1 2 2 3 Opeating tempeatue C Fig. 3.2 Life adjustment value fo opeating tempeatue 3. Basic static load ating When stationay olling beaings ae subjected to static loads, they suffe fom patial pemanent defomation of the contact sufaces at the contact point between the olling elements and the aceway. The amount of defomity inceases as the load inceases, and if this incease in load exceeds cetain limits, the subsequent smooth opeation of the beaings is impaied. It has been found though expeience that a pemanent defomity of.1 times the diamete of the olling element, occuing at the most heavily stessed contact point between the aceway and the olling elements, can be toleated without any impaiment in unning efficiency. The basic ating static load efes to a fixed static load limit at which a specified amount of pemanent defomation occus. It applies to pue adial loads fo adial beaings and to pue axial loads fo thust beaings. The maximum applied load values fo contact stess occuing at the olling element and aceway contact points ae given below. Fo ball beaings (except self-aligning ball beaings) Fo self-aligning ball beaings Fo olle beaings 4,2 Mpa 4,6 Mpa 4, Mpa A-17
Load Rating and Life 3.6 Allowable static equivalent load Geneally the static equivalent load which can be pemitted (See Section 4.4.2 page A-23) is limited by the basic static ating load as stated in Section.. Howeve, depending on equiements egading fiction and smooth opeation, these limits may be geate o lesse than the basic static ating load. In the following fomula (3.9) and Table 3.4 the safety facto S can be detemined consideing the maximum static equivalent load. So CoPo3.9 Table 3.4 Minimum safety facto values S Opeating conditions Ball beaings High otational accuacy demand 2 Nomal otating accuacy demand (Univesal application) Slight otational accuacy deteioation pemitted (Low speed, heavy loading, etc.) 1. Rolle beaings Note 1: Fo spheical thust olle beaings, min. S value=4. 2: Fo shell needle olle beaings, min. S value=3. 3: When vibation and/o shock loads ae pesent, a load facto based on the shock load needs to be included in the P max value. 3 1. 1 whee, So : Safety facto Co : Basic static ating load, N (adial beaings: Co, thust beaings: Coa) Po max : Maximum static equivalent load, N (adial: Po max, thust: Coa max) A-18
Beaing Load Calculation 4. Beaing Load Calculation To compute beaing loads, the foces which act on the shaft being suppoted by the beaing must be detemined. These foces include the inheent dead weight of the otating body (the weight of the shafts and components themselves), loads geneated by the woking foces of the machine, and loads aising fom tansmitted powe. It is possible to calculate theoetical values fo these loads; howeve, thee ae many instances whee the load acting on the beaing is usually detemined by the natue of the load acting on the main powe tansmission shaft. 4.1 Load acting on shafts 4.1.1 Load facto Thee ae many instances whee the actual opeational shaft load is much geate than the theoetically calculated load, due to machine vibation and/o shock. This actual shaft load can be found by using fomula (4.1). K fwkc 4.1 whee, K Actual shaft load Nkgf fw Load facto (Table 4.1) KcTheoetically calculated value Nkgf 4.1.2 Gea load The loads opeating on geas can be divided into thee main types accoding to the diection in which the load is applied; i.e. tangential (Kt), adial (Ks), and axial (Ka). The magnitude and diection of these loads diffe accoding to the types of geas involved. The load calculation methods given heein ae fo two geneal-use gea and shaft aangements: paallel shaft geas, and coss shaft geas. Fo load calculation methods egading othe types of gea and shaft aangements, please consult NTN Engineeing. K t 19.116 H D N pn 4.2 1.916 H D kgf pn Ks KttanSpu gea4.2a K t tan Helical gea4.2b cos K Kt 2 Ks 2 4.3 Ka KttanHelical gea 4.4 whee, KtTangential gea load (tangential foce), N KsRadial gea load (sepaating foce), N KRight angle shaft load (esultant foce of tangential foce and sepaating foce), N KaPaallel load on shaft, N H Tansmission foce, kw n Rotational speed, /min DpGea pitch cicle diamete, mm Gea pessue angle Gea helix angle Ks Kt Fig. 4.1 Spu gea loads (1)Loads acting on paallel shaft geas The foces acting on spu and helical paallel shaft geas ae depicted in Figs. 4.1, 4.2, and 4.3. The load magnitude can be found by using o fomulas (4.2), though (4.4). Ks Kt Ka Table 4.1 Load facto fw Amount of shock Vey little o no shock Light shock Heavy shock fw 1.1.2 1.21. 1.3. Application Electic machines, machine tools, measuing instuments. Railway vehicles, automobiles, olling mills, metal woking machines, pape making machines, ubbe mixing machines, pinting machines, aicaft, textile machines, electical units, office machines. Cushes, agicultual equipment, constuction equipment, canes. Fig. 4.2 Helical gea loads Kt K Ks Dp Fig. 4.3 Radial esultant foces A-19
Beaing Load Calculation Because the actual gea load also contains vibations and shock loads as well, the theoetical load obtained by the above fomula should also be adjusted by the gea facto fz as shown in Table 4.2. Table 4.2 Gea facto fz Gea type Pecision gound geas (Pitch and tooth pofile eos of less than.2 mm) Odinay machined geas (Pitch and tooth pofile eos of less than.1 mm) (2)Loads acting on coss shafts Gea loads acting on staight tooth bevel geas and spial bevel geas on coss shafts ae shown in Figs. 4.4 and 4.. The calculation methods fo these gea loads ae shown in Table 4.3. Heein, to calculate gea loads fo staight bevel geas, the helix angle =. The symbols and units used in Table 4.3 ae as follows: Kt Tangential gea load (tangential foce), N Ks Radial gea load (sepaating foce), N Ka Paallel shaft load (axial load), N H Tansmission foce, kw n Rotational speed, /min Dpm Mean pitch cicle diamete, mm Gea pessue angle Helix angle Pitch cone angle In geneal, the elationship between the gea load and the pinion gea load, due to the ight angle intesection of the two shafts, is as follows: KspKag4. KapKsg4.6 fz 1.1.1 1.11.3 whee, KspKsgPinion and gea sepaating foce, N KapKagPinion and gea axial load, N Fo spial bevel geas, the diection of the load vaies depending on the diection of the helix angle, the diection of otation, and which side is the diving side o the diven side. The diections fo the sepaating foce (Ks) and axial load (Ka) shown in Fig. 4. ae positive diections. The diection of otation and the helix angle diection ae defined as viewed fom the lage end of the gea. The gea otation diection in Fig. 4. is assumed to be clockwise (ight). Kag Ksg Ktg K tp Kap Ksp Fig. 4.4 Loads on bevel geas δ β K s K a K t D pm 2 Fig. 4. Bevel gea diagam Table 4.3 Loads acting on bevel geas Pinion Rotation diection Helix diection Clockwise Counte clockwise Clockwise Counte clockwise Right Left Left Right Unit N Tangential loadkt Kt 19.116 H Dpmn 1.91 6 H Dpmn Diving side KsKt tan cos cos tansin KsKt tan cos cos tansin Sepaating foceks Diven side KsKt tan cos cos tansin KsKt tan cos cos tansin Axial load Ka Diving side KaKt tan sin cos tancos KaKt tan sin cos tancos Diven side KaKt tan sin cos tan KaKt tan sin cos tancos A-2
Beaing Load Calculation 4.1.2 Chain / belt shaft load The tangential loads on spockets o pulleys when powe (load) is tansmitted by means of chains o belts can be calculated by fomula (4.7). Kt 19.1 16 H N Dpn 4.7 1.916 H kgf Dpn whee, KtSpocket/pulley tangential load, N H Tansmitted foce, kw DpSpocket/pulley pitch diamete,mm Fo belt dives, an initial tension is applied to give sufficient constant opeating tension on the belt and pulley. Taking this tension into account, the adial loads acting on the pulley ae expessed by fomula (4.8). Fo chain dives, the same fomula can also be used if vibations and shock loads ae taken into consideation. 4.2 Beaing load distibution Fo shafting, the static tension is consideed to be suppoted by the beaings, and any loads acting on the shafts ae distibuted to the beaings. Fo example, in the gea shaft assembly depicted in Fig. 4.7, the applied beaing loads can be found by using fomulas (4.1) and (4.11). FA ab F1 d F2 4.1 b cd FB a F1 c F2 4.11 b cd whee, FARadial load on beaing A, N FBRadial load on beaing B, N F1, F2Radial load on shaft, N Kf bkt4.8 whee, KSpocket o pulley adial load, N f bchain o belt facto (Table 4.3) a b Beaing A Beaing B Table. 4.4 chain o belt facto f b Chain o belt type f b F F Chain (single) 1.21. F! F@ V-belt 1.2. c d Timing belt 1.11.3 Flat belt (w / tension pulley) 2.3. Fig. 4.7 Gea shaft Flat belt 3.4. F1 Loose side Dp K F2 Tension side Fig. 4.6 Chain / belt loads A-21
Beaing Load Calculation 4.3 Mean load The load on beaings used in machines unde nomal cicumstances will, in many cases, fluctuate accoding to a fixed time peiod o planned opeation schedule. The load on beaings opeating unde such conditions can be conveted to a mean load (Fm), this is a load which gives beaings the same life they would have unde constant opeating conditions. (1) Fluctuating stepped load The mean beaing load, Fm, fo stepped loads is calculated fom fomula (4.12). F1, F2... Fn ae the loads acting on the beaing; n1, n2...nn and t1, t2... tn ae the beaing speeds and opeating times espectively. whee: Fm Fi p ni ti 1p 4.12 ni ti p3 p13 F F1 Fo ball beaings Fo olle beaings F2 Fm (3) Linea fluctuating load The mean load, Fm, can be appoximated by fomula (4.14). Fm Fmin2Fmax F Fmax Fmin 3 4.14 Fm Fig. 4.1 Linea fluctuating load (4) Sinusoidal fluctuating load The mean load, Fm, can be appoximated by fomulas (4.1) and (4.16). case (a) case (b) Fm.7Fmax 4.1 Fm.6Fmax 4.16 t Fn F n1 t1 n2t2 nn tn Fig. 4.8 Stepped load Fmax Fm (2) Consecutive seies load Whee it is possible to expess the function F(t) in tems of load cycle to and time t, the mean load is found by using fomula (4.13). whee: Fm 1 to Ft p d t to o p3 p13 1p 4.13 Fo ball beaings Fo olle beaings F Fmax a Fm t F F(t) b Fig. 4.11 Sinusoidal vaiable load t Fm to to t Fig. 4.9 Time function seies load A-22
Beaing Load Calculation 4.4 Equivalent load 4.4.1 Dynamic equivalent load When both dynamic adial loads and dynamic axial loads act on a beaing at the same time, the hypothetical load acting on the cente of the beaing which gives the beaings the same life as if they had only a adial load o only an axial load is called the dynamic equivalent load. Fo adial beaings, this load is expessed as pue adial load and is called the dynamic equivalent adial load. Fo thust beaings, it is expessed as pue axial load, and is called the dynamic equivalent axial load. (1) Dynamic equivalent adial load The dynamic equivalent adial load is expessed by fomula (4.17). whee, PDynamic equivalent adial load, N FActual adial load, N FaActual axial load, N X Radial load facto Y Axial load facto The values fo X and Y ae listed in the beaing tables. whee, PoStatic equivalent adial load, N F Actual adial load, N Fa Actual axial load, N XoStatic adial load facto Yo Static axial load facto The values fo Xo and Yo ae given in the espective beaing tables. (2) Static equivalent axial load Fo spheical thust olle beaings the static equivalent axial load is expessed by fomula (4.21). PoaFa2.7F4.21 whee, PoaStatic equivalent axial load, N Fa Actual axial load, N F Actual adial load, N Povided that F / Fa. only. (2) Dynamic equivalent axial load As a ule, standad thust beaings with a contact angle of 9 cannot cay adial loads. Howeve, self-aligning thust olle beaings can accept some adial load. The dynamic equivalent axial load fo these beaings is given in fomula (4.18). PaFa1.2F4.18 whee, PaDynamic equivalent axial load, N FaActual axial load, N FActual adial load, N Povided that F / Fa. only. 4.4.2 Static equivalent load The static equivalent load is a hypothetical load which would cause the same total pemanent defomation at the most heavily stessed contact point between the olling elements and the aceway as unde actual load conditions; that is when both static adial loads and static axial loads ae simultaneously applied to the beaing. Fo adial beaings this hypothetical load efes to pue adial loads, and fo thust beaings it efes to pue centic axial loads. These loads ae designated static equivalent adial loads and static equivalent axial loads espectively. (1) Static equivalent adial load Fo adial beaings the static equivalent adial load can be found by using fomula (4.19) o (4.2). The geate of the two esultant values is always taken fo Po. PoXo FYo Fa4.19 PoF 4.2 A-23
Beaing Load Calculation 4.4.3 Load calculation fo angula ball beaings and tapeed olle beaings Fo angula ball beaings and tapeed olle beaings the pessue cone apex (load cente) is located as shown in Fig. 4.12, and thei values ae listed in the beaing tables. When adial loads act on these types of beaings the component foce is induced in the axial diection. Fo this eason, these beaings ae used in pais (eithe DB o DF aangements). Fo load calculation this component foce must be taken into consideation and is expessed by fomula (4.22). a Fa F Load cente Fa F a Load cente Fa.F 4.22 Y The equivalent adial loads fo these beaing pais ae given in Table 4.. Fig. 4.12 Pessue cone apex Table 4. Beaing aangement and dynamic equivalent load Beaing aangement Load condition Axial load Equivalent adial load DB aangement DF aangement DB aangement DF aangement Bg1 F1 Bg2 Bg1 Fa Fa F2 F1 Bg2 F2 Fa Fa Bg2 Bg1 F2 F1 Bg2 F2 Bg1 F1.F1.F2 Fa Y1 Y2.F1.F2 Fa Y1 Y2.F2.F1 Fa Y2 Y1.F2.F1 Fa Y2 Y1 Fa1.F2 Fa Y2.F2 Fa2 Y2.F1 Fa1 Y1 Fa2.F1 Fa Y1.F1 Fa1 Y1 Fa2.F1 Fa Y1 Fa1.F2 Fa Y2.F2 Fa2 Y2 P1XF1Y1 P2F2 P1F1 P2XF2Y2 P1F1 P2XF2Y2 P1XF1Y1 P2F2 Note 1: The above ae valid when the beaing intenal cleaance and peload ae zeo. 2: Radial foces in the opposite diection to the aow in the above illustation ae also egaded as positive..f2 Fa Y2.F1 Fa Y1.F1 Fa Y1.F2 Fa Y2 A-24