SELECTION  OF THE BEARINGS'DIMENSION  

                  Even under normal operational conditions , some fish scale damages ( called peeling or flake ) 
            will be caused on the surfaces of the tray and  the  rolling bodies due to fatigue of the  materials 
            afterthe repeatedly alternative load effected  upon  the surfaces of the rolling bodies and the tray
            duringthe loaded rotation of the bearings..
                  The total  number of revolutions  before  the happening of this operational rolling fatigue is 
            called"fatigue life " of the bearings
                  Considering the dispersion of material fatigue itself, this fatigue should be studied from the 
            viewof statistics.
                  So when a lot of same bearings rotate under the same conditions,rolling fatigue will not occur 
            on 90% of those bearings. The total number of revolutions of them is called "basic rated life of the
            bearings"(i.e. the life time with 90% reliability).
                  When  the  rotation  speed remains fixed , the life can be also expressed  with total times of 
            revolutions.
                  In practical operation, damages other than operational fatigue may occur(for example abrasion,
            burnt ,creeping , erosion , indentation , breakage etc) . These extra damages can be avoided through 
            suitable selection ,mounting and lubricating .

            Basic rated dynamic load
                    The basic rated dynamic load shows  the rolling fatigue-resistance of the bearing ( i .e . load 
             capacity) . This means the constant pure radical load ( for centripetal bearings) or central axle load
            (for thrusting bearings ) is effected in a definite direction , the inner ring rotates with fixed outer 
            ring (or vise versa ) . The basic rated life can reach 1 million revolutions under this load. The basic
            rated dynamic loads of the centripetal  bearings and  thrusting bearing  are called radical basic rated
            dynamic load or axle rated dynamic load separately, expressed with Cr and Ca . The values are listed in
            the Bearing Dimension List.
             Basic rated life
                    Equation (1) shows the relationship among basic rated dynamic load, equivalent dynamic load and 
             the basic rated life time .When the bearings are rotated at a fixed speed , it would be more convenient
             to express life with time. Please see equation (2).Furthermore, life time is expressed with distance(km)
             when used for railroad vehicles or cars. Please refer to equation (3).

               Therefore,for operational conditions of the bearing, assuming the equivalent dynamic load as P, the
         speed as n, the bearing basic rated dynamic load necessary to satisfy the designed life should be calcul-
         ated from equation(4).The size of the bearing can be decided only if we can get the satisfactory figure of
         the bearing from Bearing Dimension List.

        [Reference]it can be also expressed in following expressions  with life factor (fh) or speed factor(fn)
         L10h=500fhp..................................................................(5)
         Life factor : fh=fn  C/P......................................................(6)
         Speed factor : fn=(106 / 500x60n)1/p=(0.03n)-1/p..............................(7)
         fh , fn and f10h are easily found with calculation chart (reference chart)

       Reference chart  The relationship among speed (n)/speed factor (fn) and life factor (fh)/life (L10h)
       The correction as per temperature on the basic rated dynamic load and the dimension stabilization
           When bearings are used under high temperature , the material structure will change with the decrease of its 
       hardness. The basic rated dynamic load will be less than that under normal temperatures. Once there are changes 
       in material structure, it will not return back to its original even when the temp becomes normal.Therefore under
       high temperature , the value of the basic rated dynamic load list must be multiplied by a temperature factor in 
       List 3 to make necessary corrections.
           When bearings are to be used under 120 ℃  for a long time, dimension stabilization must be handled because
       of the big dimensional changes in normally heat-treated bearings.
           List 4 shows the dimensional stabilization code and the operational temp ranges.
           But hardness will decrease after dimensional stabilization. Sometimes, the basic rated dynamic load will 
       also be lowered.
           Table 3,  Temperature Factor                     Table 4, Dimensional code  and stabilization treatment

            
            Correcting the rated life time
              Equation 10 shows the basic rated life time with 90% reliability. In some cases, the consideration is 
       given to those with more than 90% reliability.
              Besides special materials may prolong the life time of bearings. Also the operational conditions such 
       as basic lubricating will effect the life of the bearings .  The life time after correction on the basis of 
       above mentioned factors is called corrected rated life time which can be calculated with equation below:

   Lna= a1 a2 a3 L10…….........................................................(8)

               Here: 
             Lna:corrected life time,106 revolutions
             (the life of reliability of 100-n% after considering factors such as bearing characteristic data and
              operational conditions (i.e. failure rate n%)
              L10:(reliability 90%)
               a1:reliability factor
             a2:characteristic data factor
             a3:operational condition factor
             Special attention should be given to the strength of the bearing and its casing when reliability over 
             90% is used for Lna selective bearing dimension. 

             But under conditions listed below, a3 < 1 should be used.
             lThe lubricating moving viscosity decreases in operation
             ball bearing......less than 13mm2/s{13cSt}
             roller bearing......less than 20mm2/s{20cSt}
             lThe speed is extremely low
             The product of rolling body times speed is less than 10000
             lThere are impurities mixed in lubrications.
             lThe relative slope between inner and outer rings is very big
                 remarks 1:When bearings are used in high temperature and the hardness is decreased , basic rated 
             dynamic load must be corrected
                Remarks2: Even special material is used with a2 >1 , if the lubricating condition is not suitable.
                The result of a2  x  a3 >1 can hardly be reached . In the case of a3<1 , Generalview shows a2≤1 . 
                Due to the difficulty of separating a2 from a3, one factor of a23 is suggested .
              The life time of multi bearing system
                  In the unit with more than two bearings, in most cases , the failure of only one bearing will cause 
             the failure of the whole unit. So when all bearings used are regarded as a bearing system, the rated life
             of this system can be calculated with equation below:

                                1/Le=1/L1e  + 1/L2e +1/L3e + ................................................(9)

                Where,
                L : the rated life of the whole bearing system
                L1, L2 , L3 ...... :  the rated lives of different bearings
                E: constant
                e=10/9 ......ball bearings
                e= 9/8 ......roller bearings
                (mean value should be used then mixed)
                Example:
                       For an axle supported by two roller bearings.Assuming the rated life of one bearings is 50000 
                hrs while the  rated life of the other is 30000 hrs, then , from equation 9  , the rated life of the 
                whole bearing system should be :
                             1/L9/8=1/500009/8 + 1/300009/8              L=20000h
              This means the rated life of the whole bearing system is shorter than the shortest life of the single
           bearing .This is a very important result which reminds us that in a bearing unit with over two different
           types, if the life time of the whole bearings system is to be considered,special attention must be given
           to this point.
              lThe necessary bearing life requested mechanically
                  It is not an economical way to over prolong the life of the bearing . The best way is to decide a
            necessary life of the bearing as per the mechanically operational conditions.
              Table 6     Bearing necessary life (for reference)

Operational condition

Short-time or intermittent
reliable  operation

Non-frequen but 
reliableoperation
            

Intermittentbut long
 time operation
             

Continuous orover 
8 hrs operation 

24 hrs continuousoperation             

             The load effected on the bearing includes the weight of the article supported by the bearing , the 
        transmission forces of the gears or belts, the loads resulted from  the mechanical operations and so on 
        and so forth.
             It is hardly possible to determine the load through a simple calculation because most of the loads
        are changeable with the uncertainty of its degree and nature . Therefore the way with theoretical calc-
        ulation value multiplied by an experience factor is used in determination of the practical bearing load.
             Load factor
             Though the radical or axle loads effected on the bearings can be got as per the general mechanical 
        way.The practical loads on the bearings are often greater than the calculated value due to the vibration
        and impact of mechanism. Thus , the theoretically calculated value should be often multiplied by  a load 
        factor related to the mechanical vibration and impact with an expression as below:
             Table 7 : load factor fw

                                      F=fw ．Fc  ....................................................................(10)

                    Here ,F : practical load,N { Kg f};Fc:theoretical load , N { Kg f};Fw:load factor (table 7).

          The load during belt or chain transmission
               The  theoretical load  effected on the belt shaft during its  transmission can be calculated from the 
          belt effective transmission force.But during the calculation of practical load, effective transmission must
          be multiplied by load factor ( fw ) related to the mechanical vibration or impact and the belt factor ( fb)
          which is related to the tension or the belt.
               Furthermore, a chain factor (the same as belt factor) must be multiplied in chain transmission.
               For this effect, please see equation (11).        
                                                                  6
                             Fb= 2M/DpXfwXfb=19.1x10  W/DpnXfwXfb = ........................(11)
                   Where,
                     Fb: the practical load on shafts of pulley or chain wheel,N{kgf}
                      M: torque of pulley or chain wheel,mN.m{kgf.mm}
                      W: transmission power,Kw
                     Dp: diameters of pulley or sprocket element,mm
                      n: speed,rpm
                     fw: load factor(see table 7)
                     fn: belt (chain ) factor(see talbe 8)
                    Table 8 Belt (chain) factor fb

               The load during gear transmission
               the theoretical loads effected on the gear includes tangential load (Kt),radical load (Kr) and
          axle load (Ka) . They can be calculated through mechanical method item  (2) (a) (b) (c) as per the 
          transmssion power and the type of the gears.
               But during the practical calculation of loads, the theoretical load must be multiplied with the
          mechanical vibration and impact factor (fw ...Table 7) and the gear factor ( fg ...Table 9) which is 
          related to the gear precision.
               Table 9  Gear Factor fg