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Mechanical Design                                                          Rolling Contact bearings

                              Rolling contact bearings
6.1 Types of rolling contact bearings
   Friction between moving parts can not be eliminated entirely, but often it is
reduced most effectively by using some form of rolling bearings. There are
many types of rolling contact bearings which suit different applications. The
most common types are, See fig.(6.1):
   1.    Ball bearings
        1.1. Single row ball bearing
        1.2. Double row ball bearing
        1.3. Self alignment ball bearing
        1.4. Angular contact ball bearing
        1.5. Thrust ball bearing
   2. Roller contact bearings
      2.1. Taper roller bearing
      2.2. Straight roller bearing
      2.3. Conical roller bearing
      2.4. Concave roller bearing
      2.5. Thrust roller bearing
      2.6. Needle bearings




                                                                Roller thrust
                                                  Ball thrust     bearing
                               Spherical roller                                 Radial tapered
    Ball bearing     Roller                        bearing
                                thrust bearing                                  roller bearing

        Fig. (6.1) Cut view of different types of rolling contact bearings
The loading on roller contact bearings can be
classified into three groups:
       1. Solely radial loading
       2. Solely axial loading
       3. Combined radial and axial loading
            Ball and roller bearings are
manufactured in several series, the most popular
ones are shown in fig (6.2). Within each of these      Extra   Light   Medium    Heavy
series is a wide range of different bearing sizes.     light
Heavy series bearings have the greater load               Fig. (6.2) Series of ball
carrying capacity but extra light series bearings                 bearings
run at higher speeds, assuming the bearings have
the same bore diameter and of similar internal construction.
 Dr. Salah Gasim Ahmed                                                                      YIC        1
Mechanical Design                                                Rolling Contact bearings


6.2 Standardisation of ball bearings:
       Through the effort of the society of Automotive Engineers (SAE) the
manufacturers of radial ball bearings have adopted the international standard
dimensions, according to which the light series is designated by the number
200, the medium by 300 and the heavy by 400. The last two digits of a standard
bearing number designate the bore diameter which comes in multiple of 5 mm,
see fig. (6.3)

6.3 Main parts of a typical ball bearing



                                  6309

                Bearing type   Series number     Bore diameter
                     Fig. (6.3) Bearing designation number
            The main parts of a typical ball bearing are :
          1. The outer ring, (outer
        race).                                            Ball                  Ball
          2. The inner ring ,(inner                                           retainer
        race).
          3. The    rolling     elements,
        (ball).
          4. The ball retainer (the cage)
See fig. (6.4)
6.4 Selection of ball bearings:                        Inner
       In selecting a ball bearing from                 ring                 Outer ring
trade catalogue for specific installation
three main points must be considered:
1. The bearing must be of the series           Fig. (6.4) Main parts of a typical ball bearing
   best suited to the installation, in
   regard to both capacity and
   dimensions.
2. The type of bearing selected, radial,
   thrust or combined must be suitable for the type of imposed load.
3. The size of the bearing must be such as to give the required length of service
   with sufficient assurance.

   In the majority of applications ball bearings have to resist some combination
of radial and thrust loads. The bearing rating is always referred to a radial load.
There for the combined load must be reduced to an equivalent radial load.

 Dr. Salah Gasim Ahmed                                                          YIC          2
Mechanical Design                                                   Rolling Contact bearings

               Various catalogues give different methods of reduction. In general the
               equivalent load Fe may be computed by the equation:
                              Fe = XFr + YFa                                               (6.1)
               Where,
                   Fe : equivalent radial load
                   Fr : actual radial load
                   Fa : actual axial load
               X and Y are coefficients which depends on the ratio Fa/Fr. For most bearings
               The values given in table (6.1) are suitable.
                                                  Table (6.1) Values of X and Y
e of bearing          Y              X
p groove             1.5             1
ular contact          1             0.5
aligning             2.5            0.5

                      Experiments have shown that the life of a ball bearing is a function of the
               load it carries. It also showed that the service life of a ball bearing is inversely
               proportional to the value of the load it carries raised to power 3. In other words
               it can be expressed by the equation

                      Ln =   (C)     3
                                                                                                   (6.2)
                               Fe
               Where,
                   C: dynamic specific capacity of bearing.
                   Ln: Life of bearing in millions of revolution.
                   Fe : Equivalent load
                      Table (6.4) shows the dynamic specific capacity for SKF bearings. SKF
               engineers introduced speed factor and life factor which can be taken from fig.
               (6.5) and fig. (6.6) respectively. The required dynamic capacity can be obtained
               from the equation:
                                         f s Fe f h
                              Fc ≥                                                                 (6.3)
                                             fn
               Where
                  fs: safety factor
                  fn : speed factor
                  fh : life factor
                  Fc : dynamic capacity of the bearing

                                                          Bearing life

                                                                                  Life in working
                                                             Class of machine
                                                                                       hours
                 1      Instruments and apparatus that are used only seldom.
                Dr. Salah Gasim Ahmed                                                              YIC         3
Mechanical Design                                                    Rolling Contact bearings

         Demonstration apparatus, mechanisms for operating
                                                     sliding doors
  2                                               Aircraft engines     2000 - 1000
         Machines used for short periods or intermittently and
         whose brake down would not have serious
         consequences; hand tools, lifting tackles in
  3                                                                    8000 - 4000
         workshops, hand operated machines, generally
         agricultural machines, cranes in erecting shops,
                                               domestic machines
         Machines working intermittently and where
         breakdown would have serious consequences.
  4      Auxiliary machines in power stations, conveyor plant         12000 - 8000
         for flow production, lifts cranes for piece goods;
                                 machine tools used infrequently
         Machine for use 8 hours per day and fully utilized:
  5                                                                   20000 - 12000
           .stationary electric motors, general purpose gear units
         Machine for use 8 hours per day and fully utilized:
  6      machines for engineering industry generally: cranes          30000 - 20000
                   for bulk goods, ventilating fans, countershafts
         Machines for continuous use 24 hours per day:
         Separators, compressors, pumps, mine hoist,
  7                                                                   60000 - 40000
         stationary electric machines, machines in continuous
                                  operations on board naval ships
         Machines required to work ith high degree of
         reliability 24 hours per day: pulp and paper
  8      machinery; public power plants, mine pumps, pumps           200000 - 100000
         in water works, machinery in continuous operation on
                                            board merchant ships

6.5 Installation of ball bearings:

      In the installation of ball bearings the following points must be
considered separately:

   1.   The shaft must be designed to take the inner ring (race)., see fig. (6.7)
   2.   A suitable mounting must be designed for the outer ring (race).
   3.   Lubrication must be provided for the bearing
   4.   Methods of sealing the lubricant and preventing penetration of foreign
        matter must be provided.




 Dr. Salah Gasim Ahmed                                                              YIC          4
Mechanical Design                                           Rolling Contact bearings




Example 1

     Determine the load capacity of a single row deep-groove SKF bearing –
SKF 10, medium series, that must run 2000 hours at 700 rpm.

Solution:

    From table (6.4) C = 10400 lb




            Fig. (6.7) A method of fastening ball bearing to a shaft
    From fig.(6.5) fn = 0.36

    From fig.(6.6) fh = 1.58

                                 f s Fe f h
Hence from equation (6.3) Fc ≥       fn

            Fc f n
    Fe =
            fs fh

Take safety factor fs = 1
            10400 x0.36
     Fe =
              1x1.58

     Fe = 2370


Example 2

      A shaft is supported by two bearings. One of the bearings carries a radial
load of 200 lb and an axial load of 500 lb with minor shocks. The shaft runs at
230 rpm and operates 10 hours per day for 5 days per week. Select a suitable
 Dr. Salah Gasim Ahmed                                                     YIC          5
Mechanical Design                                          Rolling Contact bearings

ball bearing with a service life of 2 years if the diameter of the shaft can be
varied between 3 16 and 3 1 .
                 15
                          2


Solution
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 Dr. Salah Gasim Ahmed                                                    YIC          6

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MET 304 Bearings notes

  • 1. Mechanical Design Rolling Contact bearings Rolling contact bearings 6.1 Types of rolling contact bearings Friction between moving parts can not be eliminated entirely, but often it is reduced most effectively by using some form of rolling bearings. There are many types of rolling contact bearings which suit different applications. The most common types are, See fig.(6.1): 1. Ball bearings 1.1. Single row ball bearing 1.2. Double row ball bearing 1.3. Self alignment ball bearing 1.4. Angular contact ball bearing 1.5. Thrust ball bearing 2. Roller contact bearings 2.1. Taper roller bearing 2.2. Straight roller bearing 2.3. Conical roller bearing 2.4. Concave roller bearing 2.5. Thrust roller bearing 2.6. Needle bearings Roller thrust Ball thrust bearing Spherical roller Radial tapered Ball bearing Roller bearing thrust bearing roller bearing Fig. (6.1) Cut view of different types of rolling contact bearings The loading on roller contact bearings can be classified into three groups: 1. Solely radial loading 2. Solely axial loading 3. Combined radial and axial loading Ball and roller bearings are manufactured in several series, the most popular ones are shown in fig (6.2). Within each of these Extra Light Medium Heavy series is a wide range of different bearing sizes. light Heavy series bearings have the greater load Fig. (6.2) Series of ball carrying capacity but extra light series bearings bearings run at higher speeds, assuming the bearings have the same bore diameter and of similar internal construction. Dr. Salah Gasim Ahmed YIC 1
  • 2. Mechanical Design Rolling Contact bearings 6.2 Standardisation of ball bearings: Through the effort of the society of Automotive Engineers (SAE) the manufacturers of radial ball bearings have adopted the international standard dimensions, according to which the light series is designated by the number 200, the medium by 300 and the heavy by 400. The last two digits of a standard bearing number designate the bore diameter which comes in multiple of 5 mm, see fig. (6.3) 6.3 Main parts of a typical ball bearing 6309 Bearing type Series number Bore diameter Fig. (6.3) Bearing designation number The main parts of a typical ball bearing are : 1. The outer ring, (outer race). Ball Ball 2. The inner ring ,(inner retainer race). 3. The rolling elements, (ball). 4. The ball retainer (the cage) See fig. (6.4) 6.4 Selection of ball bearings: Inner In selecting a ball bearing from ring Outer ring trade catalogue for specific installation three main points must be considered: 1. The bearing must be of the series Fig. (6.4) Main parts of a typical ball bearing best suited to the installation, in regard to both capacity and dimensions. 2. The type of bearing selected, radial, thrust or combined must be suitable for the type of imposed load. 3. The size of the bearing must be such as to give the required length of service with sufficient assurance. In the majority of applications ball bearings have to resist some combination of radial and thrust loads. The bearing rating is always referred to a radial load. There for the combined load must be reduced to an equivalent radial load. Dr. Salah Gasim Ahmed YIC 2
  • 3. Mechanical Design Rolling Contact bearings Various catalogues give different methods of reduction. In general the equivalent load Fe may be computed by the equation: Fe = XFr + YFa (6.1) Where, Fe : equivalent radial load Fr : actual radial load Fa : actual axial load X and Y are coefficients which depends on the ratio Fa/Fr. For most bearings The values given in table (6.1) are suitable. Table (6.1) Values of X and Y e of bearing Y X p groove 1.5 1 ular contact 1 0.5 aligning 2.5 0.5 Experiments have shown that the life of a ball bearing is a function of the load it carries. It also showed that the service life of a ball bearing is inversely proportional to the value of the load it carries raised to power 3. In other words it can be expressed by the equation Ln = (C) 3 (6.2) Fe Where, C: dynamic specific capacity of bearing. Ln: Life of bearing in millions of revolution. Fe : Equivalent load Table (6.4) shows the dynamic specific capacity for SKF bearings. SKF engineers introduced speed factor and life factor which can be taken from fig. (6.5) and fig. (6.6) respectively. The required dynamic capacity can be obtained from the equation: f s Fe f h Fc ≥ (6.3) fn Where fs: safety factor fn : speed factor fh : life factor Fc : dynamic capacity of the bearing Bearing life Life in working Class of machine hours 1 Instruments and apparatus that are used only seldom. Dr. Salah Gasim Ahmed YIC 3
  • 4. Mechanical Design Rolling Contact bearings Demonstration apparatus, mechanisms for operating sliding doors 2 Aircraft engines 2000 - 1000 Machines used for short periods or intermittently and whose brake down would not have serious consequences; hand tools, lifting tackles in 3 8000 - 4000 workshops, hand operated machines, generally agricultural machines, cranes in erecting shops, domestic machines Machines working intermittently and where breakdown would have serious consequences. 4 Auxiliary machines in power stations, conveyor plant 12000 - 8000 for flow production, lifts cranes for piece goods; machine tools used infrequently Machine for use 8 hours per day and fully utilized: 5 20000 - 12000 .stationary electric motors, general purpose gear units Machine for use 8 hours per day and fully utilized: 6 machines for engineering industry generally: cranes 30000 - 20000 for bulk goods, ventilating fans, countershafts Machines for continuous use 24 hours per day: Separators, compressors, pumps, mine hoist, 7 60000 - 40000 stationary electric machines, machines in continuous operations on board naval ships Machines required to work ith high degree of reliability 24 hours per day: pulp and paper 8 machinery; public power plants, mine pumps, pumps 200000 - 100000 in water works, machinery in continuous operation on board merchant ships 6.5 Installation of ball bearings: In the installation of ball bearings the following points must be considered separately: 1. The shaft must be designed to take the inner ring (race)., see fig. (6.7) 2. A suitable mounting must be designed for the outer ring (race). 3. Lubrication must be provided for the bearing 4. Methods of sealing the lubricant and preventing penetration of foreign matter must be provided. Dr. Salah Gasim Ahmed YIC 4
  • 5. Mechanical Design Rolling Contact bearings Example 1 Determine the load capacity of a single row deep-groove SKF bearing – SKF 10, medium series, that must run 2000 hours at 700 rpm. Solution: From table (6.4) C = 10400 lb Fig. (6.7) A method of fastening ball bearing to a shaft From fig.(6.5) fn = 0.36 From fig.(6.6) fh = 1.58 f s Fe f h Hence from equation (6.3) Fc ≥ fn Fc f n Fe = fs fh Take safety factor fs = 1 10400 x0.36 Fe = 1x1.58 Fe = 2370 Example 2 A shaft is supported by two bearings. One of the bearings carries a radial load of 200 lb and an axial load of 500 lb with minor shocks. The shaft runs at 230 rpm and operates 10 hours per day for 5 days per week. Select a suitable Dr. Salah Gasim Ahmed YIC 5
  • 6. Mechanical Design Rolling Contact bearings ball bearing with a service life of 2 years if the diameter of the shaft can be varied between 3 16 and 3 1 . 15 2 Solution …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. …………………………………………………………………………………………..…………………….. Dr. Salah Gasim Ahmed YIC 6
  • 7. Mechanical Design Rolling Contact bearings Exercises 1. The main shaft in a reduction gear-box is shown in fig.(1). The shaft is to be supported by two deep groove ball bearing at A and D. In addition to the radial loads the shaft carries an axial load of 175 lb. Determine the bearings loads and select suitable single row deep groove bearings if the shaft rotates at 1200 rpm and operates 7 hours per day, five days a week for five years. Take factor of safety = 1.5. The maximum diameter of the shaft at both ends should not exceed 30 mm 100 lb 2 in 250 lb 3 in 1 in A Gear B 175 lb Gear C D Fig.(1) 2. Select suitable deep groove ball bearings for the spindle of a woodworking machine revolving at 1200 rpm. One bearing is subjected to a radial load of 600 lb and the other carries a radial load of 820 lb. An axial load of 310 lb is acting along the machine spindle. The machine is to be used 8 hours per day and 5 days a week, and a service life of 10 years is desired. The diameter of the spindle is 2 in. and can be turned down slightly. 3. A reduction gear-box is shown in fig.(2). It consists of two helical gears fixed to shafts X and Y. Shaft X is supported by two single row deep groove ball bearings. On shaft X, the bearings and the helical gear are located as follows: The distance between the centre of pulley and centre of bearing A = 35 mm, The distance between the centre of pulley and centre of helical gear = 90 mm, The distance between the centre of pulley and centre of bearing B = 135 mm. Dr. Salah Gasim Ahmed YIC 7
  • 8. Mechanical Design Rolling Contact bearings The helical gear exerts the following loads on shaft X: Radial load = 100 lb Tangential load = 150 lb Axial load = 50 lb Bearing A Shaft X Bearing B Shaft Y Fig.(2) 4. Determine the bearings loads and select suitable single row deep groove bearings if the shaft rotates at 1500 rpm and operates 8 hours per day, seven days a week for five years. Take factor of safety = 1.5 5. A shaft supported by two ball bearings: A and B is shown in fig. (3). The shaft carries two pulleys with radial loads 250 lb and 600 lb. An axial load of 300 lb is acting along the shaft in the direction indicated by the arrow. The shaft runs at speed of 1500 rpm for 8 hours per day and 5 days a week, and a 2 inch 2 inch 1 inch 600 Lb 300 Lb Bearing A Bearing B 250 Lb Fig. (3) service life of 10 years is desired. The minimum diameter of the shaft is not less than 1 inch. Select suitable ball bearings. Dr. Salah Gasim Ahmed YIC 8
  • 9. Mechanical Design Rolling Contact bearings 6. Determine the load capacity of a single row deep-groove SKF bearing – SKF 15, heavy series, that must run 3000 hours at 600 rpm. Fig. (4) shows a shaft supported by two ball bearings and runs at 1000 rpm. A radial and axial loads act on the shaft with minor shocks. If the shafts operate for 16 hours per day and total service life required is 3 years select suitable bearings for the shaft. The minimum diameter off both ends of the shaft is not less than 9 mm. 7. Select suitable ball bearings for the spindle of a woodworking machine revolving at 1200 rpm. One bearing is subjected to a radial load of 600 lb 900 lb 8 inch 4 inch 150 lb B A Fig. (4) and a thrust load of 450 lb; the other carries only a radial load of 650 lb. The machine is to be used 8 hour per day and 5 days a week, and a service life of 10 years is desired. The diameter of the spindle is 2 in. and can be turned down slightly. 8. A ball bearing is to be used on a drill press operating at 3000 rpm with a 250 lb maximum thrust load and 500 lb radial load. The press will be operated five 8-hour days a week but will be idle 20% of the time. Determine thr type and size of the bearing (a) if it should last 1 year. (b) if it should last 2 years. 9. Determine the radial capacity of an SKF 6211-Z bearing running at 500 rpm and carrying an axial load of 500 lb, for 2 years of continuous service. 10.A shaft is supported by two bearings 16 in apart and carries a bevel gear of 7.75 in pitch diameter. The gear is at 6 in from one end of the shaft. The gear produces a radial load of 2150 lb and a thrust load of 625 lb when rotating at 525 rpm. .Determine : (a) The shaft diameter if the shaft is made of SAE1045 steel and (b) The proper type and size of ball bearings to be used on each end of the shaft. The desired life is 2 years at 50 hour/week. Dr. Salah Gasim Ahmed YIC 9
  • 10. Mechanical Design Rolling Contact bearings Table (6.2) Safety factors for MRB ball bearings Safety factor, life Safety factor, life of 5 to 10 years of 10 to 20 years Load conditions Intermittent 10 hours per day Continuous Continuous Steady load 0.5 ------ 1 1.5 2 3 Light shock 1 ------- 2 2.5 3 4 Moderate shock 2 ------- 3 3.5 4 5 Severe shock 3-------- 4 4.5 5 6 Table (6.1) Values of X and Y f bearing Y X roove 1.5 1 r contact 1 0.5 gning 2.5 0.5 Table (6.3) Over-all dimensions of radial ball bearings SAE (Bore of inner race (d Outside diameter D mm (Width B (mm Bearing 200 300 400 200 300 400 Number mm in series series series series series series 00 10 0.3937 30 35 …… 9 11 …… 01 12 0.4724 32 37 …… 10 12 …… 02 15 0.5906 35 42 …… 11 13 …… 03 17 0.6693 40 47 62 12 14 17 04 20 0.7874 47 52 72 14 15 19 05 25 0.9843 52 62 80 15 17 21 06 30 1.1811 62 72 90 16 19 23 07 35 1.3780 72 80 100 17 21 25 08 40 1.5748 80 90 110 18 23 27 09 45 1.7717 85 100 120 19 25 29 10 50 1.9685 90 110 130 20 27 31 11 55 2.1654 100 120 140 21 29 33 12 60 2.3622 110 130 150 22 31 35 13 65 2.5591 120 140 160 23 33 37 14 70 2.7559 125 150 180 24 35 42 15 75 2.9528 130 160 190 25 37 45 16 80 3.1496 140 170 200 26 39 48 17 85 3.3465 150 180 210 28 41 52 18 90 3.5433 160 190 225 30 43 54 19 95 3.7402 170 200 …… 32 45 …… 20 100 3.9370 180 215 …… 34 47 …… 21 105 4.1339 190 225 …… 36 49 …… 22 110 4.3307 200 240 …… 38 50 …… Dr. Salah Gasim Ahmed YIC 10
  • 11. alignin groove groove Angula contact -row self- deep- deep- -row row Table (6.4)Specific dynamic capacity of SKF ball bearings, in Pounds row g r- Double Double Single- Single- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 2 3 4 2 3 4 2 3 4 …… …… 0 5 0 6 4 …… 0 2 2 …… …… …… …… …… 7 1 1 0 0 5 …… 0 4 1 0 0 8 …… 0 6 8 …… …… …… …… …… Mechanical Design 1 1 1 1 0 3 6 …… 0 5 2 0 6 9 …… 0 4 0 …… …… …… …… …… Dr. Salah Gasim Ahmed 1 1 1 2 0 2 1 …… 0 0 6 0 6 3 …… 0 0 6 0 0 8 …… …… …… …… 2 1 2 2 3 0 4 2 …… 0 6 1 0 5 7 …… 0 5 5 0 0 5 …… …… 0 0 7 …… 2 2 2 3 4 2 0 5 2 …… 0 2 3 0 5 6 0 0 3 0 0 8 0 0 0 …… 0 8 2 0 0 8 0 0 2 3 2 3 6 3 6 2 3 6 0 5 0 0 0 1 0 5 2 0 0 8 0 0 5 0 0 3 0 0 8 0 0 4 3 0 0 2 0 0 8 0 5 3 4 6 3 4 7 5 7 1 3 4 7 0 0 8 0 5 0 0 0 3 0 0 7 0 0 5 0 0 1 0 0 3 0 0 0 4 0 5 2 0 0 7 0 0 3 4 7 4 5 9 7 9 1 4 5 9 0 0 1 0 5 0 0 0 9 0 5 9 0 0 0 1 0 0 0 0 0 2 1 0 0 6 7 0 0 1 0 5 9 0 0 6 0 6 8 4 6 1 8 1 1 5 6 1 0 5 6 0 0 4 0 0 0 5 0 0 0 0 0 2 3 0 0 0 0 0 6 4 0 0 0 2 0 0 7 0 0 0 0 0 9 2 7 1 5 9 1 9 1 2 5 9 1 0 5 6 0 0 0 2 0 5 8 0 0 4 0 0 0 6 4 0 5 6 0 0 0 7 0 0 5 7 0 0 0 0 0 4 0 0 0 3 4 8 1 5 1 1 9 1 2 6 1 1 drives 0 0 4 0 0 0 7 2 0 5 3 0 0 0 2 0 0 3 7 0 0 8 1 0 0 3 9 0 0 5 7 0 5 3 0 0 0 2 0 0 6 6 1 1 7 1 1 1 1 2 7 1 1 0 0 0 2 0 0 3 5 0 0 8 0 0 7 3 0 0 0 9 0 0 3 4 0 0 0 2 0 0 5 0 0 0 8 0 0 7 3 0 0 3 8 1 1 8 1 1 1 2 3 8 1 1 0 0 7 2 0 0 3 6 0 5 6 0 0 3 5 0 0 8 0 0 0 6 5 0 0 0 5 …… 0 0 0 0 0 0 3 5 0 0 0 0 1 1 9 1 2 1 2 1 1 2 0 0 3 5 0 0 0 0 0 0 4 0 0 0 0 7 0 0 0 6 0 0 0 7 0 0 5 7 …… 0 0 0 1 0 0 0 7 0 0 5 5 1 2 1 1 2 1 2 1 1 2 0 0 3 6 0 0 8 2 0 0 0 1 0 0 6 8 0 0 0 8 0 0 0 8 0 0 5 0 …… 0 0 4 1 0 0 0 9 0 0 0 7 1 2 1 1 2 1 3 1 1 2 0 0 0 8 0 0 5 5 0 0 2 2 0 0 8 0 …… 0 0 6 9 0 0 5 3 …… 0 0 7 2 0 0 8 0 …… 1 2 1 2 1 3 1 2 0 0 0 0 0 0 5 7 0 0 7 3 0 0 4 2 …… 0 0 4 0 0 0 5 3 …… 0 0 3 4 0 0 8 2 …… 2 2 1 2 2 3 1 2 0 0 8 2 0 0 0 1 0 0 6 5 0 0 5 4 …… 0 0 2 3 0 0 5 5 …… 0 0 6 6 0 0 5 4 …… 2 3 1 2 2 3 1 2 0 0 5 5 …… 0 0 6 7 0 0 5 6 …… 0 0 5 8 …… …… 0 0 6 7 0 0 5 6 …… 2 1 2 2 1 2 0 0 5 7 …… 0 0 6 9 0 0 5 0 …… 0 0 0 2 …… …… 0 0 6 9 0 0 5 2 …… 2 1 3 3 1 3 0 0 0 1 …… 0 0 6 1 0 0 5 2 …… …… …… …… …… 0 0 5 4 …… 3 2 3 3 0 0 5 3 …… 0 0 0 4 0 0 5 7 …… …… …… …… 0 0 0 4 0 0 0 9 …… 3 2 3 2 3 Belt …… …… …… …… …… …… …… …… 0 0 5 7 …… …… 2 YIC 11 …… …… …… …… …… …… …… …… 0 0 0 1 0 0 0 8 …… 3 4 …… …… …… …… …… …… …… …… 0 0 5 3 …… …… 3 …… …… …… …… …… …… …… …… 0 0 0 9 0 0 5 8 …… 3 5 …… …… …… …… …… …… …… …… 0 0 5 1 …… …… 4
  • 12. Number SAE 0 0 2 0 0 5 6 8 1 5 1 Mechanical Design 0 9 2 0 5 2 Dr. Salah Gasim Ahmed 0 1 3 0 0 4 0 1 4 0 3 8 0 1 5 0 4 2 0 2 6 0 0 1 0 3 7 0 5 3 0 3 8 0 5 2 0 4 9 0 5 7 0 4 0 0 0 1 1 5 drives 1 0 0 2 1 6 2 0 0 1 1 7 3 0 5 6 1 7 4 0 0 5 1 8 5 0 0 3 1 9 6 0 0 8 1 9 7 0 0 8 1 1 1 8 0 0 9 2 1 1 9 …… 1 0 0 0 3 6 2 1 1 …… 2 2 0 0 4 0 2 2 Belt 4 …… 2 YIC 12 6 …… 2 8 …… 2 0 …… 3 2 …… 3
  • 13. Number SAE 0 0 2 0 0 5 6 8 1 5 1 Mechanical Design 0 9 2 0 5 2 Dr. Salah Gasim Ahmed 0 1 3 0 0 4 0 1 4 0 3 8 0 1 5 0 4 2 0 2 6 0 0 1 0 3 7 0 5 3 0 3 8 0 5 2 0 4 9 0 5 7 0 4 0 0 0 1 1 5 drives 1 0 0 2 1 6 2 0 0 1 1 7 3 0 5 6 1 7 4 0 0 5 1 8 5 0 0 3 1 9 6 0 0 8 1 9 7 0 0 8 1 1 1 8 0 0 9 2 1 1 9 …… 1 0 0 0 3 6 2 1 1 …… 2 2 0 0 4 0 2 2 Belt 4 …… 2 YIC 12 6 …… 2 8 …… 2 0 …… 3 2 …… 3
  • 14. Number SAE 0 0 2 0 0 5 6 8 1 5 1 Mechanical Design 0 9 2 0 5 2 Dr. Salah Gasim Ahmed 0 1 3 0 0 4 0 1 4 0 3 8 0 1 5 0 4 2 0 2 6 0 0 1 0 3 7 0 5 3 0 3 8 0 5 2 0 4 9 0 5 7 0 4 0 0 0 1 1 5 drives 1 0 0 2 1 6 2 0 0 1 1 7 3 0 5 6 1 7 4 0 0 5 1 8 5 0 0 3 1 9 6 0 0 8 1 9 7 0 0 8 1 1 1 8 0 0 9 2 1 1 9 …… 1 0 0 0 3 6 2 1 1 …… 2 2 0 0 4 0 2 2 Belt 4 …… 2 YIC 12 6 …… 2 8 …… 2 0 …… 3 2 …… 3