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GEAR REDUCER PROJECT

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GEAR REDUCER PROJECT Powered By Docstoc
					Eric Achey

Advanced Drafting and Design


                                                   Gear Reducer Design Calculations

       The documentation to follow will demonstrate the validity of my design for a 6:1 gear reducer. These will include all calculations
made toward defining the necessary components of the gear train and bearings, including complete tablatures for ease of specification
comparison and comprehension.
         Moment diagrams, system layout, and full fabrication drawings are included, and will clarify the design concept. The mechanical
requirements can be solidified during the CAD proto-typing process. The completed part and assembly drawings will enable fabrication of a
working prototype for evaluation and/or manufacture.
       Table #1 and the noted information and calculations were determined using the approximate horsepower and torque rating charts from
the Boston Gear Catalog Online, Pg. 48 & 49, for Class 1 service (Service Factor = 1.0), 100% Efficiency.
       Table #2 contains further obtainable specifications from the catalog from the detail sheets, Pg. 33 & 34, for both 6 and 8 Diametral
Pitch- metallic spur gears.
       Table #3 contains shaft and key calculations, and noted information, to determine shaft diameter, length and weight.
       Table #4 includes information and calculations to determine bearing load and service life expectation.
       All Material Specifications (material, grade, treatment processes, special features) that were available are included in the
Manufacturer’s/ Supplier’s Specification sheets enclosed with this design concept.
                                                                                                                                Achey 2
                                                  Table #1 – Gear Calculations
Gear #     Gear       HPT    Speed    Torque    Number     Diametra    Gear     Pressure      HPR         Rated         Pitch   Center
          Rotation                      (T)     of Teeth       l       Mat.      Angle      Boston Gear   Torque        Dia.    Distance
                                                   (N)       Pitch                          Cat. online    (TR)         (PD)     (CD)
                                                             (DP)                                         Boston Gear
                                                                                                          Cat. Online
 Units       ---       ---   RPM        In/lbs      ---        ---       ---     Deg.         ---       In/lbs           In.      In.
 Notes       ---        1       2          3         4          5         5         5          5                          6        7
  G1        CW         10     1800        350       14          8       Steel     20º        10.91        382           1.75     2.625
  G2       CCW         10      900        700       28          8       Steel     20º        13.88        972            3.5
  G3       CCW         10      900        700       12          6       Steel     20º        13.06        915            2.0      4.0
  G4        CW         10      300       2100       36          6        C.I.     20º        12.26       2575            6.0
Notes:
   1. Horsepower Transmitted (HPT) @ 100% Efficiency.
   2. Overall Speed Ratio = 1800 RPM / 300 RPM
           Speed Reduction Factor = 6 / 1 – 1800 RPM
           First Stage Reduction = 2 / 1 – 900 RPM
           Second Stage Reduction = 3 / 1 – 300 RPM
   3. Torque (T) = HP(63,000)/RPM
          @ S1 = 10(63,0000)/1800=350 in/lbs
          @ S2 = ( Ft = 2(350)/1.75 = 400 lbs) 400(3.5)/2 = 700 in/lbs
          @ S3 = ( Ft = 2(700)/2.0 = 700 lbs) 700(6)/2 = 2100 in/lbs
   4. For Spur Gears in Class 1 Service (Service Factor = 1.0)
           Number of Teeth (N1) for G1 from manufacture’s table. 14 @ 2:1 =
           N2 G2 = 28
           N3 G3 = 12      @ 3:1 =
           N4 G4 = 36
   5. Diametral Pitch (DP), Gear Material, Pressure Angle, & Rated Horsepower (HPR) from manufacture’s tables.
   6. Pitch Diameter (PD) = N / D.P.
           G1 = 14/8 = 1.75
           G2 = 28/8 = 3.5
           G3 = 12/6 = 2.0
           G4 = 36/6 = 6.0
   7. Center Distance (CD) = Gear 1 to Gear 2: (1.75 + 3.5)/2 = 2.625” Gear 3 to Gear 4: (2 + 6)/2 = 4.0”
                                                                                                                                                       Achey 3



                                             Table #2 – Gear Data From Manufacture’s Tables
Manufacture: Boston Gear_
Type of Gears: __Spur – 20 Deg. Pressure Angle_

                                                                           Bore
                     Diam.        #       Pitch     Outside     Stock                   Hub     Hub       Face                                Boston        Gear
Gear      Press.                                                           Size                                      Overall      Gear
                     Pitch      Teeth     Dia.        Dia.      Bore                    Dia.    Proj.     Width                                Gear         Weight
 #        Angle                                                           Max.                                       Length       Style
                     (DP)        (N)      (PD)       (OD)        (B)                    (H)      (P)       (W)                               Catalog #      (Est.)
                                                                            Req.
Units      Deg.        ---        ---       In.        In.        In.       In.         In.      In.        In.         In.         ---          ---          Lbs.
                                                                          .75*
  G1        20º         8         14       1.75        2.0        .75             .75
                                                                                        1.31     .75        1.5        2.25       Spur      YH14-3/4          1.34
                                                                          1.75*
  G2        20º         8         28        3.5       3.75       .875             1.0
                                                                                        3.06     .88        1.5        2.38       Spur       YH28 **          5.85
                                                                          .875*
  G3        20º         6         12        2.0       2.33        1.0             1.0
                                                                                        1.46     .88        2.0        2.88       Spur        YJ12-1          2.22
                                                                          2.0*
  G4        20º         6         36        6.0       6.33       1.125          1.25
                                                                                        3.5      1.5        2.0         3.5       Spur      YJ36B **         20.11
* - Maximum bore by manufacturer R.O.T. (60% of hub dia.). Required value represents acceptable bore size in accordance with hub diameter, shaft size required,
     and G3 stock bore size.
** - Require machining of bore size to indicated diameter and standard keyways of .25”W X .125”D (see machining dwgs.).

Gear Weight Estimate: Since no weights were given by the manufacturer’s online catalog, the following estimates are based on values for
steel round stock (service industry reference) at the nearest diameter to the hub diameter and projection length, and the gear face length at the
pitch diameter (to offset tooth voids).
              lb/ft              lb/ft
     G1 = (5.049/12)(.75) + (8.18/12)(1.5) = 1.34 lbs
     G2 = (24.04/12)(.88) + (32.7/12)(1.5) = 5.85 lbs
     G3 = (6.01/12)(.88) + (10.68/12)(2) = 2.22 lbs
     G4 = (32.7/12)(1.5) + (96.13/12)(2) = 5.85 lbs

Shaft Weights: From selected shaft lengths calculated for Table #3, using steel round stock values from steel service industry reference book.
    S1 = 11.97875(1.5021) = 1.5 lbs
    S2 = 9.885(2.6704) = 2.2 lbs
    S3 = 12.38(4.1724) = 4.3 lbs
                                                                                                                                  Achey 4


                                            Table #3 –Shaft & Gear Key Calculations
Shaft   HPT    Speed     Torque      Min.       Min. Shaft    Selected Selected        Gear Key      Shear    Calc.    Selected    Calc.
  #                        (T)       Shaft      Dia. (Dm2)     Shaft    Shaft            Size        Force    Min.      Gear       Shaft
                                   Dia. (Dm1)   Based on        Dia.    Length         (Based on      (P)     Key        Key       Weight
                                   Based on     Torsional        (D)     (L)           Shaft Dia.)   @ Key   Length    Length
                                    Torsion     Deflection                                (D)                 (lm)        (l)
Units           RPM       In/lbs         In.          In.        In.       In.         In.          Lbs         In.        In.        Lbs
Notes     1       ---        2            3            4          5         6           7             8          9         10         11
S1 G1    10     1800        350        .6673        .6983        .75     11.98      3/16 Sq.       933.33      .498       2.25        1.5
S2 G2    10      900        700         .841        .8798         1      9.885       1/4 Sq.        1400        .56       2.38        2.2
S2 G3    10      900        700         .841        .8798         1      9.885       1/4 Sq.        1400        .56       2.88        2.2
S3 G4    10       30       2100        1.212         1.27       1.25     12.38       1/4 Sq.        3360      1.344        3.5        4.3
Notes:
   1. Horsepower Transmitted ( HPT)
   2. Calculated Torque from Table #1 – Note #3
   3. Min. Shaft Dia. (Dm1) Based on Torque - Solid Shaft in Pure Torsion (Neglect weight of shaft and gears), Shear Stress (Ss) = 8,000
       psi (reduced to 6,000 psi for keyway strength reduction)

             S1 =                 = .6673”,    S2 =                = .841”,    S3 =                   = 1.212”

   4. Min. Shaft Dia. (Dm2) Based on Torsional Deflection - Shear Modulus for Steel, G = 12,000,000 PSI, Acceptable Limit for Torsional
      Deflection is < 1º per every 20 shaft diameters.

             S1 =                         = .6983”, S2 =                         = .8798”, S3 =                           = 1.27”

   5. Select Shaft Dia.> Dm1 or Dm2 and based on (Table 5-1, Pg 159) plus Gear Stock/Max. Bore Diameters limits.
   6. Select Shaft Length based on Gears Lengths, Container Wall Thickness, Bearing Lengths and Clearances Required.
                   PTO OA brng lgth OA hsng runout
           S1 = 2.5 + (1.484375*2) + 6.26         +.25      = 11.97875”
           S2 =         (1.5625*2)      + 6.26    + (.25*2) = 9.885”
           S3 = 2.5 + (1.6875*2)        + 6.26    + .25     = 12.385”
   7. See Table 6-5 on Page 235 of Text: “American Standard Square & Flat Keys”
   8. Shear Force (P) @ Gear Key - S1 G1 = 350/.375 = 933.33 lbs, S2 G2G3 = 70/.5 = 1400 lbs, S3 G4 = 2100/..625 = 3360 lbs
                                                                                                                            Achey 5
   9. Minimum Gear Key Length (lm) , Allowable Shear Stress = 10,000 psi –
       S1 G1 = 1.875L = 933.33/10000, L = .498”, S2 G2G3 = .25L = 1400/10000, L = .56”, S3 G4 = .25L = 3360/10000, L = 1.344”
   10. Selected Key Length (l) Should be > Calc. Min. Gear Key Length (lm) Selected lengths = OA gear length.
   11. Calculated Shaft Weight from length (see bottom of page 3)

                                        Table #4 – Bearing Load & Life Calculations
               Distance                  Radial         Radial        Radial      Selected Bearing    Rated Average       Total
              from CL of              (Separation)     Load on       Load on        Boston Gear       Life of Bearing    Load on
                             Force
     Shaft       Left                  Force (FR)        Left         Right           SF Series            (L50)          Shaft
                              (FT)
              Bearing to                Between        Bearing       Bearing           Cat. Pg.         Ref. Pg 109       (LT)
              CL of Gear                 Gears           (RL)          (RR)             99,100
     Units        In.         Lbs         Lbs            Lbs           Lbs               ----               Hrs            Lbs
     Notes         1           2           3              4              5                6                  ----           7
     S1 G1       2.771        400        145.59         95.65         52.785           ST-3/4             > 75,000        148.43
     S2 G2       2.786        400        145.59
                                                        28.04         91.42             ST-1              >75,000         119.46
     S2 G3       4.538        700        254.78
     S3 G4       4.568        700        254.78         117.2         161.99          ST-1¼S              >75,000         279.19

Notes:
   1 Distance from CL of Left Bearing to CL of Gear Determined from Layout Drawing
   2 Tangential Force (FT) - G1 G2 = 2(350)/1.75 = 400 lbs, G3 G4 = 2(700)/2.0 = 700 lbs.
   3 Radial (Separation) Force (FR) - G1 G2 = 400TAN(20º) = 145.59 lbs, G3 G4 = 700TAN(20º) = 254.78 lbs.
   4,5 Radial Load Calculations on Right and Left Bearings:
            Shaft nS1 = 2.771(145.59+1.34+1.5)-7.792 (RR), RR = 52.785 lbs, RL = 148.43 – 52.785 = 95.65 lbs.
            Shaft nS2 = 2.78625(5.85+145.59) )+3.91125(2.2)+4.53625(2.22 - 254.78) - 7.8225(RR), RR = - 91.42 lbs,
                                                                                                    RL = 119.46 – 91.42 = 28.04 lbs.
            Shaft nS3 = 4.5675(254.78+20.11)+5.065(4.3)-7.885(RR), RR = 161.99 lbs, RL = 279.19 – 161.99 = 117.2 lbs.
   6 List Manufacture & Style of Selected Bearing
   7 Total Load on Shaft
            LT S1 = 145.59 +1.34 +1.5 = 148.43 lbs
            LT S2 = 254.78 –145.59 + 5.85 + 2.22 + 2.2 = 119.46 lbs
            LT S3 = 254.78 + 20.11+ 4.3 = 148.43 lbs