Gearbox Design

Preliminary Analysis & Gear Design


  1. Compute the nominal velocity ratio (VR):
  2. Specify the trial diametral pitch (Pd) using table (13-3):
  3. Pd = ?                                                                 (tpi – teeth per inch)

  4. Specify the number of teeth on the pinion (Np):
  5. Hint: Minimum number of teeth to avoid interference for pinions having 20 pressure angles is 18

    Np = ?

  6. Compute the number of teeth on the gear (Ng):
  7. NOTE: Remember, Ng must be an integer, so round-off the value to the closest integer

  8. Check the new velocity ratio (VR) and verify if the new gear speed (ng) falls within the specified range of 460~465 rpm:
  9. &


  10. Compute the pitch diameters (dp and dg):
  11.                                                                     (in.)



  12. Check whether the center distance (C) is in the specified range ( 5"):
  13.                                                             (in.)


  14. Compute the pitch line velocity (n t):
  15.                                                             (fpm – feet per minute)


  16. Compute the transmitted load (Wt) for the specified power of 3 hp:
  17.                                                             (lb.)


  18. Specify the gear face width (F):
  19.                                                              (in.)


  20. Compute the bending stress (s tp) on the pinion teeth:
  21.                                                     (kpsi)

    Based on a reliability of 99%, the computed stress can be compared directly with the allowable stress shown in fig. (14-2) to find the required Brinell hardness for the pinion teeth and call it ‘x

    x = ?                                                                      (BHN)


  22. To evaluate the bending stress on the gear teeth (s tg), use the following equation:
  23.                                                             (kpsi)


    For the value calculated above, find the required Brinell hardness from fig. (14-2) and call it ‘z

    z = ?                                                                      (BHN)


  24. Compute the contact stress (s c) on the gear pair:
  25.                                                     (kpsi)


    Compare the computed stress with the allowable contact stress in fig. (14-3) and find the required surface hardness, call this hardness value ‘y’

    y = ?                                                                             (BHN)


  26. Specify materials for the gears, keeping in mind the fact that pinions are typically made from materials about 16% harder than those used for the gear to ensure optimum performance.



Brinell Hardness

Selection Procedure

Bending Stress on Pinion


}Use maximum value for              selecting pinion material

}Use maximum value for              selecting gear material

Contact Stress on Gear Pair


Bending Stress on Gear