Double Reduction Spur Gearbox Design

Preliminary Analysis & Gear Design


Given Data:

noutput = 50~55 rpm

Ddrum = 8 in.

F = 1 metric ton

h = 0.95 for each gear pair

VR(total) 25

wpe1.jpg (3427 bytes)


Preliminary Analysis

  1. Calculate minimum required output torque:
  2. Toutput = F Ddrum/2

  3. Calculate required power output:
  4. Poutput = Toutput noutput(avg.)/63000 hp

  5. Calculate required power input:
  6. Pinput = Poutput/h h          hp

  7. Select a standard motor from the table provided and note down the motor specification including the motor speed:
  8. Pmotor = ? hp ninput = ? rpm

  9. Check if actual output torque is greater than output torque required:
  10. Toutput = 63000 (Pmotor h 2)/noutput

  11. Check actual velocity ratio:
  12. VR(actual) = ninput/noutput

  13. Calculate velocity ratios (VR1 & VR2) for gear pairs 1 & 2 such that:
  14. VR(actual) = VR1 VR2

    NOTE: VR1 & VR2 must be selected such that their product equals the value of VR and allows the selection of integer values for numbers of teeth for all the gears

  15. Hence:

VR1 = Ng1/Np1 & VR2 = Ng2/Np2


Gear Design


  1. Specify a reasonable trial Diametral Pitch (Pd):
  2. Pd = ? (tpi - teeth per inch)

  3. Select the number of teeth on the pinion (Np):
  4. Hint:

    Minimum number of teeth to avoid interference for pinions having 20 pressure angles is 18

    Select Np= ?

  5. Calculate the Pinion Diameter (dp):
  6.   dp=Np/Pd        (in)

  7. Calculate the number of teeth on the gear (Ng):
  8. Ng = Np VR

    Round-off the calculated value to a closest integer value

  9. Calculate the Gear Diameter (dg):
  10. dg=Ng/Pd          (in)

  11. Calculate & Check the final Output Speed (ng):
  12. ng = np (Np/Ng) (rpm)

    Tip: Get np from the equation VR(actual) = np1/ng1 np2/ng2

    For the 2nd set, check if this value falls within the specified output speed range for gear # 2, i.e. (50~55 rpm)


  13. Calculate the Pitch Line Velocity (n t):
  14. n t = p dpnp/12 (ft./min.)

  15. Calculate the Tangential Force (Wt):
  16. Wt = P 33000/n t (lb.)

  17. Calculate the Face Width (F) of the gears:
  18. F = 8/Pd F 16/Pd (in.)

  19. Calculate Bending Stress on the pinion (s tp) and gear (s tg):
  20. Use 1st equation of (14-15) from the text book               (kpsi)

  21. Calculate the Contact Stress (s c) on the gear pair:
  22. Use equation (14-16) from the text book                          (kpsi)


  23. Select Materials for the pinion and gear depending upon the hardness values for each stress



Brinell Hardness

Selection Procedure

Bending Stress on Pinion


Select material using max. of X & Y for the Pinion
Contact Stress on Gear Pair


Bending Stress on Gear


Select material using max. of Y & Z for the Gear

 Repeat the gear design procedure shown above for the 2nd set of gears