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          lb.in.

  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          lb.in.

  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

 

Stress

Brinell Hardness

Selection Procedure

Bending Stress on Pinion

X

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

Y

Bending Stress on Gear

Z

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

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