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.

  2. Calculate required power output:

    3. Poutput = Toutput ´ noutput(avg.)/63000 hp

  3. Calculate required power input:

    4. Pinput = Poutput/h ´ h          hp

  4. Select a standard motor from the table provided and note down the motor specification including the motor speed:

    5. Pmotor = ? hp ninput = ? rpm

  5. Check if actual output torque is greater than output torque required:

    6. Toutput = 63000 ´ (Pmotor ´ h 2)/noutput          lb.in.

  6. Check actual velocity ratio:

    7. VR(actual) = ninput/noutput

  7. Calculate velocity ratios (VR1 & VR2) for gear pairs 1 & 2 such that:

    8. 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

  8. Hence:

VR1 = Ng1/Np1 & VR2 = Ng2/Np2

 

Gear Design

 

  1. Specify a reasonable trial Diametral Pitch (Pd):

    2. Pd = ? (tpi - teeth per inch)

  2. Select the number of teeth on the pinion (Np):

    3. Hint:

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

    Select Np= ?

  3. Calculate the Pinion Diameter (dp):

    4.   dp=Np/Pd        (in)

  4. Calculate the number of teeth on the gear (Ng):

    5. Ng = Np ´ VR

    Round-off the calculated value to a closest integer value

  5. Calculate the Gear Diameter (dg):

    6. dg=Ng/Pd          (in)

  6. Calculate & Check the final Output Speed (ng):

    7. 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)

     

  7. Calculate the Pitch Line Velocity (n t):

    8. n t = p dpnp/12 (ft./min.)

  8. Calculate the Tangential Force (Wt):

    9. Wt = P ´ 33000/n t (lb.)

  9. Calculate the Face Width (F) of the gears:

    10. F = 8/Pd £ F £ 16/Pd (in.)

  10. Calculate Bending Stress on the pinion (s tp) and gear (s tg):

    11. Use 1st equation of (14-15) from the text book               (kpsi)

  11. Calculate the Contact Stress (s c) on the gear pair:

    12. Use equation (14-16) from the text book                          (kpsi)

     

  12. 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