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

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