Homework Help: Selecting suitable gears for a gearbox

1. Aug 18, 2015

DevonZA

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. A gearbox is required to transmit 5.5 kW from a shaft rotating at 2000 rpm. The desired output speed is approximately 350 rpm. The output must rotate in the same direction as the input and along the same axis. Select suitable gears.

2. Lewis Formula: $F= \frac{Wt}{(Kv)(m)(Y)}$

3.
I get an overall ratio of 2000rpm/350rpm = 5.71

Then I choose Np=18 and NG=100 (SG1-100) because 100/18=5.5 (these teeth numbers are from standard tables provided in the textbook - I unfortunately do not have a copy with me but I can post later)

m=1 according to table 6.7 where I have chosen SG1-100

d=mN

d=(1)(Np)
= 1x18
= 18

d=(1)(NG)
=1x100
=100

V=(d/2)XnX(2pi/60)
= (18/2)X2000X(2pi/60)
= 1884.96m/s

V=(d/2)XnX(2pi/60)
= (100/2)X350X(2pi/60)
= 1832.60m/s​

Kv=6/(6 +V)
= 6/(6+1884.96)
= 3.172991496x10^-3

Kv=6/(6 +V)
= 6/(6+1832.6)
=3.263352551x10^-3​

Wt= Power/V
= 5500W/1884.96
= 2.92N

Wt= Power/V
= 5500W/1832.6
= 3N​

F= Wt/(Kv)(m)(Y)
= 2.92/(3.172991496x10^-3)(1)(0.39502)
= 2329.67

F= Wt/(Kv)(m)(Y)
= 3/(3.263352551x10^-3)(1)(0.51321)
= 1791.27​

I'm not sure what to do from here. This question actually appears in Mechanical Design by K.Maekawa, T. Obikawa, Y. Yamane, T.H.C Childs but no solution is provided.

Last edited: Aug 18, 2015
2. Aug 18, 2015

Nidum

Consider the layout of gears and number of gears needed to meet this requirement before doing any further calculations .

3. Aug 18, 2015

DevonZA

The type of gears that rotate in the same direction and along the same axis which I can think of are epicylic gears?

4. Aug 18, 2015

Nidum

More likely a simple layshaft design is expected .

5. Aug 18, 2015

DevonZA

Okay so how to do I go about selecting gears then?

6. Aug 18, 2015

CWatters

The fact that the output must be "along the same axis" has implications for the dimensions of the gears. For example the distance between the input shaft and the lay shaft must be same as lay shaft to output.

7. Aug 18, 2015

Nidum

(1) As CWatters says about centre distances .

(2) Overall gear ratio is given by ratio of first pair multiplied by ratio of second pair .

Say both ratios are the same . Therefore (ratio)^2 = 5.7 and ratio = SQRT(5.7) = roughly 2.4

Use this ratio to answer your question .

(3) Full gear calculations optimise the load carrying capability of each gear and this may lead to different ratios being chosen for more critical applications .

8. Aug 18, 2015

DevonZA

Okay so overall ratio = $\frac{2000}{350}$ = 5.714
To get the same direction of rotation I need an odd number of gears such as 3 or 5.
I will say 3 gears, therefore if all ratios between gear 1&2 and 2&3 are the same $ratio^2$ = 5.714 and ratio=$\sqrt{5.714}$
Ratio = 2.4

So if I select a spur gear with 22 teeth and one with 9 teeth as per the table I get $\frac{22}{9}$ = 2.4

9. Aug 18, 2015

Nidum

This is what a layshaft gear arrangement looks like :

.

nb : A countershaft and a layshaft are essentially the same thing though the term layshaft tends to be used in automotive industry and term countershaft more generally .

Last edited: Aug 18, 2015
10. Aug 18, 2015

sunil63

Devon I think we doing the same course ...MEE231V ?

11. Aug 18, 2015

DevonZA

Hi Sunil

Yes I am really struggling. I contacted the lecturer for help and he told me to think..
How are you coping?

12. Aug 18, 2015

sunil63

Im also really struggling man . I made a group on whatsapp do you wna be added we can work together

13. Aug 18, 2015

DevonZA

Sent you my number. Studying with UNISA is honestly the worst I have had problems from day 1.
WRT this question I think I'm almost there, I'll post the answer I get once I'm done.

14. Aug 18, 2015

DevonZA

Nidum thank you for the video!

15. Aug 18, 2015

DevonZA

How do I calculate the change in rpm between gears? I.E in gear 1 the rpm would be 2000rpm (input) in gear 2 the rpm would be..?

16. Aug 18, 2015

Nidum

Divide by gear ratios :

First pair : 2000 / 2.4 = 833 rpm

Second pair : 833 / 2.4 = 347 rpm

17. Aug 20, 2015

Christiaan

You figure this one out? Also doing unisa.... Efff!

18. Aug 20, 2015

CWatters

I'm really no expert on gears but 9 teeth sounds low. I recall reading something once about gear wear on gears with a low tooth count? Do your text books or tables say anything about wear (contact angles?) on gears with a low tooth count?