Selecting suitable gears for a gearbox

[DevonZA]

Homework Statement

Homework Equations

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.

 

[Nidum]

The output must rotate in the same direction as the input and along the same axis. Select suitable gears.

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

 

[DevonZA]

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

 

[Nidum]

More likely a simple layshaft design is expected .

 

[DevonZA]

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

 

[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.

 

[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 .

 

[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

 

[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 .

 

[sunil63]

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

 

[DevonZA]

Hi Sunil

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

 

[sunil63]

Hi Sunil

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

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

 

[DevonZA]

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

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.

 

[DevonZA]

Nidum thank you for the video!

 

[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..?

 

[Nidum]

Divide by gear ratios :

First pair : 2000 / 2.4 = 833 rpm

Second pair : 833 / 2.4 = 347 rpm

 

[Christiaan]

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

 

[CWatters]

So if I select a spur gear with 22 teeth and one with 9 teeth

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 textbooks or tables say anything about wear (contact angles?) on gears with a low tooth count?