# Design of a Gear Reducer for a Tractor

1. Oct 14, 2014

### djp012

Hello everyone,

I am a junior Mechanical Engineering major tasked with the design of a gear reducer using spur gears. We haven't studied gears in-depth up to this point and I was wondering if anyone has suggestions regarding initial design considerations or a possible starting point. Any feedback is much appreciated. Thank you in advance.

http://imageshack.com/a/img537/3594/rf9JiI.jpg [Broken]

Design Requirements:
1.) The reducer must transmit 22HP
2.) The input is from an engine with a rotational speed of 1800rpm
3.) The output delivers power at a rotational speed in the range of 330 to 335rpm
4.) The output is connected to the drive shaft of a tractor (Moderate Shock)
5.) Input/Output shafts must be in-line (as illustrated)
6.) Reducer must fit in a space no larger than 22x22in with maximum height 25in

Last edited by a moderator: May 7, 2017
2. Oct 14, 2014

### NTW

Lubrication hasn't been apparently considered, at least at this stage of the design... Perhaps the bearings are of the sealed, for-life lubrication type, but those gears will need lubrication...

3. Oct 14, 2014

### Dr.D

Write the kinematic conditions that must be met, both for the overall ratio and for the alignment of the input and output shafts. (This alignment is called a reverted train.)

You can deal with the gears as if they were smooth friction wheels with radius equal to the pitch radius of each gear.

4. Oct 14, 2014

### SteamKing

Staff Emeritus
Just out of curiosity, if you haven't studied gears in depth up to this point in your coursework, how come you have been assigned a design project using gears? Did your professor have a stroke or something?

In any event, you have been given an input power and RPM and a range of output speeds. With your limited knowledge of gears, you should be able to determine the ratio of the gears in the gearbox to give the required reduction in input speed and also to calculate the output torque of this device, which can be used to size the output shaft. Make sure that your gear arrangement adheres to the geometrical requirements specified

5. Oct 14, 2014

### Dr.D

That range on the output speeds, 330 to 335 rpm, is to give you a bit of lee way in choosing tooth numbers (which must be integers) in order to achieve the required ratio.

6. Oct 14, 2014

### Dr.D

You will need to go to a gear standard (AGMA, DIN, etc) to find the proportions and sizes for particular gears after you settle on tooth number choices. This will also give you guidance on the tooth strength as req'd to transfer the torque at each stage.

This is a complex problem, and like most design problems, you will likely have to iterate. This makes a computer formulation very attractive.

7. Oct 18, 2014

### Baluncore

You should consider an epicyclic = planetary gear train.
http://en.wikipedia.org/wiki/Epicyclic_gearing
The sun gear pinion would be driven by the engine, the outer annular gear is fixed, the planet carrier then drives the output shaft. The output rotates in the same direction, and on the same axis as the input. The planetary gears are compact with very low side forces. They are used widely in automatic transmissions. The Ferguson TE20 tractor built in the 1950s had an axial reduction box option that used planetary gears.
The wanted shaft reduction ratio = 1800 / 332.5 = 5.4137
The shaft ratio will be 1 + Na/Ns.
The tooth count ratio will be about 4.4137

Here are some possible tooth counts.
Sun, Annular, Planet, RPM out for 1800 input.
Ns, Na, Np, RPM
16, 70, 27, 334.884
17, 75, 29, 332.609
18, 80, 31, 330.612
20, 88, 34, 333.333
21, 93, 36, 331.579
22, 98, 38, 330.000
23, 101, 39, 333.871
24, 106, 41, 332.308
25, 111, 43, 330.882
26, 114, 44, 334.286
27, 119, 46, 332.877
28, 124, 48, 331.579
29, 127, 49, 334.615
29, 129, 50, 330.380
30, 132, 51, 333.333
31, 137, 53, 332.143
32, 140, 54, 334.884
32, 142, 55, 331.034
33, 145, 56, 333.708
33, 147, 57, 330.000
34, 150, 58, 332.609
35, 155, 60, 331.579
36, 158, 61, 334.021
36, 160, 62, 330.612
37, 163, 63, 333.000
38, 168, 65, 332.039
39, 171, 66, 334.286
39, 173, 67, 331.132
40, 176, 68, 333.333
40, 178, 69, 330.275
41, 181, 70, 332.432

8. Oct 21, 2014

### Dr.D

It seems to me that Baluncore is way off base here. Consider these points:

1. The assignment presents the topology of the gear train to be designed, and it most definitely is not a planetary train.

2. Planetary trains are far more expensive and complex to actually build, and that additional cost is only justified in special cases. The assignment makes it rather clear that this is not required, and therefore not justified.

3. A part intended learning process for this assignment is for the student to work through the process of fining suitable tooth numbers to meet the ratio requirements. Why does Baluncore short circuit this process by producing an extensive table of tooth number combinations.

All in all, I think that the advice of Baluncore on this problem should be totally ignored, Science Advisor though he may be.

9. Oct 22, 2014

### Baluncore

The problem presented is not complex. Iteration is not useful as the integers involved in the gear ratios restrict solution to a short table of possibilities. Being able to factorise numbers and recognising mutual primes is more important in gearbox design.

That is not necessary, nor true. Friction wheels or belts can have irrational ratios and slip. Gears and roller chains are restricted to integer ratios and are locked.

This thread is on a public forum, anyone looking for information on tractor reduction boxes who finds and reads this thread should be able to see a sensible solution to the simple task of speed reduction in heavy equipment.

The image in the OP is only referenced when showing that the input and output shafts must be in line. Spur gears are specified, that is satisfied by the use of either an epicyclic or a gearbox with an intermediate shaft.

Epicyclics will carry greater forces than standard gear systems of the same size. I find them simpler to build and lower cost. Because there are usually three or four planetary gears transferring torque, the size of the gears can be significantly smaller for the same power. An epicyclic reduction gear does not place side forces on the gear shafts. The image in the OP shows six separate bearings being required to counter those forces in an intermediate shaft box. In an epicyclic gearbox, a needle roller bearing is needed for each planet on the carrier. The input and output shafts are self-centring, input and output bearings are not required. Heavy equipment uses epicyclic reduction gears because they are both more compact and more robust. Where hydraulic motors drive large diameter wheels, an epicyclic is often used as a reduction stage.

The claim that the required tractor gearbox must be designed to handle 22HP demonstrates that it is not a real tractor, but only a toy. The early TE20 grey Ferguson tractors were 20HP and had an optional epicyclic reduction, but that was 75 years ago. The Model T Ford also used an epicyclic box over one hundred years ago, so epicyclics are certainly not difficult to build, nor expensive.

You ask me why? This thread is in the engineering, not in the homework section. I presented a table of all the reasonable epicyclic possibilities for the solution required by the OP. I did not identify the few that would be on my short list nor why I would have chosen one particular set. The ratios I provided are quite inapplicable to a standard gearbox and so are of no help in the solution that Dr.D is advocating. My table shows that many epicyclic solutions are possible. If djp012 was to do the calculations for an epicyclic solution, the table I provided would help confirm the right path to a solution. There are a few important parts of both solutions that I did not provide.

I did not apply to become a science advisor, the award was made without my knowledge. I believe it was in recognition of my experience in quite diverse corners of the scientific and engineering worlds.
Discounting the use of epicyclic gears in driveline applications would demonstrate an ignorance of current engineering practice in heavy equipment design. While I now only rebuild about one heavy tractor gearbox each year, as the owner and experienced operator of a gear hobbing machine, I believe I can claim some knowledge of that field.

I would expect an intelligent student to present a solution using an intermediate shaft system, but to also suggest that an epicyclic reducer would be a more compact and more reliable alternative. A competent student has the ability to decide who's posts to ignore without misleading advice.

10. Oct 22, 2014

### Staff: Mentor

Mentor note -- thread moved from the Engineering forums to Homework help.

@djp012 -- please check your personal conversations. Schoolwork needs to be posted in the Homework Help forums, and not in the general technical forums. Also, you are required to show your work toward the solution when posting schoolwork.

To the other responders -- remember to report misplaced schoolwork questions, rather than responding (and especially doing a student's work for them). Thank you.

11. Oct 22, 2014

### Dr.D

@Baluncore:

The first sentence of the OP said, "I am a junior Mechanical Engineering major tasked with the design of a gear reducer using spur gears." You observed that "this thread is in the engineering, not in the homework section." It seems to me to be clear that this is an academic problem, whether you see it or not. I have been a Professor of ME for quite a few years, and I can recognize a home work problem in most cases. I know for certain that I would be far more likely to ask a student to design a simple train such as the one shown before I ask him to design an epicyclic train. This is not to say that epicyclic trains do not exist, that they do not have advantages in some cases, etc, but simply that it is the common practice to ask students to design simple systems before asking them to design more complex systems.

As to whether this is a complex system or not, that is a value judgement. To a gear train expert, no it is not complex. To a novice, it is quite complex because it involves choosing tooth numbers, pitch diameters, face widths, etc -- the whole spectrum of design choices, and for a beginner, this is a complex process. While you might not find it necessary or even useful to iterate, most beginners will have to iterate several times to get it all to a workable design.

You said, "The claim that the required tractor gearbox must be designed to handle 22HP demonstrates that it is not a real tractor, but only a toy. The early TE20 grey Ferguson tractors were 20HP and had an optional epicyclic reduction, but that was 75 years ago. The Model T Ford also used an epicyclic box over one hundred years ago, so epicyclics are certainly not difficult to build, nor expensive." I am duly impressed with your expertise, but I still maintain that you are simply showing off and not helping the learning process.

You also said, "That is not necessary, nor true. Friction wheels or belts can have irrational ratios and slip. Gears and roller chains are restricted to integer ratios and are locked." This is true, but it is irrelevant. It does not invalidate my statement made to the OP to facilitate his understanding of the problem. If perchance he selects an irrational gear ratio (a contradiction in terms), he will discover the difficulty quite quickly when he starts to seek tooth numbers.

Despite the simplicity you evidently see in planetary trains, not too many others would agree, I think. My former employer who made countless number of gear trains for aerospace applications, both simple and planetary trains, always opted for a simple train if they could get the load capacity and other factors that way. But then, what did they know?

I never implied that you had asked to be a Science Advisor or anything of the sort, but only that I thought you were way off base despite having the title. I still think that; I am still quite convinced that you are way off base with helping the learning process for this student.

12. Oct 23, 2014

### Staff: Mentor

I suggest that we hold off posting further until the OP returns and replies in this thread...