Gear drive problem

I have been asked to post this question which is from a sample of questions relating to the topic of Mechanical Principles:

A compound gear train has input Gear A having 10 teeth, which drives Gear B having 36 teeth. Gears B and C are on the same shaft and Gear C drives Gear D, which has 40 teeth. Given the Velocity Ratio of the gear train is 1:12, determine the number of teeth on Gear C.

We can get the number of teeth on gear C but are confused about the ratio as written.

Thanks in anticipation of your thoughts. Jim.

1:12 Looks a fairly standard way to express a ratio to me.

What answer did you come up with for your Homework? Its a bloody big gear!

Edited By JasonB on 26/05/2017 08:15:10

I think it is 12 teeth. The question regarding the ratio is should it be 1:12 or 12:1? If it is for a threading solution for a lathe gear train then 1:12 may make sense. If direct drive gave a tpi of 1 then the calculated gear train would give a tpi of 12. If you are looking at the ratio of input rpm to output rpm then 12:1 would be the correct ratio.

Martin C

Yes for the given ratio of 1:12 you would need 1440T but for a reduction ratio of 12:1 you would only need 112T

1:12

10/36 = 0.277777

x/40   = 43.2

43.2 x 0.27777 = 12

So 40x 43.2 = 1728T

12:1

10/36 = 0.27777

x/40 = 0.3

0.3 x 0.27777 = .083333

So 40x 0.3 = 12T

Edited to correct 36T not 30T

Edited By JasonB on 26/05/2017 10:11:46

Hi Jason and Martin.

Thanks for having a go at this. We do indeed get 12 teeth but only if we use a ratio of 12:1. But as Jason said, if we use the examiners ratio of 1:12 it is a massive number of teeth !!!!!

As I understand things, the ratio of 1:12 would indicate and input of 1 and an output of 12??

Thanks chaps.

I would tend to discount the massive gear solution as it does not seem logical to have a first stage that reduces the rpm followed by such a massive increase in rpm at the second stage. However maybe this silly solution was what was required to test if the person being tested really understood the calculation process for the gears.

Martin C

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Conventional wisdom is here: **LINK**

http://www.the-warren.org/quiz/gearratios.htm

... and many other places.

MichaelG.

Not in my book. ':' means divide so 1:12 is one twelfth. For example,

• A 12:1 mix of Acid and Water means 12 parts of acid to 1 part of water. ( 12 times more acid than water, 12 acid divided by 1 water )
• A 1:12 mix of Acid to Water means 1 part of acid to 12 parts of water. ( 12 times more water than acid, 1 acid divided by 12 water)

Gear ratios confuse me because there are always two ways of looking at them depending on what you're thinking of, a change in speed or a change in torque. The velocity ratio is the opposite of the torque ratio, so a 1/12 velocity reduction is a 12 x 1 torque increase and vice versa. While I have no problem visualising this for gear pairs it's amazing how bewildered I get calculating compounds.

Dave

Edit Michael_G thinks and types faster than me...

Edited By SillyOldDuffer on 26/05/2017 09:52:49

Perhaps it was just a question to sort out those that apply the definition correctly? Or possib

y an error on the question writer's part. I prefer to use term for gear trains as speed 'reduction' or 'multiplier' - no ambiguity possible then.

I once had a degree level question that asked for the output of a one megawatt turbine if the rotor diameter was doubled. I answered ''One megawatt. Attempting to increase the output of a one megawatt turbine by a factor of four (by quadrupling the swept area) would 'let the smoke out' - ie the turbine would fail." A bit like noon and midnight - they cannot be 12am and 12pm by definition! Midnight is actually both 12am and 12pm! Noon is the meridian.

Is this yet another ambiguous question from a British GCSE? When my kids were going through this I kept on finding ambiguous or unanswerable questions, for instance find the solution to an equation which had 2 unknowns, there are an infinite number of solutions. Worst of it was the maths teacher wouldn't accept there was an issue.

However in this case both

**LINK**

and

**LINK**

agree that a 1:12 drive is speed increasing. Only an idiot would design such a train with the first 2 as quoted, so I reckon the question setter has got it wrong

Taking Duncan's first link, the results will be consistent, if unlike the method taught to me as a young engineer, as mentioned above: driver over driven (times driver over driver ... - I know the example shown is pulleys).

Driver over driven is 40/120 = 1/3 0r 0.333...

RPM of output = RPM of input * 1/3 = 100 * 1/3 = 33.33... RPM

It looks to me like the level of course is using division, as again multiplication of the input by the ratio, as I was taught.

Bill

Just an aside, Duncan ...

Do you agree that the BBC BiteSize "definition" [in your second link] is itself rather counter-productive ?

[quote]

Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley

[/quote]

... I wonder if they actually understand the word 'ratio'

MichaelG.

You do have to watch out for what examiners are after. My career included a spell in Systems Analysis which is about understanding business processes so that they can be computerised. Back then we were taught that most business units don't properly understand the detail of their own processes and that embarrassed staff and managers will make answers up rather than admit they don't know what they're talking about.

As flushing out the truth was an important part of systems analysis, it wasn't unknown for exam questions to contain deliberate ambiguities and mistakes that you were meant to identify and explain how you would deal with in the real world. In comparison, provided you could do the maths, the numeric questions were a doddle because they were logical.

So when you answered the turbine question:

• the 'it will make smoke answer' got full points, or
• you got told off for failing to calculate a theoretical answer and explain what was needed to uprate the turbine, or
• you got credit for spotting a badly worded question and they fixed it, or
• you were punished for not understanding what they meant!
• no-one made any comment one way or the other.

I've no idea what the right answer would be. I hate exams!

Dave

Edited By SillyOldDuffer on 26/05/2017 13:46:22

I got a distinction rating for that paper, so I reckon my result and reasoning/explanation was more than adequate. Most, I believe, answered 4MW and were probably marked as correct. The problem arose, I think due to the first part of the question being about a described turbine and the later part using the definite article rather than the indefinite article. It was a low mark question anyway. At least it was not a 'multiple guess' question like a lot of the GCSE papers these days!

The ratio of 12:1 gives quite different 'answers' depending on whether you are measuring speed (rpm, etc) or torque as the input and output. One goes up as the other goes down. So, as written, the term 'velocity ratio' is quite helpful (even if it is rpm that we are measuring, not speed in a given direction as such. Get back into pedant's corner).

Those with an eye for precision will tend to put the numbers round the logical way; those with an eye for neatness will generally start with 1:

As an ex-examiner, I would try to give most marks to an answer which recognised the duplicity involved, and took account of it.

Cheers, Tim

.

It may ease the pain, Tim, if you assume 'angular velocity ratio'.

MichaelG.

Just to be a bit thick, if you double the size of the disc, but reduce the speed to half, the blade speed stays the same and so the blade root stress is reduced (mass * velocity squared / radius). However you have double the blade area to pass steam through, so why can't you double the steam flow and hence power output. It wouldn't be terribly convenient as you'd be generating 25 hz. All UK electricity generating staem turbines run at 3000 rpm, and have 2 pole generators. This probably limits disc diameter via root stress.

What i learnt in engineering classes too many years ago was that if there was any ambiguity in the question then your answer should always be preceded by a statement giving your understanding of the question. That way you could never be wrong as you were always answering what you thought the question was asking, even if this was different from what the examiner intended.

That being said, my understanding of the conventional expression of gear ratios is the ratio of the input speed to the output speed, as is the norm for automotive gearboxes and differentials, but unfortunately most of my engineering textbooks from the 70's seem to be inconsistent in this matter. Some of the worked examples confuse the issue by giving a gear ratio of 3:1 and then stating the driving gear is to be the smaller of the gears.

Duncan, the reported question does not mention either steam or turbine disks, the use of the work rotor makes me think of a car's turbocharger turbine. The turbine disks on a gas turbine may be spinning in the region of 15000 rpm at a lot higher temperature than a steam turbine. Doubling the disk diameter would probably result in a design that could not take the stresses unless the rpm is reduced. What seems like a simple question on a test paper could have a complex answer. I think people who had done the course would know what the expected answer would be based on coursework covered.

Martin C

I doubt you've got a one megawatt turbocharger on your car. Same argument applies if it's a gas turbine, double the diameter, halve the rotor speed, double the gas area, double the power.