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Tractor Talk Discussion Forum

Gearing and Math Question ....

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Gyro Gearloose

11-13-2005 05:20:50




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I was at a science exhibit yesterday and there was a large display of gears, gear ratios, etc. and how & why gearing systems work as they do. I think this question has been asked here before but it came to mind yesterday so here goes. Suppose you had two low-gear gearing systems, both with a 1:2 ratio of the drive gear to the driven gear. For simplicity sake (not practicality) lets say the two systems that were being compared were system A and B as follows:

System A - the drive gear has 10 teeth and the driven gear has 20 teeth. Basic ratio is 1:2.

System B - the drive gear has 15 teeth and the driven gear has 30 teeth. Basic ratio is 1:2.

Now suppose that the materials from which the gearing systems were made were modified so that system A and system B had exactly the same overall weight so that wouldn't come into play (at least in our example it wouldn't). Nor would other factors such as dimensional size, friction, etc. between the two systems. We are just talking about the math comparison between the two setups.

My question is this, if you (or an engine or whatever power source) were driving these systems against a load of some type (same load for both A and B), would you (or whatever power source you were using) be using or expending the same amount of force or power in both? For example, if you had two identical bicycles with these different gearing systems and were pedling up a hill, would you feel that both bicycle trips were as easy (or as difficult) as the other?

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Tim B in MA

11-15-2005 11:02:14




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
Gyro, your question is too hypothetical. You are basically asking if the performance (in terms of energy required to do work) of two gear arrangements would be different if the only difference were that one setup had a third more teeth than the other, and assuming same diameters, same mass, same amount of friction. Clearly they would perform the same under those circumstances. The affect of teeth size will likely alter things that your hypothetical question dissallows: at a minimum, friction and smoothness of operation. The finer tooted system is likely to be more efficient in the real world.

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Thack

11-13-2005 22:39:19




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
"would you (or whatever power source you were using) be using or expending the same amount of force or power in both?"

No! The affect comes from the number of teeth in the drive gear and tire rev's per mile for your bicycles.

So if you had 30" tires on both you would need 10 drive/8.05 driven on one and 15 drive/12.08 driven to get the same 672 tire revs per mile.

The gears you choose are good for taking measure, such as a speedometer.

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Joe(TX)

11-13-2005 19:20:06




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
I will try to answer from a mechanical engineers view point.
If the gears are the same diameter; The ones with the fewer teath will require sligntly more power. The reason is that the teeth are thicker and the friction would be higher. The thicker teeth would however be able to transmit more torgue if the gears are the same width. the tradeoff is that the thicker teeth are not as smooth. Speed is another factor to consider.
I hope I have not gotten too deep in the "enginnering mode" and confused everyone.

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MarkB_MI

11-13-2005 15:51:05




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
If you discount friction, there would be no difference. However, in the real world there are always friction losses. I have no idea which setup would be more efficient, but no doubt one would be slightly more efficient than the other.



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Ranger John

11-13-2005 11:14:48




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
When it comes to gears and pulleys one should think of them as continous levers. What creates the mechanical advantage is the radius of each wheel. When you build the ratio of r1 over r2 you get the mechanical advantage. If r1/r2 > 1 then you increase speed and decrease force. Of course the opposite is also true.

As for the size of the teeth, they need to be nearly the same for smooth operation.

When it gets to be fun is when you have angles cut in the teeth. Using a bit of trig and calculus to can minimize the shearing of teeth in high torque usage.

But in agreement with other posters the size doesn"t make much difference except that the larger might give you more tooth contact which will give you more resistance to breakage.

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Old Pokey

11-13-2005 10:47:50




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
I would change the example to a something different. The bicycle has a chain that will have an effect even if weight and all that were eliminated. And as Sid is concerned about, are you working with the same size gears, and just sizing the teeth different, or are you sizing the diameter different and using the same gear pitch?

2 to 1 is 2 to 1 period. In order to gain any advantage knowledge, you need to leave in at least one of the other factors that make each equasion different from the other. I believe anyway.

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Sid

11-13-2005 07:02:41




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
I am not an engineer nor a math expert, but I do have a question. As I understand the question the gears in A and B are the same diameter. You have the same ratio in both set ups. But the teeth in example A are going to be bigger. It seems to me that you are going to have a slight advantage because of the different size of the teeth. Wont the larger teeth have a slight leverage effect? It seems to me that A would have a slight advatage over B.

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Mike (WA)

11-14-2005 14:27:57




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 Re: Gearing and Math Question .... in reply to Sid, 11-13-2005 07:02:41  
In a chain drive situation, the "pitch" of the teeth (that is, the distance between tooth "points", if you will) has to be the same for the chain to work. The gears will vary in diameter, depending on the number of teeth.



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Coloken

11-13-2005 06:10:48




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
Are you asking if 2 to 1 is the same as 2 to 1?
The answer is all ways yes, even if 2000 to 1000. You say to eliminate friction, size, and such, so the Only thing left, is there mught be more vibration with the lower number teeth. Depends on the type of teeth.



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John T

11-13-2005 06:06:57




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
Gyro, although this is more of a mechanical engineering question and I graduated as an electrical engineer, the physics and conservation of energy issues still intrigue me and we still had to study lots of physics n mechanical stuff.

When you discounted the effects of friction and weight (isnt that what you said or intended?) and are left with only the straight gear ratios, I see NO DIFFERENCE, i.e both rides would be the same. Not more or less difficult.

Remember, we cant create or destroy energy, only change its form. Thats why in the real world of friction the tractors drawbar HP is less then on the clutch pulley, cuz of the HP requirements necesary to turn all the gears and the friction n heat losses. It got used up and converted to heat energy cuz of the gear friction so theres less available on the drawbar.

If your bicycle has frictionless and weightless gears, I see the effort the same to turn the crank/pedals regardless if it were a 10/20 or 15/30 gear set up.

So, until proven otherwise, "Thats my story n Im stickin to it" lol

John T

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Richard H.

11-13-2005 07:12:20




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 Re: Gearing and Math Question .... in reply to John T, 11-13-2005 06:06:57  
John, the 15/30 would be have to run smoother is all I can think of. Just curious, where were you an E.E. at? Richard H in Ind. L.U. 481



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John T

11-13-2005 15:35:20




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 Re: Gearing and Math Question .... in reply to Richard H., 11-13-2005 07:12:20  
I retired as an EE from the Naval Surface Warfare Center, Crane, Indiana back in 1991. I was into electronics earlier but then finished as a power distribution engineer later. I was too young to do nuttin so I went back to law school now have a small semi retired law practice.

You an EE also??

John T



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Richard H.

11-14-2005 06:22:08




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 Re: Gearing and Math Question .... in reply to John T, 11-13-2005 15:35:20  
John, no Iam not an EE, just an electrician out of 481 in Indpls. I have worked with several engineers over the years. It"s just your name and demeanor seem very familier. Have a good day, Richard



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IaGary

11-13-2005 05:42:24




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 Re: Gearing and Math Question .... in reply to Gyro Gearloose, 11-13-2005 05:20:50  
In my opinion force verses mass would be the same for both A and B. Only difference would be more weight in ex.B thus it would be stronger. My 2 cents.



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UncleTom

11-13-2005 09:14:56




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 Re: Gearing and Math Question .... in reply to IaGary, 11-13-2005 05:42:24  
Im no engineer either but The 15\30 would most likely have a heavyier rotating mass there fore a very slight power loss. The 15\30 would also be stronger because of more tooth contact of the bigger drive gear.



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