Perhaps you mean 'modulus'?

If so, then its a relationship that describes the toughness of a material.

(wikipedia is your friend)

Can you give an example so that we can deduce the context?

Sir,

     It is not modulus.........I mean, the term "module" that we use to mention in gears.

Eg : 1module = 1 addendum of gear

referance link : http://en.wikipedia.org/wiki/Gear#Standard_pitches_and_the_module_system

One learns something each day.

Well, from the article (and I confess, I've had plenty of exposure to gears but have never heard this term), the module is "the pitch diameter in millimeters divided by the number of teeth"

The teeth mesh at the 'pitch diameter' - which is, for all intents and purposes, the average of the minimum and maximum diameters of the gear. The smaller the module, the 'toothier' is the gear. The larger, the coarser it becomes.

That's clear as day.

I imagine that low module gears have better efficiency till some point at which the teeth are too slender to support the torque. High module gears will be more robust, but will have poor leverage efficiency as the mesh points will be not colinear with the shaft centres and you'll get sliding losses.

No doubt Google can help you from here - oh wait - let me spend 5 seconds.

Check page 7 of this:

http://www.estomad.org/documenten/D2_1/D2_1%20Document%201%20%20Literature%20survey%20gears.pdf

and page 50 of this

http://www.diva-portal.org/smash/get/diva2:397023/FULLTEXT01.pdf

'Modulus' is not a terribly strong driver of gear efficiency it seems. 

I may be limited in my English vocabulary here...  Like with screws, there is some need for a standardisation of the bits and pieces that go together in toothwheel and similar assemblies such as gears, linear drives, bevel gears, worm drives. The modulus is (part of) defining such a standard.

The most simple aspect of this is that parts sharing the same modulus in principle go together, tooth size etc. fit; parts with different moduli won't go together.

In case of a spur gear, the geometrical meaning is the following: Assume you have a toothwheel with 40 teeth. if it is of modulus 1 then it has a nominal diameter of 40 mm (nominal diameter is somewhere near half 'teeth hight'). That means that the travel per tooth is pi times modulus mm.

You may want to look up technical drawings in the online catalogues of vendors of such objects. the link below is an example from Germany, you can switch the language to English, though.

www.maedler.de

Thank you ,Sir for your explanations.

@Kai Fauth @James Garry 

I will study the articles posted by you and let me digest the concepts. If I am not clarrified with the question, I will comment below

See my small additions in the application,

please.

Thank you very much , Sir @Alexander Nikolaevich Petrovskiy. You have given an expression where the module is directly relaed to the gear efficiency. Can you please send me the referance link for your attachment?

Dear Mr. Harish Swaminathan, see page 42 in the application file. But this Russian.

Translator: https://translate.google.ru/

Thank you sir

Module is not always equal to the addendum. Module is just defined as m = p / pi

where p is the pitch and pi=3.14. It is a sort of scale factor and gives an idea of the dimensions of the gear, but the effective high of the theet depend on the addendum and dedendum coefficients ha* and hf*.

Sir,

      The module is defined by the above formula given by you. But when you design a gear, how will you physically measure the module?

Geometrically speaking the module is just a scale factor for a gear. For instance all geometrical features of a spur gear with m=2mm are two times bigger than the corresponding features of a m=1mm gear, provided that the number of teeth, nominal pressure angle and the whole depth, fillet radius, backlash and profile shifting coefficients are the same. All linearly affected magnitudes (i.e. root stress including stress concentration, sliding velocity etc.) increase either proportional (sliding velocity) or inversely proportional to it (root stress), while others (i.e. contact stress) follow a non-linear relationship. Regarding the efficiency of a gear pair it is mainly dominated by the sliding velocities of the gears in mesh along their path of contact, therefore the bigger the module the higher the losses for a given angular velocity and transmission ratio.  

module indicates size of gear

The module of a gear, defined as the ratio of the circular pitch by the number π,  is the measure of the gear as V. Spitas has put it,

Involutometry is the process of measuring the geometry of gears. AGMA standards have all details of verifying the dimensions of a constructed gear and therefore its module by measuring the diametral pitch. Other agencies like ISO, DIN etc. have the same or similar processes. Also, circulating books contain part of these measuring techniques. For example, if you have a spur gear with Z teeth and outside diameter D then, if the gear has no modifications,  the module shoud be D/(Z+2). Professor V. Spitas is active in gearing and may help you.

One salient point is that if you are picking gears from a catalogue, say, then they must all have the SAME module or else they will not mesh! Put simply, the module is the pitch diameter divided by the number of teeth.

It might be worth adding that gear module is sometimes "misunderstood". For example, I have just ordered some gears that "claim" to have a module of 0.5, but the pitch diameter is given as 21.1mm and the number of teeth is 30, so "somebody" has made a mistake in the gear catalogue. Fortunately, the module doesnt matter as long as it is the same for all the gears.