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The Pinion is a small part in combination with gear where it is needed to transform the motion to gear as a result the spinning motion and contacts of the teeth to the gear materiel is more ( as pinion has less number of teeth than gear) the result is over heating and wear and tear are comparatively more that the counterpart . 

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In general, pinion is used as a driving gear in a machine. They are used to transferring more torque to the gear. And we already know torque is directly proportional to power transmitted. More the torque and more power can be transmitted. Apart from cyclic loading at higher speed, the pinion also faces a large amount of shear stress since torque is directly proportional to shear stress and due to its lesser polar moment of inertia, the value of shear stress increases proportionally. Show in order to avoid it from shear failure we have to use better material. If we increase the polar moment of inertia, it means its size will be increases which is not desirable for power transmitting. So pinions are made of Superior material than gear.

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What is the relation between number of cycles of pinion and its wear?

no. Of cycles is related with every mechanical component. On the basis of no. Of cycles every mechanical component is designed for safe working.

For more u can Google s-n curve.

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Totally agree with the comments above from an engineering perspective, the pinion might also be subject to a torsional force that the material would have to dissipate, the teeth being of a smaller size there is more chance of a stress raiser being created around the base of the teeth.  However, you've got to remeber that these design considerations are application specific, and if they can calculate that the cheaper material is strong enough why use a better one that will generally cost more?  If you can calculate that is will only encounter a limited number of cycles per year and it will take hundreds of years to break - why bother?

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Akeel A. Abdullah ia the first who answer correct and clear the concept about material selection in pinion gear and all comments after Akeel`s comment are identical to his answer

Great answer Akeel

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There is a problem with the original question. The term "superior material" is undefined. What is a "superior material"? Is it superior with respect to strength? With respect to wear? With respect to heat conduction? With respect to workability? With respect to ductility? With respect to toughness? Etc, etc. Until this is defined, the question is not very meaningful.

DrD

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for a give condition 

1.the SURFACE SPEED /velocity of pinion is much more than the gear (DEPend on radio),to withstand equal life the pinion should be heat treated to more hardness than the gear NEED NOT BE SUPRER MATERIAL

one case  study i came across 

the machine is rotary furnace with a diameter od 3000mm to run with friction drive a pinion of 200mm the drum RPM is 10/mt(not gear and pinion) 

velocity of drum /furnace is 94.2meters per minute material MS

velocity of pinion is 6.2 meters per minute material en8 equal to ms

the raitio 15.1 which mean the pinion running faster than the drum by 15 times  here the life of pinion is 6month when compare to drum 10+years 

tto increase the life of pinion from 6month to 120 month heatreated the pinion to 36 to 40 rc the life become equal 

this is an actual condition in an industry

this information as per my knowldge

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The surface speed between two gears are exactly the same, otherwise there would be slip.

The load, or force, between two gear teeth are exactly the same, otherwise they would violate the conservation of force.

The larger of the two (in this case, the gear) has a much greater shear area, which means it sees a lower toque-induced shear stress. Recall that the stress = torque / polar moment i.e. Tau = torque / J, where J = pi * (D^4-d^4) /32.

It is true that each tooth on the larger gear has more time to cool down after making contact with the pinion because there are more teeth. But it is also usually true that the pinion's teeth are in contact with cooling oil for longer and more often.

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