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If the above theory had been correct all points on curves. "A," "B" and "C" would have fallen on one curve. It therefore follows that when based on the present generally accepted theory, measurements of contact drop cannot be duplicated unless always measured on the same size of brush.

CONTACT RESISTANCE IS INDEPENDENT OF THE CONTACT AREA

Contact resistance is not determined by the area involved although prevailing opinion appears to be to the contrary. A considerable number of tests have been made to determine what factors influence contact resistance between two conductors. (See article on "Electrical Contact Resistance" by F. W. Harris in the Electric Journal for July, 1913, P. 637; Also Article on "Contact Resistance of Large Conductors" by Arne R. Enger in Electric Journal of July, 1924, P. 316.) As a result of these tests the following laws were outlined:

"1-All other conditions being constant, the voltage across a contact joint will increase directly with the current, or the joint between two materials behaves exactly like a resistance.

"2-Where the conditions of the surfaces in contact are not affected thereby, the voltage across the contact will vary inversely with the pressure.

"3-The resistance between the materials depends directly on the internal resistance of the materials, those having a low resistance having also a low contact resistance.

"4-The resistance between contacts depends not upon their area but only on the total pressure with which they are forced together."

Before attempting to apply these laws to brush contact resistance, the mechanical nature of the contact should be thoroughly understood. The theory upon which the above laws are based is that the contact under light pressure will be at three points and that as the force pressing the conductors together

is increased these small areas of contact, by a process of breaking down, or bending, will increase in size and number. This theory has been referred to as the "three point contact theory."

This theory can be easily understood when the surfaces are rough and irregular, as the points of contacts can be observed without the use of a microscope. However, the same thing applies to comparatively smooth surfaces even though the greater part of the surfaces may be separated by only a few one hundred thousandths of an inch.

It appears as though the investigations from the results of which the above laws were formulated, covered stationary contacts. However, it can be shown that in general they apply equally well to brush contact resistance.

The contact between moving or sliding conductors at any instant of time will be the same as for stationary conductors. It is, however, to be expected that after the conductors or brushes have become thoroughly "worn in," the contacts will shift rapidly from place to place over the contact surface of the conductor or brush. In all other respects they will behave

exactly like stationary conductors.

Because of the hardness of the material and the comparatively light pressure used on carbon brushes, it is doubtful if the average number of "contact points" in contact with the commutator is ever very great, especially when held in a box type brush holder. In this connection it should be remembered that few commercial commutators are perfectly round and that each part of the commutator is worn or ground away by more than one brush. Therefore no one brush is ever ground to a "perfect fit."

From the foregoing it will be seen that there are only a very few points of very small area in contact with the commutator at any one time and when the commutator is standing still all the current from commutator to brush or vice versa must pass through these very small conducting portions. Now, when the commutator begins to move, some of these contacts are broken and new contacts are formed at other parts of the surface. It

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will be assumed that as the contact points are broken, small arcs are formed for very short interval of time. These arcs are in parallel with the other solid conductors. The percentage of current following through the arcs under normal conditions is usually very small. We therefore in studying contact resistance will confine the discussion principally to the solid material forming the contact.

In applying the first law, given above, to brush contact resistance, it should be remembered that carbon and graphite material have a negative temperature coefficient of resistance, and that therefore the resistance will decrease as the current is increased due to the higher temperature. The contact drop, therefore, will not increase in direct proportion to the current. The resistance of the small arcs in parallel with the solid conducting material also have the same characteristics.

It is believed that no one will question the correctness of the second law if interpreted to mean that the voltage drop decreases when the brush pressure increases.

Carbon and graphite have from 200 to 400 times the resistance of copper. If the third law is true, practically all resistance at the contact will be in the brush and according to the "three point contact theory" this resistance is at the face of the brush. It therefore can be assumed that practically all the heat produced by the contact resistance is produced in the material within .01 inch from the face of the brush. The expenditure of such an amount of electrical energy in such a small amount of material probably heats the material forming the "point contacts" to a rather high temperature.

It has been noted that the contact drop at the positive brush is less than the contact drop at the negative brush. This, at first thought, may seem to be contrary to the third law. However, this phenomenon appears to be the result of two causes working together. One is thermal-electric, and the other is that, due to arcing, the material in the face of the positive brush is brought to a higher temperature than the material in

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