What are washers for? When you attach a bolt to something using a nut, it is clear what the roles of the nut and bold are. 

The more you tighten the bolt the more secure your fastening. However, you are often also told to use a washer as well.

I know this somehow prevents the bolt from loosening but from a physics/mathematics point of view, what is the role of the washer?
 A: *

*Some (smooth or Teflon) washers are used to reduce friction while tightening allowing for greater torque application and thus higher axial loads on the bolt.

*Some washers increase the friction between the parts to prevent it from loosening up

*Some split (or lock) washers act like a spring maintaining pressure in contact during thermal or elastic expansion and/or helps prevent unwinding of the nut by digging in the base material.

*Some washers have a ratcheting surface to fix the nut in a particular orientation

*Some washers are thick in order to re-distribute the contact pressure and soften the damage to the clamped body

*Some washers are there to separate dissimilar metals to avoid galvanic corrosion

*Some (belleville) washers reduce the stiffness of the connection in order to take up deformation better.


... the list goes on ...
A: From here

"A humble flat washer is used for many purposes, some proper and some not. The two most common proper purposes are:
  To distribute the pressure of the nut or bolt evenly over the part being secured, reducing the chance of damage thereto, andTo provide a smooth surface for the nut or bolt to bear on, making it less likely to loosen as a result of an uneven fastening surface."

A: Some washers are to keep the nut from loosening, but not the one you show.  The kind of washer you show is to present the pressing force of the nut or bolt head over a larger area.
This can be particularly useful when the bolt goes thru soft material.  The bare nut might dig into the material in a unacceptable way, or even punch thru due to the high pressure.  The washer distributes the same force over a larger area, thereby lowering the pressure.
In some cases, the washer is also to allow for easier turning of the bolt head or nut.  If the nut digs into the material a bit, it will be hard to turn, and possibly damage the material if it is turned anyway.  The washer decouples the turning motion of the nut from the material.  The rubbing happens between the nut and the washer, and mostly just a steadily increasing pressure is presented to the material.
Then there are lockwashers, which have a different purpose altogether.  They are deliberately designed to dig into the material and the nut, preferentially in the direction of the nut being loosened.  Ideally this forms a sortof ratchet mechanism such that it requires more torque to loosen the nut than to tighten it.  This will help keep the nut in place.  Lockwashers are usually used in cases where the overall unit will be subjected to vibration or varying loads that could cause the nut to loosen over time.  There is enough friction between a normal nut, the bolt, and the material, that for static loads the nut is not going to undo itself.
A: Interesting evolution of the nut-and-washer: nut with built in washer. It helps understand some of the above answers:
Built in lockwasher

this one will "bite" evenly over a large radius - improving the torque with which the nut is held once it is tightened.
If you imagine the contact surface being smooth instead (sorry, don't have a good picture showing it) you end up with a nut that doesn't "dig" when you tighten it. Imagine that you have a soft surface: as you tighten the nut, it starts to sink into the surface, and now it will "plough" material up in front of it if you continue to torque it. This wall of material will make it harder to keep tightening (you can't turn to tighten, but the axial force may not be very high) - at the same time, it would be easy for the nut to loosen (there is a wall in front, but not behind). A smooth washer - whether built in or not - prevents that from happening. I will try to get a picture...
A: A washer helps to distribute the load of the bolt or another fastener.
