All machines involving mechanical operations can never be free from this inherent opposing force of resistance called friction, normally created due to the interactions between their various moving parts.

Since every machine normally requires an effort input for producing the desired actions with the output loads, friction may be generated with and during either of these operations.

Friction associated with the applied effort may be defined or rather considered as an additional effort that may be required to overcome this.

Friction associated with the actions produced at the output of the machine may be considered as an additional load or an additional resistance that needs to be overcome. In order to increase efficiency and minimize these unwanted oppositions in a machine, evaluating and calculating friction in a machine becomes important.

## Calculating Machine Friction

Let’s consider the above possibilities with a particular machine with the following notations:

*P* = Actual effort required for producing an action at the output of the machine, with friction taken into consideration

*P’* = Ideal effort, same as above, but having virtually no friction involved

*W* = Actual actions implemented by the machine over an output load, with friction being taken into account

*W’* = Ideal implementations by the machine, just as *W*, but without any frictional resistance into its path.

It can be simply envisaged that in the above discussion *P* and *W *will be greater than *P’* and *W’* respectively due to the additional frictional resistances.

Therefore it becomes obvious that *(P – P’)* will be equal to the additional effort required to overcome the additional frictional resistance *(W’ – W)* and will be equivalent to the additional actions done by the machine over the load at the output.

Now according to the formula of machine efficiency, *η = M.A./V.R., *where *M.A.* is the Mechanical Advantage and *V.R.* is the Velocity Ratio and *η* is the efficiency of the machine.

We know that with ideal machines the efficiency will be always equal to 1.

Substituting 1 in the above equation gives:

*η = M.A./V.R.,*

1 =* M.A./V.R.,*

*Or V.R. = M.A.*

However since M.A. is actually the ratio of weight lifted upon to the effort applied, may also be expressed as *W/P, *the above equation becomes:

*V.R. = W/P,*

As discussed above, with an ideal machine the required effort is *P’*, substituting this in the above equation gives:

*P’ = W/V.R.*

We have already studied that *(P – P’)* is equal to the magnitude of the generated friction, if expressed in terms of effort we get:

*P – P’ = P – W/V.R.*

Therefore the required additional effort to overcome friction may be finally expressed as:

*F (effort) = P – W/V.R.—————————— ( i )*

We also know that an effort *P* will operate a load *W’* in case the friction is neglected and the same will operate a load *W* in case the friction is taken into account.

Since W/P = V.R.

Considering the machine to be an ideal one (without friction), we substitute W’ in place of W in the above expression and get:

*W’/P = V.R.*

Or *W’ = P **× V.R.*

But since (W’ – W) is actually the friction, if expressed in terms of load we gat:

W’ – W = (P × V.R.) – W,

Therefore the additional frictional resistance that needs to be overcome may be finally expressed as:

*F(load) = (P **× V.R.) – W—————————- ( ii )*

Equations ( i ) and (ii ) provides us with expressions and simple solutions regarding how to measure friction in machines.

## References

Comprehensive Elements of Mechanical Engineering, By Rajput, Engineering Mechanics, (pg.378), By S. Gujral (Google Books)

My Course Book: Applied Mechanics and Strength of Material By R.S. Khurmi.