# Coefficient of Friction in Cable Pulling Tension from Conduit Bends

Pulling equations for straight conduit sections and conduit bends. You will also learn about applied friction theory and multi-bend tests.

## Definition of Coefficient of Friction

COF is a measure of the frictional resistance to movement. It is calculated by measuring the force required to slide an object across a surface. In cable pulling, the COF varies with the cable jacket and conduit materials; the conduit condition; the temperature; and, of course, lubricant choice. In cable pulling, the friction measure is most useful when developed from pulling real cables into conduits to mimic field conditions.

## Pulling equations – straight conduit sections

Tension estimation based on the COF is calculated using the cable pulling equations. As discussed previously, the basic equation for a straight pull section looks like this:

 Straight Section Equation Straight Conduit: Tout = Tin + LWμ Where: Tout = Tension Out Tin = Tension In L = Length of Straight Run W = Weight of Cable (per length) μ = Coefficient of Friction

Note that the tension is additive based on incoming tension, the cable weight and friction.

## Pulling equations – conduit bends

The force required to pull a cable increases in a different way as it is pulled into a conduit bend. This force is dependent on the tension entering the bend (incoming tension), as well as the bend angle and the friction. The force added around a bend assumes the form of the “capstan equation”.

 Bend Section Equation Conduit Bend: Tout = Tin * eμθ Where: Tout = Tension Out Tin = Tension In μ = Coefficient of Friction θ = Angle of Bend (radians) e = Natural Log Base

## Everyday application of friction theory

The equation style gets it name from the mechanics of a capstan. The load force using a capstan can be dramatically increased by increasing in the number of wraps (θ), the friction surface on the drum (μ), or by increasing the holding force.

But when pulling cable around a bend, the bend angle, friction coefficient, and incoming tension are established and they determine the pulling tension.

Looking at the equation, we see that the incoming tension is multiplied by the eμθ factor. For a COF of 0.10 and a bend of 90 degrees the multiplication factor is 1.17. But for a a COF of 0.80 and 90 degree bend, the factor is 3.51. So, the lower COF adds 17% to the incoming tension while the higher adds 251%. Small changes in μ (friction coefficient) have a significant effect on bend tension. Accurate friction coefficients are needed for the best correlation of calculated tension with field-measured tension.

## Using a multi-bend test to measure COF

Polywater’s Friction Table is a quick way to measure COF between different surfaces using a large variety of lubricants. Our multi-bend test methods can measure additional effects. A multi-bend test can measure how well lubricant stays coated as the cable travels through conduit bends. We have used this test to study lubricant quantity, cable fill, pulling through water, and multiple-cable pulls.

In a multi-bend test, a weight is added to the cable to produce a known incoming tension. The cable is pulled through a series of bends using a constant speed motor, and the pull tension is measured using a load cell. These tension data are measured at regular intervals, typically every half-second. The force required to pull the cable through the bends is used to calculate the COF. This test complements the friction table test, but requires more time and materials to develop meaningful results.

A accurate estimate of pull tension is the goal of accurate COF measurement. Cables have maximum tension limits based on conduct size and material. It is important not to exceed these limits during installation. Raceway planning and tension estimation in combination with the use of a high-performance lubricant is an excellent way to stay below maximum tension limits.

A related consideration is the cable sidewall tension (crush) limits. This force occurs when cable is pulled through a bend. More on sidewall pressure: