Contact Pressure Vs Traction Vs Deformation in a wire

[ounvme]

Homework Statement

A .1in aluminum wire is being pulled from a coil between 2 1in steel rollers. One roller is fixed to the driving motor while the other roller is loaded with a force to provide traction. What is the maximum force that can be applied before the wire is plastically deformed by the traction roller? What is the maximum traction force the system is capable of using the maximum force on the traction roller before deformation? Does this traction force exceed the tensile strength of the wire? The coefficient of static friction is assumed to be .61 and the material will yield at 18000PSI.

Homework Equations

I assume that Spherical Contact equations should be used

The Attempt at a Solution

I have calculated the maximum tension allowed in the wire but I am not able to figure out the maximum force applied to the wire before deformation radially. My guess is the principle stress in the z direction should be less than 18000PSI but I am also not sure of this.

YIELD STRENGTH 18000 PSI
CROSS SECTIONAL AREA (in²) 0.007853982 in²
ULTIMATE YIELD STRENGTH 141.3716694 lb

 

[haruspex]

Many of those who might be able to assist you on this forum will not be familiar with the equations, so please post them. Please be sure to define the variables.