Contact Pressure Vs Traction Vs Deformation in a wire

In summary, the conversation discusses the maximum force that can be applied to a 0.1in aluminum wire before it is plastically deformed by a traction roller. The maximum traction force and whether it exceeds the wire's tensile strength is also considered. The coefficient of static friction is assumed to be 0.61 and the material will yield at 18000PSI. The equations used are assumed to be Spherical Contact equations, but the maximum force applied to the wire before deformation radially is still unknown. The yield strength of the wire is 18000 PSI and the cross-sectional area is 0.007853982in², resulting in an ultimate yield strength of 141.3716694lb. Further information,
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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
 
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  • #2
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.
 

1. What is contact pressure?

Contact pressure refers to the force per unit area that is exerted on an object when it comes into contact with another object. In the context of a wire, it is the force applied on the surface of the wire when it is in contact with another surface.

2. What is traction?

Traction is the force that is generated when a wire is pulled or stretched. It is a measure of the resistance of the wire to deformation. The higher the traction, the more force is required to stretch or deform the wire.

3. What is deformation in a wire?

Deformation in a wire refers to any change in the shape or size of the wire when a force is applied to it. This can include stretching, bending, or compressing the wire. Deformation is directly related to the amount of force applied to the wire.

4. How are contact pressure, traction, and deformation related?

Contact pressure, traction, and deformation are all interrelated. When a force is applied to a wire, it will experience contact pressure on the surface that is in contact with another object. This contact pressure will result in traction, which is the force required to deform the wire. The amount of deformation that occurs in the wire will depend on the amount of traction and the properties of the wire, such as its material and thickness.

5. How can contact pressure, traction, and deformation be measured in a wire?

Contact pressure, traction, and deformation can be measured using various methods, including strain gauges, force sensors, and extensometers. These instruments can measure the amount of force applied to the wire, the amount of deformation that occurs, and the resulting contact pressure. Other factors, such as temperature and surface roughness, should also be taken into account when measuring these properties in a wire.

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