How to calculate roller/wheel maximum load?

[lobosta]

Dear all,

I would like to know how to calculate the maximum load that a roller/wheel can stand under set conditions. The roller/wheel works in a sliding door and it rolls along a stainless steel rail.

I think I have to use contact stresses equations and so on but after reading several books and forums about this topic I am a bit confuse as there are a lot of different equations to use to calculate the same thing.
Which is the most simple and more accurate equation to use?

I leave some random data to give you an idea for what I am looking for:

Roller/wheel material: polyacetal homopolymer, POM-H
Young modulus: 2800MPa
Poisson coef: 0.35
Yield strength: 79MPa
Dynamic friction coef: 0.3; static: 0.2

OD (outer diameter)= 30mm
ID (inner diameter) = 15mm
Width= 10mm

No T requirements.

I am not looking for the results; I am more interested in the equation and how to calculate.

Hope somebody can help me,

 

[Achy47]

Thank you.



Thank you for your question. I would approach this problem by first understanding the mechanics of the roller/wheel in the sliding door system. The main factors that will affect the maximum load that the roller/wheel can withstand are the material properties, geometry, and the contact stresses between the roller/wheel and the stainless steel rail.

To calculate the maximum load, we need to consider two main failure modes: yielding of the roller/wheel material and excessive contact stresses. Yielding occurs when the applied load exceeds the yield strength of the material, causing permanent deformation. Excessive contact stresses occur when the contact pressure between the roller/wheel and the rail is too high, leading to failure of the material at the contact point.

To determine the maximum load for yielding, we can use the following equation:

P = A * σ_y

Where P is the maximum load, A is the cross-sectional area of the roller/wheel, and σ_y is the yield strength of the material. In this case, A can be calculated using the outer and inner diameters and the width of the roller/wheel. The yield strength for POM-H is 79MPa, as provided in your data.

To calculate the maximum load for excessive contact stresses, we can use the Hertzian contact stress equation:

σ_max = (3P/2πab^2) * (1-ν^2)

Where σ_max is the maximum contact stress, P is the applied load, a is the radius of the roller/wheel, b is the radius of the rail, and ν is the Poisson coefficient. In this case, a = 15mm and b = 30mm.

To ensure that the roller/wheel can withstand the maximum load without excessive contact stresses, we need to make sure that the maximum contact stress is lower than the yield strength of the material. This can be achieved by adjusting the dimensions of the roller/wheel or the rail, or by using a different material with a higher yield strength.

In conclusion, the most accurate and simple equations to use for calculating the maximum load of a roller/wheel in a sliding door system would be the yielding equation and the Hertzian contact stress equation. However, it is important to note that there may be other factors to consider, such as the dynamic friction coefficient, which can affect the performance of the roller/wheel. I hope this helps and please let me know if you