Thermal expansion of a metal round disk with hole in the middle

[tbone_nl]

This is my first post on this forum because I have a question that I cannot seem to answer myself.

At my working place we have a machine where a metal conveyor belt is running through a section of the machine where the temperature is constant at 320 degrees Celcius. On this conveyor belt are metal round disks with a hole in the middle.

I know that when such a disk is heated from room temperature to higher temperature, the inner diameter of the disk (so in fact the diameter of the hole) gets smaller (right ?)

I also know that the outside diameter of the disk itself will get larger.

But the question is: how do I calculate this ?

Let's say the outer diameter of the disk is 10 cm and the inner diameter of the hole is 8 cm at room temperature. How do I calculate these diameters at 320 C.

I need an answer badly because inside the hot part of the machine there is resitricted space and we want to put disks through the machine that fit at room temperature, but we are not sure if they fit at high temperature. We can easily test this, but there is a risk that we damage the machine if the disks would become to large.

The disks are in the machine long enough to reach 320 C themselves before they arrive at this restriction.

Many thanks in advance.

 

[nasu]

All dimensions (inner diameter or radius included) will increase when temperature is increased.
The hole gets bigger when the temperature is increased.
A good approximation is given by the formula for linear expansion
l=lo(1+alpha * deltaT)
where lo is the initial value of the linear dimension (diameter, thickness, etc), alpha is the coefficient of thermal expansion for the material and deltaT is the increase in temperature.
For common metals alpha has typical values of the order of 10^(-5). So for a temperature increase of 300 Celsius, I would expect that the change in dimensions will be of the order of a few percent.

 

[Redbelly98]

a disk is heated from room temperature to higher temperature, the inner diameter of the disk (so in fact the diameter of the hole) gets smaller (right ?)

Actually, no, the hole gets larger. This is a common misconception.

 

[Lsos]

Yeah, it get larger. They even asked me this question at my current job interview. I answered that "it gets larger" even though I did have a hint of a doubt in my mind.

The guy then said "are you sure?"...but luckily he started laughing before I managed to say "No..."

 

[sardar]

I can provide some information and guidance on your question about thermal expansion of a metal round disk with a hole in the middle. First of all, thermal expansion is a physical phenomenon where a material expands or contracts in response to changes in temperature. This is due to the fact that as temperature increases, the molecules in a material have more energy and vibrate more, causing them to take up more space and expand.

In the case of your metal round disk with a hole in the middle, the inner and outer diameters will indeed change as the temperature increases. In general, the change in length (or in this case, diameter) of a material can be calculated using the coefficient of thermal expansion (CTE) and the change in temperature. The CTE is a constant that is specific to each material, and it represents the amount of change in length (or diameter) per unit change in temperature.

To calculate the change in diameter of your metal disk, you will need to know the CTE of the specific type of metal it is made of. Once you have that information, you can use the following formula:

ΔD = D₀ * α * ΔT

Where:
ΔD = change in diameter
D₀ = initial diameter
α = coefficient of thermal expansion
ΔT = change in temperature

So in your case, if the initial diameter of your disk at room temperature is 10 cm and the CTE of the metal is 0.00002 (which is a typical value for most metals), and the change in temperature is 320°C - room temperature (let's assume it is 25°C), then the change in diameter would be:

ΔD = 10 cm * 0.00002 * (320°C - 25°C) = 0.058 cm

Therefore, the new diameter at 320°C would be 10.058 cm.

It's important to note that this calculation assumes a uniform change in temperature throughout the entire disk. In reality, the temperature may not be exactly 320°C at all points on the disk, and the CTE may vary slightly depending on the specific composition of the metal. Additionally, other factors such as the shape and thickness of the disk can also affect the amount of thermal expansion.

In order to ensure that the disks will still fit in the restricted space at 320°C, you may want to consider adding a safety margin to