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# Thermal Expansion of a Cylinder

## Thermal Expansion of a Cylinder

(OP)
My applogies if this is a repost, but the search function isn't working.

I know the most accurate way to calculate the change in diameter of a cylinder due to thermal expansion is to use an FEA, but I don't have access to software at the moment.  I want to know how good an approximation I will get using a staight linear calculation on the diameter itself?

Does anyone have experience in this that can tell me?  Thank you.

Orchid Consulting

### RE: Thermal Expansion of a Cylinder

Is the cylinder, hollow and symmetric? What are the boundary conditions---ie uniform internal and external pressure, uniform inside and outside temp? What are the end conditions?

### RE: Thermal Expansion of a Cylinder

If the temperature is uniform, and the ends are not restrained, then figuring on the diameter like you're doing will be exactly right- it won't be a FEA problem.  The cylinder just gets larger in every dimension as it heats up.

If it's restrained in someway, or has temperature variations, then it might get more involved.

### RE: Thermal Expansion of a Cylinder

(OP)
Thanks, at this point the cylinder is solid (with a few surface features machined into it, but for arguments sake lets say it's smooth).  Outside temperature is uniform when in operation.  The ends are restrained by a spring loaded seal, so there is an applied load but it can expand.

Thanks for the replies.  At this point we're willing to expiriment.  Our surface features could lead to some warping or other issues, so being off 0.001" on the tolerance is to be expected anyway.  We do our testing at our machine shop so we can make changes on the spot.

Orchid Consulting

### RE: Thermal Expansion of a Cylinder

If the ends are restrained, you'll get an axial load as it heats up.  In that case, you get some additional lateral expansion due to Poisson's effect, which may or may not be significant in your case.

### RE: Thermal Expansion of a Cylinder

Orchidconsult,

If you want an easy linear calculation for determing the change diameter (or radius) with respect temperature use the following equation:

dR = Ro * alpha * dT

alpha = thermal expansion (approx 7.2 x 10^-6)
dT = change in temperature

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