Metal annular ring growth at elevated temperature

[petertha]

Can anyone guide me to the proper formula/methodology to evaluate the diameter increase of say a liner or cylinder under elevated temperature? I first assumed I could just multiply any dimension such as the bore or OD by the thermal coefficient to get the new dimension at new temperature. Now I'm not so sure. Maybe I should be multiplying the coefficient by the largest dimension (the OD) and scaling the original ID proportionately?

I'm trying to get a feel for 2 modes:
- heating the aluminum cylinder only & dropping in the CI liner at ambient & which is a slight interference fit to the cylinder at ambient.
- more importantly come removal time, heating the cylinder+liner combination to some temperature so the two parts can be removed. Here I can no longer apply different temperature, both parts will rise together.

Here is how my spreadsheet is evolving, but I'm lacking the proper underlying formula.

 

[Cogsy]

I've never had to do such calcs on a ring so can't help with any formulas but I can say you definitely can't apply the linear coefficient to things such as bore or OD and get correct expansion. The thermal coefficient relates to material expansion only and the 'void' of the bore or ID will not contribute to the expansion. You might get some indication of expansion magnitude by applying the linear coefficient over the wall thickness (i.e. treating the liner as a flat bar and examining the thickness change) but the ring shape is going to confound things. I'm sure there's formulas out there somewhere though as it's a common thing to do.

I'm not sure how much heating will hep you for removal though. Certainly the aluminium will expand more than the liner material and should reduce the press fit by some amount, but I would expect the comparatively small volume of aluminium (especially at the bottom of the fin grooves) and relatively thick liner will mean it won't reduce by much (maybe even at all if the mismatch in volumes is high).

 

[petertha]

Just curious, any Edwards 5-cyl builders out there? That design is quite similar to my radial in this regard. The Edwards plans specify a min/max for the cylinder ID and liner OD. Going by these numbers the possible interference can range from 0.0000" to 0.0015". What I'm not sure of is the design intent of the upper interference range (0.0015"). Are the liners meant to be removable or are they considered rather permanent?

The other data points I have for liner/cylinder relative diameter interference are from Ohrndorf at .01mm (=.0004") and Jung at .02mm (0.0008"). Jung says the following: To ensure optimum heat transfer, the cylinder liners must be shrunk into the cylinders. The inner diameter of the cylinder is about 0.02 mm smaller than the respective outer diameter of the liners to unscrew. After uniform heating of the aluminum cylinder by means of gas burner or hot plate (to about 200 ° C), the cold liners are inserted into the cylinder. Ohrndorf instructions are sparse, just the liner OD dimension +above cylinder bore dimension.

Well I made a slight error interpreting the drawings because one has to hop back & forth between 2 engines with shared parts but modified dimensions. But at least I was consistent across the liners & cylinders so its fixable. I'm sitting at about 0.0015" interference right now. I put the cylinder in my mini toaster oven at 425F for 5 minutes. The liner dropped in effortlessly. But the heat shrink force also caused my bores to shrink. Before installation they were are all sitting -.0001" of target bore, but once shrunk in the cylinder are ~ 0.001" undersize. I could leave them with increased interference but represents more tedious lapping work to bring to size.

Removing the liner using the same 425F temperature soak on the assembly did not work well. I tried a heat gun at 550F (it probably wasn't actually that hot or uniform). I then resorted to butane torch which I was loath use, but I cornered the assembly in some fire bricks & slowly danced it around evenly from a distance. I've had to do this on the odd RC engine purely because of fuel varnish 'glue'. Fortunately no permanent distortion could be measured once everything was cool.

So now because the liner bores are lapped accurately & the ODs are all finished ~0.0015" oversize, I figure the easiest remedy is to lap the cylinder ID's. This will increase their bore to some lesser target interference dimension. I measured some RC engines & they seem to be in the 0.0005" range but they are used so not quite sure I trust them. Usually they part ways with mild heat gun, say 300F?

 

[Charles Lamont]

Petertha, your first assumption was correct. It is easy to overthink this.

 

[Asm109]

change in length= CTE*Dimension*Change in temp.
CTE Coefficient of Thermal Expansion.
Dimension is ID, OD, wall thickness, Length. It matters not.