Expanded Thermal-Expansion Chart

Thank you for the proposed solutions sent in to us in response to the “Thermal-expansion Challenge” problem given to you at the end of my Differential Metal Expansion – Part 1 article on Thermal Expansion. Here’s the answer to the problem that readers were asked to solve!

**The problem for readers to solve was this:** What room temperature radial clearance should be used for the carbide-stainless combination shown in Fig.2 if it were going to be brazed at 1950F (1065C) in a vacuum furnace, and a 0.0015″ (0.040 mm) radial clearance was desired at brazing temperature?

**Our answer:** In order to reach an optimal radial gap clearance of about 0.0015″ (0.040 mm) at brazing temperature, our calculations show that you would need to start with a fairly “loose” radial clearance at room temperature of about 0.0135″/0.34mm (diametrical clearance of 0.027″/0.68mm) between the inner 302-stainless insert and the outer tungsten carbide sleeve-ring. How was this calculated?

**Explanation:** Since we cannot assume that readers have access to other brazing resources to answer this, other than the thermal-expansion chart we included in the article, we wanted to see how folks would use the chart in the article to “solve” this problem.

So, to determine the expansion of the stainless steel from room temperature up to brazing temperature, i.e., 70F to 1950F (about 20C to 1065C), it was necessary to extrapolate the thermal-expansion curve for 302-stainless up to 1950F/1065C (our original chart published in the article only went up to about 1800F/980C).

### See the “Expanded” Thermal-Expansion Chart

The extrapolation results in a predicted total expansion of about 0.021 inch per inch of thickness (or diameter). The carbide curve shows an expansion of only 0.009 inch per inch of thickness (or diameter) over this same temperature range. To make it easier to solve this problem, let’s start by letting the outside diameter (O.D.) of the stainless and the inside diameter (I.D.) of the carbide ring each have exactly a 1.0″ radius as a “starting position” for our calculations. Thus, the total expansion for the metal parts in this assembly when hearted up to 1950F can be read directly from their respective curves as 0.021″ and 0.009″. Thus, when heated from room temp up to 1950F (1065C), the 1.0″-dia stainless bar will grow 0.021″ in diameter, but the carbide-ring’s ID will only increase by 0.009″. Thus, the diameter of the stainless bar will grow more than the ID of the hole in the carbide ring, and the radial gap between them will actually get smaller as the temperature rises. Remember, the ID of the carbide ring does not get smaller when heated, but gets larger, just like the OD of the stainless bar. So this becomes only a differential expansion issue! The ID of the carbide ring does not shrink when heated, but gets larger, just like the outside diameter of the stainless bar.

The amount of the expansion of the outer member minus the amount of expansion of the inner member gives the net gap-clearance change. Thus, 0.009″-0.021″ = -0.12″ net diametrical gap “shrinkage” per inch of diameter (because the result of this calculation is a negative number), times “2” (because the stainless bar is actually 2-inches in diameter), for a total diametrical brazing-gap shrinkage of 0.024″! However, we do not want this amount of change (“shrinkage”) to close up the gap completely! When that “shrinkage” has happened, we still want there to be room for the brazing filler metal (BFM) to flow through the joint. That’s why we asked that the “final” resultant radial-clearance at brazing temperature still be 0.0015″ (0.003″ diametrical gap clearance). Thus, the starting gap clearance at room-temp needs to be 0.024″ + 0.003″ = 0.027″ diametrical — i.e., a 0.0135″-radial clearance (in order to provide a 0.0015″ radial-clearance at brazing temp).

Congratulations to **Travis Grohoske of Triumph Group** in Ohio for coming closest with his estimate of 0.0067″-radial clearance at room temperature for this assembly! He probably was assuming a 1-inch diameter bar. Thus, for a 2-inch diameter stainless bar, he would have had an answer of 0.0134″ radial clearance needed. Wow!