Machine Screw Pull-Out Capacity

[Gerrha]

I am a retired scientist and off/on for many years I planned to build a small liquid fuel rocket engine. My son recently got me interested again so I am back working on the project. This engine will never leave the ground. It is for fun and also for my son and I to learn many new things along the way. As a starting point, the design will have a combustion chamber with a round injector plate on the top. They will be bolted together. These parts are fairly small, less than 3" in diameter, so the screws also need to be small as in #4 through maybe #8. Our current design would use 8, 6-32 socket-head cap screws with a thread engagement of 1/2". The material is copper, and the chamber pressure is 500-psig. The thing will be operated remotely, so if it blows up no harm will be done, but the point of the project is to learn what is required for a proper design. This bolt arrangement has become a question for me. It looks good on paper, but from an engineering consideration, is our bolt arrangement adequate or not?

I have searched many sources and cannot find this type of information. However, it must be out there somewhere. Could someone please help us with this?

 

[dgeesaman]

It's hard to give crisp answers because I can't visualize what you're showing.

The primary questions are:
1) will the applied load put the screws be in shear or pure tensile/tear-out?
2) how flat and consistent will the mating surfaces be under the screws?
3) what strength is expected for the screw material and for the copper?
4) when you say 1/2" thread engagement and screws, those keywords have me visualizing a tapped hole in solid copper that is deeper than 1/2" and has the screw engaging 1/2". Please confirm this is correct as opposed to a screw/nut setup.

I can offer that for standard steel bolts screwed directly into tapped holes in soft materials like copper, I would aim to have (1.5x to 2.0x screw diameters) of thread engagement. This follows rules of thumb that say the full tearout strength is reached in 1.0-1.25x for high strength materials and more engagement is required for lower strength materials. 1/2" seems like more than enough there.

 

[Gerrha]

Thanks for your reply. Your questions are all things I have thought about as well and this is what I can answer.

1. Pure tear-out tensile. There should not be any shear.
2. The surfaces will be flat and very smooth because there will be o-rings involved to keep the combustion gases where they are supposed to be. The surface finish will be specified at Ra 16.
3. The screws planned as of now, will be stainless steel A286 with 160K psi tensile strength and 120K psi yield strength. I have assumed 10K PSI yield strength for the copper.
4. You are correct in that the plan is for blind tapped holes in the solid copper injector plate that are deep enough to provide 1/2" thread engagement. This depth can be adjusted if needed. Also, the tap used will be selected to provide 75% thread. For the planned 6-32 screw, this is a tap drill of 0.1065" diameter.

Thanks!

 

[lucky-guesser]

I had a similar conundrum a few years back on a project, couldn't find any data so just ended up having to do my own tests.

Agreed with dgeesaman, if you have 1/2" engagement I would suspect that would be plenty. Wouldn't surprise me if you broke the bolt before getting it to pull out. Assuming pure tension loads of course.

 

[Gerrha]

There must be some sort of guidance out there.

There is an o-ring seal between the combustion chamber and injector plate. The OD of that o-ring is 2.637" and the chamber pressure at maximum engine capacity is 500-psig. That will equate to about 2750-lbs of force pushing those two plates apart. There must be some way to determine the number of 6-32 screws (4, 6, 8, 12?) that will be safe under those conditions or maybe not safe at all and a larger screw is needed.

 

[Stick.]

Screw thread Calculations - Roy Mech

roymech.org

That covers the basics of calculating the capacity of a screw and tapped hole. I can't say if copper requires any special considerations not covered there, but that may be worth looking into.

 

[Gerrha]

Thanks for that link and information. It took me a while to go through it.

Here is what I calculated for a 6-32 screw used in a situation like this. I hope it is correct. I feel I am on very thin ice with the final three calculations (highlighted below), which were not in the link. I sort of made the final three calculations based on what seemed logical to me, but I am not sure. If what I have is correct, then in theory, two 6-32 screws would be sufficient for my expected 2750 pounds. I plan to use 8. Does that make sense? Also, the calculations show that a thread engagement length of 0.36" should be adequate and I plan for 0.5".

Thanks for the help!

Parameter	6-32 screw	Calculation
D, basic screw diameter, inch	0.138	Given
TPI, threads/inch, inch-1	32	Given
Ts, screw material tensile strength, psi	160000	Given
Cs, copper tensile strength, psi	45000	Given
P, thread pitch, inch	0.03125	P = 1/TPI
At, tensile stress area, inch2	0.00927685	At = p * (D - 0.938194 * P)2/4
Ds, tensile stress diameter, inch	0.10868144	Ds = 2 * (At/p)1/2
Dp, pitch circle diameter, inch	0.1177025	Dp = D - 0.64952 * P
Le, length of thread, screw, inch	0.10	Le = 2 * At/(0.5 * p * Dp)
Asss, thread shear area, screw, inch2	0.0185537	Asss = Le * 0.5 * p * Dp
J, material strength factor, unitless	3.56	J = Ts/Cs
Le2, length of thread, copper, inch	0.36	Le2 = J * Le
Assc, thread shear area, copper, inch2	0.06596873	Assc = Le2 * 0.5 * p * Dp
Ss, strength, screw, lbs	1484	Ss = Ts * At
Sst, strength, screw threads, lbs	2969	Sst = Ts * Asss
Sct, strength, copper threads, lbs	2969	Sct = Cs * Assc

 

[EdStainless]

I think that 45ski for Cu is being optimistic, 32ksi is more appropriate unless you have a specific alloy in mind.
And the yield will only be 10-15ksi

 

[Gerrha]

Thanks, that is good information. If I use 32 ksi for the copper, the updated table is shown below. This ups the required thread engagement length to 0.5" which is what I was planning all along. That is good news - assuming my calcs above are correct.

Are the final three calculations correct? What they tell me is that the screw will break before the threads will pullout and that a single screw can take approximately 1450 pounds of tension before breaking. That seems to me a lot of force for a small 6-32 screw.

Parameter	6-32 screw	Calculation
D, basic screw diameter, inch	0.138	Given
TPI, threads/inch, inch-1	32	Given
Ts, screw material tensile strength, psi	160000	Given
Cs, copper tensile strength, psi	32000	Given
P, thread pitch, inch	0.03125	P = 1/TPI
At, tensile stress area, inch2	0.00927685	At = p * (D - 0.938194 * P)2/4
Ds, tensile stress diameter, inch	0.10868144	Ds = 2 * (At/p)1/2
Dp, pitch circle diameter, inch	0.1177025	Dp = D - 0.64952 * P
Le, length of thread, screw, inch	0.10	Le = 2 * At/(0.5 * p * Dp)
Asss, thread shear area, screw, inch2	0.0185537	Asss = Le * 0.5 * p * Dp
J, material strength factor, unitless	5.00	J = Ts/Cs
Le2, length of thread, copper, inch	0.50	Le2 = J * Le
Assc, thread shear area, copper, inch2	0.09276852	Assc = Le2 * 0.5 * p * Dp
Ss, strength, screw, lbs	1484	Ss = Ts * At
Sst, strength, screw threads, lbs	2969	Sst = Ts * Asss
Sct, strength, copper threads, lbs	2969	Sct = Cs * Assc