Bolt toque vs tension

Discussion in 'Physics' started by strantor, Feb 16, 2015.

1. strantor Thread Starter AAC Fanatic!

Oct 3, 2010
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I'm trying to find a "rough" / "general" formula for the tensile force caused by a bolt torqued to a specific value.

All I have found so far are formulas a whole page wide, and over-simplified calculators; nothing in between. If anybody knows a rough formula where I can input torque ft-lbs, coefficient of friction, and TPI, that would be great. I know it would not be exact, but whatever; I just need "a number" to go with.

But that is not my main purpose here. My question is: how is it possible to calculate the tensile force without inputting the thread pitch?

For example the formula here.

or the calculator here.

In the above calculator I input:
456 in-lbs torque
.5" diameter
.18 coefficient of friction
and it returns 5067 lbs of tension.

How can it know that without knowing the thread pitch? The 1/2" bolts in question are coarse thread, but if they were fine thread, they would create a higher tension for a given torque, wouldn't they? The calculator doesn't know if I'm talking coarse thread or fine thread, so what gives?

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2. wayneh Expert

Sep 9, 2010
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This one?
Most of them do seem to use thread pitch.

3. shortbus AAC Fanatic!

Sep 30, 2009
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Why? The thread pitch only has to do with the pull out strength of the threaded material. Nothing to do with the clamping force of the bolt. The clamp force come from the amount the bolt actually stretches. This is why on a racing/high performance engine they measure the overall length of the connecting rod cap bolts now instead of just torquing them to a certain value.

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4. #12 Expert

Nov 30, 2010
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That works if you can get a measuring device on both ends of the bolt, but it is more difficult in a blind hole, isn't it?

Another way to say that: Can you measure the head bolts that way?

5. wayneh Expert

Sep 9, 2010
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Perhaps, but pitch does affect the torque required to turn the bolt, at a given degree of bolt elongation.

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Mar 31, 2012
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7. shortbus AAC Fanatic!

Sep 30, 2009
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You can't. But that's how they determine the 'torque setting' for a blind hole bolt. They put a bolt through tow pieces of metal, with a nut. Then measure the torque it takes to give the stretch required. Bolt torque is one of those, "more art than science" things. That's one reason they went to the 'torque to yield' measurement on engine cylinder head bolts. Torque to a certain value, that is lower than a "standard" bolt torque, the turn "X" degrees past that torque. And if the head gasket needs changing, you also have to buy new head bolts.

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8. shortbus AAC Fanatic!

Sep 30, 2009
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Not really in the 'real world'. The torque is needed is a combination of bolt tensile strength, friction between the underside of the bolt head and part surface. The thread pitch doesn't add that much compared to the other things.

9. #12 Expert

Nov 30, 2010
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Gee, these people who design cars are always finding ways to make them cheaper. Do the new bolts come with the gasket for about 10 cents extra or are the bolts free because they saved the manufacturer so much money making the car?

What will they think of next? Installing about 20 microprocessors in each car?

10. WBahn Moderator

Mar 31, 2012
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That doesn't seem to make much sense. I'm thinking of something like an old style bumper jack for a car. What you seem to be saying is that the thread pitch shouldn't have much of an effect on the amount of torque it takes on the jack handle to raise the car, yet if I change the thread pitch then I change the amount by which the car raises for each rotation of the lead screw. If the torque needed to do that didn't change much, then I could drastically change the power input vs. power output relationship because the power input is the torque x rotational speed of the handle and the output power is the force on the jack arm x the vertical speed of it.

11. #12 Expert

Nov 30, 2010
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I also find it counter intuitive to think the slope of the threads has little to do with torque v force. (The bumper jack example demonstrates this well.) I have taps and dies from 13 TPI to 32 TPI. That seems significant to me. Am I going, "out of context" here? Is the sentence about, "little difference" missing the part about, "when considering the same size bolt"? Do the, "formulas" apply to everything from a 6-32 to a 1/2-13 thread? If the formula is valid, why measure stretch? Apparently the formula is not valid!

12. wayneh Expert

Sep 9, 2010
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The various online calculators add about 10% to the torque for a fine pitch versus a coarse pitch.

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13. shortbus AAC Fanatic!

Sep 30, 2009
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You can't use the 'screw jack' to compare to bolt torque. The screw in a jack isn't constrained by a 'clamp force'. It, the jack is moving something, not stretching. After the friction of the bolt head interface is involved, the threads don't turn much, compared to the tension in the bolt shank.

When I was an apprentice, the company did a lot of work for Babcock & Wilcox R&D lab. They had a bunch of special threads for some of the test fixtures and didn't have torque ratings for them. We did a job of making samples of the threads in a 'known' good metal then torquing and measuring to find correct torque values. Special (for the time) torque wrenches with electronic data collection outputs were used.

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14. #12 Expert

Nov 30, 2010
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Excuse me for being fossilized, but you just demonstrated that torque values can be used to tighten bolts, as we have done for a century. What's up with this, "measuring the stretch"? How did we make all those machines work for the last hundred years by merely using the recommended torque? Are modern engine blocks so flimsy that a torque wrench can't be trusted to arrive at the right tension range without risk of stripping the threads out of the block or the connecting rods?

15. WBahn Moderator

Mar 31, 2012
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In his defense, he did specify high-performance engines. Also, I can imagine that today's engines (and other things) are more finicky as we keep getting more power out of smaller and lighter engines. At some point what was "good enough" a couple decades ago just isn't good enough any longer. I would imagine that, for most things, torque values are still good enough.

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16. WBahn Moderator

Mar 31, 2012
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I understand what you are saying, but I'm not sure to what degree I agree with it (which is not saying that you are wrong, just that I am having a hard time visualizing things in a way to see that you are right).

I can picture two ways of building a screw jack and one of them definitely falls into the description you offer. But the one I had in my first car doesn't and would seem to be subject to the same forces as your "clamping force" description. In that one the leadscrew hung from the top plate (it didn't even touch the bottom of the case) and so the flange that was the bottom of the crank handle worked just like a bolt head in terms of the frictional effect and the leadscrew was in tension due to the load.

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17. wayneh Expert

Sep 9, 2010
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It's worth noting that this is not an ordinary bolt application, but one where the tension on the non-threaded portion of the bolt is the important feature. Thread friction has a relatively lower impact on the torque.

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18. strantor Thread Starter AAC Fanatic!

Oct 3, 2010
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I have trouble wrapping my head around why/how torque is unrelated to pitch. I can see I won't be able to submit as evidence any examples of screws moving things, so I'll try to limit it to torque and bolt stretch. I will look at extremes:

Say I have a bolt 1/2" with 0 TPI. I know, that's not a bolt, it's a 1/2" shaft with slot cut in it. I put 37ft*lbs of torque on the head with a wrench. The 0TPI "bolt" is pulled into the nut with 0Lbs of tension and all 37lbs of torque is directed toward twisting the head off the bolt.

Now I substitute a 1/2"-13TPI bolt. I put 37Lbs of torque on it, and the rotational torque is transferred to linear force along the pitch, which is a slope of 1:13. So my linear force, not considering friction, tooth form, et. al. should be (according to me, maybe wrong) roughly as shown:
37 ft*lbs =
444in*lbs

444in*lbs * 13threads/1in. = 5,772lbs of tension.

That's suspiciously close the 5,853 lbs given by the chart below for a lubricated 1/2"-13TPI bolt (what I ended up using for my "a number" from post #1). Although it is curious that the number from the chart is HIGHER than my number. I would have expected it to be lower, considering friction and all. I guess that bolt stretch relieves some of the tension.

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19. wayneh Expert

Sep 9, 2010
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Torque results from the static friction presented by the area of all mating surfaces, plus the work required to further stretch the bolt. Both of these increase with the tension on the bolt.

Lower angle thread pitch (higher number per inch) makes it easier (lower torque) to stretch the bolt because you stretch it less for a given travel of the wrench. But more threads also adds to the surface area, and this appears to more than offset the mechanical advantage of the lower angle. As I noted earlier, the models calculate a higher torque for fine pitch bolts. I believe your table shows the same.

20. WBahn Moderator

Mar 31, 2012
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How are you getting that the slope is 1:13?

The circumference of the thread is nominally pi/2 inches, or 1.57", so the slope of the incline of the thread is (1/13)"1.57)" or ~1:20.