BOLT CLAMP FORCE / THREAD STRETCH 3

[Matt206]

Background:
A simple relatively accurate formula to relate Torque to Clamp Force is: T = (F)(D)(K).
Where D --= Diameter of bolt, T = Torque, Lets ignore K for this.
I am encountering a situation where a screw designed like #1 has an appropriate clamp force with the hand toque that we are able to generate. While a screw designed like #2 does not achieve the appropriate clamp force.
Thread type, thread engagement, material, is all exactly the same. As the above formula suggests, the diameter difference is the reason for the difference in holding force. I can actually feel the stretch that I am looking for when turning the smaller screw.

Question:My question is WHY does Diameter have an impact on this? I would think it would be cross sectional-area of the screw, But after drilling a through-hole in the larger diameter screw to decrease the cross sectional area (with the intention of making it function as a thinner spring to generate more stretch) this did not impact the clamp force.
If unable to change thread type, engagement, and diameter – I am unable to achieve the required clamping force with a given torque.

Picture 1:

Picture 2:

 

[hydtools]

http://www.danlocgroup.com/news-blog.html/2016/09/21/understanding-bolting-preload/

Ted

 

[chez311]

Matt206,

Glad I could help! Theres alot of misconceptions surrounding bolts and the interrelationship of torque, friction, and preload - something about using twisting forces to create pulling forces...

Sounds like you were able to modify the tooling to allow the operators to apply more torque. FYI while it definitely does something, standard WD-40 is a surprisingly poor lubricant. Any moly-based lubricant will do a far better (and more consistent) job - however if you're just utilizing a screwdriver you might be right, the amount of torque you can apply by hand might just never be enough. You'd be surprised what difference a little leverage makes.

 

[chez311]

Necking down the screw reduces the spring rate resulting in more stretch for a given load.

While that would certainly allow more bolt stretch, OP stated he wants to increase preload for a given torque, not just the amount the bolt stretches for a given torque.

Lets use the formula in the link you provided:

Nut Turns = preload / (spring rate * pitch)
Solve for preload = Nut Turns * spring rate * pitch

If as you say you decrease the spring rate (stiffness) of the bolt you have to increase the rotation (nut turns) just to achieve the same preload - which all else being equal should result in the same applied torque as well. As I said all you've accomplished is stretching the bolt further while achieving the same preload.

 

[rb1957]

can you drill a bore into the shank ? this would reduce the stiffness of the bolt.

another day in paradise, or is paradise one day closer ?

 

[handleman]

Umm... He already tried that. In the OP.

 

[dvd]

It is also possible to warm the fastener and let it shrink to tension.

 

[SwinnyGG]

You said this is for a biotech application... are you threading this screw into an organic material, and/or is the screw creating its own thread as it is being driven?

If so, it's going to behave VERY differently than a machined metal part with threads cut in it.

Secondly- it is often helpful to remind yourself that a bolt or screw is really a spring; a bolt applies clamp load by storing energy as it is stretched during tightening.

But after drilling a through-hole in the larger diameter screw to decrease the cross sectional area (with the intention of making it function as a thinner spring to generate more stretch) this did not impact the clamp force.

Imagine you have a fish scale which weights 1 lb with a spring rate of 5 lb/in. Hang a 5 lb weight from it. The scale deflects 1 inch, reads 5 lb, and you're holding a total of 6 lbs in your hand.

Now replace that scale with another scale weighing 1 lb, but with a spring rate of 1 lb/in. Hang your 5 lb weight again. The scale still reads 5 lb, you're still holding 6 lb total in your hand, but the weight now deflects 5 inches.

Drilling a hole through the grip length area of a bolt is exactly the same as changing the spring rate of the scale. You're changing the spring rate of the bolt, meaning it will stretch more at any given load, but you are not effecting the load applied or the total force in any meaningful way.

 

[Matt206]

So I still am trying to understand this concept fully – and will greatly appreciate it if someone can clear it up. If we are looking at the logic that CHEZ provided:

“Your only inputs are the friction coefficient and normal force. The additional factor which needs to be considered with a fastener is the diameter - which is essentially a moment arm through which the friction force is reacted. Larger diameter = larger moment arm = larger amount of torque to overcome the same amount of friction.”

So from this I understand why a small bolt is able to overcome more friction force because of the smaller moment arm. But I don’t understand why this would actually increase the holding force – Wouldn’t a smaller moment arm “loosen” more easily because it would require less force (pretty much the vise-versa situation)

Let me know if I didn’t clarify my confusion well enough

JGKRI thanks for the example -- I do understand that, and that was my initial intuition, but I asked anyway because I figured I might have been confused about the whole concept due to my confusion specified above

 

[SwinnyGG]

So from this I understand why a small bolt is able to overcome more friction force because of the smaller moment arm. But I don’t understand why this would actually increase the holding force – Wouldn’t a smaller moment arm “loosen” more easily because it would require less force (pretty much the vise-versa situation)

The actual energy used to stretch the screw and apply preload (F=kx when treating the screw as a spring) can be estimated by taking the energy input to the system during tightening, and then subtracting the energy dissipated by friction heating of all the various interfaces (thread on thread, bolt head on washer, washer on part, etc).

For your case, you can only apply a fixed amount of torque- meaning your energy input into the system is fixed.

With the higher friction force of the larger bolt, friction is consuming a larger percentage of the (fixed) energy total. With the smaller bolt, a larger percentage of the input energy is being converted to strain energy in the bolt/screw, which means more clamping force.

 

[chez311]

Matt206,

A smaller diameter bolt does not overcome more friction force, it just takes less torque to overcome the same amount of friction. To use an arbitrary case with the simplified equation, 1000 lbs of preload in a 0.25" diameter fastener and 0.375" diameter both with k-values of 0.1 (in reality they would not be identical but probably pretty similar - lets treat them the same for the example ONLY) would result in a friction term of F*K = 100 lbs for both fasteners, which is the friction force that both fasteners, regardless of diameter, need to overcome to generate 1000 lbs of axial preload. The difference is that this friction force acts through different length moment arms resulting in T = F*D*K = 25 in*lbs and 37.5 in*lbs to overcome this friction force for the 0.25" and 0.375" fasteners respectively. Thats a 50% increase in torque required for the larger fastener to achieve the same preload as the smaller one! So the smaller fastener will then require less torque to apply the same preload - the caveat of course being that a smaller fastener will be able to handle less preload (tensile load) because of its smaller cross-section (ie: stresses will be much higher with a smaller cross section for the same tensile load - therefore, as follows intuitively, the smaller fastener will fail at a lower load) and so at a certain point you will have to jump up to a larger diameter fastener depending on the preload required.

Theres so many other factors that can be brought into play, but I'm ignoring them for the sake of simplifying the torque/friction/preload relationship. If you really want to simplify things, all you're doing is using torque to drive a wedge in order to stretch the fastener. The friction force acting on the wedge stays the same so the actual force opposing motion is the same, but as that wedge gets further from the axis of rotation, the moment which is opposing motion increases.

 

[rb1957]

Are you saying that applying the same torque to both your bolts give different preloads/stretches ?
We'd expect this ... the smaller bolt would stretch more than the larger one (for the same torque).

Adding a bore "should" make the bigger bolt softer ... but you say it didn't ... what d/D did you use ?
d = bore diameter, D = pin shaft diameter

You want the prescribed amount of stretch ?
for a limited amount of torque ??

another day in paradise, or is paradise one day closer ?

 

[hydtools]

The larger bolt with the hole is still constrained from stretching by the full length thread engagement.

Ted

 

[handleman]

OK... Looking back and re-reading the OP, the desired outcome is Clamping Force. Unless the original problem was misstated, stretchin' don't enter into it. All stretch does is maintain said clamp force against vibration etc. after it is created. If you make a "stretchy" section of the fat bolt, it will retain its smaller clamping force better against vibration due to the increased stretch, you'll get more turns before it stops rotating, but it will not increase clamping force for the same torque.

If clamp force is the requirement, then, all else being equal, it is impossible (in a world where friction exists) to achieve the same clamping force given a fixed torque with a larger diameter bolt. That's it. Period. This is a slight simplification, but frictional resistance torque = axial force (aka clamping force) times friction coefficient TIMES RADIUS.

 

[chez311]

Adding a bore "should" make the bigger bolt softer ... but you say it didn't

It did.. it stretched the bolt further to achieve the same preload. This is as expected.

You want the prescribed amount of stretch ?
for a limited amount of torque ??

No.. OP says they want an increased preload NOT just increased bolt stretch.

The larger bolt with the hole is still constrained from stretching by the full length thread engagement.

I'm sorry, I don't really know how to interpret that statement. Constrained how?

 

[chez311]

handleman,

Fully agreed, I think I said as much several times which is why I told OP either increase the torque applied or reduce friction coefficient. Looks like OP was able to change tools for the operator to apply more torque (leverage available with T-handle vs. round handled screwdriver).

a Hand powered screwdriver is used, cannot change the screwdriver, but tested a T-handle screwdriver and was able to achieve the clamp needed

 

[Matt206]

I didnt realize that increases stretch without increased clamp load would aid for screw vibrating loose.
This is really what I am trying to get at, though I have not said it before, Im only dealing with a inch long screw with quater inch of thread engagement so I dont know if Ill realistically be able to get enough stretch. As I have already tried the boring out and this had no effect, I could try taking down shaft above the threads like mentioned above, Does this really have that large of an impact on holding tight to vibration, any guesses?

 

[chez311]

Are you having issues with the current joint with loose fasteners in service?

 

[Matt206]

yes but I wanted to avoid all the typical comments that will probably come about bold vibrating loose, because they will be inapplicable to my situation. So i wanted to pose the question just as simple and direct as possible. I cannot use any modified threads, sealer, any rubber, nords-lock washer, (really any washer or c-clip) ect. ect. ect.

 

[rb1957]

why the focus on the stretch of the bolt ?

most would say "I want this much preload (or clamp up)", not "I need this much stretch".

if you want to increase the preload (or the clamp up), then you need to increase the stiffness of the bolt.

if you want to increase the stretch of the bolt, then you need to reduce the stiffness of the bolt.

another day in paradise, or is paradise one day closer ?

 

[hydtools]

It sounds like there is about 3/4 inch of bolt length that can be necked down. The necked down diameter should equal the thread root diameter to minus tolerance. The increased stretch, elongation, will help prevent loosening under cyclic loads. Use as generous a fillet radius as you can under the head and at the thread to prevent creating risers.

Ted