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# Why does bolt preload decrease as friction increases?

## Why does bolt preload decrease as friction increases?

(OP)
I'm relatively new to bolted joint design and analysis, and want to master the subject. I've read statements that say something like "friction eats up preload". This makes sense, but I want to understand more clearly the physical mechanism behind it.

I have thought about this for about an hour, and want to confirm that what I assume is accurate. This is what I have come up with (assuming a bolt is being rotated into a tapped hole at some fixed torque input):
• Preload: is ultimately dependent on the bolts axial travel.
• Axial travel: is directly related to the degree of rotation.
• Rotation: stops when there is a reaction torque acting on the bolt that is equal and opposite to the input torque.
• Reaction torque: is the product of the reaction frictional forces and associated radial moment arms (requires integration).
• Frictional force: is the product of the normal force (related to preload), and the friction coefficient.
Therefore given the same torque input, increased friction coefficient means that less preload is needed to generate an equilibrium reaction torque, which means the bolt will reach equilibrium with less rotation, resulting in less axial advancement. Thus, there is not as much clamping force (preload). Would you say this is accurate?

### RE: Why does bolt preload decrease as friction increases?

I think you've got it.

So, in order to get somewhat close to the expected preload using a torque value, friction must be carefully controlled. Otherwise, another method will have to be used to ensure proper preload, such as the use of some type of load indicator or a turn-of-the-nut method.

### RE: Why does bolt preload decrease as friction increases?

CamJPete:
I think you generally have the right idea, but may be saying it a bit bass-acwords. Try thinking of it this way…, more inherent friction within the threads requires more torque just to turn the bolt. Thus, less input torque is available to advance the bolt, which of course, also increased the friction within the threads as the bolt tightens. The preload actually happens because the bolt elongates (not just axial travel or rotation) as the joint parts are clamped tighter. You should replace your ‘axial travel’ with axial elongation. The relative elastic stiffness of the various joint parts also comes into play in these calcs. Clamping two pls. of lead (low E, modulus of elasticity) together, with a large steel nut, bolt and washers, will allow plenty of bolt travel/rotation, but not much bolt elongation or preload. Alternatively, the same bolt on two well fitted (flat) steel pls. (much higher E, in ksi) will cause much more bolt elongation per unit of travel/rotation, and thus greater preload. Take a look at some good Strength of Materials, Theory of Elasticity and Machine Design text books for bolted connection design.

### RE: Why does bolt preload decrease as friction increases?

There is a great reference for bolted joints called NASA-STD-5020. One can find this with a google search.

### RE: Why does bolt preload decrease as friction increases?

(OP)

I have read through my machine design chapter on bolted joints several times, and am currently reading through NASA-STD-5020. I am familiar with the equations of T = KDP, and rearranged, P = T/KD, and concepts of joint stiffness. Yes, elongates is probably more accurate. I was assuming axial travel was equating with elongation as the head hits the material, but that is a better description.

What I was hoping to confirm was the physical reason for there being less preload if there is more friction. The statement of "friction requires more torque to turn the bolt" was what I kept reading, but I never could state why that affects preload. Perhaps another way of saying that same thing is "friction means the same torque will turn the bolt less".

I started pondering this question as other engineers at my company have informed me that the presence or absence of a steel washer (against an aluminum part) will affect preload because of the friction. If I specify XX lbf-in torque on the drawing, I wanted to understand how the same torque input could mean less preload without a washer. As I understand it, there is nothing inherently bad about the friction (galling aside), so long as you account for it in the joint design and specify "more torque to turn the bolt".

Perhaps another way of saying this is "if I want to achieve some preload, I have to ensure that the bolt elongates (simplistically) by P/k (load/stiffness)...remembering that higher friction can prevent that from happening if you don't increase your torque." I'm beating a dead horse now.

HotRod, I like your summary. Friction must be carefully controlled or you might not get what you think you're getting.

### RE: Why does bolt preload decrease as friction increases?

Yeah, and it's difficult to control or get predictable friction. Consequently, torque is almost always a very imprecise measure of bolt tension.

For applications where tension in the bolt is not required, we'll direct the contractor to use stick wax to lube the bearing faces and threads and use the "full effort of a worker" using a wrench of a specified length to achieve a "snug tight" condition.

For anchor bolts requiring preload, we use the aforementioned "snug tight" wording, and then have them turn the nut another so much of a turn (usually 1/4 turn total in 2 passes). Many times we check those later using our own hydraulic wrench, which is about all you can do on a 2" or larger anchor bolt. Our wrench will generate up to 6,000 ft-lbs of torque, and when they're tightened properly, they don't budge.

For tensioned high-strength bolts, most often twist-off bolts are used, which is a torque based way of tensioning them, but the fabrication and prep for those is fairly consistent. Otherwise, load indicating washers are required.

### RE: Why does bolt preload decrease as friction increases?

You can also look at it from a work viewpoint.

The input work of torque x rotation goes into

Preload work of tension x stretch

Friction work of tension x much rotation.

### RE: Why does bolt preload decrease as friction increases?

This old f*** didn't note anyone saying anything about pitch, or angle of slope the nut has to rise as it travels up along the bolt. The more threads per length unit of bolt, the easier the resistance to turning the nut. Like a car traveling up a hill. The steep one is more difficult.

### RE: Why does bolt preload decrease as friction increases?

(OP)
Thanks oldestguy. That brings up a good point of clarification. As I understand it, the equation of P = T/KD states that the preload is inversely proportional to the nut factor. The nut factor is often empirically derived, but I've seen a statically derived equation for the nut factor that is a function of the friction coefficients, pitch diameter, and lead angle (among other variables).

Perhaps my original question was more focused on the physical mechanism for why friction itself affects preload, rather than why the nut factor does. But you've given me some additional information to extend that idea to the nut factor. Thank you.

MintJulep, work is an interesting way to look at it. I'm not fully understanding your equations though. Are you saying that torque * rotation = tension * stretch (+/-/or?) tension * much rotation? Could someone provide a more formal equation that states this clearly? Thanks.

### RE: Why does bolt preload decrease as friction increases?

Sorry, I typed my first post on my phone. much --> mu

Input torque x input rotation = (bolt tension x bolt elongation) + (bolt tension * mu * rotation)

### RE: Why does bolt preload decrease as friction increases?

Something you might want to consider is that measuring torque is only a proxy for actual bolt preload, and honestly not a very accurate one. When assembling a bolted joint, the goal is to preload the fastener to a defined stress value. This elastic deformation creates the clamping force that the fastener uses to hold whatever you're attaching together.

Measuring this preload directly is challenging, and requires more expensive, high-precision equipment. It is often not feasible to do this kind of direct measurement. What is easy to measure, however, is the installation torque. So the T = KDP equation is an empirically derived way to relate torques and bolt preload. The fastener resists turning for two reasons - firstly, turning is applying a force to a fastener via the geometry of the threads. Secondly, the friction between the bolt or nut head, and the mounting surface also resist turning. So theoretically, if you can determine your frictional forces perfectly, you can determine the amount of force that goes into stretching the bolt, based on the materials and geometry. Of course, in reality, it is quite difficult to determine actual installation friction (environmental factors can affect it quite a bit - humidity, temperature, cleanliness of surfaces, etc). This is where the nut factor comes in - while people have attempted to determine an engineering basis, it's primarily determined empirically, by testing various fastener joints and measuring the true preload with some of the fancier equipment I mentioned above. The empirical nut factor came first, before anyone tried to derive a real formula for it.

So to summarize, the reason friction affects preload, is that the installation torque is applied to two different things - stretching the fastener, and turning the fastener against its mounting surface. If you need more torque simply to turn the fastener, that means less torque goes to preloading. There are methods of preloading fasteners that don't require turning or torquing at all - hydraulic bolt stretchers, and preheating a fastener before installation to preload it by the shrinking cooling.

### RE: Why does bolt preload decrease as friction increases?

"Measuring this preload directly is challenging, and requires more expensive, high-precision equipment."

Actually, direct tension indicators accomplish this rather well, at a fairly nominal cost in materials. Standard load indicating washers require only a feeler gauge to check. The fancier "squirter washers" that squirt dye out when the bolt reaches the specified tension, don't even require that.

### RE: Why does bolt preload decrease as friction increases?

HotRod10: Interesting, I haven't come across those types of washers before. The maximum of 1-1/2" would limit their application at my shop, but for larger diameter fasteners, we will often use jack-bolt tensioners (the generic name for Supernuts and Superbolts from Nordlock), to minimize the required installation torque. The design of supernuts also lets us tension to a higher percentage of the fastener yield strength, as we have more confidence in the torque/preload relationship.

I'm curious about the downsides of these tension indicating washers - if they work so well, how is it that they aren't more widely used?

### RE: Why does bolt preload decrease as friction increases?

The downside to the standard washers is that someone has to carefully check the gap with a feeler gauge at each bolt. The squirter type is a fairly new technology, so it suffers from the bias of unfamiliarity, but is gaining popularity.

For new bridge construction and rehabilitation projects with a significant number of bolts, we see almost exclusively twist-off bolts, because it's easy to see that they're tensioned, and the variation in final tension is within the tolerance for what we require.

### RE: Why does bolt preload decrease as friction increases?

For critical joints using common fasteners, ultrasonic extensometers have been used in the field for 50+ years among other nondestructive methods and aren't overly expensive in the grand scheme of things - a couple thousand \$USD.

### RE: Why does bolt preload decrease as friction increases?

That's interesting, CWB1. I hadn't heard of those. Maybe the tension for the bolts for our joints isn't considered critical. A few grand is not bad if number of bolts to be checked is sufficiently large. Looks like they would work really well for checking tension on already-tensioned bolts, which would be difficult to do any other way, but I'm not sure how convenient it would be for getting the correct tension during installation. They would have to be tightened and then checked, and then adjusted, and checked again, correct?

### RE: Why does bolt preload decrease as friction increases?

Correct. The transducers are quick to attach, usually via magnets so its not an overly slow or laborious process but it is more of a QA check than an installation technique.

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