How a Bolt Works : Keeping it all together

Bolts are a crucial part of today’s modern world. They are used in a vast range of applications – from home garden tools, bicycles, vehicles, aircraft and even the defense and aerospace industry. If it were not for bolts, our world would start to fall apart.

If you've ever thought about how a bolt works, you may think it's a simple matter of finding the right sized bolt for the hole, and then tightening it as much as you can so it doesn't come undone.

It might seem that simple – but the truth is that bolts work because of a relatively complex combination of design features and mechanical properties that hold them in place. Some of the important characteristics are:

  • the type of bolt
  • physical dimensions
  • thread density
  • and the materials it's formed from

An improperly installed fastener can fail by becoming loose or breaking completely. In this article we are going to look at how bolts work, how to install them correctly and some things you should look out for when installing fasteners.

Bolt thread

A bolts thread is really just an extension of an "inclined plane" that has been wrapped around a shaft.

When the bolt is turned, it forces the complementary nut or slot to move up the inclined plane. Torque or turning force is used to increase pressure on the nut to make it climb up the thread. When the thread runs out, the tension in the bolt increases to press the mating parts together. As a rule of thumb, the narrower a thread is, the more pressure it can apply.

When we look at a bolt, we discover that the reason it works so well is because of a perfect balance between 3 different forces.

  • Fp = Preload Force
  • Fc = Clamping Force
  • Ft = Tension Force

As you will soon discover, this balance is represented mathematically with the formula Fc = Fp – Ft

Fp – Preload Force

Preload force (Fp) is the tension that is caused by tightening the bolt. It causes the threads to engage and hold the parts together.

Now, if you imagine that the area marked with the letters Fp is a spring, you can begin to understand what Preload force is.

Before the bolt is tightened, the spring is loose and has no tension in it. At this point the bolt has no preloaded force.

But as you tighten the bolt and nut, you eventually get to a point where the nut can't move any further along the thread (because of the parts between it) and our imaginary spring needs to be stretched to get any further movement. The tightening of the spring stores energy that we can use to hold things together.

Now remove the imaginary spring and think about our bolt again. The more the bolt is rotated and tightened against the parts in the middle, the more the bolt stretches and generates tension withing the shaft itself. In this case the shaft of the bolt is workign like a virtual spring and the force that is built-up is called the "Preload" tension.

Ft – Tension Force

The next thing we need to consider is the fact that the joint we are bolting together has forces that are trying to make it come apart. The joint may be part of a bigger assembly and the forces may not be coming directly from the location of the joint. Examples include connecting rod bolts, flywheel bolts and airhead cylinder studs.

When a bolt is properly fastened, the preload force generated by tightening the bolt against the joint is the key to a strong and reliable joint. The stored preload force cancels out the tension forces acting on the joint. It's only when the tension forces are larger than the stored preload forces that joint will start to come apart.

Fc – Clamping Force

Other than dealing with shear forces, the other force involved in the joint is called the clamping force.

The clamping force (Fc) is the difference between the preload force and the tension force (Ft) on the joint. It is created by the head of the bolt and the face of the nut (or washer) against the joint. This is the force that holds the parts together.

Lets go back to our mathematical formula Fc = Fp – Ft

When the tension force (the force pulling the joint apart) is increased beyond the preload force (the force stored inside the bolt shaft), the joint will come apart.

If you think about this from a mathematical point of view:

When Ft is greater than Fp, the calculation of Fc will result in a negative number.

This makes complete sense and is certainly the case when the bolt is undone.

It is important to note that once a bolt is tightened, the value of Fp doesn't change until the tensile force (Ft) is greater than the preload force (Fp). Fp is a constant and the joint stays together because the value of Fc (clamping force) changes to offset the change in the Tension force (Ft).

In simple terms, the strength of a joint is limited to the strength of the bolt and higher preload forces result in a better joint as they stop the parts from moving or loosening.

Joints with soft gaskets are an exception to the rule that higher preload values are better. High loads can damage a gasket and cause leaks.

Shear Forces

The other type of load working on a joint is called shearing force (Fs).

Unlike the other forces that were working longitudinally along the length of the bolt, this force is working across the the bolt shaft and can literally tear (or shear) the bolt in half. An example of this type of joint is a shock absorber mount or a driveshaft flange.

In a joint that is loaded to resist shear, the friction between the parts keep them from moving. It's the job of the bolt to increase the friction between the parts to a point where the joint cannot move under load. In fact, in a properly loaded joint, the friction of the joint bears the load instead of the bolt or fastener itself. The bolt achieves this by using the preload force to increase the clamping force – which in turn increases the friction on the joint.

How do you set preload

Because preload tension can be so important, we need to have a way to calculate and apply it to a joint.

Luckily the mathematicians have come to the rescue and given us a way that we can apply an exact preload by using a torque wrench and a bit of maths.

The formula we use to calculate Fp is:

Fp = T / (D x K)

T is the torque (which we can measure with a torque wrench)
D is the thread diameter
K is a tightening factor that matches the assembly conditions

and if we know the Fp value we want in advance, we can reorganize the formula to calculate the required torque instead:

T = Fp x D x K

 

Torque

You have probably seen that most manufacturers specify the torque required for critical fasteners. The values have not been selected at random and have a direct correlation to the strength of the join they are being applied to.

Once we know the amount of torque we need to create a given proload force, we can use a torque wrench to increase the tension in the bolt. This, in turn, increases the clamping and preload forces.

Unfortunately, torque is not an exact way of generating preload.

When we go back to our formula Fp = T / (D x K), the value we use for K is a theoretical value that only applies in a perfect world.

K Factor or Nut Factor

"K" is a complex factor that is made up of several parts. The best way to explain this is to look at the torque formula by J.Bickford "Introduction to the Design and Behavior of Bolted Joints, 2nd Ed.", 1990 (attributed to N. Motosh, 1976)

In this version of the torque formula, D and K have been combined and are represented by the part between the brackets.

Most of the variables can be easily obtained and relate directly to the thread pitch, radius of the head and radius of the thread. However, two of the variables are based on friction – and this can't be easily controlled in the real world.

Causes for the change in friction can be found everywhere. Some common causes include working with different surface finishes, materials, hardness and lubrication. Because of variations of friction in real life, the torque required to apply a specific preloading force can be out by up to 35% (on unlubricated bolts).

There are lots of ways to improve the consistency of the friction and related K-value.

  • Connections should turn freely with no binding
  • Repair damaged threads with appropriate tap or die
  • Remove dirt and debris
  • Clean with spray cleaner and compressed air
  • Strictly follow the manufacturers specification for thread lubrication

One area that deserves particular attention is the application of lubricants or anti-seize paste. When a manufacturer specifies that a bolt should be assembled dry, it may be tempting to add an anti-seize paste to prevent rust and to make the bolt easier to remove later. The application of lubricant reduces friction and results in a much greater preload than the manufacturer intended. In an extreme case, this may make the bolts stretch beyond their intended limit and make them more likely to fail completely.

For critical applications the variation can be reduced to +/- 10% with the help of special preload indicating washers, and with the help of strain gauges, the variation can be reduced to as low as +/- 1%.

Preload measuring method Error
Operator Feel +/- 35%
Torque Wrench +/- 25%
Angle Torquing +/- 15%
Load Indicating Washers +/- 10%
Fastener Elongation +/- 5%
Strain Gauges +/- 1%

 

Because of the large variations, manufacturers build allowances into their torque settings to ensure that the fastener will hold at both ends of the variation spectrum.

The following video demonstrates some effective ways the variation can be reduced

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