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How does a bolt work in physics?

02 Dec.,2024

The Way Bolts Work Is Far More Fastenating Than You Think

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Dear Autopians. It&#;s time. It&#;s time to go deep. Deep into the depths of engineering nerdom. Do you want to know the physics behind how bolts work (they work essentially like springs)? Do you wonder how automakers decide which bolt size to use? Are you curious how they come up with fastener installation torque specs? Do you wonder how much of that force you put on a ratchet actually goes into creating a clamp load versus how much is just overcoming thread friction? These are the things you will learn as we go down a path that many have tried and failed to travel. So grab the hand of the person next to you &#; it&#;s dark down there &#; and follow me as I guide you into the wonderful, fascinating world of the most ubiquitous and much maligned component in all of engineering: the fastener &#; a component more complex and interesting than most people give it credit for. Yes folks, it&#;s time to learn about the lowly nut and bolt.

[Welcome to Huibert Mees&#;s column, where the former Ford GT/Tesla Model S suspension engineer gets to write whatever he wants on The Autopian. -DT]

So what exactly is a bolt? At its most basic, a bolt is a clamp. It is no more than a small version of a C-clamp (or G-clamp for those of you on the other side of the pond). If you want to hold two things together temporarily, you use a C-clamp. If you want to hold them together permanently, use a bolt. Stated more technically:

&#;A bolt is a device that provides a clamping force between two or more surfaces such that the surfaces cannot move relative to each other under normal service loads.&#;

There are essentially two types of joints that bolts are asked to clamp together: Shear and Tensile. In a shear joint, the bolt is used to provide sufficient friction between two or more surfaces such that there is no movement possible between the surfaces. In a tensile joint, the bolt is used to provide sufficient preload in the joint that under normal loads there is no separation possible between the surfaces.

First, let&#;s talk about shear joints.

Shear Joint

A bolt uses friction to ensure that two or more objects are held together and do not move relative to each other when they are subjected to the normal forces the objects are designed for. The part about not moving is key here. A bolt must not allow ANY movement between the objects, not even a tiny bit. There must be enough friction between the objects that they cannot move at all. Even a tiny bit of movement means that the bolt has failed to do its job and the joint will eventually fail and break. Therefore, the bolt has to be strong enough and tight enough to provide the necessary friction, so we need to know exactly how much force the joint has to resist. That is step number one.

A Bolt Acts Like A Spring

So, how does a bolt provide the friction we need? A bolt is really just a simple spring, albeit a very stiff one. When you push and pull on a spring, it develops a force which is governed by the equation:

F = K x X

Where X is the amount the spring is being stretched (or compressed) and K is the stiffness of the spring. Multiply those two together and you get the force in the spring. Here&#;s an example: Suppose we have a spring that has a stiffness of 15 lb/in, in other words, it takes 15 lb of force to stretch or compress the spring one inch. If we want to compress this spring 2 inches, we would need:

F = 2&#; x 15 lb/in = 30 lb

The same thing happens in a bolt. [Editor&#;s note: The equation above shows the spring equation since we&#;re making an analogy. In reality, the relationship between force, strain, and stiffness of a metal bolt is , which is stress = elastic modulus x strain. But it&#;s the same idea. -DT]. When we tighten the bolt, the threads of the bolt are trying to pull the nut closer to the head of the bolt. But, the object we are trying to clamp (a steel plate, a suspension bushing, a bracket, etc.) is in the way and stops the nut from being able to get closer to the bolt head. The only way the nut can keep turning is for the bolt to stretch just like a spring. Of course, like a spring, this gets harder and harder the more you try to stretch the bolt which is why it gets harder and harder to turn a nut the more you tighten it. We can imagine a similar thing happening to the objects being clamped by the bolt; they have a stiffness as well and we can think of them as springs that instead of being stretched, are being compressed by the force of the bolt.

Once the bolt is tightened, the force in the bolt &#;spring&#; and the force in the object &#;spring&#; are the same and push against each other in the area under the head of the bolt. They also push against each other in the area between the two objects. This is where the friction is generated that keeps the objects from moving.

Determining The Bolt Needed For The Job

So now that we know how to use a bolt to create friction between two objects, how do we know that is enough? As I said earlier, the first thing we need to know is how much force the joint has to be able to withstand. With that knowledge, we can then determine how strong the bolt has to be, i.e. how much clamping force the bolt has to be able to provide.

Let&#;s do an example. Suppose we have two steel plates that are going to be bolted together and we need to be able to pull on these plates with a force of 1,000 lb. Something like this:

The amount of friction between two objects is governed by the following equation:

F_friction = mu x N

Where N is the force pushing the two objects together (the clamping force from the bolt, in this case) and mu is the &#;coefficient of friction&#; for the materials the objects are made of. When two materials are pushed against each other, the force it takes to make them slide depends on the materials. For instance, put a block of steel on a concrete surface and it will not slide very easily. Put that same block of steel on a teflon surface and it will slide much more easily. In both cases, the force (N in our equation) pushing the block against the concrete or teflon is just the weight of the block and is always the same. The difference is the coefficient of friction, which is much higher in the case of the concrete than it is in the case of the teflon.

The coefficient of friction is a number that is determined by testing different materials in a laboratory and is a number usually between 0 and 1. There are instances where the number can be higher than one but they are rare. Very sticky tires can have a mu value higher than one, for instance. Zero is also not common because that would mean there is no friction at all which I&#;m pretty sure would be physically impossible. In most cases though, mu will be somewhere between 0.1 and 0.6 with the majority of materials, like steel against steel, the value that most engineers use is 0.2.

Now let&#;s go back to our example. We now know what mu is (0.2) and we know how much friction we need (1,000 lb), but we don&#;t know N yet. Re-arranging our formula we can solve for N:

N = F_friction / mu

N = / 0.2

Therefore

N = 5,000 lb

Now that we know how much clamp force the bolt has to be able to provide, we need to pick a bolt that is big enough to provide that much force.

Like anything else, if you tighten a bolt enough, eventually it&#;s going to break. There is a limit to how much clamping force a bolt can provide before it fails. Failure in this case means the bolt has stretched too far and is now longer than it was originally. If we tighten a bolt up to the point of failure and then loosen it, it will come back to the same shape and length as it was before. If we tighten a bolt beyond the point of failure then it will have permanently stretched and will be longer than it was. This is typically seen as a necking down of the bolt shank and looks a bit like this:

So how do we know how much a particular bolt can take before it fails? We need to know something called the &#;proof load&#; of the bolt. This can be easily found online and will depend on the size of the bolt and the grade, or property class, of the bolt. A 1/4-inch &#;grade 5&#; bolt will not be as strong as a 1/4-inch &#;grade 8 bolt,&#; for example, even though they are the same size. Proof load tables look something like this:

Let&#;s see which bolt would work for our application. Let&#;s look at grade 5 bolts since they are easy to find and cheap. Going down the grade 5 column we see that we do not get above 5,000 lb until we get to a &#;-inch 16 threads per inch (&#;-16) bolt which has a max load of 6,510 lbs. It looks like this bolt would work perfectly in our example.

Determining How Much You Need To Tighten The Bolt (Torque Spec)

Now that we have chosen a bolt to hold our plates, we need to decide how much we should tighten it. There are many tables available that will tell you how much you can tighten a &#;-16 bolt, but they make a lot of assumptions about the type of materials being clamped together, the method for tightening (hand tightening, pneumatic torque wrench, DC nut runners, etc.) and the condition of the parts (are they clean, is there some dirt or oil still on them, etc.). We want to be much more precise than that. This requires physical testing. We need to make some samples of our parts and we need to get sample bolts and nuts. It is important these samples are made as close as possible to the final manufacturing method. This means getting the samples from the same suppliers that will provide the parts once we start production.

Once we have our samples we need to run two tests on them: torque to failure and shear-load to slip. The torque to failure test will tell us what torque we need to specify and the shear-load to slip will tell us if all our calculations and assumptions were right and we have enough clamp load to resist our 1,000 lb force. Both tests require some very special and expensive equipment so we usually send it out to one of a few companies that do this type of work.

Torque to Failure

In the torque to failure test, we will assemble the parts with the bolts and nuts and then tighten the nut or bolt until it breaks. While doing this we will measure the angle, or amount of rotation of the nut or bolt, and the torque we have to apply to make the nut or bolt rotate. Plotting them against each other we get something like this:

There are 5 important areas marked on this graph: run-down, transition, elastic tightening, plastic tightening, and failure.

Rundown: This is the part where the parts are not quite pushed up against each other and the nut is still only finger tight

Transition: In this area the parts are starting to touch each other and any imperfections in the surfaces are slowly pushed flat. If the surfaces aren&#;t quite flat or there is some dirt between them, this is where that is pushed flat and or squashed.

Elastic Tightening: This is the important one. This is where the bolt is stretching without failing and where the clamping force is being generated.

Plastic Tightening: Here is where the bolt is starting to fail. The shank is stretching permanently (this is called plastic deformation) and starting to neck down. You can see how the clamp force is actually reducing the more you tighten the bolt.

Failure: The final area is where the bolt actually fails and snaps in two. Torque drops to zero since it now takes nothing to spin the bolt anymore.

Once we have this graph we can look at where the elastic tightening area transitions into the plastic tightening area. In this case it happens at about 30 ft-lb. From this we could conclude that we can tighten our bolt to 30 ft-lb before we start to fail the bolt. But that&#;s just this particular bolt. If we were to grab another bolt out of the same box of bolts and run the test again it might start to fail at a slightly different torque, maybe 30.5 ft-lb or 29.7 ft-lb &#; we don&#;t know. So, to better understand the boundaries of bolt torque, we need to do this same test a few more times because even though all the parts may have been made the exact same way, there are always minor differences between them.

Usually we will run this test six to 10 times using new parts each time. We then get six to 10 graphs which will all show a slightly different transition point between the elastic and plastic areas. We will then use statistical methods to come up with a torque below which we can ensure that no bolts will fail &#; within 99.999% accuracy. Let&#;s assume in our case the result of these calculations turns out to be 28 ft-lb. That means we can be almost guaranteed that any bolt we pick will not fail when we tighten it to this torque spec.

Tool Variability

The next thing we need to do is to understand how this bolt will be tightened in our production plant. Every tool has some variability when used. In other words when you use a torque wrench to tighten a bolt, the actual torque is never exactly what the torque wrench says. If you set a torque wrench to 28 ft-lb and tighten a bolt, the actual torque might in fact be 27.5 ft-lb or 28.2 ft-lbs. It will rarely be exactly 28 ft-lb.

How close the torque wrench can consistently get to the value you are asking for will depend on the type of tool you are using. A DC nut runner has a very high accuracy while an air impact wrench has less accuracy. Let&#;s suppose the torque wrench we are using has an accuracy of +/- 5%. This means if we set the wrench for 28 ft-lb, we will actually get anywhere between 26.6 and 29.4 ft-lb. That&#;s a range of 2.8 ft-lb overall and it means that half of the time we will be over-tightening bolts. So, if we know that we can never go over 28 ft lb without risking failing some of the bolts, and if we know the range is 2.8 ft lb, then we should target a torque of 28 &#; 2.8/2 = 26.6 ft-lb. That way, using the torque wrench we&#;ve chosen, the max we will get is 26.6 + 5% = 27.9 ft lb and the lowest we will get is 26.6 &#; 5% = 25.3 ft lb. Doing that will assure we never go over 28 ft-lb and we will never cause any bolts to fail.

Shear Load to Slip

We are now set to run our second and last group of tests, which is the shear load to slip. For these tests we will assemble another six to ten sets of parts using the torque spec we calculated by adjusting the torque to failure test results with tooling variability considerations (for this, we&#;d use super accurate, expensive torque wrenches that are constantly calibrated). So in this case, we&#;d torque to 26.6 ft-lbs, and then we&#;d use a press to push the two parts being clamped in a way that puts the bolt into shear.

As we push on each sample, we will measure the force and the position of the press. What we&#;re looking for is a very small jump in the position of the plate we are pushing on. This means the plate has slipped and we have reached the maximum force the joint can handle. This is the shear load to slip: the load in the shear direction required to make the joint slip. Do this for all the samples and apply the same type of statistics we used in the torque to failure tests to find the lowest shear load we could expect any future joint to be able to handle. If this load is higher than our 1,000 lb load then the joint is good and we can proceed with production. If not, then we need to go back to the drawing board and use a larger bolt.

So now that we know how much torque we need to hold the joint together, where does all that torque actually go? We know the object here is to stretch the bolt, but how much of the torque we apply is actually going to stretching the bolt? Here is a breakdown in a case where we tighten the bolt and hold the nut:

As you can see, only about 10% of the torque we apply to the bolt causes it to stretch. The other 90% goes into the friction between the bolt and the object and into the threads of the nut. [Editor&#;s Note: If you live in Michigan or any other rust-belt state, that figure goes from 90 to 99.%. -DT].

The Tensile Joint

Now let&#;s look at the tensile joint. What happens when we have a joint that is in tension instead of shear? Cylinder head bolts are a good example of this type. Engine combustion is trying to lift the head off the block and the head bolts pull it back down to contain the pressure in the cylinders. There is nothing pushing the head sideways so there is no shear load here. In this case, we are not asking the bolts to create friction, they are instead creating a pre-load that the pressure of combustion is trying to overcome. Here is what I mean by that.

Imagine a bolt, represented by the spring above, clamping a cylinder head with a force of 1,000 lbs. That is the preload being applied by the bolt. You need to apply a force greater than 1,000 lbs to overcome this preload and cause the head to become unclamped.

Here&#;s another way to think about it. If I put you inside a box and then sit on it, you will have to push up on the lid with a force greater than my weight in order to lift the lid and get out of the box. If I weigh 200 lb and you can only push up with a force of 100 lb then you will never be able to lift the lid. The other part of this is that I will never know you are pushing up against the lid until you overcome my weight. I cannot feel you pushing with 100 lb of force because the lid has not moved. In the same way, a bolt clamping a cylinder head will not know that an external load is being applied until that load exceeds the preload in the bolt ( lb in the case of the diagram above).

This is the principle that keeps cylinder heads in place and sealed to the block. Add the clamp load of all the head bolts together and you will have the force that the combustion pressures have to overcome in order to lift the head off the block. If the pressures never exceed this total clamp load then the head will always stay in place and the seal will remain intact. This is why it&#;s so critical to tighten head bolts correctly. Too little torque means there isn&#;t enough preload in the bolts, and every time a cylinder fires, the combustion pressures can lift the head up ever so slightly and cause a small leak that will get worse and worse as time goes by.

A Look At Bolts Used For Suspension Bushings

Let&#;s take a look at another usage of bolts, this time in a suspension. In most cars, the suspension arms are bolted to the body of the car or to a subframe using clevis joints.

Notice that the suspension arm is being clamped on two sides by the subframe while a single bolt goes through everything and holds it all together. If we look at this joint in cross section, it might look something like this:

A key thing to remember here is that before the bolt is tightened, there is a gap in the joint to make it easier to install the bushing between the two body brackets. If it were a tight fit then it would be difficult to install on the factory floor, so these joints are always designed with a small gap like this:

As the bolt then gets tightened, the first thing that happens is the body bracket is pulled towards the bushing to close the gap. Of course, it takes some force to close this gap since we have to bend the steel of the body bracket as we tighten the bolt and that force has to be provided by the bolt. This means that not all the force in the bolt is available to provide the friction we need to keep the bushing in place. Depending on how stiff the steel of the body bracket is, this can have a significant impact on the design of the joint and the suspension engineer must take this into account.

[Editor&#;s note: I&#;d like to show how this looks on a Jeep control arm. It works the same way in a wishbone-style arm. Basically, the metal sleeve at the center of the bushing gets squished against the unibody (or in some cases, the frame/subframe), so when the suspension moves and the arm rotates, the sleeve doesn&#;t, causing the rubber to flex. This is how many of your suspension parts move in a quiet, controlled manner.

Here&#;s a look at a Jeep XJ lower control arm:

Contact us to discuss your requirements of Friction Bolt. Our experienced sales team can help you identify the options that best suit your needs.

And here&#;s the opening in the unibody where it slots before being squeezed by a big bolt:

-DT]

On the positive side, there are now two surfaces reacting to the force coming from the suspension, so we now get twice the amount of friction force for the same clamp load coming from the bolt. Our friction equation now looks like this:

F_friction = mu x N x 2

This is a big help and means we can use a smaller bolt to do the same job as we had in our plate example above. This is called a double shear joint while the plate example was a single shear joint.

Here, as in the plate example, once we have a design, we would make sample parts and do the exact same torque to failure and shear load to slip testing to determine the installation torque and make sure the whole joint will withstand the forces we expect the suspension to endure.

Well, you&#;ve survived your first deep dive into the world of fasteners and lived to tell the tale. We&#;ve only just scratched the surface here but if you want to learn more, I can highly recommend a book called &#;An Introduction to the Design and Behavior of Bolted Joints&#; by John H. Bickford. He can take you many levels deeper than I can and should be required reading for anyone who designs bolted joints for a living.

Screw mechanism

Mechanism that converts motion, and forces, from rotational to linear

For the screw as a fastener, see screw . For other uses, see screw (disambiguation)

Animation showing the operation of a screw. As the screw shaft rotates, the nut moves linearly along the shaft. This is a type called a lead screw. A machine used in schools to demonstrate the action of a screw, from . It consists of a threaded shaft through a threaded hole in a stationary mount. When the crank on the right is turned, the shaft moves horizontally through the hole.

The screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force.[1] It is one of the six classical simple machines. The most common form consists of a cylindrical shaft with helical grooves or ridges called threads around the outside.[2][3] The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut can rotate around a stationary screw shaft.[4][5] Geometrically, a screw can be viewed as a narrow inclined plane wrapped around a cylinder.[1]

Like the other simple machines a screw can amplify force; a small rotational force (torque) on the shaft can exert a large axial force on a load. The smaller the pitch (the distance between the screw's threads), the greater the mechanical advantage (the ratio of output to input force). Screws are widely used in threaded fasteners to hold objects together, and in devices such as screw tops for containers, vises, screw jacks and screw presses.

Other mechanisms that use the same principle, also called screws, do not necessarily have a shaft or threads. For example, a corkscrew is a helix-shaped rod with a sharp point, and an Archimedes' screw is a water pump that uses a rotating helical chamber to move water uphill. The common principle of all screws is that a rotating helix can cause linear motion.

History

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Wooden screw in ancient Roman olive press

The screw was one of the last of the simple machines to be invented.[6] It first appeared in Mesopotamia during the Neo-Assyrian period (911-609) BC,[7] and then later appeared in Ancient Egypt and Ancient Greece.[8][9]

Records indicate that the water screw, or screw pump, was first used in Ancient Egypt,[10][11] some time before the Greek philosopher Archimedes described the Archimedes screw water pump around 234 BC.[12] Archimedes wrote the earliest theoretical study of the screw as a machine,[13] and is considered to have introduced the screw in Ancient Greece.[9][14] By the first century BC, the screw was used in the form of the screw press and the Archimedes' screw.[10]

Greek philosophers defined the screw as one of the simple machines and could calculate its (ideal) mechanical advantage.[15] For example, Heron of Alexandria (52 AD) listed the screw as one of the five mechanisms that could "set a load in motion", defined it as an inclined plane wrapped around a cylinder, and described its fabrication and uses,[16] including describing a tap for cutting female screw threads.[17]

Because their complicated helical shape had to be laboriously cut by hand, screws were only used as linkages in a few machines in the ancient world. Screw fasteners only began to be used in the 15th century in clocks, after screw-cutting lathes were developed.[18] The screw was also apparently applied to drilling and moving materials (besides water) around this time, when images of augers and drills began to appear in European paintings.[12] The complete dynamic theory of simple machines, including the screw, was worked out by Italian scientist Galileo Galilei in in Le Meccaniche ("On Mechanics").[9]:&#;163&#;[19]

Lead and pitch

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Lead and pitch are the same in single-start screws, but differ in multiple-start screws

The fineness or coarseness of a screw's threads are defined by two closely related quantities:[5]

The lead is defined as the axial distance (parallel to the screw's axis) the screw travels in one complete revolution (360°) of the shaft. The lead determines the mechanical advantage of the screw; the smaller the lead, the higher the mechanical advantage.
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The pitch is defined as the axial distance between the crests of adjacent threads.

In most screws, called "single start" screws, which have a single helical thread wrapped around them, the lead and pitch are equal. They only differ in "multiple start" screws, which have several intertwined threads. In these screws the lead is equal to the pitch multiplied by the number of starts. Multiple-start screws are used when a large linear motion for a given rotation is desired, for example in screw caps on bottles, and ball point pens.

Handedness

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Right-hand and left-hand screw threads

The helix of a screw's thread can twist in two possible directions, which is known as handedness. Most screw threads are oriented so that when seen from above, the screw shaft moves away from the viewer (the screw is tightened) when turned in a clockwise direction.[21][22] This is known as a right-handed (RH) thread, because it follows the right hand grip rule: when the fingers of the right hand are curled around the shaft in the direction of rotation, the thumb will point in the direction of motion of the shaft. Threads oriented in the opposite direction are known as left-handed (LH).

By common convention, right-handedness is the default handedness for screw threads.[21] Therefore, most threaded parts and fasteners have right-handed threads. One explanation for why right-handed threads became standard is that for a right-handed person, tightening a right-handed screw with a screwdriver is easier than tightening a left-handed screw, because it uses the stronger supinator muscle of the arm rather than the weaker pronator muscle.[21] Since most people are right-handed, right-handed threads became standard on threaded fasteners.

Screw linkages in machines are exceptions; they can be right- or left-handed depending on which is more applicable. Left-handed screw threads are also used in some other applications:

Screw threads

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Different shapes (profiles) of threads are used in screws employed for different purposes. Screw threads are standardized so that parts made by different manufacturers will mate correctly.

Thread angle

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The thread angle is the included angle, measured at a section parallel to the axis, between the two bearing faces of the thread. The angle between the axial load force and the normal to the bearing surface is approximately equal to half the thread angle, so the thread angle has a great effect on the friction and efficiency of a screw, as well as the wear rate and the strength. The greater the thread angle, the greater the angle between the load vector and the surface normal, so the larger the normal force between the threads required to support a given load. Therefore, increasing the thread angle increases the friction and wear of a screw.

The outward facing angled thread bearing surface, when acted on by the load force, also applies a radial (outward) force to the nut, causing tensile stress. This radial bursting force increases with increasing thread angle. If the tensile strength of the nut material is insufficient, an excessive load on a nut with a large thread angle can split the nut.

The thread angle also has an effect on the strength of the threads; threads with a large angle have a wide root compared with their size and are stronger.

Standard types of screw threads: (a) V, (b) American National, (c) British Standard, (d) Square, (e) Acme, (f) Buttress, (g) Knuckle

Types of threads

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In threaded fasteners, large amounts of friction are acceptable and usually wanted, to prevent the fastener from unscrewing.[5] So threads used in fasteners usually have a large 60° thread angle:

In machine linkages such as lead screws or jackscrews, in contrast, friction must be minimized.[5] Therefore, threads with smaller angles are used:

Uses

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A screw conveyor uses a rotating helical screw blade to move bulk materials.

The screw propeller, although it shares the name screw, works on very different physical principles from the above types of screw, and the information in this article is not applicable to it.

Distance moved

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The linear distance d {\displaystyle d\,} a screw shaft moves when it is rotated through an angle of α {\displaystyle \alpha \,} degrees is:

d = l α 360 &#; {\displaystyle d=l{\frac {\alpha }{360^{\circ }}}\,}

where l {\displaystyle l\,} is the lead of the screw.

The distance ratio of a simple machine is defined as the ratio of the distance the applied force moves to the distance the load moves. For a screw it is the ratio of the circular distance din a point on the edge of the shaft moves to the linear distance dout the shaft moves. If r is the radius of the shaft, in one turn a point on the screw's rim moves a distance of 2πr, while its shaft moves linearly by the lead distance l. So the distance ratio is

distance ratio &#; d i n d o u t = 2 π r l {\displaystyle {\mbox{distance ratio}}\equiv {\frac {d_{in}}{d_{out}}}={\frac {2\pi r}{l}}\,}

Frictionless mechanical advantage

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A screw jack. When a bar is inserted in the holes at top and turned it can raise a load

The mechanical advantage MA of a screw is defined as the ratio of axial output force Fout applied by the shaft on a load to the rotational force Fin applied to the rim of the shaft to turn it. For a screw with no friction (also called an ideal screw), from conservation of energy the work done on the screw by the input force turning it is equal to the work done by the screw on the load force:

W i n = W o u t {\displaystyle W_{in}=W_{out}\,}

Work is equal to the force multiplied by the distance it acts, so the work done in one complete turn of the screw is W i n = 2 π r F i n {\displaystyle W_{in}=2\pi rF_{in}\,} and the work done on the load is W o u t = l F o u t {\displaystyle W_{out}=lF_{out}\,} . So the ideal mechanical advantage of a screw is equal to the distance ratio:

M A i d e a l &#; F o u t F i n = 2 π r l {\displaystyle \mathrm {MA} _{ideal}\equiv {\frac {F_{out}}{F_{in}}}={\frac {2\pi r}{l}}\,}

It can be seen that the mechanical advantage of a screw depends on its lead, l {\displaystyle l\,} . The smaller the distance between its threads, the larger the mechanical advantage, and the larger the force the screw can exert for a given applied force. However most actual screws have large amounts of friction and their mechanical advantage is less than given by the above equation.

Torque form

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The rotational force applied to the screw is actually a torque T i n = F i n r {\displaystyle T_{in}=F_{in}r\,} . Because of this, the input force required to turn a screw depends on how far from the shaft it is applied; the farther from the shaft, the less force is needed to turn it. The force on a screw is not usually applied at the rim as assumed above. It is often applied by some form of lever; for example a bolt is turned by a wrench whose handle functions as a lever. The mechanical advantage in this case can be calculated by using the length of the lever arm for r in the above equation. This extraneous factor r can be removed from the above equation by writing it in terms of torque:

F o u t T i n = 2 π l {\displaystyle {\frac {F_{out}}{T_{in}}}={\frac {2\pi }{l}}\,}

Actual mechanical advantage and efficiency

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Because of the large area of sliding contact between the moving and stationary threads, screws typically have large frictional energy losses. Even well-lubricated jack screws have efficiencies of only 15% - 20%, the rest of the work applied in turning them is lost to friction. When friction is included, the mechanical advantage is no longer equal to the distance ratio but also depends on the screw's efficiency. From conservation of energy, the work Win done on the screw by the input force turning it is equal to the sum of the work done moving the load Wout, and the work dissipated as heat by friction Wfric in the screw

W i n = W o u t + W f r i c {\displaystyle W_{in}=W_{out}+W_{fric}\,}

The efficiency η is a dimensionless number between 0 and 1 defined as the ratio of output work to input work

η = W o u t / W i n {\displaystyle \eta =W_{out}/W_{in}\,}

W o u t = η W i n {\displaystyle W_{out}=\eta W_{in}\,}

Work is defined as the force multiplied by the distance moved, so W i n = F i n d i n {\displaystyle W_{in}=F_{in}d_{in}\,} and W o u t = F o u t d o u t {\displaystyle W_{out}=F_{out}d_{out}\,} and therefore

F o u t d o u t = η F i n d i n {\displaystyle F_{out}d_{out}=\eta F_{in}d_{in}\,}

F o u t F i n = η d i n d o u t {\displaystyle {\frac {F_{out}}{F_{in}}}=\eta {\frac {d_{in}}{d_{out}}}\,}

M A = F o u t F i n = η 2 π r l {\displaystyle MA={\frac {F_{out}}{F_{in}}}=\eta {\frac {2\pi r}{l}}\,}

or in terms of torque

F o u t T i n = 2 π η l {\displaystyle {\frac {F_{out}}{T_{in}}}={\frac {2\pi \eta }{l}}\qquad \,}

So the mechanical advantage of an actual screw is reduced from what it would be in an ideal, frictionless screw by the efficiency η {\displaystyle \eta \,} . Because of their low efficiency, in powered machinery screws are not often used as linkages to transfer large amounts of power but are more often used in positioners that operate intermittently.[5]

Self-locking property

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Large frictional forces cause most screws in practical use to be "self-locking", also called "non-reciprocal" or "non-overhauling". This means that applying a torque to the shaft will cause it to turn, but no amount of axial load force against the shaft will cause it to turn back the other way, even if the applied torque is zero. This is in contrast to some other simple machines which are "reciprocal" or "non locking" which means if the load force is great enough they will move backwards or "overhaul". Thus, the machine can be used in either direction. For example, in a lever, if the force on the load end is too large it will move backwards, doing work on the applied force. Most screws are designed to be self-locking, and in the absence of torque on the shaft will stay at whatever position they are left. However, some screw mechanisms with a large enough pitch and good lubrication are not self-locking and will overhaul, and a very few, such as a push drill, use the screw in this "backwards" sense, applying axial force to the shaft to turn the screw. Other reasons for the screws to come loose are incorrect design of assembly and external forces such as shock, vibration and dynamic loads causing slipping on the threaded and mated/clamped surfaces.[26]

A push drill, one of the very few mechanisms that use a screw in the "backwards" sense, to convert linear motion to rotational motion. It has helical screw threads with a very large pitch along the central shaft. When the handle is pushed down, the shaft slides into pawls in the tubular stem, turning the bit. Most screws are "self locking" and axial force on the shaft will not turn the screw.

This self-locking property is one reason for the very large use of the screw in threaded fasteners such as wood screws, sheet metal screws, studs and bolts. Tightening the fastener by turning it puts compression force on the materials or parts being fastened together, but no amount of force from the parts will cause the screw to turn backwards and untighten. This property is also the basis for the use of screws in screw top container lids, vises, C-clamps, and screw jacks. A heavy object can be raised by turning the jack shaft, but when the shaft is released it will stay at whatever height it is raised to.

A screw will be self-locking if and only if its efficiency η {\displaystyle \eta \,} is below 50%.[27][28][29]

η = F o u t / F i n d i n / d o u t = F o u t F i n l 2 π r < 0.50 {\displaystyle \eta ={\frac {F_{out}/F_{in}}{d_{in}/d_{out}}}={\frac {F_{out}}{F_{in}}}{\frac {l}{2\pi r}}<0.50\,}

Whether a screw is self-locking ultimately depends on the pitch angle and the coefficient of friction of the threads; very well-lubricated, low friction threads with a large enough pitch may "overhaul". Also considerations should be made to ensure that clamped components are clamped tight enough to prevent movement completely. If not, slipping in the threads or clamping surface can occur.[26]

References

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