[The following is unfinished and lacks diagrams, but may still be of limited interest.]

Chain Drive -- Operation and Wear

Most bicycles built since 1900 use chain drive. Other drive schemes have been tried -- direct drive, shaft drive, levers, cables, and so on. However, chains have demonstrated the best combination of cost, weight, efficiency, strength, durability, gearing choices, and choice of rider position.

Chains have many good properties: they can be loaded heavily; operate with bad alignment; can demonstrate good efficiency despite having hundreds of wear surfaces which are lubricated poorly and continually bathed in abrasives; and can operate reliably despite chain and sprocket wear and even significant damage to the chain and sprockets.

Chains are simple in principle, but complex in actual operation. This note explains basics of chain operation, how the chain changes with wear, and several significant effects that come from seemingly-minor design decisions. For more detail, see a reference on industrial chains [1].

Chain Construction

Common bicycle chain is made of four or five distinct parts: outer plates, inner plates, pins, bushings, and rollers. The outer plates are pressed on to pins, forming a single unit. For a five-part (bushed) chain, the inner plates are pressed on to bushings. For four-part chains, each inner plates forms half the bushing. For both types, pins rotate inside bushings, allowing the chain to flex. Rollers are hoops which rotate around the bushings, allowing the chain to roll easily (with low friction) on and off the teeth of sprockets. The parts are assembled as shown in the following diagram.

The following diagram shows a typical 4-part chain.

Most derailleur bike chains made since about 1990 are made of four parts, with the side plates formed to provide the bushing surface. This design is a compromise and is discussed in more detail below.

The chain pitch is the distance between pins. The nominal pitch is the pitch when the chain is new. For all but a few vintage bicycles, the pitch is 1/2 inch — 0.500 inches. Bushings do not fit tightly around pins, so the pitch should be measured with the chain under light tension. The following diagram shows the pitch of a chain under light tension, including slack between the pins, bushings, and rollers.

As the chain wears, the pitch increases. For example, a derailleur chain is worn out when the pitch increases by 1%, giving an actual pitch of 0.505 inches.

Note that the actual pin-to-pin spacing is uneven on a worn chain. The outer plates hold the pins rigidly, so even as the chain wears, two pins in the same outer plate always have the same spacing. However, pin/bushing wear increases the distance between pairs of pins which are connected by bushings and inner plates. Thus, the pitch of these links is longer by the amount of wear at both ends of the inner plate that connects them.

Note also that roller/bushing wear does not affect pitch or the distance between rollers. So, for example, a new (unworn) chain with loose rollers runs the same as a new chain with close-fitting rollers.

Sprockets have teeth (cogs), and the chain has rollers which rest on the teeth. The sprocket also has a pitch, which is the distance between faces of the teeth. The teeth are arranged in a circle and the faces are sloped, so the tips are farther apart than the roots of the teeth. Thus, the nominal pitch is the distance between faces near the root, but the sprocket actually has a range of spacings from the root to the tip.

A bicycle uses a chain moving between a pair of sprockets. The front sprocket on a bike is often called a ``chainwheel''. The individual teeth on sprockets are called ``cogs'', though the term is sometimes confusingly applied to rear sprockets. For example, a 17-cog sprocket is sometimes called a ``17 cog''.

Basic Chain Operation

The operation of a chain is usually the same for both front and rear sprockets. The only important difference is that a front sprocket has taut side of the chain move on to the sprocket and the loose side move off; on the rear, the loose side moves on and the taut side moves off. In the following, ``sprocket'' is used to mean either front or rear. When there is a difference, ``front'' and ``rear'' will be added as needed.

The simplest view of chain drive operation is that the chain is hooked over the teeth of the front and rear sprockets; when you pedal, the front sprocket pulls the chain, and the chain pulls the rear sprocket.

In more detail, as you pedal, the chain is pulled off the last tooth of the rear sprocket, and the chain straightens. When the chain straightens, there is motion between the pin and bushing. The motion is called articulation. When the chain reaches the front sprocket, it is pulled on to the first tooth of the front sprocket, and it again articulates. The chain continues around the front sprocket to the slack side, where it repeats the process but this time under low tension.

As the chain articulates under load, there is rubbing between the pin and bushing. The rubbing is one source of drivetrain friction -- and friction means ``reduced drivetrain efficiency''. The rubbing is also one source of chain wear. Note that a chain link articulates under load twice per circuit: once when the chain is pulled off the rear sprocket, and again when it is pulled on to the front sprocket. Although the chain also articulates on the slack side, the small chain tension means friction and wear are small compared to those effects when the links are on the taut side.

The roller turns as the chain is pulled off the last tooth of the rear sprocket, and it turns again as the chain is pulled on to the front sprocket. The roller is under load as it turns, and there is rubbing between the roller and bushing and also some rubbing between the roller and the tooth. The rubbing is another source of friction, but bushing/roller wear does not affect chain pitch and sprocket wear is usually much slower than chain wear.

As an aside, some industrial chains use no rollers, but eliminating rollers increases friction and thus hurts efficiency and also wears the chain and sprockets faster.

The wear and friction from pivoting is increased by greater tension in the joint, by a larger angle of articulation, and by bending more links per second. Using this information, we can show a first principle of chain drives: larger sprockets and more chain is heavier, but also gives a longer service and better efficiency.

Consider, for example, riding a given hill either using a 26-tooth chainring and 13-tooth rear sprocket or using a 52-tooth chainring and 26-tooth rear sprocket. Both provide the same gear ratio. The 52-tooth chainring is twice the diameter of the 26-tooth chainring, so the chain is under half the tension for the same overall gear ratio. The 52-tooth chainring also articulates each link half as sharply, since twice as many links are used to wrap around the chainring. Note, however, that the 26-tooth chainring only pulls half as many links per second. Thus the larger chainring has two factors helping it and one factor hurting it. Thus, drivetrain efficiency for a given gear ratio increases with increasing sprocket size.

When a chain is under load -- pulling on a rear sprocket or being pulled by a front sprocket -- the chain is actually balanced on the sprocket teeth. The tooth face is at an angle to the chain tension, so the chain wants to roll up the face. In order to do so, it must pull along the next link of chain. The next link is also resting on a tooth, so it resists the pull of the first link. However, with the second link under tension, the second link also wants to roll up the face of its tooth. Thus, the second pulls on the third, which pulls on the fourth, and so on around the sprocket.

The amount of chain tension passed from link to link around a sprocket depends on both the steepness of the tooth face, and also on the angle from one link to the next. The tooth face steepness depends on design decisions by the maker. The angle from one link to the next depends on the number of teeth on the sprocket.

The ejecting force is the tendency of a link to roll up the face of a tooth. When the tooth face is fairly shallow, the ejecting force is high. Thus, the second link must exert a large force on the first link to keep the first link from rolling up and off its tooth. Since the second link is under a lot of tension, it passes a lot on to the third link, and so on. When the tooth face is fairly steep, there is little ejecting force on the first link, and so less is passed on to the second and subsequent links.

The angle between links also affects the amount of tension passed from link to link. If the sprocket is small, then each link pulls fairly directly against the ejecting force of the earlier link. However, if the sprocket is large, then even a small ejecting force requires the next link to be at high tension to have a component which can resist that force.

There are several effects from tension passed link to link. If a large tension is passed between links, then the load on any one sprocket tooth is less because a given load is shared among more sprocket teeth. Sharing improves sprocket durability by reducing the load/unload forces which can fatigue the teeth. Sharing also reduces the roller load, and in particular reduces the load where the roller is rolling on or off a tooth. That reduces both friction and wear for the sprocket, roller, and bushing.

Note, however, that while sharing reduces the bushing/roller load, sharing does not affect the pin/bushing load for inner links pulling on outer links, and sharing actually increases the pin/bushing load for outer links pulling on inner links.

[Diagram 11 -- pin/bushing loads under high/low sharing for both pin-pull-bushing and bushing-pull-pin.]

Tension is passed from link to link in percentages. For example, consider a configuration which passes 60% of the link tension to the tooth and 40% to the next link. The next link will then pass 60% of its load to its tooth and 40% to the following link, and so on. Thus, the chain tension after one tooth is 40%, after two teeth is 0.4 * 0.4 = 16%, after three teeth is 0.4 *0.4 * 0.4 = 6.4%, and so on.

The following table shows how load is distributed across sprocket teeth, depending on how the load is taken at each tooth. For example, if 90% of the load is taken by a tooth, then the 1st tooth takes 90% of the total chain tension and passes 10% to the 2nd tooth. The second takes 90% of that 10% load, or 9%, then passes 1% to the third tooth. The table columns show the fraction of total tension taken at each tooth; for example, 0.2 means each tooth takes 20% of the chain tension at that tooth. The table rows show the tooth number; for example, 3 is the third tooth. The final row shows the remaining tension in the chain; for example, 0.05 means that after going over 6 teeth the remaining chain tension is 5% of the tension in the tight upper run of chain, so 5% is passed on to the 7th tooth, or if the chain runs over only 6 teeth, the slack side tension is 5% of the tight side tension.

In practice, bicycle teeth tend to be fairly steep and thus share load among few teeth; the left side of the table above is given to lend intuition to the effect of tooth profile.

The chain on the ``slack'' side is under tension. The tension is small compared to the original load, and the just the weight of the chain may be enough to keep the chain from riding up the tooth faces. Nonetheless, the slack-side tension is still an issue: if the minimum slack-side tension is just 0.1% of the chain tension, then a chain under 500kgf tension requires the slack side still requires at least 0.5kgf (about 1 pound) of tension to hold the load.

Non-derailleur bikes use shallower tooth angles in order to share load better among sprockets and thus reduce the risk of broken teeth. When a chain starts to ``ride up'' on a sprocket, the slack side simply goes taut. Note the highest tooth load is always the first tooth to engage the tight side of the chain.

Derailleur bikes use steeper tooth angles, since the maximum slack-side tension is determined by the derailleur spring tension, and high slack-side chain tension hurts shifting and makes the derailleur heavier.

Non-derailleur drivetrains also engage close to 180 degrees of the sprocket, while derailleur drivetrains sometimes engage as little as 120 degrees. A smaller angle of wrap means the derailleur drivetrain has fewer teeth engaged, and correspondingly higher slack-side tension.

Note also that derailleur bikes also sometimes have rear sprockets as large as 38 teeth, sometimes as small as 9 teeth, and commonly have as few as 11 teeth. Non-derailleur bikes rarely have fewer than 10 teeth and usually between 16 and 22 teeth. The wide range of sprocket sizes might suggest a wide range of tooth shapes; or it might suggest the tooth shape is designed for the worst case and is a bad compromise for the common case. Note, however, that small sprockets have a steeper link angle and thus less secondary link tension is needed to resist a given ejecting force. Thus, a single tooth shape can do a good job across a range of sizes.

Do note, however, that smaller sprockets are still at a disadvantage for durability. First, the steeper link angle means the smaller sprockets concentrates more chain load on just one tooth at a time. That raises peak tooth forces and thus increases both wear and fatigue. There are also fewer teeth on a small sprocket, so there is less material to share the wear.

Chain Wear

Chain wear is of special interest to cyclists because chains can wear out faster than most other bike parts, and because a worn chain can quickly damage the sprockets, which may cost several times what a chain costs.

As the chain wears, the pitch increases and the chain rides higher on the sprocket teeth, at a larger pitch. However, since the tension around the sprocket is uneven, it does not ride at a fixed radius. For example, on the rear sprocket, the chain enters at some tension and travels down to the root of the tooth. As tension is applied, it then rolls up the tooth faces until it is pulled off.

Similarly, as the chain engages the front sprocket under tension, it starts high. As the chain is pulled around the front sprocket, it is under less and less tension, and it gradually rolls down the tooth face, then rises up again as it exits to the bottom run.

A new chain always engages the teeth near the bottom of the tooth. As it engages and disengages, there is relatively little motion and thus relatively little wear of the chain or the sprockets. As the chain wears, the amount of motion increases. Thus, a worn chain wears more quickly; it also wears out the sprockets more quickly. A worn chain also gives worse drivetrain efficiency.

As the chain moves up and down the teeth, it wears them. Each tooth wears the same, so the sprocket pitch does not change. However, the tooth face shape changes. Most wear occurs where the chain is highly loaded, which is in the last few engaged teeth, which is where the chain rides highest on the teeth. Wear gradually forms a pocket. Although all teeth wear equally, the unloaded portion of the tooth above the pocket does not wear. The tooth thus develops a ``hooked'' profile.

Note that the chain does not wear the very tip of the tooth. The position of the chain on the tooth depends on the chain tension -- the higher the tension, the higher the chain rides. Since the chain rarely operates with its highest tension, the chain rides below the tip of the tooth. However, the tip cannot be removed, or else high loads will cause the chain to roll off the tooth and skip.

The hooked profile causes problems when an unworn chain is used on a worn sprocket. An unworn chain has a shorter pitch and so the slack part of the chain runs closer to the tooth face than the slack part of a worn chain. When the chain load is increased, the tight part of the chain pulls the slack part around to be even closer to the tooth faces. On a rear sprocket, the slack part of the chain cannot clear the overhang of the hook, and the chain skips under load. On a front sprocket, the chain cannot disengage the sprocket and so gets pulled up in to the space between the chainring and the frame (``chain suck'').

Note that a shallow tooth face can wear more before skipping occurs with a new chain.

Chain Alignment

The discussion so far has focused on chains running in a straight line. Derailleur chains often run misaligned, with sprockets which are parallel but offset.

Misalignment has several effects. One is to wear the sides of the sprocket teeth where the inner plates slide on and off under load. Side loads are relatively small so wear is relatively slow, but over time the wear can make the sprocket teeth narrower so that the faces wear more quickly.

A misaligned chain concentrates the ``bend'' in one pin/bushing joint at a time. The misaligned joint thus concentrates the load over a very small area. Unfortunately, this is also the joint which is articulating under load. In such situations, wear can increase out of proportion to the area reduction. A four-part chain may have an advantage since the inner links can move separately, but the link on the ``inside'' of the bend has less distance to go and so will be slacker, reducing any advantage.

There are no published results on the efficiency of misaligned chains. Some simple but inaccurate experiments suggest drivetrain efficiency goes down sharply. The experimental results are inconclusive, but suggest a more accurate study would provide interesting results.

Note that some industrial applications use a ``curve'' chain in which the bushings have an ``hourglass'' shape to allow misalignment. I do not know if the pin has a matching shape, but if it does the pin is weaker; if it does not, the pin is subject to great pin shear (see below). At any rate, in industrial applications, running at an angle is enough of an issue it gets a special chain.

Some applications also use a ``step'' chain in which there is a large gap between the inner and outer plates, allowing the chain to be at an offset without bushing misalignment. A step chain has higher pin shear; the gap between inner and outer plates also makes the chain wider, and thus unsuitable for bike drivetrains.

Another effect of misalignment is it requires larger side-to-side gaps between the chain plates. It is unclear whether the large gaps help allow grit in to the chain to accelerate wear on the pins and bushings.

Bicycle Chain Design

Most one-speed and hub-geared bicycles use a five-part chain with 3mm spacing between the inner plates and a bushing width of about 5mm. Most derailleur-equipped bicycles use a narrower chain, with those made after 1990 often having 2mm or less between inner plates and a maximum bushing width of 4mm or less. The narrower chain is used to allow a stack of sprockets to fit in the narrowest possible width.

Running a chain between offset sprockets causes loads which tend to break side plates and push the side plates off the pins.

Since about 1990 it has also been common to shape the sprockets so the chain can move more easily from sprocket to sprocket, thus making it possible to shift under higher loads. Shifting under load places yet more loads on the chain.

In the 1950's, it became feasible to fit bicycles with front sprockets as small as 26 teeth using commercial equipoment. In the 1980's it became common to fit bicycles with front sprockets as small as 24 teeth, and in the 1990's it became common to fit bicycles with sprockets as small as 20 teeth. Though uncommon, some commercial setups allow chainrings as small as 16 teeth.

Peak chain forces are ultimately limited by traction, but smaller sprockets are often used to achieve a given gear ratio with smaller and lighter sprockets, but at the expense of higher chain tension. Smaller sprockets are thus often used in a way that gives riders greater leverage on the chain, further increased chain tension and misalignment/shifting forces, and thus further increased chain wear and failure rates.

A lower chain profile helps shifting under load, but reduces the amount of material which is taking the load. At the same time, chain widths have been decreasing, making it impractical to gain strength by using thicker side plates. [Diagram 22 -- side profile inner+outer; inner-only with bushing, reduced profile showing less material.]

Two design changes were introduced around 1990 to compensate for the increased chain loads and failure rates: special pins and four-part chains. The following text considers these in turn.

One change is a ``mushroom'' head on the ends of the pins. The pin is inserted and is then deformed to form a lip which provides extra holding force for the side plates.

Enlarging the pin ends improves the side load capacity, but also makes chain disassembly and reassembly more complex. Some chains thus use special links or pins. Reassembling a chain without the special parts weakens the chain against side loads. Some chains require a special tool to ``peen'' the pin and give it the mushroom shape. These tools may be more expensive and not portable enough to use for field service and repair.

A second change is a four-part chain, which uses a special inner plate that is formed to make both the side plate and the bushing. The side plate is thus stronger or may be made smaller without losing strength, since the same material is used as both a structural element and as a bushing.

Although a four-part chain side plate improves load capacity, it introduces new problems. First, the formed side plate is radiused. Radiused side plates increase pin bending loads. That, in turn, increases the outer plate bending failures and makes it easier for the outer plate to come off the pin.

The radiused side plate also decreases bushing area, and there is also a gap between the two side plates. These factors both reduce the total bushing area, which in turn increases wear rates and may increase friction.

The gap in the middle of the bushing also provides more paths and more total area for contaminants to enter and for lubricants to be washed out. The problem is further exagerated because the chain is laterally flexible for shifting; because lateral flexibility requires side-to-side clearances within the chain; and because the two side plates are not rigidly connected and so can move independently -- helping to pump contaminants in and lubricants out. Thus, while four-part chains retain lubricant in dry conditions, wet and muddy conditions can quickly clean the chain of lubricants.

A four-part chain also makes the side plate and the ``bushing'' out of a single piece of material. Thus, the material for the bushing/side plate is a compromise between the best bushing material and the best side plate material.

For these reasons, four-part chains typically give about half the service life of five-part chains of similar dimensions. It is likely that drivetrain efficiency is also reduced, but efficiency data, if there is any, is not publicly available.

Chain Lubrication

There are industrial chains of similar construction and loading to bike chains. When they are run in a clean oil bath, they can have service lives that corresponds to hundreds of thousands of kilometres of cycling. In contrast, five-part derailleur chains rarely give more than 20,000 kilometres of service; four-part derailleur chains rarely give more than about 10,000 kilometres of service. In dirty use, chains can wear in less than 1,000 kilometres.

Chain wear is caused by grit and poor lubrication. For bicycles, grit is often the most severe problem, as grit can pierce protective lubricant films.

Grit is a problem because the bike chain is continually dirtied by grit, dust, and mud. Even in dry conditions, the chain is exposed to a stream of dirt thrown up by the front tire. In wet conditions a greater stream is kicked up and it provides a liquid to carry the grit in to the chain and also wash out lubricant.

Road dirt can be very abrasive: consider that silicon carbide and silicon dioxide are the primary ingredients in both common sand and grinding compound, and that the other major ingredient in grinding compound is oil.

Dirt sticks easily to a heavily-oiled chain. Flexing the chain then carries the dirt in to the bushings. The hard particles break through the lubricant that separates the pin from the bushing, gouging out metal and causing wear. The wear particles are also abrasive, causing more wear.

A lightly-oiled chain also attracts grit, but the light lubrication does not act as a wick to move the grit in to the bearing surfaces.

Lubricating a chain with dirt on the surface will carry the dirt in to the load bearing surfaces. Thus, for best drivetrain life and efficiency, the chain should be cleaned before it is lubricated, and the surface should be cleaned again after lubrication to remove surface oil which can attract and hold dirt.

Thorough cleaning is done with the chain off the bike, as the chain must be immersed in solvent and then flexed in order to float out the wear particles. ``On-bike'' chain cleaning tools lack sufficient solvent volume and soaking time to dissolve and float out the inner dirt.

Since dirt is the primary cause of chain wear, most lubricants do a good job, except those which attract and wick in grit at a high rate.

Some poor lubricants give surpisingly good service life. For example, solid lubricants such as wax do not move under surface tension. Thus, once load has pushed the wax out from the bushing surface, it does not flow back in, and the chain runs unlubricated. In compensation, however, dry lubricants typically do not attract dirt. Thus, a waxed chain fails due to poor lubrication, but in compensation, wear is not further aggrevated by dirt. Chain life with wax is typically worse than with oil, but is surpisingly good considering that wax is a poor lubricant, and in dry (not rainy/muddy) service, some riders report better chain life using wax than using liquid lubricants.

Some lubricants are wax in a solvent suspension. The goal is that the wax does not attract dirt, and the solvent suspension allows frequent reapplication with the chain still on the bicycle (without removing the chain and washing it). These lubricants tend to be expensive to use compared to ordinary oil or conventional waxing, because the lubricant cost is high compared to oil or wax, and because they must be reapplied frequently. However, the drivetrain tends to remain relatively clean, which is an advantage where an oiled chain otherwise gets clothes and other items dirty, and in dry conditions users often report good chain life, albeit with the inconvenience of frequent lubricant reapplication.

Some lubricants are washed off easily by water, and most lubricants are washed off easily by mud. Water serves as a good lubricant while the chain is wet, and even mud can be a slight lubricant. However, upon drying the chain may have no remaining lubrication, and the chain will typically be dirty inside as well.

TODO

The Regina CX-S had asymmetric side plates. The inner plates had a vertical ``recess'' so the chain did not have to rise as far in order to clear the sprocket teeth. The asymmetric side plates faced the center with the recess towards the axle.

[Picture? Diagram?]

References

[1] ``Chains for Power Transmission and Material Handling'' by the American Chain Association, published by Marcel Dekker, Incorporated, Copyright 1982.