The car Transmission Bible - how transmissions and gearbox work including manuals, automatics, clutch, CVT, crash gearboxes, differentials, limited-slip differentials, 2wd, 4wd, awd and much more.

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Transmission, or gearbox?

That question depends on which side of the Atlantic you're on. To the Europeans, it's a gearbox. To the Americans, it's a transmission. Although to be truthful, the transmission is the entire assembly that sits behind the flywheel and clutch - the gearbox is really a subset of the transmission if you want to split hairs.
Either way, this page aims to deal with the whole idea of getting the power from your engine to the ground in order to move your car (or bike) forwards.

Manual gearboxes - what, why and how?

From the Fuel & Engine Bible you know that the pistons drive the main crank in your engine so that it spins. Idling, it spins around 900rpm. At speed it can be anything up to 7,500rpm. You can't simply connect a set of wheels to the end of the crank because the speed is too high and too variable, and you'd need to stall the engine every time you wanted to stand still. Instead you need to reduce the revolutions of the crank down to a usable value. This is known as gearing down - the mechanical process of using interlocking gears to reduce the number of revolutions of something that is spinning.

A quick primer on how gears work

In this case I'm talking about gears meaning 'toothed wheel' as oppose to gears as in 'my car has 5 gears'. A gear (or cog, or sprocket) in its most basic form is a flat circular object that has teeth cut into the edge of it. The most basic type of gear is called a spur gear, and it has straight-cut teeth, where the angle of the teeth is parallel to the axis of the gear. Wider gears and those that are cut for smoother meshing are often cut with the teeth at an angle, and these are called helical gears. Because of the angle of cut, helical gear teeth have a much more gradual engagement with each other, and as such they operate a lot more smoothly and quietly than spur gears. Gearboxes for cars and motorbikes almost always use helical gears because of this. A side effect of helical gears is that if the teeth are cut at the correct angle - 45 degrees - a pair of gears can be meshed together perpendicular to each other. This is a useful method of changing the direction of movement or thrust in a mechanical system. Another method would be to use bevel gears.

Spur gears

Helical gears

The number of teeth cut into the edge of a gear determines its scalar relative to other gears in a mechanical system. For example, if you mesh together a 20-tooth gear and a 10-tooth gear, then drive the 20-tooth gear for one rotation, it will cause the 10-tooth gear to turn twice. In this case, the larger gear is the input gear. Each tooth on the input gear meshes with one tooth on the output gear. There are 20 teeth on the input gear and only 10 on the output gear. It follows then that for one rotation of the input gear, the output gear will turn twice. This creates a gear ratio of 20 teeth to 10 - 20:10 or 2:1. This is known as gearing up.
Gearing down is exactly the same only the input gear is now the one with the least number of teeth. The output gear is the larger one and now, for every turn of the input gear, the output gear turns half a revolution. In this case it becomes a gear ratio of 10:20, or 1:2.
By meshing many gears together of different sizes, you can create a mechanical system to gear up or gear down the number of rotations very quickly. As a final example, imagine an input gear with 20 teeth, a secondary gear with 40 teeth and a final gear with 50 teeth. From the input gear to the secondary gear, the ratio is 1:2 - half. From the second gear to the final gear, the ratio is 4:5 - four fifths. The total gear ratio for this system is (1/2) * (4/5) which works out to be 1/2.5, or 0.4. ie. for one turn of the input gear, the output gear turns 0.4 times.
Collections of helical gears in a gearbox are what give the gearing down of the speed of the engine crank to the final speed of the output shaft from the gearbox. The table below shows some example gear ratios for a 5-speed manual gearbox (in this case a Subaru Impreza).

Gear	Ratio	RPM of gearbox output shaft when the engine is at 3000rpm
1st	3.166:1	947
2nd	1.882:1	1594
3rd	1.296:1	2314
4th	0.972:1	3086
5th	0.738:1	4065

Final drive - calculating speed from gearbox ratios. It's important to note that in almost all vehicles there is also a final reduction gear. This is also called a final drive or a rear- or front-axle gear reduction and it's done in the differential with a small pinion gear and a large ring gear (see the section on differentials lower down the page). In the Subaru example above, it is 4.444:1. This is the final reduction from the output shaft of the gearbox to the driveshafts coming out of the differential to the wheels. So using the example above, in 5th gear, at 3000rpm, the gearbox output shaft spins at 4065rpm. This goes through a 4.444:1 reduction in the differential to give a wheel driveshaft rotation of 914rpm. For a Subaru, assume a wheel and tyre combo of 205/55R16 giving a circumference of 1.985m or 6.512ft (see The Wheel & Tyre Bible). Each minute, the wheel spins 914 times meaning it moves the car (914 x 6.512ft) = 5951ft along the ground, or 1.127 miles. In an hour, that's (60minutes x 1.127miles) = 67.62. In other words, knowing the gearbox ratios and tyre sizes, you can figure out that at 3000rpm, this car will be doing 67mph in 5th gear.

Making those gears work together to make a gearbox

If you look at the image below you'll see a the internals of a generic gearbox. You can see the helical gears meshing with each other. The lower shaft in this image is called the layshaft - it's the one connected to the clutch - the one driven directly by the engine. The output shaft is the upper shaft in this image. To the uneducated eye, this looks like a mechanical nightmare. Once you get done with this section, you'll be able to look at this image and say with some authority, "Ah yes, that's a 5-speed gearbox".

So how can you tell? Well look at the output shaft. You can see 5 helical gears and 3 sets of selector forks. At the most basic level, that tells you this is a 5-speed box (note that my example has no reverse gear) But how does it work? It's actually a lot simpler than most people think although after reading the following explanation you might be in need of a brain massage.
With the clutch engaged (see the section on clutches below), the layshaft is always turning. All the helical gears on the layshaft are permanently attached to it so they all turn at the same rate. They mesh with a series of gears on the output shaft that are mounted on sliprings so they actually spin around the output shaft without turning it. Look closely at the selector forks; you'll see they are slipped around a series of collars with teeth on the inside. Those are the dog gears and the teeth are the dog teeth. The dog gears are mounted to the output shaft on a splined section which allows them to slide back and forth. When you move the gear stick, a series of mechanical pushrod connections move the various selector forks, sliding the dog gears back and forth. In the image below, I've rendered a close-up of the area between third and fourth gear.

When the gearstick is moved to select fourth gear, the selector fork slides backwards. This slides the dog gear backwards on the splined shaft and the dog teeth engage with the teeth on the front of the helical fourth gear. This locks it to the dog gear which itself is locked to the output shaft with the splines. When the clutch is let out and the engine drives the layhshaft, all the gears turn as before but now the second helical gear is locked to the output shaft and voila - fourth gear.

Grinding gears. In the above example, to engage fourth gear, the dog gear is disengaged from the third helical gear and slides backwards to engage with the fourth helical gear. This is why you need a clutch and it's also the cause of the grinding noise from a gearbox when someone is cocking up their gearchange. The common misconception is that this grinding noise is the teeth of the gears grinding together. It isn't. Rather it's the sound of the teeth on the dog gears skipping across the dog teeth of the helical output gears and not managing to engage properly. This typically happens when the clutch is let out too soon and the gearbox is attempting to engage at the same time as it's trying to drive. Doesn't work. In older cars, it's the reason you needed to do something called double-clutching.
Double-clutching, or double-de-clutching (I've heard it called both) was a process that needed to happen on older gearboxes to avoid grinding the gears. First, you'd press the clutch to take the pressure off the dog teeth and allow the gear selector forks and dog gears to slide into neutral, away from the engaged helical gear. With the clutch pedal released, you'd 'blip' the engine to bring the revs up to the speed needed to engage the next gear, clutch-in and move the gear stick to slide the selector forks and dog gear to engage with the next helical gear.
The synchromesh - why you don't need to double-clutch. Synchros, synchro gears and synchromeshes - they're all basically the same thing. A synchro is a device that allows the dog gear to come to a speed matching the helical gear before the dog teeth attempt to engage. In this way, you don't need to 'blip' the throttle and double-clutch to change gears because the synchro does the job of matching the speeds of the various gearbox components for you. To the right is a colour-coded cutaway part of my example gearbox. The green cone-shaped area is the syncho collar. It's attached to the red dog gear and slides with it. As it approaches the helical gear, it makes friction contact with the conical hole. The more contact it makes, the more the speed of the output shaft and free-spinning helical gear are equalised before the teeth engage. If the car is moving, the output shaft is always turning (because ultimately it is connected to the wheels). The layshaft is usually connected to the engine, but it is free-spinning once the clutch has been operated. Because the gears are meshed all the time, the synchro brings the layshaft to the right speed for the dog gear to mesh. This means that the layshaft is now spinning at a different speed to the engine, but that's OK because the clutch gently equalises the speed of the engine and the layshaft, either bringing the engine to the same speed as the layshaft or vice versa depending on engine torque and vehicle speed.

So to sum up that very long-winded description, I've rendered up an animation - when you see parts of a gearbox moving in an animation, it'll make more sense to you. What we have here is a single gear being engaged. The layshaft the blue shaft with the smaller helical gear attached to it. To start with, the larger helical gear is free-spinning on its slip ring around the red output shaft - which is turning at a different speed because it's connected to the wheels. As the gear stick is moved, the gold selector collar begins to slide the dog gear along the splines on the output shaft. As the synchromesh begins to engage with the large helical gear, the helical gear starts to spin up to speed to match the output shaft. Because it is meshed with the gear on the layshaft, it in turn starts to bring the layshaft up to speed too. Once the speed of everything is matched, the dog gear locks in place with the output helical gear and the clutch can be engaged to connect the engine to the wheels again.

What about reverse?

Reverse gear is normally an extension of everything you've learned above but with one extra gear involved. Typically, there will be three gears that mesh together at one point in the gearbox instead of the customary two. There will be a gear each on the layshaft and output shaft, but there will be a small gear in between them called the idler gear. The inclusion of this extra mini gear causes the last helical gear on the output shaft to spin in the opposite direction to all the others. The principle of engaging reverse is the same as for any other gear - a dog gear is slid into place with a selector fork. Because the reverse gear is spinning in the opposite direction, when you let the clutch out, the gearbox output shaft spins the other way - in reverse. Simple. The image on the left here shows the same gearbox as above modified to have a reverse gear.

Crash gearboxes or dog boxes.

Having gone through all of that business about synchromeshes, it's worth mentioning what goes on in racing gearboxes. These are also known as crash boxes, or dog boxes, and use straight-cut gears instead of helical gears. Straight-cut gears have less surface area where the gears contact each other, which means less friction, which means less loss of power. That's why people who make racing boxes like to use them.
Normally, straight-cut gears are mostly submerged in oil rather than relying on it sloshing around like it does in a normal gearbox. So the extra noise that is generated is reduced to a (pleasing?) whine by the sound-deadening effects of the oil.
But what is a dog box? Well - motorbikes have been using them since the dawn of time. Beefing the system up for cars was the brainchild of a racing mechanic who wanted to provide teams with a quick method of altering gear ratios in the pits without having to play "chase the syncro hub ball bearings" as they fell out on to the garage floor.
Normal synchro gearboxes run at full engine speed as the clutch directly connects the input shaft to the engine crank. Dog boxes run at a half to a third the speed of the engine because there is a step-down gear before the gearbox. The dog gears in a dog box also have less teeth on them than those in a synchro box and the teeth are spaced further apart. So rather than having an exact dog-tooth to dog-hole match, the dog teeth can have as much as 60° "free space" between them. This means that instead of needing an exact 1-to-1 match to get them to engage, you have up to 1/6th of a rotation to get the dog teeth pressed together before they touch each other and engage. The picture on the right shows the difference between synchro dog gears and crash box dog gears.
So the combination of less, but larger dog teeth spaced further apart, and a slower spinning gearbox, allegedly make for an easier-to-engage crash box. In reality, it's still quite difficult to engage a crash box because you need exactly the right rpm for each gear or you'll just end up grinding the dog teeth together or having them bounce over each other. That results in metal filings in your transmission fluid, which ultimately results in an expensive and untimely gearbox rebuild.
But it is more mechanically reliable - it's stronger and able to deal with a lot more power and torque which is why it's used in racing.
So in essence, a dog box relies entirely on the driver to get the gearchange right. Well - sort of. Nowadays the gearboxes have ignition interrupters connected to them. As you go to change gear, the ignition system in the engine is cut for a fraction of a second as you come to the point where the dog teeth are about to engage. This momentarily removes all the drive input from the gearbox making it a hell of a lot easier to engage the gears. And when I say 'momentary' I mean milliseconds. Because of this, it is entirely possible to upshift and downshift without using the clutch (except from a standstill). Pull the gear out of first, and as you blip the throttle to get the engine to about the right speed, the ignition is cut just as the gears engage.
Even the blip of the throttle isn't necessary now either - advanced dog boxes can also attempt to modify the engine speed by adjusting the throttle input to get the revs to the right range first.
Of course even with all this cleverness, you still get nasty mechanical wear from cocked up gear changes, but in racing that doesn't matter - the gearbox is stripped down and rebuilt after each race.

Before the gearbox - the clutch

So now you have a basic idea of how gearing works there's a second item in your transmission that you need to understand - the clutch. The clutch is what enables you to change gears, and sit at traffic lights without stopping the engine. You need a clutch because your engine is running all the time which means the crank is spinning all the time. You need someway to disconnect this constantly-spinning crank from the gearbox, both to allow you to stand still as well as to allow you to change gears. The clutch is composed of three basic elements; the flywheel, the pressure plate and the clutch plate(s). The flywheel is attached to the end of the main crank and the clutch plates are attached to the gearbox layshaft using a spline. You'll need to look at my diagrams to understand the next bit because there are some other items involved in the basic operation of a clutch. (I've rendered the clutch cover in cutaway in the first image so you can the inner components.) So here we go.

In the diagram above, the clutch cover is bolted to the flywheel so it turns with the flywheel. The diaphragm springs are connected to the inside of the clutch cover with a bolt/pivot arrangement that allows them to pivot about the attachment bolt. The ends of the diaphragm springs are hooked under the lip of the pressure plate. So as the engine turns, the flywheel, clutch cover, diaphragm springs and pressure plate are all spinning together.
The clutch pedal is connected either mechanically or hydraulically to a fork mechanism which loops around the throw-out bearing. When you press on the clutch, the fork pushes on the throw-out bearing and it slides along the layshaft putting pressure on the innermost edges of the diaphragm springs. These in turn pivot on their pivot points against the inside of the clutch cover, pulling the pressure plate away from the back of the clutch plates. This release of pressure allows the clutch plates to disengage from the flywheel. The flywheel keeps spinning on the end of the engine crank but it no longer drives the gearbox because the clutch plates aren't pressed up against it.
As you start to release the clutch pedal, pressure is released on the throw-out bearing and the diaphragm springs begin to push the pressure plate back against the back of the clutch plates, in turn pushing them against the flywheel again. Springs inside the clutch plate absorb the initial shock of the clutch touching the flywheel and as you take your foot off the clutch pedal completely, the clutch is firmly pressed against it. The friction material on the clutch plate is what grips the back of the flywheel and causes the input shaft of the gearbox to spin at the same speed.
Burning your clutch
You might have heard people using the term 'burning your clutch'. This is when you hold the clutch pedal in a position such that the clutch plate is not totally engaged against the back of the flywheel. At this point, the flywheel is spinning and brushing past the friction material which heats it up in much the same was as brake pads heat up when pressed against a spinning brake rotor (see the Brake Bible). Do this for long enough and you'll smell it because you're burning off the friction material. This can also happen unintentionally if you rest your foot on the clutch pedal in the course of normal driving. That slight pressure can be just enough to release the diaphragm spring enough for the clutch to occasionally lose grip and burn.
A slipping clutch
The other term you might have heard is a 'slipping clutch'. This is a clutch that has a mechanical problem. Either the diaphragm spring has weakened and can't apply enough pressure, or more likely the friction material is wearing down on the clutch plates. In either case, the clutch is not properly engaging against the flywheel and under heavy load, like accelerating in a high gear or up a hill, the clutch will disengage slightly and spin at a different rate to the flywheel. You'll feel this as a loss of power, or you'll see it as the revs in the engine go up but you don't accelerate. Do this for long enough and you'll end up with the above - a burned out clutch.

Motorcycle 'basket' clutches

It's worth spending a moment here to talk about basket clutches as found on some Yamaha motorbikes. Even though the basic principle is the same (sandwiching friction-bearing clutch plates against a flywheel), the design is totally different. If nothing else, a quick description of basket clutches will show you that there's more than one way to decouple the a spinning crank from a gearbox.
Basket clutches need to be compact to fit in a motorbike frame so they can't have a lot of depth to them. They also need to be readily accessible for mechanics to be able to service them with the minimum amount of fuss, something that's near impossible with regular car clutches. A basket clutch has a splined clutch boss bolted to the shaft coming from the engine crank with strong springs. Metal pressure plates slide on to this shaft, in alternating sequence with friction material clutch plates. The clutch plates are splined around the outside edge, where they fit into slots in an outer basket - the clutch housing. The clutch housing is bolted on to the layshaft which runs back through the middle of the whole mechanism and into gearbox. Clever, but as usual, not much use without a picture, so here you go.

In operation, a basket clutch is simplicity itself. A throw-out bearing slides around the outside of the layshaft and when you pull the clutch lever, the throw-out bearing pushes against the clutch boss. The clutch boss compresses the clutch springs and removes pressure from the whole assembly. The friction plates now spin freely in between the pressure plates. When you let the clutch out, the springs push the clutch boss in again and it re-asserts the pressure on the system, crushing the friction and pressure plates together so they grip. And there you have a second type of clutch.
You should now feel proud that with all your newfound (and somewhat geeky) understanding of clutches, you can go about your business safe in the knowledge that you sort of understand how all this spinning, geared-and-splined witchcraft works.

Sequential gearboxes - what, why and how?

If you've ever watched motorsports you'll have noticed that the drivers don't have an "H" gate for their gearstick. They either jam the stick back and forth or use paddle-shifters behind the steering wheel. The paddle-shifters do the same job as the gearstick movement in this case, only using electronics to move the shifter. So what's going on in a sequential gearbox? Actually it's quite simple. A sequential gearbox is just like a manual gearbox but the selector system is different. The manual gearbox example at the top of the page showed a series of selector forks which were moved by the physical position of the gearstick. In a sequential box, those selector forks are connected to a single shaft that has corkscrew-type grooves in it. The collar that fits around this selection shaft has a ballbearing in it which sits in a recess in the collar as well as in one of the corkscrew grooves. When the gearstick is moved forwards or backwards, the selector shaft is mechanically turned by some number of degrees. That twisting motion rotates the corkscrew groove which in turn interacts with the ballbearings and the selector fork collars, forcing them to slide back and forth. Each click of the gearstick rotates the shaft another number of degrees and all the selector forks change position in one go.

That's why it's called a sequential gearbox - the gears are always selected in sequence. You can't jump from first to third, you have to go via second. Often, sequential gearboxes have a "double-click for neutral" option and when you do this, it disengages the clutch and rotates the selector shaft back around to the neutral position, just before first gear. So why design and use a sequential gearbox? Well for a start it's a simpler design than a fully-manual gearbox with less moving parts. For racing drivers it makes for much quicker gearchanges - bang the gearstick and you're up a gear nearly instantly.
If you want to see how the corkscrew groove interacts with the selector collars this animation is worth watching.
Trivia note : TipTronic type gearboxes are not sequential. See the section below for an explanation of why.

One final point on sequential boxes - if you've ridden a geared motorbike in the last 50 years or so, you've used a sequential gearbox. Most bikes are 1-down, 5-up with neutral in between first and second gear. That little gear selector pedal that you click up and down with your left foot is simply linked to a ratchet system that ratchets the selector shaft around to pick the relevant gear.

Automatic gearboxes - what, why and how?

If you're reading this in America, there's a fair chance that everything above this point in the page was totally useless to you because you don't "drive stick", you drive an automatic. Automatic gearboxes are a totally different beast. For a start they don't have a clutch pedal. For that matter they don't have a clutch at all; they have a torque converter, but we'll get on to that later.
If you took an automatic gearbox apart (and for the love of all that is Holy, please don't), you'd see an enormous collection of mechanical parts all jammed into an impossibly small space. Taking centre stage would be the planetary gearset. Not to be confused with planetary drive, a hyperspace system we've only seen on the Sci Fi channel, the planetary gearset is nowhere near as exciting. In a manual gearbox, the dog gears lock and unlock different sets of helical gears to the output shaft in order to give the various gear ratios. In an automatic gearbox, the planetary gearset produces all the different gear ratios in one go and with only one set of gears. Ok so maybe it is pretty cool, but know this - an automatic gearbox is several orders of magnitude more complicated than a manual gearbox. Read on and you'll begin to understand why getting an automatic gearbox overhauled costs so damned much.

A quick primer on how planetary gearsets work

Any planetary gearset has three main components. The sun gear, the planet gears (and their carrier) and the ring gear. Any one of these three components can be locked in place, but more importantly, any one can be the input or the output drive. Locking any two of them at the same time will always produce a 1:1 gear ratio. So how the hell does that work? One set of gears for every ratio you need? The work of the Devil? Time to get the old brain massager out again. For this example I'll talk about a planetary gearset with a ring gear that has 75 teeth and a sun gear that has 25 teeth. The following table shows how sending the input to one set of gear and locking another set can give a wide variety of gear ratios.

Input	Ouput	Locked gears	Calculation	Resulting ratio
Sun	Planet Carrier	Ring	1+(Ring/Sun)	4:1
Planet Carrier	Ring	Sun	1/(1+(Sun/Ring))	0.75:1
Sun	Ring	Planet Carrier	-Ring/Sun	-3:1 (ie. reverse)

So that table basically has one reverse and two forward gears. Need more gears? Add more planetary gearsets with different numbers of teeth and link them together. Make the ouptut of one become the input of another and you can start to multiply up the number of gears available to you. The image below shows an example planetary gearset with the planet carrier in cutaway.

Again, something like this works much better in motion. Below I've rendered an animation showing a planetary gearset in motion. In this example, the blue ring gear is locked. The input is the yellow sun gear and the output is the planet carrier. The planetary gears are the green ones, and the planet carrier is semi-transparent so you can see what's going on inside. This shows clearly how the input to the sun gear can be geared down - in this case by a ratio of 2.7:1.

Compound planetary gearsets In reality, automatic gearboxes typically use one or more compound planetary gearsets instead of chaining regular gearsets together. They look just like a regular planetary gearset from the outside, but inside there are two sun gears and two sets of intermeshing planet gears. There is still only one ring gear though. With a single compound gearset, the number of ratios available increases to 4 forward ratios and one reverse. The image below shows an example compound planetary gearset again with the planet carrier in cutaway. In my example, the planet gears are arranged as inner and outer planets. The inner ones are shorter and only engage the small sun gear and the outer planet gears. They in turn engage the larger sun gear at the bottom and the outermost ring gear. Another configuration would be to have the two sets of planet gears next to each other but slightly staggered so that only one set meshes with the ring gear. Would you believe there are people paid to come up with this stuff? Makes you wonder if you shouldn't just accept that an automatic gearbox simply works and that you don't want to know why.

I could now go on to explain to you how all the different ratios get selected but if I did, I'd lose most readers at this point and all the typing and fine imagery in the rest of the page would go to waste. For the sake of a working example, I will explain the first two gears though.
Looking at the image below, When first gear is engaged, the smaller sun gear (green) is driven from the torque converter. The planet carrier (red) tries to spin the opposite direction but because of a one-way clutch system, it locks in place which forces the ring gear (blue) to turn instead. The ring gear becomes the output from the gearbox in this case and there you have first gear. The catch is that because of the design of the compound gearset, the direction of rotation of the output shaft ought to be opposite to that of the input shaft, but it isn't. This is because the first set of planet gears engages the second set and it's the second set that turns the ring gear. Doing this reverses the direction of rotation, thus making it now the same as the input shaft.
Moving swiftly along, when second gear is engaged the input is again the small sun gear but this time the ring gear is held in place by a band and the output becomes the planet carrier.

Locking planetary gearset components

If you've got this far, congratulations, you're doing better than I did the first time I had automatics explained to me. You might now be wondering how the clutches and bands I've mentioned above actually work. Bands are literally that - they're a band wrapped around the outside of the ring gear and when tightened, they lock the ring gear in place. Bands are actuated by a lever or pivot connected to a small hydraulic piston in the gearbox housing. The image below shows how a band might work in the example I've been building up. The actuator piston actually sits in a small cylinder inside the hydraulic distributor (see later) which is built into the gearbox case. You can see the band wraps around the ring gear and when the piston is pushed down, it tightens the band and clamps the ring gear into place, locking it to the gearbox case.

The clutches are a little more complex and are used to perform functions such as locking the sun gears to the turbine or input shaft. Automatic transmission clutches are a lot like the motorbike basket clutches mentioned higher up the page. They consist of a series of pressure and friction plates with splines on the inside and outside. These are compressed by hydraulic fluid fed through channels in the various shafts to a clutch piston. Clutch springs make sure the clutch piston releases when hydraulic pressure is reduced. The example below shows how a clutch system might work to lock the ring gear to the output shaft.

The automatic gearbox hydraulic system - how it changes gears.

You've got the idea by now that hydraulics are used a lot in an automatic gearbox. They're used to pressurise the piston plate for the clutches and they're used to move the band-activation pistons up and down. In the good old days, the routing of the hydraulic fluid in the system was controlled by mechanical shift valves linked to the throttle valve on one side and the governor (see later) on the other. Those days are on the way out now and generally speaking, when you move the gear stick, you're doing nothing more than giving an input to the engine management system or engine control unit (ECU) indicating what gear you'd like to be in. The ECU then looks at engine speed, speed across the ground, current gearbox configuration and position of the gear selector and decides what the best action is. It signals solenoid shift valves inside the hydraulic system to open and close appropriately and the gearbox then changes gears as necessary.
But how does the gearbox know to go up gears when you're speeding up, and down when you're slowing down? Well there's a device called the governor attached to the output shaft of the gearbox. It's a centrifugal sensor connected into the hydraulic circuit. The faster you're going, the faster the governer spins and the more open the valve in it becomes. That in turn allows the pressure of the hydraulic circuit to rise, which then applies more pressure to different components, pistons and clutch activators and lets the gearbox shift up at the right speeds. Again, in modern cars, all this information is fed through the ECU which also takes another input from a throttle sensor or more usually a vacuum modulator. These devices allow the ECU to know how hard the engine is working - something else that's critical to how the gearbox operates. It's these inputs that can sense the sudden need for more power so that when you stuff the accelerator to the floor, the gearbox can downshift. The ECU sees a relatively sedate output shaft speed from the governor but a sudden and dramatic increase in vacuum pressure in the engine intake manifold. This is the key to dump the gearbox down a gear to get more power and quick.
Limiting gear selection. Most gearbox selectors have a '1' and '2' position. When you select one of these positions you're inhibitting the gearbox's ability to pick any gear higher than that. In a mechanical system it locks off certain portions of the hydraulic system physically so the gearbox simply cannot provide hydraulic pressure to the selector components. In a modern electronic gearbox, again you're simply telling the ECU "don't select anything higher than this". The ECU will then simply not ever send commands to open the solenoid valves to activate higher gears.
The pump. It's probably no surprise to you that all this hydraulic trickery needs some sort of pressure to work and that comes from the hydraulic pump. This is normally located in the cover of the gearbox housing itself and it draws fluid from the gearbox sump to feed the gearbox hydraulic system, the fluid cooler (basically a small radiator) and the torque converter. The pump itself is a typically a rotary displacement pump that uses the difference in pressure between the spinning centre lobe and the outer housing to suck fluid in on one side and expel it on the other.
For the uninitiated or the morbidly curious, the image below shows a highly simplified example of the rats nest of hydraulic routes in a gearbox housing. The hydraulic lines are effectively cast in the metal because doing it with rubber hoses and clamps would be so complicated and take up so much space that it would be uneconomical and unreliable to do in mass production.

Park it!

So after the long and complicated slog through all that stuff above, are you ready for something simple? Ok, here we go. "P" - the park position on an automatic gear selector. If you've ever engaged park right before you've actually stopped, you'll have heard a clicking sound followed by a thud as the gearbox locks and the car rocks forwards. The mechanism that does this is so disturbingly simple it's almost not worth rendering a picture for. Ready? How about notches on the outside of the clutch housing and a single or pair of spring-loaded catches? Seriously. The image below shows the basic idea behind the park mechanism in an automatic. When you put the gearbox in 'P' for park, the catches are deployed and they fit into the notches on the outside of the clutch housing. Simple.

Torque Converters

Just like a manual gearbox, an automatic gearbox needs a method of decoupling the constantly-spinning engine from the gearbox components. To do this it uses a torque converter which is a viscous fluid coupling (because it's full of hydraulic fluid). A torque converter consists of three basic elements. The impeller, the turbine and the stator. The impeller is attached to the torque converter housing which itself is attached to the engine flywheel. The impeller is basically a centrifugal pump. As the flywheel spins, so does the impeller and the vanes take the fluid from the central part of the torque converter and fling it to the outside creating a pumping action. The fluid then circulates around the outer edge of the torque converter and back into the turbine. The turbine is basically the opposite of the impeller - it's like a ships's propeller in that the fluid passing through it causes it to spin. The turbine is connected to the input shaft of the gearbox via a splined shaft so as the turbine spins, so does the input shaft to the gearbox. The fluid passes through the turbine from the outside towards the inside. Finally, as the fluid reaches the central core, it passes through the stator which is designed to help redirect the flow into the inner vanes of the impeller. (Without the stator, the whole system would be a lot less efficient) With this mechanism, the fluid is constantly being circulated. In the image below I've rendered the various parts of an example torque converter taken apart so you can see the internal construction.

When the engine is idling, the fluid is pumping around without a lot of force and the amount of torque on the turbine is minimal. As you accelerate, the impeller speeds up and creates larger forces on the turbine which in turn spins more quickly and with more torque. Because it's connected to the input shaft of the gearbox, this feeds more rotational speed and torque into the gearbox and the car starts to move forwards. It's because of this viscous liquid coupling that automatic gearboxes have a certain amount of 'slop' in them - the engine can rev up and down without the car actually changing speed too much. It's also the reason automatics are less fuel efficient because the torque converter uses up energy from the engine simply in its design by spinning the hydraulic fluid. In the image below I've rendered a cutaway of an assembled torque converter. The shaky yellow arrow is my attempt to show the basic circulation path of the fluid inside as it is pumped from the impeller (red) through the turbine (blue) and back through the stator (green).

For sportier vehicles or those with specialised needs, some torque converters include a hydraulic clutch. Once the car is moving and in top gear, the clutch engages and locks the turbine to the impeller. Once that happens, the whole torque converter spins as one and the viscous coupling becomes redundant - effectively the gearbox now behaves like a manual because the engine flywheel is connected directly to the gearbox input shaft. By locking all the components together, it makes the car as fuel efficient as a manual when in top gear because the energy that was being used up in the viscous coupling is no longer required. It also means instantaneous throttle response - you push the accelerator and the car accelerates instantly just as with a manual.

But why is it called a torque converter? Very simply, because it has the ability to multiply the torque from the engine 2 or 3 times in certain conditions. Basically, from a standing start, when the engine is spinning far faster than the gearbox, the whole design allows the torque from the flywheel to be multiplied. As the car gets up to speed, the multiplication factor drops until it becomes 1x once everything is in motion and the impeller and turbine are moving at almost the same speed.

Doing it yourself. In true Blue Peter fashion, you can demonstrate the principle behind a torque converter at home. Get a large bucket or bowl and a cordless drill with a paint-stirrer. Fill the bucket with water and put some bits of paper around the outside of the bucket, floating on the water. Stuff the paint stirrer in the middle and pull the trigger on the drill. To start with, the paint stirrer is spinning way faster than the water in the bucket, and the bits of paper will barely be moving. As the water in the bowl begins to speed up its circulation, the bits of paper will being circulating the bucket at speed. Eventually the water in the bowl will be circulating at almost the same speed as the paint stirrer is turning. (At this point your wife/husband will probably also be complaining that it's going all over the kitchen/bathroom - you've been warned) It's that "almost" that shows the inefficiency in a torque converter - the fluid can never spin at exactly the same speed and thus it can never impart the exact same torque and motion into the turbine. Now imagine that the bucket or bowl has vanes around the inside of it. As the water is circulating, it's going to be applying force to those vanes and given a slippery enough surface, your bucket or bowl will eventually start to spin. Voila. The drill and the paint stirrer are the input from the engine and the spinning bucket or salad bowl is the output to the gearbox.
The other way to do this is to take two desk fans and turn one on and point it at the other. Eventually the second fan will start to spin because of the air being forced past it by the first fan. This uses the same principle but with moving air instead of water and it's nowhere near as much fun to watch

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