Crossplane by Yamaha: A technical approach.

As many other MotoGP fans, and as a complete engine freak in a more particular way, I’ve been curious about the technical solutions adopted by the manufacturers at their engines, and I can say that the Yamaha M1’s (Also R1 street bike) engine is one of the most advanced that I’ve ever known. I’ll try to offer you a general vision of how this engine works, and what makes it so special.

The important thing about this engine, is that the crankshaft layout is completely different to any other engine made for a motorbike. At the beggining of the MotoGP era, when 500cc 2 Stroke were discarded in benefit of 4 Stroke engines, there were two principal solutions for the integration of the power unit into the chassis and the bike in general: V4/V5 engines (Honda, Ducati, Suzuki) and Inline engines (Yamaha, Kawasaki, Aprilia).

Over the next years, all of us have seen how inline engines disappeared from the competition, some times because the budget and non-competitive machines, and others simply because the Inline bikes couldn’t reach the V’s performance. But, first of all, we aren’t speaking about horsepower, because that is not substancial, rather than about laptimes, which is pure speed, and the really important thing.

936631742330.jpgSuzuki GSVR.jpg

The only team that featured a V4 engine, and left the Championship, was Suzuki, by the end of the 2011 season. They designed the XRE0 powerplant, which we can see above, for the GSV-R (It looks a little bit like a Honda, doesn’t it?). The only team that survived the 800 era, with a straight 4 engine, was Yamaha.

But, why? Let’s start speaking about the bike layout:

First, the V configuration allows the designers placing the engine at the chassis with the presence of less cylinders in the longitudinal axis of the bike, therefore the chassis is stiffer from the beginning. The intake goes then between the vee and the plenum is placed at the front of the chassis, so then the fuel tank is placed at the free space left by the intake at the typical fuel tank position for a bike, and also goes under the seat. This is not a difference between the two different options because the intake uses to be placed roughly at the same position. So the principal advantage in the bike layout is simply that the bike is narrower with a V engine than featuring a straight engine.

But this system has some disadvantages, which are for example, that the wheelbase usually is a bit longer, and the rear suspension configuration becomes harder because of the presence of the rear bank of cylinders.

montaje_motos_0.png
There we have the two main contenders for the Championship nowadays, the Honda RCV213 and the Yamaha M1.

Talking about engines, and comparing V’s with Straights, we have the next:

The V4, has overcome as the most succesful solution during the 4 Stroke era, because simply all the Straights with the exception of Yamaha and some private teams with BMW and Kawasaki street engines have survived. The V4, obviously, has some problems. The first, is that every component from the above each block has two copies. And we are obviously talking about four camshafts instead of two, and two gear timings instead of only one. It happens the same with the exhaust, which is splitted in two pairs, one below the engine itself (front cylinders) and other going upside to finish at the back of the seat.

A Straight engine allows us to join all four exhaust manifolds in an only exit if necessary, reducing weight and lowering the mass center of the bike. We only have a bank of cylinders that in fact is wider but has a pair of camshafts and a single gear timing group, although the crankshaft has to be longer by definition.

Then, it comes the big question. What has the Yamaha engine inside that made the difference from the other Straight engines, and that even made the bike World Champion?

The answer, is easy to be told, but hard to explain in an understandable way: This Straight four engine has the layout of any 4 cylinder engine, but has many of the advantages of a V4 engine without their disadvantages.

LEADFlat-plane-crank-590x397.jpgcrossplane.jpg

 

Here is where we start talking about four terms that are paired:

Flat plane, and Screameer: The first, has relation with the left image above, and it comes because if we make a plane that crosses the main crankshaft axis and the crankpin of each conrod, you’ll see easily that the plane is the same for all four cylinders and this is where the name comes from. The name «Screamer» came from the 500cc era, when Honda and Yamaha used the term in opposition to the  Big Bang configurations. In fact, we are naming the types of firing orders for each solution. The name «Screamer», has a direct reference with the sound that comes from a flat plane 4 cylinder engine when it revs up.

Crossplane, and Big Bang: The crossplane term, if we repeat the operation of forming planes at the axis of the bearings and the pins, comes because as we see at the image on the right, the planes would be two, and would cross at the main axis of rotation of the crankshaft. Simple as that, and yes, for example an Inline 3 or Inline 5, or 6 are also crossplane engines. The term «Big Bang», comes because if we use this configuration with a crossplane engine, three explosions come very close between them in time terms, and the other comes alone at the center of the gap produced by the other three. This is the origin of the Big Bang name, and this is why a V4 or a R1 engine sounds lower than a Screamer engine, because the apparent frequency of the explosions is higher at a Screamer engine (that has equally spaced firings) than at a Big Bang engine.

And having arrived to this point, I can say it now: A Yamaha R1/M1 behaves exactly as a 90-degree V4 engine with a flat plane crankshaft (180º spacing, pins opposite), in terms of firing order and power delivery. You can hear this and continue reading below:

Inline-4, Screamer configuration: https://www.youtube.com/watch?v=J4IBOyVAU2Q

Inline-4, Crossplane configuration: https://www.youtube.com/watch?v=MYyWa4kzkwI

V4@65º, Flat plane@180º : https://www.youtube.com/watch?v=zAAiRYwUOq0

As a demostration, and with the help of AutoCAD, I can show you how this happens. We’ll start from a V4@90º, with a 180º plane crankshaft:

v4.png

Note the number attached to each piston, because is important. What we’ll do is to put the alternative axis of the piston movement in vertical position. That means that we have to separate each piston into an individual crankpin firstly:

mult.png

As we see at this second image, we’ve separated the pistons and the rods with individual pins, and rotated them 45º. That will mean that the current rotations will be, for each cylinder, and measured clockwise:

1: -45º     4: +45º   2: -45º  3: +45º

Note at the first image, that piston 3 should be 2 and 2 should be 3, and everything will take sense. At this point, and if we have to maintain the firing order we have to «rotate back» the positions to 0, so if the alternative axis of the pistons must remain vertical, we only can rotate the pins from their initial position. If we do, given that the absolute angle between pairs of cylinders is 90º, and knowing that the crankshaft spacing at the start was 180º, we’ll get this:

cplane.png

And finally we rotate all of it 45º clockwise, we get a Crossplane crankshaft, particularly the same as the Yamaha R1 and M1 configuration. Suzuki, at their actual MotoGP GSX-RR, use also a Crossplane configuration, because the chassis suggests that it’s not V4 powered, and, obviously at this point, also because of its sound.

But it is worth using a configuration never used before in an Inline 4? And…the most important, Why?

The first answer is easy. Basically Yamaha has achieved success with their package and this is the end of the story.

The second, mainly comes from the internal dynamics of an alternative powertrain. All about maths, dynamics, fatigue, frequencies and spectrums, and a bunch of  stuff that is studied at Mechanical Engineering, which I’ll try to explain next the easiest way as possible.

Starting from the beginning, we can define the main mechanism present at every single alternative ICE (Internal Combustion Engine), which is composed from a crankshaft, a connecting rod, and a piston. The function of all of this, is the transformation of linear movement into rotational movement.

BMW_E41-4_Crank_Drive_crazy.jpg

So, we can put many of them together and here it is, we have a V10 F1 engine, made by BMW.

But, how the engine transforms air and petrol into power? This should be known, it burns all of it inside the combustion chamber, which is the space that remains between the piston and the cylinder head when the first is at the Top Dead Center. How it does it, or how is this optimised is not the plot of this story, so we’ll assume that the burning mixture pushes perfectly the piston down, as the crankshaft is forced to rotate. If you need more information, watch this animation:

https://en.wikipedia.org/wiki/Four-stroke_engine

Then, a 4 stroke engine, has 4 stages, that are intake, compression, expansion, and exhaust, in order. Simplifying, this cycle is performed by the engine once by every 2 complete crankshaft revolutions, what means that the crank rotates 720º per cycle, and that in a simple way, each cycle has 180º duration. During the expansion stroke, as the burning of air and petrol is an exothermal chemical reaction, pressure and temperature will rise.

Temperature (at this explanation will be considered a side effect) affects directly at the combustion and the thermoaerodynamics and the transport phenomena present at the combustion and at the cooling of the engine, and if everything is optimal to an acceptable point, the pressure peak reached at the cylinder when the mixture is expanding will be high enough to push the piston down easily.

When I did my Master Thesis, I designed a single cylinder Moto3 engine, so I can show you how the pressure evolves inside a cylinder with the crankshaft rotation, and considering 0º the start of the intake stroke:

Sin título.png

We can see an strong peak when starting the expansion stroke. This diagram is good for the engine we are talking about, because a Moto3 engine has barely the same principal dimensions and shape of a MotoGP engine, but instead of 4 cylinders, has only one. (Short stroke, short rod, wide piston diameter, high rpm power and torque peak)

But all of this has to happen into a machine, that has components. Therefore, the force produced over the piston, has to be combined with the inercial forces of the alternating masses presents at the mechanism, that are the piston and part of the mass of the rod (there are some methods to know the amount of the total mass to be considered as alternative, but we are not explaining that here).

So, the masses in that mechanism are like energy stores, that take the energy that phisically is transmitted from the gasses pressure, and then delivered as movement to the transmission and the rear wheel. The heavier is the mechanism, the slower an engine accelerates, and the greater the forces that it has to stand.

When we speak about a piston-rod-crank mechanism, if we schematize it, would look like this:

img1.gif

To study the kinematics of the mechanism, we «only» have to divide this system into two coordinates, x and y, take the lenghts of the crank and the rod, and if we assume as variables the angle of rotation of the crank and the angle formed between the rod and the displacement axis of the piston (linear), we have to impose mathematically that the position of the piston has a constant value, for the case of the image, at the y axis.

Once we’ve done that, differenciate the equations once, will give us the speed of the piston and the rest of the elements of the group, and if we repeat the operation, we’ll get the accelerations.

The equations, use to be referenced to the piston, and look like this:

eqs.png

Where Theta is the angle of the crank, r is the offset of the axis of the pin, referenced to the main axis of the crankshaft (which is half the stroke of the engine), and Lambda is the coefficient between r and the rod’s lenght. If we have some mathematical sight, is easy to see that if the rod’s lenght tends to infinite, Lambda becomes zero and the position, speed and acceleration of the piston would follow seniodal and cosenoidal laws.

When fast engines are designed, normally the stroke is small, and the bore is the biggest as possible, and the limitation uses to be the materials because the components have to stand with the huge loads that are generated by the huge accelerations that happen inside these machines.

For example, and speaking about numbers, in the case of the engine I designed, the bore was 81mm, the stroke was 48,5mm, and when the engine was running at 14k rpm, the acceleration peak at the piston, every time it reached the TDC, was…well…67727m/s^2, or what is the same, almost 6904G. That means, that the piston and every thing with any mass that had the same movement of the piston (the piston pin, mainly, and part of the mass of the connecting rod), would weight at that time almost 7000 times their stationary mass. If a racing piston of this dimensions weights, for example, 180g with the pin attached to it, it would mean that its apparent weight would be approximately of 1260kg at that moment. But…this is dynamics, I’m going too fast.

Before that, let’s see how the position, speed and acceleration of the piston behave, for a system with a 48.5mm stroke, and a rod lenght of 100mm:

cin.png

Note that this diagram shows three curves, that represent the reduced magnitudes of each equation calculated before. Look also how the rod’s lenght reduces the acceleration of the piston at the TBC (grey, 180º and 540º).

Then, this is the moment where we switch kinematics into dynamics. And we only have to know that an inertial force is the product from the mass by an acceleration. When we speak about which parts of the mechanism have accelerations, for a constant crank speed, the only who have are the following:

  • Piston, with it’s bearings, circlips, and pin.
  • A percentage of the mass of the connecting rod, and it’s top bearing mass, and every mass over the horizontal plane passed by it’s top axis when the rod is vertical.

The amount of mass from the rod, can be calculated by the «1/3 – 2/3» method, that considers that the 33,33% of the total mass of the rod with all it’s attachments is moving alternatively and the rest is moving rotary. A more accurate way, consists of reducing the mass of the rod to a system of two masses and considering the mass center of the rod and the bearings and bolts, but we require a computer and more time. All this is what we use to balance the crankshaft with masses on it, and counter rotating masses if neccesary.

So, if we know the masses, and the accelerations that they have, we can know the force that they withstand, and if we divide this force with the area of the piston, we can combine this with the pressure of the gasses, obtaining then a curve like this:

din.png

This graph takes into account if the pressure goes with the movement or against the movement of the mechanism, and is represented for 14000 rpm, where the inertial forces have the main paper over the cylinder pressure. Moreover, if we see how all behaves for 8000 rpm, the story is a little different:

din8k.png

Therefore, if we calculate the force over the rod, and mathematically find out how much of this forces are directed in a orthogonal way from the rotational axis of the crankshaft (then, generating a moment, or what is the same, torque), the result is the next:

torque.png

So, this is the study for a single cylinder, and we are trying to compare two different solutions for a 4 cylinder engine. Lucky of us, we have Excel and we can copy all of this and simply edit the angle where things happen, for each cylinder. Then we will compare how inertial torque and combustion torque behave for a Big Bang engine, and a Screamer engine.

If we combine the values of all the torques for a 4 cylinder configuration, for example, the diagram of the inertial torque for an screamer engine, is shown below:

IT.png

It is not a surprise, that the inertial torque is aligned by pairs, and therefore the combination is obtained by summing all the instantaneus values.

CIT.png

Then, we can see the same for the combustion torque, for an screamer type engine, at the graph below:

CT.png

So, if we combine the combustion torque for all the four cylinders, we would obtain a diagram as shown below:

CCT.png

As happens with the inertial torque, the combustion torque, due to the symmetrical configuration at the engine, gives a regular signal. If we combine the inertial torque with the combustion torque, we will obtain a very similar signal to a one acquired from a real engine.

CMT.png

As we can see, four strong pulses are transmitted from the crank, through the clutch, to the transmission, to the chain and then to the wheel and the ground. This phenomena is what the crossplane configuration tries to avoid, using a different geometry, which in combination of the inertial and combustion torque, for all the four cylinders, gives an smoother power delivery to the ground.

If we look deeper this configuration,.we’ll see that the inertial torque of all four cylinders is aligned, and therefore the forces are acting ones against the others all the time. For example, when a cylinder is at it’s power stroke, at it’s TDC, the piston that will ignite inmediately, starts the compression, at it’s TBC. This means that the piston that pushes down has to compensate the inertial force from the piston that starts going up.

If we remember, the kinematics of this mechanism says that the biggest inertial forces are reached at the dead centers of the piston stroke, because the piston speed is zero, and it’s acceleration is maximum. Then, this circumstance is making the response of the engine slower to the accelerator opening, and therefore more abrupt.

At a crossplane engine, the configuration is made as shown below:

CPIT.png

Surpringlthis configuration makes the inertia of each pair of cylinders opposed, and therefore, the resulting inertial torque is almost zero. By other side, the pistons never move in opposition, and this results in a more inmediate and precise power delivery from the engine. The resulting inertial torque would be the shown below:

CPCIT.png

So, as you can see in blue, the inertial torque of the crossplane configuration is significantly smaller than the inertial torque produced by a flat-plane crankshaft. If we look at the combustion torque, the shape of the signal should be this:

CPCCT.png

As you can see, the firing intervals are 270º-180º-90º-180º. Then the combination, produces this torque diagram for the combustion:

CPMT.png

If you take a look above, at the combustion torque for the screamer configuration, you will see fastly that the differences between them are big. This configuration has more peaks, but are more similar in value and the mean values for each configuration are the same, 148N·m. We can say that this configuration has an small «bang» at the beggining, and then a middle explosion spaced 270 degrees, and then the two last explosions spaced only 90 degrees between them. This three last explosions, happen in a short amount of time (talking relatively to an engine timing), and therefore this is why this configuration is called «big bang». About the smoothness, it is clear that this configuration has only three big peaks instead of four, as happens in an screamer engine.

The combined signal, for the torque, should be the shown below:

CPTTTT.png

Look at how the torque delivery is smoother at the crossplane option, although the mean torque is the same for the two options (that means the same power). The main advantage of the crossplane configuration, is that deliverying the power more smoothly, the rear tire is able to stand more time in good conditions, and that is so important when we speak about racing. In addition, the power delivery itself, is more «linear», what makes the engine more predictable to the gas. For example, a 2 stroke engine makes a low delivery at low rpm, but suddenly, when the flow inside the engine becomes optimal (and does it fast, when high rpm are reached), then the torque delivery comes all at one time, giving to the rider a sensation of «kick».

This sensation is reproduced by a screamer engine, but it’s not by a crossplane engine. But which is the best? Probably none of them, because it depends from the rider. Some R1 fans have stopped buying R1’s because with the introduction of the crossplane engine, the characteristic (and strong) kick of the flat-plane engine has been lost.

In my opinion as a rider, this technology should arrive more extensely to the road bikes, making them safer. In my opinion as a racing fan, I’d rather prefer a V4, but there’s no doubt that this technology is simply awesome.

I hope this article gave you a deeper view from this engine!

Greetings to all!

 

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