Yamaha sells the R1 engine like crossplane, due to the kinetic energy of parts into engine is due to each piston and the crankshaft.
Kinetic Energy of Piston and Crankshaft
The engine in rpm constant state, the pistons have a alternative movement, therefore have 0 and X kinetic energy, but the crankshaft, turn all time to the same rpm and therefore keep the energy. But the energy doesn't created nor destroyed, only transformed.
If we follow Newton's laws of motion, and law of conservation of energy, the energy of pistons must go to other part, therefore is energy, is gave and took other part of engine, in this case it is between crankshaft and other piston.
Engine Kinetic Energy
And relation between parts keep the energy constant. In the cross plane we see the piston when two piston is closed to maximum speed, the other 2 piston is closed to minium speed and then Exchange the energy between them, and together keep the energy constant
Video Yamaha crossplane explained
Analysis crossplane concept in R6 and R675
If we resolve the energy equation to provide crankshaft speed, we can calculate the speeds and pistons and crankshaft balance.
Equation to resolve the crankshaft speed
In the R1 with crossplane we can see this behaviour.
Yamaha R1 crossplane behaviour, with constant speed in crankshaft and with energy constant.
In last figure show with crankshaft energy without mass, and we can see that it is very balanced between pistons, and this configuration keep the energy with few variations.
If we see the other configuration we can see that they are less balanced or completly unbalanced.
Yamaha R6 flatplane behaviour, with constant speed in crankshaft and with energy constant.
Yamaha R675 behaviour, with constant speed in crankshaft and with energy constant.
Yamaha R6 flatplane reduced the energy changes crankshatf in 0.49%.
Yamaha R675 reduced the energy changes crankshatf in 0.20%.
Therefore the crossplane don't have enough impact in the behaviour in the rotational motion in the crankshaft, due to 99% of kinetic energy is the crankshaft.
Other aprox is the minimum crankshaft inertia, in ideal case, is due too for balance mass in the crankshaft, calculates in "Why should Yamaha to make a YZF R675?",
Basic Inertia crankshaft equation
YZF-R6 = ICrankshaft = 0,000388359 kg·m2 ;
YZF-R675 = ICrankshaft = 0,000714714 kg·m2 ;
Yamaha R6 increased the energy changes crankshaft until 20%.
Yamaha R675 increased the energy changes crankshaft until 4%.
But this behaviour could be to the R675 have more inertia, but if we put the same inertia in the two engines ICrankshaft = 0,000714714 kg·m2
Yamaha R6 reduced the energy changes crankshaft until 12%.
It only reduced the variations until 12%, 3 times more than R675.
If we compare the inertia on the engine, in speed for example 100km/h (36 m/s) of one motorbike with 250kg (180kg bike + 70kg pilot), we have 162 kJ and into engine to 11.000rpm the the energy is:
YZF-R6 ICrankshaft = 0,0200 kg·m2 ; Energy engine 13.3kJ 8,23% overall energy
YZF-R675 ICrankshaft =0,0175 kg·m2 ; Energy engine 11.7kJ, 7,22% overall energy
but we considered, that it needs more rpm for the same power in 4 cylinders against 3 cylinders, near of +20%, the energy in the 4cylinders reach 12% of engine,
If we analyze the construction of engine, we can see, that the Inertia an balance mass have inverse behaviour.
Balance mass to radio and the same inertia to radio
We can see that in we increase the mass balance, but we put near or turn axis for keep the balance, we have less inertia
Relationship of design parameters
Therefore if, we decrease the ratio an increase the mass balance, for example in we realize on drill in the crankshaft to r 30mm to axis, we can replace with lead to r 20mm and this weight provide 33% less of inertia.
with this we can see that a weight material in crankshaft, down the global inertia, but the ideal, is light material in the crankshaft with heavy mass to balance, something like that, aluminium crankshaft with lead mass balancer.
Conclusion, it is the crossplane, with current steel crankshaft, it don't provide a significative improvement, but Inertia in the engine is very important.
No hay comentarios:
Publicar un comentario