Originally Posted by serialk11r
The piston's path is "linear", but its motion is quasi-simple-harmonic (aka sinusoidal) with respect to time. [Explained before, its motion is linear but its measurement over crank angle at constant rev, or time, is quasi-sine wave]
The rod adds some complexity to this, most obviously decreasing it around TDC. The Wikipedia article varies stroke and keeps rod length constant, if you change the rod length instead, you'll see that it's increasing BDC peak acceleration. [Up to this point, it is correct.]
This can be proved simply based on the formula itself. At BDC (crank angle = 180 degree), the function sinA= 0 while cosA = -1. The acceleration equation becomes:
X" = -r(-1) - r^2/l - r4*0*1/l^3
= r - r^2/l
= r (1 - r/l)
So if you increase l, the term r/l is reduced so that (1 - r/l) increase, and thus the acceleration value increase and vice versa. Simple as that.
The reason is the piston's postion at a given crank angle is the vertical distance between a circle of radius = stroke/2 and a tangent circle of radius =rod length, vertical meaning perpendicular to the common tangent of said circles. An infinitely long rod would make the piston's motion perfectly sinusoidal. [This is where you screwed up with fancy terms and thing. How does the position of piston have any relationship with longer rod that causes faster acceleration at BDC.]
Actually, suppose at TDC, if you draw a circle at r = stroke/2 from crank center, and you draw another circle from the wrist pin of the rod connecting the piston with radius = rod length. These two circles touches, or tangent, at the crank pin. However, once you start cranking the engine, these two circles start intersecting one and another at the crank pin. The piston and wrist pin continue their linear motion along the line, while the crank pin moves around the crank circle. The crank circle remains the same while the rod circle continue to intersect until BDC, where two circles touches, or tangent, again. And then they start intersecting again until to TDC.
Now, notice that the center of the rod circle, at wrist pin, *always* travels along the line. This means that the circle of the rod *always* travel along the line. It never bounce up, or down. If It had bounce up or down to create a sinusoidal motion, the center of the circle must be moving up or down. That was not the case here with finite-length rod, and that is never the case with infinite long rod.
serialk11r, if you want to explain something, make sure you explain it right with enough detail and use the common terms. Sometime using fancy word does not mean it is more correct.
|