
Originally Posted by
Brillo
Ashtonts Your point is well taken but I wasn't trying to do a rigorous calculations since there are too many unknowns. So I made a gross assumption which was that the the inertial mass allowed the cams to spin for one second after the belt snapped - maybe more maybe less, who knows. They would have been spinning at 16.5 rps at the time of belt breakage (assuming an engine rpm of 2000 rpm) and zero after one second. That's likely close because think about how long it takes your engine to shut down after you turn the key off, and that's at idle speed (about 800 rpm). Assuming linear deceleration that would amount to about 8.25 complete revolutions (I said 16 but the point is the same). The crankshaft probably would have spun longer than the cams on account of having much more rotating mass and not having to drive the cams on account of the belt breakage. Again, without being too rigorous, that is plenty of crank and cam rotations for the pistons to come into contact with the valves on one or more cylinders and bend them. My limited experience is that on interference engines (obviously) when a timing belt breaks valves get bent. Based on your experiences or your dynamics class let us know if a more accurate assessment can be made.
I may sound like I’m being pedantic but I feel the distinction is important:
α(average) = dω/dt. In other words, average angular acceleration (deceleration in this case) is equal to the change in angular velocity over the change in time. We aren’t explicitly assuming linear angular deceleration, we’re modeling the average deceleration as constant. This is important because we don’t necessarily care about exactly how the graph of dω/dt looks (it could be parabolic, etc—the path of the velocity of you will), we only care that over the time (1s in this case) the angular velocity changes from 2000 rpm to 0 rpm.
So since we know the start and end points of the velocity and assume the start and end points of the time, we can ignore the path the velocity takes to get there because it won’t matter in our particular analysis, and instead just model it as an average. This is important because if we wanted to use this same equation to determine the position at .5s or .75s, our answer could potentially be very far off depending on what the actual path was.
Pedantry aside, I agree completely with the way you modeled it. Plugging it into my kinematics equations, I got the same output of 8 revolutions of the camshafts.
I will add, however, that assuming timing is lost immediately, and that the timing never coincides again as the cam and crank both decelerate to a stop (may or may not be a good assumption—I have no idea honestly), and that both stop at the same point (t=1s), the crank will spin 2x the distance (16 revolutions). Since the movement of the pistons is tied to the crank, and with the valves being out of time, there is the chance for damage to the valves on all cylinders for all 16 of those revolutions, caused by the pistons.
So all this effort to say what we already know: OPs valves are fucked.
If I knew a few more of the unknowns here, it might even be possible to determine how much force is being exerted on the valves when they crash against the pistons, compare it to the yeild point of the valves, and get a definitive answer to whether or not the valves (and pistons for that matter) are smashed... buuuut I’m a little lazy for that.
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