Re: interference fit

[James Marriott <marriott@micron.net>]

glen powell wrote:
> 
> Good Frank, I am getting closer to understanding, thanks.
> However, still seems to me that deceleration must approach
> zero as the piston approaches TDC and the piston does come
> to a complete stop for an instant in time. It also seems to me that
> at that instant in time after deceleration is complete and before
> downward acceleration commences that there must be an instant
> of zero deceleration coinciding with the instant of zero motion.

OK. Let's try a different--but similar--example. Throw a tennis ball
against a wall. From the instant the ball contacts the wall until the
instant it leaves the wall, it is being accelerated in a direction away
from the wall. This, even though the velocity is positive--but
decreasing--as it continues on towards the wall, and negative (ie, away
from the wall)--but increasing--as it heads away from the wall.

The differences between the two examples is that the ball is a
non-linear spring/mass system, while the piston approximates sinusoidal
motion.

> This assumption is why I cannot understand the previous assertion
>  "acceleration is highest at TDC" that started this thread. At the
> instant of transition from upward deceleration to downward
> acceleration and while the piston has no velocity at
> the instant of time that it is at TDC how can this instant be the
> point of maximum acceleration......?

Let's try to find where the acceleration is _zero_. Acceleration is
defined to be the change in velocity (ft/sec, m/sec, etc) in a unit of
time (usually sec). A favorite of Camaro drivers:  "my car does 0-60 MPH
in 7.2 secs." Here we have a change in velocity (60 MPH final velocity
minus 0 MPH start velocity equals delta-velocity of 60 MPH). We also
have a time span (7.2 secs). So this car can, at average, change its
velocity 8.3 MPH per second. A more standard form would be to work the
units around so both "time" parameters are the same. That is, "X miles
per second per second," or "X miles per second squared," or "X miles /
sec^2 ." OK. Where is the piston's velocity "changing characteristics."
Or, where does the piston _begin_ to "reverse" direction? When it
reaches its peak speed and begins to slow down, or at ~90 deg. Though it
hasn't actually changed direction, it has started to do just that by
slowing down. How can accel be zero here? Because the delta-velocity
(say from ~90.000000 to ~90.000001 deg) is zero, as both velocities are
~zero.

> Now if maximum acceleration is immediately before or after the instant
> of TDC that makes more sense to me.....

You're so close here. The thing about sinusoidal motion (caused by
objects in rotation) is that it can't be "abrupt." That is, there's no
way for the accel to go from max to zero to max all at--or even very
close to--TDC (or BDC). The reason for the max accel at TDC is that the
velocity change per time is the _greatest_ here.

hth,
James, super nerd