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# RE: interference fit

```>>> <snip>
>>> Quite simply, the acceleration of the piston is at its greatest
>>> at TDC and BDT.

Right.

>>> Is not piston acceleration zero *at TDC and *at BDC as the piston
>>> is at a dead stop at that instant in time? Perhaps
>>> de/acceleration is highest immediately TDC/BDC?

[Snip.....]

>The piston is moving up toward TDC.
>At some instant in time it will be at rest at TDC.
>For it to achieve the state of rest or 'no motion' the piston must
>decelerate to 0. At this instant in time it has no motion and no
>acceleration. The piston then must accelerate from 0 to proceed to
>move back down. So, in my primitive and prolly wrong analysis, the
>piston decelerates to 0 as it approaches TDC, @ TDC it has no motion
>and no acceleration, it then reverses direction and accelerates
>downward, so at some instant in time when upward deceleration is
>zero and the piston is motionless in space, downward acceleration is
>also zero, or it could not be motionless. There must be an instant
>in time between upward motion and downward motion where both speed
>and acceleration are both zero. (?)

>Mebbe I am wrong because it may be possible for the piston to go
>from upward deceleration to downward deceleration without reaching
>zero acceleration at TDC while it is instantaneously at rest at TDC
>and before downward deceleration

Some formulas to calculate piston acceleration, speed and distance.
Metric system.

c = Piston speed .....................................  m/s
R = Crankshaft radius ................................  m
w = Crankshaft angular velocity ......................  rad/s
a = Piston acceleration ..............................  m/s^2
s = Distance the piston has moved from TDC ...........  m
A = Crankshaft angle relative to crankshaft at TDC ...  Degree
L = Piston rod lenght ................................  m
n = Revolutions pr. second ...........................  s^-1
S = Piston stroke ....................................  m
y = Crankshaft/pistonrod relation ....................  1

n = RPM/60
w = 2*PI*n
S = 2*R
y = R/L

c = R*w*(sin(A)+y/2*sin(2*A))
a = R*w^2*(cos(A)+y*cos(2*A))
s = R*(1-cos(A)+y/2*sin(A)^2)

aTDC = R*w^2(1-y)
aBDC = -R*w^2(1-y)

As an example, if you set R=0.1_m, L=0.2_m and w=1_rad/s.

The piston acceleration will be ZERO at approx. A=68,5 Degrees, and
piston speed will be maximum. Distance the piston has moved from
TDC => s=0.042_m

The piston acceleration will be maximum at TDC and BDC, and piston
speed will be ZERO.

--
John Torset
johnt@borre.mail.telia.com
Amiga 4000

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