Why Not Consider Piston Oscillations as Simple Harmonic Motion?

[monty37]

i have asked this question before ,yet i ask again,
why should we not consider the reciprocating action of the piston as simple
harmonic motion?
harmonic oscillations are when a particle may oscillate within unequal limits
about the mean position

a special case in which limits of oscillation on either side of neutral position are equal
is simple harmonic motion,in case of the piston,the limits are the tdc and bdc.

 

[xxChrisxx]

Simple harmonic motion is a sine wave.

Real pistons with a conrod do not follow a sine path, so can't be considered simple harmonic.

An ideal case of an infinitely long conrod will bring the movement to a sine wave.

 

[monty37]

simple harmonic motion could be sine or cosine wave,but the conrod needs
to have a limit,so in case of an infinitely long conrod,how does it become Simple
harmonic motion?

 

[FredGarvin]

Just look at the definition of SHM vs. that of a piston with a connecting rod. I attached a basic Excel spreadsheet that allows you to play with the values of L (connecting rod length) and R (crank radius). As you make L larger you can see the displacement curve for the piston approach that of the SHM curve.

 

[xxChrisxx]

I've just checked up and this was all answered last time.

SHM has to follow sinusodal motion.

Real rods have a 'dwell' time that is affcted by the Rod /length to Crank Throw Ratio. (L/R) This is where the crank and conrod are still rotating, but is not piston up and down.

The lower the ratio the longer the dwell time at bdc and tdc (the teo have different values and the majority of dwell is at bdc). As the ratio increased the dwell time reduces, making the shape of the dixplacement against crank angle curve become closer to sinusodal.

When you start getting L/R ratios of 6+ you can assume that the conrod is following sinusodal motion.

In real engines this means you have to go back to pre WW2 engines. After the war L/R ratios began to reduce. Typical engines now run an L/R ratio between 1.5 and 3.

With that sort of ratio, if you want accurate answers, you can't assume shm.

 

[monty37]

i did understand from the sheet .so if i consider
an infinitely long conrod,shm can be achieved.so
currently we don't have engines with L/R ratios of 5 or more?does this
ratio affect the efficiency?

 

[xxChrisxx]

The rod length to throw ratio doesn't effect efficiency.

I could elaborste and say why it could, but it would just be confusing as its not true for every engine ans requires tuning of tiher components. So its not true to say that one ratio is more or less efficient that another.

 

[Jobrag]

For it to be SHM the rotational speed would have to be constant throughout the cycle, in an extreme case consider a large single cylinder two stroke just after fireing the piston will be moving downwards quickly as the compression part of the cycle starts the piston will slow down, not SHM. Although the effect will be reduced in multi piston engines it should still be measurable.