Piston diameter size, fricition, mathematical proof

  1. I have already asked the question of piston diameter size and efficiency in an earlier thread but i'll recap.

    My question was that is it true that the larger diameter piston have a larger propensity to overcome the mechanical loss of fricition due to the piston rings contact with the mating surface inside the piston walls.

    The resounding response was yes, but I wanted to clarify 2 factors:

    1. Would it matter if the the rings were lubricated by water instead of oil?

    2. Would it be correct to express it in a mathematical type proof by using this method:

    Circumference formula : pi * 2*radius

    Area formula : pi * radius *radius

    if we cancel out the constant pi from each equation , we have

    circumference forumla : 2 * radius

    Area forumla : radius * radius


    Thus, for any radius, we can see that the larger the radius, the area formula will have a factor of radius squared, while the circumference formula will only be radius times 2.

    Is this a mathematical type of expression we can make to show why larger pistons will be more likely to overcome piston ring friction? The fact that larger radius will have result in a larger area factor relative to the circumference of the piston?

    thanks
     
  2. jcsd
  3. brewnog

    brewnog 2,791
    Science Advisor
    Gold Member

    You're nearly there.

    The parameter commonly used is volume to surface area ratio. The main source of loss in a combustion chamber isn't due to piston ring friction (which you're correct in saying is a function of circumference) but due to heat loss (which is a function of surface area, both of the piston crown which transfers heat from the combustion gas, of the piston skirts which dissipate heat to the liner and coolant, and of the undercrosn which dissipates heat to the lube oil). Then (and only then!) do you consider ring friction.

    I don't know what you mean about using water instead of oil. Theoretically yes, but practically water is hopeless at lubricating, sealing and cleaning engine components.
     
  4. My device is not really a piston with gas combustion as much as it is a hydrualic (water) as the main substance being sealed. The device basically works in this manner:

    A chamber has an outside water seal and a seal inside. Both these seals are used to seal the passage of water and they are dynamic in nature (like a piston ring). Basically i want the chamber to be moved by water pressure from the water surrounding the chamber. The chamber will move back and forth at low speed past the water seals. The pressure driving the chamber is between 500 to 1000 Kpa. The water seal outside prevents water from passing through between itself and a certain point on the outside of the chamber wall. The water seal inside prevents water from passing between itself and the inside chamber walls.

    I figured that a larger chamber with a larger area exposure to the water pressure, even though the circumference of the o ring is also larger, would be more likely to have a tendency to move better b/c proportionately, the larger surface area more than compensates for the larger diameter (o ring friction). Thus for every larger radius chamber, the pressure pushing on the larger surface area of the bottom of the chamber, is proportionately greater than for that of a smaller radius chamber and smaller circumference o ring. Would the math example i used be correct in this scenario then?

    thanks
     
  5. brewnog

    brewnog 2,791
    Science Advisor
    Gold Member

    Yes. As bore diameter increases, your piston area (upon which your fluid acts) increases as a square; the seal contact area increases linearly.
     
  6. Thanks a lot for your help :)
     
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