0:18

So, looking at the cylinder efficiency, we've

Â got a few major sources of energy loss.

Â The first one is just the seal friction, and two major

Â seals on this, this actuator, one is right up here at

Â the rod, between the, the rod and this end cap, where

Â we've got a wiper seal with also then probably a u-cup seal.

Â And then between the, the piston hub which you can probably see better in the slide.

Â And the the outer cylinder, we got another seal.

Â Both of these have, have friction associated

Â with them as they're, as they're in motion.

Â We then have further viscus friction from the

Â fluid moving through small passages within the hydraulic cylinder.

Â So this would be a, a, a velocity related term.

Â And then we also have, have leakage in our

Â hydraulic cylinder, often, often leakage past the piston hub.

Â And hopefully less leakage past the rod, but we do sometimes get

Â leakage past the rod and, a challenge with hydraulic systems is leakage.

Â And then some other terms that, that we won't discuss too much right

Â now but fluid compressibility is another one we have to pay attention to.

Â Pressure drop through the ports, especially if you're using quick

Â disconnect ports like these that have quite a significant pressure drop.

Â So there are many places that we could

Â have energy loss, and we put this all together

Â and express it in the efficiency, which is

Â simply the output power divided by the input power.

Â So the output power of a hydraulic cylinder is the

Â force times the velocity, mechanical power coming out of it.

Â The input power is the hydraulic, which is the pressure times the flow rate.

Â Now, we take this one step further, and say let me break this up into the

Â mechanical components, really the friction components and the

Â volume metric, or the leakage, the compressibility components.

Â And I can express these separately.

Â And so, my mechanical component would, in this case would be really a, a f,

Â force efficiency, so the force of the rod,

Â divided by the, pressure times the area inlet.

Â And one thing I need to stress here is that, right

Â now I'm neglecting any pressure that would be on the downstream side.

Â So if I have pressure coming into the, into the cap side, I'm saying

Â that the, the pressure on the rod

Â side would be atmospheric pressure or vice versa.

Â So I'm neglecting that, that other pressure times area, that I'd otherwise

Â have to pay attention to that we did in our transformer lecture.

Â 2:28

We also then have volumetric.

Â And this primarily is leakage but also a compressibility term.

Â And here we have the area times the velocity in the numerator.

Â And the flow rate in the denominator.

Â So this again is relating.

Â How much flow do I have going into my,

Â my cap side and what's the velocity of my rod?

Â And I recognize some of the fluid that's going in

Â there is going to leak past the, the piston hub.

Â Some of it is going to go

Â into just compressing the, the hydraulic fluid itself.

Â So recognize that these, the mechanical and

Â the volumetric efficiencies as they're expressed right here

Â are not in terms of, of power but

Â because they are dimensionless we, we're all right.

Â And also if you multiply the, the mechanical and the volumetric efficiency.

Â You get the total efficiency, which the ratio

Â of the, the output power to the input power.

Â 3:16

So, let's do a, a quick example here applied to

Â a hydraulic cylinder similar to, to this one right here.

Â I've tried to make this as close to this cylinder as possible.

Â On the cap side we've got a 38 millimeter diameter

Â bore, our, my rod is about a 25 millimeter, diameter.

Â And I'm saying I have a flow rate going into this

Â of about 10 liters per minute at a pressure of 21 megapascals.

Â So, I'm going to take this information a little bit of information that perhaps I

Â can get from a datasheet about the

Â mechanical and the volumetric efficiency of this.

Â And from that try to calculate what the peak force and

Â a peak velocity of this cylinder would be in extension and retraction.

Â We'll focus on one, but we'll talk about how

Â to do it for, for the retraction case as well.

Â So, lemme first of all focus on an assumption that I'm going to make, and

Â this is an assumption that the down stream

Â or the non-pressure port is at atmospheric pressure.

Â So, if I'm applying pressure to the cap side to drive this in extension.

Â I'm saying that my rod side is as atmospheric pressure.

Â So, I've got my mechanical and volumetric efficiency equations here.

Â And what I need before I move on is the area of the cap or the rod side.

Â I've got a diameter, I need an area.

Â So, if I look at the extension case.

Â 4:30

The important area here would be on the cap side which is A1 on

Â the, on the diagram and the area of the cap, would

Â simply be equal to pi times the, the cylinder diameter.

Â I'll put this in 3.8 centimeters.

Â Square that, divide it by 4, and crunching the numbers, I end up with

Â an area of 11.3 square centimeters.

Â And this again is a lesson in paying attention

Â to units, as we're, as we're moving through these calculations.

Â So what I'm going to do is I'm going to take my.

Â Mechanical efficiency equation and rewrite this, such that

Â I can express it in terms of force.

Â So the peak force will just be equal to the mechanical efficiency

Â times the pressure in, which would be P1 in this case, times the area.

Â And this will be the cap side area in this case.

Â 6:29

So, what about the velocity capabilities?

Â Well, to do the velocity, I'm going to

Â simply rearrange my, lemme grab a different color here.

Â I'm going to rearrange my volumetric efficiency equation such that I

Â can get velocity and express velocity as the, let's see

Â in this case I would end up with the biometric

Â efficiency multiplied by the flow rate divided by the area.

Â 6:55

And so I plug in my numbers.

Â I'm given the fact that I have a biometric efficiency of 95% for this case, 0.95.

Â I've got a flow rate of.

Â Ten liters per minute, but again we have to

Â be careful as to what our units are here.

Â So, I'm going to keep this in time units of,

Â of minutes, but I'm going to convert it into cubic centimeters.

Â So, I'm going from ten liters, which would then be 10,000, centimeters.

Â Cubed, per minute, and, then my area

Â is 11.3 centimeters squared.

Â So, notice that I am not doing this calculation in pure

Â SI units which will be meters and meters cubed per second but.

Â Because I can, you know, have a velocity in whatever

Â units I, I'm comfortable with this, this'll work out just fine.

Â So, I crunch through the numbers here and I end up with 840, centimeters cubed.

Â 8:33

I'm only going calculate the area here because the rest of the, the work is

Â the same, but the area on the rod side, would now be equal to pi.

Â Multiplied by the, diameter of the, the, the, the entire

Â bore diameter, which would be 38, or 3.8 centimeters.

Â Square that.

Â Subtract the, diameter of the rod at 25 millimeters, or 2.5 centimeters.

Â Square that.

Â And divide all this by four.

Â 9:06

So, I can say then the area of my rod, ends up

Â being just over half of the area of the, the cap side.

Â So I end up getting 6.4, centimeters squared.

Â And then I could do the exact same thing

Â and I challenge you to do so for an exercise.

Â Calculate the exact same thing for the, for the retraction

Â case, as I have flow going into the rod side.

Â And we will then get a force and

Â a velocity that are different from the extension case.

Â 9:49

So in summary here, we discussed a couple

Â different sources of energy loss in a hydraulic cylinder.

Â Recognize that the mechanical and the volumetric losses that we see here

Â in a cylinder, the same thing applies to other hydraulic components such

Â as pumps or, you know, other spool valves and things like that

Â so we have mechanical losses, we have volumetric losses in all of those.

Â And then we applied that to an example calculation.

Â Thank you.

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Â