0:18

So, looking at the cylinder efficiency, we've

got a few major sources of energy loss.

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

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

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

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

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

And the the outer cylinder, we got another seal.

Both of these have, have friction associated

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

We then have further viscus friction from the

fluid moving through small passages within the hydraulic cylinder.

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

And then we also have, have leakage in our

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

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

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

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

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

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

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

So there are many places that we could

have energy loss, and we put this all together

and express it in the efficiency, which is

simply the output power divided by the input power.

So the output power of a hydraulic cylinder is the

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

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

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

mechanical components, really the friction components and the

volume metric, or the leakage, the compressibility components.

And I can express these separately.

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

force efficiency, so the force of the rod,

divided by the, pressure times the area inlet.

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

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

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

that the, the pressure on the rod

side would be atmospheric pressure or vice versa.

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

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

2:28

We also then have volumetric.

And this primarily is leakage but also a compressibility term.

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

And the flow rate in the denominator.

So this again is relating.

How much flow do I have going into my,

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

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

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

Some of it is going to go

into just compressing the, the hydraulic fluid itself.

So recognize that these, the mechanical and

the volumetric efficiencies as they're expressed right here

are not in terms of, of power but

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

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

You get the total efficiency, which the ratio

of the, the output power to the input power.

3:16

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

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

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

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

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

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

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

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

can get from a datasheet about the

mechanical and the volumetric efficiency of this.

And from that try to calculate what the peak force and

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

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

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

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

this is an assumption that the down stream

or the non-pressure port is at atmospheric pressure.

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

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

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

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

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

So, if I look at the extension case.

4:30

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

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

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

I'll put this in 3.8 centimeters.

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

an area of 11.3 square centimeters.

And this again is a lesson in paying attention

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

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

Mechanical efficiency equation and rewrite this, such that

I can express it in terms of force.

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

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

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

6:29

So, what about the velocity capabilities?

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

simply rearrange my, lemme grab a different color here.

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

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

in this case I would end up with the biometric

efficiency multiplied by the flow rate divided by the area.

6:55

And so I plug in my numbers.

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

I've got a flow rate of.

Ten liters per minute, but again we have to

be careful as to what our units are here.

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

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

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

Cubed, per minute, and, then my area

is 11.3 centimeters squared.

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

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

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

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

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

8:33

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

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

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

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

Square that.

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

Square that.

And divide all this by four.

9:06

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

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

So I end up getting 6.4, centimeters squared.

And then I could do the exact same thing

and I challenge you to do so for an exercise.

Calculate the exact same thing for the, for the retraction

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

And we will then get a force and

a velocity that are different from the extension case.

9:49

So in summary here, we discussed a couple

different sources of energy loss in a hydraulic cylinder.

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

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

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

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

And then we applied that to an example calculation.

Thank you.

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