0:00

So in this lecture, we'll be getting into how do we actually size a hydraulic hybrid

Â system specifically, a series system for a given application.

Â Now, the application that I've picked here happens to be a passenger car.

Â A four door passenger car very similar to a Toyota Camry, just for

Â a a vehicle that I happen to pick, and I've given the mass, the frontal area.

Â The drag coefficient so this is the aerodynamic performance of the vehicle.

Â The tire radius and the rolling resistance that we'll all need to calculate how

Â this vehicle's going to behave in a driving cycle.

Â So what I first want to do is, size all of the components or

Â the major components in my series hydraulic hybrid system.

Â And the major components being first of all the pump.

Â And then, I've got the attractive pump, I'm sorry attractive motor that's

Â driving the wheels of the vehicle and finally the accumulator.

Â So I want to size these three components and I recognize that from my earlier

Â lectures I do have additional components as well such as charge pumps and

Â other things going on in the system.

Â But, let's focus on these major components here and recognize that the other

Â components do need do exist but we're not going to focus on them right now.

Â Now, I'm going to happen to pick that this is going to be a really,

Â a passenger commuting type of vehicle, so I'm going to pick a drive cycle which is

Â the urban dynamometer driving schedule that I have shown in the lower right.

Â And this is a velocity plot versus time.

Â And you can see it goes for about thirteen hundred and some seconds.

Â And it covers about seven and a half miles, there's no grade in this so

Â it's all flat terrain.

Â But you can see it accelerates and decelerates.

Â This one speed spike up to about 25 meters per second, that's about 50 or so

Â miles per hour, just to give you a feeling of what this looks like.

Â So, this is city stop and start driving and I want to size my components.

Â So, first of all let me start with the accumulator.

Â This would be our energy storage device.

Â Now when I look back at that drive cycle, I realize I didn't have many,

Â many velocity spikes that went over about 15 meters per second.

Â So, I'm going to size my energy storage device to store all my

Â energy from a 20 meter per second breaking event.

Â So, a single storage event as I'm breaking from that speed.

Â Now, I'm going to make a few assumptions.

Â First of all, I'm going to say that the gas in my hydropneumatic accumulator is

Â going to act isothermally.

Â And that might occur if I have a, a foam in the,

Â in the nitrogen side of my accumulator which is increasing the surface area.

Â So I don't get a lot of, of temperature change as I'm compressing and

Â expanding that gas.

Â I am going to assume that I have a 2 to 1 pressure ratio.

Â Why you ask?

Â Well, that should come out of the homework that you are doing with the,

Â the accumulator part of the class.

Â And then, I am going to assume that my maximum pressure is going to be

Â 35 megapascals, 5000 psi.

Â And I am going to neglect any inefficiencies at this moment as far as

Â looking at this 20 miles per hour, 20 meter per second to us a breaking event.

Â 2:43

So with that said, let me now equate the kinetic energy of

Â the vehicle travelling at this speed to the energy stored in my accumulator.

Â So, the kinetic energy is one half mass times velocity squared.

Â I've got all of the specs for this vehicle on the right side so

Â we can plug in those numbers.

Â And we saw from our accumulator lectures that this is the, the equation for

Â the energy storage in an accumulator is the pressure.

Â The charge pressure of my accumulator times the volume of

Â the accumulator multiplied by the natural log of the pressure ratio.

Â So because I'm assuming at isothermal compression,

Â my pressure ratio is equal to my volume ratio.

Â And so, this makes it fairly easy to say that the charge pressure is going to

Â be one half of pmax and, and to just go ahead and plug that in.

Â So it allows me to simplify this just a little bit.

Â And so with that, I can rearrange this equation and solve for

Â the volume of my accumulator at 0.03 cubic meters.

Â And for those of you who probably don't think in cubic meters.

Â How big is this?

Â Well, this happens to be 30 liters of volume.

Â 3:49

So 30 liters of volume.

Â Obviously, a lot larger than this.

Â but, you know, about the size that we would have for a,

Â a vehicle fuel tank in a, in a passenger car like this.

Â So again, storing this, this storage vessel or

Â packaging this storage vessel in a passenger vehicle is not a simple thing.

Â And remember, this is only for the high pressure accumulator.

Â I still need a low pressure accumulator or a low pressure reservoir to store the oil

Â that's going to be moving in and out of my accumulator.

Â So storing all of this fluid in the vehicle and

Â the storage device is not trivial.

Â 4:21

But we have an initial storage volume for, for my accumulator and

Â I'll use this in my simulation in just a moment.

Â So we size the accumulator.

Â Now ,let's goto the tractive motor.

Â So this is the one that is driving the wheels of the vehicle.

Â And now, I'm going to size this for

Â the peak acceleration even that occurs in that drive cycle.

Â So, I took the velocity drive cycle and I basically went though the entire thing and

Â said what is the maximum acceleration.

Â And it happens to be 1.5 metters per second squared.

Â As the peak acceleration, either positive or negative or positive or

Â breaking if you will.

Â And I'm going to size the vehicle for that and I'm going to make a few assumptions.

Â First of all, I'm going to neglect any efficiencies again, I'm going to

Â neglect any road loads that are occurring during this acceleration event,

Â we'll look at road loads in just a moment.

Â And I'm going to say this is a direct drive of a hydraulic motor that's

Â driving the wheel, one wheel of the vehicle.

Â So, normally we'd be driving it through some sort of a gear box and

Â maybe we might have two of these motors driving the two separate wheels or

Â maybe four wheels of the vehicle, we could have a four wheel drive, vehicle.

Â Right now, I'm just going to be saying,

Â I've got one hydraulic motor driving and one wheel.

Â And I'm going to be sizing this for the peak power at the minimum pressure.

Â So again, I'm saying my 35 megaPacals is the peak pressure.

Â But, I'm going to drop to 17 and a half megaPascals at my lowest pressure.

Â And I'm going to size it for that low pressure.

Â 5:58

And then, I can go back to my pump equation or my motor equation in this

Â case and they say the torc is equal to the pressure times its displacement divided 2

Â pie to take care of the radiance to, to revolutions.

Â And from this, I then get the displacement of my hydraulic motor that would be

Â driving the wheels of the vehicle.

Â So, this 2.9 times 10 to the minus 4th.

Â Cubic meters per revolution.

Â So often times we don't think in, in these terms.

Â So this would then be 290, cubic centimeters per rev.

Â So this is a quite large hydraulic motor, and very often we would apply something

Â like a four to one gear box which would drop us down to a 72 cc per rev, motor.

Â So that would be a little more reasonable, or

Â maybe we might have two of them driving.

Â Left and right rear wheels or

Â left and right front wheels depending on how we're sitting at the vehicle.

Â So we've now sized the accumulator, the tractive motor, let's go ahead and

Â take care of the engine pump.

Â Now the engine pump we can operate this in a variety of different ways.

Â Remember, I said one of the benefits of a series system is that we can

Â decouple the engine from the wheels.

Â And I'm going to try and do that here and say my engine only operates in two states,

Â either on or it's running at its most efficient condition.

Â Condition, excuse me.

Â Or completely off.

Â And I'm going to cycle back on and off based on how much energy I have stored,

Â which is dictated by the pressure in the accumulator.

Â So, I'm going to run my engine pump in an on,

Â off situation, and, that's how I'm going to, to set this up.

Â Now, I'm going to size this for the road loads at the maximum speed.

Â We see our maximum speed of about 25 meters per second, and I'm going to set

Â this up to handle the aerodynamic drag, and the rolling resistance in my vehicle.

Â At that speed and again using this On/Off control.

Â 7:38

Now in my simulation im a take my assumption one step farther and

Â really say let's neglect what the engine is doing and instead treat our

Â hydraulic pump that's supplying pressure to the system as a constant flow source.

Â And this constant flow source will either be on or off.

Â So now i want a size what the flow rate is of that unit.

Â In the future we could add more complexity, if we wanted to.

Â I'm also going to neglect any inertial forces of acceleration deceleration, and

Â neglect inefficiencies in my system.

Â So, let's take a look at what these rowboats are.

Â So first of all the aerodynamic drag,

Â one-half the density of the air times the, the drag coefficient of the vehicle.

Â Times the frontal area of the vehicle, times the velocity squared.

Â So this is where the, the velocity really comes in, as being a major factor.

Â And then, I've got a rolling resistance equation here.

Â Here I'm assuming that it's independent of velocity, it is slightly dependent on

Â the velocity, especially as we get to up to higher speeds.

Â But for now, I'm using a fairly simplistic version of a rolling resistance or

Â a rolling drag, if you will.

Â And you can see the relative quantities of these two at 25 meters per second.

Â You know, the aero drag is going to be dominant on, in this region.

Â 8:48

Now, let me take those two, put them together, and

Â call that the drag force overcomer, the road load.

Â I'm going to multiply that by the velocity, and

Â that will give me the power that I need to create.

Â Now I'm going to say the power that needs to go to the vehicle is going to

Â be equal to the hydraulic power that's going to it.

Â And that will be the lowest pressure that will be operating at 17 and

Â half mega pascals multiplied by the flow rate and this is the flow rate that I'm

Â going to be sizing my Hydraulic Pump or my constant flow source at.

Â So in this case we have sized this Q as being 6.2 times 10 to the minus 4.

Â Cubic meters per second and again happens to be a number that doesn't make

Â a whole lot of since when we are thinking about cubic meters per second.

Â And if we convert this, this ends up being about 37 litres per minute, of flow.

Â And this will be again coming out of our pump motor unit.

Â 10:01

One thing I do need to mention before I jump to that,

Â is we have an additional flow source that we need to supply.

Â And this happens to be that our, our tractive motor,

Â even with reasonable efficiency, has quite a large amount of leakage through it,

Â and the leakage is fairly comparable to what we would actually size that, the,

Â the engine pump for initially for these.

Â For just the, the road loads.

Â And so based on this we hae to oversize this pump to take care of the,

Â the leakage losses that would be going on in this motor.

Â So, I just wanted to raise that before we jump onto the simulation.

Â So here's what the simulation looks like.

Â I'm going to jump over to sim hydraulics and

Â we can look at this maybe a little bit more directly.

Â So, now what I've got going on here in sim hydraulics,

Â the main components I want you to be looking at.

Â Is over here on the left side, I've got the pump, and this would be,

Â really be the engine pump that is driving the system, and

Â this is my constant flow source, so the flow coming out of his,

Â this is going through a flow sensor, so this is just measuring the flow.

Â Fluoride coming out of the engine pump and then I have a flow meter,

Â again going to a hydraulic accumulator so this is my energy storage device.

Â And then I have this going over here to attract a motor.

Â This is what's driving the wheels of the vehicle, so

Â here is the, the wheel unit that's converting.

Â By rotational domain into linear domain.

Â Linear mechanical and

Â then attached to my linear mechanical I've got a mass right here.

Â This is the mass of the vehicle and

Â then I've the road loads which are both the aerodynamic drag and

Â the rolling resistance and then I'm going to measure that and.

Â Convert it into a velocity that I can plot right here with the velocity output.

Â So that's the system and I've gone ahead and plugged in these values so

Â if you look at the tractive motor, you can see that I happen to have

Â the the displacement of 3 times 10 to the minus 4th cubic meters per round which

Â is very close to what we had sized it at, during our, our sizing just a moment ago.

Â Did the same thing for

Â the accumulator, the same thing for this hydraulic flow source.

Â And this happens to be where I'm placing the volume flow rate for that, for

Â that flow source.

Â So I'm getting a little ahead of myself because I'm starting to talk about the two

Â different control strategies here.

Â And so the first control strategy is simply,

Â how do we track the velocity that we want to be creating in this drive cycle.

Â So what I'm going to do is I'm going to take the velocity that my vehicle actually

Â has that I'm measuring here and I'm going to compare it with my drive cycles.

Â In this upper left here I've got two different drive cycles,

Â I can either switch from my sign wave or I can switch to an imput,

Â this happens to be the urba, urban dynamometer driving schedule.

Â I'll go back to my, my sign wave.

Â And so, this will be my input and in this summing block,

Â I'll compare that with what the actual velocity is.

Â I then just have a proportional controller, so I am applying some gain to

Â this and then that is going into the command signal of the tractive motor.

Â So that is the displacement control of this tractive motor.

Â So that's how I am controlling the motor or the speed of the vehicle.

Â Now, as far as the engine pump remember I'm using the,

Â the pressure in the system and so I take this pressure source right here and

Â my accumulator pressure is now being fed back to over here and I'm using this

Â relay to say when the pressure drops below a certain threshold turn on this flow

Â source when it gets above a certain threshold turn it back off.

Â And I'm cycling on and off.

Â And you can play around with this in, in your own simulation.

Â So let me first of all run this through the sign wave and

Â we can look at how this behaves.

Â 13:26

So, I will do that and here you

Â can see it tracking a velocity so on the lower right I've got the velocity.

Â The yell, the yellow happens to be my command.

Â The red or the magenta is the, the actual tracking, so

Â you can see I'm tracking that fairly well.

Â In the upper right you can see the motor command.

Â Where positive values are, you know,

Â positive traction and negative values are regenerative event.

Â And on the lower left you can see my accumulator pressure which is

Â varying with time.

Â And on the upper left, you can see the flow rate.

Â Where the yellow happens to be the flow coming out of my,

Â my engine pump which is this binary on off behavior.

Â And then the purple or the magenta is what's coming out of my accumulator.

Â Or in and out of my accumulator during energy storage events.

Â So that's how the system's going to operate with just a input.

Â Now let me go back and switch this over to the Urban Dynamometer Driving Schedule.

Â So a simple switch, and now I'm going to read this in from a file.

Â And now when I go ahead and run this, minimize this so you can see it moving.

Â Now you can see, on the lower left, my velocity is a function of time.

Â This is the driving schedule that we were looking at just a little bit ago.

Â And you can see, you know, much more aggressive behavior from what my,

Â my, displacement controller has to to do.

Â Where I have quite a few periods of regenerative events.

Â Which are causing the accumulator pressure to go up.

Â You can see the on/off behavior of my, my engine pump.

Â And you can see the, the flow going in and out of the accumulator.

Â So, a fairly dynamic interesting behavior here.

Â And what I'm going to encourage you to do in your homework,

Â is to explore this is a little bit more.

Â What happens is we change the parameters of these components as we

Â size them differently.

Â I just did a rough sizing in this case,

Â what if we start tweaking these a little bit?

Â Or what if we use a very different vehicle?

Â What if instead of a passenger vehicle, we use a large refuse truck?

Â And lets resize it for those types of situations.

Â So, with that said we looked at hydraulic hybrid vehicles from first of

Â all talking about various different architectures.

Â And then moved into, in this lecture, talking about how we

Â actually size the components and run a simulation of those using Sim Hydraulics.

Â Which then you can use to further explore how these vehicles behave.

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Â