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

system specifically, a series system for a given application.

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

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

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

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

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

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

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

the major components in my series hydraulic hybrid system.

And the major components being first of all the pump.

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

driving the wheels of the vehicle and finally the accumulator.

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

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

other things going on in the system.

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

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

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

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

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

And this is a velocity plot versus time.

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

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

it's all flat terrain.

But you can see it accelerates and decelerates.

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

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

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

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

This would be our energy storage device.

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

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

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

energy from a 20 meter per second breaking event.

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

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

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

going to act isothermally.

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

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

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

expanding that gas.

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

Why you ask?

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

the accumulator part of the class.

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

35 megapascals, 5000 psi.

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

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

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

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

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

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

we can plug in those numbers.

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

the energy storage in an accumulator is the pressure.

The charge pressure of my accumulator times the volume of

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

So because I'm assuming at isothermal compression,

my pressure ratio is equal to my volume ratio.

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

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

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

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

the volume of my accumulator at 0.03 cubic meters.

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

How big is this?

Well, this happens to be 30 liters of volume.

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So 30 liters of volume.

Obviously, a lot larger than this.

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

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

So again, storing this, this storage vessel or

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

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

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

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

So storing all of this fluid in the vehicle and

the storage device is not trivial.

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

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

So we size the accumulator.

Now ,let's goto the tractive motor.

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

And now, I'm going to size this for

the peak acceleration even that occurs in that drive cycle.

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

said what is the maximum acceleration.

And it happens to be 1.5 metters per second squared.

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

breaking if you will.

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

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

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

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

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

driving the wheel, one wheel of the vehicle.

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

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

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

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

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

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

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

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

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

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

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

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

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

driving the wheels of the vehicle.

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

Cubic meters per revolution.

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

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

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

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

So that would be a little more reasonable, or

maybe we might have two of them driving.

Left and right rear wheels or

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

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

take care of the engine pump.

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

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

decouple the engine from the wheels.

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

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

Condition, excuse me.

Or completely off.

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

which is dictated by the pressure in the accumulator.

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

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

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

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

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

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

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

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

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

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

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

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

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

neglect inefficiencies in my system.

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

So first of all the aerodynamic drag,

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

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

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

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

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

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

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

a rolling drag, if you will.

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

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

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

call that the drag force overcomer, the road load.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

the engine pump for initially for these.

For just the, the road loads.

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

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

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

So here's what the simulation looks like.

I'm going to jump over to sim hydraulics and

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

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

the main components I want you to be looking at.

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

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

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

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

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

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

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

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

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

By rotational domain into linear domain.

Linear mechanical and

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

This is the mass of the vehicle and

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

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

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

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

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

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

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

Did the same thing for

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

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

that flow source.

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

different control strategies here.

And so the first control strategy is simply,

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

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

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

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

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

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

I'll go back to my, my sign wave.

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

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

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

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

So that is the displacement control of this tractive motor.

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

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

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

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

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

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

And I'm cycling on and off.

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

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

we can look at how this behaves.

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So, I will do that and here you

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

The yell, the yellow happens to be my command.

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

you can see I'm tracking that fairly well.

In the upper right you can see the motor command.

Where positive values are, you know,

positive traction and negative values are regenerative event.

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

varying with time.

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

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

my engine pump which is this binary on off behavior.

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

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

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

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

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

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

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

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

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

my, displacement controller has to to do.

Where I have quite a few periods of regenerative events.

Which are causing the accumulator pressure to go up.

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

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

So, a fairly dynamic interesting behavior here.

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

is to explore this is a little bit more.

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

size them differently.

I just did a rough sizing in this case,

what if we start tweaking these a little bit?

Or what if we use a very different vehicle?

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

And lets resize it for those types of situations.

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

all talking about various different architectures.

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

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

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

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