IKnowNot'ing

This is a question addressed to all the rotary divinities, self-proclamed or not, of this forum.

I read in numerous places that the e/R (eccentricity over generating radius) is critical for proper operation of a wankel RE.

Can someone explain to me why it is so critical and what range should the ratio be in?

Also, does this critical ratio applies only on Rotary engines or any Wankel-based machinery (such as a compressor for ex.)?

Thanks,

IKN

tertou

I may be mistaken, but aren't e and R the determining parameters from where you can calculate the sizes of the epitrochoid chamber as well as the triangular surface of the rotor ?

As I understand, those pieces' curves are difficult to reproduce. And MAZDA probably has some expensive machinery to produce these curves, but with fixed ratios (It's just a thought, I don't know nothing, either ).
Hence the news that MAZDA might produce bigger rotor by only increasing their depth...

(I don't know why, but I'm guessing you're looking at getting more torque ? :D )

shelleys_man_06

Yes. e and R are important variables in creating the trochoid shape of rotary engines. The parametric equations the epitrochoid are as follows, in x-y coordinates -

x=e[cos(3a)]+R[cos(3a)]
y=e[sin(3a)]+R[sin(3a)]

The angle a varies from 0 to 360 degrees.

There's more on the way .

shelleys_man_06

To further answer why the eccentricity ratio is critical to performance, let's examine the equation for rounded-flank rotary engine displacement, which is

V=(3)[(3)^(1/2)]w(R^2)(e/R)

w is the rotor width
R is the rotor center-to-tip distance
e/R is the eccentricity ratio

Okay, now that we've settled this, let's look at the equation for power, which is

W[dot]=PVN

P is the brake mean effective pressure
V is the displacement
N is the angular velocity, or in layman's terms, revs.

If you plug in the original equation for V, you will notice that power is directly proportional to the eccentricity ratio (e/R). This means increasing (e/R) increases power, and decreasing it results in lower power (e/R), due to the change in displacement.

shelleys_man_06

IKN, since you have been such a good help to me, I will help you out . The eccentricity ratio determines the shape of the housing. It also determines the compression ratio. Eccentricity means that, for example, two circles that do not share the same center point. The rotor and shaft are eccentric to each other for rotary engines, like a spirograph. The eccentricity ratio applies to all Wankel rotary-type machinery, such as an oil pump, compressor, etc. The (e/R) range for flat-flanked (ideal) rotary engines is from 0 to 1/4. Why? Assuming an ideal rotary engine, the rotor housing clearance parameter, d, is given as

d=(R-e)-(e+R/2)=R/2-2e

d is actually the difference between the housing minor radius, R-e, and the distance from the housing to mid flank, e+Rcos60, which is e+R/2 (remember trigonometry ). Setting d=0, the equation goes to (e/R)=1/4, which is the critical eccentricity ratio, or (e/R)[crit]. Using the parametric equations I described above, one can realize that the lower limit for (e/R) is zero, or a circle.

Air Force RX8

Just when I thought I couldn't feel more stupid someone posts stuff like this and makes me feel even stupider...

shelleys_man_06

Don't feel bad friends. Sorry if the math isn't self-explanatory. We are here to exchange ideas. No one here is stupid .

tertou

A big thank Shelley's Man !
Now, I can go on with the math and picture it better :D

Charles R. Hill

iTrader: (7)

And, POOF, here is another mystery from my friend S.M. Since I don't have the machinery to make a whole new rotary design, I'll be happy with what I have. Thanks for giving me nightmares with the numbers, Shell.

Just kidding around,
Charles

shelleys_man_06

The parametric equations are only critical to the shape, and nothing more. Having an (e/R) of zero means that the two circles are concentric, a circular path; there is no compression, no displacement, no power. Math is fun :D.

09Factor

Hmmmm. I glad I know smart peeps to explain things like this.

shelleys_man_06

Oh yeah, I forgot. The 3 from the parametric equations comes from the fact that there is a 120 degree separation (the ideal rotor is actually a flat-flanked triangle).

bgreene

Hey shelleys_man,

In your equasions, the diplacement varies directly with e/R, and with R^2 (simplification of the formula would leave it varying linearly with both R and e).

Therefore, wouldn't the displacement - and consequetially, the power output - then increase when R increases but e remains constant (which would also reduce the ratio e/R)?

Of course, this ignores the real-world power that would be lost to spinning up bigger, heavier rotors......

shelleys_man_06

Don't simplify the equation, because then you would be missing the point of the eccentricity factor. You do make a valid point, because displacement is also proportional to power, which I already explained.

shelleys_man_06

The eccentricity ratio is a ratio between the eccentricity of the shaft with respect to the rotor center-to-tip distance. What do you get when you do simplify the equation for displacement? The result is

V=(3)[(3^(1/2)]weR

What does this equation tell us? It tells us pretty much nothing about what we are trying to find, which is the relationship between displacement and eccentricity ratio.

shelleys_man_06

Finally, before I go to Wal-Mart, here's a link that graphically explains what an epitrochoid really is.

http://mathworld.wolfram.com/Epitrochoid.html

Charles R. Hill

iTrader: (7)

Are you going to Wal-Mart to get a nitrous kit?

Charles

shelleys_man_06

It's pronounced, NOZZ :D.

shelleys_man_06

Since I am so fixated on this thread, I wanted to reply to this statement by saying that you are right. My equations are meaningless in the real world. There is a correction for this, through transient analysis, meaning it slowly decreases. In an ideal world, we could measure in steady-state from the equations, but since there is transcience involved, we could actually calculate, or at least accurately guesstimate power, torque, etc. But why go through all of the trouble? Trust me, it's not pretty, which is why we assume steady-state function. This makes plugging and chugging much easier .

IKnowNot'ing

Your formulae must be wrong. It's probably a typo. Just draw a few points to check, they should read something like :
x=e[cos(3a)]+R[cos(a)]
y=e[sin(3a)]+R[sin(a)]


All that you prove here is that power increase with Swept Volume, with intuitively makes sense. It does not help me optimise e/R as I can get any given Swept Volume (thus therotical power) with a wide range of different e/R ratios...

Here you're getting closer to what I'm looking for but you only define the absolute limits of e/R.
e/R = 0 gives you a round rotor rotating in a round housing. It's a bit like a piston engine that would have a given bore but no stroke.
e/R = 1/4 corresponds to a tringular rotor with absolutely flat sides.

Note that I have a formula that gives you the curvature radius of the rotor side that will give you complete sealing of the housing at TDC.

Also, any CR can be achieved by machining recesses within the rotor flanks. Although this CR explanation could be further investigated.

Remember the Renesis e/R ratio is 0.142857... which means that getting close to this value should give you a good Wankel IC engine.
But why?
And supposing I'm not interested in the design of a Wankel IC engine, but a Wankel compressor or another Wankel machinery, this 0.143 e/R ratio might not be optimal.

I was actually hoping someone who already know would answer the question fo me, in order to avoid to find it out by myself by a time consuming iterative process.

However, I really appreciate your help, Shelley

shelleys_man_06

Yeah. I fudged on the parametric equations.

IKnowNot'ing

I'll try three different e/R ratios for the same Swept Volume to see how it affects CR.

shelleys_man_06

Getting to that actual value for (e/R) is quite hard, well at least with the math I used. Where did you get that number from? It's pretty vague in a sense, that they just put it out like that without explaining why. That value for (e/R) is going to be different for different devices. From the formula, changing R has an effect on the eccentricity ratio. Changing e is also going to have an effect. They are dependent on each other. Also, I forgot to mention since the rotor moves in such a way that it touches the housing, those formulas I mentioned earlier, become

x=e[cos(3a)]+R{cos[a+(2n*pi)/3]}
y=e[sin(3a)]+R[sin(a+2n*pi)]

where n ranges from 0, 1, or 2, which defines the positions of the tips, which are separated by 120 degrees (almost like a triangle).

The eccentricity ratio can be found by dividing the parametric equations for the epitrochoid. How Mazda obtained the 0.143 is a design secret. You can try it out, since you already know the width of the 13B-MSP's rotor, 80 mm.

I forgot to touch on machining the rotor recesses to change the compression ratio. I think of it in terms of a dished and domed piston. Having a flat flank is obviously going to have a higher compression ratio than a recessed flank. The recess increases both minimum and maximum by the same amount, like the dish and domed piston. Also, rotor recesses help improve the shape of the long, narrow combustion pocket forming the minimum swept volume.

I would be interested in knowing why Mazda decided 0.143 as the optimal (e/R). Personally, (e/R) can only be found through experiment.

IKnowNot'ing

Here are the results of the variation of CR vs. e/R. Vs remains constant at 654cc (//Renesis). Renesis' Vrp (volume of 1 rotor pocket) estimated at 23cc. Other assumption, I calculated the CR as for a piston engine : CR = (Vs+Vch,min)/Vch,mi (Vch,min = min. comb. chamber volume).

e/R.............CR
0................67 ----- here, rotor and housing = circles
0.01...........16.3
0.05...........13.8
0.1.............11.5
0.12...........10.7
0.142857...10 ------- Renesis
0.16...........9.4
0.18...........8.9
0.2.............8.4
0.25...........7.3 ------- here, Ro (curvature radius of rotor surface) = infinite => rotor with flat flanks

However, with the rotor pockets allowing a wide range of CR anyway, there must be more than just a CR issue in this e/R ratio.

Or maybe is it just the Wankel equivalent to the also critical Bore/Stroke ratio of a piston engine?

shelleys_man_06

I'm as about as clueless as you are about other uses for (e/R). As far as I know, (e/R) determines the shape of the housing, displacement, compression ratio, and performance.