# Belt drive with elliptical cog wheel?

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#### floridapilot1

##### Active Member
Supporting Member
As we know most of the time a 4 stroke engine is driven by the flywheel. In a 4 cylinder there are 2 power strokes per revolution which keep the thing running – and give rise to the omnipresent torsional vibrations.

They might be greatly reduced in a belt drive by using an elliptical (e.g. primary) cogwheel at no expense except for the production process being more sophisticated. The trick is to compensate the higher rotational speed during the power stroke by a (very slightly) smaller leverage arm aka wheel radius at that phase of rotation. This will smooth the velocity of the belt and the prop shaft.

Consider a setting with an additional fixed deflection pulley on the tension side of the drive and a springy belt tension pulley on the return side to compensate minor variations of carbon backed belt length (see Honda B20B Belt PSRU)

Now think of a flat belt and do a first gedankenexperiment:
Imagine that on the elliptical cogwheel the arriving and departing belt fully encloses the cogwheel, 360°. When you now rotate the cogwheel all the elliptical circumference is in use, the total circumference of the belt is constant at all times (even no need for compensation by springy tension pulley).

Now the real situation:
With the two idle pulleys on the backside guide the belt in such a way that arrival and departure leg run parallel. For symmetry reasons that means that only half of the cogwheel's circumference is in use while the other half is free – all the time, almost constantly. Again “constant” belt circumference.

“Almost” means that there are minimal variations given by the fact that during revolution the effective diameter of the ellipse varies for some per mill – therefore the springy second idle pulley.

By the way, it need not be a mathematical ellipse: the shape could be adapted to the nature of the power pulse and the inertia of engine and prop side. All what is needed is 2fold symmetry.
For timing belt drives this could be a viable way to reduce driving forces for torsional vibrations using appropriate mean values for the power range in use. Production of the grooves might be more complicated, but viable.

I am aware that I am surrounded by most competent specialists here. Critics, ideas and comments are welcome.

Richard

#### Dana

##### Super Moderator
Staff member
Interesting idea. I'm not sure how it would work out in practice and it could be very difficult to work out the exact geometry as the speed variation trails the torque variation by some amount, which will vary depending on power setting and propeller load. Since the geometry is fixed, it might actually work under some conditions but make it worse under others (like when the prop is windmilling)... or it might not.

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Supporting Member
Accelerating and decelerating the mass is not as simple as an ellipse. In the end the belt has to be sized to take all that impulse. Drive side and slack side (which sorta happens on both sides alternately due to prop inertia) tensioners that are tuned to the worst pulses are could work well to tune and soften a belt system against TV. A cog belt system can probably be designed to work without but the tension required is going to make it pretty stiff. The mass of the prop can be damaging to the system.

Just as a datapoint some engines use an off center rotating mass to offset TV problems. They call them balance shafts. Same idea as you are describing but a different approach. Swing the mass in some opposite part of the timed stroke to offset the swinging of the rotating assembly. Single blade props with counter balances are a similar but simpler idea.

Billski is the vibe expert here. I think all the harmonics aren't as simple as tuning one RPM.

#### wsimpso1

##### Super Moderator
Staff member
First thing to remember is that piston engine design, dealing with firing pulses and imbalanced loads and vibrations from them have been around for over two centuries ( before gasoline piston engines, there were steam piston engines). Literally millions of smart folks have studied the problems, estimated the magnitudes, and tried out solutions to all this stuff. I don't expect anyone will figure out a new simple solution as we near the sunset of the piston engine... Almost everything that works was found early on while orders of magnitude more ideas were found wanting.

So on to why this guy's idea may not work so well.

Look at the height of the curve at peak and trough - that is ratio of pulley radius you would need, properly timed to null out the torque variation. At max power and cruise power these would be large changes in cog belt radius, not small ones. Epi-eng.com has a great discussion on vibration.

How high is it? In a four with manifold pressure close to sea level, instantaneous torques go from above twice the mean torque to seriously negative torque twice per turn of the crank. V8s go from around twice mean torque to around zero and back again. So our cog pulley geometry would get interesting indeed to accommodate this torque pattern. How does one make a sprocket with these huge swings in radius?

The shape and position of the peak and ratio of peak to trough height all change substantially with manifold pressure and rpm, so this scheme requires picking the operating condition for matching. Let's say we select max power and we somehow succeed in taking off firing pulses, then reduce power to about 25% for descent. Peak to trough ratio is now about 25% as big, but now we have a vibration that is 75% of Full Power with peaks in the negative direction. Where is the torque coming from? We are retrieving energy stored in the single largest flywheel in the system, the prop, through our varying gear ratio set. In addition, the torque peak no longer matches the position in the cycle, so we now have a sharp decel from gearing offset from the firing accel that behaves as a much higher frequency input that we must now also handle . The character of this input also varies with manifold pressure and rpm.

Then there are the 2x firing vibes. These are due to the pistons accelerating back and forth in the bores and bottom and top halves not being the same (crank and rod geometry). This is always there, and accelerations from it peak at about 1/4 of peak firing (assuming normally aspirated gasoline engine) and we are not doing anything about them here, but they too must be accommodated.

If one were running a genset at only one power setting, and gearing matched vibe for that setting, it might be OK. The rest of the world (not just airplanes) has to accommodate everything from low to high rpm and low to high torque, with both variables operated independantly. And so does even this scheme because you have to start it, run it up to speed, back down to shut off, and not have it tear itself apart in the process.

Now maybe the OP author can come up with insights that support a workable scheme. One of the best I know of is the electric damper. With an electric motor and computer controlled power electrics, you could generate in the power pulse and put power back in during the rest of the cycle. At firing peak, the electrical power requirement is around 8 times engine power. Yep, a 125 horsepower engine requires around 1000 horsepower electric motor, power electronics and capacitance for storing the power picked up from firing. That makes electric powertrains and their current batteries look compact and light. Torsional springs and engine side inertia both selected for the engine and prop needed are pretty good schemes...

Billski

#### jedi

##### Well-Known Member
Just as a datapoint some engines use an off center rotating mass to offset TV problems. They call them balance shafts.

FWIW - I believe the balance shaft is to counter the side to side (90 degrees from piston motion) in single cylinder engines and the rocking motion in multi cylinder engines, not the torsional vibrations.

From a conceptional point it may be a little more intuitive to think of it as a chain and sprocket rather than a cog belt. There have been bicycles that use an elliptical sprocket to smooth the pedal pulse of the cyclist. I have never found the chance to ride one so I can not comment on the effectiveness but I found the concept interesting. I have not seen any of those bicycles in recent years so that may tell you something.

I would be curious to know if they have survived in the marketplace. The market place is a cruel place indeed. Even many of the good ideas do not survive for one reason or another.

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#### TFF

##### Well-Known Member
It’s an interesting idea. Can’t comment on how it will work.
On the hardware side, nothing will work off the shelf. You can make something that will run at 10 rpm without effort. 2500 rpm of an engine or more, no way. Belts are way too stiff and would never track without super high tension pressure. That in its self turns into a lot of drag and a lot of structure, so it doesn’t cave in. It’s going to be heavy. Belts also do not like sharp turns, they will weaken in those places pretty quick.

#### floridapilot1

##### Active Member
Supporting Member
After these well – founded comments I think I can end this path which originated from a constant rpm – frog perspective.

My idea came up when I discovered a Volkswagen description of their new engine 211evo series.
They use this concept for camshaft drive with a toothed belt claiming some 200000km life expectancy – which is quite good for a timing belt.
It seems to work in an automobile environment, although there is also windmilling and even engine braking.

I have read epi-ing.com some time ago and followed all the Billski discussion - which both was highly interesting.

@Billski:
One thing I internalized for reduction drive arrangements is that the direction of power flow engine - prop must not change with each single revolution – in contrast to direct drive aircraft engines.
That speaks in favor for high moment of inertia of the engine flywheel, low for the prop and a guibo thing selected for first order resonance resulting in between crank and idle rpm. Sonny Furman uses a clutch plate with its inbuilt small steel springs which seems to work.
For me to learn: Why not use a dual mass flywheel with more powerful springs which has a much greater operating range than a normal clutchplate? Admittedly it is heavier than the rubber connector, however mostly contributing to the engine side.
Could a 3blade variable pitch prop 4kg / 2600kg*m² change things?

@jedi:
In a museum in Austria I have seen an old bicycle with a 4 link mechanism for the same purpose. I could ask the owner about it. His explanation is equivalent to your observation: the availability of (chain) bike gear terminated that development.

Thanks a lot

Richard

#### Aesquire

##### Well-Known Member
Shimano had semi- elliptical front sprockets on bicycles years ago to "smooth out the power strokes". Quite the far for a while.

If badly done, it hurt you.

If it was a world beater I wouldn't be the only person I see on the trails with mine.

#### wsimpso1

##### Super Moderator
Staff member
My idea came up when I discovered a Volkswagen description of their new engine 211evo series.
They use this concept for camshaft drive with a toothed belt claiming some 200000km life expectancy – which is quite good for a timing belt.
It seems to work in an automobile environment, although there is also windmilling and even engine braking.

First things first. Required reading before you get too far afield:

I am getting the impression that you believe we are treating PSRU as unsolved. Not so. PSRU have been around a long time. The inline and radial engines of WWII were almost all geared engine. There have been production engines for light planes - ever hear of a GO-480 or others? The G prefix means geared. There are a bunch of planes flying successfully with some sort of spring isolators between engine and gearsets. Autoflight, Marcotte, EPI, AeroMomentum are all examples of successful geared systems with a soft element.

My idea came up when I discovered a Volkswagen description of their new engine 211evo series.
They use this concept for camshaft drive with a toothed belt claiming some 200000km life expectancy – which is quite good for a timing belt.
It seems to work in an automobile environment, although there is also windmilling and even engine braking.

I looked, and the VW mentioned uses a cog belt drive for the cams, but that is neither unique nor a lifetime solution. Cog belts with lives only a little shorter than that fell out of favor a while ago - customers hated them - but have been coming back. Lifetime in a car engine usually means 90% whole engine reliability past 150k mile/250k km. Each system gets their own part of that pie, so systems usually need to aim for mean lives of 500k to 1M miles. If VW is claiming lifetime parts with replacement every 200,000 km, they are regressing.

The German language stuff posted in out of reach for most of us on here. I even tried to cut and paste it to a translater, but the post did not let me copy the text. The pictures clearly show a modest radius change, 3 per rev for the three cylinder and 2 per rev for the four cylinder. I suspect that this lowers the forces in the cam belt a little, allowing the pieces to be lighter. Tough to say without a translation of the page posted.

@Billski:
One thing I internalized for reduction drive arrangements is that the direction of power flow engine - prop must not change with each single revolution – in contrast to direct drive aircraft engines.

Not getting you here. In a four cylinder engine, torque at the crankshaft is typically recognized as going through two positive torque, negative torque cycles per revolution. once you get an isolation spring between engine and downstream components, the torque becomes continuous with a greatly reduced oscillating ripple superimposed. This can be in either positive or negative torque directions.

That speaks in favor for high moment of inertia of the engine flywheel, low for the prop and a guibo thing selected for first order resonance resulting in between crank and idle rpm.

Not really available in driving airscrews. Generally speaking the prop is by far the biggest inertia in the system, with nominal engine/flywheel inertia being much smaller, and the gear set/cog set is much lower again. Two ways exist to make all of this work:

Stiff System - Really stout shafts, gears, bearings, cases, light flywheel on the crank, low lash everywhere. The system has to push lowest natural frequency 2-1/2 octaves above highest firing rate while having tiny lash to keep impact loads on the splines, gear teeth, bearings, etc reasonably small. The entirety of firing pulses are fed through the driveline, and even the prop sees those pulses. This is usually kind of heavy...

Soft System - Put a spring between flywheel and the rest of the system. To be successful, the first natural frequency of the system must be at least an octave below firing frequency at lowest operating speeds. The engine oscillates, and a tiny bit of firing frequency ripple makes its way through to the rest of the powertrain. This is most of how it is done in cars/trucks, and even those big V-12's from WWII. This tends to be the light way to do things, but it does have to be engineered.

Lash is to be avoided because impact excites all sorts of vibrations while raising the loads on the parts. Lash at firing order is nicely avoided in soft systems. Lash is also nicely avoided with rubber springs. When running a prop, torques are low at low rpm, and rise with rpm squared. Rubber springs tend to be soft near zero load, and stiffen up as torque rises. Rubber springs are used in a number of PSRU, either rubber donuts or giubos.

Sonny Furman uses a clutch plate with its inbuilt small steel springs which seems to work.
Yeah, that is a soft system, like we use in cars, trucks, etc. I searched and all I found was a VP of Linked In and some sales executives. Please provide a reference so we can look at the drive mechanism you are talking about.

For me to learn: Why not use a dual mass flywheel with more powerful springs which has a much greater operating range than a normal clutchplate? Admittedly it is heavier than the rubber connector, however mostly contributing to the engine side.

DMF's are heavy. Say this with me: WEIGHT IS THE ENEMY. DMF's have long very low rate springs with a lot of friction, even statically, and many coils become firmly grounded and ineffective as rpm builds, which raises the effective spring rate hugely as we get to flying rpm. They can be used in airplanes if you can find one that maintains a low enough effective spring rate at flying rpm. They are heavy and things like giubos and clutch hubs tend to give the needed spring rates at much lower weight.

Could a 3blade variable pitch prop 4kg / 2600kg*m² change things?

It might. What are you trying to change? I wish we could run a 200 hp engine on a prop lighter than 20 kg. As I said above, props are the big inertia. To understand soft systems, you usually model them as two masses with a spring between them, then excite one of the masses. That is the crankshaft and flywheel, the prop is the other inertia. Making the two masses of similar inertia allows lighter springs, and letting the prop get heavier, requires lower spring rates, which when built to the same torque capacity, get heavier. Since weight is the enemy, lighter props is good, and we rarely see anyone adding inertia to the flywheel, we find springs with lower spring rates and enough torque capacity instead, as it is lighter...

Billski

#### AeroER

##### Well-Known Member
Sounds like "brake shoes" with fly weights and springs. Probably dampers, too.

Maybe mounted to a round or ellipsoid pulley with the drive belt.

Or with cams that expand that expand the drive pulley or allow it to relax.

Or, exploit this idea -

A fractal pulley Just Takes Money.

#### D Hillberg

##### Well-Known Member
What are you running a lawn mower engine with one piston?
Firing pulses x number of cylinders and RPM........Chitty Chitty Bang Bang

#### wsimpso1

##### Super Moderator
Staff member
Could a 3blade variable pitch prop 4kg / 2600kg*m² change things

I just read this again. something that weighs 4 kg but has 2600 kg*m^2of inertia would be impressive indeed. Radius of gyration would be sqrt(2600/4) = 25.5 m! That is 9 pounds at a radius of 80 feet for you non-metric types... I suspect a slipped decimal point someplace.

Billski

#### sming

##### Well-Known Member
That's the weight of the latest variable pitch e-props for rotax (I starter a thread here without much success. I thought it was amazing!) You should ask them one for 200HP, I'm sure they would be thrilled with a beta tester of your caliber

#### floridapilot1

##### Active Member
Supporting Member

Your impression is correct: I had followed an old thread of commercial gear redrives for Subaru engines from Florida, and the Thielert story gave a drastic example to me (both of which seem to be solved by now).
I was focused on a belt redrive of the style Geraldc mentioned in
Honda B20B Belt PSRU

As I discovered the VW story in
https://www.motor-talk.de/forum/aktion/Attachment.html?attachmentId=736094
I thought that's it! As the German text is embedded in a .jpg file I will translate it:

3cylinder engines: tri-oval thoothed wheel on the camshaft:
For opening the valves a certain amount of force is necessary. At each opening action this force acts on the valve drive and leads to vibrations at higher rotational speeds. To minimize these vibrations which are typically strong in 3-cylinder engines special toothed wheels are implemented on the camshaft. They have an increased radius at an angular distance of 120° (tri – oval).

4cylinder engines: oval CTC crankshaft – toothed wheel:
The 4cylinder engines have a so-called CTC crankshaft toothed wheel. CTC means Crankshaft Torsionals Cancellation. During the power stroke the driving belt will be slightly relaxed by a smaller radius. This reduces the tension forces and torsional vibrations of the belt drive.

The reduced forces on the toothed belt drive allows a reduction of the belt tension wheel force.
This leads to lower friction and reduced mechanical load of the whole drive.
The reduced vibrations mean a smoother operation of the belt drive.

Nothing new for you except for the placing of the cog wheel in the camshaft location for the 3cylinders. I might again speculate that they only aim at a partial compensation of the power stroke pulses as a compromise - say some 25%.
Concerning the DMF I was not aware that they are so heavy. From my car repairs I did in youth I remember that those springs mounted on the clutch plate are really small. While there is no real lash I would speculate they are fully compressed most of the time. On the other hand, the rubber elements are light, robust and in addition tolerate a certain misalignment.

My bad that I did not discover the typo in the original French page discovered by sming too:
E-props
It is based on the differences in decimal point in decimal comma in English compared to the rest of the European countries:
2.600 kg*m² for 1,70m diameter in adjacent lines on that site...
Of course 2.6 kg*m² is correct for USA – as you easily noticed.

One last question: for a soft system with adequately dimensioned rubber element my understanding is that in normal operation the torque to the prop remains positive at all times despite of fluctuations caused by trans vibes, that means the engine side on compression stroke lives from its own inertia / flywheel energy?
Can I keep this for valid?

Thanks again

Richard

#### wsimpso1

##### Super Moderator
Staff member
So, VW is attempting to reduce the torque from opening valves and maybe improve torsional vibe? Hmm. Torque from valve opening shows up between engine firing pulses, along with and smaller than the 2xfiring pulses from pistons moving up and down. Valve opening torque has a fixed part from spring compression and a speed varying part from valve mass (increases with square of rpm). So they can not fully compensate for it. Since it coincides with the larger and unavoidable 2x firing pulse train, I doubt the effect on NVH is even noticeable.

To apply this to firing pulse mitigation - no, firing pulse variation is HUGE. In even fire V8's, NA WOT pulses go from around zero to twice mean torque. Fours swing much more than that. Making the cog wheel radius compensate for that just can not be done.

On the prop, yes, moving the decimal point three places left would make for a much more reasonable radius of gyration. 4 kg is pretty light for a prop. What engine can you run with that? An 8kg flywheel would be about 0.08 kg-m^2 or about 1/30 as big as the prop cited. Even if all the rest of the engine internals doubled the inertia of that flywheel, we can easily see that the prop is big inertia compared to the engine.

Understand that resonant frequencies go up and down with square root of k/m, where k is the spring rate and m is the inertia. Increase prop inertia and frequency goes down. Lighter props raise the frequencies, so if you are building a soft system, lighter props mean you need still lower spring rates.

Also, there is such a thing as too low 1st order vibe. You have a firing order in cranking that you really should avoid too. Ideal frequency is about the same number of octaves below idle firing frequency as it is above cranking firing frequency. You do not resonate cranking, and you do not resonate idling, and you hopefully shoot right through resonance during start and shutdown.

When one builds a soft system (springs between flywheel and gearset) the engine/flywheel are vibrationally isolated from the prop, so the flywheel does have to be adequate to run the engine by itself at whatever idle speed you end up with. Specifically, AeroMomentum runs a faster idle speed than they would otherwise have liked. The trade was more flywheel weight or a higher idle speed, they raised the idle speed rather than add weight. Could they have applied a soft spring? Sure, if one was available. Their soft element is a giubo from driveshafts of existing rear wheel drive cars. They pick from what is available...

Billski

#### wsimpso1

##### Super Moderator
Staff member
One last question: for a soft system with adequately dimensioned rubber element my understanding is that in normal operation the torque to the prop remains positive at all times despite of fluctuations caused by trans vibes, that means the engine side on compression stroke lives from its own inertia / flywheel energy?

Yes. When the forcing function is substantially faster than the natural frequency, it is said to be isolating, and you get mean torque plus a ripple that is usually pretty modest compared to the mean. When we run a prop, the prop drag, even at idle, is usually large enough to keep us in positive torque all of the time. The further the firing frequency is above resonance (in octaves) the better we isolate. This is a soft system.

When the forcing function coincides with natural frequency, the system is amplifying. Match them perfectly and it amplifies big. The engineering world tries to avoid this in mechanical systems. In electronics, this is an amplifier.

Third case is when the forcing frequency is substantially slower than the natural frequency. This is essentially static load case, and every bit of vibe in the forcing end goes through the whole system. This is a stiff system.

Funny thing about all of this is that the math is identical between mechanical forced vibration and AC design for amplifying and filtering.

Billski

#### floridapilot1

##### Active Member
Supporting Member
Billksy, thank you again for your clear categorization in our latest post which confirms my physical understanding. It is all about preventing the resonance catastrophe coming from one or the other direction.
Your comment to the Volkswagen argument shows me that the knowledge of the author is different from yours...

To apply this to firing pulse mitigation - no, firing pulse variation is HUGE. In even fire V8's, NA WOT pulses go from around zero to twice mean torque. Fours swing much more than that. Making the cog wheel radius compensate for that just can not be done.

At that point I still have a problem of understanding: Yes, the firing pulse is huge, but it is damped by the integration effected by the flywheel. As a result the rotational speed is only slightly higher after the power stroke. Might that not give a chance to compensate for by the elliptical solution, albeit not for the whole engine operating spectrum, but for some 25% baseline?
Admittedly to work out such a compromise for a single homebuilt configuration would be hypothetical...

Last, but not least:
I have to apologize: I was wrong with the cited Rotax prop's MOI: I have looked once more , it is 2600 kg * cm² !!

Richard