# Belt Drives and design

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#### plncraze

##### Well-Known Member
HBA Supporter
The Geo intermittent torque can hit large numbers. Geo engines with a poorly designed reduction drive will eat a belt. I found a tech paper for a study that tore up some cog belts from the same manufacturer as mine. Unfortunately the belt they used had fiberglass reinforcement and mine, I believe, is Kevlar.

#### TFF

##### Well-Known Member
From maintaining helicopters with belt drives, one thing I know is they have to be adjusted to be just about perfect and stay perfect.

One version I work with has to run parallel top to bottom to .010” that one has a tensioner with a spring. The other is just drive and driven pulleys and it is less than .003”parallel and less than .005” side to side. Of course perfect is best.

If you can’t keep it straight, you will jump belts or stress one side and it will shred.

#### dog

##### Well-Known Member
From maintaining helicopters with belt drives, one thing I know is they have to be adjusted to be just about perfect and stay perfect.

One version I work with has to run parallel top to bottom to .010” that one has a tensioner with a spring. The other is just drive and driven pulleys and it is less than .003”parallel and less than .005” side to side. Of course perfect is best.

If you can’t keep it straight, you will jump belts or stress one side and it will shred.
What you describe suggests that any belt drive design must have an adjustment procedure/verification built in from the start. And that if possible, nice round numbers built in for initial belt tension and parallelism.

The numbers that you provided also suggest that pulley wear will contribute to tension and alignment being out of spec.

Another point is that a failure to get belt alignment in the range you suggest as a minimum could likely contribute to vibration issues that would be indistinguishable from TV or other types of vibration, and so again the ability to check alignment and tension easily is almost mandatory.

#### TFF

##### Well-Known Member
Adjustment on the idler setup is through the tension of the spring that pulls the idler and the manufacturer has a measurement of compressing the spring. The other is expanded until the tension is made. The manufacturer has a tensiometer that is a recalibrated cable tensiometer and the average running number is 2500 lbs. That’s all I can read into it. As you go through the procedure, you can feel that tightening the belt is sucking horsepower. I bet there is 4-5 hp lost. I always forget to stick that tool on the other for grins. Horsepower is 225 and 308. Belts are similar about 2 1/2 foot center to center and 9” wide. Ribs longitudinal 1/4” spacing.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Interesting discussion. I am learning form it. Natural frequencies can be figured out by modal analysis (eigenvalue calculations), but for that to be realistic one MUST know the elasticity of the belt. The method suggested by AdrianS can generate at least rough elasticity data. I do not know if the belt elasticity is linear.
As Billski mentioned one can not base belt sizing on mean torque. Designing a reduction for a piston engine is far more challenging than designing for a turboprop, because piston engines have intermittent torque. The peak torque can easily be two to three times higher than mean torque. Therefore the design must take into account those peak torques. Additionally, intermittent torque means cyclic loads - which produce fatigue. That must be taken into account too. I do not believe that belts are much fatigue-prone, but I would look into it anyway.
Another point related to belt reduction is the temperature effect. If the subject aircraft is to be flown in summer and winter at altitudes up to, say, 15000ft, then it is something the designer must check, to evaluate the need or not of a belt tensioner (hydraulic or mechanical).
The interesting thing about belt drives is that most do not include a deliberately "soft" element. Maybe the belt is torsionally softer than the other parts, but I would not count on it. Do the work and find out, then apply the info to your analysis. If no element has a lot lower spring rate than the rest then inertia and springiness of the assembly really must be included. This is easy if you have most of it modeled in a CAE system that includes a dynamic solver for assemblies. This is applied to the crank, bottom pulley, belt (tension side only) top pulley, and output shaft.

Belt springiness and weight will probably have to be determined by test and an elastic element modeled and run between top and bottom pulleys on the tension side of the system. The belt section between the pulleys should match on density, weight, and springiness of the real thing. While the springiness of the belt may not be strictly linear, it is usually modeled as linear at the belt tension expected for torque expressed at RPM. If the load vs deflection plot has much curve to it, you will want to do runs at low, medium and high torque, knowing the rpm-torque relationship of your prop (fixed pitch). If you are running a constant speed prop, you will have a range of RPM and torque to cover, but that still only means five runs of the Eigen solver - low-low, low-high, high-low, high-high, and med-med - that will give a pretty good map of resonance frequencies and modes.

Another potentially significant spring is the shafts the pulleys are hung on - When cantilevered, these shafts can be particularly springy, and this scheme is used on small V-twins and the like. When you get into fours and auto engines, the tendency is to support both ends of each pulley, and that will be significantly stiffer than cantilever shafts.

The last element is the prop. Bifilar pendulum to get the inertia, and then model a disc or bar to get the same weight and MMOI to use as the "prop".

In dynamic modeling of this sort, the parts are usually modeled simplistically - no splines, no teeth on the belt or pulleys, little of the real part's detail is included.

Billski

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#### galapoola

##### Well-Known Member
Here's a belt drive 101 question, how do the belts on my tractor cutting deck deal with all these pulse issues? It has two mini propellers bouncing over my uneven lawn, hitting stuff and becoming unbalanced over time. The engine does not have a heavy flywheel. It seems to work with single and v-twin engines that I've had.

#### plncraze

##### Well-Known Member
HBA Supporter
My bet is that it slips. That combined with low inertia blades means that the engine dominates all the other spinning masses. There is also a balance weight inside the engine too.
In regards to the soft element in belt drives Raven used a dry friction element, a clutch, in their Geo Metro reduction drives and said it would last without it. I never could find a picture of it and it is not shown in their manual. I am just going to use a clutch friction element in mine.

#### dog

##### Well-Known Member
Adjustment on the idler setup is through the tension of the spring that pulls the idler and the manufacturer has a measurement of compressing the spring. The other is expanded until the tension is made. The manufacturer has a tensiometer that is a recalibrated cable tensiometer and the average running number is 2500 lbs. That’s all I can read into it. As you go through the procedure, you can feel that tightening the belt is sucking horsepower. I bet there is 4-5 hp lost. I always forget to stick that tool on the other for grins. Horsepower is 225 and 308. Belts are similar about 2 1/2 foot center to center and 9” wide. Ribs longitudinal 1/4” spacing.
From that I get that the belt is carrying 30 some HP an inch and is tight enough that it
is deforming at the pulleys which provides the friction nessesary to transmit the power at the
cost of 1 to 2 % of the total power lost in heat.
Your first hand account fits nicely with the numbers that are generaly quoted for such systems,but is much easier for me to visiualise

TFF

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Here's a belt drive 101 question, how do the belts on my tractor cutting deck deal with all these pulse issues? It has two mini propellers bouncing over my uneven lawn, hitting stuff and becoming unbalanced over time. The engine does not have a heavy flywheel. It seems to work with single and v-twin engines that I've had.
Lawn mower belts are usually pretty long, which can make for pretty low spring rates, driving first resonance frequency low. Then you usually do not engage the clutch at low rpm, so it becomes a soft system at higher rpm, nicely isolating the engine vibe from the bladeset. Ideally that resonance is below idle speed, but if it is up near or a little above idle, so what? Relatively little energy is available there (Blades absorb power same as a prop does, with torque required correlated with rpm^2, and power required with rpm^3, so the low speed end is at really low power), so it is unlikely to get in trouble down low. And then if it does resonate, the belt can slip and the idler reduces feedback on the coast side of the firing pulse. Then most of us only engage the mower deck at higher rpm because you can kill the engine doing the engagement down low, and many of the manufacturers run min engine speed pretty high on mowers.

How is the mower different from the airplane? Props are usually a lot bigger than the mower blades; Belts are much shorter on the airplane, inches vs feet on the mower; The idler is spring loaded instead of hard adjusted or not present at all on PSRU; Mower engines really do have a bunch of flywheel for the size of the engine. So, going to a much shorter belt drives up stiffness and raises resonance rpm, the prop has a lot more MMOI from having more diameter (MMOI goes with weight and diameter^2) making it higher inertia than the mower which can drive down resonant frequency, and the hard belt arrangement that is commonly used in PSRU let's the vibration feedback over power strokes and coast strokes between power strokes.

I have not modeled a belt PSRU because I have other stuff important to me, but if any of you want to know how big each effect is, doing some measurements and some analysis will tell you a lot. And I am offering to look at your models and data if you like.

Billski

#### Martin W

##### Active Member
Most builders and manufactures will obviously use a straightedge on the sprocket face to make sure both sprockets are aligned parallel (eg: vertically) (one above the other)

But they also must be carefully aligned parallel (eg: horizontally) with zero angular difference from the output shaft to the driven shaft.

This is critical and often overlooked .

By design the Gates tooth belt has no stretch .... so if sprockets are not parallel the outside edge carries most of the load (overloaded) and the kevlar cord begins to break and fray .

Operators mistakenly blame the small flange on the outside of the sprocket for causing the edge wear .... because that is what it looks like at first glance but 90% of the time it is an angular misalignment.

.

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##### Well-Known Member
Regarding belts and torque pulses - the standard cog belt used in OHC cam drive sees a noticeable torque reversal as the cam rotates.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
By design the Gates tooth belt has no stretch ....
Untrue two different ways.

Those Gates belts may feel like they do not change length under load but I have news for you: ALL solid materials have a stress (load per unit area) vs strain change in dimension per unit length) relationship that is usually linear and completely recoverable (elastic). The slope of stress per unit strain is Young's modulus in tensile loading, and Shear modulus in shear loading. Young's modulus can be very low (plastic foams have a Young's Modulus of in hundreds to thousands of psi) to very high (tungsten carbide is around 80 Mpsi). Steel is 30 Mpsi, while Kevlar fibers range from 6-10 Mpsi, or is about 20% to 33% as stiff as steel.

Then the rubber tooth belt form molded over the Kevlar cords is much softer than the cords, and does deform in shear as it is loaded.

The total result is that the belt will have a finite and measurable deformation vs the load applied. If some one can tell me the detail geometry of cord and rubber, as well as length between sprocket contact points, I can compute a pretty good estimate of just how springy the belt is. Add in mechanical deformation of the sprockets and shafts, and we have pretty good idea of spring rate of the PSRU.

Billski

#### Martin W

##### Active Member
Untrue two different ways.

Those Gates belts may feel like they do not change length under load but I have news for you: ALL solid materials have a stress (load per unit area) vs strain change in dimension per unit length) relationship that is usually linear and completely recoverable (elastic). The slope of stress per unit strain is Young's modulus in tensile loading, and Shear modulus in shear loading. Young's modulus can be very low (plastic foams have a Young's Modulus of in hundreds to thousands of psi) to very high (tungsten carbide is around 80 Mpsi). Steel is 30 Mpsi, while Kevlar fibers range from 6-10 Mpsi, or is about 20% to 33% as stiff as steel.

Then the rubber tooth belt form molded over the Kevlar cords is much softer than the cords, and does deform in shear as it is loaded.

The total result is that the belt will have a finite and measurable deformation vs the load applied. If some one can tell me the detail geometry of cord and rubber, as well as length between sprocket contact points, I can compute a pretty good estimate of just how springy the belt is. Add in mechanical deformation of the sprockets and shafts, and we have pretty good idea of spring rate of the PSRU.

Billski
Sigh

#### TFF

I know the systems I mess with will stretch. The helicopters with the idler does get adjusted over time as does the other. The idler system is pretty simple, a couple of wrenches and a 6” ruler and do it. The non idler is more of a pain. The transmission is fixed. After tensioning the belt which is done free of the engine, the engine has to be shimmed to match. A Royal pain. There is a procedure to count the adjuster turns and subtract shims, but at some point the belt will need a complete alignment again. It does stabilize and can stay good for a long time but at some point , you could run out of shims. 4000 belt too. The first design actually used a combine belt until Gates found out they were going on helicopters for the last 40 years. #### Heliano ##### Well-Known Member Well said, plncraze and Billski about Galapoola's mower: the belt of a mower probably slips when subject to bumps and kicks, and I presume that they are "V" belts, not timing belts. And when a belt is long it lowers the natural frequencies of the assembly, probably below anything similar to the rotation of the engine/propellers. A quick comment about "V" belts: they are cheap but are the least efficient of all, which means that they transmit less power and generate more heat. Heat is equal to wear and length change. #### plncraze ##### Well-Known Member HBA Supporter Billski, thank you! A little story: I worked with a retired transmission engineer/executive from one of the big three. I said "Do you understand torsional resonance?" He looks at me and says "Yes" looking me like I was clueless (I was). I said "You should design a reduction drive for homebuilders" and he almost goes nuts and talks about how he isn't going to risk losing his a## because some idiot builds his drive wrong and the widow sues everybody. So I appreciate your help on this forum and cannot thank you enough. And just between you and me, my widow will never find out about us LOL Here is what I hope is the detail geometry of my belt. Mine is an 8mm pitch. The distance (thickness) from the top of the tooth to the bottom of the belt is 5.51 mm and the thickness between teeth is 2.3mm. The distance between contact points between the larger and smaller pulley is 317.5mm. The recommended center to center distance for my pulleys is 313.944mm (289.56-314.96). According to a brochure it is made from • Upgraded construction with fibreglass tensile cord, elastomeric teeth and backing and nylon facing. #### plncraze ##### Well-Known Member HBA Supporter If the numbers for the contact points and the center-to- center distances don't make sense it is because I had a hard time mocking up the belt and sprockets. I had the spacing on both sprockets right but the belt kept moving. #### dog ##### Well-Known Member I know the systems I mess with will stretch. The helicopters with the idler does get adjusted over time as does the other. The idler system is pretty simple, a couple of wrenches and a 6” ruler and do it. The non idler is more of a pain. The transmission is fixed. After tensioning the belt which is done free of the engine, the engine has to be shimmed to match. A Royal pain. There is a procedure to count the adjuster turns and subtract shims, but at some point the belt will need a complete alignment again. It does stabilize and can stay good for a long time but at some point , you could run out of shims.4000 belt too. The first design actually used a combine belt until Gates found out they were going on helicopters for the last 40 years.
I have a weakness for old flat belt mill gear,and rescued the wreakage of a steam powered flat
and poly v belt drive wooden box making factory,got a bunch of stuff give to me.
Mechanical nailing machines saws,whatnot.
Big solid shafts 2 and 15/16 ,and lots of smaller,under the bearing boxes were shims,
of all sized,down to thin foil shim stock under
10 thou.Somebody was fussy.
Had to have been done by hand and eye and ear.

#### galapoola

##### Well-Known Member
Lawn mower belts are usually pretty long, which can make for pretty low spring rates, driving first resonance frequency low. Then you usually do not engage the clutch at low rpm, so it becomes a soft system at higher rpm, nicely isolating the engine vibe from the bladeset. Ideally that resonance is below idle speed, but if it is up near or a little above idle, so what? Relatively little energy is available there (Blades absorb power same as a prop does, with torque required correlated with rpm^2, and power required with rpm^3, so the low speed end is at really low power), so it is unlikely to get in trouble down low. And then if it does resonate, the belt can slip and the idler reduces feedback on the coast side of the firing pulse. Then most of us only engage the mower deck at higher rpm because you can kill the engine doing the engagement down low, and many of the manufacturers run min engine speed pretty high on mowers.

How is the mower different from the airplane? Props are usually a lot bigger than the mower blades; Belts are much shorter on the airplane, inches vs feet on the mower; The idler is spring loaded instead of hard adjusted or not present at all on PSRU; Mower engines really do have a bunch of flywheel for the size of the engine. So, going to a much shorter belt drives up stiffness and raises resonance rpm, the prop has a lot more MMOI from having more diameter (MMOI goes with weight and diameter^2) making it higher inertia than the mower which can drive down resonant frequency, and the hard belt arrangement that is commonly used in PSRU let's the vibration feedback over power strokes and coast strokes between power strokes.

I have not modeled a belt PSRU because I have other stuff important to me, but if any of you want to know how big each effect is, doing some measurements and some analysis will tell you a lot. And I am offering to look at your models and data if you like.

Billski
That makes sense, plenty of stretch and slop in those systems. Thanks for the detailed explanation

#### TFF

##### Well-Known Member
Thirty years ago, I could have had a complete auto machine shop that was belt driven for free. It has been around forever. It had modern tools too. The land became valuable, the third generation liked his other business, so when dad retired, they took the “ portable “ stuff home and scrapped it. This was electric. In the middle of the room was an armature that was about 8’ in diameter that drove the belts. Looked like an electric waterwheel. They still used the cylinder grinder if someone would pay for it. It made perfectly round cylinders with a surface ten times cleaner than a boring bar and hone.