# Belt Drives and design

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#### wsimpso1

##### Super Moderator
Staff member
Solutions are being discussed here- moving resonance out of the operating range and in my case, I added flywheel mass.

Missed this earlier. Adding inertia to the engine side is very effective at lowering the primary resonance frequency, and has been applied by Ross, by me on the Jabiru power train I have mentioned, and even in road vehicles. It adds weight, but sometimes it is the solution you can apply now, and so you do it.

Billski

#### wsimpso1

##### Super Moderator
Staff member
The estimation method is used when the component exists only as an accurate drawing. It takes advantage of the fact that inertias in a component are additive. We simply break the component down into separate elements with easily calculatable weight and radius of gyration (ROG). The MMOI for each element is calculated individually, then the inertias are summed. Again, use the spreadsheet to make your life easy. I've included an example, a flywheel which can be broken into three discrete elements.

It would be nice if one of our resident professionals would review the spreadsheet equations for accuracy.

At both Ford and at Chrysler, we used a single wire method as well as the double wire method for the torsional pendulums.

#### Geraldc

##### Well-Known Member
If you are using a guibo or rubber donut would an infrared camera show up problems at certain revs?

#### dog

##### Well-Known Member
Perhaps a top end infrared camera would give some indication of instantanious heat build up ,but the horse choking wads of cash required to buy one could probably be better spent.
And if a series of runs were made at different
rpm's,just stopping the motor and useing your
hand would suffice.
Lots of mechanics will do this to trace problems.
Shaky loose or high friction things get hot.

#### DanH

##### Well-Known Member
I previously posted second mode Holzer results, with the discussion limited to frequency, and how we don't want it to drop into the upper end of the operating RPM range.

Now look at the mode shapes. Note the negative displacement value for the center inertia.

In the first mode, the two smaller inertias rotate opposite the one large inertia, in our case the propeller. However, in the second mode the small center inertia rotates opposite the two end inertias.

#### DanH

##### Well-Known Member
An interesting aside...

Billski was kind enough to review the mass moment of inertia spreadsheet from post 137, and noted the radius of gyration values did not look right. Only took me a few minutes to determine why. Some years ago, while working on the spreadsheet, I flipped open Machinery's Handbook for an ROG equation, and did not note the given axis of rotation, X or Y. What we need here is ROG for rotation around the Z axis. Duh. Different equation.

We'll get a corrected version back up when Bill has finished his review. Thanks Bill!

#### DanH

##### Well-Known Member
Ok, Bill was kind enough to check the equations, and reports them good to go. While he was doing so, I added two more handy worksheets, shaft stiffness and the effect of ratio. Radius of gyration is revised, and one accuracy tweak made. With a little care in application, the four worksheets will yield inputs accurate enough to run the Holzer code, which should help you avoid highly resonant periods. Ya'll have fun.

#### Attachments

• MMOI Worksheets - July 2021.xls
258 KB · Views: 26
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#### plncraze

##### Well-Known Member
Supporting Member
Awesome! The equivalent thing is pretty abstract and this helps. I go through Den Hartog some of the Schaum's books but it isn't always explaining it in a way I am looking for.

#### wsimpso1

##### Super Moderator
Staff member
If you are using a guibo or rubber donut would an infrared camera show up problems at certain revs?
The infrared camera will show you the temperature of things. As to showing you if you have problems, thermal lag is substantial. You would have to carefully design your experiment. If you suspect a resonance at a certain speed, maybe runs within a quarter octave of that speed should be run after you warm up the engine and establish the baseline for other parts of the operating range. Certainly run a wide range of conditions. More than a quarter octave from resonance, the giubo should run pretty close to the stuff around it, while it will warm up if it near a resonance and is thus absorbing much energy. Just shooting from the hip, I would bet you would need a minute or more at each operating point.

As a long time design of experiments guy, I would layout the range of testing (Idle to max engine rpm), all of the speeds I intended to run, and then randomize the sequence. Randomizing the sequence is important - it keeps you from learning something when it ain't so. In this case, if the giubo is warming slowly through the whole test, but you started slow and worked to fast, you will now have data that says that faster is hotter. Randomize your speed runs and the warm up will just show as noise. Better to learn nothing than to learn something that is wrong...

The trouble with this approach is that resonance tends to happen over pretty narrow range of speeds, so a slow thermal response and small speed steps can make for a pretty long test sequence. Usually in vibe measurement, we run speed sweeps. It might take us 10 to 20 seconds to run and engine up from idle to max speed, and another 10 to 20 to run back down. This way we see all speeds twice and any range with big vibe amplitudes shows up.

If you suspect a certain speed has a resonance, sure run there and run well away from there, and see if there are differences. You still may have a mystery as to what to do about it, but a hot spot in the range is a clue...

Billski

#### DanH

##### Well-Known Member
I go through Den Hartog some of the Schaum's books but it isn't always explaining it in a way I am looking for.

I know exactly what you mean....two pages of calculus followed by "Thus it can be seen...."

True story. I live in a little town with a tiny library tucked into the back of city hall. About 1999, a practicing engineer told me the best reference for torsional vibration was W. Ker Wilson's Practical Solution of Torsional Vibration Problems, so I ordered it via inter-library loan. A week later, our librarian calls and says "Dan, your books are here". "Books?", says I. Turns out Ker Wilson wrote five volumes....which I had for two weeks.

Really is a terrific practical reference, but out of print, with originals being expensive. You can find some of it online, like here, Vol 1: https://babel.hathitrust.org/cgi/pt?id=wu.89080441520&view=1up&seq=1

I'm not into "collectables", but I do have this fantasy about stumbling into all five volumes in the back of some dusty used bookstore...

#### plncraze

##### Well-Known Member
Supporting Member
I have been utilizing my library (it is fantastic!) and they have the Ker Wilson.
I have a couple questions about using Holzer from VibrationData.
When I am inputting data for the Holzer diagram it asks me if I want "Free-free" "Free-fixed" and "Fixed-fixed" for my diagram. Since I am doing a belt drive I believe the correct answer is "Free-free." Is this correct?
I am in the process of loading a cad program to read the Holzer.plt output but reading the written output I am getting "omega" numbers. Are these the critical frequencies for the shaft or something else.
These questions are very specific to the VibrationData website program. One of the reasons I am asking is that my first Omega is 0 (zero)

#### rv7charlie

##### Well-Known Member
Supporting Member

So much to learn; so little time....

edit: what are the names of vol 2 - vol 5? Maybe Google has made them available now, too.

#### rv6ejguy

##### Well-Known Member
Supporting Member
I've been involved in a number of PSRU projects and many which had/ have TV periods. It's generally obvious through direct observation- sound and feel below about 35Hz if you have a worrisome level of TV amplitude. Above this frequency, which will be in the flight range generally, the human senses are not reliable and you'll need instrumentation to detect dangerous levels of TV.

A math model as Dan has presented here is a good place to start. It helped confirm what I observed on my installation between about 1050-1300 rpm but more importantly, showed the next resonance period well above normal operating rpm.

My solution was to add 16 steel weights to my flywheel to increase MMOI. This resulted in a remarkable decrease in perceived TV down around the idle/ taxi rpm ranges.

Interestingly, almost all 4 cylinder engines with PSRUs seem to have a similar period down around this rpm range, regardless of drive type.

#### plncraze

##### Well-Known Member
Supporting Member
Here is a copy of my Holzer output if this is helpful. The first Inertia is the flywheel crankshaft and the last one is the propeller. I am trying to figure out why the first omega is zero and what the vector numbers mean. As I understand the Hz you will use the formula to convert them to rpm and this will be the resonant rpm for that part.

#### Attachments

• Holzer.txt
1.4 KB · Views: 9

##### Well-Known Member

So much to learn; so little time....

edit: what are the names of vol 2 - vol 5? Maybe Google has made them available now, too.
I jumped straight to the chapter on damping devices, where he talks about TV damping devices fitted to the Graf Zeppelin after it landed with 4 broken cranks!

#### DanH

##### Well-Known Member
Here is a copy of my Holzer output if this is helpful. The first Inertia is the flywheel crankshaft and the last one is the propeller. I am trying to figure out why the first omega is zero and what the vector numbers mean. As I understand the Hz you will use the formula to convert them to rpm and this will be the resonant rpm for that part.

Ignore the first omega. What the code calls omega 2, 3 and 4 are the three natural frequencies of interest. Why three? Because the number of natural frequencies is always equal to inertias less one, and your model has four inertias.

The vectors are mode map inputs. Positive means rotation in one direction (clockwise, for example) while negative means rotation in the opposite direction. The values are relative to the motion of inertia one, which is given a value of 1.

"Relative to" is an important concept here. The vectors don't tell how far an element actually rotates, as might be expressed in degrees, nor the resulting stress in the connecting components. Both require further calculations. Here we're just trying to find the natural frequencies, in order to design them out of the operating range. The vectors tell which parts will be oscillating the worst, if the predicted frequency is excited by a forcing frequency within the operating range. The most powerful forcing frequency is gas pressure oscillation, i.e. firing events, which is why (for an even fire four-stroke) we keep the equation for converting frequency to RPM in mind:

RPM * number of cylinders / 120 = hertz, or..
hertz * 120 / number of cylinders = RPM

Example from a previous post: This three-inertia mode map had a first mode (omega 2) vector table of...

1
0.5578
-0.7608

...so the mode map looks like this:

Next, convert hertz to RPM for your engine to see the RPM at which the predicted natural frequency will resonate. Again note, it does not tell how hard it will resonate. That requires further calculation, but we don't care very much if the natural frequencies can be moved out of the operating range.

Which brings us to the Holzer output you posted. Consider the omega 2 frequency values:

= 54.37 Hz

Convert hertz to RPM for your 3-cyl 4 stroke:

RPM = 54.37 * 120 / 3
RPM = 2175

Uh oh....if the inertia and stiffness inputs are accurate, the result (a system resonating at 2175 RPM) is undesirable. Explore other practical inertia and stiffness combinations. Doing so with calculation tools beats the crap out of building a drive and finding out it sucks, then guessing at a new configuration.

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#### plncraze

##### Well-Known Member
Supporting Member
I appreciate your reply Dan. I was wondering if that low rpm number was bad. I have Love joy coupling in between that I didn't calculate when I did this. I will play with this further. Also the shaft length can change too. I'm starting to understand why it took Ross as long as it to calculate his drive system.

#### DanH

##### Well-Known Member
I appreciate your reply Dan. I was wondering if that low rpm number was bad. I have Love joy coupling in between that I didn't calculate when I did this. I will play with this further. Also the shaft length can change too. I'm starting to understand why it took Ross as long as it to calculate his drive system.

Sketch out your model for us. And did you adjust the driven inertia for ratio?

#### wsimpso1

##### Super Moderator
Staff member
Following up on DanH response...

The Free-Free means that neither end of the system is constrained or fixed, and is appropriate to a crankshaft whirling away on one end and the prop on the other end. Fixing some spots along the chain happens when a part is anchored against vibration. A tire tread patch on pavement is pretty good for "fixed".

You have a resonance mode in the operating range at 54 Hz. Looking at the vector, Inertia 1 & 2 are accelerating together while the 3rd and 4th inertia are also accelerating together, but opposite to 1&2. Your prop and engine are vibrating opposite each other with spring 2 (between inertia 2&3) being exercised. This could be a bad thing.

Going to the next mode, that is a firing frequency at 200Hz*40 = 8000 rpm on a three cylinder engine. Firing looks safe unless you are going above 600 rpm, but 4 stroke engines have their second biggest forcing function at 2x firing, so 200Hz also gets pumped by the engine at 4000 rpm which is also inside your operating range. This is pistons going up and down in the cylinders... Now this forcing function at 2x firing tends to be about 1/4 to 1/3 of the amplitude of firing frequency - while smaller, it is usually still important. Springs 2 and 3 are both being exercised, with spring 3 being run much harder. Reading the vector, this mode has Inertia 1, 2 and 4 going the one direction while Inertia 3 is vibrating opposite the other three, and Inertia 4 is amplifying a LOT.

The last one is way up there, probably irrelevant to us. Try out some more inertia in 1 and 2, lower spring rate in 2, and higher spring rate in 3, then see if the last mode has stayed out of range high...

Typical solutions to the 54 Hz mode are:
• Increase inertia 1;
• Increase inertia 2;
• Decrease spring rate 2;
• Combinations of the above.
Typical solutions to the 200 Hz mode are to add stiffness in spring 3 to drive this mode higher.

What parts are these seven pieces? The relative size of the inertia are not really making sense to me. Usually the prop is biggest, engine and flywheel are next smaller, and the sheaves or gear sets are much smaller again... Inertia 1 and 2 are pretty small compared to inertia 4, which I am assuming is a prop, and that is OK, but inertia 3 is bigger than Inertia 1+2, which is unusual. Do you have a flywheel on the engine? Where is it in this scheme?

Then the springs... 2 is softest, but that is still about 2 to 4 times what is used in a typical diesel pickup truck damper spring with about 10 times the torque - not exactly what I would call a soft element in a little engine. The other stiffnesses are only 1-1/2 to 4 times the soft element, which means they are kind of soft.

Usually the soft element is soft while the inertia ahead of it are high to drive first mode below operating and the rest of the elements stiff to run the rest of the modes out of range high. Prop shafts are beefy SOB's as they carry the engine torque times the torque ratio of the gearset in torsion, plus they carry gyroscopic moments from that big prop inertia times prop speed times combined pitch-yaw rotation speed (rotation rates are in radian/s, inertia is in consistent units to get torque units you are designing in). When you make the prop shaft beefy enough to both be reliable under carrying torques and gyro moments and get the higher modes high enough, it tends to be pretty beefy indeed. Usually, you check it out with one set of bearings, and if it is not stiff enough/ strong enough, you go to the next size up of bearings, bump the shaft diameters to follow, through drill it to take out some weight, and check again. When you are done, somebody will try to tell you it is overbuilt. Worry not if it works.

Billski

#### DanH

##### Well-Known Member
My solution was to add 16 steel weights to my flywheel to increase MMOI. This resulted in a remarkable decrease in perceived TV down around the idle/ taxi rpm ranges.

Now if we could just convince you to (1) machine a new flywheel with a nice high-inertia ring at its perimeter, and (2) install a real honest-to-gosh engineered soft coupler to replace those horrible urethane bushings...