# How to calculate the vibration from motor

1. Mar 8, 2016

### Jeng Ho

Good evening, I have a question about calculation vibration of produced from a motor. The engine provide is 2 stroke engine, 1.3 horsepower, 3.2 kg in mass, bore size 34mm, stroke 28 mm and with maximum rotation per minute is 10500 rpm. Can I calculate the vibration produced by engine or not? Thank you for help

2. Mar 8, 2016

### jambaugh

Nope... much more information is needed. Specifically the geometry of the engine at the specific level of all the various reciprocating and rotating parts. The masses of the pistons, their positions and directions in the engine block, the sequence in which they are displaced, the offsets of the crank shaft and its nasty little non-diagonal moment of inertia tensor... Now if you disassemble the engine and do some measurements you could do a rough calc (or working from a CAD model or set of diagrams) or possibly a computer program is out there which can do a numerical approximation.

What happens when an engine vibrates is this, if you were to run the engine in a freefall environment attached to no mountings it would then move, the engine block in opposition to piston and imbalanced cam motion, so that the center of mass remains unchanged. You also get relative rotations as the engine block turns opposite the crankshaft and flywheel so that the angular momentum remains unchanged. There would also be a wobble of the engine block in opposition to a wobble of the principle axes of the crank shaft which (unless very carefully designed) will not align with the rotation axis.

When you mount the engine, if you mount it securely to a very large mass, then the moving parts will move shifting the center of mass and angular momentum vectors of the whole engine and there will be the appropriate reaction force on the mountings to prevent the engine block itself from moving. In actual cases the engine is mounted to a somewhat larger mass and the vibrations and other forces/torques are imparted on the whole structure.

Ok having said that, you can do a ballpark estimate if you are talking a single piston engine, take the mass of the piston (+ connecting rod) times half its linear displacement (the "stroke" not the volume displacement), times the angular frequency squared gives the maximum force on the piston and thus back onto the engine block. This will give you a comparable quantity. But with multiple pistons its a mess to calculate and you'd be much better off making an empirical measurement. It is not simply twice (thrice, ...) as much given two (or 3 or more) pistons and in fact might be quite less given their configuration.

[edit:] BTW angular frequency = radians per sec = 2pi * cycles per sec = 120pi * RPM.

3. Mar 17, 2016

### Rx7man

It sounds like a chainsaw, and I've thought about and studied those fairly extensively

I am not going to go into vibration due to the mechanical output of the engine, but describe how I'd look at breaking down the linear vibration in 2 axes due to the weight of the rotating parts.

I'd look at it in the 4 quadrants of rotation, 0, 90, 180, and 270 degrees from TDC.

Near TDC, the piston is essentially stopped,, but the 'big end' of the connecting rod is moving, and on the opposite side of the main bearings will be the counterweights moving in the opposite direction, you'll have an acceleration (vibration) of the main body due to the differences in weights of these two sides of the crank.
Near 90*, the piston mass will be moving, as well as the connecting rod, the ratio of accelerating masses on either side of the crank will be different than when it was at TDC.
When balancing a single cylinder engine, the counterweights will probably be designed to weigh somewhere between the two extremes, too much weight and you'll have a lot of (horizontal) vibration when near TDC and BDC, too little weight and you'll get (vertical) vibration near the 90* points

Hope this makes sense.. I can't help much with the formulas though.

4. Mar 17, 2016

### Rx7man

you would at least need to know the masses of the moving parts... Piston, BOTH ends of the connecting rod with bearings installed, and how the mass is distributed around the crankshaft to be able to get any sort of idea... If the flywheel adds external balance, the weight there would be important as well.

5. Mar 18, 2016

### CWatters

Probably easiest just to measure it.

It will make a difference what the motor is mounted on. Fix it to a ton of concrete and it won't vibrate as much as it will if held in the hand.