Crank Balancing revisited

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Crankshaft Balancing:

An imbalance in the crankshaft in relation to the reciprocating weight of the upper end causes vibration and a loss of power. Making sure your engine is balanced correctly is essential, especially if you are modifying the engine to work in a different rpm range than what it was designed for. Using a lighter wrist pin lightens the top end by 4.5 grams which is enough to make a significant difference but not enough to completely balance the crankshaft.

50% to 85% of the top end weight (piston, rings, wrist pin, bearing, upper half of connecting rod) is recommended as the weight to be "missing" in the balance holes on the crankshaft halves close to the connecting rod pin. (Making weight disappear on one side of the halves is like making it appear additionally at the opposite side.) The conrod pin adds 3.3 grams to the balance area (over what would be if no holes were made for it). In the Tony Foale information (www.tonyfoale.com/Articles/EngineBalance/EngineBalance.pdf) he said that the balance factor corresponds to the square root of the rpm. So here I list the square roots from 5,500 to 10,000 rpm:
10,000 100
9,500 97.5
9,000 94.9
8,500 92.0
8,000 89.5
7,500 86.6
7,000 83.7
6,500 80.6
6,000 77.5
5,500 74.2

So this gives us the relation of the balance factors to each other for the different max rpm. If we assume 5,500 as needing the minimal 50% balance factor then we can derive these other balance factors with the percentages changed to fractions:
10,000 .674 (67.4%)
9,500 .657
9,000 .640
8,500 .620
8,000 .603
7,500 .583
7,000 .564
6,500 .543
6,000 .522
5,500 .500

As an example of how to calculate the needed "missing" balance weight I will use the 48cc Grubee engine. What I first notice is that the existing balance holes are not the same distance from the center of the crankshaft as the connecting rod pin is. That is important because the farther a weight is from the centerpoint the more centrifugal force it has for the same rotational velocity. Using a test weight of 1kg at http://www.calctool.org/CALC/phys/newtonian/centrifugal I see that 1kg at the 36mm distance of the balance holes gives 1.9 times the centrifugal force as 1kg at the 19mm distance of the conrod pin. So the final formula will take the upper end weight, multiply it by the balance factor, add the additional weight (3.3gm) of the conrod pin, and then divide that result by 1.9. The upper half of the conrod weighs 31 grams and the piston assembly weighs 79 grams for a total of 110 grams. 110x.50=55 +3.3=58.3 /1.9=30.7gm. The two factory-placed holes of 11mm diameter equate to 23 grams of missing weight. 30.7 minus 23 equals 7.7 grams that still needs to be removed. A single extra hole of 6.3mm diameter (1/4") drilled at the same 36mm distance will remove 7.5 grams of weight. I would also buy a 1/8" drill bit to use as a starter hole. It is hard slow going drilling a hole in that metal. (Grainger has good prices on carbide bits. On their site search "jobber drill aircraft" and the size needed.

The missing weight of any hole can be calculated at http://www.ralingroup.co.uk/weights.html but you have to multiply the resultant weight of kg by 1000 to get grams. Use half of the diameter as the wall thickness.

If the lighter weight wrist pin is used then that shaves 4.5 grams off of the piston assembly to reduce the total weight from 110 to 105.5 grams. Recalculating gives 29.5 grams needing to be counterbalanced. Subtracting 23 grams leaves 6.5 needing to be removed. A 6mm (15/64") diameter hole will remove that.

Below is a picture of my crank assembly with an additional balancing hole just above the conrod pin. The 6 blue holes are lightening holes for better acceleration. The blue is foam filling half the hole. The ends of each hole were later filled with JBWeld. I used foam just to reduce the amount of expensive JBWeld used. The conrod hole and two factory balance holes are already filled with JBWeld for increased crankcase compression.
flywheel.jpg
 
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Test Results

The above is just theory. Next it has to be proven by real life tests. I am starting to do that. I just tested my 55cc engine (see engine details below) ported for 10,000 rpm but that achieved only 9100 since I just did the test runs with the standard exhaust pipe instead of an expansion chamber with the correct header length for 10,000 rpm. Anyway here are the details:
upper assembly weight: 122gm
additional balance weight removed: 9.8gm
That figures to be balanced for 5080 rpm (ie: a .48 balance factor)
The engine vibrated between 5600 and 7900 rpm and ran smooth before and after that rpm range.
So I think this test has proved the veracity of my formula so far. Next I will enlarge the extra balance hole to 15.8 gm for an rpm of 8,500 for my other 8300rpm engine and see how it runs.

Here are the square root and balance factors up to 12,000 rpm for anyone who wants them:

RPM____sqr rt
12,000__109.5
11,500__107.2
11,000__104.9
10,500__102.5

RPM____balance factor
12,000__.738
11,500__.722
11,000__.707
10,500__.691

55cc high rpm engine:
55cc Grubee cylinder/head on 48cc bottom end
port durations: 185 exhaust, 119 transfers, 125 intake
transfer port walls removed for greater transfer area
stuffed crankcase
155 psi cranking pressure
18mm Mikuni
custom intake manifold
piston port intake
slant plug head with squish band .65mm from piston
Kawasaki KX65 piston and rings (adapted for use with piston port intake)
Jaguar CDI with Kawasaki KX high voltage coil
44 tooth rear sprocket
26" wheels with mountain bike tires
peak head temperature: 425F
 
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Any one who has studied the subject knows "balanced" in this application of the word is relative, and just means "not vibrating too much".
 
Excel calculator

I've made an Excel file for calculating the counter-balance for a 48cc Grubee flywheel. It is free to download at http://www.dragonfly75.com/motorbike/48ccCounterWt.xlsx

If anyone cares to give me the following info I can make a calculator for the 69cc:
upper assembly weight (piston/wrist-pin/bearing)
inner diameter of counter-balance holes
width of each flywheel half
distance from center of crankshaft to center of counterbalance holes
 
Second test:
My other 55cc engine (ported for 8300rpm) with lighter 77.3gm upper assembly.
the additional weight removed was raised to 15.8 grams via a 9.15mm diameter hole.
Using my formula I figure the rpm for that combo is 9380.
It allowed my engine to go up to 9150 rpm (downhill) without any bothersome vibration.
so far, so good.
 
Someone gave me the dimensions for a 69cc engine and I figured what is needed for it.
With a stock piston assembly of 107.6 grams and 11.15mm counterbalance holes at 36mm from shaft center I figure a 12.6mm diameter extra hole is needed to balance the engine.
 
The machine shop let me do the drilling as they were pre-occupied. I just drilled slow and the bits didn't get too hot. I didn't use any cutting oil either. And they still feel sharp.
I have a masonry bit and it doesn't have a sharp edge to it. Don't mean it won't work but man oh man are those flywheels made of some hard-ass steel.
 
I have been through this before as i purchased a "so called" balanced and trued crankshaft (in a complete 69cc engine) from another vendor, which was tested to 9,000 rpm in pre-production development work to determine the best counter balance weight.

When receiving the package i immediately pulled off the top end to find the crankshaft counter weight holes measured in at 12mm which was up from 11mm diameter in a standard 69cc engine.

After spending time to assemble it to my SickBikeParts jackshaft system and installing the thing in my bike and giving it a test run, i was shocked as to how vicious the vibration was at normal running rpm of 3,500 to 4,500 rpm.

The vibration was completely unacceptable and many times worse than the standard engine at normal operating rpm.
Consequently engine was stripped out of my bike and returned to the vendor, upon which a standard 69cc engine was bolted in it's place.

Since that day, i have never bothered with the concept of balancing a standard engine as my research (and the maths to support it) shows that a single cylinder engine can only be balanced for a narrow rpm range at a selected rpm.
Balance the engine so that it is smoother at high rpm and it will vibrate excessively at lower rpm.
 
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