11/29/98 Single plane, no phase balance solution using two trial runs. Along with using these instructions the reader should have either BalanceB.DXF or BalanceB.JPG downloaded and maybe printed. It is assumed that the user of these instructions has a way of measuring vibration with enough precision to allow for accurate comparison. Also it is assumed that a condition of rotor unbalance is the dominant source of vibration. Using these instructions the user may "Fix" a point of unbalance correction in a rotor, (thinking in "polar" units "Y" is solved for value and sign, "X" is solved for value but is not solved for sign). I tend to like this approach because you have a 50 percent chance of balancing in three runs where the 120 degree method always takes at least four runs and is usually no more accurate. STEPS 1. Spin the rotor up and measure the original vibration value as "O" and stop the rotor. 2. Prepare a test weight "TW", and install the weight at a known radius and angle on the rotor. Record the weight value, IE. 20 grams, or 16 oz. for later use. 3. Spin the rotor up again and record the new unbalance value as "T1" and stop the rotor. If the value of "T1" is less than "O" from step 1, use a larger test weight and repeat step 3. 4. The test weight is then rotated 180 degrees from the original location at the SAME RADIUS. 5. Spin the rotor up again and record the new unbalance value as "T2" and stop the rotor. 6. Construct a polar chart using a convenient scaling from the values obtained "O", "T1" and "T2". In the case of the chart BalanceB.DXF, inches were used to denote values, (in my example "O" = 3, "T1" = 5 and "T2" = 4). IT IS IMPORTANT THAT ALL SCALING BE THE SAME IN CONVERSIONS FROM UNITS OF UNBALANCE TO UNITS OF MEASURE! 7. A circle is drawn to denote the original unbalance using a radius with the value of "O", (in my example the original unbalance value "O" is 3). 8. Where the circle intersects the "Y" axis at the top of the chart mark "POINT A, where the circle intersects the "Y" axis at the bottom of the chart mark POINT B". 9. The value "T1" is then used as a radius to construct an arc from "POINT A" towards the chart center, (in my example the original "T1" value is 5). 10. The value "T2" is then used as a radius to construct an arc from "POINT B" towards the chart center, (in my example the original "T2" value is 4). 11. If enough test weight was used for the test runs, arcs "T1" and "T2" will cross in two places. A line is now drawn from the center of the chart to either of the crossover points of "T1" and "T2". The length of this line represents the value "R" and will be needed for computing the amount of correction weight. 12 The amount of correction weight is computed with the formula ("O" X "TW")/"R" a. "O" from step #1 b. "TW" from step #2 c. "R" from step #11 *Note* To solve for my example with a 16oz. test weight being used, the correction weight would be (3 units X 16oz.)/3.39 units or 14.16oz. 13. The angle of correction is the angle "X" from "Point A" to the line that represents "R", (in the case of my example angle "X" is 102.78 degrees). 14 Place the correction weight (calculated from step #12) at a point clockwise from the original test weight location by angle "X" degrees, at the SAME RADIUS used for placing the test weight in step #2. 15 Spin up the rotor and measure the unbalance amount. If the rotor is running within expectations then the correct weight is in the right position. If not, stop the rotor, and go to step 16, otherwise see step #17. 16 Move the correction weight (calculated from step #12) at a point counter-clockwise from the original test weight location by angle "X" degrees, at the SAME RADIUS used for placing the test weight in step #2. Spin up the rotor and measure the unbalance, if the correction weight calculations and radius rules were observed the rotor should be ..2 of the original unbalance amount or better. 17. If adding weight to a correction plane is acceptable, (such as with a fan blade) the task is finished. If the weight must be removed, or removed and substituted for (such as with Muntz metal plugs), then corrections must be made 180 degrees from the locations solved for above and at the SAME RADIUS as the original test weight. Material densities for the purpose of removal may be found in a number of places, (the Machinerys Handbook comes to mind). *Note* There will be some that reason that this solution won’t work if arcs "T1" and "T2" don’t intersect. Ah-Ha, this can happen if the test weight is placed at, or very near the point of unbalance and/or is too small, when this happens another solution is needed. I would rather recommend that the weight be rotated 90 degrees or increased. I would also mention that for almost all vector balancing solutions the test weight MUST cause a 30 percent change in vibration amplitude or a 30 degree change in unbalance phase (if phase is being tracked). I also tend to like "vector construction" for solving balancing problems as it is visual and hones useful "geometric construction techniques".