Could someone tell me the formula to split weights between two locations or sum them? In addition, does anyone know of any good resources for balancing information on the web? Any help on this subject would be very helpful, thanks.

There's quite a bit of trigonometry involved, so it's not easy to post a solution. I recommend you look at "Machinery Malfunction Diagnosis and Correction" by Robert Eisenmann. Chapter 11 is about balancing and has a section on weight splitting. You can also look at Chapter 16 of "Fundamentals of Rotating Machinery Diagnostics" by Don Bently.

Personally I think plotting is the easiest and give a good graphical presentation for the maint. file.

Are you familar with this? It is very easy. Do a search on the old IRD. Still need help; re-post or mail me directly and I'll try to get you a plot with explanation.

Plotting is simple as Sam stated.

1. Plot your desired weight add (subtracts are similar) on polar graph paper.
2. Draw (construct) lines at the angles on either side of the weight add where the weight will be split
3. Construct parallel copy of one of lines drawn in 2. to connect with the other line and the weight add plotted in step 1.
4. You now have the vector solution, either measure the vector solution or complete the parallelogram and measure.

Note: In step 3. constructing parallel copies of lines can be done with a set of parallels or with two triangles- set one triangle on the line you want to translate, set the other triangle against the first triangle and slide the first triangle to position.

The numerical procedure is simplest when done as a Law of Sines application or simplify the other usual approach. Weight split angles need to be on either side of weight add angle and <180 degrees apart.

d – Desired magnitude of weight add
A1 – First weight split angle difference to desired angle
A2 – Second weight split angle difference to desired angle
a1 – First weight split magnitude
a2 – Second weight split magnitude

a1 = d*sin(A2)/sin(180-(a1+a2))
a2 = d*sin(A1)/sin(180-(a1+a2))

This message has been edited. Last edited by: William_C._Foiles,

Thanks allot Sam and William; this will be extremely helpful! Thanks for the contact info Sam. This has to be one of the best boards on the web.

Thanks William for a great explanation including the figure. I have to admit I didn't remember what the "law of sines" was. I found it here
http://hyperphysics.phy-astr.gsu.edu/hbase/lsin.html
and with that your explanation makes good sense.

One can extend hole splitting further. The December issue of "Vibrations" magazine had an article on this, perhaps with better explainations.

This message has been edited. Last edited by: William_C._Foiles,

Weight_Splitting_into_More_than_Two_Location.doc (526 Kb, 77 downloads) edited for typo

Bill,

I think I have found an error in equation 2 of your attachment. The RHS of both equations 2 and 3 are identical.

Equation 2 solves for V2. In the numerator, you have sin(abs(a-a1)). I believe it should be sin(abs(a-a2)).

I put the equations in a spreadsheet and they checked out okay with your example of 100 g-cm at 40 degrees.

Steve

Here's an excel based weight-spliting program for two weights.

Weight_Splitting.xls (60 Kb, 75 downloads) Weight Split Calculator

Thanks, equation 2 looks ok. The problem was with the second (redundant) part of equation 3 to comput V1. The first part of that equation can be used to solve (correctly) for V1. I shall edit the file, so that this is not mis-understood.

The second numerator should have had (and now does have) sin(abs(a-a2)) to solve for V1.

This was mostly filler for the rest of the story anyway. The solver given to be used with Scilab (registered trade mark of INRIA and copywrite) adds functionality to the traditional solvers.

Patrick,
Alec posted this website on another thread. You can download a calculator that will split and sum weights for you. http://www.vibronurse.com/Balance.html
It's free to download in case you are interested.

Ronnie

Dear Steve,

The Excel program you have proposed is excellent!
Thanks for sharing!

Marko Leo

Good info from everyone.

Sci Lab looks like a free version of Matlab.

Scilab is a free program with similar capabilities to Matlab if you have many installed toolboxes for the Matlab.

The linear programming tool I used is built in. Controller synthesization using many techniques is built in. I have balanced a number of machines using this.

Least squares balancing is rather simple using Scilab. I generally prefer another method, still in Scilab.

I am more used to using Matlab for plotting, but I see there are some look alike tools (that I haven't used) with more of a Matlab feel for plotting.