Tolerance stackup analysis on cartesian systems

[Koolwijk J]

I have a question regarding tolerance stackup analysis of cartesian systems.

Currently I have build a spreadsheet that can calculate the yield percentage based on given system limits. Here I can enter components with their dimensions and their tolerances. This is done with the infomation of several papers for example: "BasicTools for Tolerance Analysis of Mechanical Assemblies".

However the examples in these papers all calculate with all the components being a 3Sigma distribution and every assembly is a new product of itself. This is not my case. Let's say the gantry with gripper will pick up a product and place this on a different product and have this proces repeat indefinently.

This results in:

Fixed offset of the gantry and gripper that occure during assembly of the machine. These can be measured and will result in a measuring inaccuracy. (Fixed dimension)
Repetition accuracy of the gantry and gripper. (Variable dimension)
Productdimension. (Variable dimension)
Do I do the analysis over all three kinds of dimensions or do I just use the variable dimension? Or do I include the fixed offsets with measuring inaccuracy (Uniformly distributed?), or do I replace all of the inaccuracy of the fixed offsets for one tolerance value(Normally distributed or Uniformly distributed?

Also, in my spreadsheet, uniform distributions are just wider normal distributions. This is based on the information in "BasicTools for Tolerance Analysis of Mechanical Assemblies". When using one not to large uniform distribution and at least 5 other dimensions the results will be relatively accurate. This however gives me the idea that I shouldn't add more that one or two uniform distributions. This gives me the impression that I should add up all the fixed offsets's tolerances to one single uniform distribution.

I hope you can help.

 

[3DDave]

If you mean this paper

https://community.ptc.com/sejnu6697...20Analysis%20of%20Mechanical%20Assemblies.pdf

that paper doesn't limit the analysis to 3sigma. A wide normal tolerance is nothing like a uniform tolerance. The two aren't similar.

I don't know what you are analyzing. Is it the product of one machine or all products of all possible machines?

 

[Koolwijk J]

Yes, that´s one of the few papers I used.

Let me try to clear some stuff up:

The company, who builds assemblymachines for clients, currently has a machine for assemblying small (around 30*10*20 mm) and simple (electronic) devices. These components change per order/client and the machine has to be redesigned. This machine is based on a linear proces comparable with an filling and cappingproces of for example Coke bottles. The tolerances for an assemblystep are relatively high.

An recurring question around these machines are if the proces could be achieved with a machine based on tray handling.

For example a gantry picking up multiple products at the same time and assembling them on multiple other components. This will result in a start-stop system, but could maybe result in higher speeds, creater flexibility and/or no need for a complete redesign of the machine with every new order. The biggest bottleneck in such a machine would be the necessary accuracy for an assemblystep. Thus without designing a complete machine I would want to give insight on possible machineconcepts that should work based on tolerance analysis.

When researching tolerance analysis they all speak of all products being part of the final product. Every dimension is different in every assembly (also shown in the linked paper). Also normal distributions are calculated by replacing them for a normal distribution with a compensating factor. The effect of this shouldn´t be noticable when using multiple normal distributions in the calculation. However I want to do a tolerance analysis on for example a gantry setup picking up 10 components and assembling (placing) those on 10 other components. In this case the dimensions of the 20 diffent components could change every cycle, but the measured fixed offset of a gantry wouldn't change.

Is there a way of doing a tolerance analysis of such systems, where the dimensions of the products actual can vary and measured offsets will always be fixed?

I created an Excel sheet for calculating the yield on given tolerances, including a Monte Carlo simulation with the uniform distributions being actually uniform. When I calulate the yield and Z-scores of the given tolerances and compare those with the Monte Carlo simulations, they are pretty much the same. Even when using multiple normal distributions.
I feel like I could use those calculations since they work with the simulations. Calculating with actual normal distributions would require a whole different approach.

 

[3DDave]

Position to position the offset from nominal is variable, so they would have a distribution, and be handled as a variable.

Other than that, any fixed offset would be directly added to the error calculated by adding the statistical distributions if you wanted to analyze the machine after it is built.