Selective assembly of machined parts based on requisite clearance and interference fits

Hello friends,

I need to select pairwise parts based on fits. Shaft A can be paired with Hole B only if there is a clearance of 20 to 30 microns in between them. I have 10 nos each of Shaft A and Hole B which are to be paired with each other according to this criterion. All the shafts and holes have unique identification numbers like A,B,C...The program I need to write should give me the identification no of the pairs of holes and shafts pairwise as an output. This is the first step. In the second step the Hole B is to be paired with Part C based on another dimension where an interference fit of say 30-40 microns is desired. Finally the program should give me an output of combinations like ShaftA-HoleD-PartF as one possible combination. As an input to the program I shall feed the part identification nos of the shafts, holes and parts and their sizes as a coloumn vector. Thank you for your support.

[dpb]

So, what have you done so far and where did you get stuck?

Some comments -- If you have only N of each part and they're being randomly selected from a population unless the populations are graded or the manufacturing tolerances are very good, it's likely (or at least possible) there won't be a possible solution for all.

It would seem the first would be pretty straightforward to just sort the two lists and take the largest Hole with largest shaft that meets the tolerance gap. If it's not the first of both, then you just ran into the problem of there not being a solution that would match up all ten with this selection of pieces-parts.

The second step would essentially be the same sequence from smallest to largest -- it's possible also it would seem that you could manage to match the first condition on one set and the second on another; not all of which would match both.

What's the desired output if either of those conditions arises--only full three-piece sets or the two-set combinations that are feasible besides?

[Subrata Chakrabarti]

I am still thinking where to start. I will be happy if I can solve the first part at least where I have paired the holes with the shafts based on the desired clearance band. The program I want to write should give me the identification nos of the pairwise holes and shafts which fulfils the criterion.

[dpb]

Again, per usual, if you would expect somebody to play around and try to solve your problem for you, supplying a set of typical data would go a long ways towards helping...

Did you try the sort solution direction I suggested above?

[Subrata Chakrabarti]

Hello dpb,

Apologies for the delay in responding. I have constructed a fictitious table in order to convey the question in a more effective manner. I have in the first coloumn a list of names(identities) whose dimensions are given in column 2. These dimensions are to be matched with the ones which appears in the 4th column( those of F to J) . I have set a criteria that their difference should be more than 0.3 and less than 0.5 for them to pair. Once a pairing is made, the corresponding cell member should go out of contention for selection when the loop re-runs.The same thing is to be repeated for the next set whose dimensions are given in the columns 5-7. In the end I expect combinations like [A G M], [B I N] etc. This is what I could do so far:

[a,b]=xlsread('lsrv.xlsx',1);
n=5;
for i=1:n
  for j=1:n
    if (((a(i,1)-a(j,2))>0.3) & ((a(i,1)-a(j,2))<0.5));
      break
      a(j,2)
      b(j,1)
      b(j,2)
      T=[a(j,2) b(j,1) b(j,2)];    
    end
  end
  t=xlswrite('Book2.xlsx',T) 
end

[dpb]

Thanks for the data, but raises at least as many Q? as provides answers! :)

What are the two measurements for and how are they to be used?

Is the original idea of a shaft in a bore w/ interference and the second some other distance no longer in play?

Is the idea match the nearest difference or make as many matches as possible with the selection of parts available?

[Subrata Chakrabarti]

Hello dpb,

Thank you for your response. Hope you are fine.

Basically we are matching parts identified in coloumns 1 and 3 with their respective dimensions given in coloumns 2 and 4 and forming pairs.For eg based on the criteria of min 0.3 mm and max 0.5 mm difference, parts A & G can form a pair but parts D & I cannot. There could unpaired members at the end if they do not fulfil the criteria.Once paired the member goes out of contention in future pairs.

In the second part , we repeat the exercise with dimensions given in coloumns 5 & 7( which belongs to parts mentioned in coloumns 3 and 6, respectively).Here the criteria could be something else.

At the end, I expect to get groups in sets of 3 as the output.

Dimensions given in both coloumns 4 & 5 belong to parts mentioned in coloumn 3.

Thank you for your attention. Have a nice day.

[dpb]

Is there any penalty or bonus for pairing nearest matches or is the objective the most matches (use the most parts with fewest left over)?

Are measurements such that dimension 2 is always >= dimension 4 as shown in example data or can there be cases where dimension 4 > dimension 2?

You didn't reply about the original problem question -- has the intent/description there gone away? That seemed pretty reasonable; in some ways more so than the present as far as real.

For the above, if the point is match most possible, then simply sorting and pairing the first from Part 1 with first from Part 2 that is within tolerance would provide the most matches possible until and if the last one(s) are out.

Here that would pair

>> tLSRV
tLSRV =
  5×7 table
    Var1     Var2    Var3     Var4    Var5    Var6     Var7
    _____    ____    _____    ____    ____    _____    ____
    {'E'}    5.6     {'H'}      5     2.3     {'M'}    2.7 
    {'D'}    5.4     {'F'}    4.9     2.1     {'L'}    2.9 
    {'B'}    5.2     {'G'}    4.8     2.2     {'K'}      3 
    {'A'}    5.1     {'J'}    4.7     2.5     {'O'}    3.2 
    {'C'}      5     {'I'}    4.6       2     {'N'}    3.3 
>> 

{D,H} {B,F},{A,G},{C,J}

{E} is unusable with these mates.

It also seems there might/should be some limit on a total or other global measurement...if these are some length, then perhaps the two match within that tolerance but the overall length is too long???

Dunno w/o knowing more of what the actual situation would be, but that would be one solution as the problem is formulated now.

[dpb]

Dear Sir,

At the end we need to match as many triplets as we possibly can fulfilling the criteria.

There are no penalties/bonus for doing that. Is it possible to include a penalty or bonus in order to make the code more robust? That would be a good learning experience though not strictly essential for this case per se.

Yes coloumn 2 is always greater than or equal to coloumn 4.

Unused pairs will be replaced/reworked at the end of the exercise.

Thanks a lot for your perseverance.

Regards,

Subrata

[MOVED TO COMMENT -- DPB]

[dpb]

OK. Gotta' go to the field now, but look at it this way...with that as the limit without the previous constraint, think of it like this--

If you sort Part 1 and 2 sizes in descending order, if first Part 1 (largest now, remember) is too large to match up with the largest of Part 2, then it certainly won't match with any of the rest. That throws it out entirely of this lot. That's the situation here with this data set with "E".

So, then you are left with starting to find match for second-largest--it may as well match with largest of Part 2 (presuming in spec) and just go from there.

With this criterion, there's no need for any comparison of one to all the rest, just match 'em up making sure they are within tolerances. Can do that in one pass in a loop and probably can be vectorized to not even need to code the loop altho I've not thought that out entirely as yet.

Then, when you have those pairs, resort the Part 2 and Part 3 dimensions and do same thing with whatever is that criterion limit. If there's no more constraint than simply the difference in dimension, then the same logic works.