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# Din 5480 - Dimensions across measuring circles

## Din 5480 - Dimensions across measuring circles

(OP)
Now i've done a search on this site and have seen numerous threads around this subject, but they don't seem to fully answer my question (as they often revert to looking up values from the tables in DIN 5480-2). I'm putting together a spreadsheet that automatically calculates all the data that is listed in the data table in section 9 (Figure 6) of DIN 5480-1. The idea behind these spreadsheet is that the designer need not use the DIN standard or need to look up tables. They simply define the module, no. teeth, tolerance, etc. The final information in the data table concerns the inspection dimensions between pins (Hubs - M1) and across pins (Shafts - M2). Now to determine this you need to solve for β. The standard gives you a BASIC program to iterate to the solution:

10 Print "inv(BETA)"
20 Input B
30 V=0.5
40 A=1/TAN(V)-1/(V+B)
50 If ABS(A)>0.000001 then V=A+V:GOTO 40
60 BETA=(A+V)*57.29577951
80 End

Now, I wanted to use circular references to determine the value, to avoid macro enabling the workbook or needing the user to click any buttons. I'm having issues with the result. Has anyone any experience with this or has done similar? I'd appreciate any guidance you might be able to offer.

cheers,

### RE: Din 5480 - Dimensions across measuring circles

If you create an user defined function, then it is used like any built-in functions.
We used the Inv() function (it calculated the involute function of an angle), AInv() function (calculated the angle from it's known involute), and others to simplify our spreadsheets. The AInv() function included the Newton's approximation loops.
You can probably lock the spreadsheet and still keep the macros active. The user has to enter some initial values and select the precision, fit, tolerances - it is hard to do it without macros/VBA programming.

### RE: Din 5480 - Dimensions across measuring circles

(OP)
Thanks for the suggestion. I will admit, that's not something I have done before in Excel / VB. Any further guidance or instruction would be useful. How would one interpret the computer program as described in DIN 5480 into VB, and where does the involute function feature in this? Apologies, i'm still a little lost.

Cheers.

### RE: Din 5480 - Dimensions across measuring circles

(OP)
Thanks, but I don't want to double-post though.

What books are you referring to?

### RE: Din 5480 - Dimensions across measuring circles

In 1992 Harry Cheng proposed a derivation of an explicit solution of the inverse involute function where (inv f) is known and the angle (f) is to be found. Using the "asymptotic" series f(f) = inv-1(ff), the explicit equation becomes:

Where (q) = Tan(f) - f

f = (3q)1/3 - (2q)/5 + (9/175) (3)2/3 (q)5/3 - (2/175) (3)1/3 (q)7/3 - (144/67375) (q)3 + (3258/3128125) (3)2/3 (q)11/3 - (49711/153278125) (3)1/3 (q)13/3...........

### RE: Din 5480 - Dimensions across measuring circles

bennygod,

http://www.excelfunctions.net/Excel-Books.html#VBA...

spigor,
I did not know about that approximation. Newton's method worked for me fine. Not that hard to derive it if one remembers what we were taught long time ago in school. Or if one knows where to look ...

### RE: Din 5480 - Dimensions across measuring circles

(OP)
Ok, I have a simple Do While loop running in VB. I guess I have a bit of an issue with the program as given in Din5480 Part 15. It describes the program as follows:

10 PRINT "inv(BETA)"
20 Input B
30 V=0.5
40 A=1/TAN(V)-1/(V+B)
50 If ABS(A)>0.000001 then V-A+V:GOTO 40
60 BETA=(A+V)*57.29577951
80 End

My issue is with lines 10 and 20. Why Print Inv(BETA) and not use it? Is Line 20 an error and actually Input B is Inv(BETA)? I would've thought finding the Inverse of Inv(BETA) would involve using Inv(BETA)?

So I guess my question is, in the program, is B referring to Factor B as calculated for either the internal or external spline, or is it referring to Inv(BETA), or is it a combination of both that is a typo in the standard?

Thanks,

### RE: Din 5480 - Dimensions across measuring circles

The Print statement is a reminder to the user of the function.
It looks like there are errors in the program.
Line 50 "V-A+V" makes no sense; I think it should be "V=A+V"
Line 70 is missing a closing quote character for "Grad"

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