My Method
I developed this method after not having much luck getting consistent "Good Knurls". I tried the CP Method first and then moved to Hunt & Peck, did a ton of research and tried minimizing all the other variables, and none really gave consistent results greater than about 70-80% of the time. Eventually I turned back to figuring out what my tools actually were and moved toward developing an algorithm for that Integer Ratio for My Tools.
The first tool I got was a bit loose and pretty sure one of the wheel pins wasn't perpendicular. I spent an hour or so shimming it up a bit and made it better but still didn't make good, consistent knurls no matter what I did. In all fairness and Thanks, I called LMS and actually spoke with Chris about the tool. We spoke at length about my processes and shimming and he offered and sent me a replacement tool. This one was much better and made decent knurls about 70% of the time using the CP Method. Thank You Chris!
Based on the LMS specs for the tools I have, they should be 33TPI, 21TPI, & 14TPI diagonal knurls, meaning I have CP Tools. Additionally there were no markings on the knurls so I was not absolutely sure they actually were 33, 21, & 14TPI as these are from across the Pacific pond, and might be metric for all I knew.
I also did some more research and a couple of these led to what I came up with. First was "Conrad's Easy Knurling Method". He brought forward the idea of actually measuring your tools by rolling them on an ink pad, then on paper and measuring the distance between lines...Who Would a Thunk! It seemed pretty inaccurate but turns out, if you are careful you can get within a couple of Tenths to the measured and calculated pitch. Thank You Conrad!!
Next was a YouTube Video by a man (ghostses) mightily determined to help others solve these issues. He presents a 4 part series and on the first he takes you through a spreadsheet/PDF that he made trying to relate CP Distance between teeth to an incremental list of Integer Ratios. His spreadsheet is correct, however the issue is in assuming the TPI is actually 14, 21, & 33 and that it is a true integer as we saw on the CP page, but he was absolutely on the right track. Thank You Ghostses!
Fortunately 25+ years of Excel/spreadsheet experience gave me a clue where I wanted to take My Method. First it involved physically measuring my tools and counting teeth on them, then applying basic formulas from the results. Second was to use Conrad's method and measure Ink on Paper, then apply the basic formulas to those and compare the two. Like I said above, they were amazingly close in values and in the final form have a 4th digit insignificance, especially for the Mini.
The Measurements
I measured the OD of each tool with Mitutoyo digital calipers and found the Course was exactly .7500, the Medium and Fine were .7450 and all had about .0015 TIR (total indicated runout or simply, out of round). Then I counted teeth and they were: 27, 41, & 62 respectively. This gave me enough to crunch numbers. Here is a table from my spreadsheet for the measured and calculated values.
Measured & Calculated Values for LMS, Diagonal Knurls
Notice these are the basic formulas from the ANSI Standard because the Dot measurement allowed me to calculate the rest. P can only be approximate because there is no way of knowing what the imaginary Dnt is for these tool so I used Dot, which we know is very close from the ANSI Method. If we round the TPI to Integers they are considerably different than 14, 21, & 33. These values should be Normal TPI, they are however Angular Knurls so if we back calculate the Transverse CP by dividing these values by (Cos 30=.866) we get 13.2319, 20.2277, & 30.5882. So, we could make a case that the Stated Pitches were in Transverse Values because we now know that TPI are Approximate values, even in Transverse.
The important values here are Pot and CP/π because they will be used in the final calculations. Pot is the CP on the Major Diameter (measured), basically the circumference divided by number of teeth. By plugging π back into the equation for CP/π it drops out and leaves Dot/Nt giving us the actual PF (pitch factor) based on the actual number of teeth on the tool. As a proof you can multiply this value by Nt and it will give you the actual Dot of the tool (.02778 x 27=.7500) or (.7500/27=.02778).
I basically went way around the block on this to ensure that I had all the numbers for empirically testing the final calculated material values.
Empirical Measurements
Next step in the development was to use Conrad's method as a backup proof. I cleaned all tools, found an ink pad and rolled them on paper to get as many points of measurement as possible. Here is my paper...sorry its a bit fuzzy but click on it to zoom in (Cntl++).
As you can see there were 5 measurements on each wheel up to 70 marks; these were then divided by the number counted (30, 40, 50, etc.) to arrive at a CP value for each measurement. Next was to average the 5 measurements to get an average distance between each mark for a large number (sample) of teeth. Note: I measured at the top of the marks so it would be like a Transverse TPI measurement. Then the average CP value was divided by π to get the PF...same as above.
Here is a table with the results to compare to the Measured and Calculated values, above.
Ink Pad Measured Values for LMS, Diagonal Knurls
As you can see these important values are Very Close to the measured and calculated values. In fact the CP/π average difference is .000303...meaning that either value could be used in the next step of creating the Look Up Table.
The Look Up Table
The next step in the development is based on Knowing that getting a good knurl depends on finding an Integer Ratio between the Tool and Work Material diameters, like Ghostses pointed out. To do this I created a table for multiples of the CP/π value for each tool up to about 3". This is because the LMS tool will only go up to 2" and even with the new chuck, I have yet to work material much bigger than about 2.75" on the Mini. Here is a sample of what the table looks like:
Lookup Table - Knurl Pitch - Multiples of AVG CP/π
These initial table values are primarily to show the Integer multiplier times the CP/π in each column (3 x .0268=.0805, etc.). The ability to knurl any material this small is likely impossible because of tooth depth. Typical stock sizes of 1/4" or larger begin around Multiplier 9 and end at 250 for a 3" fine pitch. We can now move on to the calculator.
The Calculator
The Calculator is fairly straight forward and uses an Excel function called "Lookup" for the multiplier table values. Lookup will look through a column of numbers (table) and find the nearest value to a number you place in an adjacent cell. What this means is: if we put our material value in a cell and then have Lookup search through a column of numbers, it will return the nearest value to the cell we build the function in. A picture is probably worth a thousand words here.
The following table shows the Lookup values for Course, Medium and Fine tools for 7/16" (.4375) material from my spreadsheet.
The Calculator for Work Material Diameter
These returned values provide a choice as to which pitch tool I want to use and a value to turn the stock material to, with High Hopes for achieving a good knurled part...All I ever asked for since the beginning.
End Notes
Developing this calculator was fun. However, it does not take in to account the tooth height because I don't have a way to measure it accurately. If I had a way, I believe pretty much all the formulas for DP could be used because we are using actual number of teeth and Dot measured. It would then be the most accurate because it allows for figuring the imaginary Nominal Diameter which is tied in throughout the calculations. It may be possible to measure with a thread mic, a 3 wire system or an Optical Comparator. The difficulty with CP tools and getting full specs is that their manufacture processes may not be as consistent as required by the ANSI Standard, especially if tooth depth is derived as a percentage of the Illusive CP.
Also keep in mind that Knurl Tools will wear over time, especially on hard metals, and will change their size and shape slightly...so keep them clean and keep an eye on them for wear.
Epilogue
I have created a working spreadsheet to calculate material sizes based on My Method which will calculate SAE & Metric material diameters for your knurl wheels. If you would like an Excel version of it you can purchase it for a modest $5 at HomemadeTools.net of which the first 1000 copies proceeds will be donated to this great forum.
Also, keep in mind there are many variables involved in Knurling as described on previous pages. Just because we have a cool spreadsheet doesn't mean we get Good Knurls every Time. In the final page of the Knurling Saga I will describe Techniques I learned and use, to minimize the other variables and how to Achieve the Illusive Good Knurl...as often as possible...~¿@