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ANSI Method

The ANSI Standard (B94.6-1984) is for Knurls and Knurling and covers knurling tools with standardized diametral pitches and their relation to the work material.  The standard covers straight, diagonal, and diamond knurling on cylindrical surfaces up to 1" material. 

It is based on the Pitch Diameter of the material to be knurled using a Standard Knurling tool with several defined Diametral Pitches (64, 96, 128 & 160), with 96 being the preferred for simplified tooling.  Using this standard assures good knurl tracking (teeth meshing in successive revolutions) and allows one to use standardized material sizes in fractions of 1/64" & 1/32" (normal Stock Diameters).  What this means is if you are working with a piece of 1/2" stock and use a 1" 96DP tool you will get 48 lines on your stock (96 x .50)...a direct ratio.

Diametral Pitch (P) is defined as the basic blank diameter divided by the number of teeth in the circumference of the work (P=Nt/Dnt) The key here is that you work from stock material, as in the 48 lines in 1/2" stock above, because the tool is standardized.

Knurl Tools

The standard also defines the tooling.  However, for the tooling "P" is defined as the number of teeth in the circumference divided by the Nominal Diameter.  As you can see in my reproduction drawing from the Machinery's Handbook the Nominal Diameter (Dnt) is outside the diameter of the finished knurl tool.  I exaggerated the drawing because the small print in the book is a bit misleading.   



Here are the basic formulas.
Machinery's Handbook Definitions
Based on Std. Material Ø with Knurl tools having Std. Diametral Pitches (P) of 64, 96*, 128, & 160
P = Diametral pitch of Knurl = Nt/Dnt
Dnt = Nominal diameter of knurl = Nt/P
Nt = No. Teeth on Knurl = P x Dnt
**Pnt = Circular Pitch on nominal Diameter = π/P
**Pot = Circular Pitch on Major Dia. =  πDot/Nt
Dot = Major Diameter of Knurl = Dnt-(Nt*Q/π)
= Tracking correction factor= Pnt-Pot
* Note: The 96 Diametral pitch Knurl should be given preference in the interest of tool simplification.
** Note: For diagonal knurls, Pnt and Pot are transverse circular pitches which are measured in the plane perpendicular to the axis of rotation.

All of these confusing and convoluted definitions become clearer after close examination of the specs for the knurling tool and associated notes! The following charts are reproduced from the Handbook and more technically pertinent to the manufacture of the knurl tool...however this first one gives you the basic information to work with the Material and formulas above, too. Confusing at best, and as my father used to say, "A mouse built to government specs is an elephant!".

Note: the highlighted 3/4"Dnt x 3/8"F x 1/4"A knurl gives you 72 teeth for a 96P knurl.  It is the number of teeth around the circumference (96 x .75 = 72).  Keep in mind this is the Nominal Diameter and is basically imaginary until you review the next table below.

 

In the above table you will notice the 3/4"Dnt knurl has a Major Diameter of .7440± with the rest of the pertinent data (tooth depth, root radius, as well as the Q factor mentioned in the formulas above) used to manufacture the tool itself. How these Major Diameters were actually derived is in the formula above for Dot; in this case 72t-((72t x .0002618Q)/π) = .7440
 
Note: the actual number of teeth are used in the formula and Not the DP number of teeth because we are using a Nominal 3/4" knurl.

Q factor is an empirical correction factor needed to insure good tracking because of all the variables like: material hardness, elasticity of holder and penetration of the work during the first revolution of the material. This allows one to find the actual Circular Pitch (Pot) needed at the major diameter of the knurl. In this case it is (π x .7440Dot)/72Nt = .0325...in other words the tool Circumference (Cir.= π*D) divided by the number of teeth is the actual Circular Pitch of the tool.  Pnt is the Circular Pitch on the Nominal Diameter and through the formula we have π/96 = .0327.  Notice in this case we used the actual Diametral Pitch P of 96, because any 96P tool will have the same radial distance on the Nominal Diameter between teeth, no matter what size it is. 

This drawing of a 3/4" tool is a 1:1 scale CAD drawing and dimensioned directly without any changes.  Hopefully you can see the detail...pick on it to open in another tab and zoom in if necessary.


Note: In the drawing, the Pot dimension was selected from the apex of the two adjacent teeth, where as the Pnt dimension was selected from the intersection of the radii through the teeth at the points intersecting Dnt.  Basically this shows the .0002 difference between Pot & Pnt is the radial difference of .006 between Dot & Dnt.

Intermission

Hopefully after all of this you haven't spun out in Diurnal Circles and Pitched all of this Diametrically into the Circular File...Nominally with a Q factor force! @¿@  My Dad used to tell the story of the Mugwump bird in the Alps...when it first leaves the nest it flies up higher and higher in ever decreasing circles until it is such a tight circle that its head goes up its rear and it Squawks, MUGWUMP.  Somehow I thought the story fitting...We are almost home now, with only a few more formulas to Actually "Make Chips" with Standard Pitch knurl tools.

Knurling

The following are the formulas that are applicable to Knurled Work (Making Chips).  They are very similar to the above but are applied to the Materials.

Here are the basic formulas.
Formulas Applicable to Knurled Work
for Straight or Diagonal Knurling with Straight or Diagonal tooth cylindrical Knurling Tools Set with the Knurl Axis Parallel with Work Axis. 
P = Diametral pitch = Nw/Dw
Dw = Work Blank diameter = Nw/P
Nw = No. Teeth on Work = P x Dw
a = "addendum" of tooth on work = (Dow-Dw)/2
h = Tooth depth (see Table 2)
Dow = Knurled Diameter (outside diameter after knurling) = Dw + 2a

As you can see the formulas here are similar ratios to the ones above but the names have been changed to protect the guilty! 8-)  However, there are still some circular references with Dow, Dw and the new "addendum".

Armed with all of this, lets run through an example of creating a straight knurled piece with Standardized Knurl Tools and try to solve all the math.

We'll start with 1/2" stock and a 1" 96P straight tool.  We know that a 1" 96P tool will have 96 teeth on it, so we should get 48 lines on the 1/2" stock...so our Nw will be 48, our Dw will be .500 and P will be 96 (48/.500).  For all practical purposes this is all that's required to make good knurls with Standard DP Knurls.

The only rub comes in if you have a critical Dow for a press fit spline joint which means you need to know or figure the OD after knurling.  For all practical purposes the "Addendum" is the mid point between the root and apex of a tooth or 1/2h.  Table 2 tells us that h for a 1" 96P straight tool is .024 so the addendum is .012.  Notice the formulas for "a" and Dow either divide by 2 or add (2 x a).  In the case above our Dow should be (.500 + .024 = .524) and our "a" for this tool will always be (.024/2 = .012)


Epilogue

The real issue I've had with the Standard is multiplicity of meanings applied to the word Knurl and how it applies to the act of knurling, the tool design, and the result of the operation.  Additionally the use of the word Nominal is one of those old throw backs to how pipe and tubing are specified rather than what it's actual size is.  This has always been problematic to work with and communicate with others.  In My Opinion, Terms should always be defined first and simply in a standard.  I have written many SOP's and Company Standards over the years and always followed this rule...just gets people on the same page from the get go. ;-)

After reading this diatribe I hope you can see the simplicity of using standardized knurling tools on standard stock sizes.  Creating a knurled piece doesn't really use a lot of detailed math.  As you can see in the example, it's
basically simple Integer ratios, once you get how they were derived...hopefully I helped with that here. 

To me the only issue with using these is getting the basic Course, Medium, and Fine pitches on your work and being able to choose the appropriate DP Tool to achieve the basic three types.  This is because the standard also alludes to finer pitches having some issues with tooth tracking and probably why they recommend that 96DP as the "Preferred" pitch.

The Standard also contains two other important specs.  First, they have associated tolerances in three classes (I, II, & III).  They cover tolerance on final OD dimensions and Work Diameter before knurling. 
  1. Class I is very loose and generally for knobs and handles without critical dimensions. 
  2. Class II is for straight knurling only, to control the OD and tighter than Class I. 
  3. Class III is the tightest for straight knurls, mainly for close or press fits.
Second, the standard requires that all standard DP knurl tools be stamped with the following:
  1. for straight knurls the DP
  2. for diagonal, to indicate its DP, Helix Angle and Hand of angle (LH, RH)
As I have said previously, it is always about Knowing what tool you actually have.  If you buy Standard DP Tools they should be stamped appropriately.  However, because there is an older standard based on CP (Circular Pitch) and tools are still being made to these specs, the Standard also gives us some wherewithal to actually figure out what we have, when its not stamped.   On subsequet pages I will try to explain this, and how to use what you actually have.

CP Method, Hunt & Peck, My MethodPJ's Knurl Calc, Techniques