02-22-2018, 06:08 PM
(This post was last modified: 03-03-2018, 03:15 PM by Mike Brubacher.)

### Brubacher/Svancara

### Rockwell C Differential Comparitor

This calculator computes the change in hardness from one HRC number to another

"instructions"> Enter the first HRC value in the box and then the second HRC value in the next box. Click "CALC". Answer will be displayed as a percent (%) change. Click "RESET" to clear boxes. Visit bessex.com for a full explanation of this calculation, or go to edgeonup.com to download this calculator.

Copyright 02/26/2018 Brubacher/Svancara - The above calculator is optimized for Google Chrome Browsers. It may display differently in other browsers.

Comments on the calculator program for determining percentage change of hardness between two Rockwell C hardness numbers

In the thread “Rockwell C Linearity Study” of the BESS Exchange forum we presented a simple formula which tells us the percentage change of hardness between two immediately following HRC numbers (e.g. between HRC 60 and HR 61).

For the use in the hardness difference calculator we derived a equation for determining the relative difference in hardness for two arbitrary Rockwell hardness numbers (e.g. HRC1 = 50 and HRC2 = 60).

The formula looks like this:

The above equation sums up our efforts expended during the last year on a better understanding of the Rockwell C hardness scale. This equation represents the mathematical formula for determining the relative difference in hardness of one Rockwell C hardness number to another. The above calculator function reports that difference as a percentage. When we first began this project we did not hold out much hope for actually solving the problem of putting the Rockwell C (HRC) into well defined and meaningful terms but rather were hoping just to make it a bit more meaningful in relative terms. Our expectations were tempered by the fact that, simply, this question has been asked for a hundred years and never, to the best of our knowledge, answered. Given the prevalence and commonality of the HRC test method, that would give anyone pause when contemplating this question. In the end though, the question was substantially answered in not one, but three, while related, still different and independent approaches. Since all three of these methods, each independently arrived at, seem to support each other, it gives us some confidence in the correctness of our efforts. In view of the fact that most of us had not even a good idea or guess as to the relevance of one HRC number to another, we feel that the calculator can make a real contribution to our understanding and use of the HRC scale.

The first of our efforts resulted in the generation of a study of the geometric attributes of the HRC indenter itself . That study resulted in the following chart:

This chart calculates and then compares the percentage change in surface area of the HRC indenter in .002mm increments. While this chart does not represent the answer, it does make a significant contribution in setting the path to the answer. The equation listed at the top of this page draws on some of the work done by George and Robert Vickers and incorporates information drawn from elements of the chart. For those who may not be aware, the Vickers uses a very different method than HRC in calculating hardness. Vickers hardness calculations are made by measuring the area of the indentation and then factoring in the force applied. The relevance of the Vickers work to this project can simply be described as this; the Vickers Hardness Scale is linear. Scales that are linear lend immediate and intuitive relevance to their output i.e. assuming that the scale's increases are in an ascending order, then 50 is twice as much as 25 and 100 is four times as much as 25.

The HRC cannot be linear due to the fact that it utilizes a constant force (load) and a constantly changing indenter impingement area. Therefore, materials of various hardness are tested under various circumstances. There is no "apples for apples" with the standard HRC scale unless one is always testing the same hardness of material.

Fortunately the HRC test method does provide us with a key bit of information; we know the depth of indenter penetration into the sample. The force or "load" is constant with the HRC and since the HRC indenter is of a well known geometry, we can then calculate the surface area impinging on the test sample. This then leaves us with more of "Vickers Like" calculation of hardness.

A third checkpoint in this process then is simply this; just as the conversion graph above demonstrates , we can take advantage of the many different types and styles of Vickers to Rockwell C converters available. Many of these seem to vary somewhat in their interpolations but, generally, they support our equation. The process here is a simple one when proving the calculator's general correctness. If the Vickers is linear then its correspondence with any two HRC numbers (within the accuracy constraints of the conversion) must be linear as well. Find a converter and then pick any two HRC values and their corresponding Vickers values. Simply calculate the percentage difference between the two Vickers numbers and compare with our calculator result. Due to the vagaries of the various conversion charts the comparisons aren't likely to be precise but you should find that they are proximate.

Here then is another method and an exercise in comparing our calculator results to our earlier chart results; enter any two HRC values that are immediately proximate to each other i.e. 60-61 or 32-33 and then compare our calculator result to the corresponding chart result. The result will be nearly precise.

Acknowledgement:

Our thanks to Wade Bevan for his help in the construction of this web-based calculator program.