|
The determination of uncertainty associated with Rockwell hardness
measurements is a relatively new concept for many users of Rockwell
hardness as well as for laboratories engaged in hardness calibrations, such as
test block standardizing agencies. Traditionally, the acceptance criterion for
Rockwell hardness measurements has been through the use of acceptability
tolerances. This has been true for most all aspects of the Rockwell method
including measurements made as part of the direct and indirect verifications
of hardness machines and the standardization of test blocks.
Tolerance limits will continue to be used in Rockwell hardness. They provide
general criteria for determining whether a Rockwell hardness machine is
operating at an acceptable level of performance. What the acceptability
tolerance limits do not indicate is the accuracy in the measurements made
with the hardness machine. When it is important that the measurement
accuracy be known, then the uncertainty in the measurements should be
determined.
8.3.1 Uncertainty Limits
Uncertainty values are usually written as numerical limits bracketing the
measurement value. Stating a measurement value in this way tells the user
that the “true value" of the measurement would fall somewhere within these
uncertainty bounds. As an example of uncertainty as it might apply to Rockwell
hardness, consider a standardized hardness block that is certified with a value
of 25.3 HRC ± 0.4 HRC. In this example, the 25.3 HRC value is the certified
average hardness of the block, and the ± 0.4 HRC is the uncertainty in this
certified value. This means that although the standardizing agency estimated
the average hardness value of the test block to be 25.3 HRC, the “true value"
would fall somewhere within 24.9 HRC to 25.7 HRC. For a complete
understanding of this measurement and uncertainty, the values should be
accompanied with a brief statement defining what the uncertainty interval
represents. This statement should usually indicate the statistical process used
to calculate the uncertainty and state the confidence level of the uncertainty
interval.
It is important to understand the difference between uncertainty intervals,
such as given in the example above, and acceptance tolerance limits
traditionally provided with commercial test blocks. In the example above, the
± 0.4 HRC states that the standardizing agency can only estimate the “true"
average hardness of the test block and that the “true value" falls somewhere
within ± 0.4 HRC of 25.3 HRC. In contrast to these uncertainty limits, the
certified value marked on commercial test blocks in the United States has
included tolerance limits that reflect an ASTM acceptability requirement.
This requirement states that when using the test block to conduct an indirect
verification or daily check of a hardness machine, the machine’s measurement
value must fall within these limits. As a rule, the acceptance tolerances have
been stated in the same format as demonstrated above for uncertainty
statements, for example 25.3 HRC ± 1.0 HRC. These are clearly two
different concepts.
8.3.2 Highest Reference Standard
Before the level of uncertainty can be determined, the laboratory must
choose a reference standard to which the measurement value will be
compared. For example, the level of error in a Rockwell hardness machine
might be determined by comparing the result of a measurement made on a
standardized test block with the test block’s certified hardness value. It then
follows that the certified value of the test block also includes a level of error
with respect to another reference standard, typically the performance of the
hardness machine used to standardize it. The performance of the standardizing
hardness machine also includes a level of error with respect to a higher-level
reference standard, and so it goes to the highest level of reference.
The highest level of reference to which a measurement value is compared
might be referred to as the “true value." The level of error in the measurement
is then determined with respect to this “true value" taking into account the
errors at each of the reference levels between the measurement value and the
“true value". Ideally, the highest level of reference should be an internationally
agreed upon standard. In some cases, international agreement does not exist;
consequently national reference standards (i.e., NIST in the United States) are
typically considered the highest reference level. At present, this is the case for
Rockwell hardness.
8.3.3 Calculation of Rockwell Hardness Uncertainties
Over the past decade, there has been an increasing industry trend towards
obtaining quality program accreditation, as well as obtaining accreditation for
testing and calibration facilities. A common element of most of these programs
is the requirement for reporting the uncertainty of measurement data. As a
result, users of Rockwell hardness have struggled to develop procedures to
determine the uncertainty of Rockwell measurements.
Currently, there are no generally agreed upon U.S. or international methods
for calculating the measurement uncertainty of a Rockwell hardness machine
or the uncertainty in the certified value of standardized test blocks. A reason
for this may be that, until recently, there has been very little desire or need
by industries that use Rockwell hardness to use uncertainty values. Also, the
determination of Rockwell hardness uncertainty is not as straightforward as
it would seem.
For example, suppose the uncertainty is to be calculated by combining all of
the sources of error together. The errors associated with the hardness machine
are typically not in hardness units, but they are in other units, such as force,
length, and time. In order to determine an uncertainty in the hardness measurement,
the relationships between how these errors affect the hardness value must be
determined, often by experiment. Amplifying this problem is the fact that these
relationships vary by Rockwell scale and hardness level and are often material
dependent. In addition, the errors associated with a diamond indenter are difficult
to identify and more difficult to relate to errors in hardness. Thus, it is clear that
determining the hardness uncertainty by assessing the individual components of
the hardness machine is extremely difficult to accomplish.
A different approach to determining Rockwell hardness uncertainty is to
assume that by passing a direct and indirect verification, the errors in the
individual operating components of the hardness machine are small enough
that the indirect verification measurements are not the result of multiple large
errors offsetting each other. Thus, the individual machine components can be
considered to be operating together as a single component. The individual
operating components include the force application system, depth measuring
system, indenter, test cycle, and the remaining parts of the machine frame
and test specimen support system. By considering the hardness machine as
a single component, the uncertainties may be estimated with respect to the
overall performance of the hardness machine without having to assess the
uncertainty contributions for each of the separate machine components.
When this approach is used, the most significant sources of error have been
determined to be the following:
(1) Repeatability in the performance of the hardness machine.
(2) Reproducibility in the day-to-day performance of the hardness machine,
including operator influence.
(3) Resolution of the measurement indicating display.
(4) Uncertainty in the certified average hardness value of the reference test
block.
(5) Non-uniformity in hardness across the surface of the test block or test
material.
(6) Bias in the hardness machine measurement with respect to the reference
standard to which traceability is claimed.
(7) Determining the hardness machine measurement bias.
(8) Correcting for the measurement biases.
(9) The remaining bias in the hardness machine after a correction for bias is
made.
As this guide is being written, there are efforts both internationally and
within the United States to develop general procedures to assist Rockwell
hardness standardization laboratories and users of Rockwell hardness in
evaluating their measurement uncertainty. In the United States, the ASTM has
initiated the development of such a procedure, and the ISO is to take up this
issue at the next committee meeting of ISO TC164/SC 3 subcommittee on
hardness testing in 2001.
Back
|
