Load Cell Stability – How It Can Kill Your Uncertainty Budget
Load cells are a combination of metal, strain gauges, adhesive, and more. Like humans, every measuring instrument is subject to aging. Load cells age from mechanical stress or fatigue and overtime this ensures that there will be some instability in the system. This cannot be prevented, but it can be detected and corrected by setting the appropriate calibration cycle. Load cell stability or drift is usually assumed to be the amount of change in the entire cell system from one calibration cycle to the next. It is the relative standard uncertainty of a reference force transducer’s long-term instability. In an uncertainty budget, load cell drift can be referred to as either the reference standard instability or the reference standard stability.
Load cell stability can impact the following:
- Potentially consume your uncertainty budget
- Cause the force measuring device to be out of tolerance
- Cause all measurements between the last calibration and the current calibration to be recalled
- Raise the accuracy specification of the system
Calibrating load cells for more than 50 years, Morehouse has observed all kinds of instabilities from different manufacturers. Most load cells we see are categorized as either general purpose or those calibrated in accordance with more stringent standards, such as ASTM E74 or ISO 376. We are going to discuss both types of load cells and their typical instability characteristics. In each case, we will start with the general uncertainty contributors, then progress to what we normally observe and give recommendations for improvement.
The systems are each broken down into Good, Common, and Bad. Systems that fall into the Good category are usually those by reputable manufacturers who understand load cells and indicating systems. The Common category may consist of suboptimal combinations, such as an excellent load cell and an average indicator or an excellent indicator and an okay load cell. In the Poor category, one or both components are probably not suitable for the end user’s overall uncertainty needs.
Typically, general-purpose load cells are more inexpensive and are paired with indicating systems which also contribute towards drift. The requests we see on these systems is generally for a 10-pt. calibration. The accuracy specifications are usually 0.05 % to 1 % of full scale.
Figure 1: Typical Instability Numbers for Various Load Cells
The long-term instability of the reference force transducer is determined either from previous calibrations or by estimations of similar systems until the actual values can be obtained. Figure 1 above shows the instability Morehouse typically observes on general-purpose load cells.
Next, we will discuss calculating expanded uncertainty and how reference standard stability (or instability) affects overall expanded uncertainty.
General Purpose Load Cells
Typical contributions for the CMC uncertainty of General Purpose load cells are:
Type A Uncertainty Contributions
2) Repeatability or Non-Repeatability of the Reference Standard.
3) Repeatability of the Best Existing Device (and technician)
4) Repeatability and Reproducibility
Type B Uncertainty Contributions
5) Resolution of the Best Existing Device
6) Reference Standard Resolution* If Applicable
7) Reference Standard Uncertainty
8) Reference Standard Stability (our topic today)
9) Environmental Factors
10) Other Error Sources
11) Specified Tolerance * If Not Listed and making ascending measurements only. If making Ascending and Descending Measurements Use Static Error Band (SEB) or a combination of Non-Linearity and Hysteresis. If the force measuring device is calibrated with an indicator and set up to have a tolerance, then it may not be necessary to include non-linearity or SEB.
*Note: if the device is going to be used at points different from the points it was calibrated at than SEB, Non-Linearity, or Hysteresis may need to be used.
12) Hysteresis * (Only if the Device is Used to Measure Decreasing Forces and SEB was not used)
Figure 2: Expanded Uncertainty Budget with 0.2 % instability
With general-purpose load cells, it is common to observe systems with accuracy specifications lower than the instability observed from one calibration to the next. If the accuracy requirement is for 0.1 % of full scale and the instability from one calibration to the next is 0.2 %, it becomes nearly impossible to claim 0.1 % accuracy as your tolerance. Figure 2 shows the uncertainty of 0.2 % instability on a 10,000 lbf load cell. This accounts for approximately 95.90 % of the uncertainty contribution.
When accounting for reference standard stability in an uncertainty budget, stability can be treated as type A or B. Most calibration laboratories claim instability as type B uncertainty contributor with a rectangular distribution. This means that instability of 0.2 % would be divided v3 (or 1.732) which is about 0.115 %.
Now let’s think about that. A calibration laboratory is claiming 0.1 % accuracy on their scope and their device’s instability is accounting for 115 % of their accuracy statement alone. I guess this is a case of accounting for more than the 100 % allowable. The solution to this problem is often simple. Either shorten the calibration frequency or purchase better equipment. This could mean upgrading the indicator, load cell, or both.
Next, let’s assume the end-user decided it would be much less expensive to buy a better load cell than to shorten the calibration interval. A year after the purchase, the reference standard stability is observed to be 0.05 % or 5 lbf on a 10,000 lbf load cell.
Figure 3: Expanded Uncertainty Budget with 0.05 % instability
In this example, shown in Figure 3, the Reference Standard Stability still is the largest contribution to the Expanded uncertainty. However, the end-user can now actually claim 0.1 % of full scale and have a bit of room to maintain the accuracy from one calibration to the next. In fact, the instability can go as high as 0.077 % and they could still be within the 0.1 % of full scale!
Figure 4: Morehouse Calibration Grade Load Cells
The Morehouse calibration grade load cell with PSD hand-held indicator will typically maintain an accuracy of 0.1 % of full-scale year over year with instability accounting for about 0.05 % of overall accuracy. If an accuracy of 0.05 % or better is required then we recommend a different meter, most likely either the Gauge Buster 2 or the Morehouse 4215.
Devices Calibrated in Accordance with the ASTM E74 Standard (Usually Metrological Grade Load Cells and Indicators)
Note: This section can be used for the devices calibrated in accordance with ASTM E74 and used for ASTM E4 and other calibrations for determination of the CMC uncertainty. The ASTM E4 Annex gives additional detail on how to calculate the measurement uncertainty for the ASTM E4 verification/calibration.
The contributions for the CMC uncertainty are:
Type A Uncertainty Contributions
1) ASTM LLF reduced to 1 Standard Deviation (ASTM LLF is reported with k= 2.4)
2) Repeatability with the Best Existing Device
3) Repeatability and Reproducibility
Type B Uncertainty Contributors
1) Resolution of the Best Existing Device
2) Reference Standard Resolution* If Applicable
3) Reference Standard Uncertainty
4) Reference Standard Stability (our topic today)
5) Environmental Factors
6) Other Error Sources
All uncertainty contributions should be combined, and the Welch-Satterthwaite equation should be used to determine the effective degrees of freedom for the appropriate coverage factor for a 95 % confidence interval. Figure 5 below shows typical numbers Morehouse has observed regarding instability. ASTM calls this “change from previous”.
Figure 5: Typical Instability Numbers for ASTM Load Cell Calibrations
Note: In this example, anything over 0.16 % of the applied force is bad because we are discussing ASTM calibrations and section 11.2.1 of ASTM E74-18 states “Force-measuring instruments shall demonstrate changes in the calibration values over the range of use during the recalibration interval of less than 0.032 % of reading for force-measuring instruments and systems used over the Class AA verified range of forces and less than 0.16 % of reading for those instruments and systems used over the Class A verified range of forces.” The assumption is that most end-users are using the force-measuring instruments for calibration in accordance with ASTM E4 and would like to comply with the ASTM E74 standard. That requires a calibration interval of two years.
Section 11.2.2 states “Force-measuring instruments not meeting the stability criteria of 11.2.1 shall be recalibrated at intervals that shall ensure the stability criteria are not exceeded during the recalibration interval.” Basically, the standard says that if the criteria are not met, then the calibration interval must be shortened until it is met.
Through our experience, we have rarely observed Bad load cells meet the stability criteria if the calibration interval was shortened to one year. If stability is higher than 0.16 % and everything else remains constant (e.g. the cell has not been overloaded), then the recommendation is to replace the load cell.
Let’s look at two examples with comparing a reference standard stability of 0.16 % (Figure 6) to a typical Morehouse HADI system with Ultra-Precision Class or better load cell with 0.01 % stability (Figure 7).
Figure 6: ASTM E74 Expanded Uncertainty with 0.16 % stability
Figure 7: ASTM E74 Expanded Uncertainty with 0.01 % stability
The actual load cell in this test is a Morehouse Ultra Precision 10,000 lbf load cell with an ASTM lower limit factor (llf) of 0.25 lbf. Assuming everything else remains the same, in both scenarios the Reference Standard Stability is the largest contribution to uncertainty. Often, this isn’t the case. Load cells with bad instability often have much higher llfs than better load cells. A load cell with 0.16 % stability will usually have an llf worse than 2 lbf.
However, the purpose of this blog is to show the impact of stability on a load cell system and how it should impact your decisions when purchasing a load cell system. If stability is bad, the system will probably not meet your accuracy requirements. In general, I would say repeatability, reproducibility, and stability are the most important characteristics when evaluating a load cell system. Adapters play a huge role in actual results, and careful attention to purchasing the right adapters must also be considered. For more information on the proper adapters, Morehouse has a technical paper that can be downloaded here.
Figure 8: Morehouse HADI calibration system
The Morehouse Ultra-Precision Load Cell with the HADI system will typically maintain an ASTM Class A verified range of forces from 2 % of capacity (accuracy at the time of calibration of 0.005 %) or better year over year. Instability accounts for 50 % or less of the overall uncertainty budget, usually below 0.02 % of applied force (0.01 % or better instability from year to year).
If I can stress anything, it is reference standard stability that must be considered in any uncertainty budget and overall system accuracy should be adjusted accordingly. Manufacturers often highlight short-term accuracy and discount drift from their accuracy specifications. We know that instability largely depends on how equipment is used, the number of load cycles, the age of the material, the strain gauge bond, electronics, and more. Instability is a number best quantified when comparing one calibration against another with all other things being equal. Load cell drift is often overlooked and should not be discounted when considering system accuracy.
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