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How to Reduce the Biggest Error Contributor in Temperature Calibration

​There are many error sources when performing temperature calibration in a dry-block and very often it is necessary to make an uncertainty budget. The list of error sources is long and comprises:

By Henrik Bendsen, Product Manager of JOFRA temperature calibrators

Henrik Bendsen, Product Manager of JOFRA temperature calibrators

Henrik Bendsen, Product Manager of JOFRA temperature calibrators

  • ​Axial gradient
  • ​Horizontal gradient
  • ​Temperature coefficient
  • Load
  • Resolution
  • Stability
  • Drift
  • Hysteresis
  • Insert
  • Insert age
  • Curve fit error

Normally, the specifications of a temperature calibrator is based on tests performed under “ideal conditions”. For example, the load of the insert is kept at a minimum during these “ideal conditions”, which means that the calibrator is only loaded with a reference sensor. This scenario differs from the conditions when the calibrator is actually used by the end-user for calibrating a big diameter sensor, or even more sensors calibrated at the same time. Both are scenarios that can cause errors in your calibration results if you do not take precautions.

So, what can you do to reduce error in your temperature calibration? Well, the two biggest contributors to error are the load of the calibrator and the axial gradient, so let’s take a closer look at those.

Error Due to Load

If a calibrator is loaded with a 10 mm diameter sensor the error caused by this load can easily get to 0,15°C or more depending on the calibrator being used. The error from load is not a fixed value but is dependent on the sensor diameter of the UUT (Unit Under Test).

The error caused by load can very easily be reduced to a tenth or less just by using an external reference in the insert together with the UUT sensor. The external sensor can be as a stand alone together with an external handheld thermometer or, maybe even better, the external reference can be connected directly to the calibrator.

By connecting the external reference sensor to the calibrator, the reference sensor can serve two purposes at the same time. First of all it serves as the reference indicating the accuracy, but at the same time it is used as the controlling sensor.

By using an external reference sensor the error caused by load is dramatically reduced.

Temperature Calibration - Maskiner

Error Due to Axial Gradient

The ideal way to calibrate is in a bath with very high stirring and thus getting a very high temperature homogeneity around the sensor that is calibrated. There are several reasons why this is not a practical solution though. Bath calibrators are often big and heavy and therefore not practical for on-site calibration. On top of that there is a safety issue with the risk of spilling hot oil, and the sensors being “polluted” with silicone oil.

For these reasons a dry-block calibrator is often the chosen solution when performing on-site calibration. The term homogeneity is now replaced by axial and radial gradients as we move from a liquid bath to a dry-block.

Due to the relatively small diameters of the insert in a dry-block calibrator, the error steaming from radial gradient is normally very small, typically 0,01°C. The error from axial gradient is normally far higher even with a relatively small load. Moreover, the error contribution from axial gradient is changing with different loads and different temperatures.

How to Minimise Errors from Axial Gradients

The first step to take to minimise error from axial gradient is to choose a calibrator with a dual-zone design as these types of calibrators have a main heating zone at the lower part of the calibrator and a top zone performing compensation for the heat loss. The dual-zone calibrators are supplied with special internal sensors that can measure the temperature at the two zones, and that can control the energy from the individual zones.

By doing this they are able to equalise the temperature differences. To make this system efficient the “zone” sensors needs to be placed in the insert alongside and very close to the UUT sensor.

To minimise the axial gradient to an absolute minimum these zone sensors should influence directly on the energy distribution to the two heating zones. The system that makes the dual-zone calibrators able to equalise the temperature difference is called DLC (Dynamic Load Compensation) and is typically only available on top-model temperature calibrators on the market.

The value of the difference in temperature from the bottom of the calibrator and 60 mm up is shown in the display of the calibrator and the value is used by the controller to minimise the axial gradient. End result is that the DLC system makes a dry-block perform like a bath in regard to temperature homogeneity and tells the user what temperature contribution is inside the calibrator.

Temperature Calibration -

What Are the Important Benefits of the DLC System?

So, to sum up, by using a dry-block calibrator with a DLC system you not only ensure that big diameter sensors are calibrated without losing accuracy due to heat conduction, you also save time on calibrating multiple sensors simultaneously.

The displayed difference temperature value for the axial gradient indicates when the optimum temperature homogeneity is achieved in the dry-block, and when the load has minimum influence on the calibration result. When the difference temperature value is close to zero, the calibration technician knows that the calibration results are reliable.

But there is also the impact of the uncertainty budget to take into consideration. So, let’s take a look at how using a dry-block with a DLC system impacts this.

What Is the Impact on the Uncertainty Budget?

The biggest error in the uncertainty budget is by far the axial homogeneity. By using the value of the difference temperature measurement, and putting the reading in the uncertainty budget, the overall uncertainty with K=2 can be reduced from 0,185°C to 0,034°C.   

Uncertainty budget: Calibrator loaded with ø 10 mm sensor with no gradient control

​1

​Temperature of reference thermometer

121,003

​2

​Uncertainty reference thermometer (k=2)

​0,015

​Normal

​0,0075

​3

Resolution of RTC temperature indicator

​0,001

Square

​0,0003

​4

​Hysteresis effect

​0,008

Square

​0,0046

​5

Axial temperature homogeneity

0,159

Square

0,0918

6

Radial temperature homogeneity

​0,004

Square

​0,0023

​7

​Loading effect

​0,004

Square

​0,0023

​8

Stability in time

​0,003

Square

​0,0017


​121,003

​k=1

​0,092


​Geometrical sum

​k=2

0,185


Uncertainty budget: Calibrator loaded with ø 10 mm sensor with gradient control

​1

​Temperature of reference thermometer

121,003

​2

​Uncertainty reference thermometer (k=2)

​0,015

​Normal

​0,0075

​3

Resolution of RTC temperature indicator

​0,001

Square

​0,0003

​4

​Hysteresis effect

​0,008

Square

​0,0046

​5

Axial temperature homogeneity

0,024

Square

0,0139

6

Radial temperature homogeneity

​0,004

Square

​0,0023

​7

​Loading effect

​0,004

Square

​0,0023

​8

Stability in time

​0,003

Square

​0,0017


​121,003

​k=1

​0,017


​Geometrical sum

​k=2

0,034

Conclusion

With a DLC system in a dry-block calibrator you can get calibration results that are extremely close to the results achieved if the same calibration was performed in a bath as the dry-block performs bath-like homogeneity. The dry-block performs as a calibration bath but without the disadvantages such as heavy weight, slow calibration and the risk of hot-oil-spills.

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