Calculating Measurement Ranges and Tolerances

This article applies to: All Brookfield laboratory viscometers

Looking at the Brookfield catalog, you may notice minimum and maximum measurements that cover a huge range of viscosities. For example, the RV DV2T gives a range from 100cP to 40,000,000cP. This is the overall range of the instrument and encompasses every spindle and speed combination the instrument is capable of. The working range of an instrument is determined for each measurement method, and is calculated based on the instrument torque, spindle, and spindle speed. If any of these factors change, then the working range of the instrument will also change.

In this article, we will discuss how to calculate and understand the working range of your viscometer, as well as discuss the uncertainty or tolerance that is applied to each measurement taken with the instrument.

This article will reference tables and figures in Appendix A of More Solutions to Sticky Problems.

Understanding working ranges

Every Brookfield laboratory viscometer has a range of viscosities it is able to measure given a particular spindle and speed selection. This working range will be significantly narrower than the overall ranges given for the instrument.

The basic reading given by a Brookfield viscometer is a unitless value of “percent torque” (%) between the values of 0% and 100%. On legacy analog instruments, this is also called the “Dial reading”. This value is what is used to calculate the viscosity reported by the instrument.
A VALID viscosity measurement can be taken between 10% and 100%.
Below 10%, and the instrument may still report a value, but this value will not be accurate. Above 100%, your instrument will state “EEEE” for the viscosity, this is the over-torque error.
The 100% torque value is referred to as the full-scale range.

If you are trying to take a measurement, and the instrument is displaying an over-torque error (“EEEE”), or displaying a very low measurement torque (below 10%), then you can adjust your measurement method to alter the instruments working range to better fit your sample.

Calculating a working range

Every spindle produced by Brookfield has a spindle factor. These factors are empirically calculated functions that allow for a simple conversion between percent torque and viscosity. Spindle factors are listed in Appendix A of More Solutions to Sticky Problems, and are given in the form [number]/N, where N is the selected spindle speed in RPM. A spindle will have multiple factors that depend on the torque of the instrument it is installed on, so make sure to note which instrument you are calculating for (LV, RV, HA, HB, etc.)

To arrive at the viscosity reading being measured by an instrument, you can take the above factor, and multiply it by the percent torque, or dial reading. This will give a viscosity value in centipoise (cP).

For example, if an RV-04 spindle was being used on an RV torque instrument at 20RPM and the torque value displayed was 62.3%, you could determine the viscosity reading using the factor 2000/N from Appendix A of More Solutions to Sticky Problems in the following equation:

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Substituting in the appropriate values, we get the below result.

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Using the above equation, we can determine the working range of a particular measurement using the knowledge that the minimum valid percent torque is 10%, and the maximum is 100%.

Continuing with the above example, we can calculate the working range of an RV viscometer with the RV-04 spindle at 20RPM as follows:

Understanding and calculating measurement tolerances

Every measurement taken with a Brookfield instrument has some amount of uncertainty associated with it. This uncertainty is denoted as a measurement tolerance, where the actual viscosity of the fluid being measured can be within a specified range of the measured viscosity. The uncertainty or tolerance of measurements is given as a percentage of the full-scale range, or 100% torque value.

• For standard spindles (RV-03, LV-01, HV-05, etc.), the tolerance is +/- 1% of the full-scale range.

• For cone and plate viscometers, the tolerance is +/- 1% of the full-scale range.

• For accessories such as the small-sample adapter, Enhanced UL adapter, etc. the tolerance is +/- 2% of the full-scale range.

These tolerances can be calculated using the same equations above and substituting the tolerance percent into the percent torque position. Continuing with the same example of the RV instrument with an RV-04 spindle at 20RPM, this would give a measurement tolerance of:

This means that any measurement taken with an RV instrument using an RV-04 spindle at 20RPM would have an tolerance of +/- 100cP. Since this is based on the full-scale range, it is not affected by the actual viscosity being measured. Below are some examples of how this tolerance is applied.

Notice that even though both measurements carry the same tolerance, the tolerance applied to measurement 2 results in a lesser overall range of possible viscosities compared to the nominal. This is due to the tolerance being based on the full-scale range of the measurement. The closer the measurement torque to the full-scale range, or 100%, the smaller overall effect the tolerance might have.

There are plenty of situations where it might not be feasible to design tests for the maximum possible torque reading, but in general, readings of higher torque percent will have lower overall uncertainty.