High Inertia Rheometer Design

Rheometer designs with high inertia limit your ability to produce accurate rheological data.

With any combined motor and transducer rheometer (traditionally known as stress controlled rheometer), the contribution of the inertia of the moving parts to the measurement is an extremely important consideration.  We learn from Newtonian Physics that F (force) = M (mass) x A (acceleration), or in rotary terms, T (torque) = I (moment of inertia) x A (angular acceleration).  This fundamental equation shows that the less inertia a system has, the less torque it will take to meet a desired acceleration rate. Therefore, it is advantageous to minimize inertia to in order to maximize acceleration. In a rheometer, minimizing motor inertia allows most of the motor’s torque to accelerate the sample, not ‘wasting’ much of the motor’s torque accelerating its own inertia.

Consider the schematic of a combined motor and transducer rheometer (Figure 1).  The input to make a rheological measurement is torque (current to the motor), regardless of whether the control mode is strain or stress.  When torque is applied to the motor, part of that drive torque goes into accelerating the motor, while part deforms the sample.  As the inertia of the moving parts of the rheometer increases, more of the applied torque is taken up by accelerating the motor, and less of the applied torque is taken up by deforming the sample.

Keeping the inertia as low as possible is important in step rate experiments, fast sweep flow curves, and any dynamic test - especially those at high frequency and/or on low viscosity fluids.  Inertia is an often-overlooked specification when evaluating a combined motor and transducer rheometer.  For example, many rheometers specify a maximum drive frequency of 100 Hz (628 rad/s).  However, the maximum obtainable frequency is actually dependent on the viscosity of the sample and the inertia of the rheometer.  This fact is easily observed by running frequency sweeps on various silicone oil standards.

Figure 2 shows a comparison of three frequency sweeps on Cannon viscosity standards.  In this example the rheometer is a low inertia design (such as TA Instruments drag cup design) with total system inertia of about 17 μN.m.s². Silicone oil standards are Newtonian over the measurable frequency range of a shear rheometer.  It is easily observed that:

• The S600, with a Newtonian viscosity of ~ 1,000 mPa.s at 25°C, shows a constant magnitude of the complex viscosity, η*, to the maximum frequency of 628 rad/s. 
• The S60 (η ~ 100 mPa.s), η* begins to increase at a frequency of about 100 rad/s.
• The S3 (η ~ 3 mPa.s), η* starts to increase at 5 rad/s. 

The apparent increase in viscosity is due to the inertia of the moving parts of the rheometer.  

Figure 3 shows data obtained on a rheometer with a high inertia design (inertia ~ 93 μN.m.s² ), istypical of an electrically commutated motor (ECM).  Note when testing under the same conditions, accurate results on the S600 standard can not even be achieved to the maximum frequency. Conducting simple experiments on silicone oil standards demonstrates why comparing frequency specifications, without considering inertia, does not provide a true comparison of instrument performance.

It is easy to see that a well-designed rheometer using a drag cup motor has a significant low inertia advantage over one using an ECM motor. TA Instruments AR-Series rheometers provide the low inertia design important for precise and accurate viscoelastic characterization of low viscosity structured materials

Beware of high inertia!