Dynamic forces are widespread in industrial force measurement. When measuring such forces, precision can be improved by compensating the forces produced by the force introduction components’ inertia. The following method description details how to compensate the inertia using the integrated acceleration sensors from the DR force transducer range. The benefit is that you need no prior knowledge of the mass or acceleration values.

The problem of mass inertia

In dynamic testing, acceleration of assembly components such as clamping tools or sample holders produces mass inertia effects. Alongside the desired test force F_test, dynamic excitation produces an undesired inertial force F_inert through the multiplication of the assembly components’ mass and acceleration. F_inert distorts the measured force value F_meas. For the force transducer, a distinction between force applied to the sample and undesired inertial forces is impossible without further modification.

F_meas = F_test + F_inert

However, measuring the acceleration along the force measurement axis facilitates determination of the undesired force F_inert and allows it to be compensated by applying an opposing, equal force F_comp:

F_meas = F_test + F_inert + F_comp

Where F_comp = - F_inert will produce a correct measurement of the testing force on the sample:

F_meas = F_test

Mechanical model

The model comprises three components: the actor (e.g. hydraulic cylinder), the force transducer with integrated MEMS acceleration sensors and the assembly components in the form of connected, moving masses (MEMS = microelectromechanical system).

• The assembly components (moving mass) need to be installed on the force transducer’s ‘oscillating side’.
• The force transducer’s ‘rigid side’ needs to be attached to the actor.

Basic test setup for compensation

The strain gauges used in the force transducer are wired together to form a Wheatstone bridge and convert an applied mechanical load to an electric signal. Depending on your requirements, use a precision DMS measuring signal amplifier with an analogue or digital output signal. The system used for electric signal processing must be capable to determine and process the peak-to-peak amplitudes of the measured dynamic signal. Using the peak-to-peak amplitudes eliminates the influence of the various phase changes in the signals used for compensation.

In the DR force transducers, the acceleration sensors are located as close as possible to the force measurement axis. The MEMS components convert applied acceleration to an electric output voltage. The systems are radiometric, which means that the output voltage depends directly on the supply voltage. This makes a stable power supply imperative. Here, too, the measuring system needs to be capable of calculating the output signal’s peak-to-peak amplitude.

Determining compensation

The compensation parameters need to be determined taking into account the assembly components’ mass but without contact to the specimen. During the test, we require F_test = 0.

To identify the settings for F_comp, excite the system using harmonic load cycles across the entire testing frequency range. When doing so, record the force transducer signal F_meas, which under free oscillation is equivalent to the uncompensated inertial force F_inert because there is as yet no contact with the sample. Also record the associated acceleration sensor signal. Conduct a test series with varying amplitudes and frequencies according to your requirements.

Example:

Calculate the proportionality parameter for compensation.

In our example, this is:  F_inertSS = 3/2 · a_ySS

Depending on your test requirements (amplitudes, frequencies), it may be necessary to perform not only a linear correction but to also calculate the second and higher orders. Combine the force signal and acceleration signal according to:

F_comp = - F_inert

The result is F_meas = 0 across the entire test range. The compensation ‘pulls’ the inertial forces back to the value of the desired dynamic force.

Once you have determined and applied the compensation settings, you can clamp the sample. The measured force F_meas will no longer be affected by the undesired inertial forces.