Load cell mathematical model

Question

I'm studying a solution for a weight measuring system that's affected by enviroment vibration - a load cell fixed on a "shaky" frame. My first thought was to use a 3-axis accelerometer (or IMU) so I could measure the forces being applied to the measurand on the load cell and then start building a digital compensation technique while comparing the weight and acceleration readings.

I'd like to simulate a control system to validate this method and further study the effects of mechanical interferences on signal noise, however I can't seem to find a ready-made load cell mathematical model (similar to a matlab DC motor model), nor any literature that shows how to bring up such a model.

I will appreciate any suggestions of a starting point of where to study mathematical modelling of these transducers, or any didatic work already published, having in mind I have limited knowledge about mechanical engineering and alike.

EDIT:

Here's some results my colleague obtained some months ago, where the weight was sampled with an ADS1220 and an analog low-pass filter @ 15Hz. I have no data on the sampling frequency or accelerometer model whatsoever.

Answer 1

There is no standard mathematical model of a load cell, since pretty much every load cell is different. You need the mechanical models of:

• the load attached to the load cell,
• the load cell transducer,
• the support structure the load cell is mounted on,
• the IMU and its attachement to the support structure.

In case of a very light and rigid IMU, the mechanical model may be trivial - just reading out the linear and angular position and rate data from the dynamic model of the support structure.

To model just the load cell, you need a mass-ful finite element model of the transducer, and a time-invariant model (transfer function) of the data acquisition channels. Then the two have to be connected together. The output of the FEM - the strains at the strain gage sites - would be fed to the DAQ transfer function, perhaps adding random noise too.

Then you need a model of what is actually attached to the load cell. This may be integrated into the model of the transducer for simplicity - if it's a rigid body. Otherwise, you'll have to couple the loads on the transducer structure to the model of the load.

A 10kg cube of steel bolted to a load cell is a very different beast than, say, a 10g cube of steel - both due to vastly different rigid body inertia, but also because the 10kg cube is large enough to stiffen up the transducer structure. Most load cells respond favorably when things attached to them - both on the support side and the load side - are rigid. A small, concentrated load in the case of a 10g steel cube may actually end up measuring worse. And that's just for rigid stuff.

Now assume you have a box half-full of sand attached to the load cell. Or a box half-full of water. Or completely filled with water. All three of those behave very differently. You may not care much, but your goal is - presumably - to inertially compensate a load cell. The load places inertial loads on it too!

I have limited knowledge about mechanical engineering and alike.

You may do best using actual hardware in some test setup similar to the final application. Accurate modeling of the system may be much harder than just getting something to work at least a bit in the physical world.