Force measurement system - relating output voltage to Force - strain gauges

[mh1985]

Homework Statement

I'm struggling with this, I have series of data for the deflection of a cantilever beam and the corresponding output voltages from a strain gauge, wheatstone bridge and amplifier circuit.

I'm trying to find the relation between voltage output and force, i.e. Force = K x voltage (K = constant) but I don't have the force.

Homework Equations

Also I've been given the equation for

Bending moment M = F * Length at gauge

Stress on top surface of beam σ= d/2 * M/1

Output voltage = R2/R* Vs* Kg *ε

Where Kg = gauge factor

The Attempt at a Solution

I think Force can be found from 3EId /L^3 , where d = deflection, E= youngs modulus, I = 2nd moment of area. But still think I'm missing something.

I've already found another constant for output voltage = K x deflection, if that is relevant.

Using 3EI/L^3, I get 5171.3 which can then be multiplied by deflection to give the Force - not sure if this is correct?

Hoping someone has done a similar experiment before and can help in some way please?

 

[KataKoniK]

Hello,

It seems like you are on the right track in your attempt at finding the relation between voltage output and force. The equation you have for bending moment and stress on the top surface of the beam is correct. However, I would like to clarify a few things that may help you in your solution.

Firstly, the equation for bending moment should be M = F * Length at gauge * (1/2 - d/L), where d is the deflection and L is the length of the beam. This takes into account the change in length of the beam due to the deflection.

Secondly, the equation for stress on the top surface of the beam should be σ = d * M / (2 * I), where I is the moment of inertia of the beam. This takes into account the cross-sectional area of the beam.

Now, coming to your attempt at finding the force using 3EI/L^3, this equation is correct, but the value you have calculated (5171.3) seems a bit high. I would suggest double-checking your calculations and making sure you are using the correct units for all the variables.

Additionally, you mentioned that you have found another constant for output voltage = K x deflection. This is relevant as it can help you in determining the value of K. You can use this constant and the equation for output voltage to find the value of K, which can then be used in the equation for force.

I hope this helps. If you have any further questions or need clarification on any of the equations, please don't hesitate to ask. Good luck with your experiment!