Week 07 - Computer-Controlled Machining
This week I thought about the flexure plate I need, if I want to use strain gauges and how to specifiy the dimensions and material.
First of all it is important that the properties of the material stay nearly the same over the whole lifetime. That would be much easier, then trying to compensate for changes in the material. There will, however, be a temperature related factor for the strain gauges, but the compensation can be achieved by arranging them in a clever way.
Preliminary calculations
I need to start with some assumptions for the dimensions of the anemometer.
Length of the lever arm: \(l=300\)
Diameter of the sphere at the end of the lever: \(d=60\)
What will the resulting momentum be?
My requirement is measuring up to \(v=75m/s\)
The formula for the aerodynamic drag force is:
The area is \(A=\pi/4*d^2=2827mm^2\)
The density of humid 10°C warm air at sealevel can be estimated as \(\rho=1200g/m^3\)
Because there will occur a turbulent flow at higher wind speeds, the \(c_w\) value depends on the Reynolds number.
The Reynolds number can be calculated as follows:
\(\upsilon\) is the kinematic viscosity which is around \(14m^2/s*10^{-6}\)
That leads us to a Reynolds number of \(Re = 320000\)
Now we can assume, that the flow is undercritically turbulent and therefore \(c_w=0,4\).
Using that in the formula from above, the drag force results to
Now there will be a bit more force present due to the drag force of the arm itself, but I will neglect that for now.
The resulting momentum is
I get the feeling, that this is very little momentum for the maximum design wind speed. I might need to enlarge the sphere or lengthen the lever arm, but that isn't ideal for the final product.
The strain gauges I ordered have a footprint of 7,1 mm x 4,5 mm. Therefore I would like to have a minimum width of 8mm for the flexure plate. The tensile limit for them is 2 %.
The typical aluminium sheet you can get here is from AlMg3 with a yield strength of \(70N/mm^2\).
Hooke's-Law shows the permissible elongation for the AlMg3 alloy of:
That means, I can only utilize half of the measuring range of the strain gauge.