Pressure Sensors Calculations

The absolute pressure at any given depth = (liquid density x depth below surface x acceleration due to gravity) + barometric pressure at the surface.

The gauge pressure at any given depth = liquid density x depth below surface x acceleration due to gravity

Does that help?

This may be a start:

http://www.analog.com/UploadedFiles/Associated_Docs/324635617948502532074843652499435765318149061216540223Fsect4.PDF

The formula you can use depend on the pressure range and the diameter of the diaphragm. The comparison of theoretical computations and the actual results shows that a good correlation is more obtained with relatively large ratios D/t where D is the diameter and t the thickness. Usually the diaphragm angular deformation (du/dr with u the axial deformation under pressure and r the radius) is considered zero on the periphery where the membrane (diaphragm) is welded to the sensor body. The maximal bending occurs on the periphery (stresses directed radially) and in the center (where stresses are equal in both directions radial and tangential). If you use a strain gage for pressure transducers you will see how the resistances are designed in order to feel the stresses in above mentioned directions.

The problem in designs as you mention with welded membranes is the fatigue which could lead to cracks at the periphery.

For the relationships for computing you can look in any book for material resistance where they are printed usually under in the chapter "circular plates".

If you want to obtain better results it recommendable to turn the sensitive element from a high resistance steel together with the ream and weld the ream to the body.

This will allow you to make a radius and reduce the stress concentration. This component can be optimized by FEA. If you do not have it I can do it but this cannot be a free service. If you are interested mail directly.

Hi all,

Diaphragm pressure transducer are based on what in strength of materials can be a model of "clamped circular plate uniformly loaded".

The problem is well known and you can find it in any strength of materials book under "flexure of plates and shells" (I've studied this case in Timoshenko Vol.2 35 years ago).

There are strain gages "rosettes" specially designed for diaphragm pressure transducers and most of manufacturers have it in their catalogues (Vishay Micromeasurements Division, HBM, etc).

For calculation of stresses, following formulae apply:

σ_t = 3P/8t²[R²(1+ν) - r²(1+3ν)]

σ_r = 3P/8t²[R²(1+ν) - r²(3+ν)]

Where:

σ_t= Tangential stress

σ_r = Radial stress

P = Pressure

t = plate thickness

R = plate radius

r = radius of plate position in which stress are calculated

ν = Poisson ratio of material used

Maximum stresses occur at edge of plate in radial direction (limiting condition)

For additional information regarding strain gage pressure diaphragm calculation you can take a look in the following link:

http://www.vishay.com/docs/11060/tn5101.pdf (sorry, link no longer available)

I saw that you were given the indications already. I would like to give you a + information. The equations are based on the assumption of perfect clamping of the membrane. In fact the periphery is not perfect clamped at the contact with the body which ever design you choose. This leads to an angle not nil and a reduction of the strains. The sensitivity will be less. This is the reason i indicated that only when ratio d/t is big the results are about the same. In fact this angle is equivalent to a clamping on a diameter bigger than the geometrical one. Do not be surprised by the differences.

You're right. Real things usually doesn't behave as theoretically perfect models. This is explained in the Tech Note whose link I've included in my previous post.

But I've work a lot with this and if the ratio d/t is enough big (about 20 times) and the deflection of the center of the plate is low, the efect of non perfect clamping is negligible and measurements of the transducer follows the theoretical model.

Anyway it's necessary to get a compromise between d and t according to the rated pressure of the transducer, taking into account the material selected.

And remember the initial question:

Can any one please suggest me,how to start calculation...Pls

You are right but if he starts he will come to and end (hopefully) and surprises are always at the end!