1. University of New Haven
Department of Mechanical Engineering
ME 427
April 19, 2005
Pressure Transducer Design Problem
Authors: Mudar Al-Bayat, Franco Pezza and Walter Yamben.
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2. Table of Content
Abstract 3
Introduction 3
Equipment 5
Procedure 7
Results and Discussions 7
Conclusions 11
Recommendations 11
Reference 11
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3. Abstract
The purpose of this project is to optimize the beam design of a pressure transducer
for the use of a strain gage.
Introduction
The two basic elements of a pressure transducer are the membrane and the beam,
which are usually encapsulated in a rigid body or container (figure 1).
(Figure 1. A cross section view of a schematic pressure transducer)
The pressure, acting on the flexible membrane, loads the beam at the center where is in
contact with the membrane. This load deforms the beam and the deformation is measured
and recorded at the top of the beam, where the strain is detected. The strain along the top
of the beam (path) varies of intensity. In fact, starting from the centerline, the strain goes
from a minimum to a peak tensile stress, then goes to zero and reaches a peak
compressive stress. The behavior of the strain is also symmetric respect the centerline.
For this problem, the following assumptions are to be considered:
• The pressure to be sensed passed directly to the beam by the membrane.
• The beam is in plane stress.
Also, because of symmetry, only one half of the beam is used for calculations.
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4. A strain gage is mounted on the top of the beam and detects any strain of the beam. The
data is recorded and elaborated by a converter. The design objectives are the followings:
• To ease in the bonding of strain gages and facilitate assembly, gages are to be
mounted on the top surface of the beam.
• To obtain temperature compensation, the beam should have equal areas of
tension, and equal areas of compression, on the top of the surface (see figure 2).
• To facilitate bonding of gages and reduce errors in placement gages, the beam
should have areas of constant tension and compression on the top surface.
• To facilitate fabrication, there is a minimum width, there should be no interior
corners, and all curves should be smooth to avoid stress concentrations and
therefore premature failure of the transducer due to fatigue.
• Because of the strain-indicator apparatus that is to be used, there is a
predetermined strain level for a pressure of 1000 psi.
The design of the beam should also follow the following requirements:
1. On the top surface maximum tension and compression should be equal +/- 1%.
2. At a pressure of 1000 psi, the strain read should be 600 µ-strain.
3. The maximum tension and compression should be constant over an area of 0.3+/-
1% inches long per unit depth minimum.
4. The largest Von Mises in the beam at 1000 psi should be less than 25% of the
yield stress.
5. Beam is to be made of stainless steel with Young’s modulus of 29,000 kpsi,
Poisson’s ratio 0.2700, and yield stress 60 kpsi.
(Figure 1b. 3-D Section view of a schematic pressure transducer)
Equipment
The equipment used for this design problem is Ansys 8.1 Finite Elements
Analysis Software and Solidworks 2004 CAD Software.
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5. Procedure
To shape and size the cross section of the beam in order to achieve the expected
result, the trial & error method was adopted with the support of the Ansys software.
Starting from the beam cross section (half of it) as in figure 2a, some material was
removed in critical section such that the plot of the strain on top of the beam was within
the specifications.
(Figure 2a. Starting shape and size of the beam)
From the starting shape, the meshing and the plot of the x-direction strain (εx) of the
beam obtained from Ansys was the following showed in figure 2b and 2c. On the same
plot is also the curve of the ideal εx.
( Figure 2b. The load, the constrain, the symmetry and the mesh of the beam)
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6. (Figure 2c. The εx plot of the starting shape, compared to the ideal curve)
The approach token to solve the problem is represented in figure 3, where the curved line
represent the shape we guessed to give acceptable results.
( Figure 3. The target shape)
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7. With the use of Ansys we modified the curve to fit the best result for our design problem,
which was to obtain a strain curve plot along the top of the beam as per figure 4.
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