Stress Analysis Project 01
- 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. 1
- 2. Table of Content Abstract 3 Introduction 3 Equipment 5 Procedure 7 Results and Discussions 7 Conclusions 11 Recommendations 11 Reference 11 2
- 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. 3
- 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. 4
- 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) 5
- 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) 6
- 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. 7