# Modal Analysis of Load Cell

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Advanced Finite Element Analysis: MEC 6440

Project 1: Modal Analysis of S-beam Load Cell

11/2/2012

Modal Analysis of an S-beam load cell

Contents

Summary 2

Introduction: 2

Objectives: 2

Theory of Modal Analysis: 2

Original Design: 3

Analysis Procedure: 4

Results and Assessment 5

Results: 5

Assessment of the results: 6

Redesign: 7

Analysis of Redesign: 9

Conclusions: 10

Bibliography 10

Summary

A Finite Element analysis was carried out on an S-beam load cell using ANSYS APDL. The first modal frequency was found to be in the operating frequency range of the load cell. A different design was proposed and its Modal Analysis was performed to show that its First modal frequency was sufficiently outside its operating frequency range.

Introduction:

A load cell is Transducer which converts force to measurable electrical output signals.

Load cells are designed to deform proportionally under applied forces only in a particular direction (other directions are rigidly supported to prevent any deflection). Strain gauges are rigidly connected to load cells so as to convert these deflections into proportional electrical signals.

S-beam type load cells are designed both tensile and compressive forces. Hence they are often used to measure alternating tensile and compressive forces.

Objectives:

To perform Modal Analysis of the S-beam load cell

To check its Dynamic response for Frequencies less than or equal to 1500Hz

To identify the source of poor performance and propose a new design

To analyse the new design using Finite Element Methods

Theory of Modal Analysis:

The Matrix form of Equation for a system under vibrations is:

[M]{u ̈} + [C]{ů} + [K]{u} ={f}

where

[M] is Mass matrix

[C] is Damping matrix

[K] is Stiffness matrix

{f} is Matrix for applied loads

For modal analysis there no external loads. Damping is also neglected.

Hence we have the equation:

⌊M⌋{u ̈ }+[K]{u}=0

For a linear system the solution for the displacement is assumed periodic:

{u}={∅}cos⁡(ωt)

{u ̈ }=-ω^2 {∅}cos⁡(ωt)

ω are the Vibration frequencies.

∅ represent the mode shapes - the shape assumed by the structure when vibrating at frequency

Hence we get:

⌊K⌋{∅}= λ [M]{∅}

where, λ =ω2

Using Cholesky factors, above Equation can be converted to a Standard Eigenvalue Problem of the form:

[K]{ ∅} = λ {∅}

Standard Eigenvalue problems can be solved by various numerical methods, the most commonly used for Modal Analysis in ANSYS APDL being Block Lanczos [1].

Original Design:

The geometry of the load cell is shown in the figure .The load cell is constructed of stainless steel (316) with properties as follows:

Modulus of Elasticity 193 GPa

Poisson's Ratio 0.3

Density 7.99 g/cm3

Figure 1: Geometry of S-beam Load cell

The central cavity houses the strain gauge whereas the two holes at the top and bottom are provided so that the load cell can be bolt to a testing rig.

Analysis Procedure:

The Finite Element Analysis was performed on the software ANSYS APDL on remotely accessed computers called Iceberg. The geometry was created using standard modeling tools in units of millimeters. Units of material properties like modulus of elasticity and density were proportionally changed to millimeters for consistency. Multiple tetrahedral free mesh were generated by varying global element sizes and refining the mesh at certain areas where maximum deflection and stress was expected (NOTE: Modal Analysis does not give exact deflection or stress values, but the values are relative to give an indication of zones with expected high deflection and stress).Figure shows the picked areas where the mesh was refined.

Figure 2: Areas where mesh is refined

Element SOLID 285 was chosen for the mesh. It is a 4-node solid element suitable for 3-d applications and recommended over SOLID 185 8-node element when tetrahedral mesh is generated [2]. Boundary conditions were applied to restrict the motion of the load cell only in axial direction. This was achieved by adding zero displacements

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