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Lab 9: Stress and Strain Measurement and Analysis - Prof. Anthony Duva, Lab Reports of Mechanical Engineering

Instructions and theory for a lab experiment focused on stress and strain measurement using a strain gauge system and finite element analysis (fea). Students will learn to set up the system, calibrate it, and compare results with fea and theoretical calculations. Equipment list, setup instructions, and lab procedures are included.

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Uploaded on 08/19/2009

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Lab 9- Stress and Strain
Introduction
One critial, primary, must-satisfied design criteria for mechanical engineering is that the
actual stress in part or components during operations must be less than allowable stress specified
by the design engineering. The allowable stress of the materials is generally specified by the
material manufacturer and is a known variable for design engineers. The key issue is how to
find out the actual stress of the components.
Generally, three approaches are equally used in mechanical engineering, which are
theoretical prediction (calculation), finite element analysis (FEA) and strain & stress
measurement (testing).
When the geometry of components and loading conditions are simple, design engineers
can provide very acuurate theretical prediction of the actutal stresses in the components. When,
the geometry and loading conditions are complicated, design engineers can implement different
approaches to simplify the actual models into a handable models, the theroreticla pridction of
which can still be provided. In words, design engineers can always provide therotical prediction
of the actual stresses and use these as a starting point.
Finite element analysis (FEA) is a very powerful tool for predicting the sctual stresses,
which is a numeraical techniques and acquire to use computers, which is one of common tools
availabe for every design engineering. FEA can deal with very complicated geometry and
loading conditions. FEA can also provide relative accurate results acceptable by mose of design
engineers supposed that loading conditions, boundary conditions and initial conditions are
correctly considered.
In reality, both the theroretical prediction and FEA results of the actual stress of the
compoments must be verified by testing if components are critical components in the machine
or equipment. If the testing is properly carried out, the testing results will be results design
engineers must trust and use.
In this strain & stress lab, we will try to use three of approaches mentined above to carry
out the strain & stress evaluation. This lab illustrates the use of a strain gage. The gage is
bonded near the clamped end of a cantilever beam. Predetermined deflections are applied to the
free end of the beam. The strain gage measures the axial elongation of the beam. The therotical
caculation and FEA on the cantilever beam will also part of the lab. Three results will be
compared and discussed.
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Lab 9- Stress and Strain

Introduction

One critial, primary, must-satisfied design criteria for mechanical engineering is that the

actual stress in part or components during operations must be less than allowable stress specified

by the design engineering. The allowable stress of the materials is generally specified by the

material manufacturer and is a known variable for design engineers. The key issue is how to

find out the actual stress of the components.

Generally, three approaches are equally used in mechanical engineering, which are

theoretical prediction (calculation), finite element analysis (FEA) and strain & stress

measurement (testing).

When the geometry of components and loading conditions are simple, design engineers

can provide very acuurate theretical prediction of the actutal stresses in the components. When,

the geometry and loading conditions are complicated, design engineers can implement different

approaches to simplify the actual models into a handable models, the theroreticla pridction of

which can still be provided. In words, design engineers can always provide therotical prediction

of the actual stresses and use these as a starting point.

Finite element analysis (FEA) is a very powerful tool for predicting the sctual stresses,

which is a numeraical techniques and acquire to use computers, which is one of common tools

availabe for every design engineering. FEA can deal with very complicated geometry and

loading conditions. FEA can also provide relative accurate results acceptable by mose of design

engineers supposed that loading conditions, boundary conditions and initial conditions are

correctly considered.

In reality, both the theroretical prediction and FEA results of the actual stress of the

compoments must be verified by testing if components are critical components in the machine

or equipment. If the testing is properly carried out, the testing results will be results design

engineers must trust and use.

In this strain & stress lab, we will try to use three of approaches mentined above to carry

out the strain & stress evaluation. This lab illustrates the use of a strain gage. The gage is

bonded near the clamped end of a cantilever beam. Predetermined deflections are applied to the

free end of the beam. The strain gage measures the axial elongation of the beam. The therotical

caculation and FEA on the cantilever beam will also part of the lab. Three results will be

compared and discussed.

Lab tasks

  1. Set up a strain measurement system including wiring Quarter Bridge, configuring SC-

signal conditioning, configuring DAQ channel and compiling a strain VI.

  1. Conduct 8 strain measurements under the predetermined defection at the free end of the

cantilever beam. The maximum allowable deflection in this lab will be less than 0.5”.

  1. Theoretical prediction of the strain under the pre-determined deflection for the cantilever

beam.

  1. FEA results of the strain under the pre-determined deflection for the cantilever beam by

using Solidworks.

  1. Submit test procedure and final project test report

Objectives

 Understand the strain measurement system and be able to set up this system for strain

measurement.

 Be able to calibrate the system and properly interpret the measurement results

 Comparison measurement with FEA and theoretical calculation

Equipment List

 Computer running Windows

 LabVIEW version 8.

 SCC-SG01 quarter bridge module

 SC-2345 signal conditioning with cable for connection between SC-2345 and DAQ device

 NI PCI 6221 DAQ device

 Strain Gage (SGD-6/120-LY13)

 Flexor - Cantilever beam

Setup

Computer-based measurement systems are used in a wide variety of applications. In

laboratories, in field services and on manufacturing plant floors, these systems act as general-

purpose measurement tools well-suited for measuring voltage signals. However, many real-world

sensors and transducers require signal conditioning before a computer-based measurement

system can effectively and accurately acquire the signal. The front-end signal conditioning

system can include functions such as signal amplification, attenuation, filtering, electrical

isolation, simultaneous sampling, and multiplexing. In addition, many transducers require

excitation currents or voltages, bridge completion, linearization, or high amplification for proper

and accurate operation. Therefore, most computer-based measurement systems include some

form of signal conditioning in addition to plug-in data acquisition (DAQ) devices. For more

Strain and deflectiuon relationshin on a cantilever beam

By mounting strain gages to the surface (top and/or bottom) of a cantilever beam, you can

measure the axial deformation of the beam (the deformation along the length of the beam) when

a transverse load or a predetermined deflection input is applied to the end of the beam. The

amount of deformation can be related to the strain using the previous gage factor equation.

Figure 2 shows a strain gage bonded to the top surface of the cantilever beam.

Figure 2. Cantilever Beam with a Strain Gage Mounted on the Top

When a load (P) is applied at the end of the beam, the deflection of the beam will be:

L x

EI

Px y  3 

6

2

3

3

EI

PL δ  (2)

Where

P is the loading applied at the free end of the cantilever beam

E is the Young’s modules

I is the moment of inertial. For a rectangular beam,

12

3 bt I . t is the thickness of the beam

and b is the width of beam.

L is the distance from the fixed end to the location of loading

x is the longitudinal axis

 is the deflection at the loading location.

If we use the deflection as an input to replace the applying loading, from equation (2), we can

determine the equivalent force as:

3

L

EIδ

P  (^) (3)

Plugging equation (3) into equation (1), we have:

  (^) ( 3 )

2

3

2 2

L x

L

x

L x

EI

Px

y

Based on theory of beam, we have the following relationship between the bending moment and

deflection:

2

2

dx

d y MEI (5)

Plugging the equation (4) into equation (5), we have:

   L x

L

L x EI

L

EI

dx

d y

M EI

2 3 3

2 3 3

(6)

According to the theory of beam, the tensile stress () along the x-axis at the top surface is given

as:

I

t M

x

Plugging equation (6) into equation (7), we have:

 L x 

L

t E

I

t

M

x

3 2

From Hook’s law, we have

 L x 

L

t

E

x

3 2

If the strain gage is installed at location Ls, the strain in the strain gauge will be

  S

L L
L

t

3 2

Figure 4 A quarter Wheatstone Bridge

If R 1 =R 2 , and R 3 =R 4 , But we replace R 4 with an active strain gauge. Then any change in

the strain gauge resistance will unbalance the bridge and produce a nonzero output voltage. If

the nominal resistance of the strain gage is designated as RG, then the strain-induced change in

resistance R can be expressed as R=RG ×GF×. We have

4

GF

2

GF 1

1

4

0 GF  

  

  

EX

V

V

Lab procedures

Before the Day of the Lab

Download and study following documents before you come to lab

 “Measuring strain with strain gauges” by National instruments

http://zone.ni.com/devzone/cda/tut/p/id/

 “SCC-SG Series strain gage modules”, http://www.ni.com/pdf/manuals/371073b.pdf

 “SCC tutorial series: SCC-SG0x”, http://zone.ni.com/devzone/cda/tut/p/id/

 “SC-2345/2350 Carrier User Manual and Specifications”,

http://digital.ni.com/manuals.nsf/websearch/09FC2D464C3C38A1862571850066A

8D

 “SCC quick start guide”,

http://digital.ni.com/manuals.nsf/websearch/5587D12C545D7ED9862570600070E

 Strain gauge information of “SGD-6/120-LY13”

http://www.omega.com/Pressure/pdf/SGD_LINEAR1-AXIS.pdf

 Lectures related strain gauge measurement

 Flexor user manual (available in lab)

Lab section one

In section one, you should complete following tasks:

 Set up the Flexor cantilever beam in which two strain gages (one on top surface and

one on bottom surface) have been installed

 Wiring two quarter bridges by using SCC-SG01 modules

 Plug the SCC-SG01 modules in SC-2345 signal conditioning

 Connect SC-2345 signal conditioning to DAQ device (PCI 6221), which has be

installed in computer.

 Configure SC-2345 signal conditioning

 Create VI which can indicate the strains and save measurement

 Offset null of the quarter bridge by using the potentiometers in SCC-SG01 modules.

Follow these steps to complete lab section one:

  1. Install the aluminum beam in Flexor as shown in figure 5

b. Plug the modules in any SC- 2345 socket J1 ~J8.

  1. Connect SC-2345 with DAQ device (NI PCI 6221)
  2. Configure SC-2345 signal conditioning as a DAQ accessory
  3. Configure strain channels for LABview – Configure the channel so that the readout of the

signal is strain

  1. Create a VI which will indicate the readouts of strain signal channel and can save the data

(Note: The strain signal is in strain (in/in). It is recommended that you will convert it in

the unit .

  1. Offset Nulling

a. Create a graph for the readout of strain gage channel.

b. Set the scales for the graph at ±5000  in order to see the strain signal.

c. While monitoring the channel input voltage, rotate the appropriate trimming

potentiometer with a flathead screwdriver until you read less than ± 100 .

d. Next, decrease the input range (use ± 1000 ) and repeat step c.

e. Next, decrease the input range (use ± 100 ) and adjust the potentiometer and

try to do your best to reach less ± 20 .

f. You have successfully nulled the system offset.

  1. After nulling the quarter bridge, defelct the beam to see whether the signal in LABview is

changed or not. If you see the signal change, you sucessfully set up the strain

measurment system.

Lab section two

In section two, you should complete following tasks:

 Conduct 8 strain measurements under the predetermined defection at the free end of

the cantilever beam. The maximum allowable deflection in this lab will be less than

 Conduct the theoretical prediction of strain for the cantilever beam at the

predetermined deflection.

 Compare the measurement with theoretical prediction.

Do analyze the data to check whether results are reasonable or not. If not, try to

figure out what is wrong and prepare to rerun it in lab three section.

  1. Nulling Quarter Bridge.
  2. Then, let loading screw to touch the beam and have 1~2 in deflection
  3. Nulling the quarter bridge again and record the signal

Deflection

 (^) (or   (^) )

Measurement on top

strain gage

or

Measurement on bottom

strain gage

or

Theoretical prediction

Note: Create your own table to show the relative error.