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# Introduction to Sensors and Data Analysis

## ME 3263 Fall 2018

ME 3263 Lab Report Rubric

Labs 0 and 1 have a 3-page limit and 2-figure limit. Labs 2-6 have a 5-page limit and 4-figure limit. You can add additional pages and figures in an Appendix. The Appendix will not be formally graded, but you can use it to refer to data, methods, or diagrams that are relevant.

The report is scored 0-100. Over 70 is passing. Late submissions receive 10 point penalty per day.

Part of your "writing assignments" grade is based upon the reports that you make the final edits and improve the flow. The first author listed will get credit for the writing assignment portions. Take turns as first author and co-author. The group shares the pass/fail grade for the "lab report" grade.

# ME3263 Introduction to Sensors and Data Analysis (Fall 2018)

## Lab #5 Mass Measurement Device with Cantilever beam

Lab 5 github files

# Mass measurement contest

In the mass measurement contest, you will use natural frequency shifts to determine the mass of an object. There are three locations you can mount the object as seen in Figure 1, where the object is mounted in position 2. The experimental procedure only involves measuring natural frequency with the mass mounted in different positions. You can create an engineering model as we will do with experimental results from Ghatkesar et al. 2007 [1], as described in section 2.

You can use the modal analysis in Ansys [2] and apply a point mass to get predicted changes in natural frequencies. This will create a table of values for your given cantilever for known masses for interpolation as described in section 3.

Rules of Contest

1. The masses must not leave the lab

2. You cannot mount other known masses to the cantilever

3. You must report your uncertainty in your mass measurement to enter the competition

4. You must report your serial number "TJM 01-TJM 12" to enter the competition

5. You may use the following tools and software: strain gage or accelerometer (not both), calipers, Ansys, Labview, Python, Matlab, and Excel

Winners of the contest

There will be two sets of winners for the contest:

1. Lab group with the most accurate mass measurement calculated with $A=|m_{reported}-m_{actual}|$

2. Lab section with the most precise mass measurement calculated with $P=\sum_{i=1}^{N}(m_{reported}-m_{actual})^2$

Where $A$ is the accuracy, $P$ is the precision, $m_{reported}$ is the reported mass from your experiment, and $m_{actual}$ is the actual mass of the object, and $N$ is the total number of lab groups in a section. The group and section with smallest A and P, respectively will win prizes. The prizes are as such

1. ** $100 cash prize** put into your student accounts ($50/group member for group of 2)

Lab #5 report should include details of the following

3. Your predicted results from Ansys

4. Your final calibration process for measuring a mass based upon natural frequency changes

## Lab #4 Predicting Natural Frequencies with the Finite Element Method

### What is the Finite Element Method?

The Euler-Lagrange dynamic beam equation is an example of a partial differential equation (PDE). These equations are common in many engineering applications e.g. solid mechanics, electromagnetics, fluid mechanics, and quantum mechanics. The finite element method solves PDEs. The FEM process involves two steps to create matrices for a computer algorithm solution. First, the PDE is integrated from the strong form to the weak form. Second, an approximation of the variable "shapes" within each "element" is created to convert the integrals and derivatives into matrices (1). For elements with nodes only at vertices, such as cubes (hexahedrons) or pyramids (tetrahedrals), the "shape" function is linear for displacement.

Lab 4 github files

## Lab #3 Measuring Natural Frequencies

### What are natural frequencies

In free vibration (i.e., no external forcing), structural components oscillate at specified frequencies or combinations of frequencies. Since these vibrations are unforced, the associated frequencies are referred to as natural frequencies; it's how the system vibrates if left to behave on its own. In contrast, driven linear systems vibrate at the driving frequency. An amplification of the response (called resonance) occurs when the driving frequency coincides with one of the natural frequencies. In short, the system is driven at a frequency at which it likes to vibrate. Large amplitude oscillations are the result. So it is important to know what the natural frequencies are a priori so you can avoid driving the system into resonance.

Lab 3 github files

# Lab #2 - Static beam deflections with strain gage

## What is a Strain Gage?

A strain gage consists of a looped wire that is embedded in a thin backing. Two copper coated tabs serve as solder points for the leads. See Figure 1a. The strain gage is mounted to the structure, whose deformation is to be measured. As the structure deforms, the wire stretches (increasing its net length ) and its electrical resistance changes: $R=\rho L/A$, where $\rho$ is the material resistivity, $L$ is the total length of the wire, and $A$ is the cross sectional area of the wire. Note that as $L$ increases, the cross sectional area changes as well due to the Poisson contraction; the resistivity also changes.

Figure 1: a) A typical strain gage. b) One common setup: the gage is mounted to measure the x-direction strain on the top surface. It's engaged in a quarter bridge configuration of the Wheatstone bridge circuit.

# Lab #1 - Measurements of machining precision and accuracy

Lab 1 github files

Outline and figures due in week 4 at beginning of lab

Final report due day before lab by 11:59pm

How can you measure something?

All measurements have traceable standards. There are seven base units in SI - meter (length), second (time), Mole (amount of substance), Ampere (electric current), Kelvin (temperature), Candela (Luminous intensity), and kilogram (mass) 1. Any measurement you make should have some method to check against a reference. In this lab, we will use calipers that measure dimensions i.e. meter 1E-3 (length). Calipers can always be verified to work with gage blocks.

Sources of measurement variations

No measurement is exact. No surface is compeletely flat. Every measurement you make has two types of uncertainties, systematic and random. Systematic uncertainties come from faults in your assumptions or equipment.

# Lab #0 - Introduction to the Student t-test

Outline and figures due Wed 9/5 by 5pm

Final report due Thu 9/13 by 5pm

Lab 0 interactive notebook in ipynb jupyter notebook

We use statistics to draw conclusions from limited data. No measurement is exact. Every measurement you make has two types of uncertainties, systematic and random. Systematic uncertainties come from faults in your assumptions or equipment. Random uncertainties are associated with unpredictable (or unforeseen at the time) experimental conditions. These can also be due to simplifications of your model. Here are some examples for caliper measurements:

In theory, all uncertainies could be accounted for by factoring in all physics in your readings. In reality, there is a diminishing return on investment for this practice. So we use some statistical insights to draw conclusions.

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