Introduction to measurements for mechanical engineers

Set of Jupyter notebooks, prepared by Prof. Alex Liberzon, School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University for the course that is called in many places as “Mechanical Measurements Lab 1” or “Theory and Design of Mechanical Measurements”, “Introduction to Measurements for Mechanical Engineers”, etc.

This book does not replace the course materials, but rather organizes it in Jupyter and Markdown notebooks. We hope is useful as an assistance learning material for undergraduate engineering laboratory courses. It is an open source project and any contribution is welcome ( contact us on Github ).

Textbook and relevant books:

This course follows the [Figliola and Beasley, 2020]. It is also recommended to consult with [Dunn and Davis, 2017] and [Wheeler and Ganji, 2009]

Table of contents

Theory of experiments and measurements

• Standardization
• Laboratory Notebook
• Uncertainty 101
• Uncertainty in simple terms from IAEA
• Short summary of the ``Measurement good practice guide ‘’ by NPL
• Simple example of mechanical measurement with uncertainty analysis
• Using AI tools to learn uncertainty
• How to estimate the uncertainty of a slope for static calibration or regression
• General measurement system diagram
• Significant digits

Statistics for measurements

• Very basic review of some statistics terms
• Probability Distributions and the Central Limit Theorem
• Lecture 5 - probability and statistics
• Histogram
• Let’s create our own histogram
• Now we can load some real long sample of turbulent temperature fluctuations
• Chi-square test
• Lecture 6
• Outliers

Calibration

• Sensitivity estimate example
• Micrometer calibration using gage block
• Second half: use the calibrated micrometer to measure the diameter of a cylinder
• Calibration and uncertainty analysis - virtual experiment
• Calibration of non-linear (logarithmic) function
• Hysteresis and regression analysis example

Analog to digital (A/D) and D/A

• Mimic A/D conversion
• Analog to digital (A/D) and Digital to Analog (d/A) conversion example
• Sampling, clipping and aliasing
• Digital to Analog conversion using sinc

Signal processing

• Digitizing the signal using pure Python
• Using FFT the right way to find the correct spectrum
• Fourier transforms
• Symbolic evaluation of Fourier coefficients
• Using FFT-based filter to reduce noise
• FFT demo of a real, periodic signal
• Given periodic signal, sampling frequency and total time

Dynamic signals

• Log decrement method
• 1st order dynamic system
• Example of pre-measurement design
• Step responses of dynamical systems
• Plot power spectrum of experimental data
• Spectrum example
• Fast Fourier Transform (FFT) of a sum of two sine signals
• Lab Worksheet: Measurement of Unknown Mass using Vibrating Beam

Copyright Information

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References

[DD17]

P.F. Dunn and M.P. Davis. Measurement and Data Analysis for Engineering and Science. CRC Press, 4 edition, 2017.

[FB20]

R.S. Figliola and D.E. Beasley. Theory and Design for Mechanical Measurements. Wiley, 2020.

[WG09]

A.J. Wheeler and A.R. Ganji. Introduction to Engineering Experimentation. Prentince Hall, 2009.