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I How to find Area of Hysteresis?

  1. Jun 11, 2016 #1
  2. jcsd
  3. Jun 11, 2016 #2

    Simon Bridge

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    welcome to PF;
    hint: use calculus.
     
  4. Jun 21, 2016 #3
    how to use calculus here i have never done .
     
  5. Jun 21, 2016 #4

    SteamKing

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    Then why do you need to know the area of the hysteresis loop?
     
  6. Jun 22, 2016 #5
    I have studied calculus but no idea how too apply ?
     
  7. Jun 22, 2016 #6

    Simon Bridge

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    Since you have studied calculus, you known how to use it to find the area under a curve.
    That is pretty much the definition of "integration".

    Perhaps if you ptovided an example?
     
  8. Jun 22, 2016 #7

    billy_joule

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    Does this ring any bells?
     
  9. Jun 22, 2016 #8

    Nidum

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    If the hysteresis loop is plotted from test data then there will be no immediately available equations defining the shape of the up going and down going curves forming the loop .

    To use calculus you need to find the equations of curves which are best fit to the plot curves . There are standard ways of doing this .

    Alternatively you can use numerical methods . There are standard ways of doing this also .
     
  10. Jun 22, 2016 #9

    Nidum

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    Numerical methods :

    (1) Overlay the plot onto squared paper . Count the number of squares enclosed by the loop . Use a rule to decide when to include or exclude partial squares .

    (2) Divide the plot into many slices with equally spaced horizontal or vertical lines . Estimate the area in each slice and sum .

    (3) If you want to get more sophisticated look up : Trapezium Rule , Simpson's Rule and Gaussian Quadrature .

    (Have a look at Gaussian Quadrature anyway for general interest - it is fascinating how a very small number of ordinate samples can give very accurate answers)
     
  11. Jun 22, 2016 #10

    Nidum

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    When I started in the DO we sometimes used a Planimeter . Now we use facilities within our CAD software .

    There are downloadable apps for working out areas enclosed by curves .
     
  12. Jun 23, 2016 #11
    OK, How to find equation of curve?
     
  13. Jun 23, 2016 #12
    hello i understand planimeter
     
  14. Jun 23, 2016 #13
  15. Jun 23, 2016 #14
    You could weigh the paper any calibrate it to the area. Fun experimental/hands on way to integrate without calculus, kids love it and you can talk about error.
     
  16. Jun 23, 2016 #15

    Nidum

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    The easy way :

    http://uk.mathworks.com/products/curvefitting/

    http://uk.mathworks.com/videos/curve-fitting-toolbox-overview-61198.html

    (You can do the integration in Mathworks as well if you want to)

    The moderately easy way :

    Choose simple functions which give the right sort of curve shapes to fit your plot and scale them to best fit . Sometimes easier to break plot curve into segments and use different functions for each segment .

    Commonly used functions : linear , polynomial , exponential and sine/cosine .

    Slightly more formal way :

    https://en.wikipedia.org/wiki/Curve_fitting#Fitting_lines_and_polynomial_functions_to_data_points
     
  17. Jun 23, 2016 #16

    Nidum

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  18. Jun 23, 2016 #17
    hello,

    How to drawn second degree polynomial, like this?
     
  19. Jun 23, 2016 #18

    NascentOxygen

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    SDRFG, can you attach a neat plot of your hysteresis loop, with the measured points clearly shown?

    Do you intend using a software package to find a polynomial of best fit? (I expect wolfram alpha would do this for you.)
     
  20. Jun 23, 2016 #19
    i want to learn by hand in paper
     
  21. Jun 23, 2016 #20

    NascentOxygen

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    Please attach your plot.
     
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