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In the measurement of surface roughness, height of 20 successive peaks and troughs were measured from a datum and were: 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35 and 20 μm. If these measurements were obtained over a length of 20 mm, determine the C.L.A. (i.e. R a ), R.M.S and R z values of the rough surface. B) Determine the grade of roughness in case of R a value.?
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In the measurement of surface roughness, height of 20 successive peaks...
Measurement of Surface Roughness


Given


  • Height of 20 successive peaks and troughs = 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35, and 20 μm

  • Length of measurement = 20 mm



To Find


  • C.L.A (i.e. R a )

  • R.M.S value

  • R z value

  • Grade of Roughness in case of R a value



Solution


C.L.A (i.e. R a )


  1. Find the arithmetic mean of the measured heights
    R a = 1/n Σ(zi)

  2. R a = (33+25+40+22+35+18+42+25+35+22+36+18+42+22+31+21+36+18+35+20)/20

  3. R a = 28.7 μm



R.M.S value


  1. Find the square of each measured height
    z²i = zi²

  2. Find the mean of the squares of the measured heights
    (Σ(z²i))/n

  3. Find the square root of the mean value
    RMS = √((Σ(z²i))/n)

  4. RMS = √((33²+25²+40²+22²+35²+18²+42²+25²+35²+22²+36²+18²+42²+22²+31²+21²+36²+18²+35²+20²)/20)

  5. RMS = 34.3 μm



R z value


  1. Arrange the measured heights in ascending order
    20, 21, 22, 22, 25, 25, 31, 33, 35, 35, 35, 36, 36, 40, 42, 42, 42

  2. Find the difference between the highest and lowest measured heights
    R z = 42 - 20 = 22 μm



Grade of Roughness in case of R a value


  • R a = 28.7 μm

  • From the table of surface roughness grades, R a falls under the grade of N9

  • N9 indicates a rough surface finish

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In the measurement of surface roughness, height of 20 successive peaks and troughs were measured from a datum and were: 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35 and 20 μm. If these measurements were obtained over a length of 20 mm, determine the C.L.A. (i.e. R a ), R.M.S and R z values of the rough surface. B) Determine the grade of roughness in case of R a value.?
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In the measurement of surface roughness, height of 20 successive peaks and troughs were measured from a datum and were: 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35 and 20 μm. If these measurements were obtained over a length of 20 mm, determine the C.L.A. (i.e. R a ), R.M.S and R z values of the rough surface. B) Determine the grade of roughness in case of R a value.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In the measurement of surface roughness, height of 20 successive peaks and troughs were measured from a datum and were: 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35 and 20 μm. If these measurements were obtained over a length of 20 mm, determine the C.L.A. (i.e. R a ), R.M.S and R z values of the rough surface. B) Determine the grade of roughness in case of R a value.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the measurement of surface roughness, height of 20 successive peaks and troughs were measured from a datum and were: 33, 25, 40, 22, 35, 18, 42, 25, 35, 22, 36, 18, 42, 22, 31, 21, 36, 18, 35 and 20 μm. If these measurements were obtained over a length of 20 mm, determine the C.L.A. (i.e. R a ), R.M.S and R z values of the rough surface. B) Determine the grade of roughness in case of R a value.?.
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