Measurement of Geometrical Errors in Manufacturing Flatness

METU Department of
Mechanical Engineering
ME410
Experiment 1
Straightness and Flatness Measurements on a
Surface Table
Instructor Assoc. Prof. Dr. E. İlhan KONUKSEVEN
Assistant Cem Türkeş
Group D3
Team Samet Baykul
Hamza Arif Raza
Abdul Ahad Naeem
Prepared by
Samet Baykul
December 7, 2018

ii
ME 410 Experiment 1 August 1, 2019
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also
declare that, as require by these rules and conduct, I have fully cited and
referenced all material and results that are not original to this work.
Name, Last Name : Samet Baykul
Signature :

1. Abstract
In this report, we will measure the straightness of line segments at certain intervals
and calculate the flatness of a surface through these measurements. We will discuss
how this measurement works. We will also discuss the results and possible errors.
2. Nomenclature
Surface Straightness: The standard form of straightness is a 2-D tolerance that is
used to ensure that a part is uniform across a surface or feature. It is defined as the
variance of the surface within a specified line on that surface.
Flatness references how flat a surface is regardless of any other datum’s or features.
(1)
Talyvel: Talyvel is a brand name for an instrument for setting horizontal lines. This
instrument consists of an induction transducer. A conductive pendulum is held between
the two halves of the induction transducer. So, whenever the instrument tilts the
pendulum also tilts giving rise to an electric impulse. This impulse can be measured by a
galvanometer and thus the amount of tilt can be known. (2)
3. Objective
• Learn to use Talyvel in order to measure the straightness of lines on a surface
table,
• To determine the flatness of the whole table from measurements,
• Discuss about important outcomes and possible errors.

2
4. Introduction
There are two feet of the device used in the measurement. We place these feet on
the correct order and read the value on the screen. There is a pendulum inside the device.
This pendulum works with gravity and gives an angle relative to the elevation difference
of the two feet. By using this angle, the difference between these points on the straight
line can be calculated.
5. Theory and Experimental Procedure
Accurately measuring the flatness of a surface allows us to test whether the product
is within the given tolerance values or not. Since an infinite number of lines pass through
a surface, an absolute flatness measurement is not possible at least by the method used
in this experiment. However, after measuring the straightness of a certain number of lines
distributed homogeneously on the surface, surface flatness can be calculated according
to these values effectively. This report shows how to do process and discuss possible
errors.

3
6. Data and Results
6.1. Surface Table
Measurements were done by using Talyvel on the determined surface. Each interval
is 150 mm.

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6.2. Lines of Test
The results shown in seconds.
Position AC AE AG GC GE CE BF HD
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 21 10 65 35 -10 50 30 8
3 8 7 110 50 0 100 70 0
4 -6 14 - 65 -14 - - -19
5 - 16 - 75 - - - -
These results were transformed into height difference with formula (7.1).
Position AC AE AG GC GE CE BF HD
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 15.3 7.3 47.3 25.4 -7.3 36.4 21.8 5.8
3 5.8 5.1 80.0 36.4 0 72.7 50.9 0
4 -4,4 10.2 - 47.3 -10.2 - - -13.8
5 - 11.6 - 54.5 - - - -

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6.3. Correction of Data
6.3.1. AC Line
Cumulative Error Correction Height Relative to ACG
0 0 0
0 +1.5 1.5
21 +3.0 24
8 +4.5 12.5
-6 +6.0 0
6.3.2. AG Line
0 0 0
0 -36.7 -36.7
65 -73.3 -8.3
110 -110.0 0
6.3.3. GC Line
0 0 0
0 -15.0 -15
35 -30.0 5
(42.5 midpoint) -37.5 5
50 -45.0 5
65 -60.0 5
75 -75.0 0

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6.3.4. AE Line
0 0 0
0 -1.7 -1.7
10 -2.3 7.7
(8.5 midpoint) (-3.5) 5
7 -4.7 2.3
14 -5.8 8.2
16 -7.0 9
6.3.5. CE Line
0 0 0
0 -30.3 -30.3
50 -60.7 -60.7
100 -91.0 9
6.3.6. GE Line
0 0 0
0 +5.8 5.8
-10 +11.5 -1.5
0 +17.2 17.2
-14 +23.0 9

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6.3.7. BF Line
Cumulative Error Initial Correction Correction Error to ACG
0 24 0 24
0 24 -31.8 -7.8
(15 midpoint) 39 (-47.8 midpoint) -8.8 (It should
be close to 5)
30 54 -63.7 -9.7
70 94 -95.5 -1.5
6.3.8. HD Line
Cumulative Error Initial Correction Correction Error to ACG
0 -22.5 0 -22.5
0 -22.5 -0.9 -23.4
8 -14.5 -1.8 -16.3 (It should
be close to 5)
0 -22.5 -2.8 -25.3
-19 -41 -3.7 -45.5

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6.3.9. Results
These results are given as angle values in seconds. These values can be easily
converted to micrometer using formula 7.1.
0 +1.5 +24 +12.5 0
0
-8.3
-36.7
-15
+5.8 -1.5 +17.2 +9
-60.7
-30.3
-45.5-22.5
+5
+7.7
-1.7
+2.3
+8.3
+5
+5
+5

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7. Sample Calculations with Uncertainty Analysis
7.1. Converting from Angular Rotation to Linear Rise or Fall
h(in µm) = p*150*1000/(3600*180)*q(in seconds)
For 21 seconds ->
h = p*150*1000/(3600*180)*21
h = 15.27 µm

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8. Discussion and Conclusion
• The results are consistent within themselves except for a few points. Middle
points on BF and HD lines contradicts with some previous points as shown on
the tables.
• There are multiple errors caused by measurement.
o The biggest error source is the feet on which the device is placed do
not proceed on a straight line.
o Again, the roughness of the surface area below the feet on which the
device is placed may cause the device to lie in a different way than it
should.
Nowadays, surface flatness measurement can be done with better modern methods.
However, it is important to learn the basics of this measurement and to be aware of
possible sources of errors.

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References
(1) (n.d.), https://www.gdandtbasics.com/straightness/
(2) (11 May, 2018), https://en.wikiversity.org/wiki/Talyvel

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Appendices
A.1. Principles of “Talyvel” Electronic Level
Source: (11 May, 2018), https://en.wikiversity.org/wiki/Talyvel

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A.2. Surface Flatness and Flatness Tolerance Representation
Source: (n.d.), https://www.gdandtbasics.com/straightness/

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