In the manufacturing industry, someone once estimated that there are more circular workpieces than flat workpieces, ranging from screws, nuts, gaskets, to cylinders and bearings. The application of circular shapes is indeed very high. Today, the editor will talk to you about the topic of "roundness" in the field of measurement (reference standards: ISO/DIS 1101:2017, ISO 5459).
"roundness"
In JIS B0621-1984 "Definition and Expression of Form and Position Deviation",
Roundness is defined as "the size of a geometrically perfect circle that deviates from a circular shape",
The expression method is recorded as "roundness is a circular shape (C) is sandwiched by two concentric circles on the geometry, when the distance between the two concentric circles is the smallest, use (f) to represent the radius difference between the two circles, and the roundness Expressed in mm or μm."
For rotating components, the immediate problem is usually how to evaluate their true circular "shape". This starts with the "roundness tolerance".
What is "roundness tolerance"?
The roundness tolerance zone means that the tolerance zone is between two concentric circles of the same section. As shown in the figure below, the extraction circle should be limited within the tolerance zone between two coplanar concentric circles whose radius difference is t.
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Why do roundness and cylindricity tolerances occur? Usually there are these reasons:
Poor roundness and cylindricity caused by vibration of processing machinery
Poor roundness and cylindricity due to deterioration of rotating parts of processing machines
Poor roundness and cylindricity due to poor shape of center hole
Poor roundness and cylindricity caused by deformation in previous processing during centerless grinding
Distortion of workpieces caused by improper holding jigs or holding methods for ring parts
Poor roundness caused by abrasion of cutting tools, poor installation, vibration, etc.
Deformation caused by heat treatment after finishing, etc.
How to measure and evaluate roundness, what methods are there?
Evaluation of roundness
There are many evaluation methods for roundness, each method has its own characteristics and advantages, usually we will choose according to the needs of the workpiece...
Simple measurement methods, such as:
diameter method
The diameter of the roundness is directly read by a measuring tool such as a micrometer.
This simple measurement method is very simple and easy to operate. But when evaluating triangular and pentagonal equal-diameter strain circles, it is easy to be mistakenly measured as a perfect circle if it is not a perfect circle.
three point method
The three-point method can obtain the roundness data through [V-shaped block + micrometer / gauge + bench].
However, the tangent at the support point selected in the three-point method is different, and may not be measured correctly. The center of the reference cannot be determined, and errors may occur due to the up and down movement of the object to be measured as it rotates.
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Measurement methods based on relevant standards, such as:
radius method
The radius method uses the difference between the maximum radius value and the minimum radius value obtained when the workpiece rotates once to evaluate the roundness. In the evaluation method as shown in the figure below, the measurement results are also easily affected by the horizontal movement of the workpiece.
The tolerance zone is between two concentric circles on the same section
Central approach
The detection method of the center method is mostly used for more precise measurement requirements. The data of roundness detection depends on the reference circle. Different evaluation methods of the test circle will lead to different center positions of the reference circle, which will affect the axial position of the measured circular feature.
Least Squares Circle LSC
By fitting a circle to the measured profile, the sum of squares of deviations of the profile data from the circle is minimized, and the circularity value is then defined as the distance between the maximum deviation of the profile from the circle (highest peak to lowest valley) .
ΔZq=Rmax-Rmin, the symbol of roundness value expressed by LSC
Minimum zone circle MZC
Encloses the measured profile by positioning two concentric circles such that their radial difference is minimized. Define the circularity value as the radial separation of the two circles.
ΔZz=Rmax-Rmin , express the symbol of roundness value by MZC
Minimum circumscribed circle MCC
Creates the smallest circle that can enclose the measured profile. The circularity value is then defined as the maximum deviation of the profile from this circle
It is often used in the evaluation of shafts, rods, etc.
ΔZc=Rmax-Rmin , expresses the symbol of roundness value by MCC.
Maximum inscribed circle MIC
Creates the largest circle that can enclose the measured profile. The circularity value is then defined as the maximum deviation of the profile from this circle.
ΔZi=Rmax-Rmin , the symbol of the roundness value is represented by MIC.
In the process of evaluating roundness, in order to reduce or eliminate unnecessary noise, the obtained contour is usually filtered.
Influence of the filter on the measured profile
According to different measurement requirements, the filtering methods are also different, and the filter cut-off values are also different. (UPR: fluctuation per revolution), as shown in the figure below, it can be seen that the influence of the filter setting on the measured profile is different.
Without filter:
Low pass filter:
Bandpass filter:
And as evaluators, what can these graphics tell us?
Analysis of measurement charts
Figure: Chart of measurement results
1UPR component
1 UPR: Only one wave remains after filtering:
The 1UPR component represents the eccentricity of the workpiece relative to the axis of rotation of the measuring instrument. The amplitude of the waveform depends on the adjustment of its level.
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2UPR component
2UPR components may indicate:
① Insufficient level adjustment of measuring instruments;
② Circular runout due to incorrect installation of the workpiece on the machine tool forming its shape;
③ The shape of the workpiece is oval in design, such as in IC engine pistons.
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3~5UPR component
May mean:
① Deformation due to overtightening of the retaining chuck on the measuring instrument.
②Loose deformation due to stress release when unloading from the fixed chuck of the processing machine tool.
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5~15 UPR component
Usually indicates an unbalanced factor in the machining method or process of producing the workpiece.
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15 (more) UPR components
15 (or more) UPR conditions are usually self-induced by tool chatter, machine vibration, coolant delivery effects, material inhomogeneities, etc.
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The main parameters for evaluating roundness
parameter
meaning
RONt
Measured value of roundness, which represents the difference between the maximum value of the positive circularity curve and the minimum value of the negative circularity curve or the sum of the absolute values
RONp
The measured value of the peak height of the roundness curve, indicating the maximum value of the perfect roundness curve
RON
The roundness measure , which represents the absolute value of the minimum of the negative roundness curve
QUR
Square root mean square measure of roundness, representing the square root mean square of the roundness curve
The above is only excerpted from LSCI ""
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Finally, let's take a look at what tools and instruments are there for measuring roundness?
Common Tools/Instruments for Evaluating Roundness
micrometer:
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Roundness measuring instrument:
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CMM:
