Undulations Per Revolution (UPR) data in the roundness graphs Measurement result graphs Filtering
Effect of Filter Settings on the Measured Profile ISO 12181-2: 2011* 4 Profiles can be filtered in various ways to reduce or eliminate unwanted detail, with a cut-off value set in terms of undulations per revolution (upr). The effect of different upr settings is shown in the diagrams below, which illustrate how the measured roundness value decreases as lower upr settings progressively smooth out the line.
2CR filter ISO 4291: 1985* 3 75%
Gaussian filter ISO 12181-1: 2011* 5 50%
90
Standard Attenuation rate
Unfiltered
Δ Zq=22.14 µm
0
180
0
0
90
180
270
360
270 Terms and abbreviated terms ISO 12181-1: 2011 * 5 A 1 UPR condition indicates eccentricity of the workpiece relative to the rotational axis of the measuring instrument. The amplitude of undulation components depends on the leveling adjustment. Abbreviated terms Terms Angle
0 Least squares reference line Least squares reference plane Local cylindricity deviation Local flatness deviation 90 180 Angle Least squares reference circle Least squares reference cylinder
90 LSCI LSCY LSLI LSPL LCD 270 LFD LRD LSD MICI
Δ Zq=16.60 µm
Δ Zq=20.72 µm
Δ Zq=22.04 µm
Δ Zq=12.35 µm
Low-pass filter
0
180
0
270
360
A 2 UPR condition may indicate: (1) insufficient leveling adjustment on the measuring instrument; (2) circular runout due to incorrect mounting of the workpiece on the machine tool that created its shape; (3) the form of the workpiece is elliptical by design as in, for example, an IC-engine piston. Local roundness deviation Local straightness deviation
15 upr
50 upr
150 upr
500 upr
Maximum inscribed reference circle Maximum inscribed reference cylinder Minimum circumscribed reference circle Minimum circumscribed reference cylinder
Band-pass filter
Δ Zq=18.76 µm
Δ Zq=14.50 µm
Δ Zq=17.61 µm
90 MICY MCCI MCCY MZCI MZCY MZLI MZPL UPR 270
0
180
0
0
90
180
270
360
Angle Minimum zone reference circles Minimum zone reference cylinder Minimum zone reference lines Minimum zone reference planes Undulations per revolution
15-150 upr
15-500 upr
50-500 upr
A 3 to 5 UPR condition may indicate: (1) Deformation due to over-tightening of the holding chuck on the measuring instrument; (2) Relaxation deformation due to stress release after unloading from the holding chuck on the machine tool that created its shape.
90
Evaluating the Measured Profile Roundness ISO 12181-1: 2011* 5 , ISO 4291: 1985* 3 Roundness testers use the measurement data to generate reference circles whose dimensions define the roundness value. There are four methods of generating these circles, as shown below, and each method has individual characteristics so the method that best matches the function of the workpiece should be chosen. Each method results in a different center position for the reference circles and therefore affects the axial location of the circular feature measured.
0 Parameters and abbreviated terms ISO 12181-1: 2011 * 5 Reference element* 0 180
Abbreviated terms
0
90
180
270
360
Parameter
Minimum zone
Minimum circumscribed
Least square
Minimum inscribed
270
Angle
Cylinder taper Generatrix straightness deviation
CYLtt STRsg STRIc CYLp FLTp RONp STRp CYLt FLTt RONt STRt CYLv FLTv RONv STRv CYLq FLTq RONq STRq STRsa
✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
90
Least Square Circle (LSC)
Minimum Zone Circles (MZC)
0 Local generatrix straightness deviation Peak-to-reference cylindricity deviation Peak-to-reference flatness deviation Peak-to-reference roundness deviation Peak-to-reference straightness deviation 0 90 0 Peak-to-valley cylindricity deviation Peak-to-valley flatness deviation Peak-to-valley roundness deviation Peak-to-valley straightness deviation 0 90 0 Reference-to-valley cylindricity deviation Reference-to-valley flatness deviation Reference-to-valley roundness deviation Reference-to-valley straightness deviation Root-mean-square cylindricity deviation 0 Root-mean-squareflatness deviation Root-mean-square roundness deviation Root-mean-square straightness deviation Straightness deviation of the extracted median line 0 90 0 0
180
A circle is fitted to the measured profile such that the sum of the squares of the departure of the profile data from this circle is a minimum. The roundness figure is then defined as the difference between the maximum deviation of the profile from this circle (highest peak to the lowest valley).
Two concentric circles are positioned to enclose the measured profile such that their radial difference is a minimum. The roundness figure is then defined as the radial separation of these two circles.
180
270
360
Angle
270
A 5 to 15 UPR condition often indicates unbalance factors in the machining method or processes used to produce the workpiece.
✓
✓
✓ ✓ ✓ ✓
90
✓
✓
180
180
270
360
J
Δ Zz = Rmax-Rmin Δ Zz: A symbol indicating roundness value by MZC.
Angle
Δ Zq = Rmax-Rmin Δ Zq: A symbol indicating roundness value by LSC.
270
90
Minimum Circumscribed Circle (MCC)
Maximum Inscribed Circle (MIC)
180
180
270
360
The smallest circle that can enclose the measured profile is created. The roundness figure is then defined as the maximum deviation of the profile from this circle. This circle is sometimes referred to as the ‘ring gage’ circle.
The largest circle that can be enclosed by the profile data is created. The roundness figure is then defined as the maximum deviation of the profile from this circle. This circle is sometimes referred to as the `plug gage' circle.
Angle
270
A 15 (or more) UPR condition is usually caused by tool chatter, machine vibration, coolant delivery effects, material non-homogeneity, etc., and is generally more important to the function than to the fit of a workpiece. ✓ ✓
✓
90
* The reference elements to which the parameter can be applied.
0
180
0
0
90
180
270
360
Δ Zc = Rmax-Rmin Δ Zc: A symbol indicating roundness value by MCC.
Δ Zi = Rmax-Rmin Δ Zi: A symbol indicating roundness value by MIC.
Angle
270
90
0 *1 ISO/DIS 1101: 1996 Geometrical Product Specifications (GPS) - Geometrical tolerancing - Tolerancing of form, orientation, location and run-out *2 ISO 5459 Technical drawings - Geometrical tolerancing - Datums and datum-systems for geometrical tolerances *3 ISO 4291: 1985 Methods for the assessment of departure from roundness - Measurement of variations in radius *4 ISO 12181-2: 2011 Geometrical Product Specifications (GPS) - Roundness - Part2: Specification operators *5 ISO 12181-1: 2011 Geometrical Product Specifications (GPS) - Roundness - Part 1: Vocabulary and parameters of roundness 0 90 270 0 180
180
270
360
Angle
J-28
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