WO2011069219A1 - A system for the measurement of the deviations from form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum - Google Patents

A system for the measurement of the deviations from form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum Download PDF

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Publication number
WO2011069219A1
WO2011069219A1 PCT/BG2010/000025 BG2010000025W WO2011069219A1 WO 2011069219 A1 WO2011069219 A1 WO 2011069219A1 BG 2010000025 W BG2010000025 W BG 2010000025W WO 2011069219 A1 WO2011069219 A1 WO 2011069219A1
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Prior art keywords
measurement
run
wandering
work
sections
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PCT/BG2010/000025
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French (fr)
Inventor
Nikola Dimitrov Panchev
Dimitar Ivanov Diakov
Hristo Kirilov Radev
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Nikola Dimitrov Panchev
Dimitar Ivanov Diakov
Hristo Kirilov Radev
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Publication of WO2011069219A1 publication Critical patent/WO2011069219A1/en

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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B23MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23QDETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q17/00Arrangements for observing, indicating or measuring on machine tools
    • B23Q17/20Arrangements for observing, indicating or measuring on machine tools for indicating or measuring workpiece characteristics, e.g. contour, dimension, hardness
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00Measuring arrangements characterised by the use of mechanical techniques
    • G01B5/20Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures
    • G01B5/201Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures for measuring roundness
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00Measuring arrangements characterised by the use of mechanical techniques
    • G01B5/24Measuring arrangements characterised by the use of mechanical techniques for measuring angles or tapers; for testing the alignment of axes
    • G01B5/25Measuring arrangements characterised by the use of mechanical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes
    • G01B5/252Measuring arrangements characterised by the use of mechanical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes for measuring eccentricity, i.e. lateral shift between two parallel axes

Definitions

  • the invention applies to a system for the measurement of the deviations from form and position of the surfaces and axes of important big rotational work-pieces in the field of the heavy- and transportation machine-building and energetics.
  • work-pieces are e.g. turbine shafts, crankshafts of heavy motors, etc.
  • the deviation from roundness of the two rings and the deviation from flatness of the front face of one of them are either preliminary known or negligibly small. Transferring the measurement results of the radial and axial run-out to the virtual primary datum is done by making correction in these results that exclude the influence of both the wandering radial and axial run-out.
  • the work-piece is based on either vee-blocks, or centers, or its own bush bearings during the measurement process, and the radial and axial run-out are determined by the means of universal length measuring instruments (measuring heads and different types of electronic sensors) that are part of automated or non-automated measurement systems.
  • the primary measurement information is processed according to appropriate algorithms and programs by a computer, which is a part of the measurement system.
  • the measurement of the big shafts is performed during repair- or test operations, when they are based on their own bush bearings, because of their specific properties (e.g. turbine shafts weight up to 120 tones and their length is in the range from 10 to 12 meters), and the access to their end faces is either difficult or even impossible, respectively the mounting of the etalon rings is also either difficult or even impossible. This limits the application of this method.
  • the aim of the invention is to create a system for the measurement of the form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum without the use of etalon rings fixed (mounted) to the end faces of the measured work-pieces when the access to these faces is either difficult or impossible.
  • the virtual primary datum - the datum axis - is determined as a straight line, which passes through the centroids of the points of the instantaneous axes of rotation in two cross-sections, I-I and II-II , from the rotational surfaces of the work-piece, which are marked in advance.
  • Both the radial and the wandering run-out in these sections are determined by the means of a device built on the basis of a multi-stage self- aligning prism.
  • each point of the prism's body circumscribes a circle, which is equidistant to the root- mean-square circle of the profile of the section, in which the prism is mounted.
  • the device can be realized in two different types: A and B.
  • a measuring rod which contacts with the measured profile, is born in the body of the prism.
  • the travel of the measuring rod is measured, respectively the deviation from roundness of the profile is measured by the first measuring head, and the run-out of the work-piece in the given section is measured by the second head.
  • the run-out which is measured by the second measuring head, combines the eccentricity, the deviation from roundness, and the wandering run-out.
  • the difference between the indications of the two measuring heads contains the wandering run-out and the eccentricity, which can be determined by the means of an appropriate roundness graph.
  • a measuring rod whose measuring tip contacts with the measured profile, is born in the body of the multi-stage self-aligning prism.
  • the travel of the body of the prism and the measuring rod are simultaneously measured by the means of two measuring heads, which are fixed to the base where the work-piece is mounted.
  • the indications of the first measuring head reflect the wandering run-out and the eccentricity of the center of the root-mean-square circle of the measured profile
  • the indications of the second measuring head reflect the run-out of the profile, i.e. the deviation from roundness, the eccentricity and the wandering run-out.
  • a roundness graph is drawn using the indications of the first measuring head, by the means of which the wandering run-out and the eccentricity are determined. Corrections are made from the wandering run-out data, to exclude its influence on the run-out results in all measured cross-sections, including the two in question.
  • the deviations from form and position of the measured surfaces and axes are calculated by the means of appropriate algorithms and programs using the corrected values of the run-out.
  • the difference between the indications of the two measuring heads contains the deviation from roundness, and the eccentricity of the measured profile, which can be determined by the means of an appropriate roundness graph.
  • Figure 2 Schematic diagram of a measuring device for the evaluation of the wandering run-out, the eccentricity, and the deviation from roundness in the cross-section in question - Type A.
  • Figure 3 Schematic diagram of a measuring device for the evaluation of the wandering run-out, the eccentricity, and the deviation from roundness in the cross-section in question - Type B.
  • the application of the invention is explained by the schematic diagram for measurement, which is shown on figure 1.
  • the work-piece is based on vee- blocks, centers or on its own bush bearings, which represent the datum 5, towards which the radial run-out is measured.
  • the radial run-out in the corresponding cross-sections is measured by the means of the measuring heads 3.
  • This run-out includes the deviation from roundness of the measured profile, the eccentricity, and the wandering run-out.
  • the deviation from roundness, the eccentricity, and the wandering run-out of the surfaces of two cross-sections I-I and II-II, marked in advance, are evaluated by the means of the measuring devices 2 and 4. Corrections for the determined wandering run-out are made in the indications of all measuring heads, and the wanted deviations from form and position are calculated by the means of appropriate programs using the corrected run-out values.
  • the device contains multi-stage self-aligning prism 2, in the body of which the measuring rod 3 is mounted, and whose measuring tip contacts with the work-piece 1 profile in the measured cross-section.
  • the measuring heads 4 and 6 which are mounted along the line of measurement, the run-out is simultaneously measured, respectively towards the body 2 of the prism and the datum 5.
  • the indications A 4 of the measuring head 4 reflect the deviation from roundness towards root-mean-square circle of the measured profile
  • the indications A 6 of the measuring head 6 reflect the deviation from roundness, the eccentricity and the wandering run-out, i.e.:
  • the difference between the two indications reflects the eccentricity and the wandering run-out.
  • Corrections are made in the run-out values in all measured cross-sections using the determined values of the wandering run-out in the marked cross- sections, and by the means of these corrected values the deviations from form and position of the surfaces and axes of the measured work-piece are calculated using appropriate programs.
  • the device contains multi-stage self-aligning prism 2, in the body of which the measuring rod 3 is mounted, and whose measuring tip contacts with the work-piece 1 profile in the measured cross-section.
  • the measuring heads 4 and 6 which are mounted on the datum 5 along the line of measurement, the run-out is simultaneously measured, respectively of the body of the measured profile.
  • the indications A 4 of the measuring head 4 reflect the eccentricity and the wandering run-out of the center of the root-mean-square circle of the measured profile
  • the indications A 6 of the measuring head 6 reflect the deviation from roundness, the eccentricity and the wandering run-out, i.e.:
  • the difference between the two indications reflects the deviation from roundness.
  • Corrections are made in the run-out values in all measured cross-sections using the determined values of the wandering run-out in the marked cross- sections, and by the means of these corrected values the deviations from form and position of the surfaces and axes of the measured work-piece are calculated using appropriate algorithms and programs.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • A Measuring Device Byusing Mechanical Method (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The invention applies to a system for the measurement of the deviations from form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum, which contains datums (vee-blocks, centers, body's own bush bearings) to support the measured part, measuring heads for the measurement of the radial run-out in n cross - sections of the surfaces of revolution of the work -piece and two devices for the measurement of the wandering run-out into two cross - sections of the work-piece marked in advance, on the basis of which wandering run-out corrections are made of the measurement results of the radial run-out in all measured cross - sections and the deviations from form and position are calculated on the basis of the corrected results. The device for the measurement of the wandering radial run-out contains a multi-stage self - aligning prism and a plurality of measuring heads appropriately located in the line of measurement.

Description

A System for the Measurement of the Deviations from Form and Position of the Surfaces and Axes of Rotational Work-pieces
Towards a Virtual Primary Datum
Nikola Panchev, Dimitar Diakov, Hristo Radev
Engineering field:
The invention applies to a system for the measurement of the deviations from form and position of the surfaces and axes of important big rotational work-pieces in the field of the heavy- and transportation machine-building and energetics. Such work-pieces are e.g. turbine shafts, crankshafts of heavy motors, etc.
Former state of the technics:
A method is known for the measurement of the deviations from form and position of the surfaces and axes of important big rotational work-pieces in the field of the heavy- and transportation machine-building and energetics using the results of measurement of the radial and axial run-out of the corresponding surfaces and a subsequent processing of the primary information without any requirements for the accuracy of the virtual primary datum - the virtual datum axis, which is a straight line, passing through the centroids of the points of the simultaneous axes of rotation in the cross-sections of two rings that are fixed to the end faces of the work-piece approximately co-axial to its geometric axis. The deviation from roundness of the two rings and the deviation from flatness of the front face of one of them are either preliminary known or negligibly small. Transferring the measurement results of the radial and axial run-out to the virtual primary datum is done by making correction in these results that exclude the influence of both the wandering radial and axial run-out.
The work-piece is based on either vee-blocks, or centers, or its own bush bearings during the measurement process, and the radial and axial run-out are determined by the means of universal length measuring instruments (measuring heads and different types of electronic sensors) that are part of automated or non-automated measurement systems.
The primary measurement information is processed according to appropriate algorithms and programs by a computer, which is a part of the measurement system.
The measurement of the big shafts is performed during repair- or test operations, when they are based on their own bush bearings, because of their specific properties (e.g. turbine shafts weight up to 120 tones and their length is in the range from 10 to 12 meters), and the access to their end faces is either difficult or even impossible, respectively the mounting of the etalon rings is also either difficult or even impossible. This limits the application of this method.
Technical nature of the invention:
The aim of the invention is to create a system for the measurement of the form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum without the use of etalon rings fixed (mounted) to the end faces of the measured work-pieces when the access to these faces is either difficult or impossible.
The virtual primary datum - the datum axis - is determined as a straight line, which passes through the centroids of the points of the instantaneous axes of rotation in two cross-sections, I-I and II-II , from the rotational surfaces of the work-piece, which are marked in advance.
Both the radial and the wandering run-out in these sections are determined by the means of a device built on the basis of a multi-stage self- aligning prism.
When the prism is mounted on the shaft and turned relatively to it, each point of the prism's body circumscribes a circle, which is equidistant to the root- mean-square circle of the profile of the section, in which the prism is mounted. The device can be realized in two different types: A and B.
Type A:
A measuring rod, which contacts with the measured profile, is born in the body of the prism. By the means of two measuring heads, one of which is fixed to the body of the prism, and the other is fixed to the datum where the work- piece is based, the travel of the measuring rod is measured, respectively the deviation from roundness of the profile is measured by the first measuring head, and the run-out of the work-piece in the given section is measured by the second head. The run-out, which is measured by the second measuring head, combines the eccentricity, the deviation from roundness, and the wandering run-out.
The difference between the indications of the two measuring heads contains the wandering run-out and the eccentricity, which can be determined by the means of an appropriate roundness graph.
These data are used to make corrections to exclude the influence of the wandering run-out in the run-out measuring results in all the measured cross- sections, including the two in question. The deviations from form and position of the measured surfaces and axes are calculated from the corrected values of the radial run-out by the means of appropriate algorithms and programs.
Type B:
A measuring rod, whose measuring tip contacts with the measured profile, is born in the body of the multi-stage self-aligning prism.
The travel of the body of the prism and the measuring rod are simultaneously measured by the means of two measuring heads, which are fixed to the base where the work-piece is mounted. The indications of the first measuring head reflect the wandering run-out and the eccentricity of the center of the root-mean-square circle of the measured profile, and the indications of the second measuring head reflect the run-out of the profile, i.e. the deviation from roundness, the eccentricity and the wandering run-out.
A roundness graph is drawn using the indications of the first measuring head, by the means of which the wandering run-out and the eccentricity are determined. Corrections are made from the wandering run-out data, to exclude its influence on the run-out results in all measured cross-sections, including the two in question.
The deviations from form and position of the measured surfaces and axes are calculated by the means of appropriate algorithms and programs using the corrected values of the run-out.
The difference between the indications of the two measuring heads contains the deviation from roundness, and the eccentricity of the measured profile, which can be determined by the means of an appropriate roundness graph. Description of the included figures:
Figure 1. Scheme for the measurement of the deviations from form and position of the surfaces and axes of a rotational work-piece towards a virtual primary datum using the measurement system proposed in the invention:
1. Measured work-piece
2. and 4. Devices to determine the wandering run-out and the deviation of roundness in the corresponding cross-sections
3. Measuring heads
5. Datum (bush bearings, centers, vee-blocks) I-I and II-II - Cross-sections marked in advance
Figure 2. Schematic diagram of a measuring device for the evaluation of the wandering run-out, the eccentricity, and the deviation from roundness in the cross-section in question - Type A.
1. Measured work-piece
2. Multi-stage self-aligning prism
3. Measuring rod
4. Measuring head
5. Datum
6. Measuring head
Figure 3. Schematic diagram of a measuring device for the evaluation of the wandering run-out, the eccentricity, and the deviation from roundness in the cross-section in question - Type B.
1. Measured work-piece 2. Multi-stage self-aligning prism
3. Measuring rod
4. Measuring head
5. Datum
6. Measuring head
Example for the application of the invention
The application of the invention is explained by the schematic diagram for measurement, which is shown on figure 1. The work-piece is based on vee- blocks, centers or on its own bush bearings, which represent the datum 5, towards which the radial run-out is measured.
The radial run-out in the corresponding cross-sections is measured by the means of the measuring heads 3. This run-out includes the deviation from roundness of the measured profile, the eccentricity, and the wandering run-out. The deviation from roundness, the eccentricity, and the wandering run-out of the surfaces of two cross-sections I-I and II-II, marked in advance, are evaluated by the means of the measuring devices 2 and 4. Corrections for the determined wandering run-out are made in the indications of all measuring heads, and the wanted deviations from form and position are calculated by the means of appropriate programs using the corrected run-out values.
The schematic diagram of a device for the determination of the wandering run-out, the eccentricity, and the deviation from roundness in the marked cross- sections (Type A) is shown on figure 2.
The device contains multi-stage self-aligning prism 2, in the body of which the measuring rod 3 is mounted, and whose measuring tip contacts with the work-piece 1 profile in the measured cross-section. By the means of the measuring heads 4 and 6, which are mounted along the line of measurement, the run-out is simultaneously measured, respectively towards the body 2 of the prism and the datum 5. The indications A4 of the measuring head 4 reflect the deviation from roundness towards root-mean-square circle of the measured profile, the indications A6 of the measuring head 6 reflect the deviation from roundness, the eccentricity and the wandering run-out, i.e.:
A4 -> deviation from roundness,
A6 -> deviation from roundness + eccentricity + wandering run-out.
The difference between the two indications reflects the eccentricity and the wandering run-out.
A6 - A4 -> eccentricity + wandering run-out.
Using these differences a roundness graph is drawn, which in turn is used do evaluate the eccentricity and the wandering run-out.
Corrections are made in the run-out values in all measured cross-sections using the determined values of the wandering run-out in the marked cross- sections, and by the means of these corrected values the deviations from form and position of the surfaces and axes of the measured work-piece are calculated using appropriate programs.
The schematic diagram of a device for the determination of the wandering run-out, the eccentricity, and the deviation from roundness in the marked cross- sections (Type B) is shown on figure 3.
The device contains multi-stage self-aligning prism 2, in the body of which the measuring rod 3 is mounted, and whose measuring tip contacts with the work-piece 1 profile in the measured cross-section. By the means of the measuring heads 4 and 6, which are mounted on the datum 5 along the line of measurement, the run-out is simultaneously measured, respectively of the body of the measured profile. The indications A4 of the measuring head 4 reflect the eccentricity and the wandering run-out of the center of the root-mean-square circle of the measured profile, and the indications A6 of the measuring head 6 reflect the deviation from roundness, the eccentricity and the wandering run-out, i.e.:
A 4 -> eccentricity + wandering run-out,
A6 -> deviation from roundness + eccentricity + wandering run-out.
The difference between the two indications reflects the deviation from roundness.
A6 - A4 -> deviation from roundness.
Using the indications A4 of the measuring head 4 a roundness graph is drawn, which in turn is used do evaluate the eccentricity and the wandering radial run-out.
Corrections are made in the run-out values in all measured cross-sections using the determined values of the wandering run-out in the marked cross- sections, and by the means of these corrected values the deviations from form and position of the surfaces and axes of the measured work-piece are calculated using appropriate algorithms and programs.
Bibliography:
Figure imgf000010_0001
(Radev Hr., A method for the measurement of the deviations from form and position of surfaces and axes of rotational work-pieces towards a virtual primary datum, invention patent #65461 )
Figure imgf000011_0001

Claims

Patent claims
1. The system for the measurement of the deviations from form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum, which contains datums (vee-blocks, centers, body's own bush bearings) to support the measured part, measuring heads for the measurement of the radial run-out in n cross-sections of the surfaces of revolution of the work- piece, characterized by devices for the measurement of the wandering run-out into two cross-sections of the work-piece marked in advance, on the basis of which, corrections are made in the measurement results of the radial run-out in all measured cross-sections and the deviations of form and position are calculated on the basis of the corrected results.
2. A device for the measurement (evaluation) of the radial wandering runout in two cross-sections of the work-piece marked in advance according to claim 1 , which contains a multi-stage self-aligning prism, characterized by the fact that the travel of the measuring rod, born in the prism body, is simultaneously measured by the means of two measuring heads, fixed along the line of measurement, one of which is mounted on the prism body, and the other one is mounted on the datum; the wandering run-out is calculated and corrections are made by the difference between the indications of the two measuring heads.
3. A device for the measurement (evaluation) of the radial wandering runout in two cross-sections of the work-piece marked in advance according to claims 1 and 2, which contains a multi-stage self-aligning prism, characterized by the fact that the travel of the prism body and the measuring rod, born in prism body, are simultaneously measured by the means of two measuring heads, fixed along the line of measurement, which are mounted on the datum; by the difference of their indications the eccentricity, and the deviation from roundness are evaluated, whilst the wandering run-out is calculated, and corrections are is fixed to the datum, and the wandering radial run-out is defined as the difference between the indications of the two measuring heads.
The measuring heads of the device of the second type are fixed to the datum, and the first one measures the travel of the prism body, whereas the second one measures the travel of the measuring rod. The indication of the first measuring head is used to determine the wandering run-out, and the difference between the indications of the two measuring heads is used to determine both the eccentricity and roundness deviation.
PCT/BG2010/000025 2009-12-09 2010-12-02 A system for the measurement of the deviations from form and position of the surfaces and axes of rotational work-pieces towards a virtual primary datum WO2011069219A1 (en)

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CN102749059A (en) * 2012-07-20 2012-10-24 上海交通大学 Dual-feed type device for measuring roundness and cylindricity
CN102980502A (en) * 2011-09-06 2013-03-20 陈波 Caliper and operation method for symmetrical degree testing of large diameter shaft component key groove
CN102997828A (en) * 2012-11-16 2013-03-27 无锡麦铁精密机械制造有限公司 Coaxiality gauge
ES2415776R1 (en) * 2011-12-23 2013-10-11 Univ Catalunya Politecnica System and method of measuring the transverse displacement of a rotating physical axis
CN103968744A (en) * 2013-01-25 2014-08-06 宝钢特钢有限公司 Measurement alignment tool of coupling
CN105189034A (en) * 2013-01-21 2015-12-23 博特克创新有限责任公司 Machine and method for machining large shafts comprising eccentric parts
CN106103899A (en) * 2014-03-03 2016-11-09 西门子股份公司 There is the rotor part on surface for checking concentricity
JP2017173288A (en) * 2016-03-16 2017-09-28 株式会社東京精密 Method for calculating amount of core deviation of circularity measuring machine and circularity measuring machine
CN110174037A (en) * 2019-06-26 2019-08-27 湖北博利特种汽车装备股份有限公司 A kind of axis class processing detection device
FR3093175A1 (en) * 2019-02-21 2020-08-28 Safran Aircraft Engines SYSTEM FOR MEASURING BENDING SURFACE DEFORMATION OF A MATERIAL
CN111899632A (en) * 2020-09-07 2020-11-06 中国人民解放军陆军工程大学 Shaft measurement skill training device for teaching

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US6568096B1 (en) * 1999-02-22 2003-05-27 Obschestvo s Ogranichennoi Otvetctvennostju “Tekhnomash” Device and method for measuring shape deviations of a cylindrical workpiece and correcting steadying element and correcting follower for use therewith

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SU510638A1 (en) * 1971-05-10 1976-04-15 Специальное Конструкторское Бюро По Проектированию Шлифовального Оборудования Device for measuring non-roundness
US4176461A (en) * 1974-05-03 1979-12-04 Spetsialnoe Knostruktorskoe Bjuro PO Proektirovaniju Shlifovalnogo Oborudovania Device for measuring the deviation of object with nominally circular cross-section from the round shape
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Cited By (16)

* Cited by examiner, † Cited by third party
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CN102980502A (en) * 2011-09-06 2013-03-20 陈波 Caliper and operation method for symmetrical degree testing of large diameter shaft component key groove
ES2415776R1 (en) * 2011-12-23 2013-10-11 Univ Catalunya Politecnica System and method of measuring the transverse displacement of a rotating physical axis
CN102749059A (en) * 2012-07-20 2012-10-24 上海交通大学 Dual-feed type device for measuring roundness and cylindricity
CN102997828A (en) * 2012-11-16 2013-03-27 无锡麦铁精密机械制造有限公司 Coaxiality gauge
CN105189034A (en) * 2013-01-21 2015-12-23 博特克创新有限责任公司 Machine and method for machining large shafts comprising eccentric parts
CN103968744A (en) * 2013-01-25 2014-08-06 宝钢特钢有限公司 Measurement alignment tool of coupling
CN106103899B (en) * 2014-03-03 2017-11-17 西门子股份公司 Rotor part with the surface for checking concentricity
CN106103899A (en) * 2014-03-03 2016-11-09 西门子股份公司 There is the rotor part on surface for checking concentricity
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JP2017173288A (en) * 2016-03-16 2017-09-28 株式会社東京精密 Method for calculating amount of core deviation of circularity measuring machine and circularity measuring machine
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