This standard specifies the method of determining the roundness error by using three measuring points of the measuring sensor, separating the errors, and calculating the radius change, as well as the accuracy evaluation of the instrument. This standard is applicable to the evaluation of the deviation of the part contour from the ideal circle by using any of the following centers of circles under given conditions after contour transformation: a. The center of the smallest area circle; b. The center of the least squares square circle; c. The center of the smallest circumscribed circle; d. The center of the largest inscribed circle. In addition to being applicable to the measurement of roundness of general accuracy, the method specified in this standard is also applicable to the measurement of roundness of high-precision parts and parts whose length, diameter or weight exceeds the range of general instrument use. JB/T 5996-1992 Three-point method for roundness measurement and accuracy evaluation of its instrument JB/T5996-1992 Standard download decompression password: www.bzxz.net

Mechanical Industry Standard of the People's Republic of China
JB/T 5996-1992
Roundness measurement
Three-point method and accuracy evaluation of instruments
Published on July 17, 1992
Implementation by the Ministry of Machinery and Electronics Industry of the People's Republic of China on July 1, 1993
Mechanical Industry Standard of the People's Republic of China
Roundness measurement
Three-point method and accuracy evaluation of instruments
Subject content and scope of application
JB/T 5996-1992
This standard specifies the method of determining the roundness error by sampling at three points of the measuring sensor, separating the errors and calculating the radius change, and the accuracy evaluation of the instruments.
This standard is applicable to the deviation of the wheel set of a part from the ideal circle under given conditions after contour transformation, using any of the following centers: a. The center of the smallest area circle;
b. The center of the least square square circle
c. The center of the smallest circumscribed circle:
d. The center of the largest inscribed circle.
The method specified in this standard can be used for roundness measurement of general accuracy, and is also applicable to roundness measurement of high-precision parts and parts whose length, diameter or weight exceeds the range of general instrument use. Note: The given conditions include the position angles of the three measuring sensors, the number of discrete sampling points, the form of the three measuring sensor contacts and the position of the measuring surface. 2 Reference standards
Shape and position tolerance codes and their notation
Roundness measurement terms, definitions and parameters
Methods for evaluating roundness errors
Radius variation measurement
3 Terms and codes
Measuring plane
An imaginary plane passing through the measuring points, which coincides with the measured section of the part. Note: When measuring roundness errors, the measured section of the part is an imaginary plane perpendicular to the axis of the part. 3.2 Measuring direction
The direction of the radius change reflected on the measuring plane. 3.3 Three-point roundness measurement
Roundness measurement in the measuring direction using three measuring sensors or other measuring instruments placed on the same measuring plane and at a certain angle to each other. As shown in the figure.
Approved by the Ministry of Machinery and Electronics Industry on July 17, 1992, and implemented on July 1, 1993
Reference point
JB/T 5996-1992
In the roundness measurement of the three-point method, the measuring point where the measured contour has no shape distortion. Minimum area circle
Encloses the displayed contour, and
Two concentric circles with the smallest radius difference.
Least square circle
A circle with the smallest sum of squares of the distances from the displayed contour to the circle. 3.7
Minimum circumscribed circle
The smallest possible circle of the displayed contour circumscribed to the axis. 3.8:
Maximum inscribed circle
The largest possible circle of the displayed contour inscribed to the hole. Assessment code
The assessment code consists of △Z plus a superscript letter indicating the corresponding assessment center. See the table. Code
Three-point roundness measurement principle and instrument
4.1 Measurement principle
Evaluation center
Minimum area circle center
Minimum square circle center
Minimum circumscribed circle center
Minimum inscribed circle center
Subscript
The principle of three-point roundness measurement is to compare the radial deviation of corresponding points on the contour of the measured part with the ideal reference point contained in the three-point roundness measurement equation. The three-point method generally determines the roundness error through data processing in a discrete sampling manner. This measurement method can eliminate the influence of the rotation error of the measuring instrument (device) on the measurement, or through error separation calculation, "simultaneously obtain
the roundness error of the test piece and the rotation error of the measuring instrument (device) itself. 4.2
Measuring instrument
Consists of rotary shaft system, measuring sensor, electric signal processor and computer data processing system. For measuring instruments, they are generally composed of base,!
Online measuring instruments, the base and rotary shaft system can be replaced by the corresponding parts of the processing machine itself. Assessment of instrument accuracy
When assessing instrument accuracy, standard test pieces with certain shapes and certain values ​​specified in Appendix
(reference pieces) can be used. The instrument measurement error is expressed in absolute error and relative error, and the absolute error and relative error corresponding to the cross section and any angular position of the cross section (i.e. the angular position corresponding to a certain sampling point) should be calculated respectively. The error values ​​should meet the specified requirements. Measuring equation
JB/T5996-1992
Appendix A
Measurement equation for roundness measurement by three-point method
(reference)
is the profile of the measured section, in which O is the profile center, O\ is the rotation center, and ? are the relative position angles of the three measuring sensors. Y
Assume that the output signals of the three measuring sensors are: A (の), B (の), C (8), then: A(6)
In the formula: r (o) -
Profile of the measured section:
-The change of the rotation center 0\ with the rotation angle 0 6-The starting position angle:
-The initial position angle of the rotation center. Www.bzxZ.net
In order to eliminate the influence of 5 (の),
is set as formula ():
is the three measuring sensors, 9
the influence coefficients of the three measuring sensors are C, C, C respectively, and let (+e)
. Thus, the measurement equation for measuring roundness by the three-point method is obtained as formula (:
S(0)Cr(o)
Wherein: S (θ) is the combined signal of the three measuring sensors, which can be expressed as formula (S()CA(O)
Equation () can generally be expressed by discrete Fourier transform. Transformation, matrix adjustment and generalized inverse matrix derived from functional analysis are used to solve. B1 Position angle
JB/T5996-1992
Appendix B
Position angle of measuring sensor
(reference)
The three measuring sensors should be located in the same measuring plane. To avoid distortion, the number of sampling points should generally be equal to the number of reference points. The mutual position angles of the three measuring sensors and the number of reference points N should generally satisfy the following relationship: Let: be,
The number of points N is:
The three angles The greatest common factor angle between degrees is recorded as: △@N
(, 0, yuan)
In addition, when selecting the relative position angles, in addition to minimizing the calculation error, the size of the equation (C, C and the requirements of the instrument structure design should also be considered. Appendix C
Standard parts (reference parts) for three-point instrument accuracy evaluation
C1 standard parts
position), then the influence coefficient
in the reference
) is used to test the accuracy of the three-point roundness measuring instrument. In order to fully reflect the instrument (device) The method distortion that may occur should use any form of standard parts shown in Figure and Figure
. The boss of the standard part is generally obtained by coating method, and its height is generally times the instrument resolution. The boss size α×b can be determined according to specific requirements. The diameter of the standard part (the diameter of the sphere for the spherical standard part) is divided into two types, and the specific value can be selected according to needs; the length L and material type of the cylindrical standard part can be determined according to requirements. Se
This example uses the measurement reference point number N equal to
Calculation and radius change calculation.
JB/T 5996-1992
Appendix D
Calculation Example
(Reference)
is used as an example to illustrate the selection of the positions of the three measuring sensors. The selection of the mutual position angles of the three measuring sensors is obtained by the formula in the appendix
:
is the greatest common factor angle that satisfies and
is
. The influence coefficient C2 is calculated by the formula (
):
The synthesis of the measured values ​​of the three measuring sensors
is calculated by the formula (
Where: C
|"The options are:
The synthetic results of the measured S (9) in this example are shown in Table CB (6)
Calculate the radius change
Calculate the radius change, that is, solve the measurement equation (cc(o)
). This equation can generally be solved by discrete Fourier transform, matrix adjustment and generalized inverse matrix solution derived from functional analysis. The following takes the generalized inverse matrix solution method as an example to give the calculation formula for the calculation result (
The calculation results are shown in Table
The value of matrix A and the calculation of 4rA4S
③The calculation of A is complex and time-consuming, and should generally be calculated by computer programming. Note: ① In the table, e is the element in the generalized general A. JB/T 5996-1992
Calculate the roundness error
The roundness error is:
Additional explanation:
The method specified in JB/T5996-1992
The roundness error can be calculated by the factory. In this example, when the evaluation reference circle is the least squares square circle Az
This standard is proposed and managed by the Mechanical Standardization Research Institute of the Ministry of Machinery and Electronics Industry. This standard was drafted by the Mechanical Standardization Research Institute of the Ministry of Machinery and Electronics Industry, Jilin University of Technology, and Changchun Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences.
The main drafters of this standard are Chen Yuexiang, Xiao Huai, Gan Yongli, Bai Shufang, and Jin Guangshan. People's Republic of China Mechanical Industry Standard Roundness Measurement Three-point Method and Accuracy Evaluation of Instruments Published and Distributed by Mechanical Science Research Institute Printed by Mechanical Science Research Institute (Beijing Shouti South Road First Edition in June First Printing in June Price 2 Mechanical Industry Standard Service Network:
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