CN114739344A - Roundness error online measurement method and system - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- G—PHYSICS
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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Abstract
The invention provides a roundness error online measurement method and a roundness error online measurement system, which are simple in structure, convenient to operate, simple to install and capable of achieving online measurement. The method comprises the steps that only one displacement sensor is used, and a plurality of measuring points on the circular profile of the workpiece to be measured are measured when the workpiece to be measured rotates for a circle; obtaining corresponding radius measurement values at the measurement points according to the sensor readings at the measurement points and the radius values of the workpiece to be measured; according to a polar coordinate system of a measuring point on a workpiece to be measured, selecting the radial direction of any measuring point in the polar coordinate system as the X direction, establishing a rectangular coordinate system by taking the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measured value of each measuring point; solving the least square circle center of the track formed by all the measuring points according to the rectangular coordinates of each measuring point; and taking the distance from each measuring point to the least square circle center as an actual radius value of each measuring point, and obtaining the roundness error of the workpiece to be measured on line.
Description
Technical Field
The invention relates to the field of cylindrical grinding processing on-line measurement, in particular to a roundness error on-line measurement method and a system.
Background
The roundness error directly affects the fitting accuracy, the revolution accuracy, the vibration, the noise and the like of the parts, thereby reducing the service life thereof. The continuous development of modern industry puts forward higher and higher requirements on the roundness error of a rotary workpiece, so that the improvement of the roundness precision of the workpiece in the machining process has great significance. However, in the prior cylindrical grinding process, the roundness error of the rotary workpiece is mainly ensured by the precision of the machine tool. The profile data of the excircle of the workpiece can not be measured on line in the machining process, and the roundness error can not be compensated.
If the roundness error is measured on line in the machining process, namely the workpiece to be measured takes the machine tool spindle as a rotating shaft, the rotation error of the separation spindle must be considered. The error separation methods commonly used at present include two major types, namely a multipoint method and a multi-step method. The multipoint method is to use a plurality of sensors, distribute the sensors around a measured object according to a certain position, simultaneously acquire data and then process the data. The method has high requirements on the installation angle of the sensor, and simultaneously has the problem of harmonic suppression, and at present, the method has a lot of researches on the aspect. The multi-step method is also called a transposition method, namely, the measured workpiece is respectively measured after rotating for one time or multiple times relative to the measuring head by a set angle, and then the rotation error of the main shaft is separated through data processing. However, the multi-step method requires multiple repositioning, is complicated in operation, cannot realize online measurement, has few measurement points, and cannot fit the circular profile of the workpiece to generate subsequent compensation data. The requirement of the modern industry on the measurement of the roundness error cannot be met.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a roundness error online measurement method and a roundness error online measurement system, which have the advantages of simple system structure, convenience in operation and simplicity in installation and can realize online measurement.
The invention is realized by the following technical scheme:
an on-line measuring method for roundness error comprises,
measuring a plurality of measuring points on the circular profile of the workpiece to be measured when the workpiece to be measured rotates for a circle by using only one displacement sensor;
obtaining corresponding radius measurement values at the measurement points according to the sensor readings at the measurement points and the radius values of the workpiece to be measured;
selecting the radial direction of any measuring point in the polar coordinate system as the X direction according to the polar coordinate system of the measuring point on the workpiece to be measured, establishing a rectangular coordinate system by taking the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measured value of each measuring point;
solving the least square circle center of the track formed by all the measuring points according to the rectangular coordinates of each measuring point;
and taking the distance from each measuring point to the least square circle center as an actual radius value of each measuring point, and obtaining the roundness error of the workpiece to be measured on line.
Optionally, the radius measurement is calculated by the following formula,
mi＝R+ei；
wherein m isiIs the radius measurement value at the measurement point i, R is the radius of the workpiece to be measured, eiIs the reading deviation at the measurement point i.
Optionally, let the sensor index at any point i of measurement be HiDefining the minimum value of the index of all measurement points as Hmin. Defining the reading deviation at point i as ei：
The reading deviation e at the measuring point iiIs calculated by the following formula,
ei＝Hi-Hmin；
wherein HiFor measuring the sensor index at any point i, HminIs the minimum value of the readings of all the measurement points.
Optionally, the rectangular coordinates of the measurement points in the rectangular coordinate system are obtained as follows,
wherein x iskIs the abscissa, y, of the kth measurement pointkIs the ordinate, θ, of the kth measuring pointkAnd theta is the included angle between any two adjacent measuring points.
Optionally, the least square circle center (x) of the track formed by all the measuring pointsc,yc) The following conditions are satisfied,
wherein R iscIs the least square radius, xkIs the abscissa, y, of the kth measurement pointkAnd N is the ordinate of the kth measuring point and the number of measuring points.
Optionally, the roundness error of the workpiece to be measured obtained on line is expressed as follows,
ε＝max{rk}-min{rk}；
wherein ε represents a roundness error, rkIs the actual radius value of the workpiece at the k-th measurement point.
Alternatively, the actual radius value of the workpiece at the k-th measurement point is expressed as follows,
wherein x iskIs the abscissa, y, of the kth measurement pointkIs the ordinate of the kth measuring point, (x)c,yc) And forming the least square circle center coordinates of the tracks of all the measuring points.
An on-line roundness error measuring system comprises,
the displacement sensor is used for measuring a plurality of measuring points on the circular profile of the workpiece to be measured when the workpiece to be measured rotates for one circle;
the calculation module is used for obtaining corresponding radius measurement values of the measurement points according to the sensor readings at the measurement points and the radius values of the workpiece to be measured;
the system comprises a polar coordinate system, a rectangular coordinate system and a measuring point measuring device, wherein the polar coordinate system is used for selecting the radial direction of any measuring point in the polar coordinate system as the X direction according to the polar coordinate system of the measuring point on a workpiece to be measured, the origin of the polar coordinate system is used as the origin to establish the rectangular coordinate system, and the rectangular coordinate of each measuring point in the rectangular coordinate system is obtained according to the corresponding radius measured value of each measuring point;
the system comprises a plurality of measuring points, a plurality of sensors and a plurality of sensors, wherein the plurality of measuring points are used for measuring the distance between the measuring points and the center of a least square circle;
and the method is used for obtaining the roundness error of the workpiece to be measured on line by taking the distance from each measuring point to the least square circle center as the actual radius value of each measuring point.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the method, the actual measurement process is analyzed to obtain the measured value after the spindle rotation error is introduced, the measured value obtained by rotating the workpiece for one circle is represented in polar coordinates, a circle with the unchanged radius of the formed graph is found, and the spindle rotation error is separated only by separating the position of the circle from the origin of the coordinates due to the influence caused by the spindle rotation error, so that the spindle rotation error can be separated by solving the least square circle center of the track of the measured point; the main shaft rotation error can be separated by only using one displacement sensor, the problem that the multi-step method cannot carry out online measurement is solved, and the problems that the multi-point method needs accurate installation angles and harmonic suppression are also avoided. Therefore, the contour data of the outer circle of the workpiece can be measured in the machining process, then X-C linkage machining is carried out to compensate the roundness error, and great help is provided for improving the machining precision of the roundness of the workpiece.
Drawings
FIG. 1 is a flow chart of a method as described in an example of the invention;
FIG. 2 is an analysis diagram of the measurement process in an example of the present invention;
FIG. 3 is a polar plot of the measurements described in the examples of the present invention;
FIG. 4 is a graph showing the radius measurement m of each measuring point based on the sensor readings in the present exampleiA schematic diagram;
FIG. 5 is a schematic diagram of the rectangular coordinate system established according to the measurement points in the embodiment of the present invention;
in the figure: 1. a workpiece to be tested; 2. and a displacement sensor measuring head.
Detailed Description
The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.
The invention discloses a roundness error online measurement method based on a single-point method. The method is characterized in that the method comprises the following steps of calculating the rotation error of a measuring point, calculating the rotation error of the measuring point, and calculating the least square circle center of the measuring point. And recalculating the radius value of each measuring point based on the solved least square circle center to obtain the radius deviation value of each measuring point, thereby evaluating the roundness of the workpiece and fitting the outer edge profile of the workpiece.
The invention discloses an online roundness error measuring method, which comprises the following steps,
s0, only using one displacement sensor, measuring a plurality of measuring points on the circular outline of the workpiece to be measured when the workpiece to be measured rotates for a circle;
s1, obtaining corresponding radius measurement values at the measurement points according to the sensor readings at the measurement points and the radius values of the workpiece to be measured;
specifically, the workpiece rotates for one circle to measure N points, and the index of a sensor at any measuring point i is set to be HiThe minimum value of the readings of all the measurement points is HminThereby obtaining the registration deviation e of each measuring pointiEstimating a workpiece radius value R based on the previous procedure; based on R and eiObtaining radius measured value m at each measuring pointi；
Wherein the measured workpiece radius R is used in place of the reference radius R defined in the present inventionbIt is based on the conclusion from geometric analysis: the degree of deviation of the actual circle center of the workpiece from the theoretical rotation center caused by the rotation error of the main shaft is irrelevant to the radius of the workpiece.
S2, according to a polar coordinate system of a measuring point on a workpiece to be measured, selecting the radial direction of any measuring point in the polar coordinate system as the X direction, establishing a rectangular coordinate system with the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measurement value of each measuring point;
wherein, the polar diameter direction of any measuring point in the polar coordinate system is selected as the X direction, the origin of the polar coordinate system is taken as the origin to be taken as a rectangular coordinate system, and the coordinate (X) of each measuring point in the rectangular coordinate system is obtainedk,yk)；
S3, solving the least square circle center of the track formed by all measuring points according to the rectangular coordinates of each measuring point;
wherein, the least square circle center (x) of the track formed by N measuring points is solved based on the coordinates of each measuring pointc,yc) Thereby realizing the purpose of separating the rotation error of the main shaft; the actual measurement process is analyzed to obtain a measured value after the main shaft rotation error is introduced, the measured value obtained by rotating the workpiece for one circle is represented in polar coordinates, a circle with the unchanged radius of the formed graph is found, and the influence caused by the main shaft rotation error only enables the position of the circle to be separated from the origin of coordinates. It follows that: and solving the least square circle center of the measuring point track to separate the main shaft rotation error.
S4, taking the distance from each measuring point to the least square circle center as the actual radius value of each measuring point, and obtaining the roundness error of the workpiece to be measured on line.
Wherein the least square circle center (x) is obtained based on the solutionc,yc) And taking the distance from each measuring point to the center of the least square circle as an actual radius value of each measuring point, then calculating the radius deviation of each measuring point, evaluating the roundness error of the workpiece, and fitting the circular profile of the workpiece.
Specifically, in step S1, the radius measurement value m at the measurement point is solvediComprises the following steps:
(1-1) As shown in FIG. 2, an absolute coordinate system XOY is established. Wherein the point O is the ideal rotation center of the main shaft. Assuming that the main shaft is in pure radial run-out and pure angular swing, the instantaneous rotation center O of the main shaft is adjusted1The motion of (a) is decomposed into simple harmonic vibrations in the X and Y directions. Let O be1The simple harmonic motion in the X direction is:
in formula 1), AxIs O1The amplitude of the vibration in the X-direction,
for the angle of rotation of the workpiece relative to the initial position
At the initial position of the workpiece, at this time O1At the rightmost end);
(1-2) rotating the workpiece at a constant speed at an angular speed omega in a counterclockwise direction. When the workpiece rotates to any angle
When the workpiece is in contact with the sensor measuring head, the point A is set. Let m be the radius measurement value after the spindle rotation error is introduced, expressed as the distance between the theoretical rotation center O and the measurement point, so that the radius measurement value m at point AA：
because the rotation error of the main shaft is a tiny amount relative to the radius of the workpiece, the following can be directly obtained:
this gives:
(1-3) rotation angle of workpiece
The measured value m of the radius is used as the polar angle and the measured value after one rotation of the workpiece is expressed on the polar coordinates, as shown in fig. 3. It can be seen that the measured values obtained by one rotation of the workpiece form a pattern on polar coordinates which is still a circle with a radius R. The effect of spindle rotation error is simply to move the position of the circle away from the origin of coordinates.
From which two conclusions can be drawn.
Conclusion one: in the actual measurement process of the workpiece, although the spindle rotation error cannot be directly separated from the measurement result, the representation of the measurement value in the polar coordinate system can still accurately depict the actual shape of the circular contour of the workpiece. Then, it is sufficient if the least-squares center (i.e., O in FIG. 3) of the profile can be found based on the shape indicated by the measurement value1) The distance between each measuring point and the circle center of the least square can be regarded as the actual radius of the measuring point, the radius deviation of each point is calculated according to the calculated actual radius, then the roundness error can be evaluated according to the radius deviation of each point, and the circular contour of the workpiece can be obtained by a curve fitting method.
And a second conclusion: actual circle center O of workpiece caused by rotation error of main shaft1Deviation from polar origin O is AxIndependent of the radius value R of the workpiece itself.
(1-4) in actual measurement, the sensor can only measure a limited number of measuring points on the circular profile. If the workpiece rotates for a circle at a constant speed, the number of points measured by the sensor is N. Let the radius measurement at the ith measurement point be miDefining the smallest measurement value as the reference radius RbAs shown in fig. 4. Apparent reference radius RbIs unknown, but results two are obtained from steps (1-3): the degree of the deviation of the actual circle center of the workpiece from the theoretical rotation center caused by the rotation error of the main shaft is irrelevant to the radius of the workpiece. Therefore, before the roundness is measured, the radius value R can be estimated according to the previous procedure, and then R is used for replacing RbThe solution of the least square circle center is not influenced;
(1-5) let the sensor index at any point i of the measurement be HiDefinition ofThe minimum value of the index with the measuring point is Hmin. Defining the reading deviation at point i as ei：
ei＝Hi-HminThis is formula 6);
thus the measured value m of any point iiCan be expressed as:
mi＝Rb+ei＝R+eithis is formula 7);
as shown in fig. 4;
in step S2, a rectangular coordinate system is established to represent each measurement point position (x)k,yk) Comprises the following steps:
(2-1) since it is unknown which measuring point corresponds to which measuring point in the actual measuring process
The initial position of the time, or a point at which the initial position is likely not measured at all. Therefore, when a coordinate system is established based on actual measurement data, a measurement point can be selected at will, and a rectangular coordinate system is established by taking the direction of the polar diameter as an X axis. As shown in fig. 5.
(2-2) let the measurement point that intersects the positive half axis of the X-axis be the 0 th measurement point, so for the kth measurement point, its coordinates are:
in the formula 9), the reaction mixture is,
θkk θ this is formula 9)
In the formula 9), θ is an included angle between any two adjacent measuring points, and includes:
so far, each point capable of describing the actual circular contour of the workpiece is represented in a rectangular coordinate system, and preparation is made for the next work of calculating the least square circle center of the contour.
In step S3, the least squares circle center is calculated as follows,
setting the least square circle of the workpiece circle profile as:
wherein the least squares circle center is (x)c,yc) Least square radius of Rc
The actual radius at any measuring point i can be obtained based on the least square circle center:
the actual radius value r at point iiAnd least square radius RcThe deviation of (a) is defined as:
δi＝ri-Rc
the objective function of the least squares method is then:
i.e. the least square circle center (x)c,yc) Should make sure that
wherein R iscIs the least square radius, xkIs the abscissa, y, of the kth measurement pointkAnd N is the ordinate of the kth measuring point and the number of measuring points.
In step S4, the actual radius value at each measurement point is solved, and the following steps are included to evaluate the roundness error of the workpiece:
(4-1) actual radius value at each measurement point:
formula 11), rkThe actual radius value of the workpiece at the k-th measuring point;
the roundness error is the maximum actual radius minus the minimum actual radius:
ε＝max{rk}-min{rkthis is formula 12).
The invention also discloses a roundness error on-line measuring system, which comprises,
the displacement sensor is used for measuring a plurality of measuring points on the circular profile of the workpiece to be measured when the workpiece to be measured rotates for one circle;
the calculation module is used for obtaining corresponding radius measurement values at the measuring points according to the sensor readings at the measuring points and the radius values of the workpiece to be measured;
the system comprises a polar coordinate system, a rectangular coordinate system and a measuring point measuring device, wherein the polar coordinate system is used for selecting the polar diameter direction of any measuring point in the polar coordinate system as the X direction according to the polar coordinate system of the measuring point on a workpiece to be measured, establishing the rectangular coordinate system by taking the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measuring value of each measuring point;
the system is used for solving the least square circle center of the track formed by all the measuring points according to the rectangular coordinates of the measuring points;
and the method is used for obtaining the roundness error of the workpiece to be measured on line by taking the distance from each measuring point to the least square circle center as the actual radius value of each measuring point.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method or system. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the computing modules of the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (8)
1. An on-line roundness error measuring method is characterized by comprising the following steps,
measuring a plurality of measuring points on the circular profile of the workpiece to be measured when the workpiece to be measured rotates for a circle by using only one displacement sensor;
obtaining corresponding radius measurement values at the measurement points according to the sensor readings at the measurement points and the radius values of the workpiece to be measured;
selecting the radial direction of any measuring point in the polar coordinate system as the X direction according to the polar coordinate system of the measuring point on the workpiece to be measured, establishing a rectangular coordinate system by taking the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measured value of each measuring point;
solving the least square circle center of the track formed by all the measuring points according to the rectangular coordinates of each measuring point;
and taking the distance from each measuring point to the least square circle center as an actual radius value of each measuring point, and obtaining the roundness error of the workpiece to be measured on line.
2. A roundness error on-line measuring method according to claim 1, wherein said radius measurement value is calculated by the following formula,
mi＝R+ei；
wherein m isiIs the radius measurement value at the measurement point i, R is the radius of the workpiece to be measured, eiIs the reading deviation at the measurement point i.
3. The on-line roundness error measuring method according to claim 2, wherein the sensor index at any point i of measurement is HiDefining the minimum value of the index of all measurement points as Hmin(ii) a Defining the reading deviation at point i as ei：
Said measurement beingIndex deviation e at point iiIs calculated by the following formula,
ei＝Hi-Hmin；
wherein HiFor measuring the sensor index at any point i, HminIs the minimum value of the readings of all the measurement points.
4. An on-line roundness error measuring method according to claim 1, wherein the rectangular coordinates of each measurement point in the rectangular coordinate system are obtained as follows,
wherein x iskIs the abscissa, y, of the kth measurement pointkIs the ordinate, θ, of the kth measuring pointkAnd theta is the included angle between any two adjacent measuring points.
5. A roundness error on-line measuring method according to claim 4, wherein the least square circle center (x) of the locus formed by all the measuring pointsc，yc) The following conditions are satisfied,
wherein R iscIs the least square radius, xkIs the abscissa, y, of the kth measurement pointkAnd N is the ordinate of the kth measuring point and the number of measuring points.
6. The on-line roundness error measuring method according to claim 1, wherein the roundness error of the workpiece to be measured obtained on-line is expressed as follows,
ε＝max{rk}-min{rk}；
wherein ε represents a roundness error, rkAt the k-th measurement pointActual radius value of the workpiece.
7. A roundness error on-line measuring method according to claim 6, wherein the actual radius value of the workpiece at the k-th measuring point is expressed as follows,
wherein x iskIs the abscissa, y, of the kth measurement pointkIs the ordinate of the kth measuring point, (x)c，yc) And forming the least square circle center coordinates of the tracks of all the measuring points.
8. An on-line roundness error measuring system is characterized by comprising,
the displacement sensor is used for measuring a plurality of measuring points on the circular profile of the workpiece to be measured when the workpiece to be measured rotates for one circle;
the calculation module is used for obtaining corresponding radius measurement values at the measuring points according to the sensor readings at the measuring points and the radius values of the workpiece to be measured;
the system comprises a polar coordinate system, a rectangular coordinate system and a measuring point measuring device, wherein the polar coordinate system is used for selecting the polar diameter direction of any measuring point in the polar coordinate system as the X direction according to the polar coordinate system of the measuring point on a workpiece to be measured, establishing the rectangular coordinate system by taking the origin of the polar coordinate system as the origin, and obtaining the rectangular coordinate of each measuring point in the rectangular coordinate system according to the corresponding radius measuring value of each measuring point;
the system comprises a plurality of measuring points, a plurality of sensors and a plurality of sensors, wherein the plurality of measuring points are used for measuring the distance between the measuring points and the center of a least square circle;
and the method is used for obtaining the roundness error of the workpiece to be measured on line by taking the distance from each measuring point to the least square circle center as the actual radius value of each measuring point.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115393972A (en) * | 2022-08-30 | 2022-11-25 | 四川航天烽火伺服控制技术有限公司 | Method for detecting normal section deviation of roller thread |
| CN115752344A (en) * | 2022-11-15 | 2023-03-07 | 上海羿弓精密科技有限公司 | Method for detecting phase included angle of crankshaft of RV reducer |
| CN117308855A (en) * | 2023-11-15 | 2023-12-29 | 季华实验室 | Rotating mechanism, measuring device, installation method, data measuring and processing method |
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| CN117308855A (en) * | 2023-11-15 | 2023-12-29 | 季华实验室 | Rotating mechanism, measuring device, installation method, data measuring and processing method |
| CN117308855B (en) * | 2023-11-15 | 2024-04-05 | 季华实验室 | Rotating mechanism, measuring device, installation method, data measuring and processing method |
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