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CN109141225A - Shafting five, six degree of freedom error measurement method and measuring system based on Circular gratings - Google Patents

Shafting five, six degree of freedom error measurement method and measuring system based on Circular gratings Download PDF

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Publication number
CN109141225A
CN109141225A CN201710464459.0A CN201710464459A CN109141225A CN 109141225 A CN109141225 A CN 109141225A CN 201710464459 A CN201710464459 A CN 201710464459A CN 109141225 A CN109141225 A CN 109141225A
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measured
plane
shaft
displacement
measurement
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CN109141225B (en
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王笑
王笑一
张书涛
张波
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Henan University of Science and Technology
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Henan University of Science and Technology
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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
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The present invention relates to a kind of shafting five, six degree of freedom error measurement method and measuring system based on Circular gratings.More than two measurement planes are arranged in interval on the axial position of the measured axis of shafting, Circular gratings are set at the position that detection measured axis corresponds to each measurement plane, and reading head corresponding with Circular gratings is set in each measurement plane, if axis moves, measured axis tangential displacement when measuring Plane Rotation will change, to generate the in-plane displancement in detection plane of measured axis, due to the opposite variable that the displacement is relative initial position, the influence of the circularity of measured axis itself not will receive.

Description

Shafting five, six degree of freedom error measurement method and measuring system based on Circular gratings
Technical field
The present invention relates to a kind of shafting five, six degree of freedom error measurement method and measuring system based on Circular gratings.
Background technique
Precise rotary shaft, which ties up in many precision machineries, application, and the cutter measured axis or workpiece such as precision machine tool are tested Axis, the turntable measured axis of gear measuring center, gear integrated error tester worm screw measured axis and gear measured axis, roundness measuring equipment Workpiece measured axis etc. belong to precision rotating shafting.
Ideal shafting does not have error, and measured axis is in addition to revolution without the movement of other freedom degrees at work.But it is practical Shafting have error, in revolution, along each freedom degree error motion can all occur for measured axis.It is tested in precision rotating shafting Axis is the rigid space motion of six degree of freedom relative to movement made by fixed reference in revolution, can behave as measured axis Run-out error, axial float error and the heeling error in two orthogonal shaft sections.The movement of rotary axis system Error directly affects the detection accuracy of machine finish and instrument, therefore how accurately to measure axial system error, improves shafting Rotating accuracy is always the research emphasis being machined with metrology and measurement field.
Existing axial system error measurement method is intended to be arranged in shafting high-precision standard ball as tested surface, using electricity The radial linear movement pick-up of sense formula, condenser type or optical reflection type carries out the measurement of axial system error.Therefore it is tested datum level Form error can be mixed into the measurement result of axial system error, the separation of rotating error of axis and measured piece itself error with axis movement Key difficulties as axial system error measurement.Axial system error measurement in main error separating method have multipoint method, reverse method and Multistep processes.It is measured axis revolution that wherein reverse method and multistep processes, which can efficiently separate measured axis turn error and the premise of deviation from circular from, Repeatability is good for error；For non-repeatability axial system error, traditionally only can just be measured using multipoint method.In multiple spot The line-of-sight course being most widely used in method measures measured axis using three linear movement pick-ups, can be one to measured axis The Radial mixing in section is separated with deviation from circular from.The turn error for measuring measured axis six-freedom degree needs to arrange More sensors are just able to achieve.The sensor that existing multipoint method measuring principle uses is mainly inductance type or condenser type principle Linear movement pick-up and gradient sensor based on reflective optic measuring principle.These sensors exist more serious It is non-linear, when drift, temperature drift the problems such as, need calibrate and demarcate after could use, progressive is needed when number of sensors is more Can matching, the difficulty of system debug is larger, thus it is most be applied to researching and analysing under laboratory condition, seldom prolonged application in Production scene.In addition, existing measured axis turn error test method, which usually will install standard ball in shaft end, is used as tested benchmark, Arrange that multiple linear movement pick-ups constitute measuring system around it again, the levels of precision of linear movement pick-up installation site is direct The precision of measurement result is influenced, therefore structure is complicated for measuring system, test condition is required high, it is difficult to be integrated at low cost The on-line measurement and compensation of rotating error of axis are realized in the instrument product of volume production, it most importantly can be straight by the deviation from circular from of side Connect the measurement result for influencing product, low measurement accuracy.
Summary of the invention
The purpose of the present invention is to provide a kind of shafting measuring systems that measurement accuracy is high；The present invention also provides one kind simultaneously Shafting five degree of freedom error measurement method based on Circular gratings, the shafting six degree of freedom error measurement method based on Circular gratings.
To achieve the above object, the shafting five degree of freedom error measurement method of the invention based on Circular gratings uses following skill Art scheme:
Technical solution 1: the shafting five degree of freedom error measurement method based on Circular gratings, on the axial position of measured axis between Every more than two measurement planes are arranged, are corresponded in detection measured axis and Circular gratings are set at each position for measuring plane, and Reading head corresponding with Circular gratings is set in each measurement plane and passes through reading head and corresponding Circular gratings when measured axis rotates Cooperation detection measured axis tangential displacement to obtaining displacement and rotational angle of the measured axis at the measurement plane, according to Measured axis calculates the beat amount of measured axis in the displacement of each measurement plane, in conjunction with the rotational angle and beat amount of measured axis Be calculated measured axis rotation when except measured axis axial float displacement in addition to five freedom degrees kinematic parameter rule to Obtain the kinematic error of measured axis.
Technical solution 2, on the basis of technical solution 1: there are two the measurement planes, on one of two measurement planes The quantity of reading head be m, quantity of the reading head in another measurement plane is n, and m >=2, n >=2, m+n >=5.
Technical solution 3, on the basis of technical solution 2: setting two measurement planes is respectively plane P1 and plane P2, flat Face P1 is with theoretical centre of gyration O1Coordinate system X is established for origin1O1Y1, with theoretical centre of gyration O on plane P22For origin foundation Coordinate system X2O2Y2, O1O2Wire definition be Z axis, if the initial reading of each reading head be 0, the side of rotating counterclockwise about the z axis To for positive direction, H1i(t) displacement of Circular gratings tangential direction is indicated, then measured axis is in X1O1Y1The displacement of coordinate plane and by Survey the rotation angle of axis are as follows:
In formula, RO, Circular gratings exradius；The rotation angle of θ (t), Circular gratings；
When the reading head on plane P2 is evenly distributed in a circumferential direction, measured axis is around O2The rotation angle θ of point2(t) are as follows:
When the reading head on plane P2 is not in a circumferential direction uniformly distributed, then enable:
θ2(t)=θ1(t),
Then measured axis is in X2O2Y2The displacement of coordinate plane are as follows:
Displacement coordinate Tx (t), Ty (t) in the six degree of freedom coordinate of measured axis spatial movement and around initial coordinate axis X, Y, the rotational coordinates Rx (t) of Z, Ry (t), Rz (t) are as follows:
L is the distance between plane P1 and P2 in formula.
Technical solution 4, on the basis of technical solution 3: as the O found out1x(t) and O1y(t) absolute value is greater than the set value When, the compensation of nonlinear effect is carried out to calculated result, that is,
Nlc in formula1xAnd nlc1yIt is in advance in laboratory conditions by experiment by the non-of the higher instrument acquisition of precision Linear compensation function.
Technical solution 5, on the basis of technical solution 4: the setting value is 100 microns.
Shafting six degree of freedom error measurement method based on Circular gratings of the invention adopts the following technical scheme that
Technical solution 1: the shafting six degree of freedom error measurement method based on Circular gratings, on the axial position of measured axis between Every more than two measurement planes are arranged, are corresponded in detection measured axis and Circular gratings are set at each position for measuring plane, and Reading head corresponding with Circular gratings is set in each measurement plane and passes through reading head and corresponding Circular gratings when measured axis rotates Cooperation detection measured axis tangential displacement to obtaining displacement and rotational angle of the measured axis at the measurement plane, simultaneously The displacement for detecting measured axis axial float calculates the beat amount of measured axis according to measured axis in the displacement of each measurement plane, Rotational angle, axial float in conjunction with measured axis are displaced and axial direction when measured axis rotates except measured axis is calculated in beat amount The kinematic parameter rule of six-freedom degree other than play displacement is to obtain the kinematic error of measured axis.
Technical solution 2, on the basis of technical solution 1: there are two the measurement planes, on one of two measurement planes The quantity of reading head be m, quantity of the reading head in another measurement plane is n, and m >=2, n >=2, m+n >=5.
Technical solution 3, on the basis of technical solution 2: setting two measurement planes is respectively plane P1 and plane P2, flat Face P1 establishes coordinate system X1O1Y1 using theoretical centre of gyration O1 as origin, using theoretical centre of gyration O2 as origin on plane P2 Establish coordinate system X2O2Y2, the wire definition of O1O2 is Z axis, if the initial reading of each reading head is 0, about the z axis counterclockwise Rotation direction is positive direction, and H1i (t) indicates the displacement of Circular gratings tangential direction, then measured axis is in X1O1Y1 coordinate plane The rotation angle of displacement and measured axis are as follows:
In formula, RO, Circular gratings exradius；The rotation angle of θ (t), Circular gratings；
When the reading head on plane P2 is evenly distributed in a circumferential direction, measured axis is around O2The rotation angle θ of point2(t) are as follows:
When the reading head on plane P2 is not in a circumferential direction uniformly distributed, then enable:
θ2(t)=θ1(t),
Then measured axis is in X2O2Y2The displacement of coordinate plane are as follows:
The displacement of the play of measured axis axial direction is Oz(t)；
Displacement coordinate Tx (t), Ty (t), Tz (t) in the six degree of freedom coordinate of measured axis spatial movement and around initial coordinate Rotational coordinates Rx (t), Ry (t), the Rz (t) of axis X, Y, Z are as follows:
L is the distance between plane P1 and P2 in formula.
Technical solution 4, on the basis of technical solution 3: as the O found out1x(t) and O1y(t) absolute value is greater than the set value When, the compensation of nonlinear effect is carried out to calculated result, that is,
Nlc in formula1xAnd nlc1yIt is in advance in laboratory conditions by experiment by the non-of the higher instrument acquisition of precision Linear compensation function.
Technical solution 5, on the basis of technical solution 4: the setting value is 100 microns.
Shafting measuring system of the invention adopts the following technical scheme that
Technical solution 1: the shafting measurement error system based on Circular gratings, including multi-point displacement sensor subsystem, data Acquisition subsystem and Data Analysis Services subsystem, the multi-point displacement sensor subsystem include at least two in measured axis Axial direction on it is spaced for detecting measured axis in the radial displacement of corresponding position and the rotational angle of measured axis Displacement sensor component, the displacement sensor component include the Circular gratings for being mounted on measured axis and rotating with measured axis Disk and the reading head being correspondingly arranged with the periphery of Circular gratings disk, the data acquisition subsystem and the multi-point displacement sensor Subsystem and Data Analysis Services subsystem are conductively connected that the data of multi-point displacement sensor subsystem are acquired and passed Be defeated by the Data Analysis Services subsystem, thus make the Data Analysis Services subsystem according to measured axis at different locations Radial displacement calculate the beat amount of measured axis, and combine the rotational angle of measured axis when measured axis rotation is calculated except axis To play displacement other than other five freedom degrees kinematic parameter rule to obtain the kinematic error of measured axis.
Technical solution 2, on the basis of technical solution 1: the multi-point displacement sensor subsystem further includes for detecting The shaft position sensor of the axis play displacement of measured axis.
Technical solution 4, on the basis of technical solution 1 or 2: there are two the displacement sensor components, and the displacement passes The Circular gratings disk of sensor component is between the upper and lower m every the quantity of a corresponding reading head in setting, two Circular gratings, another is right The reading head quantity answered is n, and m >=2, n >=2, m+n >=5.
The beneficial effects of the present invention are: the shafting six degree of freedom error measurement method of the invention based on Circular gratings is in axis More than two measurement planes are arranged in interval on the axial position of the measured axis of system, correspond to each measurement plane in detection measured axis Position at Circular gratings are set, and corresponding with Circular gratings reading head is set in each measurement plane, it is logical when measured axis rotation Reading head is crossed with the tangential displacement of the cooperation detection measured axis of corresponding Circular gratings to obtain measured axis at the measurement plane Displacement and rotational angle, while the displacement of measured axis axial float is detected, according to measured axis in the position of each measurement plane Move the beat amount of measured axis of calculating, rotational angle, the axial float in conjunction with measured axis are displaced and beat amount be calculated by The kinematic parameter rule of six-freedom degree when surveying axis rotation in addition to the displacement of the axial float of measured axis is to obtain measured axis Kinematic error, measured axis rotation when, if axis moves, tangential displacement will when measuring Plane Rotation for measured axis It changes, so that the in-plane displancement in detection plane of measured axis is generated, due to the phase that the displacement is relative initial position To variable, the influence of the circularity of measured axis itself not will receive.
Detailed description of the invention
Fig. 1 is the principle signal of the embodiment of the shafting six degree of freedom error measurement method of the invention based on Circular gratings Figure；
Fig. 2 has schematic illustration when 9 sensors for the multi-point displacement sensor subsystem in Fig. 1；
Fig. 3 is the stereoscopic schematic diagram of Fig. 2；
Fig. 4 has stereoscopic schematic diagram when 6 sensors for the multi-point displacement sensor subsystem in Fig. 1；
Fig. 5 is the plane P1's in the embodiment of the shafting six degree of freedom error measurement method of the invention based on Circular gratings Measurement of in-plane motion schematic diagram；
Fig. 6 is the plane P2's in the embodiment of the shafting six degree of freedom error measurement method of the invention based on Circular gratings Measurement of in-plane motion schematic diagram；
Fig. 7 is the spatial movement measuring principle of the shafting six degree of freedom error measurement method of the invention based on Circular gratings Figure；
In attached drawing: 1, reading head；2, shaft position sensor；3, the first grating disc；4, the second grating disc.
Specific embodiment
Embodiments of the present invention are described further with reference to the accompanying drawing.
The specific embodiment of shafting six degree of freedom error measurement method based on Circular gratings of the invention, such as Fig. 1 to Fig. 7 Shown, the measuring system is using the Circular gratings be used widely in industry spot as main sensors part, with Circular gratings Reading head is as tangential displacement sensor, it is established that the strong axial system error of high-precision, high reliability, environmental suitability measures system System realizes the measurement of shaft error.The measurement method is analyzed and is handled by the reading to each sensor, and axis is obtained It is the coordinate of six-freedom motion.
As shown in Figure 1, the measuring system consists of three parts: (1) multi-point displacement sensor subsystem, (2) data are adopted Subsystem, (3) Data Analysis Services subsystem.
Wherein, multi-point displacement sensor subsystem consists of three parts: (1) in the position of the axially different position installation of measured axis Displacement sensor component, the displacement sensor component include the two Circular gratings disks installed at the different location of measured axis；(2) exist The multiple reading heads arranged around Circular gratings disk；(3) linear movement pick-up being arranged in the end of axis.First grating disc 1 and The distance between two planes locating for two grating discs 2 should structure allow in the range of select as far as possible it is larger, with improve measurement essence Degree.First grating disc, 1 surrounding arranges m reading head, and 2 surrounding of the second grating disc arranges n reading head, and the number of reading head meets M >=2, n >=2, m+n >=5.Reading head around Circular gratings disk can be evenly distributed in the circumferential direction, can also uneven cloth It sets.One or more can be set in the linear movement pick-up of axis direction setting, can be set in one end of axis, can also divide The both ends of axis are not set.The number for the grating reading head arranged in Fig. 3 is more, shares eight, can there is more redundant digit According to for corroborating each other, examining and determine certainly for measuring system is realized；The grating reading head number arranged in Fig. 4 is less, and cost is relatively low.It is real When the application present invention of border, the number and arrangement mode of reading head can be with the differences in Fig. 3, Fig. 4, but measuring principle used is The same；Interval on the axial position of measured axis can also be set, multiple Circular gratings are set to form multiple measurement planes.
Data acquisition subsystem by each reading head, the interface circuit of sensor, Data acquisition and storage hardware circuit and Relevant software composition, effect is the reading for synchronously recording each reading head, the Data Analysis Services subsystem after being Data are provided.Data acquisition subsystem can be realized with motion control card, the counter card of finished product, can also develop dedicated be based on The data acquisition device of MCU, DSP, FPGA.
The measurement of each reading head, sensor that Data Analysis Services subsystem obtains data acquisition subsystem and records Data are analyzed and are calculated, and the six-freedom motion coordinate data of tested measured axis is therefrom obtained.Data Analysis Services subsystem System mainly completes its function by software, and related software may operate at embedding assembly machine platform, also may operate in and be based on The industrial computer system of PC also may operate on cloud computing platform or other computer platforms.
The magnitude very little of measured axis error when rotated in precision bearing system, two of plane locating for two Circular gratings disks are mutually The circular runout of vertical direction is usually no more than 100 microns, and the distance between two planes are far longer than 100 microns, therefore The six degree of freedom rigid space motion of measured axis can be approximately decomposed into mutually independent Rigid Planar a little in two planes Movement and along measured axis axis direction translation a little.Likewise, since error magnitude is very when rotated for precision bearing system measured axis Small, the change in location between Circular gratings disk and reading head is seldom, therefore reading head can be counted normally in the measurements.
The measurement method, which refers to, analyzes and calculates measured axis from the measurement result that each reading head, sensor obtain It is the method for the six-freedom motion coordinate data of measured axis.Total process is first calculated separately in two Circular gratings disk planes The coordinate of the rigid body three degree of freedom of plane motion a little, calculating rigid body then in conjunction with shaft position sensor, space is transported a little The coordinate of dynamic six-freedom degree.
Measurement method comprises the steps of:
(1) coordinate system is established.
As shown in Fig. 5, Fig. 6 and Fig. 7, the label of plane locating for the first grating disc 1 is plane locating for the second grating disc 2 Label be.Coordinate system X is established on plane P11O1Y1, point O1For the theoretical centre of gyration.Coordinate is established on plane P2 It is X2O2Y2, point O2For the theoretical centre of gyration.Reference axis X1With X2In parallel, Y1With Y2In parallel. O1O2Line and reference axis X1,Y1, X2,Y2It is all vertical, it is defined as Z axis.The error of the measured axis centre of gyration line of this method measurement is relative value, therefore point O1And point O2It does not need highly precisely to determine its position.It can be first considered that initial position locating for axis is exactly O when starting measurement1、 O2Point, then again O after being measured1、O2Point position correction to survey orbit of shaft center Least Square Circle the center point, The purpose for the arrangement is that convenient show measurement result to graphically.
(2) coordinate of the three degree of freedom of plane motion a little of Circular gratings disk is calculated in plane P1.
As shown in figure 4, i-th of reading head H in note plane P11iLocating azimuth is θ1i, i=1,2 ..., m.Azimuth With X1Axis forward direction be 0 °, using around the direction that center O rotates counterclockwise as positive direction.If the initial reading of each reading head is 0, It is H in the reading of i-th of reading head of moment t1i(t)。H1i(t) displacement of Circular gratings tangential direction is indicated, with length evaluation. Then in t moment, rigid body is with basic point coordinate O1(O1x(t),O1y(t)) rotation angle θ of translation and rigid body around O point1(t) it is represented by
In formula, ROFor the exradius of Circular gratings；θ (t) is the rotation angle of Circular gratings namely the rotation angle of measured axis Degree.
As the O found out1x(t) and O1y(t) it when absolute value is greater than the set value, needs to carry out non-linear effect to calculated result The compensation answered, the setting value are 100 microns, certainly can also be other numerical value, i.e.,
Nonlinear compensation function nlc in formula1xAnd nlc1yIt is higher by precision by testing in laboratory conditions in advance Instrument obtain.For general precision bearing system, due to O1x(t) and O1y(t) absolute value very little (being no more than 100 microns), Can without nonlinear compensation, even
(3) the three degree of freedom coordinate of the plane motion a little of Circular gratings disk is calculated in plane P2.
As shown in fig. 6, i-th of reading head H in note plane P22iLocating azimuth is θ2i, i=1,2 ..., n.Azimuth With X2Axis forward direction is 0 °, around center O2The direction rotated counterclockwise is positive direction.
It is H in the reading of i-th of reading head of moment t if the initial reading of each reading head is 02i(t)。H2i(t) table Show the displacement of Circular gratings tangential direction, with length evaluation.
Rigid body is calculated first around O2The rotation angle θ of point2(t).When n reading head in plane P2 around the second grating disc 2 exists When circumferencial direction is uniformly distributed, have
In formula, ROFor the exradius of Circular gratings；θ2It (t) is the rotation angle of Circular gratings 2.
When n reading head is not that circumferencial direction is uniformly distributed, then enable
θ2(t)=θ1(t)
Namely rotation angle is not calculated by plane P2, and directly adopt rotation of the rotation angle of plane P1 as plane P2 Gyration.The purpose for the arrangement is that in some cases, in order to save cost, only can arrange two in sensitive direction in plane P2 An a or even reading head.
Rigid body is with basic point coordinate O2(O2x(t),O2y(t)) translation is represented by
As the O found out2x(t) and O2y(t) it when absolute value is greater than the set value, needs to carry out nonlinear effect to calculated result Compensation, the setting value be 100 microns, certainly, setting value may be other numerical value, i.e.,
Nonlinear compensation function nlc in formula2xAnd nlc2yIt is to be obtained in advance by experiment.For general accurate axis System, due to O2x(t) and O2y(t) absolute value very little (be no more than 100 microns), can without nonlinear compensation, even
(4) measured axis axially translation coordinate is calculated.
As shown in Figure 3 and Figure 4, axially translation coordinate can be calculated measured axis by the reading of axial linear movement pick-up, Using the arithmetic mean of instantaneous value of each axial linear movement pick-up as measured axis axial direction translation coordinate value, it is denoted as Oz(t)。
(5) the six degree of freedom coordinate of measured axis rigid space plane motion is calculated.
As shown in fig. 7, selected measured axis on plane P1 with O1The point of coincidence is the basic point of rigid space motion.Work as rotation When to moment t, due to the influence of axial system error, O1Point moves to O1' at.The six degree of freedom coordinate of rigid space motion is with base Translation coordinate Tx (t), Ty (t), Tz (t) and the rotational coordinates Rx (t), Ry (t), Rz (t) around initial coordinate axis X, Y, Z put. This six coordinates can be calculated by following formula:
In formula, L is the distance between plane P1 and P2.
According to the fortune of the parameter of above-mentioned six coordinates you can get it compared with the theory movement parameter of standard axle measured axis Dynamic error, in rotation, if axis moves, measured axis tangential displacement when measuring Plane Rotation will occur measured axis Variation, so that the in-plane displancement in detection plane of measured axis is generated, since the displacement is that the opposite of relative initial position becomes Amount, not will receive the influence of the circularity of measured axis itself.
The embodiment of shafting five degree of freedom error measurement method based on Circular gratings of the invention, it is described based on Circular gratings The embodiment of shafting five degree of freedom error measurement method and the above-mentioned shafting six degree of freedom error measurement method based on Circular gratings The difference is that being not provided with shaft position sensor, the survey of other five freedom degrees in addition to axial float is displaced only is carried out Amount.
The embodiment of shafting measuring system of the invention, for example above-mentioned axis based on Circular gratings of axial system error measuring system It is the measuring system in the embodiment of six degree of freedom error measurement method, repeats no more.

Claims (10)

1.基于圆光栅的轴系五自由度误差测量方法，其特征在于：在被测轴的轴向位置上间隔设置两个以上的测量平面，在检测被测轴对应每个测量平面的位置处设置圆光栅，并在每个测量平面上设置与圆光栅对应的读数头，被测轴转动时，通过读数头与对应的圆光栅的配合检测被测轴的切向位移从而得出被测轴在该测量平面处的位移以及转动角度，根据被测轴在各个测量平面的位移计算出被测轴的偏摆量，结合被测轴的转动角度以及偏摆量计算得出被测轴转动时除被测轴的轴向窜动位移以外的五个自由度的运动参数规律从而得出被测轴的运动误差。1. A five-degree-of-freedom error measurement method for a shaft system based on a circular grating, characterized in that: two or more measurement planes are set at intervals on the axial position of the measured shaft, and at the position corresponding to each measurement plane of the measured shaft The circular grating is set, and the reading head corresponding to the circular grating is set on each measurement plane. When the measured shaft rotates, the tangential displacement of the measured shaft is detected by the cooperation of the reading head and the corresponding circular grating to obtain the measured shaft. The displacement and rotation angle at the measurement plane, according to the displacement of the measured shaft in each measurement plane, the yaw amount of the measured axis is calculated, and the rotation angle and the yaw amount of the measured axis are combined to calculate the rotation of the measured axis. The motion parameters of the five degrees of freedom except the axial displacement of the measured shaft are obtained to obtain the motion error of the measured shaft. 2.根据权利要求1所述的基于圆光栅的轴系五自由度误差测量方法，其特征在于：所述测量平面有两个，两个测量平面的一个上的读数头的数量为m，另一个测量平面上的读数头的数量为n，且m≥2，n≥2，m+n≥5。2. The method for measuring five-degree-of-freedom errors of a shaft system based on a circular grating according to claim 1, wherein the measurement plane has two, and the number of reading heads on one of the two measurement planes is m, and the other is m. The number of reading heads on a measuring plane is n, and m≥2, n≥2, m+n≥5. 3.根据权利要求2所述的基于圆光栅的轴系五自由度误差测量方法，其特征在于：设两个测量平面分别为平面P1和平面P2，在平面P1以理论回转中心O1为原点建立坐标系X1O1Y1，在平面P2上以理论回转中心O2为原点建立坐标系X2O2Y2，O1O2的连线定义为Z轴，设各个读数头的初始读数为0，绕Z轴的逆时针转动方向为正方向，H1i(t)表示圆光栅切线方向的位移量，则被测轴在X1O1Y1坐标平面的位移和被测轴的旋转角度为：3. the five-degree-of-freedom error measurement method of the shaft system based on the circular grating according to claim 2, is characterized in that: suppose that two measurement planes are respectively plane P1 and plane P2, in plane P1, take theoretical center of rotation O 1 as origin Establish the coordinate system X 1 O 1 Y 1 , and establish the coordinate system X 2 O 2 Y 2 on the plane P2 with the theoretical center of rotation O 2 as the origin, and the connection line of O 1 O 2 is defined as the Z axis. The reading is 0, the counterclockwise rotation around the Z axis is the positive direction, and H 1i (t) represents the displacement in the tangential direction of the circular grating, then the displacement of the measured axis on the X 1 O 1 Y 1 coordinate plane is the same as the measured axis. The rotation angle is: 式中，RO、圆光栅的外圆半径；θ(t)、圆光栅的旋转角度；In the formula, R O , the outer circle radius of the circular grating; θ(t), the rotation angle of the circular grating; 当平面P2上的读数头在圆周方向上均布时，被测轴绕O2点的旋转角θ2(t)为：When the reading heads on the plane P2 are evenly distributed in the circumferential direction, the rotation angle θ 2 (t) of the measured shaft around the point O 2 is: 当平面P2上的读数头在圆周方向上不是均布时，则令：When the reading heads on the plane P2 are not uniformly distributed in the circumferential direction, then let: θ2(t)＝θ1(t)，θ 2 (t)=θ 1 (t), 则被测轴在X2O2Y2坐标平面的位移为：Then the displacement of the measured axis in the X 2 O 2 Y 2 coordinate plane is: 被测轴空间运动的六自由度坐标中的位移坐标Tx(t)、Ty(t)、Tz(t)和绕初始坐标轴X、Y、Z的旋转坐标Rx(t)、Ry(t)、Rz(t)为：Displacement coordinates Tx(t), Ty(t), Tz(t) and rotation coordinates Rx(t), Ry(t) around the initial coordinate axes X, Y, Z in the six-degree-of-freedom coordinates of the measured axis space motion , Rz(t) is: 式中L为平面P1和P2之间的距离。where L is the distance between planes P1 and P2. 4.根据权利要求3所述的基于圆光栅的轴系五自由度误差测量方法，其特征在于：当求出的O1x(t)和O1y(t)的绝对值大于设定值时，对计算结果进行非线性效应的补偿，即， 4. the five-degree-of-freedom error measurement method of the shaft system based on circular grating according to claim 3, is characterized in that: when the absolute value of the obtained O 1x (t) and O 1y (t) is greater than the set value, Compensation for nonlinear effects is performed on the calculation results, that is, 式中的nlc1x和nlc1y是事先在实验室条件下通过实验由精度更高的仪器获取的非线性补偿函数。The nlc 1x and nlc 1y in the formula are the nonlinear compensation functions obtained by the instrument with higher precision through experiments in advance under laboratory conditions. 5.基于圆光栅的轴系六自由度误差测量方法，其特征在于：在被测轴的轴向位置上间隔设置两个以上的测量平面，在检测被测轴对应每个测量平面的位置处设置圆光栅，并在每个测量平面上设置与圆光栅对应的读数头，被测轴转动时，通过读数头与对应的圆光栅的配合检测被测轴的切向位移从而得出被测轴在该测量平面处的位移以及转动角度，同时检测被测轴轴向窜动的位移，根据被测轴在各个测量平面的位移计算出被测轴的偏摆量，结合被测轴的转动角度、轴向窜动位移以及偏摆量计算得出被测轴转动时除被测轴的轴向窜动位移以外的六个自由度的运动参数规律从而得出被测轴的运动误差。5. A six-degree-of-freedom error measurement method for a shaft system based on a circular grating, characterized in that: two or more measurement planes are set at intervals on the axial position of the measured shaft, and at the position corresponding to each measurement plane of the measured shaft The circular grating is set, and the reading head corresponding to the circular grating is set on each measurement plane. When the measured shaft rotates, the tangential displacement of the measured shaft is detected by the cooperation of the reading head and the corresponding circular grating to obtain the measured shaft. The displacement and rotation angle at the measurement plane, and the axial displacement of the shaft to be measured is detected at the same time, the deflection of the shaft to be measured is calculated according to the displacement of the shaft to be measured in each measurement plane, combined with the rotation angle of the shaft to be measured , axial movement displacement and yaw amount are calculated to obtain the motion parameters of the six degrees of freedom except the axial movement displacement of the measured shaft when the measured shaft rotates, so as to obtain the motion error of the measured shaft. 6.根据权利要求5所述的基于圆光栅的轴系六自由度误差测量方法，其特征在于：所述测量平面有两个，两个测量平面的一个上的读数头的数量为m，另一个测量平面上的读数头的数量为n，且m≥2，n≥2，m+n≥5。6. The method for measuring six-degree-of-freedom errors of a shaft system based on a circular grating according to claim 5, characterized in that: there are two measurement planes, and the number of reading heads on one of the two measurement planes is m, and the other is m. The number of reading heads on a measuring plane is n, and m≥2, n≥2, m+n≥5. 7.根据权利要求6所述的基于圆光栅的轴系六自由度误差测量方法，其特征在于：设两个测量平面分别为平面P1和平面P2，在平面P1以理论回转中心O1为原点建立坐标系X1O1Y1，在平面P2上以理论回转中心O2为原点建立坐标系X2O2Y2，O1O2的连线定义为Z轴，设各个读数头的初始读数为0，绕Z轴的逆时针转动方向为正方向，H1i(t)表示圆光栅切线方向的位移量，则被测轴在X1O1Y1坐标平面的位移和被测轴的旋转角度为：7. the six-degree-of-freedom error measurement method based on circular grating according to claim 6, is characterized in that: suppose that two measurement planes are respectively plane P1 and plane P2, in plane P1, take theoretical rotation center O 1 as origin Establish the coordinate system X 1 O 1 Y 1 , and establish the coordinate system X 2 O 2 Y 2 on the plane P2 with the theoretical center of rotation O 2 as the origin, and the connection line of O 1 O 2 is defined as the Z axis. The reading is 0, the counterclockwise rotation around the Z axis is the positive direction, and H 1i (t) represents the displacement in the tangential direction of the circular grating, then the displacement of the measured axis on the X 1 O 1 Y 1 coordinate plane is the same as the measured axis. The rotation angle is: 式中，RO、圆光栅的外圆半径；θ(t)、圆光栅的旋转角度；In the formula, R O , the outer circle radius of the circular grating; θ(t), the rotation angle of the circular grating; 当平面P2上的读数头在圆周方向上均布时，被测轴绕O2点的旋转角θ2(t)为：When the reading heads on the plane P2 are evenly distributed in the circumferential direction, the rotation angle θ 2 (t) of the measured shaft around the point O 2 is: 当平面P2上的读数头在圆周方向上不是均布时，则令：When the reading heads on the plane P2 are not uniformly distributed in the circumferential direction, then let: θ2(t)＝θ1(t)，θ 2 (t)=θ 1 (t), 则被测轴在X2O2Y2坐标平面的位移为：Then the displacement of the measured axis in the X 2 O 2 Y 2 coordinate plane is: 被测轴轴向的窜动的位移为Oz(t)；The axial displacement of the measured shaft is O z (t); 被测轴空间运动的六自由度坐标中的位移坐标Tx(t)、Ty(t)、Tz(t)和绕初始坐标轴X、Y、Z的旋转坐标Rx(t)、Ry(t)、Rz(t)为：Displacement coordinates Tx(t), Ty(t), Tz(t) and rotation coordinates Rx(t), Ry(t) around the initial coordinate axes X, Y, Z in the six-degree-of-freedom coordinates of the measured axis space motion , Rz(t) is: 式中L为平面P1和P2之间的距离。where L is the distance between planes P1 and P2. 8.根据权利要求7所述的基于圆光栅的轴系六自由度误差测量方法，其特征在于：当求出的O1x(t)和O1y(t)的绝对值大于设定值时，对计算结果进行非线性效应的补偿，即， 8. The six-degree-of-freedom error measurement method of a shaft system based on a circular grating according to claim 7, is characterized in that: when the absolute value of the obtained O 1x (t) and O 1y (t) is greater than the set value, Compensation for nonlinear effects is performed on the calculation results, that is, 式中的nlc1x和nlc1y是事先在实验室条件下通过实验由精度更高的仪器获取的非线性补偿函数。The nlc 1x and nlc 1y in the formula are the nonlinear compensation functions obtained by the instrument with higher precision through experiments in advance under laboratory conditions. 9.基于圆光栅的轴系测量误差系统，其特征在于：包括多点位移传感器子系统、数据采集子系统以及数据分析处理子系统，所述多点位移传感器子系统包括至少两个在被测轴的轴向上间隔设置的用于检测被测轴在对应位置处的径向位移以及被测轴的转动角度的位移传感器组件，所述位移传感器组件包括用于安装在被测轴上并随被测轴转动的圆光栅盘以及与圆光栅盘的外周对应设置的读数头，所述数据采集子系统与所述多点位移传感器子系统以及数据分析处理子系统导电连接从而将多点位移传感器子系统的数据采集并传输给所述数据分析处理子系统，从而使所述数据分析处理子系统根据被测轴在不同位置处的径向位移计算出被测轴的偏摆量，并结合被测轴的转动角度计算得出被测轴转动时除轴向的窜动位移以外的其他五个自由度的运动参数规律从而得出被测轴的运动误差。9. A shafting measurement error system based on a circular grating, characterized in that it includes a multi-point displacement sensor subsystem, a data acquisition subsystem and a data analysis and processing subsystem, and the multi-point displacement sensor subsystem includes at least two A displacement sensor assembly arranged at intervals in the axial direction of the shaft and used to detect the radial displacement of the measured shaft at the corresponding position and the rotation angle of the measured shaft, the displacement sensor assembly includes a displacement sensor assembly for being installed on the measured shaft and following the direction of the measured shaft. A circular grating disk rotated by the measured shaft and a reading head corresponding to the outer circumference of the circular grating disk, the data acquisition subsystem is electrically connected with the multi-point displacement sensor subsystem and the data analysis and processing subsystem to connect the multi-point displacement sensor The data of the subsystem is collected and transmitted to the data analysis and processing subsystem, so that the data analysis and processing subsystem calculates the deflection of the measured shaft according to the radial displacement of the measured shaft at different positions, and combines the measured shaft with the measured shaft. The rotation angle of the measured shaft is calculated to obtain the motion parameters of the other five degrees of freedom except the axial displacement when the measured shaft rotates, so as to obtain the motion error of the measured shaft. 10.根据权利要求9所述的基于圆光栅的轴系测量误差系统，其特征在于：所述位移传感器组件有两个，所述位移传感器组件的圆光栅盘上下间隔设置，两个圆光栅中的一个对应读数头的数量为m，另一个对应的读数头数量为n，且m≥2，n≥2，m+n≥5。10 . The shaft system measurement error system based on circular grating according to claim 9 , wherein there are two displacement sensor assemblies, the circular grating discs of the displacement sensor assembly are arranged at intervals up and down, and the two circular gratings are arranged at intervals. 11 . One of the corresponding number of reading heads is m, and the other corresponding number of reading heads is n, and m≥2, n≥2, m+n≥5.
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CN114440766A (en) * 2022-01-12 2022-05-06 北京交通大学 A System for Simultaneously Measuring the Motion Errors of Rotary Axes with Six Degrees of Freedom
CN114440766B (en) * 2022-01-12 2023-12-26 北京交通大学 System for simultaneously measuring six-degree-of-freedom motion errors of rotating shaft
CN116399271A (en) * 2023-02-23 2023-07-07 河南科技大学 A device and method for measuring the overall error of gears based on double-sided meshing

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