CN100491897C - Diameter and parallel multiple-position measurement method for roller roundness error and machine tool principal axis movement error - Google Patents

Abstract

The invention relates to a method for diameter and parallel multi-bit measuring roller roundness error and machine spindle motion error, including two displacement sensor diameter disposed on the periphery of the measurement section of the measured roller, one of which used as reference position sensor, while another as measurement sensor with one parallel setting displacement sensor, keeping relative movement with roller surface on different measurement position through roller multi-displacement, obtaining the redundant information of the detected section surface of the roller, establishing corresponding multi-bit roundness error separation equation, and converting the time domain signal in the collected redundant information to the frequency domain signal and analyzing, separating on-machine the roundness error of eccentric rotating motion roller and motion error of the main spindle, thereby realizing the measurement and separation of roller roundness and machine spindle motion error. The invention which is easy to be applied is capable of solving the roundness error online measurement problem of eccentric rotating motion roller, and can be extended to the online measurement and separation of the roundness error of common spindle part and machine spindle motion error.

Description

The method of diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error

Technical field

The present invention relates to the method for a kind of diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error.A displacement transducer during diameter is provided with is as the reference position sensor, parallel in addition two as survey sensor, process roll repeatedly transposition is done relative motion in different measuring position and roller surface circle, obtain the redundant information of roll cross-sections surfaces, and set up corresponding multidigit deviation from circular from and separate equation, and the time-domain signal that will collect in the redundant information transforms to frequency domain analysis, to make the eccentric deviation from circular from of roll and the kinematic error of main shaft of rotatablely moving at machine separates, realize the deviation from circular from and the spindle motion error on-machine measurement of breaker roll, according to the actual requirements, this measuring method can be reduced to diameter two point measurement methods, any angle also can be set carry out random measurement, thereby improve measuring accuracy.

Background technology

Along with the fast development of iron and steel metallurgy and automobile industry, more and more higher to the accuracy requirement of sheet metal.In order to suppress high-precision sheet material, it is excellent in important that the quality of roll just seems.Wherein the surface quality of the circularity of roll and roll is the main factor of decision sheet material precision, and the final mass of roll is determined by roll grinder, so that the height of CNC roll grinder measuring accuracy also plays a part is very important.When tradition CNC roll grinder measurement mechanism is measured circularity, the setting-up eccentricity of roll and the spindle motion error of lathe and the deviation from circular from of roll are mixed.These traditional roll measurement mechanisms do not have the function that the machine tool system error is separated with the deviation from circular from of roll now.Along with people's breaker roll high precision, high efficiency pursuit, processed roll is implemented on-machine measurement, and the roll deviation from circular from can be separated with the machine tool system error, not only can improve measuring accuracy, and the data after separating can also be used for the compensation control of digital control processing, help improving the machining precision and the efficient of roll.

Summary of the invention

The objective of the invention is to propose the method for a kind of diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error, can realize roundness error of workpiece and the on-line measurement of machine tool chief axis kinematic error.

For achieving the above object, the present invention adopts following technical proposals:

The method of a kind of diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error, it is characterized in that measuring the periphery in cross section at tested roll, diameter is provided with two displacement transducers, wherein first displacement transducer is as the reference position displacement transducer, and the triple motion sensor of second displacement transducer and a setting in parallel is as survey sensor, process roll repeatedly transposition is done relative motion in different measuring position and roller surface circle, obtain the redundant information on roll measured section surface, set up corresponding multidigit deviation from circular from and separate equation, and the time-domain signal that will collect in the redundant information transforms to frequency domain analysis, to make the eccentric deviation from circular from of roll and the kinematic error of main shaft of rotatablely moving at machine and separate, the measurement that realizes breaker roll circularity and machine tool chief axis kinematic error with separate.

The concrete operations step is as follows:

(1) first displacement transducer and second displacement transducer of the setting of correction diameter are in the x direction of principal axis, and triple motion sensor and x axle clamp angle are

(2) measure first by three displacement transducers (1,2,3) measurement 3 1A, 1B and 1C, the record 1A point position and the data of surveying, the 1A point is as the reference position point; Measure for the second time roll be rotated counterclockwise (π-

) degree, by two second parallel displacement transducers and 2 2B of triple motion sensor measurement and 2C, 1C goes to reference point 1A position, is designated as 2A/1C, and as new reference point; Measure for the third time to the K time all with measuring process for the second time, K order triple motion sensor measurement position is put with the 1st second displacement transducer institute location and is overlapped in theory, can carry out duplicate measurements in error range;

(3), realize multiple-position measurement through the measuring process in the step (2):

If N is a Displacement Measurement sensor sampling number weekly, x _i(n) be to measure for the i time, in the measuring process corresponding point be iA (i=2,3 ..., corresponding kinematic error is all important on x and y axle in the time of K-1); , r (n) is the deviation from circular from of measured roll, and to establish δ (n) be spindle motion error, establishes roll rotation K time, value is through three and measure down for K time and establish an equation:

y＝Ae (1)

In the formula:

The displacement transducer output y that y-K time measures _i(n) the K rank column vector of Gou Chenging;

Obtain the deviation from circular from of K reconstruct and the K+1 rank column vector that spindle motion error constitutes after e-K transposition of tested roll process;

M-K+1 row are measured the output coefficient matrix.

y＝(y ₁(n)，y ₂(n)…，y _N(n)) ^T (2)

$e={(r\left(n\right),r(n+\frac{N}{K}),\·\·\·,r(n+\frac{K-1}{K}N),\mathrm{\δ}\left(n\right))}^T---\left(3\right)$

(4) setting is provided with the weights coefficient vector according to measuring mechanism:

$C=({\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_3\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K,\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K)$

$=(1,-\frac{1}{N-1},-\frac{K}{2N-K},\&CenterDot;\&CenterDot;\&CenterDot;,-\frac{1}{N-1},-\frac{1}{N-1},\&CenterDot;\&CenterDot;\&CenterDot;,1)---\left(4\right)$

The coefficient number that wherein contains kinematic error x component is N, and the coefficient number that contains the y component is 2N/K;

(5) C premultiplication matrix equation (2) is: $\mathrm{Cy}=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{c}_i{y}_k\left(n\right)=\mathrm{Me}+\mathrm{H\&delta;}$

Wherein $\mathrm{H\&delta;}=\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i{y}_i\left(n\right)=\mathrm{Me}---\left(5\right)$

(6) top (5) formula is carried out Discrete Fourier Transform (DFT), " time delay-phase shift " character of using DFT simultaneously can solve the frequency-domain expression of the deviation from circular from of measured roll:

R(l)＝Y _n(l)/G(l)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_{i+1}{e}^{i\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/K}=c_1{\mathrm{<figure-callout\; id="0"\; label="e"\; filenames="C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^0+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+\&CenterDot;\&CenterDot;\&CenterDot;+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Ω＝(e ⁰，e ^j2πl/K，e ^j2×2πl/K，…，e ^j2×4πl/K，e ^{j2×(N-1)πl/K})；

(7) solve deviation from circular from sequence and machine tool chief axis rotation error sequence at last:

$\begin{array}{cc}r\left(n\right)={\mathrm{DFT}}^{-1}\left[\frac{Y_n\left(l\right)}{G\left(l\right)}\right]& (n=\mathrm{0,1,2}.....N-1)\end{array}$

In the formula

It is right to represent Carry out inverse-Fourier transform;

(8) then deviation from circular from sequence r (n) the substitution formula that solves in (7): δ (n)=y ₀(n)-r (n) promptly obtains spindle motion error.

The present invention compared with prior art, the present invention has following outstanding substantive distinguishing features and remarkable advantage: be easy to implement, solved and done the rotatablely move deviation from circular from on-machine measurement problem of workpiece of off-centre, the on-machine measurement that can be generalized to the deviation from circular from of common big axial workpiece and machine tool chief axis kinematic error with separate.

Description of drawings

Fig. 1 is the diameter of an example of the present invention and the apparatus structure synoptic diagram of parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error.

Fig. 2 is a roll measuring principle synoptic diagram of the present invention.

Fig. 3 measures the roll location synoptic diagram first time in the measuring principle shown in Figure 2.

Fig. 4 measures the roll location synoptic diagram second time in the measuring principle shown in Figure 2.

Fig. 5 is the synoptic diagram of measurement roll location for the third time in the measuring principle shown in Figure 2.

Embodiment

Details are as follows in conjunction with the accompanying drawings for a preferred embodiment of the present invention:

The method of this diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis error adopts measurement mechanism shown in Figure 1: two cover ball screw assembly, s 5,8 and 9 are installed on measurement bay 4, drive by servomotor 6,7 and 10 respectively, it is the boundary line of ball screw assembly, 9 that ball screw assembly, 8 needs to set critical localisation, in order to avoid bump with ball screw assembly, 9 in the measuring process.The measuring head of the two sensors 1 that diameter is settled and 2 measuring head and the sensor 3 parallel with sensor 2, the three is installed in respectively on gage beam 15,11 and 16, drive the roll 13 that contacts on the center bearing bracket 14 by ball screw assembly, 5,8 with 9 respectively, thereby realize the measurement of different-diameter roll.The measuring head of the measuring head of first displacement transducer 1 and second displacement transducer 2 should be positioned on the line of centres of roll 13, and the angle that the line of centres of the measuring head of triple motion sensor 3 and roll 13 and horizontal axis form is

Here adopt the symmetrical expression sampling, triple motion sensor 3 and x axle clamp angle

Require to satisfy

Wherein K is the roll number of revolutions.Ordinary surveying (triple motion sensor 3 and x axle clamp angle

) can only need to use first displacement transducer 1 and second displacement transducer 2 to carry out the diameter measurement, triple motion sensor 3 is stand-by.High-acruracy survey (sensor 3 and x axle clamp angle

) can reduce triple motion sensor 3 and x axle clamp angle

Carry out multiple-position measurement.Require and to change by the position of regulating ball screw assembly, 8 according to measuring accuracy

The angle.

The schematic diagram of this diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error method as shown in Figure 2.Proofread and correct first displacement transducer 1 and second displacement transducer 2, two displacement transducer lines are intersected at a point, and this point overlaps with roll 13 centers, is designated as 0 point, according to the measuring accuracy requirement, set the angle that the line of centres of the measuring head of triple motion sensor 3 and roll 13 forms and be

When a certain cross section was begun to measure, first displacement transducer 1, second displacement transducer 2 were positioned at horizontal level, and initial measurement point 1A coincides on first displacement transducer 1 and the roll 13.Measure for the first time by first displacement transducer 1, second displacement transducer 2 and triple motion sensor 3 and measure 1A, 1B and 1C at 3, the record 1A point position and the data of surveying, the 1A point is as the reference position point.Measure for the second time roll 13 be rotated counterclockwise ( ) degree, measure 2B, 2C at 2 by parallel first displacement transducer 2, second displacement transducer 3,1C goes to reference point 1A position, be designated as 2A/1C, and as new reference point, measure for the third time to the K time all with measuring process for the second time, need to prove, K order triple motion sensor 3 measuring positions are put with 2 locations of the 1st time second displacement transducer and are overlapped in theory, can carry out duplicate measurements in error range.(N is a sampling number, and N=2K) Department of Survey's train value of individual position, while roll 13 turn round wants accurate calibration can to obtain N at last.Roll 13 is as shown in table 1 with respect to the rotation angle of measuring starting point 1A, and the anglec of rotation situation of each roll 13 location points is referring to Fig. 3 _ 1, Fig. 3 _ 2, Fig. 3 _ 3.

Table 1 roll is measured the initial 1A point anglec of rotation

Corresponding sensor	Angle (degree)
		1	0
/	180
		/	240
...	...

Table 2 roundness measurement workpiece rotational frequency recommendation n unit: rpm

Roller diameter mm	250～500	500～630	630～1250	Greater than 1250
					n	5～10	4～8	3～5	Less than 3

The measurement that roll circularity is separated with the machine tool chief axis kinematic error is when measuring the circularity in roll 13 a certain cross sections, roll rotational speed n reference table 2, and the measuring head that is installed in the measuring head of first displacement transducer 1 on the measurement bay 1 and second displacement transducer 2 is relative static.

The concrete operations step of above-mentioned measuring method is as follows:

(1) first displacement transducer 1 and second displacement transducer 2 of the setting of correction diameter are in the x direction of principal axis, and triple motion sensor 3 with x axle clamp angle is

(2) measure first by 1,2,3 measurements of three displacement transducers 3 1A, 1B, 1C, the record 1A point position and the data of surveying, the 1A point is as the reference position point.For the second time measuring roll 13 is rotated counterclockwise

Degree, measure 2B, 2C at 2 by two first parallel displacement transducers 2 and triple motion sensor 3,1C goes to reference point 1A position, be designated as 2A/1C, and as new reference point, measure for the third time to the K time all with measuring process for the second time, need to prove, K order triple motion sensor 3 measuring positions are put with 2 locations of the 1st time second displacement transducer and are overlapped in theory, can carry out duplicate measurements in error range;

(3), realize multiple-position measurement through (2) measuring process.

The schematic diagram of diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error method as shown in Figure 2.If N is a Displacement Measurement sensor sampling number weekly, x _i(n) be to measure for the i time, in the measuring process corresponding point be iA (i=2,3 ..., corresponding kinematic error is all important on x and y axle in the time of K-1); , r (n) is the deviation from circular from of measured roll, and to establish δ (n) be spindle motion error, establishes roll rotation K time, value is through three and measure down for K time and establish an equation:

y＝Ae (1)

In the formula:

The sensor output y that y-K time measures _i(n) the K rank column vector of Gou Chenging;

Obtain the deviation from circular from of K reconstruct and the K+1 rank column vector that spindle motion error constitutes after e-K transposition of tested roll process;

M-K+1 row are measured the output coefficient matrix.

y＝(y ₁(n)，y ₂(n)…，y _N(n)) ^T (2)

$e={(r\left(n\right),r(n+\frac{N}{K}),\&CenterDot;\&CenterDot;\&CenterDot;,r(n+\frac{K-1}{K}N),\mathrm{\&delta;}\left(n\right))}^T---\left(3\right)$

(4) setting is provided with the weights coefficient vector according to measuring mechanism:

$C=({\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_3\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K,\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K)$

(4)

$=(1,-\frac{1}{N-1},-\frac{K}{2N-K},\&CenterDot;\&CenterDot;\&CenterDot;,-\frac{1}{N-1},-\frac{1}{N-1},\&CenterDot;\&CenterDot;\&CenterDot;,1)$

The coefficient number that wherein contains kinematic error x component is N, and the coefficient number that contains the y component is 2N/K.

(5) C premultiplication matrix equation (2) is: $\mathrm{Cy}=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{c}_i{y}_k\left(n\right)=\mathrm{Me}+\mathrm{H\&delta;}$

Wherein $\mathrm{H\&delta;}=\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i{y}_i\left(n\right)=\mathrm{Me}---\left(5\right)$

(6) top (5) formula is carried out Discrete Fourier Transform (DFT), " time delay-phase shift " character of using DFT simultaneously can solve the frequency-domain expression of the deviation from circular from of measured roll:

R(l)＝Y _n(l)/G(l)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_{i+1}{e}^{i\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/K}=c_1{\mathrm{<figure-callout\; id="0"\; label="e"\; filenames="C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^0+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+\&CenterDot;\&CenterDot;\&CenterDot;+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Ω＝(e ⁰，e ^j2πl/K，e ^j2×2πl/K，…，e ^j2×4πl/K，e ^{j2×(N-1)πl/K})

(7) solve deviation from circular from sequence and machine tool chief axis rotation error sequence at last:

$\begin{array}{cc}r\left(n\right)={\mathrm{DFT}}^{-1}\left[\frac{Y_n\left(l\right)}{G\left(l\right)}\right]& (n=\mathrm{0,1,2}.....N-1)\end{array}$

In the formula

It is right to represent

Carry out inverse-Fourier transform.

(8) then deviation from circular from sequence r (n) the substitution formula that solves in (7): δ (n)=y ₀(n)-r (n) can obtain spindle motion error.

Measuring principle

As shown in Figure 1, around tested roll 13 circular sections, dispose three displacement transducers 1,2 and 3, set up coordinate system xoy, the position that O ' takes advantage of the heart for a certain moment workpiece cross section two, then δ at its intersection point O place _x(θ) and δ _y(θ) be the component of roll spindle motion error on x and y change in coordinate axis direction.

R is the mean radius of roll, and D is the spacing between the triple motion sensor 3 and second displacement transducer 2, and this moment, the output equation of three displacement transducers 1,2,3 was respectively:

x ₁(θ)＝-r(θ)+δ _x(θ) (1)

x ₂(θ)＝r(θ)+δ _x(θ) (2)

Wherein,

Can calculate by geometric relationship shown in Figure 2:

Then have:

Right

Make Taylor series expansion, omit high-order in a small amount after, then have:

Comprehensively (3), (5), (6) and (7) formula can get

During measurement, usually around 13 1 weeks of roll making uniformly-spaced data sampling, note

Be sampling interval, N ₁Be sampling number weekly, then have

(p is normal integer).The discretize data of displacement transducer reading, measured workpiece shape error and kinematic error correspondingly just should be designated as x respectively _i(n), r (n+ki), δ _x(n) and δ _y(n) (i=1,2,3).So the reading equation of three displacement transducers just becomes:

x ₁(n) the roll forming data message that is illustrated in first displacement transducer, 1 position correspondence is to measure the measured data message in triple motion sensor 3 positions last time, when measuring first: x ₁(1)=-r (1)+δ _x(1) (11)

When roll 13 rotates to last the K time, the roll forming data message of first displacement transducer, 1 position correspondence is the measured data messages in K-1 order triple motion sensor 3 positions, triple motion sensor 3 positions and second displacement transducer 2 the first time measuring position coincide.

y＝(y ₁(n)，y ₂(n)…，y _N(n)) ^T (12)

$\left.\begin{array}{c}{y}_1\left(n\right)=x_{\mathrm{KB}}\left(n\right),y_2\left(n\right)=x_{1B}\left(n\right)=x_{\mathrm{KC}}\left(n\right)\\ y_3\left(n\right)=x_{2A}\left(n\right),y_4\left(n\right)=x_{3B}\left(n\right)\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ y_K\left(n\right)=x_{(K-1)B}\left(n\right),\\ y_{(K+1)}\left(n\right)=x_{\mathrm{KA}}\left(n\right)\\ y_{(K+2)}\left(n\right)=x_{1A}\left(n\right),y_{(K+3)}\left(n\right)=x_{2B}\left(n\right)\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ y_{\left(N\right)}\left(n\right)=x_{(N-1)A}\left(n\right)\end{array}\right\}$ System of equations 1 (13)

$e={(r\left(n\right),r(n+\frac{N}{K}),\&CenterDot;\&CenterDot;\&CenterDot;,r(n+\frac{K-1}{K}N),\mathrm{\&delta;}\left(n\right))}^T---\left(14\right)$

If y=Me y=Me+H δ (15)

A, B, the C correspondence be respectively first, second and triple motion sensor 1,2,3.M is that the K+1 row are measured the output coefficient matrix, and H is the kinematic error matrix of coefficients, and δ is the kinematic error mapping matrix.

Following parameter is set:

N: survey sensor is sampling number weekly;

R (n): be the deviation from circular from of measured roll;

δ (n): be spindle motion error;

x _i(n): be the i time measurement, corresponding iA in the measuring process (i=2,3 ..., corresponding kinematic error is all important on x and y axle in the time of K-1);

y _i(n): the sensor output that is i measurement point;

c _k: be weights coefficient constant;

G (l): for the frequency transfer function of measurement-piece-rate system also claims the weight function of error separating, l overtone order;

Ω: be the phase shift twiddle factor of error separating.

Be provided with the weights coefficient vector

$C=({\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">c</figure-callout>}}_3\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K,\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K)$

(16)

$=(1,-\frac{1}{N-1},-\frac{K}{2N-K},\&CenterDot;\&CenterDot;\&CenterDot;,-\frac{1}{N-1},-\frac{1}{N-1},\&CenterDot;\&CenterDot;\&CenterDot;,1)$

C premultiplication matrix equation (12) is: $\mathrm{Cy}=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{c}_i{y}_k\left(n\right)=\mathrm{Me}+\mathrm{H\&delta;}---\left(17\right)$

Wherein $\mathrm{H\&delta;}=\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i{y}_i\left(n\right)=\mathrm{Me}---\left(18\right)$

Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i{y}_i\left(n\right)=\mathrm{Me}---\left(19\right)$

y _n(n)-be that displacement transducer is to N the weighted sum of putting the deviation from circular from that records.

Obtain real roll deviation from circular from r (n) expression formula, formula (19) is carried out Discrete Fourier Transform (DFT), " time delay-phase shift " character of using DFT simultaneously can solve the frequency-domain expression of the deviation from circular from of measured roll:

R(l)＝Y _n(l)/G(l) (20)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_{i+1}{e}^{i\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/K}=c_1{\mathrm{<figure-callout\; id="0"\; label="e"\; filenames="C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^0+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+\&CenterDot;\&CenterDot;\&CenterDot;+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="C200710040589E00151.png,C200710040589E00161.png"\; state="\{\{state\}\}">e</figure-callout>}}^j---\left(21\right)$

Ω＝(e ⁰，e ^j2πl/K，e ^j2×2πl/K，…，e ^j2×4πl/K，e ^{j2×(N-1)πl/K}) (22)

In the formula: G (l) also claims the weight function of error separating for the frequency transfer function of measurement-piece-rate system, and it has characterized and has been transported to the transitive relation of going in the composite signal after each harmonic component of circularity is weighted.Obviously when closing l=0, G (l) ≡ 0 is arranged, this shows that such method produces the zeroth order harmonic wave and suppresses, and that is to say that this method can not reflect by the dimensional variations of roll.In fact we also are the true form profiles of only being concerned about measured roll, and the zeroth order harmonic wave does not influence the application of the deviation from circular from isolation technics of this method thus.

Ω is the phase shift twiddle factor of error separating.

Formula (20) is the fundamental equation that diameter and parallel multiple-position method deviation from circular from separate.For overtone order l arbitrarily, if its weight function G (l) ≠ 0, the component of its deviation from circular from this order harmonics all can be provided by formula (20), if (20) are contrary Fourier transform (DFT ^-1) then can simultaneously according to roll deviation from circular from curve, adopt measuring system software can obtain the deviation from circular from of roll through contour curve (11) equation of the deviation from circular from after the error separating.

$\begin{array}{cc}r\left(n\right)={\mathrm{DFT}}^{-1}\left[\frac{Y_n\left(l\right)}{G\left(l\right)}\right]& (n=\mathrm{0,1,2}.....N-1)\end{array}---\left(23\right)$

In the formula

It is right to represent Carry out inverse-Fourier transform.

The discrete form of deviation from circular from sequence r (n) the difference substitution formula (12) (14) that solves in (24), can obtain spindle motion error then:

δ(n)＝y ₀(n)-r(n) (24)

Just can calculate the deviation from circular from and the machine tool chief axis rotation error of measured workpiece respectively by formula (23) and (24), thereby reach the result that deviation from circular from is separated with systematic error.

Compared with prior art, the present invention has following outstanding substantive distinguishing features and remarkable advantage: calculate simple, solved the deviation from circular from on-machine measurement problem of doing the eccentric rotary Moving Workpieces, the on-machine measurement that also can be generalized to the deviation from circular from of common large axial workpiece and machine tool chief axis kinematic error with separate.

Claims (2)

1. the method for a diameter and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error, it is characterized in that measuring the periphery in cross section at tested roll (13), diameter is provided with two displacement transducers (1,2), wherein first displacement transducer (1) is as the reference position sensor, and the triple motion sensor (3) of second displacement transducer (2) and a setting in parallel is as survey sensor, process roll (13) repeatedly transposition is done relative motion in different measuring position and roll (13) surface circle, obtain the redundant information on roll (13) measured section surface, set up corresponding multidigit deviation from circular from and separate equation, and the time-domain signal that will collect in the redundant information transforms to frequency domain analysis, onlinely will make the eccentric deviation from circular from of roll and the kinematic error of main shaft of rotatablely moving and separate, the measurement that realizes breaker roll circularity and machine tool chief axis kinematic error with separate.

2. the method for diameter according to claim 1 and parallel multiple-position measurement roll deviation from circular from and machine tool chief axis kinematic error is characterized in that the concrete operations step is as follows:

(1) first displacement transducer (1) and second displacement transducer (2) of the setting of correction diameter are in the x direction of principal axis, and triple motion sensor (3) with x axle clamp angle is

(2) measure first by 3 1A of three displacement transducers (1,2,3) measurement, 1B and 1C, the record 1A point position and the data of surveying, the 1A point is as the reference position point; For the second time measuring roll is rotated counterclockwise

Degree is measured 2 2B and 2C by second displacement transducer (2) and triple motion sensor (3), and 1C goes to reference point 1A position, is designated as 2A/1C, and as new reference point; Measure for the third time to the K time all with measuring process for the second time, adopt the symmetrical expression sampling, require to satisfy

K order triple motion sensor (3) measuring position is put with the 1st second displacement transducer (2) institute location and is overlapped in theory, can carry out duplicate measurements in error range;

(3), realize multiple-position measurement through the measuring process in the step (2):

If N is a Displacement Measurement sensor sampling number weekly, x _i(n) be the i time measurement, corresponding point are iA (i=2 in the measuring process, 3, K-1) corresponding kinematic error is all important on x and y axle the time, and r (n) is the deviation from circular from of measured roll, and to establish δ (n) be spindle motion error, if roll rotation K time, value is through three and measure down for K time and establish an equation:

Y=Ae (1), in the formula::

The displacement transducer output y that y-K time measures _i(n) the K rank column vector of Gou Chenging;

Obtain the deviation from circular from of K reconstruct and the K+1 rank column vector that spindle motion error constitutes after e-K transposition of tested roll process;

M-K+1 row are measured the output coefficient matrix.

y＝(y ₁(n)，y ₂(n)…，y _N(n)) ^T (2)

$e={(r\left(n\right),r(n+\frac{N}{K}),\&CenterDot;\&CenterDot;\&CenterDot;,r(n+\frac{K-1}{K}N),\mathrm{\&delta;}\left(n\right))}^T---\left(3\right)$

(4) setting is provided with the weights coefficient vector according to measuring mechanism:

$C=(c_1,c_2,c_3\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K,\&CenterDot;\&CenterDot;\&CenterDot;,c_{K-1},c_K)$

$=(1,-\frac{1}{N-1},-\frac{K}{2N-K},\&CenterDot;\&CenterDot;\&CenterDot;,-\frac{1}{N-1},-\frac{1}{N-1},\&CenterDot;\&CenterDot;\&CenterDot;,1)---\left(4\right)$

The coefficient number that wherein contains kinematic error x component is N, and the coefficient number that contains the y component is 2N/K;

(5) C premultiplication matrix equation (2) is: $\mathrm{Cy}=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{c}_i{y}_k\left(n\right)=\mathrm{Me}+\mathrm{H\&delta;}$

Wherein $\mathrm{H\&delta;}=\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i{y}_i\left(n\right)=\mathrm{Me}---\left(5\right)$

(6) top (5) formula is carried out Discrete Fourier Transform (DFT), " time delay-phase shift " character of using DFT simultaneously can solve the frequency-domain expression of the deviation from circular from of measured roll:

R(l)＝Y _n(l)/G(l)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_{i+1}{e}^{i\&times;j2\mathrm{\&pi;l}/K}=c_1{e}^0+c_1{e}^{j2\mathrm{\&pi;l}/K}+\&CenterDot;\&CenterDot;\&CenterDot;+c_1{e}^{j2\mathrm{\&pi;l}(N-1)/K}$

Ω＝(e ⁰，e ^j2πl/K，e ^j2×2πl/K，…，e ^j2×4πl/K，e ^{j2×(N-1)πl/K})；

(7) solve deviation from circular from sequence and machine tool chief axis rotation error sequence at last:

$\begin{array}{cc}r\left(n\right)={\mathrm{DFT}}^{-1}\left[\frac{Y_n\left(l\right)}{G\left(l\right)}\right]& (n=\mathrm{0,1,2}.....N-1)\end{array}$

In the formula

It is right to represent Carry out inverse-Fourier transform;

(8) then deviation from circular from sequence r (n) the substitution formula that solves in (7): δ (n)=y ₀(n)-r (n) promptly obtains spindle motion error.

Images