CN101033936A - Method for measuring error of roller roundness and kinematic error of machine tool main axle using antipodal two points six positions - Google Patents

Abstract

The invention relates to a method about diametrical two points and six level measuring roll roundness error and machine tool spindle error., it makes the analysis when time-finite signal collected by two displacement sensors which are set according to diametrical method during six different displacement measuring changes into frequency domain, it makes separation of roundness error of roll which makes eccentric rotatoexercise and spindle motion error, and it realizes measures online about roundness error of roll and spindle motion error, thus, it improves the precision of measuring.

Description

The method of two 6 measurement roll deviation from circular froms of diameter and machine tool chief axis kinematic error

Technical field

The present invention relates to the method for two 6 measurement roll deviation from circular froms of a kind of diameter and machine tool chief axis kinematic error.It is to do relative motion according to three transpositions of two displacement transducers process rolls of diameter setting in six different measuring positions and roller surface circle, obtain the redundant information of roll cross-sections surfaces, and set up six circle of position degree error separating equations, 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, can 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 two 6 measurement roll deviation from circular froms of a kind of diameter and machine tool chief axis kinematic error.When in-process measurement, by of the measurement of 2 displacement sensors of diameter, obtain the redundant information on workpiece to be machined surface, and set up dynamic deviation from circular from and separate equation six positions, 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 two 6 measurement roll deviation from circular froms of a kind of diameter and machine tool chief axis kinematic error, it is characterized in that doing relative motion in six different measuring positions and roller surface circle according to three transpositions of two displacement transducers process rolls of diameter setting, obtain the redundant information of roll cross-sections surfaces, and set up six circle of position degree error separating equations, and the time-domain signal that will collect in the redundant information transforms to frequency domain analysis, the measurement that realizes breaker roll circularity and machine tool chief axis kinematic error with separate.

As shown in Figure 1, two cover ball screw assembly, s 2 and 5 are installed on the measurement bay 1, are driven by servomotor 3 and 4 respectively.The two sensors measuring head 7 and 10 that diameter is settled is installed in respectively on gage beam 6 and 11, drives the roll 8 that contacts on the center bearing bracket 9 by ball screw assembly, 5 with 2 respectively, thereby realizes the measurement of different-diameter roll.Sensor head 7 and 10 should be positioned on the line of centres of roll 8.

The schematic diagram of two 6 measurement roll deviation from circular froms of diameter and machine tool chief axis kinematic error method as shown in Figure 2.Two sensor P are set respectively ₁, P ₄(10), and allow two sensor lines intersect at the O point, promptly overlap with the roll center.Open when a certain cross section begun to measure sensor P ₁(7), P ₄(10) be positioned at horizontal level, P ₁(7) with roll on initial measurement point A coincide.When measuring for the second time, roll is that benchmark turns clockwise 60 °, sensor P with the A point ₂(7 '), P ₅(10 ') are positioned at horizontal level, the value of sampling.When measuring for the third time, roll is that benchmark turns clockwise 120 °, sensor P with the A point ₃(7 "), P ₆(10 ") are positioned at horizontal level, the value of sampling.In measuring process, roll is measured with reference to starting point A wheel measuring three times, and two sensors obtain Department of Survey's train value of six positions altogether, and accurate calibration is wanted in roll revolution simultaneously.Roll is as shown in table 1 with respect to the rotation angle of measuring starting point A.

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

Corresponding sensor	Angle (degree)
		P 1(7)、P 4(10)	0
P 2(7′)、P 5(10′)	60
		P 3(7″)、P 6(10″)	120

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 a certain cross section of roll, roll rotational speed n reference table 2, and the two survey sensor heads 7 that are installed on the measurement bay 1 are relative with 10 static.

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

(1) through diameter two sensors 7[P ₁(7), P ₂(7 '), P ₃(7 ")] and 10[P ₄(10), P ₅(10 '), P ₆(10 ")] three transpositions, realize that measuring its formula for six is: y=Aey=(y ₀(n), y ₁(n), y ₂(n), y ₃(n), y ₄(n), y ₅(n)) ^T

$e={(r\left(n\right),r(n+\frac{N}{6}),r(n+\frac{2N}{6}),r(n+\frac{3N}{6}),r(n+\frac{4N}{6}),r(n+\frac{5N}{6}),\mathrm{\δ}\left(n\right))}^T$

$A=\left[\begin{array}{ccccccc}1& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

N: survey sensor is sampling number weekly;

y _k(n): the output that sensor is ordered at n when being the K time measurement;

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

δ (n): be spindle motion error;

The sensor output y that measures for y:6 time _kThe 6 rank column vectors that constitute;

E: tested roll obtains the deviation from circular from of 6 reconstruct and the 7 rank column vectors that spindle motion error constitutes after through 3 transpositions;

The A:7 row are measured the output coefficient matrix;

y _n(n): the weighted sum that is the sensor output deviation from circular from that begins of 6 datum marks;

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;

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

$C=({\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="A20071001968100122.png"\; state="\{\{state\}\}">c</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_4,c_5)=(1,-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5});$

(3) with C premultiplication matrix equation (1) and launch:

$\mathrm{Cy}=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})+\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k$

Wherein $\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=\mathrm{\&delta;}\left(n\right)(1-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5})=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6});$

(4) top (3) 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)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{K=0}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="0"\; label="c\; k\; e"\; filenames="A20071001968100122.png"\; state="\{\{state\}\}">c</figure-callout>}}_k{e}^{}{}^{0\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/6}=c_0{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_2{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+$

$c_3{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_4{e}^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}\&times;4/6}{c}_5{e}^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}\&times;5/6}$

$=1-\frac{1}{5}\underset{k=1}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Ω＝(e ⁰，e ^j2πl/6，e ^j2×2πl/6，e ^j2×3πl/6，e ^j2×4πl/6，e ^j2×5πl/6)；

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

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

In the formula

It is right to represent

Carry out inverse-Fourier transform;

(6) then deviation from circular from sequence r (n) the substitution formula that solves in (5): δ (n)=y ₀(n)-r (n) can obtain spindle motion error.

Measuring principle of the present invention

The schematic diagram of two 6 measurement roll deviation from circular froms of diameter and machine tool chief axis kinematic error method as shown in Figure 2.If N is a survey sensor sampling number weekly, y _k(n) be the output that sensor is ordered at n when measuring for the K time, r (n) is the deviation from circular from of measured roll, and to establish δ (n) be spindle motion error, and the K value is as shown in table 3, measures down through three and 6 times to establish an equation:

The corresponding survey sensor table of table 3 K value (K=0,1,2,3,4,5)

K	0	1	2	3	4	5
							Survey sensor	P 1(7)	P 2(7′)	P 3(7″)	P 4(10)	P 5(10′)	P 6(10″)

y＝Ae (1)

In the formula:

The sensor output y that measures for y-6 time _kThe 6 rank column vectors that constitute;

The tested roll of e-obtains the deviation from circular from of 6 reconstruct and the 7 rank column vectors that spindle motion error constitutes after through 3 transpositions;

The A-7 row are measured the output coefficient matrix.

y＝(y ₀(n)，y ₁(n)，y ₂(n)，y ₃(n)，y ₄(n)，y ₅(n)) ^T (2)

$e={(r\left(n\right),r(n+\frac{N}{6}),r(n+\frac{2N}{6}),r(n+\frac{3N}{6}),r(n+\frac{4N}{6}),r(n+\frac{5N}{6}),\mathrm{\&delta;}\left(n\right))}^T\&CenterDot;\&CenterDot;\&CenterDot;\left(3\right)$

$A=\left[\begin{array}{ccccccc}1& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 1& 1\end{array}\right]\&CenterDot;\&CenterDot;\&CenterDot;\left(4\right)$

Be provided with the weights coefficient vector

$C=(c_0,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_4,c_5)=(1,-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5})\&CenterDot;\&CenterDot;\&CenterDot;\left(5\right)$

With C premultiplication matrix equation (1) and launch:

$\mathrm{Cy}=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})+\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k$

Wherein $\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=\mathrm{\&delta;}\left(n\right)(1-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5})=0\&CenterDot;\&CenterDot;\&CenterDot;\left(6\right)$

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

$y_n\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})\&CenterDot;\&CenterDot;\&CenterDot;\left(7\right)$

y _n(n)-be the weighted sum of the sensor output deviation from circular from that begins of 6 datum marks.

Obtain real roll deviation from circular from r (n) expression formula, formula (7) 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) (8)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{K=0}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="0"\; label="c\; k\; e"\; filenames="A20071001968100122.png"\; state="\{\{state\}\}">c</figure-callout>}}_k{e}^{}{}^{0\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/6}=c_0{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_2{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+$

$c_3{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_4{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{c}_5{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\&CenterDot;\&CenterDot;\&CenterDot;\left(9\right)$

$=1-\frac{1}{5}\underset{k=1}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Ω＝(e ⁰，e ^j2πl/6，e ^j2×2πl/6，e ^j2×3πl/6，e ^j2×4πl/6，e ^j2×5πl/6) (10)

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 (8) is the fundamental equation that two 6 method deviation from circular froms of diameter 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 (8), if (8) 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.

$r\left(n\right)={\mathrm{DFT}}^{-1}\left[\frac{Y_n\left(l\right)}{G\left(l\right)}\right](n=\mathrm{0,1,2}\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;N-1)\&CenterDot;\&CenterDot;\&CenterDot;\left(11\right)$

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 (2) (3) that solves in (12), can obtain spindle motion error then:

δ(n)＝y ₀(n)-r(n) (12)

Just can calculate the deviation from circular from and the machine tool chief axis rotation error of measured workpiece respectively by formula (11) and (12), thereby reach the result that deviation from circular from is separated with systematic error.

The present invention compared with prior art, the present invention has following outstanding substantive distinguishing features and remarkable advantage: calculate simple, solved and done the rotatablely move deviation from circular from on-machine measurement problem of workpiece of off-centre, the on-machine measurement that also 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 a measurement mechanism synoptic diagram of the present invention.

Fig. 2 is two 6 method measuring principle synoptic diagram of diameter of the present invention.

Embodiment

Details are as follows in conjunction with the accompanying drawings in concrete enforcement of the present invention:

As shown in Figure 1, drive ball screw assembly, 5 and 2, make the diameter that is installed on gage beam 6 and 11 settle two sensors measuring head 7 and 10 to be positioned on the line of centres of roll 8 by servomotor 3 and 4.In measuring process, roll is measured with reference to starting point A wheel measuring three times, and two sensors obtain Department of Survey's train value of six positions altogether, and accurate calibration is wanted in roll revolution simultaneously.Roll is as shown in table 1 with reference to the rotation angle of starting point A with respect to measuring, roll rotational speed reference table 2.

Symbol description:

N: survey sensor is sampling number weekly;

y _k(n): the output that sensor is ordered at n when being the K time measurement;

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

δ (n): be the motion of main shaft mistake;

The sensor output y that measures for y:6 time _kThe 6 rank column vectors that constitute;

E: tested roll obtains the deviation from circular from of 6 reconstruct and the 7 rank column vectors that spindle motion error constitutes after through 3 transpositions;

The A:7 row are measured the output coefficient matrix;

y _n(n): the weighted sum that is the sensor output deviation from circular from that begins of 6 datum marks;

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.

Roll is in the method for machine circularity and the measurement of machine tool chief axis kinematic error, and concrete steps are:

(7) through diameter two sensors 7[P ₁(7), P ₂(7 '), P ₃(7 ")] and 10[P ₄(10), P ₅(10 '), P ₆(10 ")] three transpositions, realize that measuring its formula for six is: y=Ae

y＝(y ₀(n)，y ₁(n)，y ₂(n)，y ₃(n)，y ₄(n)，y ₅(n)) ^T

$e={(r\left(n\right),r(n+\frac{N}{6}),r(n+\frac{2N}{6}),r(n+\frac{3N}{6}),r(n+\frac{4N}{6}),r(n+\frac{5N}{6}),\mathrm{\&delta;}\left(n\right))}^T$

$A=\left[\begin{array}{ccccccc}1& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

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

$C=({\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="A20071001968100122.png"\; state="\{\{state\}\}">c</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_3,{\mathrm{<figure-callout\; id="4"\; label="c"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">c</figure-callout>}}_4,c_5)=(1,-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5})$

(9) with C premultiplication matrix equation (1) and launch:

$\mathrm{Cy}=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})+\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k$

$\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=\mathrm{\&delta;}\left(n\right)(1-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5})=0$ Occurred first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})$

(10) top (3) 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)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{K=0}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="0"\; label="c\; k\; e"\; filenames="A20071001968100122.png"\; state="\{\{state\}\}">c</figure-callout>}}_k{e}^{}{}^{0\&times;\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;l}/6}=c_0{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_1{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_2{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+$

$c_3{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+c_4{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{c}_5{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

$=1-\frac{1}{5}\underset{k=1}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20071001968100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Ω＝(e ⁰，e ^j2πl/6，e ^j2×2πl/6，e ^j2×3πl/6，e ^j2×4πl/6，e ^j2×5πl/6)

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

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

In the formula

It is right to represent

Carry out inverse-Fourier transform.

(12) then deviation from circular from sequence r (n) the substitution formula that solves in (5): δ (n)=y ₀(n)-r (n) can obtain spindle motion error.

Claims (2)

1. the method for two 6 measurement roll deviation from circular froms of a diameter and machine tool chief axis kinematic error, it is characterized in that doing relative motion in six different measuring positions and roller surface circle according to two displacement transducers (7) and three transpositions of (10) process roll of diameter setting, obtain the redundant information of roll cross-sections surfaces, and set up six circle of position degree error separating equations, and the time-domain signal that will collect in the redundant information transforms to frequency domain analysis, the measurement that realizes breaker roll circularity and machine tool chief axis kinematic error with separate.

2. the method for two 6 measurement roll deviation from circular froms of diameter according to claim 1 and machine tool chief axis kinematic error is characterized in that the concrete operations step is as follows:

(13) through diameter two sensors 7[P ₁(7), P ₂(7 '), P ₃(7 ")] and 10[P ₄(10), P ₅(10 '), P ₆(10 ")] three transpositions, realize that measuring its formula for six is: y=Ae

y＝(y ₀(n)，y ₁(n)，y ₂(n)，y ₃(n)，y ₄(n)，y ₅(n)) ^T

${e=(r\left(n\right),r(n+\frac{N}{6}),r(n+\frac{2N}{6}),r(n+\frac{3N}{6}),r(n+\frac{4N}{6}),r(n+\frac{5N}{6}),\mathrm{\&delta;}\left(n\right))}^T$

$A=\left[\begin{array}{ccccccc}1& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

N: survey sensor is sampling number weekly;

y _k(n): the output that sensor is ordered at n when being the K time measurement;

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

δ (n): be spindle motion error;

The sensor output y that measures for y:6 time _kThe 6 rank column vectors that constitute;

E: tested roll obtains the deviation from circular from of 6 reconstruct and the 7 rank column vectors that spindle motion error constitutes after through 3 transpositions;

The A:7 row are measured the output coefficient matrix;

y _n(n): the weighted sum that is the sensor output deviation from circular from that begins of 6 datum marks;

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;

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

$C=(c_0,c_1,c_2,c_3,c_4,c_5)=(1,-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5},-\frac{1}{5});$

(3) with C premultiplication matrix equation (1) and launch:

$\mathrm{Cy}=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6})+\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k$

Wherein $\mathrm{\&delta;}\left(n\right)\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k=\mathrm{\&delta;}\left(n\right)(1-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5}-\frac{1}{5})=0$ Realized first separating, separated spindle motion error δ (n) earlier and only contained the expression formula of roll deviation from circular from:

$y_n\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{y}_k\left(n\right)=\underset{k=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_{k}r(n+\frac{\mathrm{kN}}{6});$

(4) top (3) 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)

$G\left(l\right)=\mathrm{C\&Omega;}=\underset{K=0}{\overset{5}{\mathrm{\&Sigma;}}}{c}_k{e}^{0\&times;j2\mathrm{\&pi;l}/6}=c_0{e}^{j2\mathrm{\&pi;lk}/6}+c_1{e}^{j2\mathrm{\&pi;l}/6}+c_2{e}^{j2\mathrm{\&pi;l}\&times;2/6}+$

$c_3{e}^{j2\mathrm{\&pi;l}\&times;3/6}+c_4{e}^{j2\mathrm{\&pi;l}\&times;4/6}{c}_5{e}^{j2\mathrm{\&pi;l}\&times;5/6}$

$=1-\frac{1}{5}\underset{k=1}{\overset{5}{\mathrm{\&Sigma;}}}{e}^{j2\mathrm{\&pi;lk}/6}$

Ω＝(e ⁰，e ^j2πl/6，e ^j2×2πl/6，e ^j2×3πl/6，e ^j2×4πl/6，e ^j2×5πl/6)；

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

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

In the formula

It is right to represent

Carry out inverse-Fourier transform;

(6) then deviation from circular from sequence r (n) the substitution formula that solves in (5): δ (n)=y ₀(n)-r (n) can obtain spindle motion error.

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