CN103983227B - A kind of eccentric spindle rotation error measuring method and device of being removably installed - Google Patents

Abstract

The present invention discloses a kind of eccentric spindle rotation error measuring method and device of being removably installed, comprise displacement sensor installing holder, displacement sensor, grating encoder, signal cable, data handler and computer, measuring process by three kinds of optional modes, displacement sensor is measured, first obtain main shaft deviation from circular from other component except an order harmonics based on three point method principle, secondary separation is carried out again according to the algorithm provided, separate eccentric for installation from revolution error, obtain the pure radial motion error value of main shaft. being separated from main shaft gyration motion error by the eccentric error that the deviation from circular from of main shaft profile, standard ball and sensor are installed on the one hand, separation algorithm amount is little. on the other hand, only adopt a displacement sensor, avoid the measuring error that the sensor performance difference adopting three sensors to bring in common three point method error separating technology is introduced.

Description

A kind of eccentric spindle rotation error measuring method and device of being removably installed

Technical field

The present invention relates to a kind of precision instrument and manufacture measuring method, particularly relate to a kind of eccentric spindle rotation error measuring method and device of being removably installed.

Background technology

High-precision main shaft, air bearing are the key parts of the accurate equipment such as precision finishing machine, precision centrifuge, disc driver, high-accuracy rotating machine and steam turbine, in the numerous factors (such as: processing Thermal Error, structure error, power chain error, spindle rotation error etc.) affecting precision optical machinery working accuracy, part's machining errors has what the most directly affect be main shaft gyration motion error, and its precision is the key of restriction precision optical machinery processing, high-precision rotary. Along with the working accuracy of lathe reaches submicron even nanometer scale, the part's machining errors that spindle rotation error causes becomes the major influence factors of restriction precision optical machinery working accuracy. Correlation test shows that the part deviation from circular from that precision turning is processed about has 30%��70% to be cause by the spindle rotation error of lathe, and the precision of lathe is more high, and the ratio of its main shaft gyration motion error shared by various processing error source is more big.

When current spindle rotation error measuring principle and technique means can not fundamentally change, owing to cannot directly desirable axle center be measured, and by the measurement of standard ball, standard bar or main shaft outline being recorded indirectly the radial motion error size of main shaft, so must inevitably be mixed into the installation bias equal error source of the shape error of standard ball, standard bar itself or main shaft outline, surface waviness, surfaceness and standard ball, standard bar. Therefore, the key of main shaft gyration motion error measurement technology is error separate. When measuring accuracy enter submicron even nanometer scale time, the deviation from circular from that is mixed in take off data, surfaceness and installing eccentric etc. will highlight, and even can mask the small radial motion error of main shaft. Therefore must take effective method, radial motion error is accurately separated from measuring result. Traditional motion of main shaft revolution error measurement method is as adopted dial indicator to measure the diameter run-out of main shaft, and measuring accuracy is very low, can not be separated from radial motion error by the deviation from circular from of main shaft.

At present, main shaft gyration motion error measurement method mainly contains reversal process, multistep processes and many survey head methods. Although correlative study shows that three kinds of methods respectively have relative merits, but as long as appropriate design parameter, three kinds of methods can reach nanometer measurement precision. But, reversal process and multistep processes are mainly used to the deviation from circular to part and detect, can not online, the radial motion error of real-time measuring shaft system. Multipoint method mainly contains two-point method, three point method, four-point method etc. according to the number installing sensor, after Japanese scholars Ozono in 1966 proposes classical frequency domain Three Point Method for Error Separation of Roundness first, this technology has become one of current error separating technology widely used most. Its advantage is can the radial motion error of on-line real time monitoring axle system.

Based in the deviation from circular from of three point method and spindle rotation error measuring technology, how to reduce the harmonics restraint of error separate, to reduce measuring error transmission be the key improving error separate precision. The known main shaft gyration motion error measurement method based on three point method error separating technology mainly contains based on frequency-domain and time-domain two kinds at present. Due to a humorous suppression in rank, cause the eccentric error installing bias containing standard ball in spindle rotation error measuring result, three sensor axis intersection points do not overlap with center of turning circle and introduce. For this problem, Chinese patent a kind of modified version three point method revolution error, deviation from circular from method of calculation (patent application publication number: CN103363921A, author Niu Baoliang, Zhang Rong) a kind of deviation from circular from based on three point method and revolution error separating method are proposed, its principal feature is the translation and the weighted mean that utilize three sensor output signals, and utilize frequency domain filtering, an order harmonic component of shape error is separated from deviation from circular from and revolution error. In addition, the virtuous minister in ancient times of Xi'an University of Technology's thunder at its Ph D dissertation (based on the cylindricity Technology of Precision Measurement research of error separate, Xi'an University of Technology's Ph D dissertation, 2007) a kind of Time-Domain algorithm is adopted by deviation from circular from, spindle rotation error and bias is installed to be separated in. These methods are deepened and have been developed error separating technology, but still there is the deficiencies such as computing complexity. And, in measuring based on the deviation from circular from of three point method and spindle rotation error, the error how selected sampling number and how to avoid three displacement sensor performance differences to introduce be submicron even nanometer scale high precision measure the problem considered.

Summary of the invention

The object of the present invention is just to provide a kind of bias and only need spindle rotation error measuring method and the device of a displacement sensor of being removably installed in order to solve the problem.

The present invention is achieved through the following technical solutions above-mentioned purpose:

The eccentric spindle rotation error measuring apparatus that is removably installed of the present invention, comprise displacement sensor installing holder, displacement sensor, grating encoder, signal cable, data acquisition unit, data handler and computer, institute's displacement sensors is installed on institute's displacement sensors installing holder, institute's displacement sensors installing holder is installed near main shaft excircle place, it is provided with space between institute's displacement sensors clamper and main shaft outline, described grating encoder is installed on main shaft sleeve, described grating encoder and institute's displacement sensors are all connected with described data handler by described signal cable, described data handler is connected with described computer.

Specifically, institute's displacement sensors installing holder is the displacement sensor installing holder that can simultaneously install one or three displacement sensor.

The eccentric spindle rotation error measuring method that is removably installed of the present invention, comprises the following steps:

(1) displacement sensor clamper is arranged on main shaft excircle, and and main shaft outline between there is space, displacement sensor is arranged on displacement sensor clamper, regulates the distance between the survey head of displacement sensor and main shaft outline to correct position; Arranging the main shaft gyration displacement sensor sampling number of a week is N;

(2) drive shaft rotates, and taking a point of beginning of main shaft outline as the first sampling point of displacement sensor, is designated as A point, and main shaft revolves and turns around, and sensor sample exports N number of value, is designated as { S successively₀(0),S₀(1),S₀(2),��,S₀(N-1) }; And using the x-axis of sensor sensing direction of principal axis corresponding for initial for displacement sensor first sampling point as surving coordinate system;

(3) in the following manner by displacement sensor along main shaft profile angle of rotation ��, this angle is the angle of first sensor and the 2nd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₁=�� N/2 ��, P₁For integer:

Mode: displacement sensor clamper maintains static, utilize the location function-driven main shaft angle of rotation �� of grating encoder, the second time first sampling point making displacement sensor is the position relative to first sampling point distance alpha angle in step (2), is designated as B point;

(4) using B point as first sampling point, main shaft revolves and turns around, and displacement sensor sampling exports N number of value, is designated as { S successively₁(0),S₁(1),S₁(2),��,S₁(N-1) };

(5) measuring process of repeating step (3) and (4), the difference is that displacement sensor is �� along main shaft profile angle of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₂=�� N/2 ��, P₂For integer, with the position that displacement sensor is new, being designated as C point, as first sampling point, main shaft revolves and turns around, and sensor sample exports N number of value, is designated as { S successively₂(0),S₂(1),S₂(2),��,S₂(N-1) };

(6) data are exported based on three groups of displacement sensors in step (2), (3), (4), (5), other value r (n) except an order harmonic component of main shaft deviation from circular from can be obtained according to the frequency domain in three point method error separate principle or time domain method, n=1,2,3,, N-1;

(7) the output data S of three displacement sensors is utilized₀(n)��S₁(n)��S₂(n) and deviation from circular from r (n) except an order harmonic component separated, Errors in Radial Rotation Error of Spindle can be obtained by solve linear equations by following algorithm:

$\left[\begin{array}{ccc}\cos (2\mathrm{\π}n/N)& \sin (2\mathrm{\π}n/N)& \cos (2\mathrm{\π}n/N)\\ \cos \left(2\mathrm{\π}\right(n+P_1)/N)& \sin \left(2\mathrm{\π}\right(n+p_1)/N)& \cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ \cos \left(2\mathrm{\π}\right(n+P_2)/N)& \sin \left(2\mathrm{\π}\right(n+p_2)/N)& \cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right);$

Improving as one: in the algorithm of described step (7), according to the three pure Radial mixing �� (��) of rank Solving Linear main shaft, �� (��) can be expressed as containing deviation from circular from one order harmonics A₁And B₁, containing deviation from circular from one order harmonics A₁Not containing B₁, containing deviation from circular from one order harmonics B₁Not containing A₁, all containing deviation from circular from one order harmonics A₁And B₁Totally four kinds of forms.

The useful effect of the present invention is:

The present invention is a kind of eccentric spindle rotation error measuring method and device of being removably installed, compared with prior art, the eccentric error that the deviation from circular from of main shaft profile, standard ball and sensor are installed is separated by one aspect of the present invention from main shaft gyration motion error, and separation algorithm amount is little. On the other hand, only adopt a displacement sensor, avoid the measuring error that the sensor performance difference adopting three displacement sensors to bring in common three point method error separating technology is introduced, there is the value promoted the use of.

Accompanying drawing explanation

Fig. 1 is the hardware architecture diagram of the present invention;

Fig. 2 is the method flow diagram of the present invention;

Fig. 3 is that position conversion mode one schematic diagram installed by displacement sensor;

Fig. 4 is that position conversion mode two schematic diagram installed by displacement sensor;

Fig. 5 is that position conversion mode three schematic diagram installed by displacement sensor.

In figure: 1-main shaft, 2-displacement sensor installing holder, 3-displacement sensor, 4-main shaft outline first sampling point A, 5-main shaft outline first sampling point B, 6-main shaft outline first sampling point C, angle between 7-main shaft outline first sampling point A and first sampling point B, angle between 8-main shaft outline first sampling point A and first sampling point C, the installation sensor hole of 9-displacement sensor installing holder, the installation sensor hole of 10-displacement sensor installing holder, the installation sensor hole of 11-displacement sensor installing holder, 12-grating encoder, 13-signal cable, 14-data acquisition unit, 15-signal conditioner, 16-computer.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described:

As shown in Figure 1: the eccentric spindle rotation error measuring apparatus that is removably installed of the present invention, comprise displacement sensor installing holder (2), displacement sensor (3), grating encoder (12), signal cable (13), data handler and computer (16), displacement sensor (3) is installed on displacement sensor installing holder (2), displacement sensor installing holder (2) is installed near main shaft (1) excircle place, it is provided with space between displacement sensor clamper (2) and main shaft (1) outline, grating encoder (12) is installed on main shaft (1) axle sleeve, grating encoder (12) and displacement sensor (3) are all connected with data handler by signal cable (13), data handler is connected with computer (16), displacement sensor installing holder (2) is the displacement sensor installing holder that can simultaneously install one or three displacement sensor.

As shown in Figure 2: the eccentric spindle rotation error measuring method that is removably installed of the present invention, comprises the following steps:

(1) displacement sensor clamper (2) is arranged on main shaft (1) excircle, and and main shaft (1) outline between there is space, displacement sensor (3) is arranged on displacement sensor clamper (2), regulates the distance between the survey head of displacement sensor (3) and main shaft (1) outline to correct position; Arranging main shaft (1), to return the displacement sensor sampling number that circles be N;

(2) drive shaft (1) rotates, taking a point of beginning of main shaft (1) outline as the first sampling point of displacement sensor (3), it is designated as A point, main shaft (1) revolves and turns around, displacement sensor (3) sampling exports N number of value, is designated as { S successively₀(0),S₀(1),S₀(2),��,S₀(N-1) }; And using the x-axis of displacement sensor (3) sensitive axes direction corresponding for initial for displacement sensor (3) first sampling point as surving coordinate system;

(3) by one of following three kinds of modes by sensor along main shaft (1) profile angle of rotation ��, this angle is the angle of first sensor and the 2nd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₁=�� N/2 ��, P₁For integer:

First kind of way: displacement sensor clamper (2) maintains static, utilize location function-driven main shaft (1) the angle of rotation �� of grating encoder (12), the second time first sampling point making displacement sensor (3) is the position relative to first sampling point distance alpha angle in step (2), is designated as B point;

2nd kind of mode: rotary displacement transducer clamper (2), displacement sensor clamper (1) is made to drive displacement sensor (3) along the same cross section angle of rotation �� of main shaft (1) profile, keep displacement sensor (3) axially not beat at main shaft (1) as far as possible, and displacement sensor (3) sensitive axes orientation of its axis main shaft (1) center of turning circle;

The third mode: displacement sensor clamper (2) is designed to install the shape of three displacement sensors (3) simultaneously, angle between first displacement sensor (3) installation position and the 2nd displacement sensor (3) installation position is designed to �� angle, angle between first displacement sensor (3) installation position and the 3rd displacement sensor (3) installation position is designed to �� angle, three displacement sensors (3) are installed the design of the angle between position and are met minimum harmonics restraint condition, three displacement sensors (3) are installed position and are designated as A respectively, B, C point, wherein A point is the initial sampling point of displacement sensor (3) in step (1), displacement sensor (3) is installed to B point from A point transfer, keep displacement sensor (3) sensitive axes orientation of its axis main shaft (1) center of turning circle as far as possible,

(4) using the new position of displacement sensor (3) as first sampling point, main shaft (1) revolves and turns around, and sensor sample exports N number of value, is designated as { S successively₁(0),S₁(1),S₁(2),��,S₁(N-1) };

(5) measuring process of repeating step (3) and (4), the difference is that displacement sensor (3) is �� along main shaft (1) profile angle of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₂=�� N/2 ��, P₂For integer, with the position that displacement sensor (3) is new, being designated as C point, as first sampling point, main shaft (1) revolves and turns around, and sensor sample exports N number of value, is designated as { S successively₂(0),S₂(1),S₂(2),��,S₂(N-1) };

(6) data are exported based on three groups of displacement sensors in step (2), (3), (4), (5), other value r (n) except an order harmonic component of main shaft (1) deviation from circular from can be obtained according to the frequency domain in three point method error separate principle or time domain method, n=1,2,3,, N-1;

(7) the output data S of three displacement sensors (3) is utilized₀(n)��S₁(n)��S₂(n) and deviation from circular from r (n) except an order harmonic component separated, Errors in Radial Rotation Error of Spindle can be obtained by solve linear equations by following algorithm:

$\left[\begin{array}{ccc}\cos (2\mathrm{\π}n/N)& \sin (2\mathrm{\π}n/N)& \cos (2\mathrm{\π}n/N)\\ \cos \left(2\mathrm{\π}\right(n+P_1)/N)& \sin \left(2\mathrm{\π}\right(n+p_1)/N)& \cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ \cos \left(2\mathrm{\π}\right(n+P_2)/N)& \sin \left(2\mathrm{\π}\right(n+p_2)/N)& \cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right)$

In formula: A₁��B₁For sine in surving coordinate system of Fourier's frequency domain one order harmonic component of deviation from circular from, cosine coefficient, the revolution error value that �� (n) is main shaft (1); The cycle of deviation from circular under polar coordinates system is 2 ��, for sampling number N, has: r (n+N)=r (n).

Embodiment 1:

As shown in Figure 1: displacement sensor (3) is arranged on displacement sensor clamper (2), the sensitive axes alignment main shaft outline edge of displacement sensor (3) or standard ball, after main shaft (1) rotating speed is stable, taking grating encoder (12) as triggering and signal for locating, main shaft (1) turns clockwise a circle, displacement sensor (3) gathers N number of displacement data, is designated as S₀(��). As shown in Figure 2, displacement sensor clamper (2) and displacement sensor (3) keep not moving, drive shaft (1) turns clockwise �� angle, as the first sampling point of displacement sensor (3), main shaft (1) turns clockwise a circle, displacement sensor (3) gathers N number of displacement data, is designated as S₁(��); Displacement sensor clamper (2) and displacement sensor (3) keep not moving, drive shaft (1) turns clockwise �� angle, as the first sampling point of displacement sensor (3), main shaft (1) turns clockwise a circle, displacement sensor (3) gathers N number of displacement data, is designated as S₂(��). Three displacement datas are respectively and export data S₀(��)��S₁(��)��S₂(��), wherein �� represents main shaft corner, and they contain deviation from circular from r (��), the standard ball of main shaft (1) and sensor installation is eccentric and spindle rotation error �� (��), have following relation:

$\left\{\begin{array}{c}{S}_0\left(\mathrm{\θ}\right)=r\left(\mathrm{\θ}\right)+x\left(\mathrm{\θ}\right)\\ S_1\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\α})+x\left(\mathrm{\θ}\right)cos\mathrm{\α}+y\left(\mathrm{\θ}\right)sin\mathrm{\α}\\ S_2\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\β})+x\left(\mathrm{\θ}\right)cos\mathrm{\β}+y\left(\mathrm{\θ}\right)sin\mathrm{\β}\end{array}\right.---\left(A\right)$

In formula: x (��) and y (��) is respectively the horizontal component of Errors in Radial Rotation Error of Spindle in surving coordinate system and vertical component.

Displacement sensor is exported data for (3) three times and carries out weighted sum, Rational choice weights coefficient c₁��c₂, revolution error can be separated from sensor reading. That is:

S (��)=S₀(��)+c₁S₁(��)+c₂S₂(��)=r (��)+c₁r(��+��)+c₂r(��+��)(B)

In formula (B), weights coefficient c₁��c₂Get:

$c_1=-\frac{sin\mathrm{\β}}{sin(\mathrm{\β}-\mathrm{\α})},c_2=\frac{sin\mathrm{\α}}{sin(\mathrm{\β}-\mathrm{\α})}---\left(C\right)$

The round shape error of axle system has footpath tropism and periodicity two main geometric properties, and the cycle is 2 ��. Formula (B) is made fourier transformation, it is possible to obtain the frequency domain character value of main shaft deviation from circular from:

$R\left(n\right)=S\left(n\right)/(1+c_1{e}^{j2{\mathrm{\πnp}}_1/N}+c_2{e}^{j2{\mathrm{\πnp}}_2/N})---\left(D\right)$

Upper formula (D) is done inverse Fourier transform, the time-domain value of deviation from circular from can be obtained, but no matter how how angle [alpha], �� design, fourier transformation one order harmonic component of deviation from circular from is always suppressed, this order harmonic component be displacement sensor install eccentric (if installation code ball simultaneously, then also comprising standard ball installs eccentric) cause, on measuring accuracy and the evaluation not impact of deviation from circular from, but this measuring error all enters spindle rotation error, affect the measuring accuracy of spindle rotation error. For this reason, based on No. three displacement sensor data, it is to construct following algorithm:

$\left\{\begin{array}{c}{S}_0\left(n\right)=A_1\cos (2\mathrm{\π}n/N)+B_1\sin (2\mathrm{\π}n/N)+r\left(n\right)+\mathrm{\δ}\left(n\right)\cos (2\mathrm{\π}n/N)\\ S_1\left(n\right)=A_1\cos \left(2\mathrm{\π}\right(n+p_1)/N)+B_1\sin \left(2\mathrm{\π}\right(n+p_1)/N)+r(n+p_1)+\mathrm{\δ}\left(n\right)\cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ S_2\left(n\right)=A_1\cos \left(2\mathrm{\π}\right(n+p_2)/N)+B_1\sin \left(2\mathrm{\π}\right(n+p_2)/N)+r(n+p_2)+\mathrm{\δ}\left(n\right)\cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right.---\left(E\right)$

I.e. system of linear equations:

$\left[\begin{array}{ccc}\cos (2\mathrm{\π}n/N)& \sin (2\mathrm{\π}n/N)& \cos (2\mathrm{\π}n/N)\\ \cos \left(2\mathrm{\π}\right(n+P_1)/N)& \sin \left(2\mathrm{\π}\right(n+p_1)/N)& \cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ \cos \left(2\mathrm{\π}\right(n+P_2)/N)& \sin \left(2\mathrm{\π}\right(n+p_2)/N)& \cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right)$

According to this system of linear equations, for n=1,2 ..., N, separates above-mentioned three rank systems of linear equations and can obtain isolating deviation from circular from and installing eccentric pure Errors in Radial Rotation Error of Spindle value.

Embodiment two:

As shown in Figure 1: displacement sensor (3) is arranged on displacement sensor clamper (2), sensitive axes alignment main shaft (1) the outline edge of displacement sensor (3) or standard ball, after main shaft (1) rotating speed is stable, taking grating encoder (12) as triggering and signal for locating, main shaft (1) turns clockwise a circle, displacement sensor gathers N number of displacement data, is designated as S₀(��). As shown in Figure 3: turn clockwise displacement sensor clamper (2) angle [alpha], as displacement sensor (3) first sampling point, main shaft (1) turns clockwise a circle, and displacement sensor (3) gathers N number of displacement data respectively, is designated as S₁(��). Then turn clockwise displacement sensor clamper (2) angle beta, as displacement sensor (3) first sampling point, main shaft (1) turns clockwise a circle, and displacement sensor (3) gathers N number of displacement data respectively, is designated as S₂(��). Three displacement datas are respectively and export data S₀(��)��S₁(��)��S₂(��), wherein �� represents main shaft (1) corner, they contain deviation from circular from r (��), the standard ball of main shaft (1) and bias installed by sensor and main shaft (1) turns round error delta (��), have following relation:

$\left\{\begin{array}{c}{S}_0\left(\mathrm{\θ}\right)=r\left(\mathrm{\θ}\right)+x\left(\mathrm{\θ}\right)\\ S_1\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\α})+x\left(\mathrm{\θ}\right)cos\mathrm{\α}+y\left(\mathrm{\θ}\right)sin\mathrm{\α}\\ S_2\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\β})+x\left(\mathrm{\θ}\right)cos\mathrm{\β}+y\left(\mathrm{\θ}\right)sin\mathrm{\β}\end{array}\right.---\left(a\right)$

In formula: x (��) and y (��) is respectively the horizontal component of Errors in Radial Rotation Error of Spindle in surving coordinate system and vertical component.

Displacement sensor is exported data for (3) three times and carries out weighted sum, Rational choice weights coefficient c₁��c₂, revolution error can be separated from sensor reading. That is:

S (��)=S₀(��)+c₁S₁(��)+c₂S₂(��)=r (��)+c₁r(��+��)+c₂r(��+��)(b)

In formula (b), weights coefficient c₁��c₂Get:

$c_1=-\frac{sin\mathrm{\β}}{sin(\mathrm{\β}-\mathrm{\α})},c_2=\frac{sin\mathrm{\α}}{sin(\mathrm{\β}-\mathrm{\α})}---\left(c\right)$

The round shape error of axle system has footpath tropism and periodicity two main geometric properties, and the cycle is 2 ��. Formula (b) is made fourier transformation, it is possible to obtain the frequency domain character value of main shaft deviation from circular from:

$R\left(n\right)=S\left(n\right)/(1+c_1{e}^{j2{\mathrm{\πnp}}_1/N}+c_2{e}^{j2{\mathrm{\πnp}}_2/N})---\left(d\right)$

Upper formula (d) is done inverse Fourier transform, the time-domain value of deviation from circular from can be obtained, but no matter how how angle [alpha], �� design, fourier transformation one order harmonic component of deviation from circular from is always suppressed, this order harmonic component installs eccentric causing, on measuring accuracy and the evaluation not impact of deviation from circular from, but this measuring error all enters main shaft (1) revolution error, affects the measuring accuracy of main shaft (1) revolution error. For this reason, based on No. three displacement sensor (3) data, following algorithm is built:

$\left\{\begin{array}{c}{S}_0\left(n\right)=A_1\cos (2\mathrm{\π}n/N)+B_1\sin (2\mathrm{\π}n/N)+r\left(n\right)+\mathrm{\δ}\left(n\right)\cos (2\mathrm{\π}n/N)\\ S_1\left(n\right)=A_1\cos \left(2\mathrm{\π}\right(n+p_1)/N)+B_1\sin \left(2\mathrm{\π}\right(n+p_1)/N)+r(n+p_1)+\mathrm{\δ}\left(n\right)\cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ S_2\left(n\right)=A_1\cos \left(2\mathrm{\π}\right(n+p_2)/N)+B_1\sin \left(2\mathrm{\π}\right(n+p_2)/N)+r(n+p_2)+\mathrm{\δ}\left(n\right)\cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right.---\left(e\right)$

I.e. system of linear equations:

$\left[\begin{array}{ccc}\cos (2\mathrm{\π}n/N)& \sin (2\mathrm{\π}n/N)& \cos (2\mathrm{\π}n/N)\\ \cos \left(2\mathrm{\π}\right(n+P_1)/N)& \sin \left(2\mathrm{\π}\right(n+p_1)/N)& \cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ \cos \left(2\mathrm{\π}\right(n+P_2)/N)& \sin \left(2\mathrm{\π}\right(n+p_2)/N)& \cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right)$

According to this system of linear equations, for n=1,2 ..., N, separates above-mentioned three rank systems of linear equations and can obtain isolating deviation from circular from and installing eccentric Errors in Radial Rotation Error of Spindle value.

Embodiment three:

As shown in Figure 1 and Figure 4: displacement sensor clamper (2) is designed to have the shape of three displacement sensor open holess, the angle design that three displacement sensors are installed between positions is respectively: the angle that position installed by first displacement sensor and the 2nd displacement sensor is installed between position is the angle that position installed by ��, first displacement sensor and the 3rd displacement sensor is installed between position is ��. First displacement sensor (3) is arranged on the position (11) of clamper, sensitive axes alignment main shaft outline edge or standard ball, after main shaft (1) rotating speed is stable, taking grating encoder (12) as triggering and signal for locating, main shaft (1) turns clockwise a circle, displacement sensor (3) gathers N number of displacement data, is designated as S₀(��). Displacement sensor (3) is taken off from displacement sensor clamper position (11) be in place successively respectively displacement sensor clamper position (9) and position (10), sensitive axes alignment main shaft outline edge or standard ball, main shaft (1) revolves successively respectively clockwise and turns around, and displacement sensor (3) gathers N number of displacement data respectively successively. Three displacement datas are respectively and export data S₀(��)��S₁(��)��S₂(��), wherein �� represents main shaft corner, and they contain deviation from circular from r (��), the standard ball of main shaft and sensor installation is eccentric and spindle rotation error �� (��), have following relation:

In formula: x (��) and y (��) is respectively the horizontal component of main shaft (1) Radial mixing in surving coordinate system and vertical component.

The data that export for three times of displacement sensor (3) are carried out weighted sum, Rational choice weights coefficient c₁��c₂, revolution error can be separated from sensor reading. That is:

S (��)=S₀(��)+c₁S₁(��)+c₂S₂(��)=r (��)+c₁r(��+��)+c₂r(��+��)��

Formula 2. in, weights coefficient c₁��c₂Get:

The round shape error of axle system has footpath tropism and periodicity two main geometric properties, and the cycle is 2 ��. 2. formula is made fourier transformation, it is possible to obtain the frequency domain character value of main shaft deviation from circular from:

4. upper formula is done inverse Fourier transform, the time-domain value of deviation from circular from can be obtained, but no matter how how angle [alpha], �� design, fourier transformation one order harmonic component of deviation from circular from is always suppressed, this order harmonic component installs eccentric causing, on measuring accuracy and the evaluation not impact of deviation from circular from, but this measuring error all enters main shaft (1) revolution error, affects the measuring accuracy of main shaft (1) revolution error. For this reason, based on No. three displacement sensor data, the following algorithm of component:

I.e. system of linear equations:

$\left[\begin{array}{ccc}\cos (2\mathrm{\π}n/N)& \sin (2\mathrm{\π}n/N)& \cos (2\mathrm{\π}n/N)\\ \cos \left(2\mathrm{\π}\right(n+P_1)/N)& \sin \left(2\mathrm{\π}\right(n+p_1)/N)& \cos \left(2\mathrm{\π}\right(n-p_1)/N)\\ \cos \left(2\mathrm{\π}\right(n+P_2)/N)& \sin \left(2\mathrm{\π}\right(n+p_2)/N)& \cos \left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right)$

According to this system of linear equations, for n=1,2 ..., N, separates above-mentioned three rank systems of linear equations and can obtain isolating deviation from circular from and installing eccentric Errors in Radial Rotation Error of Spindle value.

More than show and describe the ultimate principle of the present invention and the advantage of main feature and the present invention. The technician of the industry should understand; the present invention is not restricted to the described embodiments; the principle that the present invention is just described described in above-described embodiment and specification sheets; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention. The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (2)

1. the eccentric spindle rotation error measuring method that is removably installed, adopt the eccentric spindle rotation error measuring apparatus that is removably installed, the eccentric spindle rotation error measuring apparatus that is removably installed comprises displacement sensor installing holder, displacement sensor, grating encoder, signal cable, data acquisition unit, data handler and computer, institute's displacement sensors is installed on institute's displacement sensors installing holder, institute's displacement sensors installing holder is installed near main shaft excircle place, it is provided with space between institute's displacement sensors clamper and main shaft outline, described grating encoder is installed on main shaft sleeve, described grating encoder and institute's displacement sensors are all connected with described data handler by described signal cable, described data handler is connected with described computer, institute's displacement sensors installing holder is the displacement sensor installing holder that can simultaneously install one or three displacement sensor, it is characterized in that, comprise the following steps:

(1) displacement sensor clamper is arranged on main shaft excircle, and and main shaft outline between there is space, displacement sensor is arranged on displacement sensor clamper, regulates the distance between the survey head of displacement sensor and main shaft outline to correct position; Arranging the main shaft gyration displacement sensor sampling number of a week is N;

(2) drive shaft rotates, and taking a point of beginning of main shaft outline as the first sampling point of displacement sensor, is designated as A point, and main shaft revolves and turns around, and displacement sensor sampling exports N number of value, is designated as { S successively₀(0),S₀(1),S₀(2),��,S₀(N-1) }; And using the x-axis of displacement sensor sensitive axes direction corresponding for initial for displacement sensor first sampling point as surving coordinate system;

(3) in the following manner by displacement sensor along main shaft profile angle of rotation ��, this angle is the angle of first sensor and the 2nd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₁=�� N/2 ��, P₁For integer:

Mode: displacement sensor clamper maintains static, utilize the location function-driven main shaft angle of rotation �� of grating encoder, the second time first sampling point making displacement sensor is the position relative to first sampling point distance alpha angle in step (2), is designated as B point;

(4) using B point as first sampling point, main shaft revolves and turns around, and displacement sensor sampling exports N number of value, is designated as { S successively₁(0),S₁(1),S₁(2),��,S₁(N-1) };

(5) measuring process of repeating step (3) and (4), the difference is that displacement sensor is �� along main shaft profile angle of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separate principle, and its selection to be ensured that three point method harmonics restraint is minimum; Corresponding discrete value is P₂=�� N/2 ��, P₂For integer, with the position that displacement sensor is new, being designated as C point, as first sampling point, main shaft revolves and turns around, and sensor sample exports N number of value, is designated as { S successively₂(0),S₂(1),S₂(2),��,S₂(N-1) };

(6) data are exported based on three groups of displacement sensors in step (2), (3), (4), (5), other value r (n) except an order harmonic component of main shaft deviation from circular from can be obtained according to the frequency domain in three point method error separate principle or time domain method, n=1,2,3,, N-1;

(7) the output data S of three displacement sensors is utilized₀(n)��S₁(n)��S₂(n) and deviation from circular from r (n) except an order harmonic component separated, Errors in Radial Rotation Error of Spindle can be obtained by solve linear equations by following algorithm:

$\left[\begin{array}{ccc}cos(2\mathrm{\π}n/N)& sin(2\mathrm{\π}n/N)& cos(2\mathrm{\π}n/N)\\ cos\left(2\mathrm{\π}\right(n+P_1)/N)& sin\left(2\mathrm{\π}\right(n+p_1)/N)& cos\left(2\mathrm{\π}\right(n-p_1)/N)\\ cos\left(2\mathrm{\π}\right(n+P_2)/N)& sin\left(2\mathrm{\π}\right(n+p_2)/N)& cos\left(2\mathrm{\π}\right(n-p_2)/N)\end{array}\right]\·\left(\begin{array}{c}{A}_1\\ B_1\\ \mathrm{\δ}\left(n\right)\end{array}\right)=\left(\begin{array}{c}{S}_0\left(n\right)-r\left(n\right)\\ S_1\left(n\right)-r(n+p_1)\\ S_2\left(n\right)-r(n+p_2)\end{array}\right).$

2. the eccentric spindle rotation error measuring method that is removably installed according to claim 1, it is characterized in that: in the algorithm of described step (7), according to the three pure Radial mixing �� (��) of rank Solving Linear main shaft, �� (��) can be expressed as containing deviation from circular from one order harmonics A₁And B₁, containing deviation from circular from one order harmonics A₁Not containing B₁, containing deviation from circular from one order harmonics B₁Not containing A₁, all containing deviation from circular from one order harmonics A₁And B₁Totally four kinds of forms.