CN103983227A - Method and device for measuring main shaft rotary errors with capacity of installation eccentricity separation - Google Patents

Abstract

The invention discloses a method and device for measuring main shaft rotary errors with the capacity of installation eccentricity separation. The device comprises a displacement sensor installation clamping device, a displacement sensor, a grating encoder, a signal cable, a data processor and a computer. According to the measurement process, measurement is conducted by the displacement sensor according to three selectable modes with three different positions of the external profile of a main shaft serving as sampling starting points, other components, except for first-order harmonic waves, of main shaft roundness errors are obtained on the basis of the three-point method principle, secondary separation is conducted according to the provided algorithm, installation eccentricity is separated from the rotary errors, and therefore a pure rotary movement error value of the main shaft is obtained. On one hand, the roundness errors of the profile of the main shaft and eccentric errors of installation of a standard ball and the sensor are separated from the rotary movement errors of the main shaft, so that the separation operand is small. On the other hand, only one displacement sensor is adopted and measurement errors caused by a sensor performance difference because of three sensors adopted in a common three-point method error separation technology are avoided.

Description

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

Technical field

The present invention relates to a kind of exact instrument and manufacture measuring method, relate in particular to a kind of spindle rotation error measuring method and device that is removably installed eccentric.

Background technology

High-precision main shaft, air bearing are the critical components of the precision assemblies such as precision finishing machine, precision centrifuge, disc driver, high-accuracy electric rotating machine and steam turbine, for example, affecting in the many factors of precision optical machinery machining precision (: process hot error, structural failure, power chain error, spindle rotation error etc.), what part's machining errors was had to the most directly impact is main shaft gyration kinematic error, and its precision is the key of the processing of restriction precision optical machinery, high-precision rotary.Along with the machining precision of lathe reaches even nanometer scale of sub-micron, the part's machining errors that spindle rotation error causes becomes the major influence factors of restriction precision optical machinery machining precision.Correlation test shows that the part deviation from circular from of precision turning processing approximately has 30%～70%, caused, and the precision of lathe is higher by the spindle rotation error of lathe, and its main shaft gyration kinematic error shared ratio in various mismachining tolerances source is larger.

In the case of current spindle rotation error measuring principle and technological means can not fundamentally change, owing to cannot directly desirable axle center being measured, and must, by the measurement of standard ball, standard axle or main shaft outline being recorded indirectly to the gyration error size of main shaft, so just unavoidably can sneak into shape error, surface waviness, surfaceness and the standard ball of standard ball, standard axle itself or main shaft outline, the setting-up eccentricity equal error source of standard axle.Therefore, the key of main shaft gyration kinematic error measuring technique is that error separates.When measuring accuracy enters sub-micron even when nanometer scale, deviation from circular from, surfaceness and the setting-up eccentricity etc. that are blended in measurement data will highlight, and even can mask the gyration error that main shaft is small.Therefore must take effective method, gyration error is accurately separated from measurement result.Traditional motion of main shaft turn error measuring method is as adopted clock gauge to measure main shaft run-out, and measuring accuracy is very low, the deviation from circular from of main shaft can not be separated from gyration error.

At present, main shaft gyration kinematic error measuring method mainly contains reversal process, multistep processes and many gauge heads method.Respectively have relative merits although correlative study shows three kinds of methods, 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 from of part to detect, can not measure online, in real time the gyration error of axle system.Multipoint method mainly contains two-point method, three point method, four-point method etc. according to the number of sensor installation, since Japanese scholars Ozono in 1966 proposes after classical frequency domain Three Point Method for Error Separation of Roundness first, this technology has become at present one of the most widely used error separating technology.Its advantage be can on-line real time monitoring axle the gyration error of system.

In deviation from circular from based on three point method and spindle rotation error measuring technique, it is the key that improves error separation accuracy that the harmonic wave that how to reduce error separation suppresses, reduces measuring error transmission.The known main shaft gyration kinematic error measuring method based on Analyses of Error Separation Techniques mainly contains based on two kinds of frequency-domain and time-domains at present.Due to the humorous inhibition of single order, cause containing in spindle rotation error measurement result that standard ball setting-up eccentricity, three sensor axis intersection points do not overlap with the centre of gyration and the eccentric error introduced.For this problem, a kind of modified three point method of Chinese patent turn error, deviation from circular from computing method (patent application publication number: CN 103363921A, author Niu Baoliang, Zhang Rong) a kind of deviation from circular from and turn error separation method based on three point method proposed, its principal feature is to utilize translation and the weighted mean of three sensor output signals, and utilize frequency domain filtering, an order harmonic component of shape error is separated from deviation from circular from and turn error.In addition, the virtuous minister in ancient times of Xi'an University of Technology's thunder is in (the cylindricity Technology of Precision Measurement research separating based on error of its PhD dissertation, Xi'an University of Technology's PhD dissertation, 2007) in, adopt a kind of Time-Domain algorithm that deviation from circular from, spindle rotation error and setting-up eccentricity are separated.These methods are deepened and have been developed error separating technology, but still have the deficiencies such as computing complexity.And during the deviation from circular from based on three point method and spindle rotation error are measured, How to choose sampling number and error how to avoid three displacement transducer performance differences to introduce are the sub-micron problems that even nanometer scale high-acruracy survey should be considered.

Summary of the invention

Object of the present invention is just to provide in order to address the above problem a kind of bias and only need spindle rotation error measuring method and the device of a displacement transducer of being removably installed.

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

The spindle rotation error measurement mechanism that is removably installed eccentric of the present invention, comprise displacement transducer installing holder, displacement transducer, grating encoder, signal cable, data acquisition unit, data processor and computing machine, described displacement transducer is installed on described displacement transducer installing holder, described displacement transducer installing holder is installed near main shaft excircle place, between described displacement transducer clamper and main shaft outline, be provided with space, described grating encoder is installed on main shaft sleeve, described grating encoder is all connected with described data processor by described signal cable with described displacement transducer, described data processor is connected with described computing machine.

Particularly, described data processor is made up of data acquisition unit and signal conditioner; Described displacement transducer installing holder is the displacement transducer installing holder that one or three displacement transducer can be installed simultaneously.

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

(1) displacement transducer clamper is arranged on main shaft excircle, and and there is space between main shaft outline, displacement transducer is arranged on displacement transducer clamper, and the distance between gauge head and the main shaft outline of adjusting displacement transducer is to correct position; It is N that the main shaft gyration displacement transducer sampling number of a week is set;

(2) drive shaft rotation, the first sampling point (being designated as A point) taking an initial point of main shaft outline as displacement transducer, main shaft revolves and turns around, and N value of sensor sample output, is designated as { S successively ₀(0), S ₀(1), S ₀(2) ..., S ₀(N-1) }; And using sensor sensing direction of principal axis corresponding initial displacement transducer first sampling point as the x axle of measuring coordinate system;

(3) by one of following three kinds of modes by displacement transducer along main shaft profile anglec of rotation α, this angle is the angle of first sensor and second sensor in three point method error separation principle, its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₁=α N/2 π, P ₁for integer:

First kind of way: displacement transducer clamper maintains static, utilize the positioning function drive shaft anglec of rotation α of grating encoder, the first sampling point for the second time that makes displacement transducer is the position (being designated as B point) with respect to first sampling point distance alpha angle in step (2);

The second way: rotary displacement transducer clamper, make displacement transducer clamper drive displacement transducer along the same cross section of main shaft profile anglec of rotation α, holding position displacement sensor is not axially beated at main shaft as far as possible, and displacement transducer sensitive axes orientation of its axis main shaft rotation center;

The third mode: displacement transducer clamper is designed to install the shape of three displacement transducers simultaneously, angle between first displacement transducer installation site and second displacement transducer installation site is designed to α angle, angle between first displacement transducer installation site and the 3rd displacement transducer installation site is designed to β angle, angle design between three displacement transducer installation sites meets minimum harmonic wave rejection condition, three displacement transducer installation sites are designated as respectively A, B, C point, wherein A point is the initial sampled point of displacement transducer in step (1), displacement transducer is shifted and is installed to B point from A point, holding position displacement sensor sensitive axes orientation of its axis main shaft rotation center as far as possible,

(4), as first sampling point, main shaft revolves and turns around (to be designated as B point) using the new position of displacement transducer, and N value of displacement transducer sampling output, is designated as { S successively ₁(0), S ₁(1), S ₁(2) ..., S ₁(N-1) };

(5) measuring process of repeating step (3) and (4), different is that displacement transducer is β along the main shaft profile anglec of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separation principle, and its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₂=β N/2 π, P ₂for integer,, as first sampling point, main shaft revolves and turns around (to be designated as C point) using the new position of displacement transducer, and N value of sensor sample output, is designated as { S successively ₂(0), S ₂(1), S ₂(2) ..., S ₂(N-1) };

(6) three groups of displacement transducer output data based in step (2), (3), (4), (5), can obtain other value r (n) except an order harmonic component of main shaft deviation from circular from according to the frequency domain in three point method error separation principle or time domain approach, n=1,2,3,, N-1;

(7) utilize the output data S of three displacement transducers ₀(n), S ₁(n), S ₂(n) the deviation from circular from r (n) except an order harmonic component and separating, can obtain Errors in Radial Rotation Error of Spindle by solve linear equations by following algorithm:

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

Improve as one: in the algorithm of described step (7), according to three rank Solving Linear main shaft pure radially turn error δ (θ), δ (θ) can be expressed as containing deviation from circular from one order harmonics A ₁and B ₁, containing deviation from circular from one order harmonics A ₁not containing B ₁, containing deviation from circular from one order harmonics B ₁not containing A ₁, all containing deviation from circular from one order harmonics A ₁and B ₁totally four kinds of forms.

Beneficial effect of the present invention is:

The present invention is a kind of spindle rotation error measuring method and device that is removably installed eccentric, compared with prior art, one aspect of the present invention is separated the eccentric error of the deviation from circular from of main shaft profile, standard ball and installation of sensors from main shaft gyration kinematic error, and separation algorithm amount is little.On the other hand, only adopt a displacement transducer, the measuring error of having avoided adopting in common Analyses of Error Separation Techniques sensor performance difference that three displacement transducers bring to introduce, has the value of promoting the use of.

Brief description of the drawings

Fig. 1 is hardware configuration schematic diagram of the present invention;

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

Fig. 3 is displacement transducer installation site conversion regime one schematic diagram;

Fig. 4 is displacement transducer installation site conversion regime two schematic diagram;

Fig. 5 is displacement transducer installation site conversion regime three schematic diagram.

In figure: 1-main shaft, 2-displacement transducer installing holder, 3-displacement transducer, 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 sensor installation hole of 9-displacement transducer installing holder, the sensor installation hole of 10-displacement transducer installing holder, the sensor installation hole of 11-displacement transducer installing holder, 12-grating encoder, 13-signal cable, 14-data acquisition unit, 15-signal conditioner, 16-computing machine.

Embodiment

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

As shown in Figure 1: the spindle rotation error measurement mechanism that is removably installed eccentric of the present invention, comprise displacement transducer installing holder (2), displacement transducer (3), grating encoder (12), signal cable (13), data processor and computing machine (16), displacement transducer (3) is installed on displacement transducer installing holder (2), displacement transducer installing holder (2) is installed near main shaft (1) excircle place, between displacement transducer clamper (2) and main shaft (1) outline, be provided with space, grating encoder (12) is installed on main shaft (1) axle sleeve, grating encoder (12) is all connected with data processor by signal cable (13) with displacement transducer (3), data processor is connected with computing machine (16), data processor is made up of data acquisition unit (14) and signal conditioner (15), displacement transducer installing holder (2) is for can install the displacement transducer installing holder of one or three displacement transducer simultaneously.

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

(1) displacement transducer clamper (2) is arranged on main shaft (1) excircle, and and there is space between main shaft (1) outline, displacement transducer (3) is arranged on to displacement transducer clamper (2) upper, the distance between gauge head and main shaft (1) outline of adjusting displacement transducer (3) is to correct position; Main shaft (1) is set, and to return the displacement transducer sampling number that circles be N;

(2) drive shaft (1) rotation, first sampling point (being designated as A point) taking an initial point of main shaft (1) outline as displacement transducer (3), main shaft (1) revolves and turns around, N value of displacement transducer (3) sampling output, is designated as { S successively ₀(0), S ₀(1), S ₀(2) ..., S ₀(N-1) }; And using displacement transducer (3) sensitive axes direction corresponding initial displacement transducer (3) first sampling point as the x axle of measuring coordinate system;

(3) by one of following three kinds of modes by sensor along main shaft (1) profile anglec of rotation α, this angle is the angle of first sensor and second sensor in three point method error separation principle, and its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₁=α N/2 π, P ₁for integer:

First kind of way: displacement transducer clamper (2) maintains static, utilize positioning function drive shaft (1) anglec of rotation α of grating encoder (12), the first sampling point for the second time that makes displacement transducer (3) is the position (being designated as B point) with respect to first sampling point distance alpha angle in step (2);

The second way: rotary displacement transducer clamper (2), make displacement transducer clamper (1) drive displacement transducer (3) along main shaft (1) profile same cross section anglec of rotation α, holding position displacement sensor (3) is not axially beated at main shaft (1) as far as possible, and displacement transducer (3) sensitive axes orientation of its axis main shaft (1) centre of gyration;

The third mode: displacement transducer clamper (2) is designed to install the shape of three displacement transducers (3) simultaneously, angle between first displacement transducer (3) installation site and second displacement transducer (3) installation site is designed to α angle, angle between first displacement transducer (3) installation site and the 3rd displacement transducer (3) installation site is designed to β angle, angle design between three displacement transducers (3) installation site meets minimum harmonic wave rejection condition, three displacement transducers (3) installation site is designated as respectively A, B, C point, wherein A point is the initial sampled point of displacement transducer (3) in step (1), displacement transducer (3) is shifted and is installed to B point from A point, holding position displacement sensor (3) sensitive axes orientation of its axis main shaft (1) centre of gyration as far as possible,

(4) using the new position of displacement transducer (3) as first sampling point, main shaft (1) revolves and turns around, and N value of sensor sample output, is designated as { S successively ₁(0), S ₁(1), S ₁(2) ..., S ₁(N-1) };

(5) measuring process of repeating step (3) and (4), different is that displacement transducer (3) is β along main shaft (1) the profile anglec of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separation principle, and its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₂=β N/2 π, P ₂for integer, using the new position of displacement transducer (3) (being designated as C point) as first sampling point, main shaft (1) revolves and turns around, and N value of sensor sample output, is designated as { S successively ₂(0), S ₂(1), S ₂(2) ..., S ₂(N-1) };

(6) three groups of displacement transducer output data based in step (2), (3), (4), (5), can obtain other value r (n) except an order harmonic component of main shaft (1) deviation from circular from according to the frequency domain in three point method error separation principle or time domain approach, n=1,2,3,, N-1;

(7) utilize the output data S of three displacement transducers (3) ₀(n), S ₁(n), S ₂(n) the deviation from circular from r (n) except an order harmonic component and separating, can obtain Errors in Radial Rotation Error of Spindle by solve linear equations by following algorithm:

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

In formula: A ₁, B ₁for Fourier's frequency domain one order harmonic component of deviation from circular from is at sine, the cosine coefficient measured in coordinate system, δ (n) is the turn error value of main shaft (1); The cycle of deviation from circular under polar coordinate system is 2 π, for sampling number N, has: r (n+N)=r (n).

Embodiment 1:

As shown in Figure 1: displacement transducer (3) is arranged on displacement transducer clamper (2), the sensitive axes of displacement transducer (3) is aimed at main shaft outline edge or standard ball, after main shaft (1) stabilization of speed, taking grating encoder (12) as triggering and positioning signal, main shaft (1) dextrorotation is turned around, displacement transducer (3) gathers N displacement data, is designated as S ₀(θ).As shown in Figure 2, displacement transducer clamper (2) and displacement transducer (3) keep motionless, drive shaft (1) the α angle that turns clockwise, as the first sampling point of displacement transducer (3), main shaft (1) dextrorotation is turned around, displacement transducer (3) gathers N displacement data, is designated as S ₁(θ); Displacement transducer clamper (2) and displacement transducer (3) keep motionless, drive shaft (1) the β angle that turns clockwise, as the first sampling point of displacement transducer (3), main shaft (1) dextrorotation is turned around, displacement transducer (3) gathers N displacement data, is designated as S ₂(θ).Three times displacement data is respectively output data S ₀(θ), S ₁(θ), S ₂(θ), wherein θ represents angle of eccentricity, and deviation from circular from r (θ), standard ball and the installation of sensors bias that they have comprised main shaft (1) and spindle rotation error δ (θ), 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 (θ) and y (θ) are respectively Errors in Radial Rotation Error of Spindle in horizontal component and the vertical component measured in coordinate system.

Displacement transducer (3) three times output data are weighted and, Rational choice weights coefficient c ₁, c ₂, turn error can be separated from sensor reading.That is:

S(θ)＝S ₀(θ)+c ₁S ₁(θ)+c ₂S ₂(θ)＝r(θ)+c ₁r(θ+α)+c ₂r(θ+β) (B)

In formula (B), weights coefficient c1, c2 get:

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

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

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

Above formula (D) is done to inverse Fourier transform, can obtain the time thresholding of deviation from circular from, but no matter how how angle [alpha], β design, Fourier transform one order harmonic component of deviation from circular from is always suppressed, this order harmonic component is displacement transducer setting-up eccentricity (if while installation code ball, also comprise standard ball setting-up eccentricity) cause, on the measuring accuracy of deviation from circular from and not impact of evaluation, 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 transducer data, be constructed as follows algorithm:

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

Be system of linear equations:

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

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

Embodiment bis-:

As shown in Figure 1: displacement transducer (3) is arranged on displacement transducer clamper (2), the sensitive axes of displacement transducer (3) is aimed at main shaft (1) outline edge or standard ball, after main shaft (1) stabilization of speed, taking grating encoder (12) as triggering and positioning signal, main shaft (1) dextrorotation is turned around, displacement transducer gathers N displacement data, is designated as S ₀(θ).As shown in Figure 3: displacement transducer clamper (2) angle [alpha] turns clockwise, as displacement transducer (3) first sampling point, main shaft (1) dextrorotation is turned around, and displacement transducer (3) gathers respectively N displacement data, is designated as S ₁(θ).Then displacement transducer clamper (2) angle beta turns clockwise, as displacement transducer (3) first sampling point, main shaft (1) dextrorotation is turned around, and displacement transducer (3) gathers respectively N displacement data, is designated as S ₂(θ).Three times displacement data is respectively output data S ₀(θ), S ₁(θ), S ₂(θ), wherein θ represents main shaft (1) corner, deviation from circular from r (θ), standard ball and the installation of sensors bias that they have comprised main shaft (1) and main shaft (1) turn error δ (θ), 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 (θ) and y (θ) are respectively Errors in Radial Rotation Error of Spindle in horizontal component and the vertical component measured in coordinate system.

Displacement transducer (3) three times output data are weighted and, Rational choice weights coefficient c ₁, c ₂, turn error can be separated from sensor reading.That is:

S(θ)＝S ₀(θ)+c ₁S ₁(θ)+c ₂S ₂(θ)＝r(θ)+c ₁r(θ+α)+c ₂r(θ+β) (b)

In formula (b), weights coefficient c1, c2 get:

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

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

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

Above formula (d) is done to inverse Fourier transform, can obtain the time thresholding of deviation from circular from, but no matter how how angle [alpha], β design, Fourier transform one order harmonic component of deviation from circular from is always suppressed, this order harmonic component is that setting-up eccentricity causes, on the measuring accuracy of deviation from circular from and not impact of evaluation, but this measuring error all enters main shaft (1) turn error, affects the measuring accuracy of main shaft (1) turn error.For this reason, based on No. three displacement transducers (3) data, build following algorithm:

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

Be system of linear equations:

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

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

Embodiment tri-:

As shown in Figure 1 and Figure 4: displacement transducer clamper (2) is designed to the shape of three displacement transducer mounting holes, the angle design between three displacement transducer installation sites is respectively: the angle between first displacement transducer installation site and second displacement transducer installation site is that the angle between α, first displacement transducer installation site and the 3rd displacement transducer installation site is β.First displacement transducer (3) is arranged on the position (11) of clamper, sensitive axes is aimed at main shaft outline edge or standard ball, after main shaft (1) stabilization of speed, taking grating encoder (12) as triggering and positioning signal, main shaft (1) dextrorotation is turned around, displacement transducer (3) gathers N displacement data, is designated as S ₀(θ).Displacement transducer (3) is taken off to be in place successively respectively displacement sensor clamper position (9) and position (10) from displacement transducer clamper position (11), sensitive axes is aimed at main shaft outline edge or standard ball, main shaft (1) revolves and turns around successively respectively clockwise, and displacement transducer (3) gathers respectively N displacement data successively.Three times displacement data is respectively output data S ₀(θ), S ₁(θ), S ₂(θ), wherein θ represents angle of eccentricity, and deviation from circular from r (θ), standard ball and the installation of sensors bias that they have comprised main shaft and spindle rotation error δ (θ), have following relation:

$\left\{\begin{array}{c}{S}_0\left(\mathrm{\θ}\right)=r\left(\mathrm{\θ}\right)+x\left(\mathrm{\θ}\right)\\ S_1\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\α})+x\left(\mathrm{\θ}\right)\cos \mathrm{\α}+y\left(\mathrm{\θ}\right)\sin \mathrm{\α}\\ S_2\left(\mathrm{\θ}\right)=r(\mathrm{\θ}+\mathrm{\β})+x\left(\mathrm{\θ}\right)\cos \mathrm{\β}+y\left(\mathrm{\θ}\right)\sin \mathrm{\β}\end{array}\right.$ ①

In formula: x (θ) and y (θ) are respectively radially horizontal component and the vertical component of turn error in measurement coordinate system of main shaft (1).

Three times of displacement transducer (3) output data are weighted and, Rational choice weights coefficient c ₁, c ₂, turn error can be separated from sensor reading.That is:

S(θ)＝S ₀(θ)+c ₁S ₁(θ)+c ₂S ₂(θ)＝r(θ)+c ₁r(θ+α)+c ₂r(θ+β) ②

Formula 2. in, weights coefficient c ₁, c ₂get:

$c_1=\frac{\sin \mathrm{\β}}{\sin (\mathrm{\β}-\mathrm{\α})},c_2=\frac{\sin \mathrm{\α}}{\sin (\mathrm{\β}-\mathrm{\α})}$ ③

The round shape error of axle system has footpath tropism and two main geometric properties of periodicity, and the cycle is 2 π.2. formula is made to Fourier transform, can obtain the frequency domain character value of main shaft deviation from circular from:

$R\left(n\right)=S\left(n\right)/(1+c_1{e}^{j2\mathrm{\πn}{p}_1/N}+c_2{e}^{j2\mathrm{\πn}{p}_2/N})$ ④

4. above formula is done to inverse Fourier transform, can obtain the time thresholding of deviation from circular from, but no matter how how angle [alpha], β design, Fourier transform one order harmonic component of deviation from circular from is always suppressed, this order harmonic component is that setting-up eccentricity causes, on the measuring accuracy of deviation from circular from and not impact of evaluation, but this measuring error all enters main shaft (1) turn error, affects the measuring accuracy of main shaft (1) turn error.For this reason, based on No. three displacement transducer data, the following algorithm of member:

$\left\{\begin{array}{c}{S}_0\left(n\right)=A_1\cos (2\mathrm{\πn}/N)+B_1\sin (2\mathrm{\πn}/N)+r\left(n\right)+\mathrm{\δ}\left(n\right)\cos (2\mathrm{\πn}/N)\\ S_1\left(n\right)=A_1\cos (2\mathrm{\π}(n+p_1)/N)+B_1\sin (2\mathrm{\π}(n+p_1)/N)+r(n+p_1)+\mathrm{\δ}\left(n\right)\cos (2\mathrm{\π}(n-p_1)/N)\\ S_2\left(n\right)=A_1\cos (2\mathrm{\π}(n+p_2)/N)+B_1\sin (2\mathrm{\π}(n+p_2)/N)+r(n+p_2)+\mathrm{\δ}\left(n\right)\cos (2\mathrm{\π}(n-p_2)/N)\end{array}\right.$ ⑤

Be system of linear equations:

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

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

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that in above-described embodiment and instructions, describes just illustrates principle of the present invention; 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 (5)

1. a spindle rotation error measurement mechanism that is removably installed eccentric, it is characterized in that: comprise displacement transducer installing holder, displacement transducer, grating encoder, signal cable, data acquisition unit, data processor and computing machine, described displacement transducer is installed on described displacement transducer installing holder, described displacement transducer installing holder is installed near main shaft excircle place, between described displacement transducer clamper and main shaft outline, be provided with space, described grating encoder is installed on main shaft sleeve, described grating encoder is all connected with described data processor by described signal cable with described displacement transducer, described data processor is connected with described computing machine.

2. the spindle rotation error measurement mechanism that is removably installed eccentric according to claim 1, is characterized in that: described data processor is made up of data acquisition unit and signal conditioner.

3. the spindle rotation error measurement mechanism that is removably installed eccentric according to claim 1, is characterized in that: described displacement transducer installing holder is the displacement transducer installing holder that one or three displacement transducer can be installed simultaneously.

4. a spindle rotation error measuring method that is removably installed eccentric, is characterized in that, comprises the following steps:

(1) displacement transducer clamper is arranged on main shaft excircle, and and there is space between main shaft outline, displacement transducer is arranged on displacement transducer clamper, and the distance between gauge head and the main shaft outline of adjusting displacement transducer is to correct position; It is N that the main shaft gyration displacement transducer sampling number of a week is set;

(2) drive shaft rotation, the first sampling point (being designated as A point) taking an initial point of main shaft outline as displacement transducer, main shaft revolves and turns around, and N value of displacement transducer sampling output, is designated as { S successively ₀(0), S ₀(1), S ₀(2) ..., S ₀(N-1) }; And using displacement transducer sensitive axes direction corresponding initial displacement transducer first sampling point as the x axle of measuring coordinate system;

(3) by one of following three kinds of modes by displacement transducer along main shaft profile anglec of rotation α, this angle is the angle of first sensor and second sensor in three point method error separation principle, its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₁=α N/2 π, P ₁for integer:

First kind of way: displacement transducer clamper maintains static, utilize the positioning function drive shaft anglec of rotation α of grating encoder, the first sampling point for the second time that makes displacement transducer is the position (being designated as B point) with respect to first sampling point distance alpha angle in step (2);

The second way: rotary displacement transducer clamper, make displacement transducer clamper drive displacement transducer along the same cross section of main shaft profile anglec of rotation α, holding position displacement sensor is not axially beated at main shaft as far as possible, and displacement transducer sensitive axes orientation of its axis main shaft rotation center;

The third mode: displacement transducer clamper is designed to install the shape of three displacement transducers simultaneously, angle between first displacement transducer installation site and second displacement transducer installation site is designed to α angle, angle between first displacement transducer installation site and the 3rd displacement transducer installation site is designed to β angle, angle design between three displacement transducer installation sites meets minimum harmonic wave rejection condition, three displacement transducer installation sites are designated as respectively A, B, C point, wherein A point is the initial sampled point of displacement transducer in step (1), displacement transducer is shifted and is installed to B point from A point, holding position displacement sensor sensitive axes orientation of its axis main shaft rotation center as far as possible,

(4), as first sampling point, main shaft revolves and turns around (to be designated as B point) using the new position of displacement transducer, and N value of displacement transducer sampling output, is designated as { S successively ₁(0), S ₁(1), S ₁(2) ..., S ₁(N-1) };

(5) measuring process of repeating step (3) and (4), different is that displacement transducer is β along the main shaft profile anglec of rotation, this angle is the angle of first sensor and the 3rd sensor in three point method error separation principle, and its selection will ensure that three point method harmonic wave suppresses minimum; Corresponding discrete value is P ₂=β N/2 π, P ₂for integer,, as first sampling point, main shaft revolves and turns around (to be designated as C point) using the new position of displacement transducer, and N value of sensor sample output, is designated as { S successively ₂(0), S ₂(1), S ₂(2) ..., S ₂(N-1) };

(6) three groups of displacement transducer output data based in step (2), (3), (4), (5), can obtain other value r (n) except an order harmonic component of main shaft deviation from circular from according to the frequency domain in three point method error separation principle or time domain approach, n=1,2,3,, N-1;

(7) utilize the output data S of three displacement transducers ₀(n), S ₁(n), S ₂(n) the deviation from circular from r (n) except an order harmonic component and separating, can obtain Errors in Radial Rotation Error of Spindle by solve linear equations by following algorithm:

5. the spindle rotation error measuring method that is removably installed eccentric according to claim 4, it is characterized in that: in the algorithm of described step (7), according to three rank Solving Linear main shaft pure radially turn error δ (θ), δ (θ) can be expressed as containing deviation from circular from one order harmonics A ₁and B ₁, containing deviation from circular from one order harmonics A ₁not containing B ₁, containing deviation from circular from one order harmonics B ₁not containing A ₁, all containing deviation from circular from one order harmonics A ₁and B ₁totally four kinds of forms.