CN105043737A - Bearing retainer trajectory measurement method based on error separation technology - Google Patents

Abstract

The invention relates to a bearing retainer trajectory measurement method based on an error separation technology. The method comprises the steps that 1) the translation component of the axis of a retainer in X and Y directions in the radial plane of the retainer is measured; 2) according to the radius of the retainer and the translation component measured in the step 1), translation freedom degrees x and y of the retainer in X and Y directions are calculated; 3) a displacement sensor is set, and the position of the sensor in an X-Y coordinate system and the measurement value of the sensor are recorded, so as to calculate the shape error of the end face of the retainer; 4) according the position of the sensor in the X-Y coordinate system, the measurement value of the sensor and the shape error of the end face of the retainer in the step 3), rotation freedom degrees i and j of the retainer around X and Y axes and freedom degree z of axial moving are calculated; and 5) according to the freedom degrees x, y, z, I and j, the trajectory of the retainer is acquired. According to the measurement method provided by the invention, automatic measurement of the instability of the retainer is realized.

Description

A kind of retainer movement locus measuring method based on error separating technology

Technical field

The invention belongs to retainer Precision measurement field, be specifically related to a kind of retainer movement locus measuring method based on error separating technology.

Technical background

Retainer is as the important component part of bearing, the whether good turn error that directly can affect main bearing of its operation conditions, thus affect the machining precision of main shaft, therefore the research of high precision machine tool main bearing is needed to the ruuning situation of many-sided consideration retainer.Under the high precision working condition requirement conditions such as high-speed main shaft of machine tool; the normal revolution of bearing requires that retainer has very high stability; in impact for high-speed precise machine tool machining precision; main bearing retainer is as the pith of rotary part; its orbit of shaft center directly affects the turn error of whole main shaft, and then causes gross error to the machining precision of mechanical component.The orbit of shaft center of retainer is based on retainer as rotary machine part, to judging the online working order of machine, analyzes mechanical part processing precision, and pre-pyrometry, at a high speed, high-precision main shaft holds ruuning situation provides important evidence.

Error separating technology is a kind of advanced technology in Precision measurement field, the error of the error of measured workpiece and surveying instrument self can be separated by this technology, when fortune is measured in this way, measured workpiece is measurand and measuring basis, eliminate the impact of kinematic accuracy on measurand of surveying instrument self with this, thus improve the measuring accuracy of part.

At present a lot of progress is achieved to the research of retainer movement locus, some researcher is measured the turn error of retainer barycenter in sagittal plane by special measurement scheme, obtain the centroid trajectory figure under some different operating modes, but shorter mention is to the measurement of retainer axial instability.Usual centroid trajectory figure is X-Y scheme, to this instable judge also most its operation conditions of micro-judgment by people.Therefore, be badly in need of a kind of retainer movement locus measuring method, to realize the accurate measurement to retainer axial instability.

Summary of the invention

The invention provides a kind of retainer movement locus measuring method based on error separating technology, be intended to solve in prior art the defect leaning on the experience of people to pass judgment on retainer axial instability.

For solving the problem, retainer movement locus measuring method of the present invention comprises the steps:

1) retainer axle center is measured in retainer sagittal plane along translational component dX, the dY on X and Y-direction;

2) according to retainer radius R and translational component dX, dY, retainer translation freedoms x, y is in the x, y direction calculated;

3) displacement transducer is set, and the position (xA of recorded bit displacement sensor in X-Y coordinate system _m, yA _m), measurement value sensor dA _m, adopt error separating technology to isolate retainer end face shape error delta (θ _m), wherein, m represents the numbering of sensor, θ _mfor the angle from axle center to sensor measurement point direction and X-direction;

4) according to step 3) in displacement transducer position (xA _m, yA _m), measurement value sensor dA _mand retainer end face shape error delta (θ _m), calculate retainer and to have mercy on rotary freedom i, j of X and Y-axis and the degree of freedom z that collects together vertically;

5) be maintained according to x, y, z, these five degree of freedom of i, j the movement locus of frame.

Described step 2) in the computing formula of retainer translation freedoms x, y be in the x, y direction:

$x=\frac{dX}{2}-\frac{R}{2}+\frac{(R-dY)}{2}*\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}$

$\begin{array}{c}y=-(\frac{R^2}{2}+{\mathrm{dX}}^2+\frac{{\mathrm{dY}}^2}{2}+\frac{RdX}{2}-dY)/(R-dY)+\frac{(dX+R)}{2}\\ *\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}\end{array}$

Described step 4) in retainer have mercy on rotary freedom i, j of X and Y-axis and the computing formula of degree of freedom z of collecting together vertically as follows:

$\tan i\left(k\right)=\frac{\begin{array}{c}\left|{\mathrm{xA}}_0\right|*(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+\mathrm{\δ}\left(p_2\frac{2\mathrm{\π}}{N}\right)+{\mathrm{dA}}_1\left(k\right)-{\mathrm{dA}}_2\left(k\right))\\ +\left|{\mathrm{xA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}\left(p_2\frac{2\mathrm{\π}}{N}\right)-{\mathrm{dA}}_0\left(k\right)+{\mathrm{dA}}_2\left(k\right))\\ +\left|{\mathrm{xA}}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}\left(p_1\frac{2\mathrm{\π}}{N}\right)-{\mathrm{dA}}_0\left(k\right)+{\mathrm{dA}}_1\left(k\right))\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$\tan j\left(k\right)=\frac{-\left(\begin{array}{c}\left|{\mathrm{yA}}_0\right|*\left(\mathrm{\δ}\right(p_1\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-d{A}_1(k)+d{A}_2(k\left)\right)\\ +\left|{\mathrm{yA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-d{A}_0(k)+d{A}_2(k\left)\right)\\ +\left|y{A}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})-d{A}_0(k)+d{A}_1(k\left)\right)\end{array}\right)}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$z=\frac{\begin{array}{c}\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k\left)\right)\left(\right|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_1\left|\right)\\ +(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_1\left(k\right))\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_0\left|\right)\\ +(-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_2\left(k\right))\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_1|-|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_0\left|\right)\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

Wherein, p ₀=θ ₀* N/2 π, p ₁=θ ₁* N/2 π, p ₂=θ ₂* N/2 π, N are one week total numbers of sampled point, k=0 ... N-1.

Described step 1) in retainer sagittal plane arrange two for measuring the displacement transducer of dX and dY, the light that this displacement transducer sends intersects vertically mutually, intersection point is positioned on retainer axis.

Described step 3) in be provided with four displacement transducers, the plane that four displacement transducers are formed is parallel with retainer end face, and the light that sends of four displacement transducers and retainer axis being parallel, and drops on retainer.

Described retainer end face shape error delta (θ _m) computing formula as follows:

$\mathrm{\δ}\left(k\right)=F^{-1}\[\mathrm{\Δ}\left(n\right)\]=\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}\mathrm{\Δ}\left(n\right)e^{j\frac{2\mathrm{\π}n}{N}k}$

Wherein, k=0 ... N-1 is θ _mdiscrete value, Δ (n)=(n)/G (n), n=0 ... N-1, D (n)=C ₀δ (p ₀)+C ₁δ (p ₁)+C ₂δ (p ₂)+C ₃δ (p ₃), $G\left(n\right)=e^{{j2\mathrm{\πnp}}_0/N}+C_1{e}^{{j2\mathrm{\πnp}}_1/N}+C_2{e}^{{j2\mathrm{\πnp}}_2/N}+C_3{e}^{{j2\mathrm{\πnp}}_3/N},$ C ₀, C ₁, C ₂, C ₃for weighting coefficient, and C ₀, C ₁, C ₂, C ₃meet the following conditions:

$\left\{\begin{array}{c}{C}_0=1\\ C_0+C_1+C_2+C_3=0\\ -C_0\left|{\mathrm{sin\θ}}_0\right|+C_1\left|{\mathrm{sin\θ}}_1\right|+C_2\left|{\mathrm{sin\θ}}_2\right|+C_3\left|{\mathrm{sin\θ}}_3\right|=0\\ C_0\left|{\mathrm{cos\θ}}_0\right|+C_1\left|{\mathrm{cos\θ}}_1\right|-C_2\left|{\mathrm{cos\θ}}_2\right|+C_3\left|{\mathrm{cos\θ}}_3\right|=0\end{array}\right..$

The retainer movement locus measuring method that the present invention is based on error separating technology adopts error separating technology, the position of sensor is rationally set, measure retainer at radial displacement, axial displacement and end face shape error amount, calculate the rotary freedom of retainer movement track parameters X, Y, the displacement of Z-direction and X, Y-direction, thus construct the movement locus of retainer, achieve the instable automatic measurement of retainer.

Accompanying drawing explanation

Fig. 1 retainer movement locus measurement mechanism schematic diagram;

The axial measurement point geometric relationship figure of Fig. 2 retainer;

Fig. 3 retainer movement locus measuring system structural drawing;

Fig. 4 retainer track axial displacement display effect figure;

Fig. 5 retainer track radial displacement display effect figure;

Fig. 6 retainer axle center three-dimensional track figure;

The normal vector track of Fig. 7 retainer end face.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in detail.

First, the parameter affecting retainer movement locus is introduced.Retainer is a solid of revolution do not stressed in theory, retainer end face is set up radial orthogonal two coordinate axis X and Y, retainer axis sets up Z axis.In x and y direction, retainer has rotary freedom i and j of two translation freedoms x, y and X and Y-direction, and in z-direction, retainer has the rotary freedom k of degree of freedom z and the Z-direction of collecting together along Z axis.X, y, z, these five degree of freedom of i, j constitute the change of retainer track, and degree of freedom k is the fluctuation around Z axis rotating speed, does not cause change in displacement, does not form the change of retainer track.

Determine affect retainer movement locus five degree of freedom x, y, z, after i, j, provide the embodiment of rear a kind of survey calculation five degree of freedom methods below:

1) retainer is between Internal and external cycle, and for carrying out retainer sagittal plane and axial micro-displacement measurement, the present embodiment proposes measurement scheme as shown in Figure 1.By a lighter weight, have together with certain thickness cylinder connects firmly with retainer, the track of retainer is drawn the small space of Internal and external cycle.Two laser displacement sensors are arranged in sagittal plane, to measure the total displacement of retainer in sagittal plane, the light that two laser displacement sensors send is orthogonal and meet at a bit, and intersection point drops on axis, and sensor place plane is parallel with body end surface.

After setting the position of laser displacement sensor, retainer axle center translational component dX, dY along X and Y-axis can be measured.

2) according to the radius R of translational component dX, dY and retainer, retainer translation freedoms x, y is in the x, y direction calculated.

Be preferably as follows computing formula in the present embodiment to calculate retainer translation freedoms x, y in the x, y direction, but also can adopt other account forms of the prior art, will not enumerate here, formula is as follows:

$x=\frac{dX}{2}-\frac{R}{2}+\frac{(R-dY)}{2}*\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}---\left(1\right)$

$\begin{array}{c}y=-(\frac{R^2}{2}+{\mathrm{dX}}^2+\frac{{\mathrm{dY}}^2}{2}+\frac{RdX}{2}-dY)/(R-dY)+\frac{(dX+R)}{2}\\ *\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}\end{array}---\left(2\right)$

The displacement of the radial and axial measurement that retainer causes due to metamorphosis is ignored in computation process.Wherein dX, dY represent retainer axle center that sensor measurement the goes out translational component along X and Y-axis, and R is retainer radius.

3) displacement transducer is set, and the position (xA of recorded bit displacement sensor in X-Y coordinate system _m, yA _m), measurement value sensor dA _m, adopt error separating technology to isolate retainer end face shape error delta (θ _m), concrete steps are:

The present embodiment arranges four laser displacement sensors being positioned at same plane at axial direction, to measure the total displacement of retainer in axis and the deflection degree of freedom of axis, the plane at four laser displacement sensor places is parallel with body end surface, and the light that sends of four laser displacement sensors and retainer axis being parallel.Laser displacement sensor all adopts non-contacting Laser Displacement sensor.

Fig. 2 is the axial measurement point geometric relationship figure of retainer, and retainer movement track parameters i, j, z are calculated by following methods.Consider the pattern error of end face, the measured value of axial total displacement is made up of four parts: the end face shape error amount that axial play, the axial displacement caused around the rotary freedom of X-axis, the axial displacement caused around the rotary freedom of Y-axis, collection point place collect.The relational expression can deriving each degree of freedom displacement and measurement value sensor is thus as follows:

$\left\{\begin{array}{c}{\mathrm{dA}}_0=z-\left|{\mathrm{yA}}_0\right|*\tan \left(i\right)+\left|{\mathrm{xA}}_0\right|*\tan \left(i\right)+\mathrm{\δ}\left({\mathrm{\θ}}_0\right)\\ {\mathrm{dA}}_1=z+\left|{\mathrm{yA}}_1\right|*\tan \left(i\right)+\left|{\mathrm{xA}}_1\right|*\tan \left(i\right)+\mathrm{\δ}\left({\mathrm{\θ}}_1\right)\\ {\mathrm{dA}}_2=z+\left|{\mathrm{yA}}_2\right|*\tan \left(i\right)-\left|{\mathrm{xA}}_2\right|*\tan \left(i\right)+\mathrm{\δ}\left({\mathrm{\θ}}_2\right)\\ {\mathrm{dA}}_3=z+\left|{\mathrm{yA}}_3\right|*\tan \left(i\right)+\left|{\mathrm{xA}}_3\right|*\tan \left(i\right)+\mathrm{\δ}\left({\mathrm{\θ}}_3\right)\end{array}\right.---\left(3\right)$

Wherein dA _m(m gets 0,1,2,3, the sensor corresponding to expression) represents measurement value sensor, and z represents the displacement of the end face that the translation due to axis causes, namely along the degree of freedom that Z axis is collected together, and (xA _m, yA _m) represent the position of sensor position in XY coordinate, δ (θ _m) represent the end face shape error that corresponding sensor collects at sampling point position.

Below for solving end face shape error delta (θ _m) concrete mode:

Application error isolation technics solves formula (3), in order to isolate pattern error, formula (3) is multiplied by weights coefficient C respectively ₀, C ₁, C ₂, C ₃, try to achieve after derivation:

d _n(θ)＝C ₀δ(θ ₀)+C ₁δ(θ ₁)+C ₂δ(θ ₂)+C ₃δ(θ ₃)(4)

C ₀, C ₁, C ₂, C ₃meet the following conditions:

$\left\{\begin{array}{c}{C}_0=1\\ C_0+C_1+C_2+C_3=0\\ -C_0\left|{\mathrm{sin\θ}}_0\right|+C_1\left|{\mathrm{sin\θ}}_1\right|+C_2\left|{\mathrm{sin\θ}}_2\right|+C_3\left|{\mathrm{sin\θ}}_3\right|=0\\ C_0\left|{\mathrm{cos\θ}}_0\right|+C_1\left|{\mathrm{cos\θ}}_1\right|-C_2\left|{\mathrm{cos\θ}}_2\right|+C_3\left|{\mathrm{cos\θ}}_3\right|=0\end{array}\right.---\left(5\right)$

Formula (4) discretize is obtained:

d _n(k)＝C ₀δ(p ₀)+C ₁δ(p ₁)+C ₂δ(p ₂)+C ₃δ(p ₃)(6)

Wherein p ₀=θ ₀* N/2 π, p ₁=θ ₁* N/2 π, p ₂=θ ₂* N/2 π, p ₃=θ ₃* N/2 π, N are one week total numbers of sampled point.k＝0…N-1。

Discrete Fourier Transform is carried out to formula (6), can obtain:

Δ(n)＝D(n)/G(n)(7)

Wherein weight function is: $G\left(n\right)=e^{j2{\mathrm{\πnp}}_0/N}+C_1{e}^{j2{\mathrm{\πnp}}_1/N}+C_2{e}^{j2{\mathrm{\πnp}}_2/N}+C_3{e}^{j2{\mathrm{\πnp}}_3/N},$ D(n)＝C ₀δ(p ₀)+C ₁δ(p ₁)+C ₂δ(p ₂)+C ₃δ(p ₃)，n＝0…N-1

Discrete Fourier inverse transformation is carried out to formula (7), the pattern error of end face can be obtained:

$\mathrm{\δ}\left(k\right)=F^{-1}\[\mathrm{\Δ}\left(n\right)\]=\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}\mathrm{\Δ}\left(n\right)e^{j\frac{2\mathrm{\π}n}{N}k}---\left(8\right)$

During the pattern error of above-mentioned calculating end face, be provided with four displacement transducers, according to the position of four displacement transducers in X, Y, Z coordinate and the measured value of self, then adopt error separating technology to calculate δ (θ _m), as other embodiments, can also arrange 5,6 displacement transducers etc., the more computation process of displacement transducer just arranged is more complicated, and the present embodiment preferably arranges four displacement transducers to calculate the pattern error of end face.

4) according to step 3) in displacement transducer position (xA _m, yA _m), measurement value sensor dA _mand retainer end face shape error delta (θ _m), calculate retainer and to have mercy on rotary freedom i, j of X and Y-axis and the degree of freedom z that collects together vertically.

Be preferably as follows computing formula in the present embodiment to have mercy on rotary freedom i, j of X and Y-axis and the degree of freedom z that collects together vertically to calculate retainer, but also can adopt other account forms of the prior art, will not enumerate here, formula is as follows:

$\tan i\left(k\right)=\frac{\begin{array}{c}\left|{\mathrm{xA}}_0\right|*(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+\mathrm{\δ}\left(p_2\frac{2\mathrm{\π}}{N}\right)+{\mathrm{dA}}_1\left(k\right)-{\mathrm{dA}}_2\left(k\right))\\ +\left|{\mathrm{xA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}\left(p_2\frac{2\mathrm{\π}}{N}\right)-{\mathrm{dA}}_0\left(k\right)+{\mathrm{dA}}_2\left(k\right))\\ +\left|{\mathrm{xA}}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}\left(p_1\frac{2\mathrm{\π}}{N}\right)-{\mathrm{dA}}_0\left(k\right)+{\mathrm{dA}}_1\left(k\right))\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$\tan j\left(k\right)=\frac{-\left(\begin{array}{c}\left|{\mathrm{yA}}_0\right|*\left(\mathrm{\δ}\right(p_1\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-d{A}_1(k)+d{A}_2(k\left)\right)\\ +\left|{\mathrm{yA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-d{A}_0(k)+d{A}_2(k\left)\right)\\ +\left|y{A}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})-d{A}_0(k)+d{A}_1(k\left)\right)\end{array}\right)}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$z=\frac{\begin{array}{c}\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k\left)\right)\left(\right|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_1\left|\right)\\ +(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_1\left(k\right))\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_0\left|\right)\\ +(-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_2\left(k\right))\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_1|-|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_0\left|\right)\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

(9)

The measured value of three sensors is only use only in above-mentioned computing formula, the pattern error being about to the end face calculated is brought into can after in formula (3), there will be three unknown numbers, four equations, therefore only choose wherein three equations and just can solve z, tan (i), tan (j), choose first three equation in the present embodiment and solve.

5) go out retainer rotary freedom i, j in the x, y direction and axial displacement z of Z axis through above-mentioned formulae discovery, integrating step 1) in the survey calculation X, displacement x, the y in Y-direction that obtain, construct the movement locus of retainer.

Introduce a kind of retainer movement locus measuring system applying above-mentioned measuring method below, this system consists of the following components: measured bearing (with connecting firmly cylinder), non-contacting Laser Displacement sensor, data acquisition system (DAS), master system and software, and wherein data acquisition system (DAS) comprises the testing circuit supporting with non-contacting Laser Displacement sensor, acquisition module, CPU (central processing unit) and network communication module; Error separate algorithm, as the submodule of master system software, passes through programming realization.The structure of retainer movement locus measuring system as shown in Figure 3.

For a kind of single row roller bearing, will connect firmly cylinder by process after and measured bearing retainer be fixed together, selection measuring distance is 10mm, and spot diameter is 9 μm, the Spectral Confocal formula laser displacement sensor of resolution 16nm.According to aforesaid retainer movement locus measuring method, through measurement be maintained frame movement track parameters x, y, z, i, j error amount be respectively 0.18 μm, 0.14 μm, 0.09 μm, 0.33 °, 0.21 °.Respectively as shown in Figure 4, Figure 5, the normal vector track of axle center three-dimensional track and end face as shown in Figure 6, Figure 7 for the axial displacement of retainer track and the reconstruct of radial displacement Three-Dimensional Dynamic.

Be presented above concrete embodiment, but the present invention is not limited to described embodiment.Basic ideas of the present invention are above-mentioned basic scheme, and for those of ordinary skill in the art, according to instruction of the present invention, designing the model of various distortion, formula, parameter does not need to spend creative work.The change carried out embodiment without departing from the principles and spirit of the present invention, amendment, replacement and modification still fall within the scope of protection of the present invention.

Claims (6)

1., based on a retainer movement locus measuring method for error separating technology, it is characterized in that, comprise the steps:

1) retainer axle center is measured in retainer sagittal plane along translational component dX, the dY on X and Y-direction;

2) according to retainer radius R and translational component dX, dY, retainer translation freedoms x, y is in the x, y direction calculated;

3) displacement transducer is set, and the position (xA of recorded bit displacement sensor in X-Y coordinate system _m, yA _m), measurement value sensor dA _m, adopt error separating technology to isolate retainer end face shape error delta (θ _m), wherein, m represents the numbering of sensor, θ _mfor the angle from axle center to sensor measurement point direction and X-direction;

4) according to step 3) in displacement transducer position (xA _m, yA _m), measurement value sensor dA _mand retainer end face shape error delta (θ _m), calculate retainer and to have mercy on rotary freedom i, j of X and Y-axis and the degree of freedom z that collects together vertically;

5) be maintained according to x, y, z, these five degree of freedom of i, j the movement locus of frame.

2. the retainer movement locus measuring method based on error separating technology according to claim 1, is characterized in that, described step 2) in the computing formula of retainer translation freedoms x, y be in the x, y direction:

$x=\frac{dX}{2}-\frac{R}{2}+\frac{(R-dY)}{2}*\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}$

$\begin{array}{c}y=-(\frac{R^2}{2}+{\mathrm{dX}}^2+\frac{{\mathrm{dY}}^2}{2}+\frac{RdX}{2}-dY)/(R-dY)+\frac{(dX+R)}{2}\\ *\sqrt{\frac{2R^2+2RdX+2RdY-{\mathrm{dX}}^2-{\mathrm{dY}}^2}{2R^2-2RdX-2RdY+{\mathrm{dX}}^2+{\mathrm{dY}}^2}}\end{array}$

3. the retainer movement locus measuring method based on error separating technology according to claim 1, it is characterized in that, described step 4) in retainer have mercy on rotary freedom i, j of X and Y-axis and the computing formula of degree of freedom z of collecting together vertically as follows:

$\tan i\left(k\right)=\frac{\begin{array}{c}\left|{\mathrm{xA}}_0\right|*(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_1(k)-{\mathrm{dA}}_2(k\left)\right)\\ +\left|{\mathrm{xA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k)+{\mathrm{dA}}_2(k\left)\right)\\ +\left|{\mathrm{xA}}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k)+{\mathrm{dA}}_1(k\left)\right)\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$\tan i\left(k\right)=\frac{-\left(\begin{array}{c}\left|{\mathrm{yA}}_0\right|*\left(\mathrm{\δ}\right(p_1\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_1(k)+{\mathrm{dA}}_2(k\left)\right)\\ +\left|{\mathrm{yA}}_1\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k)+{\mathrm{dA}}_2(k\left)\right)\\ +\left|{\mathrm{yA}}_2\right|*\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k)+{\mathrm{dA}}_1(k\left)\right)\end{array}\right)}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

$z=\frac{\begin{array}{c}\left(\mathrm{\δ}\right(p_0\frac{2\mathrm{\π}}{N})-{\mathrm{dA}}_0(k\left)\right)\left(\right|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_1\left|\right)\\ +(-\mathrm{\δ}(p_1\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_1(k\left)\right)\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_2|-|{\mathrm{xA}}_2\left|\right|{\mathrm{yA}}_0\left|\right)\\ +(-\mathrm{\δ}(p_2\frac{2\mathrm{\π}}{N})+{\mathrm{dA}}_2(k\left)\right)\left(\right|{\mathrm{xA}}_0\left|\right|{\mathrm{yA}}_1|-|{\mathrm{xA}}_1\left|\right|{\mathrm{yA}}_0\left|\right)\end{array}}{\left|{\mathrm{xA}}_0\right|*\left(\right|{\mathrm{yA}}_1|+|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_1\right|*\left(\right|{\mathrm{yA}}_0|-|{\mathrm{yA}}_2\left|\right)+\left|{\mathrm{xA}}_2\right|*\left(\right|{\mathrm{yA}}_0|+|{\mathrm{yA}}_1\left|\right)}$

Wherein, p ₀=θ ₀* N/2 π, p ₁=θ ₁* N/2 π, p ₂=θ ₂* N/2 π, N are one week total numbers of sampled point, k=0 ... N-1.

4. the retainer movement locus measuring method based on error separating technology according to claim 1, it is characterized in that, described step 1) in retainer sagittal plane arrange two for measuring the displacement transducer of dX and dY, the light that this displacement transducer sends intersects vertically mutually, and intersection point is positioned on retainer axis.

5. the retainer movement locus measuring method based on error separating technology according to claim 1, it is characterized in that, described step 3) in be provided with four displacement transducers, the plane of four displacement transducer formations is parallel with retainer end face, and the light that sends of four displacement transducers and retainer axis being parallel, and drop on retainer.

6. the retainer movement locus measuring method based on error separating technology according to claim 1, is characterized in that, described retainer end face shape error delta (θ _m) computing formula as follows:

$\mathrm{\δ}\left(k\right)=F^{-1}\[\mathrm{\Δ}\left(n\right)\]=\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}\mathrm{\Δ}\left(n\right)e^{j\frac{2\mathrm{\π}n}{N}k}$

Wherein, k=0 ... N-1 is θ _mdiscrete value, Δ (n)=D (n)/G (n), n=0 ... N-1, D (n)=C ₀δ (p ₀)+C ₁δ (p ₁)+C ₂δ (p ₂)+C ₂δ (p ₃), $G\left(n\right)=e^{j2{\mathrm{\πnp}}_0/N}+C_1{e}^{j2{\mathrm{\πnp}}_1/N}+C_2{e}^{j2{\mathrm{\πnp}}_2/N}{C}_3{e}^{j2{\mathrm{\πnp}}_3/N},$ C ₀, C ₁, C ₂, C ₃for weighting coefficient, and C ₀, C ₁, C ₂, C ₃meet the following conditions:

$\left\{\begin{array}{c}{C}_0=1\\ C_0+C_1+C_2+c_3=0\\ -C_0\left|{\mathrm{sin\θ}}_0\right|+C_1\left|{\mathrm{sin\θ}}_1\right|+C_2\left|{\mathrm{sin\θ}}_2\right|+C_3\left|{\mathrm{sin\θ}}_3\right|=0\\ C_0\left|{\mathrm{cos\θ}}_0\right|+C_1\left|{\mathrm{cos\θ}}_1\right|-C_2\left|{\mathrm{cos\θ}}_2\right|+C_3\left|{\mathrm{cos\θ}}_3\right|=0\end{array}\right..$