CN104792276A - High-precision optical fiber detecting method for roller path curved surface in ball nut - Google Patents

Abstract

The invention discloses a high-precision optical fiber detecting method for a roller path curved surface in a ball nut. The high-precision optical fiber detecting method includes mounting the ball nut on a motion platform, and mounting an optical fiber sensor probe relative to the central axis of the ball nut by a helical angle of the ball nut; rotating the ball nut by the motion platform, enabling the optical fiber sensor probe to move linearly by one screw pitch of the ball nut by rotating the ball nut each circle, until the optical fiber sensor probe completes detection corresponding to the inner helical line along the roller path profile of the ball nut, modulating a mathematical model of the curved according to light strength of the optical fiber sensor probe, and calculating ranging data between the optical fiber sensor probe and the roller path profile; solving the actual internal helical line space coordinate according to the ranging data and transformation relation between the workpiece coordinate system of the ball nut and the normal section coordinate system of the roller path in the ball nut. Accordingly, machining accuracy of the ball nut can be completely analyzed and evaluated.

Description

A kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface

Technical field

The invention belongs to the crudy high precision test field of ball nut, relate to a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface.

Background technology

Ball guide screw nat, owing to having the features such as high-level efficiency, high precision, high rigidity, low cost, is widely used in the fields such as machinery, space flight, aviation, nuclear industry.High-speed precision ball screw pair is the critical component developing high-accuracy machinery, for high-precision ball-screw nut, the interior raceway face of its complexity considerably increases detection difficulty, traditional detection method has the methods such as fixed detector method, steel ball contact method and relative measurement, but these all belong to contact type measurement, the quick high accuracy that cannot meet ball guide screw nat detects.Realize the high precision test of ball nut, non-contact detecting can only be carried out to it.

The high precision test of ball nut, not only comprises the detection of the surface parameter (internal diameter, external diameter etc.) of nut, also comprises the detection of the interior curve surface of raceway parameter (helical pitch, lead angle etc.) of nut.And also more or less there are some shortcomings in the contactless measurement such as the machine vision of current emerging research and optical measurement, be in particular in: 1) accuracy of detection of machine vision depends on the shooting resolution of camera unduly, and the digital picture of two dimension have lost a large amount of Testing index, such as can not detect the situation and lead angle (i.e. helix angle) etc. of raceway in it, therefore cannot the crudy of thoroughly evaluating ball nut; 2) simple application fibre-optical probe detects the inside surface of ball nut, and because Fibre Optical Sensor limit by principle, for the situation that tested surface inclination angle is excessive, receive optical fiber and cannot receive reflected light, measurement result effectively cannot illustrate the precision of measured body.Therefore, in order to make up the deficiency of above present Research, need a kind of high-precision detecting method that can detect inner roller path of ball nut curved surface three-dimensional appearance newly.

Summary of the invention

The object of the present invention is to provide a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface.

For achieving the above object, present invention employs following technical scheme:

1) ball nut is installed on the moving platform, the central axis of fiber-optic sensor probe counter ball nut is installed with ball nut helix angle;

2) through step 1) after, utilize motion platform that ball nut is rotated, ball nut often rotates one week, fiber-optic sensor probe is moved linearly a ball nut pitch, until fiber-optic sensor probe completes detection along inner roller path of ball nut, then according to the mathematical model of fiber-optic sensor probe intensity modulation curve, the ranging data D={d between fiber-optic sensor probe and ball nut raceway profile is obtained ₁, d ₂..., d _n, n represents point distance measurement number;

3) the actual ball nut inner vortex volume coordinate recorded is tried to achieve according to the transformation relation of ranging data and ball nut workpiece coordinate system and inner roller path of ball nut normal section coordinate system.

Described fiber-optic sensor probe comprises symmetrically arranged two probe branches, angle is there is between two probe branches, each probe branch comprises several contact units, each contact unit comprises at least one three optical fiber pair, and described three optical fiber form by launching fiber and each reception optical fiber being symmetrically distributed in launching fiber both sides.

Each contact unit comprises a launching fiber and four root receiving fibers uniform around launching fiber.

The quantity of the contact unit of each probe branch upwards carries out respective extension with the raceway radius increase of detected ball nut at one-dimensional square.

For any one in contact unit three optical fiber pair, calculate described three optical fiber alignment two launch and accept optical fiber respectively to M corresponding separately, one of them launch and accept optical fiber is formed receiving optical fiber by the launching fiber of described three optical fiber alignments and of described three optical fiber alignments, and another launch and accept optical fiber is formed receiving optical fiber by another of the launching fiber of described three optical fiber alignments and described three optical fiber alignments:

M＝S ₁/S

(1) as | EK|≤p-r _rtime

S ₁＝0

(2) as | EK|>=p+r _rtime

S ₁＝πr _R ²

(3) p-r is worked as _r<|EK|<p+r _rtime, then must there are two symmetrical intersection points, if two intersecting point coordinates be respectively (q, y to the oval spot profile receiving plane place, fiber end face place with the corresponding fiber end face profile that receives through reflective surface in utilizing emitted light ₁), (q ,-y ₁), then

When $p-r_R<q\&le;\sqrt{{r_R}^2+p^2}$ Time

$S_1=2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})}+x_T\left]\right\}\mathrm{dy}$

When $\sqrt{{r_R}^2+p^2}<q<p+r_R$ Time

$S_1={{\mathrm{\&pi;r}}_R}^2-2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})}+x_T\left]\right\}\mathrm{dy}$

Wherein, S ₁it is the size that three optical fiber alignment one receives the capture area of fiber-optic RF; S be the launching fiber utilizing emitted light of three optical fiber alignments through reflective surface to receiving the ellipse light spot area at plane place, fiber end face place, p is the distance between axles of described launching fiber and described reception fiber-optic RF, r _rfor described reception fiber-optic RF fiber core radius, | EK| is the distance between described launching fiber center and the nearly launching fiber point of described reception fiber-optic RF end face, and a is the major semi-axis length of ellipse light spot, and b is the minor semi-axis length of ellipse light spot, x _t=| EK|-a;

So, the mathematical model of described fiber-optic sensor probe intensity modulation curve is expressed as the quotient function of described three optical fiber alignment two launch and accept optical fiber to M corresponding separately.

Described step 3) in, try to achieve the actual ball nut inner vortex volume coordinate recorded according to formula (23), formula (24) and formula (25):

(x',y',z')＝(x,y,z)+(Δd _x,Δd _y,Δd _z) (23)

$({\mathrm{\&Delta;d}}_x,{\mathrm{\&Delta;d}}_y,{\mathrm{\&Delta;d}}_z,1)=({\mathrm{\&Delta;d}}_{x_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{y_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{z_{\mathrm{nor}}},1)\&CenterDot;T^{-1}---\left(24\right)$

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}& 0\\ 0& -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& 0\\ 0& 0& 0& 0\end{array}\right]---\left(25\right)$

Wherein, (x, y, z) is inner vortex theoretical space coordinate in described workpiece coordinate system, and (x', y', z') is the actual volume coordinate recorded of inner vortex in described workpiece coordinate system, for Δ d _iprojection variation length on the coordinate system of inner roller path of ball nut normal section, i=1 ... n, { Δ d _i}={ 0, Δ d ₂..., Δ d _n}={ d ₁-d ₁, d ₂-d ₁..., d _n-d ₁, (Δ d _x, Δ d _y, Δ d _z) be Δ d _itransform to the length varying value on corresponding each change in coordinate axis direction in described workpiece coordinate system, β represents ball nut helix angle.

Beneficial effect of the present invention is embodied in:

The present invention is first by the detection of fiberoptic probe applications in inner roller path of ball nut normal section, establish the mathematical model of this fibre-optical probe intensity modulation curve, analyze the mutual transformation relation of workpiece coordinate system and inner roller path of ball nut normal section coordinate system, give the high-precision optical fiber detection method towards inner roller path of ball nut curved surface on this basis.The present invention ensures that principle the normal direction of fibre-optical probe and measured surface detects relation all the time, and can detect the three dimensional topography of inner roller path of ball nut curved surface, and testing result may be used for the machining precision that ball nut is evaluated in multianalysis.

Accompanying drawing explanation

Fig. 1 is ball nut body crudy detection system schematic diagram; Wherein, 1 is fibre-optical probe, and 2 is tested ball nut, and 3 is motion platform;

Fig. 2 is detection method and the sonde configuration figure of system; Wherein, (a) is probe installation and mode of motion, and (b) is the partial enlargement of (a), and (c) is the structure of probe branch; 4 is ball;

Fig. 3 is detection system process flow diagram;

Fig. 4 is detection system sonde configuration figure (a) and RIM-FOS fundamental diagram (b); D ₁for a sampled point of contact unit,

Fig. 5 is fibre-optical probe end face optical field distribution situation map;

Fig. 6 (a) is the relative position relation figure between workpiece coordinate system and inner roller path of ball nut normal section coordinate system; Fig. 6 (b) is inner roller path of ball nut normal section schematic shapes;

Fig. 7 is the influence curve figure that measured surface angle of inclination changes to intensity modulation characteristic;

Fig. 8 is the influence curve figure of measured surface generation lateral excursion to intensity modulation characteristic;

Fig. 9 is that measured surface changes the influence curve figure to intensity modulation characteristic with probe launching fiber end face distance.

Embodiment

Below in conjunction with drawings and Examples, the present invention is elaborated.

(1) develop a set of high-precision optical fiber detection platform towards inner roller path of ball nut curved surface, and describe composition and the detection mode of this platform in detail;

(2) then, based on the pattern feature of inner roller path of ball nut curved surface, devise a kind of special expandable type fiber-optic sensor probe, and establish the mathematical model of the intensity modulation curve of contact unit in this probe;

(3) last, the feature in conjunction with tested inner roller path of ball nut gives inner roller path of ball nut Curved dectection method.

Described step (1) comprises following particular content:

1) system towards the high-precision optical fiber detection platform of inner roller path of ball nut curved surface forms

Towards the high-precision optical fiber detection platform of inner roller path of ball nut curved surface primarily of motion platform, fibre-optical probe, data acquisition module, control module and computing machine form, as shown in Figure 1.Ball nut is placed on motion platform, the data that fibre-optical probe collects are transferred to computing machine by data acquisition module, the signal that computer disposal obtains also controls the motion of fibre-optical probe and measured piece (i.e. ball nut) in real time by control module, after completing whole data acquisition, computing machine carries out Treatment Analysis to data, obtain the physical location vector of many group inner vortexs in raceway, thus judge whether the machining precision of ball nut body meets the requirements.

2) towards the detection method of the high-precision optical fiber detection platform of inner roller path of ball nut curved surface

Ball guide screw nat is using ball as rolling body between leading screw and nut, and its raceway profile is divided into single circular arc type and bicircular arcs type, and its static acceptance index of ball guide screw nat is determined by deviation of stroke and run-out tolerance.Ball guide screw nat is in motion process, mainly change sliding friction into rolling friction by ball and raceway contact, the precision height of the raceway inside surface near nut and ball contact point determines the precision height of ball guide screw nat, for in the actual testing process of ball nut, the main raceway surface-type feature detecting surface of contact part.

As shown in Fig. 2 (a), in known ball nut body raceway normal section parameter, nut pitch P h and helixangleβ prerequisite under, the central axis of fibre-optical probe opposing nut is installed with helixangleβ, and measuring process is as Fig. 3.The CA1 ' of fibre-optical probe aims at CA1 and CA2 region on interior raceway normal section respectively with CA2 ' part, and starts image data.Ball nut often rotates one week, fibre-optical probe moves linearly a pitch inwards, after probe has detected along a certain bar inner vortex of ball nut, computing machine, by carrying out corresponding algorithm calculating after these data analyses, can evaluate the machining precision of ball nut.

Described step (2) comprises following particular content:

1) based on the pattern feature of inner roller path of ball nut curved surface, a kind of special expandable type fibre-optical probe is designed.Probe, according to the feature of inner roller path of ball nut curved surface and the metering system of detection platform, is designed to symmetrical structure, can detects two cambered surface precision of bicircular arcs type raceway profile simultaneously.Meanwhile, the optical fiber in probe is made up of contact unit, and each contact unit comprises a launching fiber and four uniform root receiving fibers around.

See Fig. 2 (b), the measuring junction of probe is made up of the CA1 ' of symmetry and CA2 ', CA1 and CA2 region (reflecting surface) on the just internal raceway normal section of end face difference of CA1 ' and CA2 ', Liang Ge branch (CA1 ' and CA2 ') there is identical composition, TF1, TF2, TF3 tri-launching fibers are had in CA1 ', TF4, TF5, TF6 tri-launching fibers are had in corresponding CA2 ', be uniformly distributed four root receiving fibers around each root launching fiber, be respectively used to the reflected light of reception four reflection directions.Due to probe Liang Ge branch CA1 ' and CA2 ' there is symmetry, with CA1 ' for research object.As Fig. 2 (c), CA1 ' branch is made up of contact unit 1, contact unit 2 and contact unit 3.Each contact unit comprises a launching fiber and four uniform root receiving fibers around, and the quantity of contact unit can increase with the raceway radius of detected ball nut body and upwards carry out respective extension at one-dimensional square, has ductility.The launching fiber TF of fibre-optical probe is sent laser, and returns to be launched through reflective surface process that the institute of equally distributed four root receiving fiber RF around optical fiber TF receives image data and be called that one gathers and walks.By TF1 and TF4 corresponding in CA1 ' and CA2 ', TF2 and TF5, and TF3 and TF6 completes the process gathering step respectively and is called collection sequence.Fibre-optical probe often completes one and gathers the ranging data that sequence will return 6 points (respectively corresponding six helixes).

Because inner roller path of ball nut profile is three-dimension curved surface, actual detected value is subject to the impact of reflecting surface in pair of orthogonal direction inclination angle, therefore, contact unit is designed to two groups of orthogonal three optical fiber to structure, three optical fiber alignments comprise a launching fiber and are positioned at the reception optical fiber of symmetry of both sides.

2) mathematical model of the intensity modulation curve of contact unit is established

Above-mentioned fibre-optical probe is based on optical intensity modulation type Fibre Optical Sensor (RIM-FOS, Reflective IntensityModulated Fiber Optic Sensor), its principle of work is as shown in Fig. 4 (a), the light that light source LD sends is irradiated to reflecting surface through launching fiber TF, the light be reflected back is by receiving fiber-optic RF, and optical signal transmission is to photoelectric detector PD.The intensity modulation function M of RIM-FOS receives luminous power that optical fiber receives (or luminous flux phi _r) luminous power (or the luminous flux phi that sends with launching fiber _t) ratio, its reflection sensor characteristic.For RIM-FOS, intensity modulation function can be write again as the function of functions about optical fiber parameter, sensor construction parameter and reflecting surface parameter.Wherein:

(1) optical fiber parameter comprises transmitting, receives fiber core radius r _t, r _r, and numerical aperture NA _t, NA _rdeng;

(2) sensor construction parameter comprises launching fiber and surrounding any one receives optical fiber that optical fiber forms to distance between axles p etc.;

(3) reflecting surface parameter comprises reflector shape factor R _c, reflecting surface angle of inclination γ, reflecting surface lateral excursion distance l, distance d, reflective surface rate δ etc. between launching fiber end face and tested physical surface.

$M=\frac{{\mathrm{\&Phi;}}_R}{{\mathrm{\&Phi;}}_T}=f(r_T,{\mathrm{NA}}_T,r_R,{\mathrm{NA}}_R,p,d,l,\mathrm{\&gamma;},R_c,\mathrm{\&delta;},k)---\left(1\right)$

Wherein k represents the comprehensive of other X factors comprising loss etc.When sensor probe configuration is determined, according to the detection mode of system, the principal element affecting intensity modulation function M derives from reflecting surface angle of inclination γ, reflecting surface lateral excursion distance (i.e. the horizontal range at reflecting surface deflection optical fiber probe emergent light center) l and reflector shape factor R _c, for the tested ball nut that is determined, in it, raceway normal section radius is constant, and emergent light is irradiated to the spot radius r on cross section _bmuch smaller than its normal section radius (i.e. reflector shape factor R _c), work as R _c/ r _bcan by R when>=50 _cregard an infinitely large quantity as, now reflecting surface is equivalent to plane reflection.For simplifying computation process, be reflecting surface by model simplification be planar environment.

As shown in Fig. 4 (b), launching fiber of popping one's head in theory is just to raceway concave bottom, and two receive optical fiber is symmetrically distributed in launching fiber TF both sides for receiving the light of reflective surface.Because fibre-optical probe and reflecting surface all have symmetry, the light intensity only received using RF1 is below as analytic target, and suppose that reflecting surface moves as just to the direction that RF1 is close, the direction towards RF1 just rotates to be.

Suppose reflecting surface isotropy, and it is non-selective to have spectrum, then the picture that the luminous flux received by RF1 is equivalent to TF sends and is multiplied by the reflection coefficient of reflecting surface by the luminous flux that RF1 receives.Therefore, expect the intensity modulation function M that optical fiber is right, be uniformly distributed the prerequisite of hypothesis at launching fiber output intensity under, a demand obtains the ratio of the light-receiving area of RF1 and the projected area of TF, then is multiplied by the reflectivity of reflecting surface.To receive the light field of fiber end face place plane for analytic target, the propagation of light field regarded as in whole process and be uniformly distributed superposing of distributing with round platform, the luminous flux now in unit area is equal, therefore has:

M1＝Φ ₁/Φ＝S ₁/S (2)

S in formula ₁for the size of RF1 capture area; S is that utilizing emitted light is through the facula area of reflective surface to reception plane place, fiber end face place; Φ ₁for receiving the luminous flux that fiber end face reception optical fiber receives; Φ receives the total luminous flux of fiber end face place planar lightfield.Calculate S step by step below ₁.Had by the relation in Fig. 4:

θ ₁＝arcsin(NA _T)

|AE|＝r _T/tanθ ₁

|BD|＝l·tanγ

|AD|＝r _T·cotθ ₁+d+l·tanγ (3)

|QP|＝d+(l-r _T)·tanγ

|EK|＝|QK|+r _T

|JK|＝|QK|+|JG|+2r _T

In Δ QPN, had by sine:

$\frac{\left|\mathrm{QP}\right|}{\sin (\frac{\mathrm{\&pi;}}{2}-{\mathrm{\&theta;}}_1+\mathrm{\&gamma;})}=\frac{\left|\mathrm{QN}\right|}{\sin (\frac{\mathrm{\&pi;}}{2}-\mathrm{\&gamma;})}---\left(4\right)$

In Δ QNK, had by sine:

$\frac{\left|\mathrm{QN}\right|}{\sin (\frac{\mathrm{\&pi;}}{2}-{\mathrm{\&theta;}}_1+\mathrm{\&gamma;})}=\frac{\left|\mathrm{QK}\right|}{\sin ({2\mathrm{\&theta;}}_1-2\mathrm{\&gamma;})}---\left(5\right)$

Obtained by formula (3), formula (4) and formula (5):

$\left|\mathrm{QK}\right|=\frac{2\sin ({\mathrm{\&theta;}}_1-\mathrm{\&gamma;})\cos \left(\mathrm{\&gamma;}\right)}{\cos ({\mathrm{\&theta;}}_1-2\mathrm{\&gamma;})}[d+(l-r_T)\tan \left(\mathrm{\&gamma;}\right)]---\left(6\right)$

In like manner, in reception fiber-optic RF 2

$\left|\mathrm{JG}\right|=\frac{2\sin ({\mathrm{\&theta;}}_1+\mathrm{\&gamma;})\sin (\frac{\mathrm{\&pi;}}{2}+\mathrm{\&gamma;})}{\cos ({\mathrm{\&theta;}}_1+2\mathrm{\&gamma;})}[d+(l+r_T)\tan \left(\mathrm{\&gamma;}\right)]---\left(7\right)$

The fibre-optical probe that three optical fiber are right, the light that middle launching fiber TF sends, after reflective surface, arrives again that fibre-optical probe is received fiber-optic RF 1, RF2 received.The optical field distribution of fibre-optical probe end face as shown in Figure 5.

In Figure 5, elliptic equation is:

$\frac{{(x-x_T)}^2}{a^2}+\frac{y^2}{b^2}=1---\left(8\right)$

The little equation of a circle that RF1 and RF2 is corresponding is respectively:

(x-p) ²+y ²＝r _R ²

(x+p) ²+y ²＝r _R ²(9)

Wherein:

a＝|JK|/2

b≈2d·tanθ ₁+r _T(10)

x _T＝|EK|-a

S＝πab

In formula, a, b represent major semi-axis length and the minor semi-axis length of ellipse light spot (namely utilizing emitted light is through the hot spot of reflective surface to reception plane place, fiber end face place) respectively; θ ₁for the numerical aperture angle (NA of launching fiber _t=sin θ ₁).According to | the length of EK| and the size of p, can be divided into following several situation:

(1) as | EK|≤p-r _rtime

S ₁＝0 (11)

(2) as | EK|>=p+r _rtime

S ₁＝πr _R ²(12)

(3) p-r is worked as _r<|EK|<p+r _rtime, then must there are two symmetrical intersection points, if two intersecting point coordinates are respectively (q, y in oval spot profile and roundlet (receiving the end profile of optical fiber) ₁), (q ,-y ₁)

When $p-r_R<q\&le;\sqrt{{r_R}^2+p^2}$ Time

$S_1=2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})}+x_T\left]\right\}\mathrm{dy}---\left(13\right)$

When $\sqrt{{r_R}^2+p^2}<q<p+r_R$ Time

$S_1={{\mathrm{\&pi;r}}_R}^2-2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})}+x_T\left]\right\}\mathrm{dy}---\left(14\right)$

Formula (3)-formula (14) is substituted into formula (2), the intensity modulation function M1 receiving fiber-optic RF 1 can be obtained, in like manner can calculate the intensity modulation function M2 (M2=S receiving fiber-optic RF 2 ₂/ S).The intensity modulation function of definition fibre-optical probe is:

$M=\frac{M1}{M2}---\left(15\right)$

Described step (3) comprises following idiographic flow:

Workpiece coordinate system: with the axis of ball nut for Z axis is Y-axis perpendicular to the arbitrary line in the face of Z axis, by right-handed Cartesian coordinate system principle determination X-axis, with the intersection point of ball nut end face and Z axis for initial point O.

Inner roller path of ball nut normal section coordinate system: with X-axis in workpiece coordinate system for inner roller path of ball nut normal section coordinate system X _naxle, with initial point O along X-axis positive dirction translation d _m/ 2 distances are inner roller path of ball nut normal section coordinate origin O _n, cross O _npoint also becomes the direction of β angle to be inner roller path of ball nut normal section coordinate system Z with Z axis _naxle, determines Y by right-handed Cartesian coordinate system principle _naxle.

1) inner roller path of ball nut surface equation modeling

Fig. 6 (b) is the normal section schematic shapes of ball nut raceway, R in figure _gfor raceway radius, e is eccentric throw, and h is location parameter.Normal plane O _nx _nz _ncan be calculated by following formula with the angle (β) of ball nut axis:

$\mathrm{\&beta;}=\arctan \frac{P}{{\mathrm{\&pi;d}}_m}---\left(16\right)$

In formula, d _m---ball nut nominal diameter; P---ball nut helical pitch.

Can learn that ball nut normal direction bicircular arcs profile is a space curve in Oxyz coordinate by coordinate conversion relation, can be expressed as

$\left\{\begin{array}{c}{x}_0=R_G\sin \mathrm{\&alpha;}-h+d_m/2\\ y_0=-(R_G\cos \mathrm{\&alpha;}-e)\sin \mathrm{\&beta;}\\ z_0=(R_G\cos \mathrm{\&alpha;}-e)\cos \mathrm{\&beta;}\end{array}\right.---\left(17\right)$

In formula, x ₀, y ₀, z ₀---the raceway normal section coordinate of point in workpiece coordinate system in shape; α---parameter, h---location parameter.

arccos(e/R _G)≤α≤arcsin((2h+d _g-d _m)/R _G) (18)

In formula, d _g---the large footpath of ball nut.

The vector representation form of this space curve is:

r＝r(δ)＝x ₀i+y ₀j+z ₀k (19)

In formula, i, j, k---workpiece coordinate system unit vector, this vector can be expressed as follows around spin the move curved surface (i.e. raceway inner helical surface) that formed of ball nut axis:

r＝(x ₀cosθ-y ₀sinθ)i+(x ₀sinθ+y ₀cosθ)j+(z ₀+sθ)k (20)

In formula, s---the distance risen under ball nut unit angle, s=P/2 π; θ---the angle (angle turned over around nut axis of namely popping one's head in) that ball nut normal section shape turns over around axis of workpiece.Position vector (x, y, z) can be obtained:

(x,y,z)＝(x ₀cosθ-y ₀sinθ,x ₀sinθ+y ₀cosθ,z ₀+sθ) (21)

2) in conjunction with the relative installation of tested ball nut and probe, the transformation relation of ball nut workpiece coordinate system and inner roller path of ball nut normal section coordinate system is established.After known ball nut raceway normal section shape and helix parameter, probe detection side is to the position constantly changed in space along with the motion of probe along OA, A point in Fig. 6 (b), and its set is a spatially spiral curve.If D={d ₁, d ₂..., d _nbe the raw measurement data that probe acquires arrives, obviously, first point can be regarded as the anallactic point of probe to tested surface, elements all in D is all subtracted upper d ₁, then obtain data matrix:

ΔD＝{d ₁-d ₁,d ₂-d ₁,...,d _n-d ₁}＝{Δd _i}＝{0,Δd ₂,...,Δd _n} (22)

From the metering system of popping one's head in, Δ d _ifor the variation of raceway profile in probe orientation, have according to principle of coordinate transformation:

(x',y',z')＝(x,y,z)+(Δd _x,Δd _y,Δd _z) (23)

$({\mathrm{\&Delta;d}}_x,{\mathrm{\&Delta;d}}_y,{\mathrm{\&Delta;d}}_z,1)=({\mathrm{\&Delta;d}}_{x_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{y_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{z_{\mathrm{nor}}},1)\&CenterDot;T^{-1}---\left(24\right)$

Wherein, (x, y, z) is inner vortex theoretical space coordinate in workpiece coordinate system, the volume coordinate that (x', y', z') records for inner vortex in workpiece coordinate system is actual, for Δ d _i(i=1 ... n) the projection variation length on the coordinate system of inner roller path of ball nut normal section, (Δ d _x, Δ d _y, Δ d _z) be Δ d _i(i=1 ... n) transform to the length varying value on corresponding each change in coordinate axis direction in workpiece coordinate system, T is transformation matrix, from Fig. 6 (a):

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}& 0\\ 0& -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& 0\\ 0& 0& 0& 0\end{array}\right]---\left(25\right)$

Formula (24) and formula (25) are substituted into the inner vortex volume coordinate that formula (23) can try to achieve actual measurement, and the curve of being tried to achieve by many groups can evaluate the crudy of inner roller path of ball nut with the contrast of theoretical logarithmic spiral curve.

Sample calculation analysis

Analyze known according to the above features of shape to inner roller path of ball nut, X-Y scheme that interior raceway is made up of two Symmetrical Circular Arcs on the coordinate system of inner roller path of ball nut normal section scans around helix and is formed, fibre-optical probe is in testing process, main conceivable data are distances of tested surface and probe launching fiber end face, the i.e. value of d, but according to the detection principle of Fibre Optical Sensor, be finally indirectly obtain d's by the luminous flux receiving fiber-optic RF 1, RF2 receives.Right intensity modulation function M1 and M2 of optical fiber is by various factors, analyze the known trueness error due to ball nut processing of feature of raceway in nut, probe acquires is caused to arrive change reflective light intensity, be in particular in measured surface run-off the straight, measured surface generation lateral excursion and by the change of side with probe launching fiber end face distance, impact is entered the size of the luminous flux receiving fiber-optic RF 1 and RF2 by these three kinds changes, thus causes the value of intensity modulation function different.Its impact on intensity modulation function is discussed respectively from this three aspect below, optical fiber parameter is set in following analytical calculation and sensor parameters is respectively: r _r=0.05mm, r _t=0.025mm, NA _t=0.56, p=0.2mm.

(1) measured surface angle of inclination changes the impact on intensity modulation characteristic

By formula (11)-formula (14), setting d=0.15mm, l are respectively 0.08mm, 0.10mm, 0.12mm, change different γ and obtain the influence curve of measured surface angle of inclination change to intensity modulation characteristic.

As Fig. 7, along with the change of γ, M1 reduces gradually, and M2 increases gradually; For same group of M1 or M2, when γ increases to forward gradually from negative sense, be that the larger M1 of l is larger for M1, M2 reduces along with the increase of l.In whole change procedure, M1 and M2 is all nonmonotonic, defines three optical fiber here to the light modulated majorant M of fibre-optical probe:

$M=\frac{M1}{M2}---\left(25\right)$

From definition, M is the quotient function of M1 and M2, can find out in the figure 7, and M is monotone decreasing in whole process, this illustrates that M can be good at illustrating when certain d and l, and the impact of γ on the modulation light intensity of measuring system is regular and compensable.

(2) measured surface generation lateral excursion is on the impact of intensity modulation characteristic

By formula (11)-formula (14), setting d=0.15mm, γ are 1.8 °, 2.0 °, 2.2 °, change different l and obtain measured surface generation lateral excursion to the influence curve of intensity modulation characteristic.

As Fig. 8, along with the change of l, M1 and M2 is all monotone increasings gradually from 0, after arriving summit again monotone decreasing last both overlap.Their quotient function M is dull in whole process.Namely the impact of l on the modulation light intensity of measuring system is also regular and compensable.

(3) measured surface and probe launching fiber end face distance change the impact on intensity modulation characteristic

According to above analysis, when γ and l changes separately time, it is regular and controlled on the impact of system, research is when γ and l changes simultaneously below, the light modulated majorant of system, about the relation of d, makes l=0.10mm, γ=1.8 °, l=0.10mm, γ=2.0 ° respectively, l=0.12mm, γ=1.8 ° and l=0.12mm, γ=2.0 °, change different d and obtain measured surface and probe launching fiber end face distance and change influence curve to intensity modulation characteristic.

As shown in Figure 9, in interval, M1 and M2 is nonmonotonic, and along with the increase of d, M1 and M2 all increases from 0, reduces gradually after peaking, and final both overlap.Fibre-optical probe light modulated majorant M is dull, the M value that each d is corresponding unique, and large than M1 and M2 of the interval range of its dullness, characterize detection system with M as seen and nonmonotonic curve both can have been made to become dullness, also can increase sensing range, improve sensitivity.

By the analysis of above three aspects, can be obtained the light modulated intensity values of M1 and M2 respectively by probe for one-shot measurement, their quotient function M (M=M1/M2) is all dull.In actual testing process, although tested surface run-off the straight or lateral excursion, but it is rule on the impact of final light modulated majorant M, by the demarcation of certain means, the impact of tested surface inclination or lateral excursion can be eliminated, thus obtaining a fore-and-aft distance d value relatively accurately, this shows that the fibre-optical probe of three optical fiber to structure is used for detecting inner roller path of ball nut precision is feasible.

(4) precision analysis of detection system

To the scarp slope range of linearity and scarp slope sensitivity S in reference literature _fdefinition, the sensitivity of define system is that curve M is at monotony interval [d ₀, d _p] in variation delta M (the Δ M=M of modulating function _p-0) with displacement variable Δ d (the Δ d=d in this interval _p-d ₀) ratio, i.e. S _f=Δ M/ Δ d.According to this definition, analytic system accuracy of detection is as table 1.

The precision analysis of table 1 detection system

By the analysis of his-and-hers watches 1 and Fig. 9, owing to introducing the definition of three optical fiber to probe light modulated majorant, increase system linearity measurement range, improve the sensitivity of system, and when l and γ changes, system sensitivity S _frelative changing value be all less than 1.2%, namely this system has good stability and reliability simultaneously, may be used for the high precision test of inner roller path of ball nut curved surface.

Claims (6)

1., towards a high-precision optical fiber detection method for inner roller path of ball nut curved surface, it is characterized in that: comprise the following steps:

1) ball nut is installed on the moving platform, the central axis of fiber-optic sensor probe counter ball nut is installed with ball nut helix angle;

2) through step 1) after, utilize motion platform that ball nut is rotated, ball nut often rotates one week, fiber-optic sensor probe is moved linearly a ball nut pitch, until fiber-optic sensor probe completes detection along inner roller path of ball nut, then according to the mathematical model of fiber-optic sensor probe intensity modulation curve, the ranging data D={d between fiber-optic sensor probe and ball nut raceway profile is obtained ₁, d ₂..., d _n, n represents point distance measurement number;

3) the actual ball nut inner vortex volume coordinate recorded is tried to achieve according to the transformation relation of ranging data and ball nut workpiece coordinate system and inner roller path of ball nut normal section coordinate system.

2. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface according to claim 1, it is characterized in that: described fiber-optic sensor probe comprises symmetrically arranged two probe branches, angle is there is between two probe branches, each probe branch comprises several contact units, each contact unit comprises at least one three optical fiber pair, and described three optical fiber form by launching fiber and each reception optical fiber being symmetrically distributed in launching fiber both sides.

3. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface according to claim 2, is characterized in that: each contact unit comprises a launching fiber and four root receiving fibers uniform around launching fiber.

4. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface according to claim 2, is characterized in that: the quantity of the contact unit of each probe branch increases with the raceway radius of detected ball nut and upwards carries out respective extension at one-dimensional square.

5. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface according to claim 2, it is characterized in that: for any one in contact unit three optical fiber pair, calculate described three optical fiber alignment two launch and accept optical fiber respectively to M corresponding separately, one of them launch and accept optical fiber is formed receiving optical fiber by the launching fiber of described three optical fiber alignments and of described three optical fiber alignments, and another launch and accept optical fiber is formed receiving optical fiber by another of the launching fiber of described three optical fiber alignments and described three optical fiber alignments:

M＝S ₁/S

(1) as | EK|≤p-r _rtime

S ₁＝0

(2) as | EK|>=p+r _rtime

S ₁＝πr _R ²

(3) p-r is worked as _r<|EK|<p+r _rtime, then must there are two symmetrical intersection points, if two intersecting point coordinates be respectively (q, y to the oval spot profile receiving plane place, fiber end face place with the corresponding fiber end face profile that receives through reflective surface in utilizing emitted light ₁), (q ,-y ₁), then

When $p-r_R<q\&le;\sqrt{{r_R}^2+p^2}$ Time

$S_1=2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})+x_T}\left]\right\}\mathrm{dy}$

When $\sqrt{{r_R}^2+p^2}<q<p+r_R$ Time

$S_1={{\mathrm{\&pi;r}}_R}^2-2{\&Integral;}_0^{y_1}\{(\sqrt{{r_R}^2-y^2}+p)-[\sqrt{a^2(1-\frac{y^2}{b^2})+x_T}\left]\right\}\mathrm{dy}$

Wherein, S ₁it is the size that three optical fiber alignment one receives the capture area of fiber-optic RF; S be the launching fiber utilizing emitted light of three optical fiber alignments through reflective surface to receiving the ellipse light spot area at plane place, fiber end face place, p is the distance between axles of described launching fiber and described reception fiber-optic RF, r _rfor described reception fiber-optic RF fiber core radius, | EK| is the distance between described launching fiber center and the nearly launching fiber point of described reception fiber-optic RF end face, and a is the major semi-axis length of ellipse light spot, and b is the minor semi-axis length of ellipse light spot, x _t=| EK|-a;

So, the mathematical model of described fiber-optic sensor probe intensity modulation curve is expressed as the quotient function of described three optical fiber alignment two launch and accept optical fiber to M corresponding separately.

6. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface according to claim 1, it is characterized in that: described step 3) in, try to achieve the actual ball nut inner vortex volume coordinate recorded according to formula (23), formula (24) and formula (25):

(x',y',z')＝(x,y,z)+(Δd _x,Δd _y,Δd _z) (23)

$({\mathrm{\&Delta;d}}_x,{\mathrm{\&Delta;d}}_y,{\mathrm{\&Delta;d}}_z,1)=({\mathrm{\&Delta;d}}_{x_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{y_{\mathrm{nor}}},{\mathrm{\&Delta;d}}_{z_{\mathrm{nor}}},1)\&CenterDot;T^{-1}---\left(24\right)$

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}& 0\\ 0& -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& 0\\ 0& 0& 0& 1\end{array}\right]---\left(25\right)$

Wherein, (x, y, z) is inner vortex theoretical space coordinate in described workpiece coordinate system, and (x', y', z') is the actual volume coordinate recorded of inner vortex in described workpiece coordinate system, for Δ d _iprojection variation length on the coordinate system of inner roller path of ball nut normal section, i=1 ... n, { Δ d _i}={ 0, Δ d ₂..., Δ d _n}={ d ₁-d ₁, d ₂-d ₁..., d _n-d ₁, (Δ d _x, Δ d _y, Δ d _z) be Δ d _itransform to the length varying value on corresponding each change in coordinate axis direction in described workpiece coordinate system, β represents ball nut helix angle.