CN104792276B - A kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface - Google Patents

Abstract

The invention discloses a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface：Ball nut is installed on the moving platform, the central axis of fiber-optic sensor probe counter ball nut is installed with ball nut helical angle；Ball nut is rotated using motion platform, ball nut is often rotated one week, make fiber-optic sensor probe one ball nut pitch of rectilinear movement, until fiber-optic sensor probe completes detection along ball nut raceway type face correspondence inner vortex, then according to the Mathematical Modeling of fiber-optic sensor probe intensity modulation curve, it is calculated the ranging data between fiber-optic sensor probe and ball nut raceway type face；Actually measured inner vortex space coordinates is tried to achieve with the transformation relation of inner roller path of ball nut normal section coordinate system according to ranging data and ball nut workpiece coordinate system, such that it is able to the machining accuracy of comprehensive assay ball nut.

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, it is related to a kind of towards inner roller path of ball nut The high-precision optical fiber detection method of curved surface.

Background technology

The features such as ball guide screw nat is due to high efficiency, high accuracy, 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 of the high-accuracy machinery of development, for High-precision ball-screw nut, the interior raceway face of its complexity considerably increases detection difficulty, and traditional detection method has solid The methods such as fixed pattern detector method, steel ball contact method and relative measurement, but these belong to contact type measurement, it is impossible to meet ball wire The quick high accuracy detection of thick stick pair of nut.The high precision test of ball nut is realized, non-contact detecting can only be carried out to it.

The high precision test of ball nut, not only including nut surface parameter (internal diameter, external diameter etc.) detection, also include The detection of the interior curve surface of raceway parameter (helical pitch, lead angle etc.) of nut.And the machine vision and optics of emerging research at present are surveyed Also more or less be present some shortcomings in the contactless measurements such as amount, be in particular in：1) the accuracy of detection mistake of machine vision Degree relies on the shooting resolution ratio of camera, and the digital picture of two dimension have lost substantial amounts of Testing index, for example, can not detect in it Situation and lead angle (i.e. helical angle) of raceway etc., thus cannot thoroughly evaluating ball nut crudy；2) it is simple Application fibre-optical probe detect the inner surface of ball nut, by Fibre Optical Sensor is limited by principle, for tested surface inclination angle mistake Big situation, receiving optical fiber cannot receive reflected light, and measurement result cannot effectively illustrate the precision of measured body.Therefore, in order to The deficiency of above present Research is made up, it is necessary to a kind of new high accuracy that can detect inner roller path of ball nut curved surface three-dimensional appearance inspection Survey method.

The content of the invention

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

To reach above-mentioned purpose, present invention employs following technical scheme：

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

2) by step 1) after, rotate ball nut using motion platform, ball nut is often rotated one week, passes optical fiber Sensor probe one ball nut pitch of rectilinear movement, until fiber-optic sensor probe completes to examine along inner roller path of ball nut Survey, then according to the Mathematical Modeling of fiber-optic sensor probe intensity modulation curve, obtain fiber-optic sensor probe and ball nut Ranging data D={ d between raceway type face₁,d₂,...,d_n, n represents point distance measurement number；

3) according to ranging data and ball nut workpiece coordinate system and inner roller path of ball nut normal section coordinate system Transformation relation tries to achieve actually measured ball nut inner vortex space coordinates.

The fiber-optic sensor probe includes symmetrically arranged two probe branches, there is folder between two probe branches Angle, each probe branch includes several contact units, and each contact unit includes at least one 3 optical fiber pair, three optical fiber Constituted to receiving optical fiber be symmetrically distributed in launching fiber both sides each one by launching fiber.

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

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

For the optical fiber pair of any one in contact unit three, three optical fiber alignment, two transmittings are calculated respectively and receives light , to each corresponding M, one of transmitting reception optical fiber is to the launching fiber by three optical fiber alignment and three light for fibre One of fine centering receives optical fiber and constitutes, another transmitting receive optical fiber to the launching fiber by three optical fiber alignment with it is described Another of three optical fiber alignments receives optical fiber composition：

M=S₁/S

(1) as | EK |≤p-r_RWhen

S₁=0

(2) as | EK | >=p+r_RWhen

S₁=π r_R ²

(3) p-r is worked as_R<|EK|<p+r_RWhen, then the reflected face of launching light reflexes to and receives ellipse at plane where fiber end face Must there are two symmetrical intersection points in circle light spot profile, with corresponding reception fiber end face profile if two intersecting point coordinates are respectively (q, y₁)、 (q,-y₁), then

WhenWhen

WhenWhen

Wherein, S₁It is three optical fiber alignments, one size of the capture area of reception fiber-optic RF；S is three optical fiber alignments The reflected face of launching fiber launching light reflexes to the ellipse light spot area received at plane where fiber end face, and p is the transmitting Optical fiber and the distance between axles for receiving fiber-optic RF, r_RIt is the reception fiber-optic RF fiber core radius, | EK | is in the launching fiber The heart receives the distance between nearly launching fiber point of fiber-optic RF end face with described, and a is the major semiaxis length of ellipse light spot, and b is ellipse The semi-minor axis length of hot spot, x_T=| EK |-a；

So, the Mathematical Modeling of the fiber-optic sensor probe intensity modulation curve is expressed as three optical fiber alignment two Transmitting receives quotient function of the optical fiber to each corresponding M.

The step 3) in, actually measured ball nut inside spin is tried to achieve according to formula (23), formula (24) and formula (25) Space of lines coordinate：

(x', y', z')=(x, y, z)+(Δ d_x,Δd_y,Δd_z) (23)

Wherein, (x, y, z) is inner vortex theoretical space coordinate in the workpiece coordinate system, and (x', y', z') is the work The actually measured space coordinates of inner vortex in part coordinate system,It is Δ d_iIn inner roller path of ball nut method The projection fastened to cross sectional coordinate changes length, i=1 ... n, { Δ d_i}={ 0, Δ d₂,...,Δd_n}={ d₁-d₁,d₂- d₁,...,d_n-d₁, (Δ d_x,Δd_y,Δd_z) it is Δ d_iTransform in the workpiece coordinate system on each change in coordinate axis direction of correspondence Length varying value, β represents ball nut helical angle.

Beneficial effects of the present invention are embodied in：

The present invention establishes optical fiber spy first by fiberoptic probe applications in the detection of inner roller path of ball nut normal section The Mathematical Modeling of head intensity modulation curve, analyzes the phase change of workpiece coordinate system and inner roller path of ball nut normal section coordinate system Relation is changed, the high-precision optical fiber detection method towards inner roller path of ball nut curved surface is given on this basis.The present invention is from original The normal direction detection relation of fibre-optical probe and measured surface is always ensured that in reason, and the three-dimensional of inner roller path of ball nut curved surface can be detected Shape characteristic, testing result can be used for the machining accuracy of comprehensive assay ball nut.

Brief description of the drawings

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

Fig. 2 is the detection method and sonde configuration figure of system；Wherein, (a) is probe installation and motion mode, and (b) is (a) Partial enlargement, (c) be pop one's head in branch structure；4 is ball；

Fig. 3 is detecting system flow chart；

Fig. 4 is detecting system sonde configuration figure (a) and RIM-FOS fundamental diagrams (b)；D₁One for contact unit is adopted Sampling point,

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 influence curve figure of the measured surface angle of inclination change to intensity modulation characteristic；

Fig. 8 is that measured surface occurs influence curve figure of the lateral shift to intensity modulation characteristic；

Fig. 9 is measured surface and influence curve figure of the launching fiber end face distance change to intensity modulation characteristic of popping one's head in.

Specific embodiment

The present invention is elaborated with reference to the accompanying drawings and examples.

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

(2) and then, the pattern feature based on inner roller path of ball nut curved surface devises a kind of special expandable type optical fiber Sensor probe, and establish the Mathematical Modeling of the intensity modulation curve of contact unit in the probe；

(3) it is last, inner roller path of ball nut Curved dectection method is given with reference to the characteristics of tested inner roller path of ball nut.

The step (1) includes following particular content：

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

High-precision optical fiber detection platform towards inner roller path of ball nut curved surface is main by motion platform, fibre-optical probe, number Constituted according to acquisition module, control module and computer, as shown in Figure 1.Ball nut is placed on motion platform, fibre-optical probe The data for collecting are transferred to computer by data acquisition module, and the signal that computer disposal is obtained simultaneously passes through control module reality When control fibre-optical probe and measured piece (ball nut) motion, when complete whole data acquisition after computer logarithm According to Treatment Analysis are carried out, the physical location vector of multigroup inner vortex in raceway is obtained, so as to judge the processing of ball nut body Whether precision meets the requirements.

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

Using ball as rolling element between leading screw and nut, its raceway type face is divided into single circular arc type to ball guide screw nat With bicircular arcs type, ball guide screw nat its static acceptance index is determined by deviation of stroke and run-out tolerance.Ball-screw Sliding friction is mainly changed into rolling friction, nut and ball by pair of nut in motion process by ball and raceway contact The precision height of the raceway inner surface near contact point determines the precision of ball guide screw nat just, for ball nut During actually detected, the raceway surface-type feature of contact surface part is predominantly detected.

As shown in Fig. 2 (a), raceway normal section parameter, nut pitch P h and helixangleβ in known ball nut body On the premise of, the central axis of fibre-optical probe opposing nut is installed with helixangleβ, measurement process such as Fig. 3.Fibre-optical probe CA1 ' and CA2 ' are partly respectively aligned to CA1 and CA2 regions on interior raceway normal section, and start gathered data.Ball nut is every Rotate one week, fibre-optical probe moves linearly a pitch inwards, detected along a certain bar inner vortex of ball nut when popping one's head in Cheng Hou, computer will carry out corresponding algorithm calculating after these data analyses, you can evaluate the machining accuracy of ball nut.

The step (2) includes following particular content：

1) the pattern feature based on inner roller path of ball nut curved surface, designs a kind of special expandable type fibre-optical probe.Visit Head according to the characteristics of inner roller path of ball nut curved surface and detection platform metering system, be designed to symmetrical structure, can examine simultaneously Survey two cambered surface precision in bicircular arcs type raceway type face.Meanwhile, the optical fiber in probe is made up of contact unit, each contact unit Comprising a launching fiber and four uniform root receiving fibers of surrounding.

Referring to Fig. 2 (b), the measurement end of probe is made up of symmetrical CA1 ' and CA2 ', and the end face difference of CA1 ' and CA2 ' is just CA1 and CA2 regions (reflecting surface) on internal raceway normal section, Liang Ge branches (CA1 ' and CA2 ') constitute with identical, There are tri- launching fibers of TF1, TF2, TF3 in CA1 ', there is tri- launching fibers of TF4, TF5, TF6, each hair in correspondence CA2 ' Penetrate around optical fiber and be uniformly distributed four root receiving fibers, be respectively used to receive four reflected lights of reflection direction.Due to the two of probe Individual branch CA1 ' and CA2 ' has symmetry, with CA1 ' as research object.Such as Fig. 2 (c), CA1 ' branches are by contact unit 1, probe Unit 2 and contact unit 3 are constituted.Each contact unit includes a launching fiber and four uniform root receiving fibers of surrounding, The quantity of contact unit can carry out respective extension with the increase of the raceway radius of detected ball nut body in one-dimensional square, have There is ductility.The launching fiber TF of fibre-optical probe is sent into laser, and reflected face reflects and is launched around optical fiber TF The process that four root receiving fiber RF of even distribution receive gathered data is referred to as a collection step.Will be corresponding in CA1 ' and CA2 ' TF1 and TF4, TF2 and TF5, and TF3 and TF6 be respectively completed collection step process be referred to as gather sequence.Fibre-optical probe often completes one Individual collection sequence will return to the ranging data of 6 points (corresponding to six helixes respectively).

Because inner roller path of ball nut type face is three-dimension curved surface, the actually detected reflected face of value is on a pair of orthogonal direction The influence at angle of inclination, therefore, contact unit is designed as two groups of orthogonal three optical fiber to structure, three optical fiber alignments are included One launching fiber and the symmetrical reception optical fiber positioned at both sides.

2) Mathematical Modeling 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 Intensity Modulated Fiber Optic Sensor), shown in its operation principle such as Fig. 4 (a), the light that light source LD sends Reflecting surface is irradiated to by launching fiber TF, the light being reflected back is by receiving fiber-optic RF, optical signal transmission to photodetection Device PD.The intensity modulation function M of RIM-FOS is to receive luminous power (or the luminous flux phi that optical fiber is received_R) sent with launching fiber Luminous power (or luminous flux phi_TThe ratio between), it reflects the characteristic of sensor.For RIM-FOS, intensity modulation function again may be used To be write as the compound function on optical fiber parameter, sensor construction parameter and reflecting surface parameter.Wherein：

(1) optical fiber parameter includes transmitting, receives fiber core radius r_T、r_R, and numerical aperture NA_T、NA_RDeng；

(2) including launching fiber and surrounding, any one reception optical fiber constitutes optical fiber to distance between axles to sensor construction parameter P etc.；

(3) reflecting surface parameter includes reflector shape factor R_c, reflecting surface angle of inclination γ, reflecting surface lateral shift distance The distance between l, launching fiber end face and tested physical surface d, reflective surface rate δ etc..

Wherein k represents the synthesis including other X factors including loss etc..Determine in sensor probe configuration In the case of, it can be seen from the detection mode according to system, the principal element of influence intensity modulation function M derives from reflecting surface angle of inclination γ, reflecting surface lateral shift distance (i.e. the horizontal range of reflecting surface deflection optical fiber probe outgoing light center) l and reflecting surface shape Shape factor R_c, for a tested ball nut for determination, its interior raceway normal section radius is constant, and emergent light is irradiated to section On spot radius r_bMuch smaller than its normal section radius (i.e. reflector shape factor R_c), work as R_c/r_bCan be by R when >=50_cRegard as It is an infinitely large quantity, now reflecting surface is equivalent to plane reflection.To simplify calculating process, by model simplification for reflecting surface is flat Face situation.

As shown in Fig. 4 (b), just to raceway concave bottom, two reception optical fiber are symmetrically distributed in launching fiber of popping one's head in theory Launching fiber TF both sides are used to receive the light of reflective surface.Because fibre-optical probe and reflecting surface are respectively provided with symmetry, below only The light intensity received using RF1 is used as analysis object, it is assumed that reflection towards RF1 close direction movement for just, towards the direction of RF1 Rotate to be just.

Assuming that reflecting surface isotropism, and it is non-selective with spectrum, then the luminous flux received by RF1 is equivalent to TF's It is multiplied by as sending and by the luminous flux that RF1 is received the reflectance factor of reflecting surface.Therefore, the intensity modulation of optical fiber pair is expected Function M, on the premise of launching fiber output intensity is uniformly distributed hypothesis, a demand obtains the light-receiving area of RF1 and the projection of TF Area ratio, multiplied by with the reflectivity of reflecting surface.It is analysis object with the light field for receiving plane where fiber end face, entirely During the propagation of light field is regarded as be uniformly distributed with round platform be distributed be superimposed, now the luminous flux in unit area is equal , therefore have：

M1=Φ₁/ Φ=S₁/S (2)

S in formula₁It is the size of RF1 capture areas；S is reflexed to where reception fiber end face for the reflected face of launching light Facula area at plane；Φ₁The luminous flux that optical fiber is received is received to receive fiber end face；Φ is where reception fiber end face The total luminous flux of planar lightfield.Calculate S step by step below₁.Had by the relation in Fig. 4：

θ₁=arcsin (NA_T)

| AE |=r_T/tanθ₁

| BD |=ltan γ

| AD |=r_T·cotθ₁+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：

In Δ QNK, had by sine：

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

Similarly, in fiber-optic RF 2 is received

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

In Figure 5, elliptic equation is：

RF1 and RF2 distinguish corresponding small equation of a circle：

(x-p)²+y²=r_R ²

(x+p)²+y²=r_R ² (9)

Wherein：

A=| JK |/2

b≈2d·tanθ₁+r_T (10)

x_T=| EK |-a

S=π ab

A, b represent that (i.e. the reflected face of launching light reflexes at plane where reception fiber end face ellipse light spot respectively in formula Hot spot) major semiaxis length and semi-minor axis length；θ₁It is the numerical aperture angle (NA of launching fiber_T=sin θ₁).According to | EK | Length and p size, following several situations can be divided into：

(1) as | EK |≤p-r_RWhen

S₁=0 (11)

(2) as | EK | >=p+r_RWhen

S₁=π r_R ² (12)

(3) p-r is worked as_R<|EK|<p+r_RWhen, then oval spot profile must have two with roundlet (receiving the end profile of optical fiber) Individual symmetrical intersection point, if two intersecting point coordinates are respectively (q, y₁)、(q,-y₁)

WhenWhen

WhenWhen

Formula (3)-formula (14) is substituted into formula (2), you can obtain receiving the intensity modulation function M1 of fiber-optic RF 1, can similarly count Calculation obtains receiving the intensity modulation function M2 (M2=S of fiber-optic RF 2₂/S).Define fibre-optical probe intensity modulation function be：

The step (3) includes following idiographic flow：

Workpiece coordinate system：As Z axis, the arbitrary line in the face of Z axis is Y-axis to axis with ball nut, by the right side Hand cartesian coordinate system principle determines X-axis, and the intersection point with ball nut end face and Z axis is origin O.

Inner roller path of ball nut normal section coordinate system：X-axis is cut as inner roller path of ball nut normal direction with workpiece coordinate system Areal coordinate system X_nAxle, d is translated with origin O along X-axis positive direction_m/ 2 distances are inner roller path of ball nut normal section coordinate origin O_n, cross O_nPoint and with Z axis into the direction of β angles be inner roller path of ball nut normal section coordinate system Z_nAxle, is sat by right-handed Cartesian Mark system principle determines Y_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_GIt is raceway radius, e is eccentric throw, h It is location parameter.Normal plane O_nx_nz_nAngle (β) with ball nut axis can be calculated by following formula：

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 song in Oxyz coordinates by coordinate conversion relation Line, can be expressed as

In formula, x₀,y₀,z₀--- coordinate of the raceway normal section point in shape in workpiece coordinate system；α --- ginseng becomes Amount, h --- location parameter.

arccos(e/R_G)≤α≤arcsin((2h+d_g-d_m)/R_G) (18)

In formula, d_g--- the big footpath of ball nut.

The vector representation form of the space curve is：

R=r (δ)=x₀i+y₀j+z₀k (19)

In formula, i, j, k --- workpiece coordinate system unit vector, the vector are spinned to move around ball nut axis and are formed Curved surface (i.e. raceway inner helical surface) can be expressed as follows：

R=(x₀cosθ-y₀sinθ)i+(x₀sinθ+y₀cosθ)j+(z₀+sθ)k (20)

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

(x, y, z)=(x₀cosθ-y₀sinθ,x₀sinθ+y₀cosθ,z₀+sθ) (21)

2) tested ball nut and the relative installation of probe are combined, ball nut workpiece coordinate system and ball is established The transformation relation of raceway normal section coordinate system in nut.Known ball nut raceway normal section shape and helix parameter it Afterwards, probe detection direction OA along Fig. 6 (b), A points constantly change in the position in space with the motion of probe, and its collection is combined into One spatially spiral curve.If D={ d₁,d₂,...,d_nIt is the raw measurement data for collecting of popping one's head in, it is clear that can be by first Individual point regards as probe to the anallactic point of tested surface, and all of element in D is subtracted into upper d₁, then data matrix is obtained：

Δ D={ d₁-d₁,d₂-d₁,...,d_n-d₁}={ Δ d_i}={ 0, Δ d₂,...,Δd_n} (22)

From the metering system popped one's head in, Δ d_iIt is variation of the raceway type face in probe orientation, according to coordinate transform Principle has：

(x', y', z')=(x, y, z)+(Δ d_x,Δd_y,Δd_z) (23)

Wherein, (x, y, z) is inner vortex theoretical space coordinate in workpiece coordinate system, and (x', y', z') is workpiece coordinate system The actually measured space coordinates of middle inner vortex,It is Δ d_i(i=1 ... n) is in inner roller path of ball nut Projection on the coordinate system of normal section changes length, (Δ d_x,Δd_y,Δd_z) it is Δ d_i(i=1 ... n) transforms to workpiece coordinate system Length varying value on middle each change in coordinate axis direction of correspondence, T is transformation matrix, from Fig. 6 (a)：

Formula (24) and formula (25) are substituted into formula (23) can try to achieve the inner vortex space coordinates of actual measurement, be asked by multigroup The crudy of inner roller path of ball nut can be evaluated with the contrast of the logarithmic spiral curve of theory for the curve for obtaining.

Sample calculation analysis

Features of shape analysis to inner roller path of ball nut according to more than understands that interior raceway is by inner roller path of ball nut The X-Y scheme of the two Symmetrical Circular Arcs composition on the coordinate system of normal section scans what is formed around helix, and fibre-optical probe is in detection During, main conceivable data are the distance of tested surface and probe launching fiber end face, the i.e. value of d, but are passed according to optical fiber The detection principle of sensor, is finally to obtain d's indirectly by receiving luminous flux that fiber-optic RF 1, RF2 receives.Optical fiber pair M1 and M2 are affected by many factors for intensity modulation function, the essence in analysis nut the characteristics of raceway seeing as ball nut processing Degree error, causes probe to collect change reflective light intensity, is in particular in that measured surface run-off the straight, measured surface occur laterally Influence is entered the reception He of fiber-optic RF 1 by skew and the change by side and probe launching fiber end face distance, these three changes The size of the luminous flux of RF2, so as to cause the value of intensity modulation function different.Discuss it to light intensity respectively in terms of three from this below The influence of modulation function, sets optical fiber parameter and sensor parameters is respectively in analysis below calculating：r_R=0.05mm, r_T= 0.025mm、NA_T=0.56, p=0.2mm.

(1) measured surface angle of inclination changes the influence to intensity modulation characteristic

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

Such as Fig. 7, with the change of γ, M1 is to be gradually reduced, and M2 is gradually to increase；For same group of M1 or M2, work as γ It is that the bigger M1 of l are bigger for M1 when being gradually increased to forward direction from negative sense, and M2 is reduced with the increase of l.Entirely becoming During change, M1 and M2 is nonmonotonic, and modulation light intensity function M of three optical fiber to fibre-optical probe is defined here：

From definition, M is the quotient function of M1 and M2, in figure 7 it is seen that M is monotone decreasing in whole process , this explanation M can be good at explanation in the case of certain d and l, and influences of the γ to the modulation light intensity of measuring system is that have Rule and compensable.

(2) there is influence of the lateral shift to intensity modulation characteristic in measured surface

By formula (11)-formula (14), d=0.15mm, γ as 1.8 °, 2.0 °, 2.2 ° are set, change different l and be tested There is influence curve of the lateral shift to intensity modulation characteristic in surface.

Such as Fig. 8, with the change of l, M1 and M2 is the gradually monotonic increase since 0 ing, reaches after summit and dullness is passed Subtract both coincidences last.Their quotient function M is dull in whole process.That is shadows of the l to the modulation light intensity of measuring system Sound is also regular and compensable.

(3) measured surface changes the influence to intensity modulation characteristic with probe launching fiber end face distance

According to more than analyze, when γ and l independent changes, its influence to system be it is regular and controllable, under When both γ and l change simultaneously, the modulation relation of the light intensity function on d of system makes l=0.10mm, γ respectively for face research =1.8 °, l=0.10mm, γ=2.0 °, l=0.12mm, γ=1.8 ° and l=0.12mm, γ=2.0 °, change different D obtains measured surface with influence curve of the launching fiber end face distance change to intensity modulation characteristic of popping one's head in.

As shown in figure 9, M1 and M2 is nonmonotonic in interval, with the increase of d, M1 and M2 increases since 0, reaches It is gradually reduced after peak value, final both overlap.Fibre-optical probe modulation light intensity function M is dull, and each d correspondences are unique M values, and its dull interval range is bigger than M1 and M2, it is seen that detecting system is characterized with M can both make nonmonotonic song Line is changed into dull, it is also possible to increase detection range, improves sensitivity.

By the analysis in terms of three above, for the modulation light intensity that one-shot measurement can respectively obtain M1 and M2 by probe Value, their quotient function M (M=M1/M2) is dull.During actually detected, although tested surface run-off the straight or Lateral shift, but its influence to final modulation light intensity function M is rule, by the demarcation of certain means, can be eliminated Tested surface inclination or the influence of lateral shift, so as to obtain a relatively accurate fore-and-aft distance d value, this shows three optical fiber Fibre-optical probe to structure is used for detecting that inner roller path of ball nut precision is feasible.

(4) precision analysis of detecting system

To the scarp slope range of linearity and scarp slope sensitivity S in reference literature_fDefinition, define system sensitivity be curve M In monotony interval [d₀,d_p] in modulation function variation delta M (Δ M=M_p- 0) with interval displacement variable Δ d (the Δ d =d_p-d₀The ratio between), i.e. S_f=Δ M/ Δs d.According to this definition, analysis system accuracy of detection such as table 1.

The detecting system precision analysis of table 1

By the analysis to table 1 and Fig. 9, due to introducing definition of three optical fiber to probe modulation light intensity function, increase and be The linear measurement range of system, improves the sensitivity of system, and when l and γ changes, system sensitivity S_fRelative changing value Respectively less than 1.2%, the i.e. system have good stability and reliability simultaneously, can be used for inner roller path of ball nut curved surface High precision test.

Claims (5)

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

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

2) by step 1) after, rotate ball nut using motion platform, ball nut is often rotated one week, makes Fibre Optical Sensor Probe one ball nut pitch of rectilinear movement, until fiber-optic sensor probe completes to detect along inner roller path of ball nut, so Afterwards according to the Mathematical Modeling of fiber-optic sensor probe intensity modulation curve, fiber-optic sensor probe and ball nut raceway type are obtained Ranging data D={ d between face₁,d₂,...,d_n, n represents point distance measurement number；

3) according to the conversion of ranging data and ball nut workpiece coordinate system and inner roller path of ball nut normal section coordinate system Relation tries to achieve actually measured ball nut inner vortex space coordinates；

The fiber-optic sensor probe includes symmetrically arranged two probe branches, there is angle between two probe branches, often It is individual probe branch include several contact units, each contact unit include at least one 3 optical fiber pair, three optical fiber to by Launching fiber receives optical fiber composition be symmetrically distributed in launching fiber both sides each one.

2. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface, its feature according to claim 1 It is：Each contact unit includes a launching fiber and uniform four root receiving fibers around launching fiber.

3. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface, its feature according to claim 1 It is：The quantity of the contact unit of each probe branch is with the raceway radius increase of detected ball nut in one-dimensional square Carry out respective extension.

4. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface, its feature according to claim 1 It is：For the optical fiber pair of any one in contact unit three, three optical fiber alignment, two transmittings are calculated respectively and receives optical fiber To each corresponding M, one of transmitting receives optical fiber to the launching fiber by three optical fiber alignment and three optical fiber One of centering receives optical fiber and constitutes, and another transmitting receives optical fiber to the launching fiber by three optical fiber alignment and described three Another of optical fiber alignment receives optical fiber composition：

M=S₁/S

(1) as | EK |≤p-r_RWhen

S₁=0

(2) as | EK | >=p+r_RWhen

S₁=π r_R ²

(3) p-r is worked as_R＜ | EK | ＜ p+r_RWhen, then the reflected face of launching light reflexes to the ellipse received at plane where fiber end face Must there are two symmetrical intersection points in light spot profile, with corresponding reception fiber end face profile if two intersecting point coordinates are respectively (q, y₁)、 (q,-y₁), then

WhenWhen

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

WhenWhen

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

Wherein, S₁It is three optical fiber alignments, one size of the capture area of reception fiber-optic RF；S is the transmitting of three optical fiber alignments The reflected face of fibre optical transmission light reflexes to the ellipse light spot area received at plane where fiber end face, and p is the launching fiber With the distance between axles of the reception fiber-optic RF, r_RBe it is described reception fiber-optic RF fiber core radius, | EK | for the launching fiber center with The distance between described reception nearly launching fiber point of fiber-optic RF end face, a is the major semiaxis length of ellipse light spot, and b is ellipse light spot Semi-minor axis length, x_T=| EK |-a；

So, the Mathematical Modeling of the fiber-optic sensor probe intensity modulation curve is expressed as three optical fiber alignment, two transmittings Receive quotient function of the optical fiber to each corresponding M.

5. a kind of high-precision optical fiber detection method towards inner roller path of ball nut curved surface, its feature according to claim 1 It is：The step 3) in, actually measured ball nut inner vortex is tried to achieve according to formula (23), formula (24) and formula (25) empty Between coordinate：

(x', y', z')=(x, y, z)+(Δ d_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 the workpiece coordinate system, and (x', y', z') sits for the workpiece The actually measured space coordinates of inner vortex in mark system,It is Δ d_iCut in inner roller path of ball nut normal direction The projection that areal coordinate is fastened changes length, i=1 ..., n, { Δ d_i}={ 0, Δ d₂,...,Δd_n}={ d₁-d₁,d₂-d₁,..., d_n-d₁, (Δ d_x,Δd_y,Δd_z) it is Δ d_iTransform to the length change corresponded on each change in coordinate axis direction in the workpiece coordinate system Value, β represents ball nut helical angle.