CN106052568B - The compensation method of screw rod type face detection device displacement sensor system installation error - Google Patents
The compensation method of screw rod type face detection device displacement sensor system installation error Download PDFInfo
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- CN106052568B CN106052568B CN201610626814.5A CN201610626814A CN106052568B CN 106052568 B CN106052568 B CN 106052568B CN 201610626814 A CN201610626814 A CN 201610626814A CN 106052568 B CN106052568 B CN 106052568B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/30—Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces
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Abstract
The invention discloses a kind of compensation methodes of screw rod type face detection device displacement sensor system installation error, include the following steps：Step 1, structure coordinate system；Step 2, determine space oblique coordinates system and lathe bed rectangular coordinate system in space relationship；Step 3, acquisition steel ball great circle outline data；Influence of the installation error to measurement steel ball of step 4, analysis light veil type displacement sensor in the horizontal plane；Step 5 seeks the installation error of light veil type displacement sensor in the horizontal plane；Influence of the installation error to measurement steel ball of step 6, analysis light veil type displacement sensor in perpendicular；Step 7 solves light veil type displacement sensor installation error in perpendicular.The method of the present invention, as benchmark, is not only increased accuracy and also avoids the clamping error for introducing steel ball using steel ball with high precision；It is using Newton iteration method to select the value near global solution as iterative initial value when solving Nonlinear System of Equations, is further improving the accuracy of convergent speed reconciliation.
Description
Technical field
The invention belongs to ballscrew type face detection fields, especially a kind of screw rod type face detection device displacement sensor system
The compensation method of system installation error.
Background technology
Ball screw assembly, is a kind of functional component often used in machine driving and in being accurately positioned.Due to being processed into
Ball-screw screw thread surface geometry parameter error after type is to property such as the positioning accuracies, moment of friction, service life of ball-screw
It can produce bigger effect, so having a great deal of practical meanings to the detection of ball-screw screw thread surface geometry parameter.
There are many kinds of the measurement methods of ball-screw raceway geometric parameter.Traditional detection method mostly uses Three-ball method, this
Not only efficiency is low for method, but also can introduce human error.And mostly use displacement sensor or optics member device during modern surveying
Part, such as industrially contourgraph is commonly used to measure the contact angle of raceway, the estimation rolling that the method also can be general by amplifying comparison
The radius of road circular arc, but it is observational measurement, measurement accuracy relies on the experience of survey crew.Or use contact type measurement side
Method, not only measurement efficiency is low for the method, but also contact stress will necessarily bring certain influence to measurement result.It is passed based on CCD
The machine vision of sensor, two and three dimensions projection are primarily limited to the precision and image processing algorithm of CCD, and measurement accuracy is at present not
High-precision requirement can be met.
Most study was the scanning survey method based on laser displacement sensor in recent years, and the method measurement efficiency is high, essence
Degree is high, can measure a variety of geometric parameters, but the coordinate system that sensor and sensor form in the good measuring system of process and assemble is past
Toward being not ideal rectangular coordinate system, the two dimension measured or 3-D graphic distortion, the influence to measurement accuracy is caused to can not be ignored.
However, finding that scholars are sensors to measuring system compensation problem most study by studying technical data both domestic and external
Influence of the drift angle to measurement result between measured workpiece, nobody went in for the study the angle between sensor and sensor
Influence of the error to measurement result, especially for Surface inspection system, the coordinate system of sensor and sensor composition is tiltedly to sit
It can lead to aliasing when mark, this is influenced than the former influence bigger.
The Chinese patent of the patent No. (200910029189.6) discloses composite errors of ball screw spiral raceway and examines automatically
Survey method and its device.Grating scale and light veil type displacement sensor cut the normal direction of ball screw spiral raceway to be measured in this device
The axial position of each point and radial position are sampled on shape curve, but optical grating ruler measurement direction and light veil type displacement sensor
Measurement direction is not right-angle relationship, furthermore the Laser emission direction of light veil type displacement sensor and optical grating ruler measurement direction nor
Right-angle relationship, the plane coordinate system formed in this way are not rectangular coordinate systems but oblique coordinates system, the number acquired under oblique coordinates system
It can lead to the contour distortion of acquisition according to processing under rectangular coordinate system is placed directly on.
Currently, since the installation of sensor misses when above-mentioned composite errors of ball screw spiral raceway automatic detection device uses
Contour distortion phenomenon caused by difference there is no good solution.It uses steel ball with high precision as benchmark for this deficiency, passes through
Composite errors of ball screw spiral raceway automatic detection device acquires the great circle outline data of steel ball, seeks great circle outline data
Relationship between the distortion factor and installation error can accurately seek the installation error of sensor, but there is no correlation in the prior art
Research.
Invention content
The purpose of the present invention is to provide a kind of compensation of screw rod type face detection device displacement sensor system installation error
Method.
The present invention adopts the technical scheme that in order to solve the above problem：A kind of screw rod type face detection device displacement sensor system
The compensation method of system installation error, includes the following steps：
Step 1, structure coordinate system, the specifically rectangular coordinate system in space of structure lathe bed and displacement sensor system composition
Space oblique coordinates system；Specially：
Step 1-1, the rectangular coordinate system in space of lathe bed is built, the rectangular coordinate system in space of lathe bed is o-x0y0z0, wherein x0
Axis is along the length direction of lathe bed, y axially parallel with leading screw0Axis is in perpendicular and x0Axis is vertical, and direction is upward, z0Axis exists
In horizontal plane with plane ox0y0Vertically, and and x0Axis and y0The rectangular coordinate system in space of axis composition follows right-hand rule；
Step 1-2, the space oblique coordinates system of structure displacement sensor system composition, oblique coordinates system o-xsyszsIn, xsAxis
For the measurement direction of grating scale, ysAxis is the measurement direction of light veil type displacement sensor, zsAxis is along light veil type laser displacement sensor
Laser emission direction, and zsAxis can be around ysAxis rotates.
The pass of the rectangular coordinate system in space of step 2, the space oblique coordinates system for determining displacement sensor system composition and lathe bed
System, and determine that the error that needs compensate is：Installation error and light veil type displacement of the light veil type displacement sensor in perpendicular
The installation error of sensor in the horizontal plane；
Determine that the relationship of the space oblique coordinates system of displacement sensor system composition and the rectangular coordinate system in space of lathe bed is：
Spatial axes xsWith spatial axes x0Relationship pass through drift angle αyAnd αzIt determines, i.e. spatial axes xsAround y0Axis rotation angle αy,
Further around z0Axis rotation angle αzX can be transformed to0Axis, wherein αyFor spatial axes xsWith plane ox0y0Between angle, αzFor space
Axis xsWith plane ox0z0Between angle；Equally, spatial axes ysAround x0Axis rotation angle βx, further around z0Axis rotation angle βzIt is convertible
To y0Axis, wherein βxFor spatial axes ysWith plane ox0y0Between angle, βzFor spatial axes ysWith plane oy0z0Between angle；
Spatial axes zsAround x0Axis rotation angle γx, further around y0Axis rotation angle γzIt may be shifted into z0Axis, wherein γxFor spatial axes zsWith it is flat
Face ox0z0Between angle, γzFor spatial axes zsWith plane oy0z0Between angle；
Assuming that 1：The length of grating scale is very long, and installation accuracy can ensure, then xsWith x0It is considered as coincidence, i.e. αy=0, αz=
0；
Assuming that 2：The measurement direction of light veil type laser displacement sensor is vertical with Laser emission direction, i.e. βx=γx, and βx
And γxParts Measurement is not influenced, it is believed that βx=γx=0；
According to hypothesis 1 and hypothesis 2 it is found that the space right-angle of the space oblique coordinates system and lathe bed of displacement sensor system composition
The relationship of coordinate system can determine by 2 drift angles, i.e. βzAnd γz, βzThe installation for being light veil type displacement sensor in vertical plane misses
Difference, γzFor the installation error of light veil type displacement sensor in the horizontal plane.
Step 3 acquires steel ball great circle outline data using screw rod type surface detection system, builds round least square fitting side
Journey, and solve the center of circle and the radius for obtaining the big circle contour of steel ball；Specially：
Step 3-1, the least square fitting equation of structure circle is：
(x in formulasi,ysi) it is the steel ball great circle outline data that goal systems acquires, i=1,2 ... n, (xc,yc) it is fitting
The center of circle, r are fit radius, and n is the quantity of acquisition；
Step 3-2, it asks local derviation to obtain equation group the equation in step 3-1 to be：
Step 3-3, to the solving equations in step 3-2, result is：
In formula, intermediate variable m1、m2、m3And m4Calculating formula it is as follows：
Influence of the installation error to measurement steel ball of step 4, analysis light veil type displacement sensor in the horizontal plane；Specifically
For：
Step 4-1, structure circle is in rectangular coordinate system ox0y0In normal equation：
(x0-x'c)2+(y0-y'c)2=r2
(x' in formulac,y'c) be circle the center of circle, r is radius；
Step 4-2, the coordinate system of the measurement axis of the Laser emission direction of light veil type displacement sensor and grating scale composition is
Oblique coordinates system, the point of the acquisition under oblique coordinates system, which is transformed into formula used under rectangular coordinate system, is：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
γz=(90 ° of-∠ xsozs) it is the installation error of light veil type displacement sensor in the horizontal plane；
Step 4-3, by formulaIt substitutes into step 4-1 to build and can obtain ellipse side in round normal equation
Journey：
It follows that can become if being placed directly on the steel ball great circle data of oblique coordinates system down-sampling under rectangular coordinate system if circle
At ellipse, elliptical long axis and x0It is parallel, if carrying out fitted ellipse using round fit equation, the radius of fitting can be caused inclined
Greatly, and and γzIt is positive and negative unrelated.
Step 5, the method according to the conclusion and step 3 of step 4, ask light veil type displacement sensor to exist using symmetrical graphing method
Installation error in horizontal plane；Specially：
Step 5-1, with zsThe current location of axis is dead-center position；
Step 5-2, z is rotated clockwisesAxis step-length is the angle of λ sizes, at this time clockwise for just, counterclockwise is negative, angle
The size precision as needed of λ is spent to determine；
Step 5-3, the steel ball of a diameter of 9.525mm is selected, step 3 is executed and seeks fit radius value；
Step 5-4, step 5-2 and step 5-3m times are repeated, the size of m is determined according to λ, and the smaller then m of λ are bigger；
Step 5-5, z is allowedsAxis is returned to dead-center position, same to repeat step 5- with identical step pitch rotation angle λ counterclockwise
2 and step 5-3m times, and the curve graph that steel ball fitting diameter value changes with rotation angle is made, curve is about actual zero position
It sets symmetrically, then the abscissa of the minimum point of curve is just γzValue；
Step 5-6, γ is acquiredzAfterwards by zsThe dead-center position of axis is set as γzPosition, increase step angle λ simultaneously adjust m weight
Multiple step 5-1-step 5-6, judges whether the curve made using symmetrical graphing method is symmetrical about zero, if asymmetric later
It then reduces step angle λ and adjustment number of repetition m repeats step 5-1-step 5-6, terminate if symmetrical.
Influence of the installation error to measurement steel ball of step 6, analysis light veil type displacement sensor in perpendicular；Specifically
For：
Step 6-1, structure circle is in rectangular coordinate system ox0y0In normal equation：
(x0-x'c)2+(y0-y'c)2=r2
(x' in formulac,y'c) be circle the center of circle, r is radius；
Step 6-2, the measure axis and the coordinate system for measuring axis composition of grating scale of light veil type displacement sensor are skew coordinates
System, the point under skew coordinates, which is transformed into formula used under rectangular coordinate system, is：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
(x in formula0,y0) it is rectangular coordinate system ox0y0In point, (xs,ys) it is oblique coordinates system oxsysIn point,
βz=(90 ° of-∠ xsoys) it is installation error of the light veil type displacement sensor in perpendicular, be clockwise at this time
Just；
Step 6-3, by above-mentioned formulaIt substitutes into step 6-1 and builds in round normal equation, obtain
Elliptic equation：
It can thus be appreciated that can become if being placed directly on the steel ball great circle data of oblique coordinates system down-sampling under rectangular coordinate system if circle
At ellipse, and contain x in formula0And y0Cross term, so elliptical long axis and x0Between at a non-90 degree angle.
Step 7, according to installation error of the light veil type displacement sensor in perpendicular in step 6 to measure steel ball shadow
It rings, to build the least square fitting equation for solving light veil type displacement sensor installation error in perpendicular, in conjunction with step
Rapid 3 solve light veil type displacement sensor installation error in perpendicular using Newton iterative.Light veil type displacement is solved to pass
Sensor installation error in perpendicular is specially：
Step 7-1, in conjunction with the oblique seat built in the least square fitting equation of the circle built in step 3-1 and step 6-2
The formula that mark system converts to rectangular coordinate system, the least square fitting equation of structure are：
(x in formulasi,ysi) it is the steel ball great circle outline data that goal systems acquires, i=1,2 ... n；
Step 7-2, it asks local derviation to obtain equation group the equation in step 7-1 to be：
Step 7-3, step 3 is executed, and using the central coordinate of circle of solution and radius as the initial value of Newton iterative to step
The equation group of rapid 7-2 is solved, and the formula of Newton iterative is：
Qk=Qk-1-B-1F
In formulaFor the solution of kth time iteration,For Jacobian matrix, B-1
For the inverse matrix of B, whereinFor the equation group in step 7-2, the solution in step 3 is used
Initial value as Newton iteration method：The condition of convergence is | | Qk-Qk-1||2<δ, δ value are according to required
Precision is determined, k ∈ (1,2 ... t) terminate iteration when iterations k is more than t, whereinIt is that light veil type displacement sensor is erecting
Installation error in straight plane.
Compared with prior art, the present invention its remarkable advantage is：1) method of the invention is in addition to the included sensing of measuring system
Device seeks installing the installation error of itself, does not need additional sensor；2) method of the invention uses steel ball with high precision conduct
Benchmark carrys out reverse installation error, does not need complicated auxiliary clamp, has the characteristics that precision is high, convenient and simple；3) side of the invention
Influence of the method using installation error to measurement steel ball, light veil type displacement sensor can not only be effectively sought using symmetrical graphing method
Installation error in the horizontal plane, and can also be artificial control accuracy；4) method of the invention seeks light using Newton iteration method
Installation error of the curtain formula displacement sensor in perpendicular is not only efficient, and precision is also high.
Further detailed description is done to the present invention below in conjunction with the accompanying drawings.
Description of the drawings
Fig. 1 is the relational graph between the space oblique coordinates system that lathe bed rectangular coordinate system and displacement sensor system form.
Fig. 2 is the experimental provision easy structure figure of the present invention.
Fig. 3 is that the present invention seeks γ using symmetrical graphing methodzCurve graph.
Fig. 4 is the multiple compensating gamma of the present inventionzγ is being asked using symmetrical graphing method afterwardszCurve graph.
Fig. 5 is present invention compensation βzThe survey result of leading screw raceway before.
Fig. 6 is present invention compensation βzThe measurement result of leading screw raceway later.
Specific implementation mode
The present invention be directed to composite errors of ball screw spiral raceway in Patent No. 200910029189.6 to detect automatically
The improvement of method, application are composite errors of ball screw spiral raceway automatic detection device.A kind of leading screw of the present invention
The compensation method of Surface inspection device displacement sensor system installation error, includes the following steps：
Step 1, structure coordinate system, the specially space of the rectangular coordinate system in space of lathe bed and displacement sensor system composition
Oblique coordinates system；
The rectangular coordinate system in space of lathe bed is o-x0y0z0, wherein x0Axis is axially put down along the length direction of lathe bed with leading screw
Row, y0Axis is in perpendicular and x0Axis is vertical, and direction is upward.z0Axis in the horizontal plane with plane ox0y0Vertically, and and x0Axis
And y0The rectangular coordinate system in space of axis composition follows right-hand rule.
The coordinate system of the composition of displacement sensor system is space oblique coordinates system o-xsyszs.Wherein xsAxis is grating scale
Measurement direction, ysAxis is the measurement direction of light veil type displacement sensor, zsLaser emission of the axis along light veil type laser displacement sensor
Direction, and zsAxis can be around ysAxis rotates, adjustment ∠ xsozsSize.
Grating scale and light veil type displacement sensor are to each point on the normal direction section shape curve of ball screw spiral raceway to be measured
Axial position and radial position are sampled.But since the coordinate system of the composition of installation error displacement sensor system is Space Oblique
Coordinate system, the data acquired under oblique coordinates system are put into, and under rectangular coordinate system the curve of acquisition can be distorted, so first will tiltedly sit
Data under mark system are transformed under rectangular coordinate system and could carry out subsequent data processing, this just needs to seek method to seek sensing
The installation error of device.
The pass of the rectangular coordinate system in space of step 2, the space oblique coordinates system of structure displacement sensor system composition and lathe bed
System, and determine that the error that needs compensate is：Installation error and light veil type displacement of the light veil type displacement sensor in perpendicular
The installation error of sensor in the horizontal plane；
Spatial axes xsWith spatial axes x0Relationship pass through drift angle αyAnd αzIt determines, i.e. spatial axes xsAround y0Axis rotation angle αy,
Further around z0Axis rotation angle αzX can be transformed to0Axis, wherein αyFor spatial axes xsWith plane ox0y0Between angle, αzFor space
Axis xsWith plane ox0z0Between angle；Equally, spatial axes ysAround x0Axis rotation angle βx, further around z0Axis rotation angle βzIt is convertible
To y0Axis, wherein βxFor spatial axes ysWith plane ox0y0Between angle, βzFor spatial axes ysWith plane oy0z0Between angle；
Spatial axes zsAround x0Axis rotation angle γx, further around y0Axis rotation angle γzIt may be shifted into z0Axis, wherein γxFor spatial axes zsWith it is flat
Face ox0z0Between angle, γzFor spatial axes zsWith plane oy0z0Between angle；
Assuming that 1：The length of grating scale is very long, and installation accuracy can ensure, then xsWith x0It is considered as coincidence, i.e. αy=0, αz=
0。
Assuming that 2：The measurement direction of light veil type laser displacement sensor is vertical with Laser emission direction, i.e. βx=γx, and βx
And γxParts Measurement is not influenced, it is believed that βx=γx=0.
According to hypothesis 1 and hypothesis 2 it is found that the space right-angle of the space oblique coordinates system and lathe bed of displacement sensor system composition
The relationship of coordinate system can determine by 2 drift angles, i.e. βzAnd γz。βzThe installation for being light veil type displacement sensor in vertical plane misses
Difference, γzFor the installation error of light veil type displacement sensor in the horizontal plane.
Step 3 acquires steel ball great circle outline data using screw rod type surface detection system, builds round least square fitting side
Journey, and solve；
Building round least square fitting equation is：
(x in formulasi,ysi) it is the steel ball great circle outline data that goal systems acquires, i=1,2 ... n, (xc,yc) it is fitting
The center of circle, r are fit radius.
It asks local derviation to obtain equation group the equation in formula (1) to be：
To formula (2) solve result be：
In formula, n is the number of gathered data point, intermediate variable m1、m2、m3And m4Calculating formula it is as follows：
Because backoff algorithm is on the basis of steel ball, the steel ball that above-mentioned steel ball generally uses high-precision and is relatively large in diameter,
Such as a diameter of 9.525mm, circularity are the steel ball of 0.2um.
Influence of the installation error to measurement steel ball of step 4, first analysis light veil type displacement sensor in the horizontal plane；
Since backoff algorithm is based on steel ball with high precision, so first structure steel ball is in rectangular coordinate system ox0y0The mark of middle projection circle
Quasi- equation：
(x0-x'c)2+(y0-y'c)2=r2 (4)
(x' in formulac,y'c) be circle the center of circle, r is radius；
Since light veil type displacement sensor has installation error in the horizontal plane, so the laser of light veil type displacement sensor
The coordinate system for measuring axis composition of the direction of the launch and grating scale is oblique coordinates system, and the point of the acquisition under oblique coordinates system is transformed into directly
Formula used is under angular coordinate system：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
Do not occur ox in formulaszsPoint under coordinate system is because z-axis is the Laser emission side of light veil type displacement sensor
To, rather than axis is measured, so by rotating xsAxis makes xsAxis and zsAxis is vertical, γz=(90 ° of-∠ xsozs) it is light veil type displacement
The installation error of sensor in the horizontal plane.
The steel ball great circle data of oblique coordinates system down-sampling are placed directly under rectangular coordinate system to be equivalent to and substitute into formula (6)
Circle can become to ellipse in formula (4)：
According to formula it is found that elliptical long axis and x0It is parallel, if carrying out fitted ellipse using round fit equation, can cause
The radius of fitting is bigger than normal, fit radius and 1/cos γzIt is directly proportional, and and γzIt is positive and negative unrelated, can be found out according to this characteristic
γzSize.
Step 5, influence of the installation error to measurement steel ball according to light veil type displacement sensor in the horizontal plane, in conjunction with step
Rapid 3 seek the installation error of light veil type displacement sensor in the horizontal plane using symmetrical graphing method.
The installation error of light veil type displacement sensor in the horizontal plane is asked to be specially using symmetrical graphing method：
1. with zsThe current location of axis is dead-center position；
2. rotating clockwise zsAxis step-length is the angle of λ sizes (clockwise for just, counterclockwise is negative, the big rootlet of angle
It is determined according to the precision of needs)；
3. selecting the steel ball being relatively large in diameter, steel ball great circle outline data seeks fitting using formula (1)-(3) half is obtained
Diameter value；
2. and 3. m times 4. repeating, the size of m is determined according to λ, and the smaller m of λ should be bigger；
5. allowing zs2. and 3. m times axis is returned to dead-center position, same to repeat with identical step pitch rotation angle λ counterclockwise, and
Make the curve graph that changes with rotation angle of steel ball fitting diameter value, curve is symmetrical about actual dead-center position, then curve
The abscissa of minimum point is just γzValue；
6. just acquiring γzAfterwards by zsThe dead-center position of axis is adjusted to the position of η, if wanting to determine whether to terminate, increases step pitch
Angle λ adjustment m repeat experiment 1. -6. see whether the curve made symmetrical, reduce step angle λ if asymmetric and adjustment repeat time
Number m repeat experiment 1. -6., terminate if symmetrical.
Step 6 analyzes influence of installation error of the light veil type displacement sensor in perpendicular to measurement steel ball again.
Since there are installation errors in perpendicular for light veil type displacement sensor, so the survey of light veil type displacement sensor
The coordinate system for measuring axis composition for measuring axis and grating scale is oblique coordinates system, and the point under skew coordinates is transformed into institute under rectangular coordinate system
Formula is：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
(x in formula0,y0) it is rectangular coordinate system ox0y0In point, (xs,ys) it is oblique coordinates system oxsysIn point, βz=
(90°-∠xsoys) it is installation error of the light veil type displacement sensor in perpendicular, at this time clockwise for just.
The steel ball great circle data of oblique coordinates system down-sampling are placed directly under rectangular coordinate system to be equivalent to and substitute into formula (9)
Circle can become to ellipse in formula (4)：
Contain x in formula0And y0Cross term, so elliptical long axis and x0Between at a non-90 degree angle.Thus may be used
Know, if oval lower half portion is bisected into left and right circular arc, respectively using least square fitting formula fitting of circle or so circle
Arc, then one bigger than normal of the radius being fitted one is less than normal, and here it is the reason of asymmetry occur when measuring bicircular arcs leading screw.
Step 7, according to installation error of the light veil type displacement sensor in perpendicular in step 6 to measure steel ball shadow
It rings, to build the least square fitting equation for solving light veil type displacement sensor installation error in perpendicular, in conjunction with step
Rapid 3 are solved using Newton iterative.
In the case where before the steel ball great circle outline data to acquisition is fitted needing that data are first transformed into rectangular coordinate system,
So being by the least square fitting equation obtained in formula (8) substitution formula (1)：
(x in formulasi,ysi) be goal systems acquisition steel ball great circle outline data, i=1,2 ... n,.
If the circularity of steel ball is sufficiently high, the random error for ignoring sensor can be using formula (11) come reverse βz, right
Unknown quantity in formula (11) asks local derviation to obtain equation group respectively：
The central coordinate of circle and radius solved using formula (1)-formula (3) is as the initial value of Newton iterative to equation group
(12) it is solved, the formula of Newton iterative is：
Qk=Qk-1-B-1F (13)
In formulaFor the solution of this iteration of kth,For Jacobian matrix, B-1
For the inverse matrix of B, whereinFor equation group (12).Since Newton iteration method is local convergence algorithm,
Want to converge to global solution, need to select initial value appropriate, so using the solution of formula (1)-formula (3)As newton
The initial value of iterative method：The condition of convergence is | | Qk-Qk-1||2<δ, δ value are come according to required precision
It is fixed, and k ∈ (1,2 ... t) terminate iteration when iterations k is more than t.
The method of the present invention, as benchmark, is not only increased accuracy and also avoids introducing steel ball using steel ball with high precision
Clamping error；Newton iteration method is being used to select value near global solution as iterative initial value when solving Nonlinear System of Equations, into
One step improves the accuracy of convergent speed reconciliation.
Further detailed description is done to the present invention with reference to embodiment.
Embodiment
The process that screw rod type surface detection system is implemented to measure to steel ball is illustrated according to Fig. 2 in Figure of description, first
First rotation hand wheel 5 adjusts handwheel to dead-center position, and steel ball small magnet or other Simple assisting devices are then suspended in light veil type
The right in the light curtain face of displacement sensor 4, steel ball and marble lathe bed 1 are connected and stationary, in driving air floating platform 3 from a left side
During moving right, the minimum point of the intersection curve of each light curtain face and steel ball is then a data point of acquisition, light curtain
Formula displacement sensor 4 measures y-coordinate value, and grating scale 6 measures x coordinate value, and air floating platform 3 can then acquire steel ball great circle from left to right
Profile lower half portion data.
For seeking installation error β of the light veil type displacement sensor in perpendicularzExist with light veil type displacement sensor
Installation error γ in horizontal planezSteel ball parameter be：Steel ball size：9.525mm, circularity 0.2um.
The installation error γ of light veil type displacement sensor in the horizontal plane is sought first with symmetrical graphing methodzMethod such as
Under：
1. adjusting handwheel 5 arrives dead-center position；
2. rotating clockwise the handwheel 5 in Fig. 2 in Figure of description, the angular dimension of rotation is 10 '；
3. seeking the radius value of steel ball using formula (1)-(3)；
2. and 3. 10 times 4. repeating；
5. rotation hand wheel 5 is returned to dead-center position, with the rotation hand wheel 5 counterclockwise of identical step pitch 10 ', it is same repeat 2. and
3. 10 times, and make the curve graph that changes with rotation angle of steel ball fitting diameter value, in bright book attached drawing shown in Fig. 3, curve about
γzPositional symmetry, the i.e. abscissa of the minimum point of curve are just γzValue, according to curve graph Primary Location γz≈-0.75°；
6. setting the dead-center position of handwheel 5 to γz≈ -0.75 ° of position increases step if wanting to determine whether to terminate
Elongation repeat experiment 1. -6. see whether the curve made symmetrical, step angle is reduced if asymmetric and adjustment number of repetition repeats
Experiment 1. -6., terminate if symmetrical.
Fig. 4 is that symmetrical graphing method is used for multiple times to reset the result figure after dead-center position in Figure of description, for convenience
Compare the measurement result that will be rotated counterclockwise and be symmetric to the right about dead-center position, it can be seen that two curves essentially coincide.It says
Bright γ at this timez≈0°。
The raceway design parameter of bicircular arcs ball-screw 2 is as follows in Fig. 2 in bright book attached drawing：
Raceway arc radius rL=rRThe contact angle α of=3.429mm, ball and arc racewayL=αR=45 °, eccentric distance eL
=eR=0.18mm, eccentric high hL=hR=0.18mm.
Same mode obtains the great circle outline data of steel ball, is substituted into formula (11)-(13), finds out drift angle βz=
0.147 °, wherein convergence precision δ=0.00000001 of Newton iteration method, iterations k=3 when convergence, iterations
It is limited to t=10 times.The backoff algorithm known to convergence precision and iterations is not only efficient, and precision is also high.
The air-floated movable platform 3 of Fig. 2 is moved along the axial direction of leading screw 2 in Figure of description, and grating scale 6 obtains leading screw method
The x coordinate value of contour curve on section, light veil type displacement sensor obtain the y-coordinate value of leading screw normal section contour curve.
Leading screw raceway outline data is obtained, left and right circular arc data are detached, the center of circle of left and right circular arc is found out using formula (1)~(3) fitting
Coordinate and radius value.Fig. 5 is compensation β in Figure of descriptionzIt uses before obtained by ballscrew type gauge detection leading screw
Result：
Raceway arc radius rL=3.4520mm, rRThe contact angle α of=3.4282mm, ball and arc racewayL=45 °
.28 ', αR=47 ° of .00 ', eccentric distance eL=0.1974mm, eR=0.1852mm, eccentric high hL=0.1942mm, hR=
0.1726mm。
Fig. 6 is compensation β in Figure of descriptionzBallscrew type gauge is used to survey the result obtained by leading screw later：
Raceway arc radius rL=3.4395mm, rRThe contact angle α of=3.4410mm, ball and arc racewayL=45 °
.59 ', αR=46 ° of .25 ', eccentric distance eL=0.1916mm, eR=0.1909mm, eccentric high hL=0.1824mm, hR=
0.185mm。
Fig. 5 and Fig. 6 in comparative illustration book attached drawing is it is found that the left radius value ratio of the leading screw raceway measured before error compensation is right
Radius value is bigger than normal, this is because βzInfluence, compensation βzAfterwards, the difference of the identical raceway of leading screw or so radius value is measured less than 2um,
Its measurement result can accurately reflect mismachining tolerance.
From the foregoing, it will be observed that the experimental data before and after comparison compensation understands that two methods can efficiently and accurately seek installation and miss
Difference, after the installation error of compensation light veil type displacement sensor, screw rod type surface detection system can accurately measure leading screw raceway type
The parameter in face.
Claims (8)
1. a kind of compensation method of screw rod type face detection device displacement sensor system installation error, which is characterized in that including with
Lower step：
Step 1, structure coordinate system specifically build the space of the rectangular coordinate system in space and displacement sensor system composition of lathe bed
Oblique coordinates system；
The relationship of the rectangular coordinate system in space of step 2, the space oblique coordinates system for determining displacement sensor system composition and lathe bed, and
Determine that the error that needs compensate is：Installation error and light veil type displacement sensor of the light veil type displacement sensor in perpendicular
Installation error in the horizontal plane；
Step 3 acquires steel ball great circle outline data using screw rod type surface detection system, builds round least square fitting equation,
And solve the center of circle and the radius for obtaining the big circle contour of steel ball；
Influence of the installation error to measurement steel ball of step 4, analysis light veil type displacement sensor in the horizontal plane；
Step 5, the method according to the conclusion and step 3 of step 4, ask light veil type displacement sensor in level using symmetrical graphing method
Installation error in face；
Influence of the installation error to measurement steel ball of step 6, analysis light veil type displacement sensor in perpendicular；
Step 7, the influence according to installation error of the light veil type displacement sensor in perpendicular in step 6 to measurement steel ball,
Come build solve light veil type displacement sensor installation error in perpendicular least square fitting equation, in conjunction with step 3
Light veil type displacement sensor installation error in perpendicular is solved using Newton iterative.
2. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, the rectangular coordinate system in space of lathe bed and the space oblique coordinates system tool of displacement sensor system composition is built in step 1
Body is：
Step 1-1, the rectangular coordinate system in space of lathe bed is built, the rectangular coordinate system in space of lathe bed is o-x0y0z0, wherein x0Axis edge
The length direction of lathe bed, y axially parallel with leading screw0Axis is in perpendicular and x0Axis is vertical, and direction is upward, z0Axis is in level
In face with plane ox0y0Vertically, and and x0Axis and y0The rectangular coordinate system in space of axis composition follows right-hand rule；
Step 1-2, the space oblique coordinates system of structure displacement sensor system composition, oblique coordinates system o-xsyszsIn, xsAxis is light
The measurement direction of grid ruler, ysAxis is the measurement direction of light veil type displacement sensor, zsAxis swashs along light veil type laser displacement sensor
Light emitting direction, and zsAxis can be around ysAxis rotates.
3. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, the rectangular coordinate system in space for the space oblique coordinates system and lathe bed that displacement sensor system forms is determined in step 2
Relationship is：
Spatial axes xsWith spatial axes x0Relationship pass through drift angle αyAnd αzIt determines, i.e. spatial axes xsAround y0Axis rotation angle αy, further around z0
Axis rotation angle αzX can be transformed to0Axis, wherein αyFor spatial axes xsWith plane ox0y0Between angle, αzFor spatial axes xsWith
Plane ox0z0Between angle；Equally, spatial axes ysAround x0Axis rotation angle βx, further around z0Axis rotation angle βzIt may be shifted into y0
Axis, wherein βxFor spatial axes ysWith plane ox0y0Between angle, βzFor spatial axes ysWith plane oy0z0Between angle；Space
Axis zsAround x0Axis rotation angle γx, further around y0Axis rotation angle γzIt may be shifted into z0Axis, wherein γxFor spatial axes zsWith plane
ox0z0Between angle, γzFor spatial axes zsWith plane oy0z0Between angle；
Assuming that 1：The length of grating scale is very long, and installation accuracy can ensure, then xsWith x0It is considered as coincidence, i.e. αy=0, αz=0；
Assuming that 2：The measurement direction of light veil type laser displacement sensor is vertical with Laser emission direction, i.e. βx=γx, and βxAnd γx
Parts Measurement is not influenced, it is believed that βx=γx=0；
According to hypothesis 1 and hypothesis 2 it is found that the rectangular space coordinate of the space oblique coordinates system and lathe bed of displacement sensor system composition
The relationship of system can determine by 2 drift angles, i.e. βzAnd γz, βzFor installation error of the light veil type displacement sensor in vertical plane, γz
For the installation error of light veil type displacement sensor in the horizontal plane.
4. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, step 3 acquires steel ball great circle outline data using screw rod type surface detection system, builds round least square fitting side
Journey, and solve and show that the center of circle of the big circle contour of steel ball and radius are specially：
Step 3-1, the least square fitting equation of structure circle is：
(x in formulasi,ysi) it is the steel ball great circle outline data that goal systems acquires, i=1,2 ... n, (xc,yc) it is the fitting center of circle,
R is fit radius, and n is the quantity of acquisition；
Step 3-2, it asks local derviation to obtain equation group the equation in step 3-1 to be：
Step 3-3, to the solving equations in step 3-2, result is：
In formula, intermediate variable m1、m2、m3And m4Calculating formula it is as follows：
5. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, step 4 analyzes influence of the installation error of light veil type displacement sensor in the horizontal plane to measurement steel ball, specifically
For：
Step 4-1, structure circle is in rectangular coordinate system ox0y0In normal equation：
(x0-x'c)2+(y0-y'c)2=r2
(x' in formulac,y'c) be circle the center of circle, r is radius；
Step 4-2, the coordinate system for measuring axis composition of the Laser emission direction of light veil type displacement sensor and grating scale is tiltedly to sit
Mark system, the point of the acquisition under oblique coordinates system, which is transformed into formula used under rectangular coordinate system, is：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
γz=(90 ° of-∠ xsozs) it is the installation error of light veil type displacement sensor in the horizontal plane；
Step 4-3, by formulaIt substitutes into step 4-1 to build and can obtain elliptic equation in round normal equation：
It follows that can become ellipse if being placed directly on the steel ball great circle data of oblique coordinates system down-sampling under rectangular coordinate system if circle
Circle, elliptical long axis and x0It is parallel, if carrying out fitted ellipse using round fit equation, the radius of fitting can be caused bigger than normal, and
With γzIt is positive and negative unrelated.
6. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, step 5 asks the installation error of light veil type displacement sensor to be in the horizontal plane specially using symmetrical graphing method：
Step 5-1, with zsThe current location of axis is dead-center position；
Step 5-2, z is rotated clockwisesAxis step-length is the angle of λ sizes, at this time clockwise for just, be counterclockwise it is negative, angle λ's
Size precision as needed determines；
Step 5-3, the steel ball of a diameter of 9.525mm is selected, step 3 is executed and seeks fit radius value；
Step 5-4, step 5-2 and step 5-3m times are repeated, the size of m is determined according to λ, and the smaller then m of λ are bigger；
Step 5-5, z is allowedsAxis is returned to dead-center position, same to repeat step 5-2 and step with identical step pitch rotation angle λ counterclockwise
It is 5-3m times rapid, and the curve graph that steel ball fitting diameter value changes with rotation angle is made, curve is about actual dead-center position pair
Claim, then the abscissa of the minimum point of curve is just γzValue；
Step 5-6, γ is acquiredzAfterwards by zsThe dead-center position of axis is set as γzPosition, increase step angle λ simultaneously adjust m repeat walk
Rapid 5-1-step 5-6, judges whether the curve made using symmetrical graphing method is symmetrical about zero later, subtracts if asymmetric
Few step angle λ and adjustment number of repetition m repetition steps 5-1-step 5-6, terminate if symmetrical.
7. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 1,
It is characterized in that, it is specific to the influence for measuring steel ball that step 6 analyzes installation error of the light veil type displacement sensor in perpendicular
For：
Step 6-1, structure circle is in rectangular coordinate system ox0y0In normal equation：
(x0-x'c)2+(y0-y'c)2=r2
(x' in formulac,y'c) be circle the center of circle, r is radius；
Step 6-2, the measure axis and the coordinate system for measuring axis composition of grating scale of light veil type displacement sensor are oblique coordinates system, will
Point under skew coordinates is transformed into formula used under rectangular coordinate system：
Then the point under rectangular coordinate system is transformed under skew coordinates formula used and is：
(x in formula0,y0) it is rectangular coordinate system ox0y0In point, (xs,ys) it is oblique coordinates system oxsysIn point, βz=(90 ° of-∠
xsoys) it is installation error of the light veil type displacement sensor in perpendicular, at this time clockwise for just；
Step 6-3, by above-mentioned formulaIt substitutes into step 6-1 and builds in round normal equation, obtain ellipse
Equation：
It can thus be appreciated that can become ellipse if being placed directly on the steel ball great circle data of oblique coordinates system down-sampling under rectangular coordinate system if circle
Circle, and contain x in formula0And y0Cross term, so elliptical long axis and x0Between at a non-90 degree angle.
8. the compensation method of detection device displacement sensor system installation error in screw rod type face according to claim 4,
It is characterized in that, step 7 solves light veil type displacement sensor installation error in perpendicular and is specially：
Step 7-1, in conjunction with the oblique coordinates system built in the least square fitting equation of the circle built in step 3-1 and step 6-2
The formula converted to rectangular coordinate system, the least square fitting equation of structure are：
(x in formulasi,ysi) it is the steel ball great circle outline data that goal systems acquires, i=1,2 ... n；
Step 7-2, it asks local derviation to obtain equation group the equation in step 7-1 to be：
Wherein βzFor spatial axes ysAround z0The angle of axis rotation；
Step 7-3, step 3 is executed, and using the central coordinate of circle of solution and radius as the initial value of Newton iterative to step 7-2
Equation group solved, the formula of Newton iterative is：
Qk=Qk-1-B-1F
In formulaFor the solution of kth time iteration,For Jacobian matrix, B-1For B's
Inverse matrix, whereinFor the equation group in step 7-2, the solution in step 3 is usedAs ox
The initial value for iterative method of pausing：The condition of convergence is | | Qk-Qk-1||2＜ δ, δ values are according to required precision
Determine, k ∈ (1,2 ... t) terminate iteration when iterations k is more than t, whereinIt is being put down vertically for light veil type displacement sensor
Installation error in face.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108168457A (en) * | 2017-12-28 | 2018-06-15 | 长春长光精密仪器集团有限公司 | A kind of cylindricity error measuring method and measuring system |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102017121344A1 (en) * | 2017-09-14 | 2019-03-14 | Liebherr-Verzahntechnik Gmbh | Method for automatically determining the geometric dimensions of a tool with a spiral-shaped machining area |
| CN111026081B (en) * | 2019-12-10 | 2021-05-11 | 苏州智加科技有限公司 | Error calculation method, device, equipment and storage medium |
| CN112129258B (en) * | 2020-08-24 | 2022-07-26 | 中车唐山机车车辆有限公司 | Scratch depth measuring method |
| CN113642271B (en) * | 2021-08-20 | 2022-07-01 | 南京航空航天大学 | Model-based aeroengine performance recovery control method and device |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004279315A (en) * | 2003-03-18 | 2004-10-07 | Ricoh Co Ltd | Surface-shape detection apparatus, positioning method, surface-shape detection method |
| CN101701798A (en) * | 2009-01-20 | 2010-05-05 | 南京理工大学 | Method and device for automatic detection of composite errors of ball screw spiral raceway |
| CN102072705A (en) * | 2010-12-20 | 2011-05-25 | 南京理工大学 | Ball screw spiral line error on-line detection method and device thereof |
| US8924003B2 (en) * | 2010-11-11 | 2014-12-30 | Fanuc Corporation | Thermal displacement compensation method and thermal displacement compensation device for machine tool |
| CN104330024A (en) * | 2014-10-15 | 2015-02-04 | 济宁中科先进技术研究院有限公司 | Small mechanical part shape and position error detection device and detection method thereof |
-
2016
- 2016-08-03 CN CN201610626814.5A patent/CN106052568B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004279315A (en) * | 2003-03-18 | 2004-10-07 | Ricoh Co Ltd | Surface-shape detection apparatus, positioning method, surface-shape detection method |
| CN101701798A (en) * | 2009-01-20 | 2010-05-05 | 南京理工大学 | Method and device for automatic detection of composite errors of ball screw spiral raceway |
| US8924003B2 (en) * | 2010-11-11 | 2014-12-30 | Fanuc Corporation | Thermal displacement compensation method and thermal displacement compensation device for machine tool |
| CN102072705A (en) * | 2010-12-20 | 2011-05-25 | 南京理工大学 | Ball screw spiral line error on-line detection method and device thereof |
| CN104330024A (en) * | 2014-10-15 | 2015-02-04 | 济宁中科先进技术研究院有限公司 | Small mechanical part shape and position error detection device and detection method thereof |
Non-Patent Citations (2)
| Title |
|---|
| 滚珠丝杠副精度保持性试验台测控系统设计;戴鹏等;《电气与自动化》;20160731;188-212页 * |
| 滚珠丝杠滚道误差测量与分析算法研究;冯虎田;《南京理工大学学报》;20101031;第34卷(第5期);575-580页 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108168457A (en) * | 2017-12-28 | 2018-06-15 | 长春长光精密仪器集团有限公司 | A kind of cylindricity error measuring method and measuring system |
| CN108168457B (en) * | 2017-12-28 | 2020-02-07 | 长春长光精密仪器集团有限公司 | Cylindricity error measuring method and system |
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