CN112859736B - Cycloid type scanning measurement trajectory planning method and system for free-form surface - Google Patents

Cycloid type scanning measurement trajectory planning method and system for free-form surface Download PDF

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CN112859736B
CN112859736B CN202110115946.2A CN202110115946A CN112859736B CN 112859736 B CN112859736 B CN 112859736B CN 202110115946 A CN202110115946 A CN 202110115946A CN 112859736 B CN112859736 B CN 112859736B
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cycloid
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measuring head
curved surface
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CN112859736A (en
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胡鹏程
黄丽华
陈吉红
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
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    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus

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Abstract

The invention discloses a cycloid type scanning measurement trajectory planning method and system for a free-form surface, belongs to the field of five-axis continuous measurement of the free-form surface, and aims to improve the dynamic performance of a machine by avoiding frequent acceleration and deceleration of a measuring head rotating shaft so as to improve the measurement efficiency. The method comprises a measuring head trajectory curve generating step, a cycloid step length determining step and a cycloid scanning trajectory expanding step. According to the invention, in the scanning measurement process, the C axis can be always kept in the same rotation direction, and can be kept at a constant angular speed when necessary, so that the vibration caused by sudden change of the rotation direction of the C axis is avoided, the dynamic performance of the measuring machine is obviously improved, the track length of the measuring head can be obviously shortened, the amount of exercise of the linear axis is reduced, and the measurement efficiency is improved.

Description

Cycloid type scanning measurement trajectory planning method and system for free-form surface
Technical Field
The invention belongs to the field of five-axis measurement, and particularly relates to a cycloid type scanning measurement trajectory planning method and system for a free-form surface.
Background
Free-form surface measurement is more and more widely applied in industrial product manufacturing, especially for parts with higher precision requirements, and among various measurement methods, a Coordinate Measuring Machine (CMM) is often the first choice for measuring free-form surfaces due to its characteristics of high precision, high efficiency and the like. Compared with a three-axis CMM (point-by-point discrete measurement) and a three-axis and two-axis CMM (three-axis linkage scanning measurement with fixed measuring head orientation), the three-axis CMM can realize high-efficiency continuous scanning measurement with simultaneous five-axis linkage, fully utilizes the geometric characteristics of a curved surface and the unique dynamic performance of a measuring machine, plans a more efficient measurement track, and has a larger application prospect and value.
Currently, research related to planning of a five-axis CMM measurement trajectory mainly focuses on generating a measurement path according to different factors such as trajectory smoothness and measurement efficiency, for example, generating a measurement trajectory by using a "guideline", adaptive partition measurement, a potential field method, a spiral scanning trajectory planning method, and the like. When the methods are used for searching for the optimal measurement track, the motion capability of a light measuring head (namely a rotating shaft AC) is tried to be fully utilized, and a heavy translation shaft (namely an XYZ shaft) with large inertia is enabled to move slowly, so that the kinematic performance of the measurement equipment is better utilized, and the measurement accuracy is ensured. In the aspect of a track planning algorithm, a currently common mode is to divide a measurement track into a measuring head track and a measuring needle tip scanning track, firstly find a measuring head track curve covering a part of a measured curved surface, and then plan a corresponding scanning motion track of a measuring needle on the measured curved surface according to the measuring head track curve, so that the measurement track can be ensured to completely cover the measured curved surface.
To the research, the AC shaft swings in a certain angle range in the measuring process, and the tip of the measuring needle is ensured to be always in contact with the measured surface, so that an oscillation-type measuring path is formed on the measured surface, but the measuring needle needs to swing back and forth in order to enlarge the scanning area, namely, the C shaft needs to continuously change the motion direction (namely, the scanning track of the tip of the measuring needle is in an oscillation type), and the vibration of the rotating shaft is inevitably caused.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a cycloid type scanning measurement trajectory planning method and system for a free-form surface, and aims to solve the problem of vibration of a rotating shaft.
In the traditional oscillation type five-axis scanning measurement, the rotation shaft is accelerated and decelerated frequently, so that the vibration of the rotation shaft is inevitably caused, and the precision, the dynamic performance of a machine and the measurement efficiency are influenced. And since the a-axis (fifth joint) is mounted on the C-axis (fourth joint), the C-axis is subjected to a larger load than the a-axis. If the frequent speed change of the rotating shaft (particularly, the C-axis) can be reduced, the vibration of the rotating shaft can be significantly reduced, and thus more excellent dynamic performance can be obtained and the measurement efficiency can be improved.
In order to achieve the above object, the present invention further improves the kinematic performance of a five-axis CMM, and is inspired by cycloid machining in a numerical control machining process, and on one hand, the present invention provides a cycloid type scanning measurement trajectory planning method for a free-form surface, including the following steps:
(1) generating a measuring head track curve: offset curved surface S for measured curved surface SrPartitioning is carried out, and corresponding measuring head tracks are generated, so that the area of a sub-region covered by each measuring head track curve is maximized, and the complete coverage of the measured curved surface is ensured;
the offset curved surface SrThe offset curved surface is an offset curved surface which takes the radius of the tip of the measuring needle as an offset distance along the normal direction of the curved surface S to be measured;
(2) a cycloid step size determining step: determining a cycloid step length by half of a cycloid scanning circle, establishing a local coordinate system for any point on the cycloid scanning circle, calculating a corresponding arch height error by a given initial step length, solving an optimization problem according to a given arch height error threshold value constraint condition, and searching for an optimal step length;
the cycloid scanning circle is along the advancing direction of the measuring head, when the C axis of the rotating shaft of the measuring head rotates for a circle around the Z axis, the measuring head moves the distance of cycloid step length along the measuring head trajectory curve, and a cycloid-shaped scanning trajectory curve tr formed on the offset curved surface1 i(ii) a The lower corner mark j represents that the cycloid scanning circle belongs to the jth measuring head track curve, and the upper corner mark i represents that the cycloid scanning circle belongs to the ith cycloid scanning circle under the measuring head track curve;
(3) expanding a cycloid scanning trajectory: using a first measuring head track curve C1As an initial point for determining a first pair of cycloid sweep circles; from the midpoint, expanding forwards and backwards respectively by a given initial step length, optimizing and iterating according to a given bow height error threshold value constraint condition to obtain an optimal cycloid step length, and generating a first pair of cycloid scanning circles; and deriving the rest cycloid scanning circles forwards and backwards by the same method until the (i + 1) th cycloid scanning circle falls outside the curved surface, discarding the track, and repeating the operation on the sub-area covered by each measuring head track curve to complete the expansion of all cycloid scanning tracks.
Further, step (1) comprises the following substeps:
(1.1) generating a measuring head track curve by the seed curve:
(1.1.1) with an offset surface SrOne boundary line of the first probe trajectory curve is used as an initial seed curve SE for searching the first probe trajectory curve1In SE1The point on the curve is used as the center of a circle, the length L of the measuring needle is used as the radius to obtain a basic circle, and an initial seed curve SE is used1Generating a tubular sweeping surface F for a sweeping axise1：
(1.1.2) sweeping the curved surface F in the tubular shapee1Upper searching the first measuring head track curve C1The following constraint requirements need to be met:
firstly, the method comprises the following steps:C1at any point c1 iAnd offset surface SrShortest distance Dist (c)1 i,Sr) Should be greater than the safety value r ═ rs+ δ wherein rsIs the safe boundary sphere radius, δ is a given minimum positive value for redundancy safety considerations;
secondly, the method comprises the following steps: c1At any position, the contact angle alpha between the measuring needle and the curved surfacecontactA given threshold should not be exceeded;
(1.1.3) the first probe trajectory curve C1Measuring head space sphere omega and offset curved surface S of any upper pointrCrossing to obtain CS1 iGo through C1All points on { c }1 1,c1 2… } at SrGenerate a series of intersecting curves { CS1 1,CS1 2… }, the envelope SE of the intersection curve1And SF1The sandwiched region is C1Covered sub-area Sr 1And establishing the following optimization problem by taking the area maximization of the sub-region as a target:
obj：max{Area(Sr 1)}
s.t.:min(Dist(c1 i,Sr))≥[r]
max(αcontact)≤[αcontact]
solving by using a sequence quadratic programming method to obtain a first optimal measuring head track curve; the measuring head space sphere omega is a space sphere which is limited by the rotatable angle of the axis of the measuring head rotating shaft A, C, takes the intersection point of the two axes as the center and takes the length of the measuring needle as the radius;
(1.2) putting the first measuring head track curve C1Corresponding sub-region boundary SF1As a second stylus trajectory curve C2And the second sub-region Sr 2Boundary SE of2Obtaining a second optimal probe trajectory curve C in the same way2And so on until the n-1 th side head track curve C is obtainedn-1；
Generating the last measuring head track curveLine CnThen, select SrAs a seed curve, generate FenThen, find Cn，Cn-1And CnThe covered subareas have repeated areas;
(1.3) homogenizing the repeat region in step (1.2):
(1.3.1) finding the minimum width Δ u of the repeated region in the u-directionminWherein the u direction is an offset curved surface SrThe direction of the upper edge of the measuring head track curve expansion;
(1.3.2) pairing SF in the u-direction over the parameter domaini-1Performing offset with an offset distance of-delta uminV (n-1) to obtain SFi′-1And the new seed curve is used as a new seed curve SE for generating the next measuring head track curvei(ii) a Generating a first probe trajectory curve C1Then, the SF is biased according to the above-mentioned method1Biasing to obtain SF1', and use SF1' Generation of a second stylus trajectory curve C2Then to SF2The same operation is performed until the n-1 st side-head trajectory curve C is generatedn-1Last trace curve C of measuring headnWill use SrGenerating another boundary of (2);
wherein n is the number of the measuring head track curves, and n-1 represents the number of adjacent regions.
Further, the obtaining of the cycloid scanning circle of a given step size in step (2) comprises the following steps:
(2.1.1) on the stylus trajectory curve, for curve segment c1 ic1 i+1Wherein c is1 iAnd c1 i+1The distance between the measuring heads is given initial step length, and the measuring heads are measured from c1 iMove to c1 i+1The C axis just rotates around the Z axis for a circle, and when the C axis rotates to any angle in the process, the C axis is positioned in a measuring head coordinate system { o; x is the number ofh，yh，zhIn the z direction, the measuring pin is aligned with the coordinate axis zhForm a plane gamma, and the plane intersects with the measuring head space sphere omega at the arc Ac；
The gauge head coordinate system { o; x is the number ofh，yh，zhThe definition is as follows: the origin of the coordinate system is positioned at the center of the measuring head, namely the intersection point of the AC rotating shafts, and the directions of the coordinate axes are respectively parallel to XYZ axes of the five-axis measuring machine and are always kept relatively static;
(2.1.2) arc AcAnd a curved surface SrIntersecting to obtain a contact point of the tip of the measuring needle and the surface of the measured curved surface, namely a measuring point on the scanning curve; the C axis rotates 2 pi around the Z axis, and all the measurement points are on the curved surface SrForming a cycloid scanning circle.
Further, the determination of the optimal cycloid step size in step (2) comprises the following sub-steps:
(2.2.1) giving an initial step size Δ s0Obtaining two adjacent initial cycloid scanning circles tr1 i、tr1 i+1Taking the first half part of two cycloid scanning circles, uniformly dividing the first half part into n sampling points, and carrying out sampling on the jth sampling point
Figure BDA0002920647340000051
And
Figure BDA0002920647340000052
establishing a local coordinate system pj i(ii) a k, f, n } and
Figure BDA0002920647340000053
wherein f is a unit tangent vector of the cycloid scanning circle at the point, n is a normal vector of the curved surface at the point, and k is a cross product of the two, namely k is f × n;
(2.2.2) curved surface S on k-n planerRadius R ofkIs SrAt the point of
Figure BDA0002920647340000054
Radius of curvature of (d) according to tr1 iPoint of
Figure BDA0002920647340000055
And tr1 i+1Upper corresponding point
Figure BDA0002920647340000056
Can calculate the phaseThe corresponding bow height error epsilon;
(2.2.3) calculating tr as described in step (2.2.2)1 iThe maximum value of the bow height error epsilon of all the sampling points is recorded as epsilonmaxGiven a bow height error threshold [ epsilon ]]The following optimization problem is established:
Figure BDA0002920647340000057
solving the optimization problem to obtain the optimal cycloid step length delta s0*。
Further, the step (3) includes the following sub-steps:
(3.1) expand forward: selecting a first probe trajectory curve C1Is taken as an initial point for determining a first pair of cycloid scanning circles and is positioned on a first measuring head track curve C1Finding the next point by the distance of the given initial step length from the middle point, obtaining the first optimal cycloid step length according to the step (2), generating a first pair of cycloid scanning circles, then sending the next point by the distance of the first optimal cycloid step length, obtaining the second optimal cycloid step length according to the step (2), generating a second pair of cycloid scanning circles, and repeating the steps until the cycloid scanning circles fall out of the curved surface;
(3.2) backward expansion: at the first probe locus curve C1Searching points by the distance of given initial step length from the middle point backward, and obtaining a cycloid scanning circle by the same method in the step (3.1);
(3.3) connecting cycloid scanning tracks: after the expansion derivation is finished, sequentially connecting the beginning of the (i + 1) th cycloid scanning circle and the tail end of the (i) th cycloid scanning circle to obtain a continuous and smooth cycloid scanning track;
and (3.4) repeating the steps (3.1) - (3.3) for each measuring head track curve to form a complete cycloid scanning measuring track.
The invention provides a cycloidal scanning measurement trajectory planning system for a free-form surface, which comprises: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is used for reading the executable instructions stored in the computer readable storage medium and executing the cycloid scanning measurement trajectory planning method for the free-form surface.
Compared with the prior art, the technical scheme of the invention has the advantages that under the condition that extra motion loads are not caused by three heavy linear motion axes of XYZ, the motion load of the measuring head rotating shaft in the five-axis CMM is greatly reduced by always keeping the C axis of the measuring head in the same rotating direction, even at a constant angular velocity (when the acceleration is zero). In numerical control machining, the TR-type cutter path has smooth track and no sharp sudden change, so that better kinematic performance can be brought to a machine tool. Similarly, the TR mode is adopted to carry out five-axis continuous scanning measurement, the kinematic performance of the five-axis CMM can be obviously improved, and therefore the measurement precision and efficiency are improved.
Drawings
FIG. 1 is a block flow diagram of the present invention;
FIG. 2 is an offset surface S of the measured surface SrA schematic diagram;
FIG. 3 is a plot of probe trajectory C generated from a seed curve1A schematic diagram;
FIG. 4 is a schematic view of a gauge head safety boundary sphere;
FIG. 5 is a schematic view of the contact angle between the measured surface and the stylus;
FIG. 6 is the intersection of the working space sphere and the curved surface and C1A schematic view of the covered sub-regions;
FIG. 7 is an optimum stylus trajectory curve C1An example schematic;
FIG. 8 is a second seed curve at Fe2Searching a second measuring head track schematic diagram;
FIG. 9 is a graph consisting of SrAnother boundary of (2) generating FenA schematic diagram;
FIG. 10 is a schematic view of the narrowest overlap region of the last two sub-regions;
FIG. 11 is a schematic view of the homogenization of the overlapping portion;
FIG. 12 is a schematic view of adjacent cycloid sweep circles;
FIG. 13 shows the coordinate system of the stylus and the arc A on the sphere of the workspacecA schematic diagram;
FIG. 14 is a schematic view of the contact point of the stylus tip;
FIG. 15 is a schematic view of a local coordinate system of arbitrary sampling points on a cycloid scan circle;
FIG. 16 is a graph illustrating deviation error for a step in the k-direction;
fig. 17 is a schematic view of the entire measurement trajectory of the measured curved surface.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 is a schematic flow chart of a method for planning a measurement trajectory in cycloid scanning for a free-form surface according to an embodiment of the present invention, where the method shown in fig. 1 includes the following steps:
(1) generating a measuring head track curve: offset curved surface S for measured curved surface SrPartitioning is carried out, and corresponding measuring head track curves are generated, so that the area of a sub-region covered by each measuring head track curve is maximized, and the complete coverage of the measured curved surface is ensured;
the offset curved surface SrIs an offset curved surface with the radius of the tip of the measuring needle as the offset distance along the normal direction of the curved surface S to be measured, as shown in figure 2;
comprising the following substeps:
(1.1) generating a measuring head track curve by the seed curve:
(1.1.1) with an offset surface SrOne boundary line of the first probe trajectory curve is used as an initial seed curve SE for searching the first probe trajectory curve1In SE1The point on the curve is used as the center of a circle, the length L of the measuring needle is used as the radius to obtain a basic circle, and the initial seed curve is usedSE1Generating a tubular sweeping surface F for a sweeping axise1As shown in fig. 3;
(1.1.2) sweeping the curved surface F in the tubular shapee1Upper searching first measuring head track C1The following constraint requirements need to be met:
firstly, the method comprises the following steps: c1At any point c1 iAnd offset surface SrShortest distance Dist (c)1 i,Sr) Should be greater than the safety value r ═ rs+ δ wherein rsIs the safe boundary sphere radius, as shown in fig. 4, δ is a given minimum positive value for redundancy safety considerations;
secondly, the method comprises the following steps: c1At any position, the contact angle alpha between the measuring needle and the curved surfacecontactAs shown in fig. 5, a given threshold should not be exceeded;
(1.1.3) the first probe trajectory curve C1Measuring head space sphere omega and offset curved surface S of any upper pointrCrossing to obtain CS1 iGo through C1All points on { c }1 1,c1 2… } at SrGenerate a series of intersecting curves { CS1 1,CS1 2… }, the envelope SE of the intersection curve1And SF1The sandwiched region is C1Covered sub-area Sr 1As shown in fig. 6, with the area maximization of the sub-region as the target, the following optimization problem is established:
obj：max{Area(Sr 1)}
s.t.:min(Dist(c1 i,Sr))≥[r]
max(αcontact)≤[αcontact]
solving by using a sequential quadratic programming method to obtain a first optimal measuring head trajectory curve, as shown in fig. 7; the measuring head space sphere omega is a space sphere which is limited by the rotatable angle of the axis of the measuring head rotating shaft A, C, takes the intersection point of the two axes as the center and takes the length of the measuring needle as the radius;
(1.2) putting the first measuring head track curve C1Corresponding sub-region boundary SF1Acting as a raw materialForming a second probe track curve C2And a second sub-region Sr 2Boundary SE of2As shown in fig. 8, a second optimal stylus trajectory curve is obtained in the same manner, and so on until all the areas of the measured curved surface are completely covered by the stylus trajectory curve.
Generating the last measuring head track curve CnThen, select SrAs a seed curve, generate FenThen, as shown in FIG. 9, C is obtainedn，Cn-1And CnThe covered subareas have repeated areas;
(1.3) homogenizing the repeat region in step (1.2):
(1.3.1) finding the minimum width Δ u of the repeated region in the u-directionminWherein the u direction is an offset curved surface SrUpward along the direction of the extension of the probe trajectory curve, as shown in fig. 10;
(1.3.2) pairing SF in the u-direction over the parameter domaini-1Performing offset with an offset distance of-delta uminV (n-1) to obtain SFi′-1(s) and using it as new seed curve SE for generating next probe trajectory curvei(ii) a Generating a first probe trajectory curve C1Then, the SF is biased according to the above-mentioned method1Biasing to obtain SF1', and use SF1' Generation of the next probe trajectory curve C2Then to SF2The same operation is carried out until the (n-1) th measuring head track curve is generated, and the last measuring head track curve CnWill use SrGenerating another boundary of (2);
when all the probe trajectories after the offset are regenerated, the repeated regions are uniformly distributed between each of the adjacent regions, as shown in fig. 11.
(2) A cycloid step size determining step: determining cycloid step length by half of cycloid scanning circle, and establishing local coordinate system { ip) for any point on cycloid scanning circlej(ii) a k, f, n, calculating corresponding height error on the k-n plane according to the given initial step length, solving the optimization problem according to the given height error threshold value constraint condition, and searching for the height errorThe optimal step length;
the cycloid scanning circle is along the advancing direction of the measuring head, when the C axis of the rotating shaft of the measuring head rotates for a circle around the Z axis, the measuring head moves the distance of cycloid step length along the measuring head trajectory curve, and a cycloid-shaped scanning trajectory curve tr formed on the offset curved surface1 iAs shown in fig. 12;
comprising the following substeps:
the step (2) of obtaining the cycloid scanning circle with a given step size comprises the following steps:
(2.1.1) on the stylus trajectory curve, for curve segment c1 ic1 i+1Wherein c is1 iAnd c1 i+1The distance between the measuring heads is given initial step length, and the measuring heads are measured from c1 iMove to c1 i+1The C axis just rotates around the Z axis for a circle, and when the C axis rotates to any angle in the process, the C axis is positioned in a measuring head coordinate system { o; x is the number ofh，yh，zhIn the z direction, the measuring pin is aligned with the coordinate axis zhForm a plane gamma, and the plane intersects with the measuring head space sphere omega at the arc AcAs shown in fig. 13;
the gauge head coordinate system { o; x is the number ofh，yh，zhThe definition is as follows: the origin of the coordinate system is positioned at the center of the measuring head, namely the intersection point of the AC rotating shaft, and the directions of the coordinate axes are respectively parallel to XYZ axes of the five-axis measuring machine and are always kept relatively static;
(2.1.2) arc AcAnd a curved surface SrIntersecting to obtain a contact point of the tip of the stylus and the surface of the measured curved surface, namely a measurement point on the scanning curve, as shown in fig. 14; the C axis rotates 2 pi around the Z axis, and all the measurement points are on the curved surface SrForming a cycloid scanning circle;
the determination of the optimal cycloid step size in the step (2) comprises the following sub-steps:
(2.2.1) giving an initial step size Δ s0Obtaining two adjacent initial cycloid scanning circles tr1 i、tr1 i+1Taking the first half part of the cycloid scanning circle, dividing the cycloid scanning circle into n sampling points uniformly, and carrying out sampling on the jth sampling point
Figure BDA0002920647340000101
And
Figure BDA0002920647340000102
establishing a local coordinate system pj i(ii) a k, f, n } and
Figure BDA0002920647340000103
as shown in fig. 15, where f is the unit tangent vector of the cycloid sweep circle at the point, n is the normal vector of the curved surface at the point, and k is the cross product of the two, i.e., k is f × n;
(2.2.2) curved surface S on k-n planerRadius R ofkIs SrAt the point of
Figure BDA0002920647340000104
Radius of curvature of (d) according to tr1 iPoint of
Figure BDA0002920647340000105
And tr1 i+1Upper corresponding point
Figure BDA0002920647340000106
The corresponding bow height error ε can be calculated, as shown in FIG. 16;
(2.2.3) calculating tr as described in step (2.2.2)1 iThe bow height error of all the sampling points in (c), the maximum value of which is recorded as ∈maxGiven a bow height error threshold [ epsilon ]]The following optimization problem is established:
Figure BDA0002920647340000107
solving the optimization problem to obtain the optimal cycloid step length delta s0*。
(3) Expanding a cycloid scanning trajectory: using a first measuring head track curve C1As an initial point for determining a first pair of cycloid scan trajectories; starting from the middle point, respectively extending forwards and backwards by a given initial step size and according to a given arch height errorOptimizing and iterating to obtain an optimal cycloid step size under a threshold constraint condition to generate a first pair of cycloid scanning trajectories; and deriving the rest cycloid scanning tracks forwards and backwards by the same method until the (i + 1) th track falls outside the curved surface, discarding the track, and repeating the operation on the sub-area covered by each measuring head track to complete the expansion of all cycloid scanning tracks.
Comprising the following substeps:
(3.1) expand forward:
selecting a first probe trajectory curve C1Is taken as an initial point for determining a first pair of cycloid scanning circles and is positioned on a first measuring head track curve C1Finding the next point by the distance of the given initial step length from the middle point, obtaining the first optimal cycloid step length according to the step (2), generating a first pair of cycloid scanning circles, then sending the next point by the distance of the first optimal cycloid step length, obtaining the second optimal cycloid step length according to the step (2), generating a second pair of cycloid scanning circles, and repeating the steps until the cycloid scanning circles fall out of the curved surface;
(3.2) backward expansion: at the first probe locus curve C1Searching points by the distance of given initial step length from the middle point backward, and obtaining a cycloid scanning circle by the same method in the step (3.1);
(3.3) connecting cycloid scanning tracks: after the expansion derivation is finished, sequentially connecting the beginning of the (i + 1) th cycloid scanning circle and the tail end of the (i) th cycloid scanning circle to obtain a continuous and smooth cycloid scanning track;
and (3.4) repeating the steps (3.1) - (3.3) for each measuring head track curve to form a complete cycloid scanning measuring track.
The above expanding derivation and connection operations are performed on each measuring head trajectory to form a complete cycloid scanning measuring trajectory, as shown in fig. 17.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A cycloid type scanning measurement trajectory planning method for a free-form surface is characterized by comprising the following steps:
(1) generating a measuring head track curve: offset curved surface S for measured curved surface SrPartitioning is carried out, and corresponding measuring head track curves are generated, so that the area of a sub-region covered by each measuring head track curve is maximized, and the complete coverage of the measured curved surface is ensured;
the offset curved surface SrThe offset curved surface is an offset curved surface which takes the radius of the tip of the measuring needle as an offset distance along the normal direction of the curved surface S to be measured;
(2) a cycloid step size determining step: determining cycloid step length by half of cycloid scanning circle, establishing local coordinate system for any point on cycloid scanning circle, calculating corresponding height error by given initial cycloid step length, solving optimization problem according to given height error threshold value constraint condition, and searching optimal cycloid step length;
the cycloid scanning circle is along the advancing direction of the measuring head, when the C axis of the rotating shaft of the measuring head rotates for a circle around the Z axis and the measuring head moves for the distance of cycloid step length along the measuring head locus curve, the cycloid-shaped scanning locus curve tr formed by the tip of the measuring needle on the offset curved surfacej iWherein, the lower corner mark j represents that the cycloid scanning circle belongs to the jth measuring head track curve, and the upper corner mark i represents that the cycloid scanning circle belongs to the ith cycloid scanning circle under the measuring head track curve;
(3) expanding a cycloid scanning trajectory: taking the middle point of a first measuring head track curve as an initial point for determining a first pair of cycloid scanning circles; from the midpoint, expanding forwards and backwards respectively by a given initial step length, optimizing and iterating according to a given bow height error threshold value constraint condition to obtain an optimal cycloid step length, and generating a first pair of cycloid scanning circles; and deriving the rest cycloid scanning circles forwards and backwards by the same method until the (i + 1) th cycloid scanning circle falls outside the curved surface, discarding the track, and repeating the operation on the sub-area covered by each measuring head track curve to complete the expansion of all cycloid scanning tracks.
2. The method for planning a measurement trajectory for cycloidal scanning of a free-form surface according to claim 1,
the step (1) includes the following substeps:
(1.1) generating a measuring head track curve by the seed curve:
(1.1.1) with an offset surface SrOne boundary line of the first probe trajectory curve is used as an initial seed curve SE for searching the first probe trajectory curve1In SE1The point on the curve is used as the center of a circle, the length L of the measuring needle is used as the radius to obtain a basic circle, and an initial seed curve SE is used1Generating a tubular sweeping surface F for a sweeping axise1：
(1.1.2) sweeping the curved surface F in the tubular shapee1Upper searching the first measuring head track curve C1The following constraint requirements need to be met:
firstly, the method comprises the following steps: c1At any point c1 iAnd offset surface SrShortest distance Dist (c)1 i,Sr) Should be greater than the safety value r ═ rs+ δ wherein rsIs the safe boundary sphere radius, δ is a given minimum positive value for redundancy safety considerations;
secondly, the method comprises the following steps: c1At any position, the contact angle alpha between the measuring needle and the curved surfacecontactA given threshold should not be exceeded;
(1.1.3) the first probe trajectory curve C1Measuring head space sphere omega and offset curved surface S of any upper pointrCrossing to obtain CS1 iGo through C1All points on { c }1 1,c1 2… } at SrGenerate a series of intersecting curves { CS1 1,CS1 2…, the envelope of the intersection curve being the initial seed curve SE1And boundary SF1，SE1And SF1The sandwiched region is C1Covered sub-area Sr 1And establishing the following optimization problem by taking the area maximization of the sub-region as a target:
obj:max{Area(Sr 1)}
s.t.:min(Dist(c1 i,Sr))≥[r]
max(αcontact)≤[αcontact]
solving by using a sequence quadratic programming method to obtain a first optimal measuring head track curve; the measuring head space sphere omega is a space sphere which is limited by the rotatable angle of the axis of the measuring head rotating shaft A, C, takes the intersection point of the two axes as the center and takes the length of the measuring needle as the radius;
(1.2) putting the first measuring head track curve C1Corresponding sub-region boundary SF1As a second stylus trajectory curve C2And the second sub-region Sr 2Boundary SE of2Obtaining a second optimal probe trajectory curve C in the same way2And so on until the n-1 th side head track curve C is obtainedn-1；
Generating the last measuring head track curve CnThen, select SrAs a seed curve, generate FenThen, find Cn，Cn-1And CnThe covered subareas have repeated areas;
(1.3) homogenizing the repeat region in step (1.2):
(1.3.1) finding the minimum width Δ u of the repeated region in the u-directionminWherein the u direction is an offset curved surface SrThe direction of the upper edge of the measuring head track curve expansion;
(1.3.2) pairing SF in the u-direction over the parameter domaini-1Performing offset with an offset distance of-delta uminV (n-1) to obtain SFi′-1And the new seed curve is used as a new seed curve SE for generating the next measuring head track curvei(ii) a Generating a first probe trajectory curve C1Then, the SF is biased according to the above-mentioned method1Biasing to obtain SF1', and use SF1' Generation of a second stylus trajectory curve C2Then to SF2The same operation is performed until the n-1 st side-head trajectory curve C is generatedn-1Last trace curve C of measuring headnWill use SrAnother boundary of (2)Generating;
wherein n is the number of the measuring head track curves, and n-1 represents the number of adjacent regions.
3. The method for planning a measurement trajectory for cycloidal scanning of a free-form surface according to claim 2,
the step (2) of obtaining the cycloid scanning circle with a given step size comprises the following steps:
(2.1.1) on the stylus trajectory curve, for curve segment c1 ic1 i+1Wherein c is1 iAnd c1 i+1The distance between the measuring heads is given initial step length, and the measuring heads are measured from c1 iMove to c1 i+1The C axis just rotates around the Z axis for a circle, and when the C axis rotates to any angle in the process, the C axis is positioned in a measuring head coordinate system { o; x is the number ofh，yh，zhIn the z direction, the measuring pin is aligned with the coordinate axis zhForm a plane gamma, and the plane intersects with the measuring head space sphere omega at the arc Ac；
The gauge head coordinate system { o; x is the number ofh，yh，zhThe definition is as follows: the origin of the coordinate system is positioned at the center of the measuring head, namely the intersection point of the AC rotating shafts, and the directions of the coordinate axes are respectively parallel to XYZ axes of the five-axis measuring machine and are always kept relatively static;
(2.1.2) arc AcAnd a curved surface SrIntersecting to obtain a contact point of the tip of the measuring needle and the surface of the measured curved surface, namely a measuring point on the scanning curve; the C axis rotates 2 pi around the Z axis, and all the measurement points are on the curved surface SrForming a cycloid scanning circle.
4. The method for planning a measurement trajectory for cycloidal scanning of a free-form surface according to claim 1,
the determination of the optimal cycloid step size in the step (2) comprises the following sub-steps:
(2.2.1) giving an initial step size Δ s0Obtaining two adjacent initial cycloid scanning circles tr1 i、tr1 i+1The first half of two cycloid scanning circles are uniformly divided inton number of sampling points, for the jth sampling point
Figure FDA0003305850430000041
And
Figure FDA0003305850430000042
establishing a local coordinate system pj i(ii) a k, f, n } and
Figure FDA0003305850430000043
wherein f is a unit tangent vector of the cycloid scanning circle at the point, n is a normal vector of the curved surface at the point, and k is a cross product of the two, namely k is f × n;
(2.2.2) curved surface S on k-n planerRadius R ofkIs SrAt the point of
Figure FDA0003305850430000044
Radius of curvature of (d) according to tr1 iPoint of
Figure FDA0003305850430000045
And tr1 i+1Upper corresponding point
Figure FDA0003305850430000046
The corresponding bow height error epsilon can be calculated;
(2.2.3) calculating tr as described in step (2.2.2)1 iThe maximum value of the bow height error epsilon of all the sampling points is recorded as epsilonmaxGiven a bow height error threshold [ epsilon ]]The following optimization problem is established:
Figure FDA0003305850430000047
solving the optimization problem to obtain the optimal cycloid step length delta s0*。
5. The method for planning a measurement trajectory for cycloidal scanning of a free-form surface according to claim 1,
the step (3) includes the following substeps:
(3.1) expand forward: selecting a first probe trajectory curve C1Is taken as an initial point for determining a first pair of cycloid scanning circles and is positioned on a first measuring head track curve C1Finding the next point by the distance of the given initial step length from the middle point, obtaining the first optimal cycloid step length according to the step (2), generating a first pair of cycloid scanning circles, then sending the next point by the distance of the first optimal cycloid step length, obtaining the second optimal cycloid step length according to the step (2), generating a second pair of cycloid scanning circles, and repeating the steps until the cycloid scanning circles fall out of the curved surface;
(3.2) backward expansion: at the first probe locus curve C1Searching points by the distance of given initial step length from the middle point backward, and obtaining a cycloid scanning circle by the same method in the step (3.1);
(3.3) connecting cycloid scanning tracks: after the expansion derivation is finished, sequentially connecting the beginning of the (i + 1) th cycloid scanning circle and the tail end of the (i) th cycloid scanning circle to obtain a continuous and smooth cycloid scanning track;
and (3.4) repeating the steps (3.1) - (3.3) for each measuring head track curve to form a complete cycloid scanning measuring track.
6. A cycloidal scanning measurement trajectory planning system for a free-form surface, comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is used for reading executable instructions stored in the computer readable storage medium and executing the cycloid scanning measurement trajectory planning method for the free-form surface according to any one of claims 1 to 5.
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