CN112414352A  Method for correcting sampling pose and measuring profile shape of measured object on camshaft  Google Patents
Method for correcting sampling pose and measuring profile shape of measured object on camshaft Download PDFInfo
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 CN112414352A CN112414352A CN202011247233.3A CN202011247233A CN112414352A CN 112414352 A CN112414352 A CN 112414352A CN 202011247233 A CN202011247233 A CN 202011247233A CN 112414352 A CN112414352 A CN 112414352A
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Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
 G01B21/00—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups
 G01B21/20—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups for measuring contours or curvatures, e.g. determining profile

 G—PHYSICS
 G01—MEASURING; TESTING
 G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
 G01B21/00—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups
 G01B21/22—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups for measuring angles or tapers; for testing the alignment of axes
 G01B21/24—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes
Abstract
The invention discloses a method for correcting the sampling pose of a measured object on a camshaft and measuring the profile morphology, which comprises the following steps of: will cam shaft coordinate system o_{0}x_{0}y_{0}z_{0}Converting into an instrument coordinate OXYZ; and (3) second correction: translating the central axis of the camshaft to the central point of the measured object to ensure that the instrument measuring head can normally sample the measured object, so that the instrument measuring head can further correct the sampling pose relative to the translated central axis of the camshaft in an instrument coordinate system; and (3) third correction: and calculating the included angle deviation of the measured object relative to a reference datum plane in a camshaft coordinate system, and converting the coordinate system of the measured object into an instrument coordinate system according to the included angle deviation, so that the instrument measuring head can correct the sampling pose relative to the outline of the measured object in the instrument coordinate system. And after the sampling pose is corrected, sampling data are obtained and corresponding profile morphology is fitted. The invention solves the problems thatAnd the problem that the downsampling path is not matched with the real contour curve of the measured object under the instrument coordinate is solved.
Description
Technical Field
The invention relates to the technical field of measurement of a measured object on a camshaft, in particular to a method for correcting a measurement pose of the measured object on the camshaft.
Background
Before the measurement process, the camshaft is clamped on an instrument rotating table and fixed through an upper tip and a lower tip of the instrument, and a connecting line of the upper tip and the lower tip of the instrument is a Z axis parallel to an instrument coordinate system. The instrument coordinate system for measuring the camshaft is OXYZ, and the coordinate system of the camshaft is o_{0}x_{0}y_{0}z_{0}The coordinate system of each object to be measured (journal, cam, etc.) is o_{k}x_{k}y_{k}z_{k}Rotation angle of theta_{k}。
The reason for the eccentric error is as follows: 1) the central axis of the camshaft is not parallel to the connecting line of the center, and a space included angle exists, so that an eccentric error, also called an installation error, is caused; 2) the measured object (journal, cam, etc.) on the camshaft has an eccentricity amount with respect to the camshaft central axis. The reason why the object to be measured is eccentric with respect to the center line of the camshaft is that: firstly, when the measured object is designed, the axis z of the measured object_{k}To the central axis z of the camshaft_{0}Are parallel, but z_{k}And z_{0}At x_{0}y_{0}With an amount of deviation in the plane. Design time z_{k}And z_{0}Unparallel or unparallel caused by machining process, not only the pose of each measured object is compared with that of reference plane x_{0}y_{0}Plane deviation included angle alpha_{k}In the reference plane x_{0}z_{0}Also internally, a deviation angle beta appears_{k}。
Before sampling, the instrument generates a corresponding sampling path according to the input design parameters of the measured object, and controls the sensor to sample according to the generated sampling path. However, due to the eccentric error of the camshaft, the generated adopted path cannot match the spatial posture of the measured object in the instrument coordinate system, so that the sensor cannot sample along the real profile curve of the measured object, and the measured object profile fitted by the sampling point finally has a large deviation from the actual profile. Therefore, how to correct the sampling pose of the measuring head of the instrument is a key for generating a sampling path which can be matched with the outline of the measured object.
Disclosure of Invention
Aiming at the technical defects, the invention provides a method for correcting the sampling pose of a measured object on a camshaft, which solves the technical problem of how to correct the sampling pose of an instrument measuring head in an instrument coordinate system to generate a sampling path capable of matching the outline of the measured object.
In order to solve the technical problems, the technical scheme of the invention is as follows: a method for correcting the sampling pose of a measured object on a camshaft comprises the following steps:
clamping a workpiece on an instrument rotary table, and vertically fixing a cam shaft on the workpiece through an instrument tip; sequentially correcting the pose of the measuring head of the instrument for three times;
first correction: will cam shaft coordinate system o_{0}x_{0}y_{0}z_{0}Converted into the coordinate OXYZ of the instrument so that the coordinate system o of the measured object_{k}x_{k}y_{k}z_{k}Along with camshaft coordinate system o_{0}x_{0}y_{0}z_{0}The initial transformation is carried out in the instrument coordinate OXYZ, so that the instrument measuring head can initially correct the sampling pose relative to the central axis of the camshaft in the instrument coordinate system;
and (3) second correction: in an instrument coordinate system, translating the central axis of the camshaft to the central point of the measured object to ensure that an instrument measuring head can normally sample the measured object, so that the instrument measuring head can further correct the sampling pose relative to the translated central axis of the camshaft in the instrument coordinate system;
and (3) third correction: and calculating the included angle deviation of the measured object relative to a reference datum plane in a camshaft coordinate system, and converting the coordinate system of the measured object into an instrument coordinate system according to the included angle deviation, so that the instrument measuring head can correct the sampling pose relative to the outline of the measured object in the instrument coordinate system.
Further, the method comprisesThe camshaft coordinate system o_{0}x_{0}y_{0}z_{0}Conversion into the instrument coordinates xyz, as follows:
respectively selecting marking points a in the positioning areas of the upper and lower workpiece references_{0}、b_{0}；
Sampling the mark points by the instrument measuring head:
sampling for the first time at the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{1}(x_{a,1},y_{a,1},z_{a,1}) And b_{1}(x_{b,1},y_{b,1},z_{b,1})；
The rotary table drives the workpiece to rotate 90 degrees from the initial position, and then secondary sampling is carried out to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{2}(x_{a,2},y_{a,2},z_{a,2}) And coordinates b_{2}(x_{b,2},y_{b,2},z_{b,2})；
The third sampling is carried out after the rotary table drives the workpiece to rotate 180 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{3}(x_{a,3},y_{a,3},z_{a,3}) And coordinates b_{3}(x_{b,3},y_{b,3},z_{b,3})；
The fourth sampling is carried out after the rotary table drives the workpiece to rotate 270 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{4}(x_{a,4},y_{a,4},z_{a,4}) And coordinates b_{4}(x_{b,4},y_{b,4},z_{b,4})；
Whether the measuring head of the analysis instrument is in the controllable range of the measuring head when the measuring head is at the four sampling positions is judged, and if not, the workpiece is clamped again; if so, determining the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis of the instrument coordinate system according to the maximum detection error of the instrument measuring head calibrated in advance;
respectively calculating the eccentric correction quantity of the central axis of the camshaft relative to the X axis and the Y axis of the instrument coordinate system according to the sampling points; and converting the camshaft coordinate system to an instrument coordinate system according to the eccentric correction amount.
Further, a camshaft coordinate system is established as follows:
sampling the upper and lower workpiece references by an instrument measuring head in an instrument coordinate system, fitting sampling points of the upper and lower workpiece references by a least square method to obtain circle center coordinates of the upper and lower workpiece references, and taking a circle center connecting line of the upper and lower workpiece references as Z of a camshaft_{0}Axis and perpendicular to Z_{0}The plane of the axis passing through the reference circle center of the lower workpiece is taken as X_{0}Y_{0}A plane;
the camshaft coordinate system is transformed to the instrument coordinate system as follows:
x′_{k}＝(x_{k}·cosα_{0}+Δx)·cosθ_{0}；
z′_{k}＝z_{k}·cosα_{0}·cosβ_{0}+Δz；
in the formula (x)_{k},y_{k},z_{k}) Represents a point on the kth measured object in the camshaft coordinate system, (x'_{k},y′_{k},z′_{k}) Represents a point (x)_{k},y_{k},z_{k}) Converting to the coordinates under the instrument coordinate system; the amount of eccentric correction of the camshaft center axis with respect to the Xaxis comprises the angle alpha of the camshaft center axis with respect to the Xaxis_{0}And a displacement amount Δ x; the amount of eccentric correction of the camshaft center axis with respect to the Yaxis comprises an angle beta of the camshaft center axis with respect to the Yaxis_{0}And a displacement amount Δ y; theta_{0}The rotation angle of the current measuring point relative to the initial measuring point is represented, and the range is 0360 degrees.
Further, the second correction is performed as follows:
selecting a mark point c in a tested area of a kth tested object_{k}Marking point c_{k}Characteristic points belonging to the middle section of the measured object; in an instrument coordinate system, an instrument measuring head respectively rotates to the following four mark points c_{k}Sampling is carried out: the initial position, the position rotated by 90 degrees relative to the initial position, the position rotated by 180 degrees relative to the initial position, and the position rotated by 270 degrees relative to the initial position respectively obtain corresponding sampling coordinates: c. C_{k,1}(x_{c,k,1},0,z_{c,k,1})、c_{k,2}(0,y_{c,k,2},z_{c,k,2})、c_{k,3}(x_{c,k,3},0,z_{c,k,3}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) (ii) a Using c_{k,1}(x_{c,k,1},0,z_{c,k,1}) And c_{k,3}(x_{c,k,3},0,z_{c,k,3}) Correction of x_{k}Offset in the axial direction by c_{k,2}(0,y_{c,k,2},z_{c,k,2}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) Correction of y_{k}The offset in the axial direction, so as to obtain the coordinates after the second correction:
z″_{k}＝z′_{k}
wherein (x'_{k},y′_{k},z′_{k}) The coordinate of the point on the kth measured object in the instrument coordinate system after the first correction is shown, (x ″)_{k},y″_{k},z″_{k}) And representing the coordinates of the point on the kth measured object under the instrument coordinate system after the second correction.
Further, in the formula, (x ″)_{k},y″_{k},z″_{k}) The coordinates of the point on the kth measured object in the instrument coordinate system after the second correction are expressed as (x ″)'_{k},y″′_{k},z″′_{k}) And (4) representing the coordinates of the point on the kth measured object in the instrument coordinate system after the third correction, wherein (x, y, z) represents the sampling pose coordinates of the instrument measuring head.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the sampling pose is gradually corrected through three times of correction, the coordinate system of the measured object is preliminarily converted into the instrument coordinate system through the first correction, so that the subsequent two corrections can be carried out in the instrument coordinate system, and simultaneously, the sampling pose of the instrument measuring head can be preliminarily corrected relative to the central axis of the camshaft in the instrument coordinate system after the first correction is completed. However, since the axis of the measured object often does not coincide with the central axis of the camshaft, the latter two corrections are also required in order to make the sampling pose conform to the profile curve of the measured object.
2. And the sampling pose in the instrument coordinate system is relatively vertical to the central axis of the camshaft, the central axis of the camshaft is translated to the central point of the measured object by the second correction, and the phenomenon that the deviation between the axis of the measured object and the central axis of the camshaft is large and exceeds the controllable range of the instrument measuring head is avoided, so that the instrument measuring head can normally sample the measured object.
3. The third correction is based on the second correction, namely, the instrument measuring head is ensured to be capable of normally sampling the measured object, then the measured object coordinate system is converted into the instrument coordinate system according to the included angle deviation of the measured object relative to the reference datum plane in the camshaft coordinate system (converted into the instrument coordinate system), namely, the central axis of the camshaft is rotated to be coincident with the axis of the measured object, and the sampling pose in the instrument coordinate system is relatively perpendicular to the central axis of the camshaft, so that the sampling pose can be relatively perpendicular to the axis of the measured object in the instrument coordinate system, and the instrument measuring head can correct the sampling pose relative to the outline of the measured object in the instrument coordinate system.
4. The invention corrects the eccentric quantity on the premise of ensuring that the measuring head of the instrument is in a controllable range, ensures the normal work of the measuring head of the instrument, avoids collision with a workpiece in the sampling process and can continuously finish sampling.
5. The method has the advantages of less number of required sampling points, high sampling efficiency and capability of conveniently and quickly correcting the eccentric error of the camshaft.
Drawings
FIG. 1 is a schematic view of workpiece clamping;
FIG. 2 shows a mark a_{0}And b_{0}Schematic diagram of the sampling process of (a);
fig. 3 is a schematic view of a controllable force range of the contact probe;
FIG. 4 is a schematic diagram of the correction of eccentricity of the central axis of the camshaft relative to the Xaxis;
FIG. 5 is a schematic diagram of the correction of the eccentricity of the central axis of the camshaft relative to the Yaxis;
FIG. 6 is a schematic diagram of the distribution of feature points on the object under test;
FIG. 7 is a schematic diagram of the correction of the measured object relative to the reference datum plane;
FIG. 8 shows the measured object relative to the reference plane x_{0}y_{0}Schematic diagram of the included angle deviation;
FIG. 9 is a diagram of the measured object relative to the reference plane x_{0}z_{0}Schematic diagram of the included angle deviation.
Detailed Description
One), first correction
Before the measurement process, the camshaft is clamped on an instrument rotary table and fixed through an upper tip and a lower tip of the instrument, and a connecting line of the upper tip and the lower tip of the instrument is a Z axis parallel to a coordinate system of the instrument. The eccentric amount is generated: the central axis of the camshaft is not parallel to the connecting line of the tip, a space included angle exists, and the central axis of the camshaft has a deviation included angle alpha compared with the central axis of the camshaft XZ_{0}The deviation angle β occurs in comparison with YZ_{0}This causes an eccentricity error, which may also be referred to as a mounting error, which is corrected for the first time.
First correction: will cam shaft coordinate system o_{0}x_{0}y_{0}z_{0}Converted into the coordinate OXYZ of the instrument so that the coordinate system o of the measured object_{k}x_{k}y_{k}z_{k}Along with camshaft coordinate system o_{0}x_{0}y_{0}z_{0}And the initial transformation is carried out into the instrument coordinate OXYZ, so that the instrument measuring head can initially correct the sampling pose relative to the central axis of the camshaft in the instrument coordinate system.
The first correction specifically comprises the following steps:
referring to fig. 1, a workpiece is clamped on an instrument rotary table, and a cam shaft on the workpiece is vertically fixed through an instrument tip;
respectively selecting marking points a in the positioning areas of the upper and lower workpiece references_{0}、b_{0}。
Referring to fig. 2, the gauge head samples the mark points, and during sampling, the gauge head and the workpiece rotate synchronously and keep relatively static, so that the movement error of the gauge head is avoided.
Sampling for the first time at the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{1}(x_{a,1},y_{a,1},z_{a,1}) And b_{1}(x_{b,1},y_{b,1},z_{b,1})。
The rotary table drives the workpiece to rotate 90 degrees from the initial position, and then secondary sampling is carried out to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{2}(x_{a,2},y_{a,2},z_{a,2}) And coordinates b_{2}(x_{b,2},y_{b,2},z_{b,2})。
The third sampling is carried out after the rotary table drives the workpiece to rotate 180 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{3}(x_{a,3},y_{a,3},z_{a,3}) And coordinates b_{3}(x_{b,3},y_{b,3},z_{b,3})。
The fourth sampling is carried out after the rotary table drives the workpiece to rotate 270 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{4}(x_{a,4},y_{a,4},z_{a,4}) And coordinates b_{4}(x_{b,4},y_{b,4},z_{b,4})。
Whether the measuring head of the analysis instrument is in the controllable range of the measuring head when the measuring head is at the four sampling positions is judged, and if not, the workpiece is clamped again; and if so, determining the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis of the instrument coordinate system according to the maximum detection error of the instrument measuring head calibrated in advance.
Respectively calculating the eccentric correction quantity of the central axis of the camshaft relative to the X axis and the Y axis of the instrument coordinate system according to the sampling points; and converting the camshaft coordinate system to the instrument coordinate according to the eccentric correction amount.
Referring to fig. 3, when the measuring head of the instrument is a contact measuring head, it is respectively determined whether the stress of the measuring head of the instrument at the four sampling positions is within the controllable stress range, and if not, the workpiece is clamped again; if yes, one third of the maximum detection error of the instrument measuring head calibrated in advance (according to the one third principle of the error) is used as the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis. A force measuring value sensor exists on the instrument, and force information can be fed back.
When the measuring head of the instrument is a noncontact measuring head, respectively judging whether the poses of the measuring head at the four sampling positions are within a controllable pose range, and if not, reclamping the workpiece; if so, taking one third of the maximum detection error of the precalibrated instrument measuring head (according to the one third principle of the error) as the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis; the position and posture of the measuring head refer to a space coordinate and a space included angle of the measuring head under an instrument coordinate system. The space coordinate refers to the coordinate of Xaxis, Yaxis and Zaxis directions under an instrument coordinate system, and the space included angle refers to the space included angle formed by the probe which can not only move along the coordinate axes but also rotate and the coordinate axes.
Referring to FIG. 4, the cylindrical coordinate system is a camshaft coordinate system, and the amount of eccentric correction of the central axis of the camshaft relative to the X axis includes an included angle α of the central axis of the camshaft relative to the X axis_{0}And a displacement amount Δ x, calculated as follows:
by pointAnd pointThe included angle between the connecting line of (A) and the Z axis is taken as the included angle alpha_{0}Wherein, a pointIs a sampling point a_{1}(x_{a,1},y_{a,1},z_{a,1}) And a_{3}(x_{a,3},y_{a,3},z_{a,3}) Middle point, point ofIs a sampling point b_{1}(x_{b,1},y_{b,1},z_{b,1}) And sampling point b_{3}(x_{b,3},y_{b,3},z_{b,3}) The middle point of (a);
included angle alpha_{0}The calculation formula of (a) is as follows:
the displacement amount Δ x is calculated as follows:
referring to FIG. 5, the cylindrical coordinate system is a camshaft coordinate system, and the amount of eccentric correction of the central axis of the camshaft relative to the Yaxis includes an included angle β of the central axis of the camshaft relative to the Yaxis_{0}And a displacement amount Δ y calculated as follows, respectively:
by pointAnd pointThe included angle between the connecting line of (b) and the Z axis is taken as the included angle beta_{0}Wherein, a pointIs a sampling point a_{2}(x_{a,2},y_{a,2},z_{a,2}) And a_{4}(x_{a,4},y_{a,4},z_{a,4}) Middle point, point ofIs a sampling point b_{2}(x_{b,2},y_{b,2},z_{b,2}) And b_{4}(x_{b,4},y_{b,4},z_{b,4}) The middle point of (a);
angle of inclusion beta_{0}The calculation formula of (a) is as follows:
the displacement amount Δ y is calculated as follows:
the camshaft coordinate system is established as follows:
sampling the upper and lower workpiece references by an instrument measuring head in an instrument coordinate system, fitting sampling points of the upper and lower workpiece references by a least square method to obtain circle center coordinates of the upper and lower workpiece references, and taking a circle center connecting line of the upper and lower workpiece references as Z of a camshaft_{0}Axis and perpendicular to Z_{0}The plane of the axis passing through the reference circle center of the lower workpiece is taken as X_{0}Y_{0}A plane;
the camshaft coordinate system is transformed to the instrument coordinate system as follows:
x′_{k}＝(x_{k}·cosα_{0}+Δx)·cosθ_{0}；
z′_{k}＝z_{k}·cosα_{0}·cosβ_{0}+Δz；
in the formula (x)_{k},y_{k},z_{k}) Represents a point on the kth measured object in the camshaft coordinate system, (x'_{k},y′_{k},z′_{k}) Represents a point (x)_{k},y_{k},z_{k}) Converting to the coordinates under the instrument coordinate system; the amount of eccentric correction of the camshaft center axis with respect to the Xaxis comprises the angle alpha of the camshaft center axis with respect to the Xaxis_{0}And displacement ofThe quantity Δ x; the amount of eccentric correction of the camshaft center axis with respect to the Yaxis comprises an angle beta of the camshaft center axis with respect to the Yaxis_{0}And a displacement amount Δ y; theta_{0}The rotation angle of the current measuring point relative to the initial measuring point is represented, and the range is 0360 degrees.
The method is used for correcting the installation error of the camshaft, and is a basis for accurately sampling the cam profile on the camshaft, so that the instrument measuring head can adjust the sampling pose on the basis of the sampling path generated according to the cam design parameters, namely the instrument measuring head can adjust the sampling pose relative to the central axis of the camshaft actually installed in an instrument coordinate system. The invention compensates the included angle and offset error, so that the measuring head of the instrument can adjust the angle to be vertical to the central axis of the camshaft, and when the measured object (such as a shaft neck 1 and a cam 2 in figure 1) is coaxial with the central axis of the camshaft, the point on the adopted path can be moved to the outline of the measured object in the instrument coordinate system.
Two), second correction
Because the central axis of the measured object on the camshaft often has an included angle deviation with the central axis of the camshaft: 1) during design, the central axis z of the measured object_{k}To the central axis z of the camshaft_{0}Parallel, at a reference level x_{0}y_{0}An internal deviation occurs; 2) design time z_{k}And z_{0}Unparallel or unparallel caused by machining process, not only the pose of each measured object is compared with that of reference plane x_{0}y_{0}The deviation included angle alpha appears_{k}At a reference datum plane x_{0}z_{0}Also internally, a deviation angle beta appears_{k}. Therefore, after the first correction, the requirement of further correction on the condition that the sampling pose is relatively vertical to the axis of the measured object under the instrument coordinate system cannot be met.
Before further correcting the sampling pose according to the included angle deviation, the instrument measuring head needs to be ensured to be capable of normally sampling the measured object, so that the second correction must be carried out: in an instrument coordinate system, the central axis of the camshaft is translated to the central point of the measured object, so that the measured object can be normally sampled by the instrument measuring head, and the sampling pose of the instrument measuring head can be further corrected relative to the translated central axis of the camshaft in the instrument coordinate system.
The second correction is specifically performed as follows:
referring to fig. 6, a mark point c is selected in the measured area of the kth measured object_{k}Marking point c_{k}Characteristic points belonging to the middle section of the measured object; in an instrument coordinate system, an instrument measuring head respectively rotates to the following four mark points c_{k}Sampling: the initial position, the position rotated by 90 degrees relative to the initial position, the position rotated by 180 degrees relative to the initial position, and the position rotated by 270 degrees relative to the initial position respectively obtain corresponding sampling coordinates: c. C_{k,1}(x_{c,k,1},0,z_{c,k,1})、c_{k,2}(0,y_{c,k,2},z_{c,k,2})、c_{k,3}(x_{c,k,3},0,z_{c,k,3}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) (ii) a Using c_{k,1}(x_{c,k,1},0,z_{c,k,1}) And c_{k,3}(x_{c,k,3},0,z_{c,k,3}) Correction of x_{k}Offset in the axial direction by c_{k,2}(0,y_{c,k,2},z_{c,k,2}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) Correction of y_{k}The offset in the axial direction, so as to obtain the coordinates after the second correction:
z″_{k}＝z′_{k}
wherein (x'_{k},y′_{k},z′_{k}) The coordinate of the point on the kth measured object in the instrument coordinate system after the first correction is shown, (x ″)_{k},y″_{k},z″_{k}) And representing the coordinates of the point on the kth measured object under the instrument coordinate system after the second correction.
Third), third correction
And (3) third correction: and calculating the included angle deviation of the measured object relative to a reference datum plane in a camshaft coordinate system, and converting the coordinate system of the measured object into an instrument coordinate system according to the included angle deviation, so that the instrument measuring head can correct the sampling pose relative to the outline of the measured object in the instrument coordinate system.
The third correction is specifically performed as follows:
referring to fig. 7 to 9, a mark point d is selected at the upper end of the kth object to be measured_{k,1}And d_{k,2}The marking point d_{k,1}And d_{k,2}X symmetrically distributed in camshaft coordinate system_{0}z_{0}Two sides of the reference datum plane; selecting a mark point d at the lower end of the kth measured object_{k,3}The marking point d_{k,3}And mark point d_{k,1}Symmetrically distributed in x parallel to the camshaft coordinate system_{0}y_{0}Parallel crossing mark point c_{k}On both sides of the reference datum plane;
respectively acquiring recording points d by instrument measuring heads_{k,1}、d_{k,2}And d_{k,3}The coordinates of (a): d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1})、d_{k,2}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,3}(x_{d,k,3},y_{d,k,3},z_{d,k,3})；
By marking point d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,2}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) Correction and reference datum plane x_{0}z_{0}Angle of inclination of beta_{k}Passing through the mark point d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,3}(x_{d,k,3},y_{d,k,3},z_{d,k,3}) Correction and reference datum plane x_{0}y_{0}Angle deviation of alpha_{k}In an ideal state, there is no angular deviation, and the calculation formula can be obtained as follows:
correcting the coordinates of the sampling points of the measured object according to the included angle deviation according to the following formula:
x＝x″′_{k}＝x″_{k}*cosα_{k}+y″_{k}*sinβ_{k}；
y＝y″′_{k}＝y″_{k}*cosα_{k}+y″_{k}*sinβ_{k}；
z＝z″′_{k}＝z″_{k}*cosα_{k}*cosβ_{k}；
wherein (x ″)_{k},y″_{k},z″_{k}) The coordinates of the point on the kth measured object in the instrument coordinate system after the second correction are expressed as (x ″)'_{k},y″′_{k},z″′_{k}) And (4) representing the coordinates of the point on the kth measured object in the instrument coordinate system after the third correction, wherein (x, y, z) represents the sampling pose coordinates of the instrument measuring head.
Four), contour shape measurement of measured object on camshaft
Generating an initial sampling path in an instrument coordinate system according to design parameters of a measured object, and correcting the sampling pose of an instrument measuring head by adopting the method for correcting the sampling pose of the measured object on the camshaft in the specific embodiment, namely correcting the coordinates of sampling points on the initial sampling path, so that the instrument measuring head corrects the sampling pose in the instrument coordinate system relative to the profile of the measured object;
and the instrument measuring head samples by adopting the corrected sampling pose to obtain sampling data of the profile of the measured object, fits a corresponding profile shape according to the sampling data, and analyzes the fitted profile shape according to the reference datum plane of the camshaft to obtain a corresponding size value.
Claims (10)
1. A method for correcting the sampling pose of a measured object on a camshaft is characterized by comprising the following steps:
clamping a workpiece on an instrument rotary table, and vertically fixing a cam shaft on the workpiece through an instrument tip; sequentially correcting the pose of the measuring head of the instrument for three times;
first correction: will cam shaft coordinate system o_{0}x_{0}y_{0}z_{0}Converted into the coordinate OXYZ of the instrument so that the coordinate system o of the measured object_{k}x_{k}y_{k}z_{k}Along with camshaft coordinate system o_{0}x_{0}y_{0}z_{0}The initial transformation is carried out in the instrument coordinate OXYZ, so that the instrument measuring head can initially correct the sampling pose relative to the central axis of the camshaft in the instrument coordinate system;
and (3) second correction: in an instrument coordinate system, translating the central axis of the camshaft to the central point of the measured object to ensure that an instrument measuring head can normally sample the measured object, so that the instrument measuring head can further correct the sampling pose relative to the translated central axis of the camshaft in the instrument coordinate system;
and (3) third correction: and calculating the included angle deviation of the measured object relative to a reference datum plane in a camshaft coordinate system, and converting the coordinate system of the measured object into an instrument coordinate system according to the included angle deviation, so that the instrument measuring head can correct the sampling pose relative to the outline of the measured object in the instrument coordinate system.
2. The method according to claim 1, wherein the camshaft coordinate system o is set to_{0}x_{0}y_{0}z_{0}Conversion into the instrument coordinates xyz, as follows:
respectively selecting marking points a in the positioning areas of the upper and lower workpiece references_{0}、b_{0}；
Sampling the mark points by the instrument measuring head:
sampling for the first time at the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{1}(x_{a,1},y_{a,1},z_{a,1}) And b_{1}(x_{b,1},y_{b,1},z_{b,1})；
The rotary table drives the workpiece to rotate 90 degrees from the initial position, and then secondary sampling is carried out to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{2}(x_{a,2},y_{a,2},z_{a,2}) And coordinates b_{2}(x_{b,2},y_{b,2},z_{b,2})；
The third sampling is carried out after the rotary table drives the workpiece to rotate 180 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{3}(x_{a,3},y_{a,3},z_{a,3}) And coordinates b_{3}(x_{b,3},y_{b,3},z_{b,3})；
The fourth sampling is carried out after the rotary table drives the workpiece to rotate 270 degrees from the initial position to obtain a mark point a_{0}And b_{0}Is sampled at coordinates a_{4}(x_{a,4},y_{a,4},z_{a,4}) And coordinates b_{4}(x_{b,4},y_{b,4},z_{b,4})；
Whether the measuring head of the analysis instrument is in the controllable range of the measuring head when the measuring head is at the four sampling positions is judged, and if not, the workpiece is clamped again; if so, determining the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis of the instrument coordinate system according to the maximum detection error of the instrument measuring head calibrated in advance;
respectively calculating the eccentric correction quantity of the central axis of the camshaft relative to the X axis and the Y axis of the instrument coordinate system according to the sampling points; and converting the camshaft coordinate system to an instrument coordinate system according to the eccentric correction amount.
3. The method for correcting the sampling pose of the measured object on the camshaft according to claim 2, wherein when the measuring head of the instrument is a contact measuring head, whether the stress of the measuring head of the instrument at four sampling positions is in a controllable stress range is judged, and if not, the workpiece is clamped again; if yes, one third of the maximum detection error of the instrument measuring head calibrated in advance is used as the eccentric correction amount delta Z of the central axis of the camshaft relative to the Z axis.
4. The method for correcting the sampling pose of the measured object on the camshaft according to claim 2, wherein when an instrument measuring head is a noncontact measuring head, whether the pose of the measuring head at four sampling positions is within a controllable pose range is respectively judged, and if not, the workpiece is clamped again; if so, taking one third of the maximum detection error of the precalibrated instrument measuring head as the eccentric correction quantity delta Z of the central axis of the camshaft relative to the Z axis; the position and posture of the measuring head refer to a space coordinate and a space included angle of the measuring head under an instrument coordinate system.
5. The method for correcting the sampling pose of the measured object on the camshaft according to claim 2, wherein a camshaft coordinate system is established as follows:
sampling the upper and lower workpiece references by an instrument measuring head in an instrument coordinate system, fitting sampling points of the upper and lower workpiece references by a least square method to obtain circle center coordinates of the upper and lower workpiece references, and taking a circle center connecting line of the upper and lower workpiece references as Z of a camshaft_{0}Axis and perpendicular to Z_{0}The plane of the axis passing through the reference circle center of the lower workpiece is taken as X_{0}Y_{0}A plane;
the camshaft coordinate system is transformed to the instrument coordinate system as follows:
x′_{k}＝(x_{k}·cosα_{0}+Δx)·cosθ_{0}；
z′_{k}＝z_{k}·cosα_{0}·cosβ_{0}+Δz；
in the formula (x)_{k},y_{k},z_{k}) Represents a point on the kth measured object in the camshaft coordinate system, (x'_{k},y′_{k},z′_{k}) Represents a point (x)_{k},y_{k},z_{k}) Converting to the coordinates under the instrument coordinate system; the amount of eccentric correction of the camshaft center axis with respect to the Xaxis comprises the angle alpha of the camshaft center axis with respect to the Xaxis_{0}And bitThe shift amount Δ x; the amount of eccentric correction of the camshaft center axis with respect to the Yaxis comprises an angle beta of the camshaft center axis with respect to the Yaxis_{0}And a displacement amount Δ y; theta_{0}The rotation angle of the current measuring point relative to the initial measuring point is represented, and the range is 0360 degrees.
6. The method according to claim 5, wherein the amount of the eccentric correction of the central axis of the camshaft with respect to the Xaxis comprises an angle α between the central axis of the camshaft and the Xaxis_{0}And a displacement amount Δ x, calculated as follows:
by pointAnd pointThe included angle between the connecting line of (A) and the Z axis is taken as the included angle alpha_{0}Wherein, a pointIs a sampling point a_{1}(x_{a,1},y_{a,1},z_{a,1}) And a_{3}(x_{a,3},y_{a,3},z_{a,3}) Middle point, point ofIs a sampling point b_{1}(x_{b,1},y_{b,1},z_{b,1}) And sampling point b_{3}(x_{b,3},y_{b,3},z_{b,3}) The middle point of (a);
included angle alpha_{0}The calculation formula of (a) is as follows:
the displacement amount Δ x is calculated as follows:
7. the method according to claim 5, wherein the amount of the eccentric correction of the camshaft center axis with respect to the Y axis includes an angle β between the camshaft center axis and the Y axis_{0}And a displacement amount Δ y calculated as follows, respectively:
by pointAnd pointThe included angle between the connecting line of (b) and the Z axis is taken as the included angle beta_{0}Wherein, a pointIs a sampling point a_{2}(x_{a,2},y_{a,2},z_{a,2}) And a_{4}(x_{a,4},y_{a,4},z_{a,4}) Middle point, point ofIs a sampling point b_{2}(x_{b,2},y_{b,2},z_{b,2}) And b_{4}(x_{b,4},y_{b,4},z_{b,4}) The middle point of (a);
angle of inclusion beta_{0}The calculation formula of (a) is as follows:
the displacement amount Δ y is calculated as follows:
8. the method for correcting the sampling pose of the measured object on the camshaft according to claim 5, wherein the second correction is specifically performed as follows:
selecting a mark point c in a tested area of a kth tested object_{k}Marking point c_{k}Characteristic points belonging to the middle section of the measured object; in an instrument coordinate system, an instrument measuring head respectively rotates to the following four mark points c_{k}Sampling: the initial position, the position rotated by 90 degrees relative to the initial position, the position rotated by 180 degrees relative to the initial position, and the position rotated by 270 degrees relative to the initial position respectively obtain corresponding sampling coordinates: c. C_{k,1}(x_{c,k,1},0,z_{c,k,1})、c_{k,2}(0,y_{c,k,2},z_{c,k,2})、c_{k,3}(x_{c,k,3},0,z_{c,k,3}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) (ii) a Using c_{k,1}(x_{c,k,1},0,z_{c,k,1}) And c_{k,3}(x_{c,k,3},0,z_{c,k,3}) Correction of x_{k}Offset in the axial direction by c_{k,2}(0,y_{c,k,2},z_{c,k,2}) And c_{k,4}(0,y_{c,k,4},z_{c,k,4}) Correction of y_{k}The offset in the axial direction, so as to obtain the coordinates after the second correction:
z″_{k}＝z′_{k}
wherein (x'_{k},y′_{k},z′_{k}) The coordinate of the point on the kth measured object in the instrument coordinate system after the first correction is shown, (x ″)_{k},y″_{k},z″_{k}) Indicating the kth measured object after the second correctionCoordinates of the point above in the instrument coordinate system.
9. The method for correcting the sampling pose of the measured object on the camshaft according to claim 5, wherein the third correction is performed as follows:
selecting a mark point d at the upper end of the kth measured object_{k,1}And d_{k,2}The marking point d_{k,1}And d_{k,2}X symmetrically distributed in camshaft coordinate system_{0}z_{0}Two sides of the reference datum plane; selecting a mark point d at the lower end of the kth measured object_{k,3}The marking point d_{k,3}And mark point d_{k,1}Symmetrically distributed in x parallel to the camshaft coordinate system_{0}y_{0}Parallel crossing mark point c_{k}On both sides of the reference datum plane;
respectively acquiring recording points d by instrument measuring heads_{k,1}、d_{k,2}And d_{k,3}The coordinates of (a): d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1})、d_{k,2}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,3}(x_{d,k,3},y_{d,k,3},z_{d,k,3})；
By marking point d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,2}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) Correction and reference datum plane x_{0}z_{0}Angle of inclination of beta_{k}Passing through the mark point d_{k,1}(x_{d,k,1},y_{d,k,1},z_{d,k,1}) And d_{k,3}(x_{d,k,3},y_{d,k,3},z_{d,k,3}) Correction and reference datum plane x_{0}y_{0}Angle deviation of alpha_{k}The calculation formula is as follows:
correcting the coordinates of the sampling points of the measured object according to the included angle deviation according to the following formula:
x＝x″′_{k}＝x″_{k}*cosα_{k}+y″_{k}*sinβ_{k}；
y＝y″′_{k}＝y″_{k}*cosα_{k}+y″_{k}*sinβ_{k}；
z＝z″′_{k}＝z″_{k}*cosα_{k}*cosβ_{k}；
wherein (x ″)_{k},y″_{k},z″_{k}) The coordinates of the point on the kth measured object in the instrument coordinate system after the second correction are expressed as (x ″)'_{k},y″′_{k},z″′_{k}) And (4) representing the coordinates of the point on the kth measured object in the instrument coordinate system after the third correction, wherein (x, y, z) represents the sampling pose coordinates of the instrument measuring head.
10. A contour shape measuring method of a measured object on a camshaft comprises the following steps: generating an initial sampling path in an instrument coordinate system according to the design parameters of the measured object, characterized in that,
the method for correcting the sampling pose of the measured object on the camshaft according to claim 1 is adopted to correct the sampling pose of the measuring head of the instrument, namely, the coordinates of the sampling points on the initial sampling path are corrected, so that the sampling pose of the measuring head of the instrument is corrected in a coordinate system of the instrument relative to the profile of the measured object;
and the instrument measuring head samples by adopting the corrected sampling pose to obtain sampling data of the profile of the measured object, fits a corresponding profile shape according to the sampling data, and analyzes the fitted profile shape according to the reference datum plane of the camshaft to obtain a corresponding size value.
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