CN112945172A - Gear tooth form deviation off-line measuring method based on three-coordinate measuring machine - Google Patents
Gear tooth form deviation off-line measuring method based on three-coordinate measuring machine Download PDFInfo
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Abstract
The application relates to the field of gear parameter measurement, in particular to a gear tooth profile deviation off-line measurement method based on a three-coordinate measuring machine, which comprises the steps of S1, preparing theoretical data; s2, establishing a measurement coordinate system S3, and enabling a measuring head of the three-coordinate measuring machine to approach the tooth surface along the normal vector direction of a to-be-measured tooth surface grid point of the tooth surface to be measured to measure, so as to obtain measured data; and S4, processing and comparing the measured data with the theoretical data to obtain the tooth profile deviation value of the measured gear. The gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine has the advantages that compared with the traditional measuring method, the gear tooth form deviation off-line measuring method is more careful in the aspect of establishing a measuring coordinate system, and compared with the traditional data processing method, the influence of part processing errors on measurement is considered, so that the result is more accurate and reliable.
Description
[ technical field ] A method for producing a semiconductor device
The application relates to the field of gear parameter measurement, in particular to a gear tooth profile deviation off-line measurement method based on a three-coordinate measuring machine.
[ background of the invention ]
With the progress of technology, the types of the gears with complex tooth surfaces are increasingly diversified, the structure complexity of the gears is gradually improved, and the traditional measuring method is difficult to measure the gears with complex structures (such as bevel gears and face gears). Especially for face gears, the traditional measuring method has the following defects: a) the establishment of a measurement coordinate system is simpler, and particularly the angular positioning is carried out, so that the measurement result is not accurate; b) the data processing is not linked with an actual measuring method, the actual measuring method can influence the data processing result to a great extent, and the actual measuring method have a matching relation; c) the data processing does not take into account the effects of machining errors.
The existing high-precision measurement usually utilizes a special gear measurement center or special measurement software, but the cost of the special measurement software and the special gear measurement center is high, and the special measurement software and the special gear measurement center are mainly embodied in different methods in the aspects of establishing a measurement coordinate system, planning a measurement path and processing data, so that the special measurement software and the special gear measurement center are difficult to realize universality among different types of gear measurement; and the existing theoretical knowledge and method are difficult to ensure the measurement precision by adopting a three-coordinate general measurement method with higher universality.
[ summary of the invention ]
The gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine has the advantages that compared with the traditional measuring method, the gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine achieves general off-line measurement of gear tooth form deviation by using general measuring software, is universal and is suitable for any gear, and the gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine has the advantages that the establishment of a measuring coordinate system is more delicate, compared with the traditional data processing method, the influence of part processing errors on measurement is considered, and therefore the result is more accurate and reliable.
The application is realized by the following technical scheme:
a gear tooth form deviation off-line measuring method based on a three-coordinate measuring machine comprises the following steps:
s1, preparing theoretical data:
s11, obtainingTaking the tooth surface equation r of the gearf；
S12, planning a grid to be detected on the rotary projection surface, wherein a tooth surface corresponding to the grid to be detected is used as a region to be detected, and a tooth surface point corresponding to the grid point on the grid to be detected is used as a tooth surface grid point to be detected;
s2, establishing a measurement coordinate system:
s21, determining o of the measurement coordinate systemmzmDirection;
s22, determining o of the measurement coordinate systemmxmOrientation and determining o of the measurement coordinate system according to the Cartesian right-hand rulemYmDirection to obtain a refined measurement coordinate system om-xmymzm；
S3, according to the tooth surface grid point to be measured planned in the step S12 and the coordinate system o established in the step S222m-xmymzmMeasuring a measuring head of a three-coordinate measuring machine to approach the tooth surface along the normal vector direction of a to-be-measured tooth surface grid point of the tooth surface to obtain measured data;
and S4, processing and comparing the measured data with the theoretical data to obtain the tooth profile deviation value of the measured gear.
2. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein the step S21 includes:
s211, determining zmShaft: manually measuring 12 points in four areas of the bottom surface of the gear under an initial coordinate system O-XYZ of a three-coordinate measuring machine, and fitting the points into a plane A1Extraction of A1Is given as zmThe axis is in the direction of A1Expressed as in O-XYZ coordinate system
z＝zA1
S212, determining a measurement origin: z is a radical ofmAfter the axial direction is determined, 8 points with the same height of the excircle are measured, and the 8 points are fit into a circle CyThe center of the circle is C under an O-XYZ coordinate systemy(x0,y0,z0) Let the origin o of the measurement coordinate systemm(xm,ym,zm) Satisfies the following conditions:
wherein d is the height or mounting distance of the gear blank.
3. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 2, wherein the step S22 includes:
s221, roughly establishing a coordinate system: the measuring needle of the three-coordinate measuring machine is touched and measured on the area near the center of the area to be measured along the direction vertical to the rotary projection plane to obtain the cylindrical coordinate (R) approximate to the central point0,β0,Z0) Winding the initial coordinate system O-XYZ of the three-coordinate measuring machine around zmRotation of axis beta0To obtain a rough-built coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1))；
S222, in the currently established rough coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1)) Then, the tooth surface is touched and measured along the normal vector direction of the center point of the tooth surface to obtain the measurement result (R) of the touch pointk,βk,Zk)；
S223, comparing the measurement radius R of the touch pointkThe measurement radius R of the theoretical central point is equal to the measurement radius R of the theoretical central point if the accuracy requirement | R is not metkIf R | ≦ epsilon, the current coordinate system is wound around zmRotation of axis betak；
S224, repeating the steps S222 and S223, and if the precision requirement | R is metkIf R is less than or equal to epsilon, outputting the current coordinate system as a refined measurement coordinate system o of the subsequent measurement tooth surfacem-xmymzm。
4. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein the step S4 includes:
s41, theoretical data processing:
s411, recording that the grid point to be measured under the theoretical measurement coordinate system is PT(i, j) normal vector is NT(i, j) with a mesh center point of PT(3,5), corresponding examplesMeasured data is PM(i, j); wherein i is 1 … 5; j ═ 1 … 9;
s412, establishing a refined measurement coordinate system o according to the step S22m-xmymzmAn angular deviation beta exists between the measured data and the theoretical datak；
S413, extracting a central point P of the measurement gridMAngle β in cylindrical coordinates of (3,5)kA grid point P to be measuredT(i, j) and a normal vector NT(i, j) winding zmRotation of axis betakAngle as new theoretical point and normal vector PT′(i,j)、NT' (i, j) wherein PT′(i,j)、NT' (i, j) is obtained by the following formula
S42, actual measurement data processing:
s421, expressing the position relation between the established refined measurement coordinate system and the theoretical measurement coordinate system by a transformation matrix as
Wherein R isxAnd RzRespectively representing a transformation matrix rotating about the x-axis and the z-axis, T representing a translation matrix, and
Xmin≤ΔX≤Xmax，Ymin≤ΔY≤Ymax，Zmin≤ΔZ≤Zmax
by least squares fitting of measured data
Wherein
T(i,j)＝[PM'(i,j)-PT'(i,j)]·NT'(i,j)
The obtained parameter valueX*，Y*，Z*，
θ*The optimal matching parameters of the measured data and the theoretical data are obtained;
s43, accurately positioning the measurement lattice PM' (i, j) fitting to NURBS surface Rm(u, v) where u, v are parameters in both the tooth width and the tooth height, and each ordinal pair (i, j) corresponds to a group (u)i,vj)，
S44, for one P on the theoretical tooth surfaceT' (i, j), construct optimization objectives as follows:
[PT'(i,j)-Rm(u,v)]×NT'(i,j)→0
obtaining an ideal measuring point PMParameter corresponding to "(" i, j) ")
Therefore, P will beM"(i, j) is expressed as follows:
s45, comparing the tooth surface with the theoretical tooth surface to obtain the tooth surface deviation
ε(i,j)＝[PT'(i,j)-PM”(i,j)]·NT'(i,j)。
5. The gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein in step S12, one point P (R, Z) on the rotation projection plane and its corresponding grid point P on the grid to be measuredT(rfZ) a relationship of
6. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein said region to be measured in step S12 is a region where the inside and outside radii of the tooth surface are shrunk inwards by 10%, the addendum is shrunk downwards by 5%, and the dedendum is shrunk upwards by 5%.
Compared with the prior art, the method has the following advantages:
the gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine has the advantages that compared with the traditional measuring method, the gear tooth form deviation off-line measuring method is more careful in the aspect of establishing a measuring coordinate system, and compared with the traditional data processing method, the influence of part processing errors on measurement is considered, so that the result is more accurate and reliable.
[ description of the drawings ]
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic diagram of planning a grid to be measured on a rotating projection plane according to an embodiment of the present application.
Fig. 2 is a schematic diagram of a theoretical measurement coordinate system of a spur gear according to an embodiment of the present application, where 10 is a tooth surface center.
FIG. 3 is a schematic diagram of a theoretical measurement coordinate system of a bevel gear according to an embodiment of the present application, where 11 is a tooth surface center.
Fig. 4 is a schematic diagram of a theoretical measurement coordinate system of a face gear according to an embodiment of the present application, where 12 is a tooth surface center.
Fig. 5 is a schematic diagram of manually touching 12 points in total in four regions of the bottom surface of the spur gear in the initial coordinate system O-XYZ of the coordinate measuring machine in step S211 of the embodiment of the present application, where 13 is a touch point.
Fig. 6 is a schematic diagram of manually touching 12 points in total in four regions of the bottom surface of the bevel gear under the initial coordinate system O-XYZ of the coordinate measuring machine in step S211 of the embodiment of the present application, where 14 is a touch point.
Fig. 7 is a schematic diagram of manually touching 12 points in total of four regions of the bottom surface of the face gear under the initial coordinate system O-XYZ of the coordinate measuring machine in step S211 of the embodiment of the present application, where 15 is a touch point.
Fig. 8 is a schematic view of the measurement coordinate system extracted in step S211 of the present application, where 16 is a contact point.
FIG. 9 shows z in step S212 according to the present embodimentmAnd after the shaft direction is determined, measuring 8 points at the same height of the outer circle of the spur gear, wherein 17 is a contact point.
FIG. 10 shows z in step S212 according to the present embodimentmAnd after the shaft direction is determined, measuring 8 points at the same height of the outer circle of the bevel gear, wherein 18 is a contact point.
FIG. 11 shows z in step S212 according to the present embodimentmAfter the axial direction is determined, 8 points of the excircle of the face gear at the same height are measured, wherein 19 is a measuring contact point.
Fig. 12 is a schematic diagram of fitting 8 points into a circle in step S212 according to the embodiment of the present application, where 20 is a contact point.
Fig. 13 is a schematic diagram of the face gear from the rough measurement coordinate system to the refined measurement coordinate system according to the embodiment of the present application, where 21 is an approximate center point of the rough measurement coordinate system, and 22 is an approximate center point of the refined measurement coordinate system.
Fig. 14 is a flowchart of refining a measurement coordinate system according to an embodiment of the present application.
Fig. 15 and 16 are schematic diagrams illustrating a relationship between measured data and theoretical data according to an embodiment of the present application.
Fig. 17 is a schematic diagram of a measurement error according to an embodiment of the present application.
[ detailed description ] embodiments
In order to make the technical problems, technical solutions and advantageous effects solved by the present application more clear and obvious, the present application is further described in 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 present application and are not intended to limit the present application.
The embodiment of the application provides a gear tooth form deviation off-line measuring method based on a three-coordinate measuring machine, which comprises the following steps:
s1, preparing theoretical data:
s11, obtaining the tooth surface equation r of the gearf；
S12, as shown in fig. 1, planning a grid to be measured on a rotational projection plane (generally, a middle plane of a tooth socket), where the size of each grid on the measurement grid may be preset according to the size of a gear, and a subsequent probe will touch and measure each grid point, where a tooth surface corresponding to the grid to be measured is used as a region to be measured, that is, a tooth surface region corresponding to the grid abcd in fig. 1, and preferably, for more efficient measurement, the region to be measured is a working region of the gear, further, the measurement region is limited such that an inner and outer radius of the tooth surface is shrunk inwards by 10%, an addendum is shrunk downwards by 5%, and a dedendum is shrunk upwards by 5%, and a tooth surface point corresponding to the grid point on the grid to be measured is used as a grid point of the tooth surface to be measured, where a point P (R, ZT(rfZ) a relationship of
S2, establishing a measurement coordinate system, determining the theoretical measurement coordinate system of the gear according to a Cartesian right-hand rule, taking a straight gear, a bevel gear and a face gear as an example, assuming that the theoretical measurement coordinate system of the gear is shown in FIGS. 2-4, a coordinate origin om coincides with a circle center (or a pitch cone point) of an upper end face, zm is collinear with a gear rotating shaft, a direction far away from the upper end face is positive, and a ym direction is a normal vector of a plane determined by a center point of a tooth surface to be measured and a zm axis:
s21, determining o of the measurement coordinate systemmzmDirection; specifically, step S21 includes S211 and S212:
s211, determining zmShaft: as shown in FIGS. 5-8, four regions of the bottom surface of the gear are manually touched at 12 points in total under the initial coordinate system O-XYZ of the coordinate measuring machine, and are fitted to a plane A1Extraction of A1Is given as zmThe direction in which the axis is located is,let A1Expressed as in O-XYZ coordinate system
z＝zA1
S212, determining a measurement origin: as in FIGS. 9-12, zmAfter the axial direction is determined, 8 points with the same height of the excircle are measured, and the 8 points are fit into a circle CyThe center of the circle is C under an O-XYZ coordinate systemy(x0,y0,z0) Let the origin o of the measurement coordinate systemm(xm,ym,zm) Satisfies the following conditions:
wherein d is the height or mounting distance of the gear blank.
S22, determining o of the measurement coordinate systemmxmOrientation and determining o of the measurement coordinate system according to the Cartesian right-hand rulemYmDirection to obtain a refined measurement coordinate system om-xmymzm(ii) a Specifically, step S22 includes S221-S224:
s221, roughly establishing a coordinate system: the measuring needle of the three-coordinate measuring machine is touched and measured on the area near the center of the area to be measured along the direction vertical to the rotary projection plane to obtain the cylindrical coordinate (R) approximate to the central point0,β0,Z0) Winding the initial coordinate system O-XYZ of the three-coordinate measuring machine around zmRotation of axis beta0To obtain a rough-built coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1))；
S222, in the currently established rough coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1)) Then, the tooth surface is touched and measured along the normal vector direction of the center point of the tooth surface to obtain the measurement result (R) of the touch pointk,βk,Zk)；
S223, comparing the measurement radius R of the touch pointkThe measurement radius R of the theoretical central point is equal to the measurement radius R of the theoretical central point if the accuracy requirement | R is not metkIf R | ≦ epsilon, the current coordinate system is wound around zmRotation of axis betak；
S224, as shown in FIG. 14, repeating the steps S222 and S223, if the precision requirement | R is satisfiedkIf R is less than or equal to epsilon, outputting the current coordinate system as a refined measurement coordinate system o of the subsequent measurement tooth surfacem-xmymzmFig. 13 is a schematic diagram of the face gear from the rough measurement coordinate system to the fine measurement coordinate system.
S3, according to the tooth surface grid point to be measured planned in the step S12 and the coordinate system o established in the step S222m-xmymzmMeasuring a measuring head 100 of the three-coordinate measuring machine to approach the tooth surface along the normal vector direction of a to-be-measured tooth surface grid point of the tooth surface to be measured, and obtaining measured data;
s4, processing and comparing the measured data with the theoretical data to obtain the tooth profile deviation value of the measured gear; step S4 includes:
s41, theoretical data processing:
s411, recording that the grid point to be measured under the theoretical measurement coordinate system is PT(i, j) normal vector is NT(i, j) with a mesh center point of PT(3,5) the corresponding measured data is PM(i, j); wherein i is 1 … 5; j ═ 1 … 9;
s412, establishing a refined measurement coordinate system o according to the step S22m-xmymzmAn angular deviation beta exists between the measured data and the theoretical datak；
S413, extracting a central point P of the measurement gridMAngle β in cylindrical coordinates of (3,5)kA grid point P to be measuredT(i, j) and a normal vector NT(i, j) winding zmRotation of axis betakAngle as new theoretical point and normal vector PT′(i,j)、NT' (i, j), FIG. 15 shows the grid 23 to be measured and the measurement grid 24 in the theoretical measurement coordinate system, and FIG. 16 shows the rotation βkThe mesh 25 to be measured in the theoretical measurement coordinate system after the angle is rotated by betakThe post-angle theoretical measurement grid 26 in the coordinate system, where PT′(i,j)、NT' (i, j) is obtained by the following formula
S42, actual measurement data processing:
s421, expressing the position relation between the established refined measurement coordinate system and the theoretical measurement coordinate system by a transformation matrix as
Wherein R isxAnd RzRespectively representing a transformation matrix rotating about the x-axis and the z-axis, T representing a translation matrix, and
Xmin≤ΔX≤Xmax，Ymin≤ΔY≤Ymax，Zmin≤ΔZ≤Zmax
by least squares fitting of measured data
Wherein
T(i,j)＝[PM'(i,j)-PT'(i,j)]·NT'(i,j)
Derived parameter value X*，Y*，Z*，
θ*The optimal matching parameters of the measured data and the theoretical data are obtained;
in actual measurement, the curved surface point touched and measured by the measuring needle is often not an ideal measuring point, as shown in fig. 17, 101 is a theoretical tooth surface, 102 is an actual tooth surface, PM"is an ideal measurement point, and the stylus has not yet touched PM"time, with the surface at point PMContact, causing measurement errors εm. To avoid this measurement error, the following steps are taken:
s43, accurately positioning the measurement lattice PM' (i, j) fitting to NURBS surface Rm(u, v) wherein u, v are teethParameters in both width and tooth height directions, each ordinal pair (i, j) corresponding to a group (u)i,vj)，
S44, for one P on the theoretical tooth surfaceT' (i, j), construct optimization objectives as follows:
[PT'(i,j)-Rm(u,v)]×NT'(i,j)→0
obtaining an ideal measuring point PMParameter corresponding to "(" i, j) ")
Therefore, P will beM"(i, j) is expressed as follows:
s45, comparing the tooth surface with the theoretical tooth surface to obtain the tooth surface deviation
ε(i,j)＝[PT'(i,j)-PM”(i,j)]·NT'(i,j)。
The gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine has the advantages that compared with the traditional measuring method, the gear tooth form deviation off-line measuring method is more careful in the aspect of establishing a measuring coordinate system, and compared with the traditional data processing method, the influence of part processing errors on measurement is considered, so that the result is more accurate and reliable.
The foregoing is illustrative of one or more embodiments provided in connection with the detailed description and is not intended to limit the disclosure to the particular forms disclosed. Similar or identical methods, structures, etc. as used herein, or several technical inferences or substitutions made on the concept of the present application should be considered as the scope of the present application.
Claims (6)
1. A gear tooth form deviation off-line measuring method based on a three-coordinate measuring machine is characterized by comprising the following steps:
s1, preparing theoretical data:
s11, obtaining the tooth surface equation r of the gearf；
S12, planning a grid to be detected on the rotary projection surface, wherein a tooth surface corresponding to the grid to be detected is used as a region to be detected, and a tooth surface point corresponding to the grid point on the grid to be detected is used as a tooth surface grid point to be detected;
s2, establishing a measurement coordinate system:
s21, determining o of the measurement coordinate systemmzmDirection;
s22, determining o of the measurement coordinate systemmxmOrientation and determining o of the measurement coordinate system according to the Cartesian right-hand rulemYmDirection to obtain a refined measurement coordinate system om-xmymzm；
S3, according to the tooth surface grid point to be measured planned in the step S12 and the coordinate system o established in the step S222m-xmymzmMeasuring a measuring head of a three-coordinate measuring machine to approach the tooth surface along the normal vector direction of a to-be-measured tooth surface grid point of the tooth surface to obtain measured data;
and S4, processing and comparing the measured data with the theoretical data to obtain the tooth profile deviation value of the measured gear.
2. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein the step S21 includes:
s211, determining zmShaft: manually measuring 12 points in four areas of the bottom surface of the gear under an initial coordinate system O-XYZ of a three-coordinate measuring machine, and fitting the points into a plane A1Extraction of A1Is given as zmThe axis is in the direction of A1Expressed as in O-XYZ coordinate system
z＝zA1
S212, determining a measurement origin: z is a radical ofmAfter the axial direction is determined, 8 points with the same height of the excircle are measured, and the 8 points are fit into a circle CyThe center of the circle is C under an O-XYZ coordinate systemy(x0,y0,z0) Let the origin o of the measurement coordinate systemm(xm,ym,zm) Satisfies the following conditions:
wherein d is the height or mounting distance of the gear blank.
3. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 2, wherein the step S22 includes:
s221, roughly establishing a coordinate system: the measuring needle of the three-coordinate measuring machine is touched and measured on the area near the center of the area to be measured along the direction vertical to the rotary projection plane to obtain the cylindrical coordinate (R) approximate to the central point0,β0,Z0) Winding the initial coordinate system O-XYZ of the three-coordinate measuring machine around zmRotation of axis beta0To obtain a rough-built coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1))；
S222, in the currently established rough coordinate system om(k-1)-(xm(k-1),ym(k-1),zm(k-1)) Then, the tooth surface is touched and measured along the normal vector direction of the center point of the tooth surface to obtain the measurement result (R) of the touch pointk,βk,Zk)；
S223, comparing the measurement radius R of the touch pointkThe measurement radius R of the theoretical central point is equal to the measurement radius R of the theoretical central point if the accuracy requirement | R is not metkIf R | ≦ epsilon, the current coordinate system is wound around zmRotation of axis betak；
S224, repeating the steps S222 and S223, and if the precision requirement | R is metkIf R is less than or equal to epsilon, outputting the current coordinate system as a refined measurement coordinate system o of the subsequent measurement tooth surfacem-xmymzm。
4. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein the step S4 includes:
s41, theoretical data processing:
s411, recording that the grid point to be measured under the theoretical measurement coordinate system is PT(i, j) normal vector is NT(i, j) with a mesh center point of PT(3,5) the corresponding measured data is PM(i, j); wherein i is 1 … 5; j ═ 1 … 9;
s412, establishing a refined measurement coordinate system o according to the step S22m-xmymzmAn angular deviation beta exists between the measured data and the theoretical datak；
S413, extracting a central point P of the measurement gridMAngle β in cylindrical coordinates of (3,5)kA grid point P to be measuredT(i, j) and a normal vector NT(i, j) winding zmRotation of axis betakAngle as new theoretical point and normal vector PT′(i,j)、NT' (i, j) wherein PT′(i,j)、NT' (i, j) is obtained by the following formula
S42, actual measurement data processing:
s421, expressing the position relation between the established refined measurement coordinate system and the theoretical measurement coordinate system by a transformation matrix as
Wherein R isxAnd RzRespectively representing a transformation matrix rotating about the x-axis and the z-axis, T representing a translation matrix, and
Xmin≤ΔX≤Xmax，Ymin≤ΔY≤Ymax，Zmin≤ΔZ≤Zmax
by least squares fitting of measured data
Wherein
T(i,j)＝[PM'(i,j)-PT'(i,j)]·NT'(i,j)
Derived parameter value X*，Y*，Z*，
θ*The optimal matching parameters of the measured data and the theoretical data are obtained;
s43, accurately positioning the measurement lattice PM' (i, j) fitting to NURBS surface Rm(u, v) where u, v are parameters in both the tooth width and the tooth height, and each ordinal pair (i, j) corresponds to a group (u)i,vj)，
S44, for one P on the theoretical tooth surfaceT' (i, j), construct optimization objectives as follows:
[PT'(i,j)-Rm(u,v)]×NT'(i,j)→0
obtaining an ideal measuring point PMParameter corresponding to "(" i, j) ")
Therefore, P will beM"(i, j) is expressed as follows:
s45, comparing the tooth surface with the theoretical tooth surface to obtain the tooth surface deviation
ε(i,j)＝[PT'(i,j)-PM”(i,j)]·NT'(i,j)。
5. The gear tooth form deviation off-line measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein in step S12, one point P (R, Z) on the rotation projection plane and its corresponding grid point P on the grid to be measuredT(rfZ) a relationship of
6. The gear tooth form deviation offline measuring method based on the three-coordinate measuring machine as claimed in claim 1, wherein said region to be measured in step S12 is a region where the inside and outside radii of the tooth surface are shrunk inwards by 10%, the addendum is shrunk downwards by 5%, and the dedendum is shrunk upwards by 5%.
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| CN114754698A (en) * | 2022-04-11 | 2022-07-15 | 重庆大学 | Surface gear tooth surface measuring point planning and on-machine measuring method |
| CN116393769A (en) * | 2023-04-17 | 2023-07-07 | 南京工大数控科技有限公司 | Grinding tooth surface deviation correction method based on additional parabolic motion |
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