CN115790452B - Gear tooth surface three-dimensional morphology moire characterization and measurement method - Google Patents

Gear tooth surface three-dimensional morphology moire characterization and measurement method Download PDF

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CN115790452B
CN115790452B CN202310064231.8A CN202310064231A CN115790452B CN 115790452 B CN115790452 B CN 115790452B CN 202310064231 A CN202310064231 A CN 202310064231A CN 115790452 B CN115790452 B CN 115790452B
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phase
measurement
grating
tooth surface
measuring
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CN115790452A (en
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杨涛
杜晓龙
马力
张妮妮
王剑龙
杨彪
王芳
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Xi'an Chishine Optoelectronics Technology Co ltd
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Xi'an Chishine Optoelectronics Technology Co ltd
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Abstract

A gear tooth surface three-dimensional morphology moire characterization and measurement method comprises the steps of obtaining a three-frame phase shift moire fringe pattern of measured tooth surface morphology information through a projection device, and realizing high-sensitivity projection moire measurement of a gear tooth surface based on a reliable phase demodulation method and a time domain phase unwrapping method so as to solve the problems that light path propagation is easy to be blocked and measurement accuracy is not high in the gear tooth surface three-dimensional morphology characterization process in the prior art; the method adopts the projection moire principle, avoids shielding by changing the light path, improves the measurement precision by utilizing the amplifying effect of moire fringes, and solves the problems of the measurement principle, the shielding of the tooth surface and the like in gear measurement.

Description

Gear tooth surface three-dimensional morphology moire characterization and measurement method
Technical Field
The invention relates to the technical field of surface structure light measurement in optical precision measurement, in particular to a gear tooth surface three-dimensional morphology Moire characterization and measurement method
Background
The assessment of the shape error of the tooth surface of the gear is an important precision index for gear manufacturing. The tooth shape and tooth direction error measuring technology of the gear is a core technological guarantee in the aspects of reducing transmission noise, improving transmission efficiency, prolonging service life and the like. The foreign novel submarine has low running noise and can hide the position of the submarine from enemy. As another example, the research of Kyoto university in Japan shows that when the gear precision reaches the micron level, the automobile gear profile is subjected to 2-3 micron micro correction, so that the automobile gear profile has better performance and longer service life.
Conventionally, tooth surface shape error measurement mainly adopts a CNC gear measuring center, and during measurement, a measuring needle is required to be contacted with a tooth surface, and then the measurement is realized by scanning point by point along a characteristic line. The increase of the resolution depends on the increase of the number of points of contact between the measuring needle and the tooth surface, so that the measuring efficiency is lower. And only a few characteristic lines, such as an involute profile, etc., on a limited number of tooth surfaces are measured in actual measurement to be approximate. Therefore, with the increasing demand for high-precision gear applications, the development of efficient, high-precision in-place detection technology for gear tooth profiles and quality grades is particularly urgent for the parameter evaluation of gears and the development of the gear industry.
In order to meet the development requirements of the current industrial technology, the gear measuring machine based on the novel principle becomes a research hotspot of the gear measuring technology, particularly a photoelectric three-dimensional measuring method, and is hopeful to greatly improve the measuring efficiency and enlarge the measuring precision lifting space due to the characteristics of non-contact and high precision, so that the gear measuring technology again shows a milestone type crossing. Meanwhile, the dense tooth surface point cloud obtained by the method is used for representing the service performance of the gear instead of characteristic curves such as tooth shape, tooth direction and the like, and a gear precision evaluation system is also changed, so that a new gear design theory is generated.
The optical measurement technology has the characteristics of high resolution and high speed, and the implementation of the optical measurement technology also comprises a stereoscopic vision method, a digital structured light method, a laser triangulation method, a holographic method, a Morse method, a heterodyne interference method and the like. The main principle is that a series of identical fringe patterns with phase shift difference are collected, then a certain phase shift algorithm is utilized to extract the measured phase, and the appearance of the measured tooth surface is recovered by phase unwrapping. The technology is simple and reliable, but requires the use of an expensive phase shifter to ensure an accurate phase shift process, thereby limiting the wide application of the method in workshop occasions with large temperature variation and vibration; in addition, the trip point generated by the phase shift algorithm is difficult to judge correctly due to the phase unwrapping process. The traditional airspace phase unwrapping method often cannot correctly unwrap the measured phase in a noisy working site; in addition, for complex parts of gears, such as gear teeth, which are easy to shade light, the traditional surface structured light method cannot accurately collect phase shift fringe patterns due to light shading, and the measuring speed is difficult to improve.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a gear tooth surface three-dimensional morphology moire characterization and measurement method, which is based on a reliable phase demodulation method and a time domain phase unwrapping method, so as to realize high-sensitivity projection moire measurement of the gear tooth surface and solve the problems that light path propagation is easy to be blocked and measurement precision is not high in the gear tooth surface three-dimensional morphology characterization process in the prior art.
In order to achieve the purpose of measurement, the technical scheme of the invention is as follows:
a gear tooth surface three-dimensional morphology moire characterization and measurement method comprises the following steps:
firstly, setting up a projection device, wherein the projection device comprises a projection system and an imaging system; the projection system comprises a point light source, a collimator, a measuring grating group consisting of a coarse grating and a fine grating, a projection lens and a semi-reflection semi-transmission mirror which are sequentially arranged on a projection light arm; the imaging system comprises a reference grating group, an imaging lens and an industrial camera which are sequentially arranged on the light receiving arm and are the same as the measuring grating group;
placing the measured tooth surface in a measurement space, starting a point light source, parallelly irradiating the light emitted by the point light source through a collimator to measure a grating group, adjusting the included angle between a semi-reflection semi-transmission mirror and an optical axis, and using the period P in the grating group 1 Shadow grating is projected to the measured tooth surface by the coarse grating to form a shadow grating fringe pattern, the shadow grating on the measured tooth surface is reflected to the surface of a reference grating group by a semi-reflection semi-transmission mirror and is received by an industrial camera without distortion, and then a three-frame phase shift moire fringe pattern containing the appearance information of the measured tooth surface is obtained
Figure SMS_1
、/>
Figure SMS_2
、/>
Figure SMS_3
；
Step two, the period is P 2 The fine grating of the measurement grating group of (2) is moved to the measurement space, P 1 ＞P 2 Repeating the first step to obtain a three-frame phase shift moire pattern:
Figure SMS_4
，/>
Figure SMS_5
，/>
Figure SMS_6
；
step three, respectively extracting phases of the two sets of collected moire fringe patterns to obtain a low-sensitivity wrapped measurement phase
Figure SMS_7
And measurement phase of high sensitivity package +.>
Figure SMS_8
；
Step four, adopting a time domain phase unwrapping method to measure the phase
Figure SMS_9
、/>
Figure SMS_10
Performing unwrapping to obtain unwrapped high sensitivity phase +.>
Figure SMS_11
；
Fifthly, calibrating the projection device, determining phase shift by utilizing a random phase shift algorithm, and establishing a phase height mapping relation, and a phase pixel coordinate and an absolute coordinate
Figure SMS_12
To obtain the tooth surface coordinates +.>
Figure SMS_13
；
And step six, sequentially rotating the gear to be measured, and repeating the steps one to five to finish the three-dimensional profile measurement of all the tooth surfaces to be measured.
Measuring phase as described in step three
Figure SMS_14
、/>
Figure SMS_15
The obtaining method is the same, and specifically comprises the following steps:
the recorded 3-frame phase shift moire pattern is represented as:
Figure SMS_16
(1)
in the above-mentioned method, the step of,
Figure SMS_19
，/>
Figure SMS_20
，/>
Figure SMS_23
respectively background, amplitude and measured phase; />
Figure SMS_18
、/>
Figure SMS_21
、
Figure SMS_22
The phase shift amounts of the first, second and third frames are respectively, ">
Figure SMS_24
A phase shift amount for the first frame; />
Figure SMS_17
Representing pixel coordinates;
assuming a known estimate of the phase shift, first, a set of variables is defined:
Figure SMS_25
，/>
Figure SMS_26
，/>
Figure SMS_27
formula (1) is written as:
Figure SMS_28
(2)/>
in the method, in the process of the invention,
Figure SMS_29
，/>
Figure SMS_30
，/>
Figure SMS_31
；
the unknown X can be solved in the least squares sense as:
Figure SMS_32
(3)
in the method, in the process of the invention,
Figure SMS_33
is->
Figure SMS_34
Thus the phase is obtained as:
Figure SMS_35
(4)
and then can obtain:
Figure SMS_36
(5)
at this time, equation (1) is updated to:
Figure SMS_37
(6)
in the method, in the process of the invention,
Figure SMS_38
at this time, the above formula (2) is rewritten in the form of a matrix:
Figure SMS_39
(7)
in the method, in the process of the invention,
Figure SMS_40
，/>
Figure SMS_41
，/>
Figure SMS_42
；
the least square meaning is as follows:
Figure SMS_43
(8)
will be
Figure SMS_44
Substituting (2), repeating the steps until meeting the convergence condition:
Figure SMS_45
(9)
in the method, in the process of the invention,
Figure SMS_46
is a predefined convergence condition,/->
Figure SMS_47
Is the iteration number, when the convergence condition is satisfied, the measurement phase +.>
Figure SMS_48
。
The method for unwrapping by adopting the time domain phase specifically comprises the following steps:
the height equality of the two measurements according to thickness is available:
Figure SMS_49
(10)
wherein the period is used in the measurement
Figure SMS_50
And->
Figure SMS_51
Two gratings of>
Figure SMS_52
The method comprises the steps of carrying out a first treatment on the surface of the The heights of the two measurements are equal +.>
Figure SMS_53
For the wrap phase diagram obtained during the precision measurement, < >>
Figure SMS_54
For the refined developed phase diagram, +.>
Figure SMS_55
For a coarsely measured parcel phase diagram, coarsely measured parcel unwrapping further has:
Figure SMS_56
(11)
the above is deformed to:
Figure SMS_57
(12)
in the above-mentioned method, the step of,
Figure SMS_58
representing the number of fringe orders, phase unwrapping, i.e. solving +.in equation (12)>
Figure SMS_59
The method comprises the steps of carrying out a first treatment on the surface of the For unwrapping the refined phase, its wrapped phase is first of all +.>
Figure SMS_60
And coarse measurement phase expansion to +.>
Figure SMS_61
The expansion method is as follows:
Figure SMS_62
the above formula (12) shows that: />
Figure SMS_63
Expressed as an integer +.>
Figure SMS_64
And the value range is->
Figure SMS_65
Is->
Figure SMS_66
The sum is then taken to be nearest and less than or equal to ++>
Figure SMS_67
And (3) rounding to obtain:
Figure SMS_68
(13)
when (when)
Figure SMS_69
In the time-course of which the first and second contact surfaces,
Figure SMS_70
(14)
when (when)
Figure SMS_71
When and when->
Figure SMS_72
At this time: />
Figure SMS_73
(15)
If it is
Figure SMS_74
：
Figure SMS_75
(16)。
Calibrating the projection device, and determining phase shift by using a random phase shift algorithm, wherein the method specifically comprises the following steps:
the transformation relationship between pixel coordinates and absolute coordinates is expressed as:
Figure SMS_76
(17)
in the above-mentioned method, the step of,
Figure SMS_77
is an internal reference matrix of the industrial camera, +.>
Figure SMS_78
、/>
Figure SMS_79
For the external matrix of the industrial camera, the pixel coordinates can be used (17)>
Figure SMS_80
Conversion to absolute coordinates>
Figure SMS_81
；
The mapping relationship of phase and height is expressed as:
Figure SMS_82
(18)
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_83
、/>
Figure SMS_84
、/>
Figure SMS_85
the matrix related to the geometric parameters and pixel coordinates of the measuring system is obtained by a calibration method, and specifically comprises the following steps:
(5.1) processing a plane calibration plate, and mounting the calibration plate on a micro-displacement platform along the edge
Figure SMS_86
Directional movement, when starting calibration, the calibration plate is placed on the reference plane, at this time +.>
Figure SMS_87
Projecting fringe patterns on the calibration plate, and collecting three random phase shift fringe patterns to obtain +.>
Figure SMS_88
Let the collected fringe pattern be expressed as:
Figure SMS_89
(19)
then the micro-displacement platform is controlled to drive the calibration plate to move a distance from the surface perpendicular to the reference surface
Figure SMS_91
At this time->
Figure SMS_94
Three phase shift fringe patterns are acquired as well>
Figure SMS_98
A series of out-of-plane displacements and corresponding phases are obtained in the same way: />
Figure SMS_92
、/>
Figure SMS_95
，
Figure SMS_97
、/>
Figure SMS_100
，/>
Figure SMS_90
，/>
Figure SMS_99
、/>
Figure SMS_101
The method comprises the steps of carrying out a first treatment on the surface of the By substituting it into the above formula (19), +.>
Figure SMS_102
、/>
Figure SMS_93
、
Figure SMS_96
；
(5.2) determining the phase shift amount by adopting a random phase shift technology, wherein the solving method of the specific phase is as follows:
the above formula (19) is rewritten as:
Figure SMS_103
(20)/>
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_104
，/>
Figure SMS_105
at this time, the above formula (20) is written as:
Figure SMS_106
(21)
in the method, in the process of the invention,
Figure SMS_107
，/>
Figure SMS_108
at this time, each fringe pattern matrix is combined into a column line by line;
from equation (21), the fringe pattern space is expressed as a multiplication of two matrices, where the vectors
Figure SMS_109
、/>
Figure SMS_110
、/>
Figure SMS_111
The base vector of the fringe space is represented in relation to the phase shift, the fringe space being at the base vector +.>
Figure SMS_112
、/>
Figure SMS_113
、/>
Figure SMS_114
The space is formed;
to solve for vectors
Figure SMS_115
、/>
Figure SMS_116
、/>
Figure SMS_117
The method of reducing the base decomposition is adopted, and the method of reducing the base spatially transforms the high-dimensional matrix into a low-dimensional matrix form, namely:
Figure SMS_118
(22)
Figure SMS_119
is->
Figure SMS_120
Basis matrix of>
Figure SMS_121
For the transformation matrix, in this case +.>
Figure SMS_122
Second column data->
Figure SMS_123
And third column data->
Figure SMS_124
The data phase shift is:
Figure SMS_125
(23)
at this time, according to the phase shift
Figure SMS_126
The phase of the calibration plate at each moving point is obtained by adopting a least square phase algorithm
Figure SMS_127
。
The beneficial effects of the invention are as follows:
1. because a random phase shift method is used, the phase shift amount does not need to be accurately calibrated, the phase is reliably extracted through iteration, a precise and expensive phase shifter is not required, the phase shift device can adapt to a complex workshop environment, strict phase shift requirements are relaxed, and the inherent random phase shift error of a phase shift technology is eliminated.
2. The measuring grating and the reference grating are composed of thick and thin gratings, so that the variable sensitivity shadow casting grating can be carried out, a time domain unwrapping strategy is formed, phase unwrapping can be completed point by point and accurately, the effect of each pixel point is different from that of airspace unwrapping, and phase accumulation errors are not generated.
3. The measuring system is an arbitrary Moire measuring structure, and does not need to calibrate structural parameters. In addition, due to the use of the semi-reflective semi-transparent mirror, the problem that the teeth face the light is blocked is solved, free transmission of the light can be realized, and the fringe image can be acquired without distortion.
4. Because moire fringes have amplification effect, high-sensitivity measurement can be realized by using a measuring element with low resolution, and an efficient way is provided for carrying out full-field and non-contact measurement of various gears such as a straight gear, a bevel gear and the like.
Drawings
FIG. 1 is a measurement system layout of the present invention.
Fig. 2 is a technical schematic diagram of the present invention.
Fig. 3 is a measurement space coordinate system relationship.
The reference numerals are explained as follows:
1 is a measured gear, 2 is a projection system, 3 is an imaging system, and 4 is a shadow grating fringe pattern; the device comprises a 5-point light source, a 6-collimator, a 7-measuring grating group, an 8-projection lens, a 9-semi-reflection semi-transmission lens, a 10-measured tooth surface, a 11-reference grating group, a 12-imaging lens and a 13-industrial camera.
Detailed Description
The invention will be described in detail below with reference to the drawings and the implementation.
Referring to fig. 1 and 2, a gear tooth surface morphology projection device comprises a projection system 2 and an imaging system 3;
the projection system 2 comprises a point light source 5, a collimator 6, a measuring grating group 7 consisting of a coarse grating and a fine grating, a projection lens 8 and a semi-reflection semi-transmission mirror 9 which are sequentially arranged on a projection light arm;
the imaging system 3 comprises a reference grating group 11, an imaging lens 12 and an industrial camera 13 which are sequentially arranged on the light receiving arm and are the same as the measuring grating group;
the light emitted by the point light source 5 in the projection system 2 irradiates the measuring grating group 7 in parallel through the collimator 6, shadow gratings are generated on the tooth surface through the semi-reflection semi-transparent mirror 9 by the projection lens 8, the shadow gratings are modulated by the shape of the measured tooth surface 10 and deform, deformed gratings are formed, moire fringes can be obtained through recording the reference grating group 11 by the industrial camera 13 through the imaging lens 12, if the position of the measuring grating is changed by adopting the phase shifter, a phase shift moire fringe pattern can be obtained, the fringe pattern has tooth surface height information, and therefore, the three-dimensional height profile of the tooth surface can be restored by demodulating the fringe pattern.
Referring to fig. 3: during measurement, a light source is started, a measured tooth surface 10 of a measured gear is moved to a measurement space of a measuring device, an included angle between an optical axis and a normal line of a semi-reflection semi-transmission mirror 9 is adjusted on a projection arm, a shadow grating fringe pattern 4 is formed on the measured tooth surface 10, and on a receiving light arm, the optical axis of an industrial camera 13 is adjusted to coincide with the normal line of the semi-reflection semi-transmission mirror 9 so as to reduce measurement errors caused by image distortion, and moire fringe pattern data is recorded. And further processing the obtained moire fringe pattern to obtain a measurement result. When measuring the next tooth surface, the gear is rotated to the next tooth surface measuring space.
A gear tooth surface three-dimensional morphology moire characterization and measurement method is specifically implemented as follows:
step one: with the projection device built, see fig. 1 and 2, the projection device comprises a projection system 2 and an imaging system 3;
the projection system 2 comprises a point light source 5, a collimator 6, a measuring grating group 7 consisting of a coarse grating and a fine grating, a projection lens 8 and a semi-reflection semi-transmission mirror 9 which are sequentially arranged on a projection light arm;
the imaging system 3 comprises a reference grating group 11, an imaging lens 12 and an industrial camera 13 which are sequentially arranged on the light receiving arm and are the same as the measuring grating group;
the light emitted by the point light source 5 in the projection system 2 irradiates the measuring grating group 7 in parallel through the collimator 6, shadow gratings are generated on the tooth surface through the semi-reflection semi-transparent mirror 9 by the projection lens 8, the shadow gratings are modulated by the shape of the measured tooth surface 10 and deform, deformed gratings are formed, moire fringes can be obtained through recording the reference grating group 11 by the industrial camera 13 through the imaging lens 12, if the position of the measuring grating is changed by adopting the phase shifter, a phase shift moire fringe pattern can be obtained, the fringe pattern has tooth surface height information, and therefore, the three-dimensional height profile of the tooth surface can be restored by demodulating the fringe pattern.
During measurement, the measured tooth surface 10 is placed in a measurement space, the point light source 5 is started, the measured tooth surface 10 of the measured gear is moved to the measurement space of the measurement device, an included angle between an optical axis and the normal line of the semi-reflection semi-transmission mirror 9 is adjusted on a projection arm, a shadow grating fringe pattern 4 is formed on the measured tooth surface 10, and the optical axis of the industrial camera 13 is adjusted to coincide with the normal line of the semi-reflection semi-transmission mirror 9 on a light receiving arm so as to reduce measurement errors caused by image distortion and record moire fringe pattern data. And further processing the obtained moire fringe pattern to obtain a measurement result. When measuring the next tooth surface, the gear is rotated to the next tooth surface measuring space.
The irradiation period is
Figure SMS_128
And is periodic by the industrial camera 13 at +.>
Figure SMS_129
After which the generated moire pattern is recorded behind the reference grating, after which the measuring grating is shifted twice, the recorded 3-frame phase-shifted moire pattern +.>
Figure SMS_130
、/>
Figure SMS_131
、/>
Figure SMS_132
；
Step two: the grating period is as in the first step
Figure SMS_133
The measurement grating and the reference grating of the device are moved into a measurement space, and a phase shift fringe pattern is acquired to obtain a three-frame phase shift moire fringe pattern: />
Figure SMS_134
，/>
Figure SMS_135
，/>
Figure SMS_136
；
Step three, a random three-step phase shift technology is applied, the phases of the two sets of collected moire fringe patterns are respectively extracted, and the low-sensitivity wrapped measurement phase is obtained
Figure SMS_137
And measurement phase of high sensitivity package +.>
Figure SMS_138
。
Measuring phase
Figure SMS_139
、/>
Figure SMS_140
The calculation method is the same, and specifically comprises the following steps:
the recorded 3-frame phase shift moire pattern can be expressed as:
Figure SMS_141
(1)
in the above-mentioned method, the step of,
Figure SMS_144
，/>
Figure SMS_146
，/>
Figure SMS_148
respectively background, amplitude and measured phase; />
Figure SMS_143
、/>
Figure SMS_147
、
Figure SMS_149
Phase shift of 3 frames, respectively->
Figure SMS_150
A phase shift amount for the first frame; />
Figure SMS_142
Representing pixel coordinates, the subsequent expressions are omitted for convenience>
Figure SMS_145
。
Assuming a known estimate of the phase shift, first, a set of variables is defined:
Figure SMS_151
，/>
Figure SMS_152
，
Figure SMS_153
formula (1) is written as:
Figure SMS_154
(2)
in the method, in the process of the invention,
Figure SMS_155
，/>
Figure SMS_156
，/>
Figure SMS_157
。
thus, the unknown X can be solved in the least squares sense as:
Figure SMS_158
(3)/>
in the method, in the process of the invention,
Figure SMS_159
is->
Figure SMS_160
Thus the phase is obtained as:
Figure SMS_161
(4)
and then can obtain:
Figure SMS_162
(5)
at this time, equation (1) may be updated as:
Figure SMS_163
(6)
in the method, in the process of the invention,
Figure SMS_164
at this time, the above formula (2) is rewritten in the form of a matrix:
Figure SMS_165
(7)
in the method, in the process of the invention,
Figure SMS_166
，/>
Figure SMS_167
，/>
Figure SMS_168
。
the least square meaning is as follows:
Figure SMS_169
(8)
will be
Figure SMS_170
Substituting (2), repeating the steps until meeting the convergence condition:
Figure SMS_171
(9)
in the method, in the process of the invention,
Figure SMS_172
is a predefined convergence condition. />
Figure SMS_173
Is the number of iterations. When the convergence condition is satisfied, the measurement phase using the coarse grating can be solved>
Figure SMS_174
；
Step four, adopting a time domain unwrapping method to extract a measurement phase
Figure SMS_175
、/>
Figure SMS_176
Performing unwrapping to obtain unwrapped high sensitivity phase +.>
Figure SMS_177
。
The principle of the phase unwrapping process is as follows: coarse and fine measurement is carried out on the measured object, and the coarse measurement phase diagram is assumed to be free of packages or easy to remove, so that the coarse measurement result can be used for guiding the fine measurement phase diagram to remove packages. By changing gratings with different periods, coarse and fine measurement is realized, and the variable-precision unwrapping method is applied to the phase shift moire to unwrap the phase. The patent provides a variable-precision phase unwrapping method based on logic judgment. The specific principle is as follows:
since the period is used in the measurement
Figure SMS_178
And->
Figure SMS_179
Two gratings of>
Figure SMS_180
. Due to the use->
Figure SMS_181
When the measurement is carried out, the obtained phase diagram has no package or the package is easy to remove, and the height of the two measurement results according to the thickness is equal to obtain:
Figure SMS_182
(10)
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_183
for the purpose of the wrap phase diagram obtained in the precision measurement, < >>
Figure SMS_184
For the precise measurement of the developed phase diagram,
Figure SMS_185
the coarsely measured package is easy to spread out for the coarsely measured package phase diagram. Further comprises the following steps:
Figure SMS_186
(11)
the above is deformed to:
Figure SMS_187
(12)
in the above-mentioned method, the step of,
Figure SMS_188
representing the number of fringe orders, phase unwrapping, i.e. solving +.in equation (12)>
Figure SMS_189
. For unwrapping the refined phase, its wrapped phase is first of all +.>
Figure SMS_190
And coarse measurement phase expansion to +.>
Figure SMS_191
The expansion method is as follows:
expansion of arctangent function
Figure SMS_192
Thus, formula (12) above shows that: />
Figure SMS_193
Can be expressed as an integer +.>
Figure SMS_194
And the value range is->
Figure SMS_195
Is->
Figure SMS_196
The sum is then taken to be nearest and less than or equal to ++>
Figure SMS_197
And (3) rounding to obtain:
Figure SMS_198
(13)
obviously, when
Figure SMS_199
In the time-course of which the first and second contact surfaces,
Figure SMS_200
(14)
otherwise, when
Figure SMS_201
When and when->
Figure SMS_202
At this time: />
Figure SMS_203
(15)
If it is
Figure SMS_204
：
Figure SMS_205
(16)
The above method is to find the fringe order
Figure SMS_206
When the value range is complete, only logic judgment method is used to quickly recover the unwrapped high-sensitivity phase +.>
Figure SMS_207
。
Step five: calibrating a projection device, wherein the transformation relation between pixel coordinates and absolute coordinates is expressed as follows:
Figure SMS_208
(17)
in the above-mentioned method, the step of,
Figure SMS_209
is an internal reference matrix for the industrial camera 13, < >>
Figure SMS_210
、/>
Figure SMS_211
For the external matrix of the industrial camera 13, the pixel coordinates can be determined by (17)>
Figure SMS_212
Conversion to absolute coordinates>
Figure SMS_213
。
The mapping relationship of phase and height is expressed as:
Figure SMS_214
(18)
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_215
、/>
Figure SMS_216
、/>
Figure SMS_217
for measuring the matrix related to the geometrical parameters and the pixel coordinates of the system, the matrix can be obtained by a calibration method, specifically:
(5.1) processing the planar calibration plate, and mounting the calibration plate on a micro-displacement platform along the edge
Figure SMS_218
Directional movement, when starting calibration, the calibration plate is placed on the reference plane, at this time +.>
Figure SMS_219
Projecting fringe patterns on the calibration plate, and collecting three random phase shift fringe patterns to obtain +.>
Figure SMS_220
Let the collected fringe pattern be expressed as:
Figure SMS_221
(19)
then the micro-displacement platform is controlled to drive the calibration plate to move a distance from the surface perpendicular to the reference surface
Figure SMS_223
(e.g. 10->
Figure SMS_228
) At this time->
Figure SMS_232
Also, three phase-shift fringe patterns can be acquired>
Figure SMS_225
. A series of out-of-plane displacements and corresponding phases can be obtained in the same way: />
Figure SMS_229
、/>
Figure SMS_234
，/>
Figure SMS_235
、/>
Figure SMS_222
，/>
Figure SMS_226
，/>
Figure SMS_231
、/>
Figure SMS_233
. Substituting it into the above formula (19) to obtain the product in the least square sense
Figure SMS_224
、/>
Figure SMS_227
、/>
Figure SMS_230
。
(5.2) because the device is an arbitrary measurement structure, the introduced phase shift amount cannot be determined, and therefore, the phase shift amount is determined by adopting a random phase shift technology, and the specific phase solving method comprises the following steps:
the above formula (19) is rewritten as:
Figure SMS_236
(20)
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_237
，/>
Figure SMS_238
. In this case, the above formula (20) can be written as:
Figure SMS_239
(21)
wherein:
Figure SMS_240
，/>
Figure SMS_241
at this time, each fringe pattern matrix is combined into a column line by line;
from equation (21), the fringe pattern space can be expressed as a multiplication of two matrices, where the vectors
Figure SMS_242
、/>
Figure SMS_243
、/>
Figure SMS_244
The base vector of the fringe space is represented in relation to the phase shift, the fringe space being at the base vector +.>
Figure SMS_245
、/>
Figure SMS_246
、/>
Figure SMS_247
In the space formed by the sheet.
To solve for vectors
Figure SMS_248
、/>
Figure SMS_249
、/>
Figure SMS_250
The invention adopts a method of reducing the base decomposition. The primordial method may spatially transform a high-dimensional matrix into a low-dimensional matrix form, i.e.:
Figure SMS_251
(22)
here the number of the elements is the number,
Figure SMS_252
is->
Figure SMS_253
Basis matrix of>
Figure SMS_254
For the transformation matrix, in this case +.>
Figure SMS_255
Second column data->
Figure SMS_256
And third column data->
Figure SMS_257
The data available phase shifts are:
Figure SMS_258
(23)
at this time, the phase of the calibration plate at each moving point can be obtained by using the least squares phase algorithm based on the above phase shift
Figure SMS_259
。
And step six, sequentially rotating the gear 1 to be measured, and repeating the steps to finish the three-dimensional profile measurement of all the tooth surfaces 10 to be measured.
The invention provides a random phase shift fringe pattern phase demodulation method capable of eliminating background and amplitude airspace changes based on the idea of random phase shift, and simultaneously develops a wrapped phase pattern obtained by correctly expanding a time domain unwrapping technology. The method adopts the projection moire principle, avoids shielding by changing the light path, improves the measurement precision by utilizing the amplifying effect of moire fringes, and solves the problems of the measurement principle, tooth surface shielding and the like in gear measurement with different domestic existing ideas.

Claims (1)

1. The method for representing and measuring the moire of the three-dimensional morphology of the tooth surface of the gear is characterized by comprising the following steps of:
firstly, setting up a projection device, wherein the projection device comprises a projection system (2) and an imaging system (3); the projection system (2) comprises a point light source (5), a collimator (6), a measuring grating group (7) consisting of a coarse grating and a fine grating, a projection lens (8) and a semi-reflection semi-transmission mirror (9) which are sequentially arranged on a projection light arm; the imaging system (3) comprises a reference grating group (11), an imaging lens (12) and an industrial camera (13) which are sequentially arranged on the light receiving arm and are the same as the measuring grating group;
placing a measured tooth surface (10) in a measurement space, starting a point light source (5), parallelly irradiating light emitted by the point light source (5) through a collimator (6) to measure a grating group (7), adjusting an included angle between a semi-reflection semi-transmission mirror (9) and an optical axis, and using a period p in the grating group (7) 1 Shadow grating is projected to the measured tooth surface (10) to form a shadow grating fringe pattern (4), the shadow grating on the measured tooth surface (10) is reflected to the surface of a reference grating group (11) through a semi-reflection semi-transmission mirror (9) and is received by an industrial camera (13) without distortion, and then the measuring grating group (7) is randomly moved twice to obtain a three-frame phase shift moire fringe pattern containing the measured tooth surface morphology information
Figure QLYQS_1
(u, v) represents pixel coordinates；
Step two, the period is p 2 The fine grating of the measuring grating group (7) is moved to the measuring space, p 1 ＞p 2 Using a period p in the set of measurement gratings (7) 2 Shadow gratings on the measured tooth surface (10) are reflected to the surface of a reference grating group (11) through a semi-reflection semi-transmission mirror (9) and received by an industrial camera (13) without distortion, and then the measuring grating group (7) is randomly moved twice to obtain a three-frame phase shift moire fringe pattern:
Figure QLYQS_2
(u, v) represents pixel coordinates;
step three, respectively extracting phases of the two sets of collected moire fringe patterns to obtain a low-sensitivity wrapped measurement phase
Figure QLYQS_3
And measurement phase of high sensitivity package +.>
Figure QLYQS_4
Step four, adopting a time domain phase unwrapping method to measure phases of low-sensitivity wrapping
Figure QLYQS_5
And measurement phase of high sensitivity package +.>
Figure QLYQS_6
Performing unfolding to obtain->
Figure QLYQS_7
High sensitivity phase after depacketizing +.>
Figure QLYQS_8
The method specifically comprises the following steps:
the height equality of the two measurement results of the coarse grating and the fine grating can be obtained:
p 1
Figure QLYQS_9
＝p 2 />
Figure QLYQS_10
(10)
wherein the period p is used in the measurement 1 Coarse grating and p 2 Fine grating of p 1 ＞p 2 ；
Figure QLYQS_11
Is->
Figure QLYQS_12
A low sensitivity phase after depacketizing;
further comprises the following steps:
Figure QLYQS_13
the above is deformed to:
Figure QLYQS_14
in the above formula, n (u, v) represents the fringe order, and the phase unwrapping is to solve n (u, v) in equation (12); for measuring phase for high sensitivity wrapping
Figure QLYQS_15
Unwrapping, first wrapping the low sensitivity wrapped measurement phase +.>
Figure QLYQS_16
And measurement phase of high sensitivity package +.>
Figure QLYQS_17
Extend to [0,2 pi ]]The expansion method is as follows:
num＞0,den＞0；
Figure QLYQS_18
num＝0,den＞0；0；
num＞0,den＜0；
Figure QLYQS_19
num＝0,den＜0；π；
num＜0,den＞0；
Figure QLYQS_20
num＞0,den＝0；3/2π；/>
num＜0,den＜0；
Figure QLYQS_21
num＜0,den＝0；2π
wherein num represents a molecule, den represents a denominator,
Figure QLYQS_22
representing extended phase, ++>
Figure QLYQS_23
During expansion, the person is at risk>
Figure QLYQS_24
Is that
Figure QLYQS_25
Figure QLYQS_26
During expansion, the person is at risk>
Figure QLYQS_27
Is->
Figure QLYQS_28
As indicated by the above formula (12),
Figure QLYQS_29
expressed as an integer n (u, v) and a value range of [0,1 ]]Is->
Figure QLYQS_30
The sum is then taken to be nearest and less than or equal to ++>
Figure QLYQS_31
And (3) rounding to obtain:
Figure QLYQS_32
when (when)
Figure QLYQS_33
In the time-course of which the first and second contact surfaces,
n(u,v)＝m(u,v)＝0 (14)
when (when)
Figure QLYQS_34
When and when->
Figure QLYQS_35
At this time:
n(u,v)＝m(u,v)-1 (15)
if it is
Figure QLYQS_36
n(u,v)＝m(u,v) (16)；
Calibrating the projection device, determining phase shift by using a random phase shift algorithm, and establishing a phase height mapping relation and a mapping relation between phase pixel coordinates and absolute coordinates x and y so as to obtain tooth surface coordinates x, y and z;
and step six, sequentially rotating the gear (1) to be measured, and repeating the steps one to five to finish the three-dimensional profile measurement of all the tooth surfaces (10) to be measured.
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