CN112268521B - Variable-angle synchronous phase shift interferometry method for gear tooth surface shape error - Google Patents
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Abstract
The invention discloses a variable angle synchronous phase shift interferometry method facing to gear tooth surface shape errors, wherein a front double optical wedge and a rear double optical wedge are arranged along a measuring light path; and a structural optical sensor is arranged along the scanning measurement optical path, and a measured gear is arranged between the front double optical wedges and the rear double optical wedges. The double optical wedges are introduced into a measuring light path, and the angle of the incident angle irradiating the measured tooth surface is quantitatively changed, so that the density distribution of interference fringes is adjusted, and the phase data processing is facilitated; the structured light sensor is introduced into an interference measurement device, and projected structured light is combined with interference measurement data through relative motion with the surface of a measured object in the measurement process, so that full-field measurement can be ensured when a large spiral angle complex spiral curved surface is measured. The measuring method of the invention introduces the spatial phase shift technology into the interference measuring device, and can obtain a plurality of phase shift interferograms through single measurement shooting, thereby simplifying the steps of the operation process and improving the anti-interference capability of the device.
Description
Technical Field
The invention belongs to the technical field of optical measurement, and relates to a variable-angle synchronous phase shift interferometry method for gear tooth surface shape errors.
Background
The precision gear is used as an important part in the advanced rail transit and industrial robot transmission device, and has the advantages of high bearing capacity, high transmission efficiency, long service life, low noise and the like, so that the high performance of the transmission device is guaranteed. In order to meet the requirements of high bearing capacity and high transmission efficiency of the transmission, the gears must have higher machining and manufacturing precision. Among various indexes of gear precision evaluation, the tooth surface shape error has great influence on the transmission efficiency, noise and service life of the whole transmission device. Therefore, the measurement of the tooth surface shape error is very important for the processing and manufacturing of high-precision gears. The laser phase-shifting interference tooth surface shape error measuring method has the advantages of no damage, high efficiency and high precision, and is an important research direction for measuring the surface shape error of the non-contact gear. The method embodies the measured physical information as phase information of an interference fringe image, and calculates the surface shape error of the complex helical curved surface by processing the interference fringe image.
The existing measuring methods for the shape error of the precise gear tooth surface are divided into two types through literature search, and the first type is a contact type measuring method, such as a three-coordinate measuring machine or a gear measuring center. This type of measurement is based on the measurement feeler sweeping the point on the side surface, and the physical information to be measured is back-calculated by coordinate measurement. However, the method has low measurement efficiency, can scratch the measured tooth surface, and can affect the measurement accuracy by factors such as measuring head radius errors and sampling errors. The second type is a non-contact measurement method based on laser interferometry, which can realize high-precision and high-efficiency measurement. Such as laser phase-shifting interferometry, as used in Design of laser interferometric system for measurement of gear flash, published by Optik of Wanjie. The method utilizes PZT to adjust the phase of a reflector to obtain a series of measured tooth surface interference fringe images after phase shifting, and the shape error of the tooth surface of the gear can be calculated after phase extraction and unpacking. Although the method can realize high-precision measurement of the gear tooth shape error, for the helical gear with a large helix angle, measurement information is incomplete because measurement light is shielded by adjacent surfaces, so that the full-field measurement of the helical gears with different tooth widths cannot be realized. In addition, the method is based on the step-by-step phase shifting of the piezoelectric ceramics, and is very easy to be interfered by the external environment to cause the reduction of the precision, thereby limiting the practical application effect of the method.
Disclosure of Invention
The invention aims to provide a variable-angle synchronous phase-shift interferometry method for gear tooth surface shape errors, and solves the problems that in the prior art, the precision is low and full-field measurement cannot be realized.
The invention adopts the technical scheme that a variable-angle synchronous phase shift interferometry facing to the gear tooth surface shape error is implemented according to the following steps:
the state equation is as follows: x (k +1) ═ Φ X (k) + Γ ω (k)
The observation equation: y (k) ═ HX (k) + v (k)
A measuring device used for a variable angle synchronous phase shift interference measuring method facing to gear tooth surface shape errors comprises a laser, the laser emits an interference measuring light path, a polarization beam splitter prism is arranged along the interference measuring light path and divides the interference measuring light path into a measuring light path and a reference light path which are mutually vertical, a light intensity regulator a, a beam expander a, a front double-light wedge, a rear double-light wedge and a measured gear are arranged between the front double-light wedge and the rear double-light wedge along the measuring light path, a reflector a, a light intensity regulator b, a beam expander b, a reflector b and a semi-reflecting and semi-transmitting mirror are arranged along the reference light path, the interference measuring light path and the reference light path are converged to the semi-reflecting and semi-transmitting mirror to form an imaging light path, a two-dimensional grating, a lens a, a diaphragm, a lens b, a phase delay array, a polaroid and a CCD camera are sequentially arranged along the imaging light path, the CCD camera (18) is electrically connected with a computer.
The invention is also characterized in that:
and (3) the detected tooth surface interference fringe image in the step (1) corresponds to the phase shift angles of 0, pi/2, pi and 3 pi/2 respectively.
And 2, after the incident angle is changed, the detected tooth surface interference fringe image respectively corresponds to the phase shift angles of 0, pi/2, pi and 3 pi/2.
in the formula:
n is the total step number of phase shift, the step 3 adopts spatial four-step phase shift, and N is 4;
i is the ith phase shift;
Ii(x, y) is the light intensity at (x, y) at the ith phase shift;
δithe phase modulation quantity at the ith phase shifting is obtained;
the two-dimensional phase unwrapping mathematical model of the fringe image of the tooth surface under measurement can be expressed as:
in the formula: phi (x, y) is a continuous phase value after unpacking; k is the number of packages.
The formula of the height difference h in the step 4 is as follows:
in the formula: λ is the laser wavelength for measurement; alpha is the incident angle of the light on the measured object.
step 5.1, further improving the filtering precision of the data fusion algorithm, carrying out weighting assignment on the measured data by using mutual information gradient weight factors, defining the change degree between two points through the mutual information of the measured result data, and carrying out mutual information gradient assignment in the x and y directions between A, B
And
is defined as:
in formula (a):
Axand AyGradient subgraphs in the x direction and the y direction with (i, j) as the center;
Bxand ByGradient subgraphs in the x direction and the y direction with (i + l, j + k) as the center are provided, l and k are real integers and represent neighborhood positions to be calculated, and the neighborhood positions are (1,0), (0,1) and (1, 1);
step 5.2, by calculating mutual information gradient and combining the formula (a) and carrying out variance statistical calculation, defining the weight factor omega of the pixel point (i, j) under an M multiplied by N size window:
in the formula:
step 5.3, step 5.2, the weight factor omega is normalized, the closer the result is to 1, the larger the mutual information is, and the weight proportion omega occupied by the information of different pixel point positions of different sensors is obtainediAt this time, the new information sequence Y after information fusion is:
in the formula:
Zi(x, y) is the interferometric measurement at point (x, y) at the ith time;
ωi(x, y) is the weighting coefficient of the ith interferometric measurement at point (x, y).
The invention has the beneficial effects that:
1. the invention can obtain the interferogram of multiple phase shifts by single shooting, reduces the shooting times, simplifies the operation process and increases the anti-interference capability of the device.
2. The invention can carry out full-field measurement on the tooth surface of the bevel gear with the large helix angle with different tooth widths, has higher precision compared with the measurement of the traditional contact method, and has larger measurement range compared with other interference methods.
Drawings
FIG. 1 is a schematic structural diagram of a measuring device used in the variable-angle synchronous phase-shift interferometry facing to the shape error of a gear tooth surface;
FIG. 2 is an interference fringe image of a measured tooth surface facing a variable angle synchronous phase shift interferometry method of gear tooth surface shape error according to the invention;
FIG. 3 is an interference fringe image of a measured tooth surface after an incident angle is changed in the variable angle synchronous phase shift interferometry method facing to the gear tooth surface shape error;
FIG. 4a is a schematic view a of an angle-changed measurement light of the variable angle synchronous phase-shift interferometry method facing the error of the gear tooth surface shape according to the present invention;
FIG. 4b is a schematic view b of an angle-changed measurement light of the variable angle synchronous phase-shift interferometry method facing the error in gear tooth surface shape according to the present invention;
FIG. 5 is a spliced graph of results of angle change measurement of the variable angle synchronous phase shift interferometry method facing to gear tooth surface shape errors;
FIG. 6 is a simulated interferogram of a variable angle synchronous phase shift interferometry method oriented to gear tooth surface shape errors of the present invention;
in the figure, 1, a He-Ne laser, 2, a polarization beam splitter prism, 3, reflectors a, 4, a light intensity regulator b, 5, a light intensity regulator a, 6, a beam expander b, a beam expander a, 8, a front double-light wedge, 9, a rear double-light wedge, 10, reflectors b, 11, a semi-reflecting and semi-transmitting mirror, 12, a two-dimensional grating, 13, lenses a, 14, a diaphragm, 15, lenses b, 16, a phase delay array, 17, a polarizer, 18, a CCD camera and 19, a computer.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A variable-angle synchronous phase shift interferometry method facing to gear tooth surface shape errors is implemented according to the following steps:
and 3, extracting a wrapping phase of the measured tooth surface according to the measured tooth surface interference fringe image obtained in the step 1 and the measured tooth surface interference fringe image obtained in the step 2 after the incident angle is changed, and performing phase unwrapping, wherein a phase inverse variance quality diagram is adopted to guide the unwrapping process, so that the phase wrapping number k of each pixel point is obtained, and the continuous phase of the measured tooth surface is obtained.
the state equation is as follows: x (k +1) ═ Φ X (k) + Γ ω (k)
The observation equation: y (k) ═ HX (k) + v (k)
A measuring device used in a variable-angle synchronous phase shift interferometry facing to gear tooth surface shape errors is structurally shown in figure 1 and comprises a laser 1, wherein the laser 1 emits an interferometry light path, a polarization beam splitter 2 is arranged along the interferometry light path, the polarization beam splitter 2 divides the interferometry light path into a measurement light path and a reference light path which are perpendicular to each other, a light intensity regulator a5, a beam expander a7, a front double-light wedge 8 and a rear double-light wedge 9 are arranged along the measurement light path, a measured gear is arranged between the front double-light wedge 8 and the rear double-light wedge 9, a reflector a3, a light intensity regulator b4, a beam expander b6, a reflector b10 and a semi-reflecting and semi-transparent mirror 11 are arranged along the reference light path, the interferometry light path and the reference light path are converged to the semi-reflecting and semi-transparent mirror 11 to form an imaging common light path, and a two-dimensional grating 12, a lens a13, a diaphragm 14, a reference grating, a reference light source and a reference light source are sequentially arranged along the imaging common light path, Lens b15, phase delay array 16, polaroid 17, CCD camera 18, and computer 19 is connected with CCD camera 18 electrically.
The light source in the device is a helium-neon laser 1, and in practice, lasers with different wavelengths can be used as the light source; the front double-optical wedge 8 and the back double-optical wedge 9 in the device are of double-optical wedge structures, and can be replaced by other optical elements capable of changing the incident light angle, such as a reflector with a multi-degree-of-freedom movement mechanism and the like.
And (3) the detected tooth surface interference fringe image in the step (1) corresponds to the phase shift angles of 0, pi/2, pi and 3 pi/2 respectively.
And 2, after the incident angle is changed, the detected tooth surface interference fringe image respectively corresponds to the phase shift angles of 0, pi/2, pi and 3 pi/2.
in the formula:
n is the total step number of phase shift, the step 3 adopts spatial four-step phase shift, and N is 4;
i is the ith phase shift;
Ii(x, y) is the light intensity at (x, y) at the ith phase shift;
δithe phase modulation quantity at the ith phase shifting is obtained;
the two-dimensional phase unwrapping mathematical model of the fringe image of the tooth surface under measurement can be expressed as:
in the formula: phi (x, y) is a continuous phase value after unpacking; k is the number of parcels.
The formula of the height difference h in step 4 is:
in the formula: λ is the wavelength of the laser used for measurement; alpha is the incident angle of the light on the measured object.
and 5.1, in order to further improve the filtering precision of the data fusion algorithm, providing mutual information gradient weight factors to carry out weighted assignment on the measured data. Mutual information is the amount of information that is common between two variables, defined in terms of information entropy. For measurement data, the degree of variation between two points can be defined by their mutual information. The measurement objects measured at different angles are the same, and although the accuracy is different, the trends of the respective results are similar, and the same variation trend is shown in a specific range. Mutual information gradient in x and y directions between two points A, B
And
can be defined as:
in formula a:
Axand AyGradient subgraphs in the x direction and the y direction with (i, j) as the center;
Bxand ByGradient subgraphs in the x direction and the y direction with (i + l, j + k) as the center, wherein l and k are real integers and represent neighborhood positions to be calculated, and are generally (1,0), (0,1) and (1, 1);
step 5.2, by calculating mutual information gradient and combining the formula a and carrying out variance statistical calculation, defining the weight factor omega of the pixel point (i, j) under the window of M multiplied by N:
in the formula:
step 5.3, step 5.2, the weight factor omega is normalized, the closer the result is to 1, the larger the mutual information is, and the weight proportion omega occupied by the information of different pixel point positions of different sensors is obtainediAt this time, the new information sequence Y after information fusion is:
in the formula:
Zi(x, y) is the interferometric measurement at point (x, y) at the ith time;
ωi(x, y) is the weighting coefficient of the ith interferometric measurement at point (x, y).
The new information sequence expressed by the formula passes through a Kalman filter, so that the fusion of measurement data results is realized.
The invention relates to a variable angle synchronous phase shift interference measurement method facing to gear tooth surface shape errors, which comprises the following working processes: in the embodiment 1, the surface of a measured surface is a precise helical gear surface, laser emitted by a helium-neon laser 1 is divided into two paths of mutually perpendicular light through a polarization beam splitter prism 2, one path of light is used as an interference measurement light path, and the other path of light is used as a reference light path; light of an interference measurement light path sequentially passes through the light intensity regulator a5, the beam expander a7 and the front double-optical wedge 8 and then obliquely irradiates the surface of a measured gear at a certain angle, at the moment, reflected light irradiates the semi-reflecting and semi-transparent mirror 11 through the deflection angle of the rear double-optical wedge 9 and enters an imaging common light path after being reflected. The light of the reference light path is transmitted through the polarization beam splitting prism 2 and then irradiated onto the reflector a3, after being reflected, the light sequentially passes through the second light intensity adjuster b4 and the beam expander b6 and then is irradiated onto the reflector b10, after being reflected, the light is transmitted through the transflective lens 11 and is converged with the measurement light, the light is diffracted and split by the two-dimensional grating 12 and then passes through the first lens a13, the diffraction light of the (plus or minus 1 and plus or minus 1) order is made to pass through the diaphragm 14, after being converted into parallel light again by the lens b15, the parallel light sequentially passes through the phase delay array 16 and the polaroid 17 which are composed of wave plates, the measurement light and the reference light are interfered and respectively generate phase shifts of 0, pi/2, pi and 3 pi/2, and at the time, the corresponding four interference fringe subgraphs are simultaneously collected by the CCD camera 18 and transmitted to the computer 19. After the measurement is finished once, the relative angle of the front double-optical-wedge 8 and the rear double-optical-wedge 9 is adjusted to realize the measurement of the variable incidence angle, and after the incidence angle is changed for many times, the results obtained by the measurement for many times are fused to obtain the measurement result of the interference light path.
The light source in the device is a helium-neon laser 1, and in practice, lasers with different wavelengths can be used as the light source; the front double-optical-wedge 8 and the back double-optical-wedge 9 in the device are of double-optical-wedge structures, and can be replaced by other optical elements capable of changing the incident light angle.
Fig. 4a and 4b are schematic diagrams of the measured tooth surface irradiated with the measuring light with different incident angles in the embodiment 1.
As can be seen in fig. 4: the irradiation ratios to the tooth surface are different when the incident angles are alpha' and alpha, so that the variable angle measurement is more flexible and the measurement range is wider when the tooth surfaces of the gear with different tooth widths are correspondingly measured. In addition, as shown in fig. 4a and 4b, the adjustment angle changes the density distribution of the interference fringes of the measured tooth surface due to the oblique imaging. The change of the density distribution enables the phases which cannot be processed at the original dense stripes to be processed and calculated, and the measurement precision is improved.
Fig. 2 and 3 show the results of the interferometric measurements obtained in example 1 at different angles. Wherein the measurement results of fig. 2 and fig. 3 are subjected to data fusion to obtain fig. 5.
The invention discloses a variable angle synchronous phase shift interferometry method facing to gear tooth surface shape errors, which has the beneficial effects that:
1. the double optical wedges are introduced into a measuring light path, and the angle of the incident angle irradiating the measured tooth surface is quantitatively changed, so that the density distribution of interference fringes is adjusted, and the phase data processing is facilitated; on the other hand, the full-field measurement can be ensured when the gear tooth surfaces with different parameters are measured.
2. The invention introduces the spatial phase shift technology into the interference measurement device, and can obtain a plurality of phase shift interferograms through single measurement shooting, thereby simplifying the steps of the operation process and improving the anti-interference capability of the device.
Claims (4)
1. A variable-angle synchronous phase shift interferometry method facing to gear tooth surface shape errors is characterized by comprising the following steps of:
step 1, placing a gear to be measured between a front double optical wedge (8) and a rear double optical wedge (9) in an interference measurement optical path, adjusting the interference measurement optical path, and when the adjustment of the interference measurement optical path is proper, shooting by a CCD camera (18) to obtain an interference fringe image of the tooth surface to be measured;
step 2, rotating the front double optical wedges (8) and the rear double optical wedges (9), changing the relative angle between the double optical wedges, changing the incident angle of the interference measurement light path irradiating the measured tooth surface of the measured gear, and setting the times of changing angle measurement of the interference measurement light path according to the actual measured tooth surface condition to obtain the measured tooth surface interference fringe image after changing the incident angle;
step 3, extracting a wrapping phase of the measured tooth surface according to the measured tooth surface interference fringe image obtained in the step 1 and the measured tooth surface interference fringe image obtained in the step 2 after the incident angle is changed, and performing phase unwrapping;
wrapping phase at target pixel point (x, y) on interference fringe of measured tooth surface
Can be calculated as follows:
in the formula:
n is the total step number of phase shift, the step 3 adopts spatial four-step phase shift, and N is 4;
i is the ith phase shift;
Ii(x, y) is the light intensity at (x, y) at the ith phase shift;
δithe phase modulation quantity at the ith phase shifting is obtained;
the two-dimensional phase unwrapping mathematical model of the fringe image of the tooth surface under measurement can be expressed as:
in the formula: phi (x, y) is a continuous phase value after unpacking; k is the number of packages;
step 4, simulating the measured tooth surface interferometry of the measured gear according to a light ray tracing principle to obtain a simulated interferogram of the measured tooth surface, registering the measured interferometry data and the simulated interferogram to calculate an incident angle corresponding to each pixel point, converting continuous phases after unpacking the measured tooth surface phases into height information of the measured tooth surface, and deducing a height difference h through a phase difference phi according to a parallel plate interference model;
step 5, performing data fusion after registration on the data obtained by multi-angle measurement, and performing weighted fusion on the multi-source measurement data and information filtering processing by means of a measurement fusion algorithm of multi-sensor Kalman filtering when performing multi-source data fusion, wherein the linear filtering model is as follows:
the state equation is as follows: x (k +1) ═ Ψ X (k) + Γ ω (k)
The observation equation: y (k) ═ HX (k) + v (k)
Step 5 is specifically implemented according to the following steps:
step 5.1, further improving the filtering precision of the data fusion algorithm, carrying out weighting assignment on the measured data by using mutual information gradient weight factors, defining the change degree between two points through the mutual information of the measured result data, and carrying out mutual information gradient assignment in the x and y directions between A, B
And
is defined as:
in formula (a):
Axand AyGradient subgraphs in the x direction and the y direction with (i, j) as the center;
Bxand ByGradient subgraphs in the x direction and the y direction with (i + l, j + k) as the center are provided, l and k are real integers and represent neighborhood positions to be calculated, and the neighborhood positions are (1,0), (0,1) and (1, 1);
step 5.2, by calculating mutual information gradient and combining the formula (a) and carrying out variance statistical calculation, defining the weight factor omega of the pixel point (i, j) under the size window of M multiplied by N:
in the formula:
step 5.3, step 5.2, the weight factor omega is normalized, the closer the result is to 1, the larger the mutual information is, and the weight proportion omega occupied by the information of different pixel point positions of different sensors is obtainediAt this time, the new information sequence Y after information fusion is:
in the formula:
Zi(x, y) is the interferometric measurement at point (x, y) at the ith time;
ωi(x, y) is the weighting coefficient of the ith interferometric measurement at point (x, y);
the measuring device used for the variable-angle synchronous phase shift interferometry method for the gear tooth surface shape error comprises a laser (1), wherein an interference measurement light path is emitted by the laser (1), a polarization beam splitter (2) is arranged along the interference measurement light path, the polarization beam splitter (2) divides the interference measurement light path into a measurement light path and a reference light path which are perpendicular to each other, a light intensity regulator a (5), a beam expander a (7), a front double-light wedge (8) and a rear double-light wedge (9) are arranged along the measurement light path, a measured gear is placed between the front double-light wedge (8) and the rear double-light wedge (9), a reflector a (3), a light intensity regulator b (4), a beam expander b (6), a reflector b (10) and a half-reflecting mirror (11) are arranged along the reference light path, and the interference measurement light path and the reference light path are converged to the half-reflecting mirror (11) to form an imaging common light path, the imaging common optical path is sequentially provided with a two-dimensional grating (12), a lens a (13), a diaphragm (14), a lens b (15), a phase delay array (16), a polaroid (17) and a CCD camera (18) along the optical path of the imaging common optical path, and the CCD camera (18) is electrically connected with a computer (19).
2. The method for the variable-angle synchronous phase shift interferometry facing the shape error of the gear tooth surface according to claim 1, wherein the measured tooth surface interference fringe image of step 1 corresponds to the phase shift angles 0, pi/2, pi and 3 pi/2 respectively.
3. The method for the interferometry facing the variable angle synchronous phase shift of the gear tooth surface shape error according to claim 1, wherein the interference fringe images of the measured gear surface after the incident angle is changed in the step 2 correspond to the phase shift angles 0, pi/2, pi and 3 pi/2 respectively.
4. The method of claim 1, wherein the formula of the height difference h in step 4 is as follows:
in the formula: λ is the laser wavelength for measurement; alpha is the incident angle of the light on the measured object.
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