CN114719806B - Digital measuring method for arc end teeth - Google Patents
Digital measuring method for arc end teeth Download PDFInfo
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- CN114719806B CN114719806B CN202210462966.1A CN202210462966A CN114719806B CN 114719806 B CN114719806 B CN 114719806B CN 202210462966 A CN202210462966 A CN 202210462966A CN 114719806 B CN114719806 B CN 114719806B
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- 238000004040 coloring Methods 0.000 claims abstract description 29
- 238000000691 measurement method Methods 0.000 claims abstract description 15
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/08—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness for measuring thickness
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a digital measurement method of arc end teeth, which adopts an ultra-high-precision three-coordinate measuring machine as digital detection and acquisition equipment of the arc end teeth, thereby realizing digital detection of the arc end teeth. And the part virtual modeling is carried out based on the scanning data, the coloring analysis is carried out on the tooth surface in a virtual coloring mode, the artificial visual recognition is replaced, the detection efficiency is improved, the tooth surface meshing quality can be accurately judged, a specific quantitative actual measurement value is provided, and an important theoretical basis is provided for batch detection of the arc end tooth and optimization of processing parameters. In addition, the two virtual models are used for meshing simulation matching, so that the optimal meshing state can be calculated, the original detection method of trial and error by means of manual tooth-by-tooth pairing is replaced, the optimal meshing tooth pair can be automatically calculated after the geometric parameter measurement of the concave tooth and the convex tooth is completed, the detection time is greatly shortened, and a foundation is laid for the digital assembly of the circular arc end tooth part.
Description
Technical Field
The invention relates to the technical field of arc end tooth measurement, in particular to a digital measurement method of arc end teeth.
Background
The arc end teeth are mainly used for connecting parts such as a vane disk, a rotor, an impeller and the like which rotate at a high speed of a modern small engine, and all rotating parts such as a compressor, a turbine and the like are connected through the arc end teeth. The circular arc end teeth are the core structures of the turbine disk and the blade disk of the aviation turboshaft engine, are designed to be matched with the convex-concave teeth in pairs for use, have very high precision requirements, bear large loads and torque in operation, have enough strength, surface area and support, and have very high interchangeability requirements. The measurement of the arc end tooth parameters is a key important detection element in the development and production processes of the aeroengine, and plays an important role in ensuring the quality of the product of the machine type. The main geometric factors involved in detection in the processing process of the arc end tooth are as follows: the detection of the tooth surface quality and the relevant dimensional form and position tolerance of the end tooth is very strict and important.
The existing arc end tooth detection method detects the part through a checking gauge, adopts a standard transmission and coloring detection mode of a standard gauge, a checking gauge, a working gauge and the part, adopts two-dimensional section detection of the checking gauge, has more manual intervention in the detection process and the data processing process, has large error and has lower detection efficiency. The coloring area judgment is visual, the measured value is not quantized, and the coloring quality judgment is greatly influenced by the coloring agent, the coloring brush and the coloring process during detection. Further, when the tooth top inspection is performed by using a depth micrometer, there is a human error, and it is impossible to detect the condition tooth top parameter (i.e., the tooth gap width is equal to the tooth top height when the tooth thickness). In addition, when radial and axial runout inspection is performed, universal measuring tools such as an indexing turntable and a dial indicator are adopted to perform radial and axial runout detection, human errors exist, and the optimal matching engagement position can only be performed by a trial-and-error method, so that the efficiency is low. In addition, the existing detection method cannot detect end tooth parameters of arc end tooth parts with larger shapes and specifications and cannot perform reverse modeling of data because the size of the gauge is limited.
Disclosure of Invention
The invention provides a digital measurement method of arc end teeth, which aims to solve the technical problems of large detection error and low detection efficiency of the existing arc end teeth detection method.
According to one aspect of the present invention, there is provided a digital measurement method of circular arc end teeth, including:
automatically scanning the contour of the arc end tooth by using a three-dimensional simulation measuring head carried by a three-coordinate measuring machine to obtain a large number of tooth surface contour data points, and calculating to obtain the geometric parameters of the arc end tooth;
virtual modeling is carried out on the part based on the scanning data, and virtual coloring analysis is carried out on the tooth surface of the arc end tooth;
and adopting two virtual models to carry out meshing simulation matching, and calculating to obtain the optimal meshing state.
Further, the process of automatically scanning the contour of the arc end tooth by using the three-dimensional simulation measuring head carried by the three-coordinate measuring machine to obtain a large number of tooth surface contour data points and calculating the geometric parameters of the arc end tooth is specifically as follows:
establishing a Cartesian coordinate system by taking an end plane of the arc end tooth as a reference;
setting theoretical parameters of the arc end teeth, and configuring scanning parameters of a three-coordinate measuring machine;
generating tooth surface grid coordinate points according to the established coordinate system and the configured scanning parameters by the three-coordinate measuring machine, and carrying out grid scanning according to the tooth surface grid coordinate points;
and obtaining the geometric parameters of the arc end teeth according to the scanning point cloud data of the three-coordinate measuring machine.
Further, the three-coordinate measuring machine performs grid scanning twice, wherein the first scanning measurement is to perform grid scanning on two working surfaces of each tooth to obtain tooth surface data of the arc end tooth, and the second scanning measurement is to perform radial scanning along the end surface of the arc end tooth to obtain tooth top height original data of the arc end tooth.
Further, the geometric parameters of the arc-shaped end tooth comprise the conditional tooth top height, and the calculation process of the conditional tooth top height is as follows:
performing three-dimensional radius compensation of the measuring head by using point data obtained by the second scanning to obtain surface point data of the arc end teeth;
converting the surface point data of each arc end tooth based on a conversion formula between a Cartesian coordinate system and a polar coordinate system by adopting an arc unfolding algorithm, and scaling the transverse axis of the polar coordinate system so as to convert the three-dimensional arc into a two-dimensional profile;
and selecting adjacent teeth and grooves from the two-dimensional profile to intercept data in a segmented mode, and finding the tooth top height when the tooth groove width and the tooth thickness are equal, so that the conditional tooth top height of each tooth is obtained.
Further, the process of virtually modeling the part based on the scan data and virtually coloring the tooth surface of the circular arc end tooth includes the following steps:
virtual modeling is carried out by utilizing the geometric parameters of the arc end teeth;
performing measuring head three-dimensional radius compensation based on the tooth surface point data of the arc end tooth to obtain tooth surface actual measurement point data of the arc end tooth;
calculating the projection length of each tooth surface actual measurement point in the normal vector direction, namely the deviation value of each tooth surface actual measurement point;
projecting coordinate values of each tooth surface actual measurement point onto an XY plane, and taking the deviation value as a Z value to obtain a two-dimensional point deviation matrix;
virtual coloring is carried out on the point deviation matrix based on the deviation value of each real measurement point, and the point deviation matrix is displayed in a two-dimensional drawing mode.
Further, the process of virtually coloring the point deviation matrix based on the deviation value of each real measurement point and displaying in a two-dimensional drawing form specifically includes:
setting tolerance variables of the deviation values, defining different colors for different tolerance variable ranges, comparing the deviation values of each real measurement point with the tolerance variable ranges to determine the coloring of each real measurement point, calculating different coloring percentages according to the number of the real measurement points, and displaying the percentages in a coloring chart.
Further, the process of performing simulation matching by adopting two virtual models and calculating to obtain the optimal engagement state specifically includes the following steps:
and carrying out meshing simulation by utilizing one concave tooth of one virtual model and a plurality of convex teeth of the other virtual model one by one, or carrying out meshing simulation by utilizing one convex tooth of one virtual model and a plurality of concave teeth of the other virtual model one by one, respectively carrying out parallelism simulation matching and coaxiality simulation matching during each meshing simulation, and obtaining a matched tooth number corresponding to the optimal matching state according to a parallelism simulation matching result and coaxiality simulation matching result of multiple meshing simulations.
Further, the process of performing parallelism simulation matching in each engagement simulation specifically includes:
after each engagement, calculating to obtain the sum of the tooth top heights of each pair of teeth, screening out the maximum value and the minimum value of the sum of the tooth top heights, and calculating to obtain the sum deviation value of the tooth top heights between the maximum value and the minimum value of the sum of the tooth top heights, wherein the smaller the sum deviation value of the tooth top heights is, the better the parallelism is.
Further, the process of performing coaxiality simulation matching during each engagement simulation specifically comprises the following steps:
after each engagement, calculating to obtain a center distance deviation value of the two parts, wherein the smaller the center distance deviation value is, the better the coaxiality is.
Further, the process of obtaining the pairing tooth number corresponding to the optimal matching state according to the parallelism simulation matching result and the coaxiality simulation matching result of the multiple meshing simulation specifically comprises the following steps:
and calculating a quadratic root value of the sum deviation value of the tooth top and the square sum of the center distance deviation value in each meshing simulation, screening out the smallest meshing state based on the calculation result of multiple meshing simulations, wherein the meshing state corresponding to the smallest meshing state is the optimal meshing state, and obtaining the concave tooth pairing tooth number and the convex tooth pairing tooth number corresponding to the optimal fitting state.
The invention has the following effects:
according to the digital measurement method for the circular arc end teeth, an ultra-high-precision three-coordinate measuring machine is adopted as digital detection and acquisition equipment for the circular arc end teeth, and the circular arc end teeth measurement method transmitted by a gauge for a long time is replaced by an automatic and digital measurement method based on a coordinate detection principle, so that the digital detection for the circular arc end teeth is realized. Moreover, the part virtual modeling is carried out based on the scanning data, the coloring analysis is carried out on the tooth surface in a virtual coloring mode, the artificial visual recognition is replaced, the detection efficiency is improved, the influence of coloring agents, coloring brushes, coloring processes and the like on the coloring quality is avoided, the tooth surface meshing quality can be accurately judged, a specific quantitative actual measurement value is provided, and an important theoretical basis is provided for batch detection and processing parameter optimization of the arc end teeth. In addition, the two virtual models are used for meshing simulation matching, so that the optimal meshing state can be calculated, the original detection method of trial and error by means of manual tooth-by-tooth pairing is replaced, the optimal meshing tooth pair can be automatically calculated after the geometric parameter measurement of the concave tooth and the convex tooth is completed, the detection time is greatly shortened, and a foundation is laid for the digital assembly of the circular arc end tooth part.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a flow chart of a digital measurement method of circular arc end teeth according to a preferred embodiment of the present invention.
Fig. 2 is a schematic flow chart of step S1 in fig. 1.
Fig. 3 is a flowchart illustrating the calculation of the conditional tooth top in step S14 in fig. 2.
Fig. 4 is a schematic diagram of a conditional tip height evaluation report of a rounded end tooth generated in a preferred embodiment of the present invention.
Fig. 5 is a schematic view of the sub-flow of step S2 in fig. 1.
Detailed Description
Embodiments of the invention are described in detail below with reference to the attached drawing figures, but the invention can be practiced in a number of different ways, as defined and covered below.
As shown in fig. 1, a preferred embodiment of the present invention provides a digital measurement method for arc end teeth, which includes the following steps:
step S1: automatically scanning the contour of the arc end tooth by using a three-dimensional simulation measuring head carried by a three-coordinate measuring machine to obtain a large number of tooth surface contour data points, and calculating to obtain the geometric parameters of the arc end tooth;
step S2: virtual modeling is carried out on the part based on the scanning data, and virtual coloring analysis is carried out on the tooth surface of the arc end tooth;
step S3: and adopting two virtual models to carry out meshing simulation matching, and calculating to obtain the optimal meshing state.
It can be understood that the digital measurement method of the arc end tooth in the embodiment adopts an ultra-high precision three-coordinate measuring machine as the digital detection and acquisition equipment of the arc end tooth, replaces the arc end tooth measurement method transmitted by a gauge for a long time with an automatic and digital measurement method based on a coordinate detection principle, and realizes the digital detection of the arc end tooth. Moreover, the part virtual modeling is carried out based on the scanning data, the coloring analysis is carried out on the tooth surface in a virtual coloring mode, the artificial visual recognition is replaced, the detection efficiency is improved, the influence of coloring agents, coloring brushes, coloring processes and the like on the coloring quality is avoided, the tooth surface meshing quality can be accurately judged, a specific quantitative actual measurement value is provided, and an important theoretical basis is provided for batch detection and processing parameter optimization of the arc end teeth. In addition, the two virtual models are used for meshing simulation matching, so that the optimal meshing state can be calculated, the original detection method of trial and error by means of manual tooth-by-tooth pairing is replaced, the optimal meshing tooth pair can be automatically calculated after the geometric parameter measurement of the concave tooth and the convex tooth is completed, the detection time is greatly shortened, and a foundation is laid for the digital assembly of the circular arc end tooth part.
It will be appreciated that, as shown in fig. 2, the step S1 specifically includes the following:
step S11: establishing a Cartesian coordinate system by taking an end plane of the arc end tooth as a reference;
step S12: setting theoretical parameters of the arc end teeth, and configuring scanning parameters of a three-coordinate measuring machine;
step S13: generating tooth surface grid coordinate points according to the established coordinate system and the configured scanning parameters by the three-coordinate measuring machine, and carrying out grid scanning according to the tooth surface grid coordinate points;
step S14: and obtaining the geometric parameters of the arc end teeth according to the scanning point cloud data of the three-coordinate measuring machine.
Specifically, a coordinate system is first established on a three-coordinate measuring machine, for example, an end plane of an arc end tooth is taken as an XY plane, a vertical end plane is upward taken as a positive direction of a Z axis, an origin is determined by an inner circle center and an end face height, and a line connecting the inner circle center and a dividing point in a tooth surface of any tooth is taken as an X axis. Of course, in other embodiments of the present invention, the position of the coordinate system may be adjusted according to actual needs. Then, theoretical parameters of the arc end tooth are set, wherein the theoretical parameters comprise two important parameters of concave teeth/convex teeth, the number of layers (selected according to the number of actual single-layer end teeth and multi-layer end teeth), the theoretical value diameter of an inner circle and the diameter of an outer circle, the tooth shape angle, the maximum top straight chamfer angle, the top chamfer angle, the maximum root fillet radius, the tooth top height, the minimum tooth depth and the arc end tooth machining: the distance between the center of the arc end tooth and the center of the cutter, the radius (curvature radius) of the cutter at the joint plane, and after the theoretical parameters of the arc end tooth are set, the working coordinate point of the tooth surface grid and the tooth top height measuring coordinate point can be automatically calculated and generated through software. Then, setting scanning parameters, wherein the specific scanning parameters comprise tooth top detection positions, the number of lines of designated scanning, fillet radius at a chamfer angle, scanning range, scanning speed, scanning acceleration, point density, scanning bias force parameters and the like, and then carrying out high-speed scanning by using an ultra-high-precision three-coordinate measuring machine. The three-coordinate measuring machine performs grid scanning twice, wherein the first scanning measurement is to perform grid scanning on two working surfaces of each tooth, the scanning point density is not lower than 20 points/mm, the scanning speed is not lower than 5mm/s, tooth surface data of the arc end tooth are obtained, the second scanning measurement is to perform radial scanning along the end surface of the arc end tooth, the diameter of a scanning circle is fixed, the scanning point density is not lower than 20 points/mm, and the scanning speed is not lower than 5mm/s, so that tooth top height original data of the arc end tooth are obtained. And then, obtaining geometrical parameters of the arc end tooth according to a large number of tooth surface profile data points obtained by scanning of a three-coordinate measuring machine, wherein the geometrical parameters comprise the tooth profile, the tooth pitch, the runout, the contact surface, the conditional tooth top height and the like. It can be understood that the three-coordinate measuring machine has higher precision requirement, the precision is controlled below 0.6 μm, and the sphericity and diameter precision of the probe are controlled below 0.08 μm. In addition, when the digital measurement is carried out on the arc end teeth, the surfaces of the arc end teeth are required to be thoroughly cleaned, and the measurement can be carried out in an environment with 20 degrees plus or minus 0.5 degree for more than 4 hours.
The conditional tooth top parameters are the most important geometric parameters of the arc end teeth, play a key role in whether the concave teeth and the convex teeth can be meshed, and as shown in fig. 3, the calculation process of the conditional tooth top is as follows:
step S141: performing three-dimensional radius compensation of the measuring head by using point data obtained by the second scanning to obtain surface point data of the arc end teeth;
step S142: converting the surface point data of each arc end tooth based on a conversion formula between a Cartesian coordinate system and a polar coordinate system by adopting an arc unfolding algorithm, and scaling the transverse axis of the polar coordinate system so as to convert the three-dimensional arc into a two-dimensional profile;
step S143: and selecting adjacent teeth and grooves from the two-dimensional profile to intercept data in a segmented mode, and finding the tooth top height when the tooth groove width and the tooth thickness are equal, so that the conditional tooth top height of each tooth is obtained.
Specifically, ball head radius compensation is performed along the three-dimensional vector direction, so that the surface point data of the arc end teeth are obtained. For example, the normal vector n of the measurement point p is set, and the actual measurement point q is calculated by increasing or decreasing the probe radiusThe calculation formula is as follows: q=p±r×n, where r represents the probe radius. Then, a three-dimensional arc is converted into a two-dimensional contour by adopting an arc unfolding algorithm so as to eliminate the influence of the polar radius. Specifically, coordinate transformation is firstly carried out, coordinate points of a Cartesian coordinate system are converted into polar coordinate points, a horizontal axis is a polar angle, a vertical axis is a polar diameter, and a conversion formula is thatWherein, (x, y) represents coordinate values in a Cartesian coordinate system, ρ represents a polar diameter, θ represents a polar angle, and thus a 2-dimensional expansion diagram of the tooth profile of the circular arc end tooth is obtained. Then, the ratio of the horizontal axis polar angle value is changed to scale, and the tooth profile is scaled down. Then, sectionally intercepting the obtained tooth profile of the arc-shaped end tooth, intercepting an adjacent tooth and groove each time, finding the tooth top when the tooth thickness and the tooth groove width are equal, namely obtaining the conditional tooth top of the tooth, sequentially calculating the conditional tooth top of each tooth, forming conditional tooth top evaluation data of the whole arc-shaped end tooth, and generating a conditional tooth top evaluation report, as shown in fig. 4.
It will be appreciated that, as shown in fig. 5, the step S2 specifically includes the following:
step S21: virtual modeling is carried out by utilizing the geometric parameters of the arc end teeth;
step S22: performing measuring head three-dimensional radius compensation based on the tooth surface point data of the arc end tooth to obtain tooth surface actual measurement point data of the arc end tooth;
step S23: calculating the projection length of each tooth surface actual measurement point in the normal vector direction, namely the deviation value of each tooth surface actual measurement point;
step S24: projecting coordinate values of each tooth surface actual measurement point onto an XY plane, and taking the deviation value as a Z value to obtain a two-dimensional point deviation matrix;
step S25: virtual coloring is carried out on the point deviation matrix based on the deviation value of each real measurement point, and the point deviation matrix is displayed in a two-dimensional drawing mode.
Specifically, the virtual modeling of the part is firstly performed by utilizing the geometric parameters of the arc end teeth. Then, point data based on the arc end teeth is enteredAnd carrying out three-dimensional radius compensation on the measuring head, firstly solving a normal vector of the coordinates of the central point of the measuring head along the measuring direction, and obtaining the coordinates of the actual contact point by increasing or decreasing the length of the radius of the measuring head on the basis of the normal vector. Because the scanned data point density of the arc end tooth surface is very high, 4 points which are not coplanar on the tooth surface are selected to solve the normal vector of the sub-micro area. Then, according to the convex-concave tooth mutual matching algorithm, the deviation value of each real measurement point is calculated, for example, the theoretical point is set as A, and the coordinates are set as (x 1 ,y 1 ,z 1 ) The unit normal vector is (i, j, k), the theoretical point A is calculated according to the theoretical parameters of the arc end tooth, the actual contact point is q, and the actual coordinate value is (x 2 ,y 2 ,z 2 ) Then vector oa=x 1 i+y 1 j+z 1 The projection length of the k and q points in the unit normal vector direction is as follows:the deviation value of the q point can be obtained. Then, deviation conversion is carried out, coordinate values of each tooth surface actual point are projected onto an XY plane, and a deviation value is taken as a Z value, so that a two-dimensional point deviation matrix is obtained. And finally, virtually coloring the point deviation matrix based on the deviation value of each real measurement point, and displaying in a two-dimensional drawing mode so as to quickly judge coloring conditions. The specific virtual coloring process is as follows:
firstly, setting tolerance variables of deviation values, defining different colors for different tolerance variable ranges, for example, defining green corresponding to the deviation values within 0 to 8 mu m, namely a good tooth surface engagement area, yellow corresponding to the deviation values within 8 mu m to 10 mu m, namely a tooth surface engagement warning area, red corresponding to the deviation values greater than 10 mu m, and a tooth surface engagement out-of-tolerance area. And then, comparing the deviation value of each real measurement point with the tolerance variable range to determine the coloring of each real measurement point, calculating the percentage of different coloring according to the number of the real measurement points, and displaying the percentage in a coloring chart. Wherein, the left tooth surface and the right tooth surface of the arc end tooth can be respectively and virtually colored, and the graphic drawing can be independently carried out.
It can be understood that the step S3 is specifically:
and carrying out meshing simulation by utilizing one concave tooth of one virtual model and a plurality of convex teeth of the other virtual model one by one, or carrying out meshing simulation by utilizing one convex tooth of one virtual model and a plurality of concave teeth of the other virtual model one by one, respectively carrying out parallelism simulation matching and coaxiality simulation matching during each meshing simulation, and obtaining a matched tooth number corresponding to the optimal matching state according to a parallelism simulation matching result and coaxiality simulation matching result of multiple meshing simulations.
The process for carrying out parallelism simulation matching during each engagement simulation specifically comprises the following steps:
after each engagement, calculating to obtain the sum of the tooth top heights of each pair of teeth, screening out the maximum value and the minimum value of the sum of the tooth top heights, and calculating to obtain the sum deviation value of the tooth top heights between the maximum value and the minimum value of the sum of the tooth top heights, wherein the smaller the sum deviation value of the tooth top heights is, the better the parallelism is.
The coaxiality simulation matching process during each engagement simulation specifically comprises the following steps:
after each engagement, calculating to obtain a center distance deviation value of the two parts, wherein the smaller the center distance deviation value is, the better the coaxiality is.
The process of obtaining the pairing tooth number corresponding to the optimal matching state according to the parallelism simulation matching result and the coaxiality simulation matching result of the multiple meshing simulation specifically comprises the following steps:
and calculating a quadratic root value of the sum deviation value of the tooth top and the square sum of the center distance deviation value in each meshing simulation, screening out the smallest meshing state based on the calculation result of multiple meshing simulations, wherein the meshing state corresponding to the smallest meshing state is the optimal meshing state, and obtaining the concave tooth pairing tooth number and the convex tooth pairing tooth number corresponding to the optimal fitting state.
It can be understood that in theory, the meshing of the convex gear and the concave gear can be realized by only three pairs of teeth, the meshing process of the actual parts belongs to over-positioning, in theory, when the parallelism is 0, the addition value of the tooth top height of the concave tooth and the tooth top height of the convex tooth of each pair of teeth should be equal, and when the sum of the tooth top height of the concave tooth and the tooth top height of the convex tooth of each pair of teeth is equalWhen the teeth are inconsistent, the parallelism deviation of the convex teeth (based on the concave teeth) can be caused. Meanwhile, in theory, after concave teeth and convex teeth are meshed, the midpoints of the joint planes of each group of teeth pairs are completely overlapped, but are influenced by manufacturing precision, the midpoints are not overlapped, and coaxiality deviation can be caused when the midpoints are not overlapped. Therefore, the invention utilizes one concave tooth of one virtual model to carry out meshing simulation with a plurality of convex teeth of the other virtual model one by one, or utilizes one convex tooth of one virtual model to carry out meshing simulation with a plurality of concave teeth of the other virtual model one by one, and the number of meshing simulation is the number of teeth. For example, if the virtual model of the part has 11 teeth in total, the engagement simulation is performed on one concave tooth of one virtual model with 11 convex teeth of the other virtual model one by one, and the total simulation is 11 times. After each engagement, the sum of the tooth top heights of each pair of teeth is calculated, 11 groups of data are obtained in total, then the maximum value and the minimum value of the sum of the tooth top heights are screened out from the 11 groups of data, and the sum deviation value delta P of the tooth top heights between the maximum value and the minimum value is calculated. Meanwhile, the center distance deviation value delta S of the two part models is calculated after each engagement. The total engagement is simulated 11 times, so that 11 groups of data of the sum deviation value and the center distance deviation value of the tooth top heights can be obtained. Then, each engagement state evaluation index is calculated based on the following formula:wherein T represents an engagement state evaluation index. And screening out the smallest one from the 11 meshing state evaluation indexes, namely, the best meshing state, obtaining the concave tooth pairing tooth number and the convex tooth pairing tooth number corresponding to the smallest value, and assembling according to the pairing tooth number in actual assembly to obtain the best meshing state.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The digital measurement method of the arc end tooth is characterized by comprising the following steps of:
automatically scanning the contour of the arc end tooth by using a three-dimensional simulation measuring head carried by a three-coordinate measuring machine to obtain a large number of tooth surface contour data points, and calculating to obtain the geometric parameters of the arc end tooth;
virtual modeling is carried out on the part based on the scanning data, and virtual coloring analysis is carried out on the tooth surface of the arc end tooth;
adopting two virtual models to carry out meshing simulation matching, and calculating to obtain an optimal meshing state;
the process of adopting two virtual models for simulation matching and calculating to obtain the optimal engagement state specifically comprises the following steps:
performing meshing simulation by utilizing one concave tooth of one virtual model and a plurality of convex teeth of the other virtual model one by one, or performing meshing simulation by utilizing one convex tooth of one virtual model and a plurality of concave teeth of the other virtual model one by one, respectively performing parallelism simulation matching and coaxiality simulation matching during each meshing simulation, and obtaining a matched tooth number corresponding to the optimal matching state according to a parallelism simulation matching result and coaxiality simulation matching result of multiple meshing simulations;
the process for carrying out parallelism simulation matching during each engagement simulation specifically comprises the following steps:
after each engagement, calculating to obtain the sum of the tooth top heights of each pair of teeth, screening out the maximum value and the minimum value of the sum of the tooth top heights, and calculating to obtain the sum deviation value of the tooth top heights between the maximum value of the sum of the tooth top heights and the minimum value of the sum of the tooth top heights, wherein the smaller the sum deviation value of the tooth top heights is, the better the parallelism is;
the coaxiality simulation matching process during each engagement simulation specifically comprises the following steps:
after each engagement, calculating to obtain a center distance deviation value of the two parts, wherein the smaller the center distance deviation value is, the better the coaxiality is;
the process of obtaining the pairing tooth number corresponding to the optimal matching state according to the parallelism simulation matching result and the coaxiality simulation matching result of the multiple meshing simulation specifically comprises the following steps:
and calculating a quadratic root value of the sum deviation value of the tooth top and the square sum of the center distance deviation value in each meshing simulation, screening out the smallest meshing state based on the calculation result of multiple meshing simulations, wherein the meshing state corresponding to the smallest meshing state is the optimal meshing state, and obtaining the concave tooth pairing tooth number and the convex tooth pairing tooth number corresponding to the optimal fitting state.
2. The method for digitally measuring the arc end tooth according to claim 1, wherein the process of automatically scanning the contour of the arc end tooth by using the three-dimensional simulation measuring head carried by the three-dimensional measuring machine to obtain a plurality of tooth surface contour data points and calculating the geometric parameters of the arc end tooth is specifically as follows:
establishing a Cartesian coordinate system by taking an end plane of the arc end tooth as a reference;
setting theoretical parameters of the arc end teeth, and configuring scanning parameters of a three-coordinate measuring machine;
generating tooth surface grid coordinate points according to the established coordinate system and the configured scanning parameters by the three-coordinate measuring machine, and carrying out grid scanning according to the tooth surface grid coordinate points;
and obtaining the geometric parameters of the arc end teeth according to the scanning point cloud data of the three-coordinate measuring machine.
3. The method for digitally measuring the circular arc end teeth according to claim 2, wherein the three-coordinate measuring machine performs grid scanning twice, the first scanning measurement is to perform grid scanning on two working surfaces of each tooth to obtain tooth surface data of the circular arc end teeth, and the second scanning measurement is to perform radial scanning along the end surfaces of the circular arc end teeth to obtain tooth top height original data of the circular arc end teeth.
4. The digital measurement method of the circular arc end tooth according to claim 3, wherein the geometric parameters of the circular arc end tooth comprise a conditional tooth top, and the calculation process of the conditional tooth top is as follows:
performing three-dimensional radius compensation of the measuring head by using point data obtained by the second scanning to obtain surface point data of the arc end teeth;
converting the surface point data of each arc end tooth based on a conversion formula between a Cartesian coordinate system and a polar coordinate system by adopting an arc unfolding algorithm, and scaling the transverse axis of the polar coordinate system so as to convert the three-dimensional arc into a two-dimensional profile;
and selecting adjacent teeth and grooves from the two-dimensional profile to intercept data in a segmented mode, and finding the tooth top height when the tooth groove width and the tooth thickness are equal, so that the conditional tooth top height of each tooth is obtained.
5. The digitized measurement method of claim 3 wherein said process of virtually modeling the part based on scan data and virtually coloring the tooth surface of the rounded end tooth comprises the steps of:
virtual modeling is carried out by utilizing the geometric parameters of the arc end teeth;
performing measuring head three-dimensional radius compensation based on the tooth surface point data of the arc end tooth to obtain tooth surface actual measurement point data of the arc end tooth;
calculating the projection length of each tooth surface actual measurement point in the normal vector direction, namely the deviation value of each tooth surface actual measurement point;
projecting coordinate values of each tooth surface actual measurement point onto an XY plane, and taking the deviation value as a Z value to obtain a two-dimensional point deviation matrix;
virtual coloring is carried out on the point deviation matrix based on the deviation value of each real measurement point, and the point deviation matrix is displayed in a two-dimensional drawing mode.
6. The method for digitally measuring the circular arc end tooth according to claim 5, wherein the process of virtually coloring the point deviation matrix based on the deviation value of each real measurement point and displaying the point deviation matrix in the form of two-dimensional drawing is specifically as follows:
setting tolerance variables of the deviation values, defining different colors for different tolerance variable ranges, comparing the deviation values of each real measurement point with the tolerance variable ranges to determine the coloring of each real measurement point, calculating different coloring percentages according to the number of the real measurement points, and displaying the percentages in a coloring chart.
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