CN112697041B - Monte carlo method-based pre-evaluation method for measurement accuracy of assembly pose - Google Patents
Monte carlo method-based pre-evaluation method for measurement accuracy of assembly pose Download PDFInfo
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Abstract
A method for pre-evaluating the measurement accuracy of an assembly pose based on a Monte Carlo method comprises the steps of evaluating a mobile device inserted or butted fixing device, and measuring the relative pose of a large part in a simulation environment, wherein the measurement comprises target point measurement, key point calculation and relative pose calculation; placing a moving device and a fixing device on the same track, moving the moving device to a set distance from the fixing device, and placing a laser tracker on the side surface between the moving device and the fixing device; a distance measuring sensor and two angle measuring sensors are arranged in the laser tracker; the invention aims to solve the problem of pre-evaluation of pose measurement precision in large-part digital assembly, and designs an assembly pose measurement simulation method.
Description
Technical Field
The invention discloses an assembly pose measurement accuracy pre-evaluation method based on a Monte Carlo method, relates to the field of digital measurement auxiliary assembly of large components, and is used for pose digital measurement simulation and pose measurement accuracy evaluation.
Background
In the fields of aviation, aerospace and ships, the product is large in size, high in precision requirement and complex in process. The assembly of large components is a key step in the production process, the primary task of which is to determine the relative position and posture between the assembled components, and the support of large-scale space measurement technology is required. The measurement essence of the commonly used measuring instruments at present is to acquire the three-dimensional coordinates of a target point under a reference coordinate system, and then perform position and attitude fitting according to the corresponding relation, so as to guide a motion mechanism to adjust the pose of a component.
Like manufacturing errors of parts and assembly errors of components, measurement errors also have an influence on assembly compatibility. In order to ensure the one-time success rate during assembly, the measurement accuracy of the pose of the component needs to be pre-evaluated before actual assembly, so that support is provided for the model selection and station planning of a digital measurement system, and the prior art does not effectively evaluate the measurement accuracy of the pose of the component before actual assembly.
Disclosure of Invention
The invention aims to provide an assembly pose measurement accuracy pre-evaluation method based on a Monte Carlo method, which aims to solve the problem of measurement accuracy of a component pose before actual assembly.
A method for pre-evaluating the measurement accuracy of an assembly pose based on a Monte Carlo method comprises the steps of evaluating a mobile device inserted or butted fixing device, and measuring the relative pose of a large part in a simulation environment, wherein the measurement comprises target point measurement, key point calculation and relative pose calculation;
placing a moving device and a fixing device on the same track, moving the moving device to a set distance from the fixing device, and placing a laser tracker on the side surface between the moving device and the fixing device; a distance measuring sensor and two angle measuring sensors are arranged in the laser tracker;
step two, adjusting the moving device andselecting a plurality of measured target points P1 and P2 … Pn related to plugging or butting on the mobile device and the fixed device according to the relative position of the fixed device, and measuring the selected plurality of measuring points one by using a laser tracker; when measuring the target point P, the distance l, the horizontal angle alpha and the vertical angle beta from the measured instrument to the target point P are set to form a polar coordinate P (l, alpha, beta)T(ii) a Similarly, measuring the distances l, the horizontal angle alpha and the vertical angle beta of the plurality of measuring points;
step three, transforming the coordinates of the target point P to be measured as follows,
calculation of P ═ (l, α, β) according to equation (1)TMeasured value in cartesian coordinate system P ═ (x, y, z)T；
From the analysis of the error source of the laser tracker, the final influence of various error factors on the coordinate measurement of the laser tracker in the measurement process is that each sensor unit introduces a measurement error of epsilon ═ epsilon (epsilon)l,εα,εβ)TAs shown in formula (2), wherein (l)*,α*,β*)TIs a true measurement value;
according to the measuring principle of the distance and the angle of the laser tracker, an appropriate probability distribution function is distributed to the uncertainty characteristic of each sensor, the items assume that all sensing units are independent from each other and are in normal distribution with the mean value of 0, and therefore a normal distribution model for obtaining the random error measured by each sensor unit is as follows:
wherein σl *Is a distanceA standard deviation reference component of the measurement error, ω represents a linear variation coefficient of the standard deviation of the distance measurement error within a measurement range thereof, l represents a measurement distance of the coordinate point, and ω · l is a linear variation component of the standard deviation of the distance measurement error; sigmaαAnd σβRespectively the standard deviation of the measurement errors of the horizontal angle and the vertical angle; in summary, the measurement model of the laser tracker can be obtained as follows:
based on the measurement model of the formula (4), a Monte Carlo method is adopted, and a probability distribution model of random errors is combined to measure standard deviation parameter sigma of errors of a sensor unit of the laser trackerl，σα，σβRandomly sampling, adding the sampling value into each sensor unit, thereby completing the simulation process of one-time measurement of the laser tracker, and converting the simulation measurement result into a Cartesian coordinate system; the measurement simulation process is circularly executed for n times to obtain a random measurement sample (xi) with the size of n1，ξ2，…，ξn) (ii) a The above samples were statistically analyzed and the uncertainty was expressed as a 2-fold standard deviation, yielding the measured uncertainty parameter (u) for the coordinate pointx，uy，uz)T；
Step four, similarly measuring a plurality of measured target points P1 and P2 … Pn like the point P, and obtaining corresponding measurement uncertainty parameters (u)x，uy，uz)T；
Step five, butt joint of the large-scale mobile device and the fixing device is taken as an example, measured points are surface points of a shaft, a hole and a butt joint surface, on the basis, the shaft, the hole and the butt joint surface can be fitted, and intersection points of axes of the shaft and the hole and the respective butt joint surfaces are obtained, so that key points are obtained, point set matching is carried out on the key points of the two components, and the relative pose of the components can be obtained;
based on the above contents, the assembly pose evaluation is realized, a Monte Carlo method is adopted to carry out measurement simulation on the relative poses of most pieces, statistical analysis is carried out on the calculated relative poses, and the fluctuation amount of the relative poses is given;
the assembly quality is characterized by the assembly characteristic, and the minimum clearance between the shaft holes can be selected according to the assembly characteristic of the butt joint of the large components connected by the multiple shaft holes, wherein:
wherein d is1The minimum distance between the upper part of the front end of the butt joint shaft and the hole wall, d2Is the minimum distance r from the lower part of the front end of the butt joint shaft to the hole wallhAnd rsRespectively, the radii of the docking hole and the docking shaft, PsAnd PhRespectively representing the coordinates of the center points of the end surfaces of the butt joint hole and the butt joint shaft fpsAnd fphRespectively representing end surface normal vectors of the butt joint hole and the butt joint shaft;
the gap is more than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1，d2)＞0；
The characteristic parameters are generated by performing least square fitting on target measuring points, and the uncertainty of the measuring points forms the measurement uncertainty of the characteristic after fitting adjustment; in the simulation system, the Monte Carlo method is adopted for resolving for multiple times, the results of the formula are solved by substituting n groups of measured values, the resolving results are changed due to the uncertainty of measurement, and the (d) is calculated1，d2) Number n > 01Then the probability q that the assembly pose satisfies the assembly requirement can be expressed as:
q is the probability that the assembly clearance is larger than 0 in multiple measurements, the probability is output as an assembly pose evaluation result, and the minimum assembly probability x can be set according to the assembly requirement and is used as the minimum allowable assembly pose evaluation probability;
step six, when the assembly pose calculation result exists in min (d)1，d2) Case of < 0, i.e. n1/n≠1, when q is smaller than a set value x, representing that the assembly pose result does not meet the assembly requirement based on the simulation analysis of the measurement system; turning to the seventh step; if the assembly pose calculation result has min (d)1，d2) Case > 0, i.e. n1Q 1, or (d) is present1，d2) If the value is greater than 0 and q is greater than a set value x, representing that the assembly pose result meets the assembly requirement, and turning to the step eight;
seventhly, re-adjusting the pose of the butt joint section of the device to be moved and the fixing device; and adjusting the posture of the section to be butted according to the resolved assembly posture result, wherein the adjusting process is as follows:
calculating coordinate value P of center point of butt joint end facesAnd PhCalculating the vector value fp of the normal of the butt joint end surface by using the difference components on three coordinate axessAnd fphAnd (3) synthesizing the two difference components by using the difference components of the movement amount caused on the three coordinate axes, and respectively moving and compensating the corresponding difference components of the moving device in three dimensions of lifting, left and right, front and back according to the synthesized difference components to ensure that the pose after adjustment meets the adjustment principle as follows:
the gap is larger than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1，d2)＞0；
After the pose adjustment is finished, turning to the second step;
and step eight, finishing the pre-evaluation.
The invention aims to solve the problem of pre-evaluation of pose measurement precision in large-part digital assembly, and designs an assembly pose measurement simulation method. And constructing a digital model of the measuring system, and generating measuring data containing measuring errors according to the instrument station and the target point to be measured. And in the assembly process, the relative pose of the component is measured by a digital measurement system in a simulation environment. And performing measurement simulation for multiple times based on a Monte Carlo method, giving the fluctuation range of the position and the posture of the component, and evaluating whether the assembly process can be smoothly completed.
Drawings
FIG. 1 is a schematic diagram of an assembly pose measurement simulation evaluation process according to the present invention;
FIG. 2 is a schematic view of the measurement principle of the laser tracker of the present invention;
FIG. 3 is a schematic diagram of a simulation measurement method of coordinates of a target point according to the present invention;
fig. 4 is a schematic diagram of an assembly characteristic calculation method according to the present invention.
Detailed Description
A method for pre-evaluating the measurement accuracy of an assembly pose based on a Monte Carlo method comprises the steps of evaluating a mobile device inserted or butted fixing device, and measuring the relative pose of a large part in a simulation environment, wherein the measurement comprises target point measurement, key point calculation and relative pose calculation;
placing a moving device and a fixing device on the same track, moving the moving device to a set distance from the fixing device, and placing a laser tracker on the side surface between the moving device and the fixing device; a distance measuring sensor and two angle measuring sensors are arranged in the laser tracker;
adjusting the relative positions of the mobile device and the fixing device, selecting a plurality of measured target points P1 and P2 … Pn related to plugging or butting on the mobile device and the fixing device, and measuring the selected plurality of measuring points one by using a laser tracker; when measuring the target point P, the distance l from the measured instrument to the target point P, the horizontal angle alpha and the vertical angle beta are set to form a polar coordinate P (1, alpha, beta)T(ii) a Similarly, measuring the distances l, the horizontal angle alpha and the vertical angle beta of the plurality of measuring points;
step three, transforming the coordinates of the target point P to be measured as follows,
calculation of P ═ 1, α, β according to equation (1)TMeasured value in cartesian coordinate system P ═ (x, y, z)T；
From the analysis of the error source of the laser tracker, the final influence of various error factors on the coordinate measurement of the laser tracker in the measurement process is that each sensor unit introduces a measurement error of epsilon ═ epsilon (epsilon)1，εα，εβ)TAs shown in formula (2), wherein (1)*，α*，β*)TIs a true measurement value;
according to the measuring principle of the distance and the angle of the laser tracker, an appropriate probability distribution function is distributed to the uncertainty characteristic of each sensor, the items assume that all sensing units are independent from each other and are in normal distribution with the mean value of 0, and therefore a normal distribution model for obtaining the random error measured by each sensor unit is as follows:
wherein σ1 *Is a standard deviation reference component of the distance measurement error, omega represents a linear variation coefficient of the standard deviation of the distance measurement error in a measurement range thereof, l represents a measurement distance of the coordinate point, and omega is a linear variation component of the standard deviation of the distance measurement error; sigmaαAnd σβRespectively the standard deviation of the measurement errors of the horizontal angle and the vertical angle; in summary, the measurement model of the laser tracker can be obtained as follows:
based on the measurement model of the formula (4), a Monte Carlo method is adopted, and a probability distribution model of random errors is combined for laserStandard deviation parameter sigma of tracker sensor unit measurement error1，σα，σβRandomly sampling, adding the sampling value into each sensor unit, thereby completing the simulation process of one-time measurement of the laser tracker, and converting the simulation measurement result into a Cartesian coordinate system; the measurement simulation process is circularly executed for n times to obtain a random measurement sample (xi) with the size of n1，ξ2，…，ξn) (ii) a The above samples were statistically analyzed and the uncertainty was expressed as a 2-fold standard deviation, yielding the measured uncertainty parameter (u) for the coordinate pointx，uy，uz)T；
Step four, similarly measuring a plurality of measured target points P1 and P2 … Pn like the point P, and obtaining corresponding measurement uncertainty parameters (u)x，uy，uz)T；
Step five, butt joint of the large-scale mobile device and the fixing device is taken as an example, measured points are surface points of a shaft, a hole and a butt joint surface, on the basis, the shaft, the hole and the butt joint surface can be fitted, and intersection points of axes of the shaft and the hole and the respective butt joint surfaces are obtained, so that key points are obtained, point set matching is carried out on the key points of the two components, and the relative pose of the components can be obtained;
based on the above contents, the assembly pose evaluation is realized, a Monte Carlo method is adopted to carry out measurement simulation on the relative poses of most pieces, statistical analysis is carried out on the calculated relative poses, and the fluctuation amount of the relative poses is given;
the assembly quality is characterized by the assembly characteristic, and the minimum clearance between the shaft holes can be selected according to the assembly characteristic of the butt joint of the large components connected by the multiple shaft holes, wherein:
wherein d is1The minimum distance between the upper part of the front end of the butt joint shaft and the hole wall, d2Is the minimum distance r from the lower part of the front end of the butt joint shaft to the hole wallhAnd rsRespectively, the radii of the docking hole and the docking shaft, PsAnd PhRespectively representing the coordinates of the center points of the end surfaces of the butt joint hole and the butt joint shaft fpsAnd fphRespectively representing end surface normal vectors of the butt joint hole and the butt joint shaft;
the gap is more than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1，d2)＞0；
The characteristic parameters are generated by performing least square fitting on target measuring points, and the uncertainty of the measuring points forms the measurement uncertainty of the characteristic after fitting adjustment; in the simulation system, the Monte Carlo method is adopted for resolving for multiple times, the results of the formula are solved by substituting n groups of measured values, the resolving results are changed due to the uncertainty of measurement, and the (d) is calculated1，d2) Number n > 01Then the probability q that the assembly pose satisfies the assembly requirement can be expressed as:
q is the probability that the assembly clearance is larger than 0 in multiple measurements, the probability is output as an assembly pose evaluation result, and the minimum assembly probability x can be set according to the assembly requirement and is used as the minimum allowable assembly pose evaluation probability;
step six, when the assembly pose calculation result exists in min (d)1，d2) Case of < 0, i.e. n1/n is not equal to 1, and when q is smaller than a set value x, the result of the assembly pose does not meet the assembly requirement based on the simulation analysis of the measurement system; turning to the seventh step; if the assembly pose calculation result has min (d)1，d2) Case > 0, i.e. n1 Q 1, or (d) is present1，d2) If the value is greater than 0 and q is greater than a set value x, representing that the assembly pose result meets the assembly requirement, and turning to the step eight;
seventhly, re-adjusting the pose of the butt joint section of the device to be moved and the fixing device; and adjusting the posture of the section to be butted according to the resolved assembly posture result, wherein the adjusting process is as follows:
calculating coordinate value P of center point of butt joint end facesAnd PhIn threeCalculating the vector value fp of the normal of the butt joint end face by using the difference component on the coordinate axissAnd fphAnd (3) synthesizing the two difference components by using the difference components of the movement amount caused on the three coordinate axes, and respectively moving and compensating the corresponding difference components of the moving device in three dimensions of lifting, left and right, front and back according to the synthesized difference components to ensure that the pose after adjustment meets the adjustment principle as follows:
the gap is larger than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1，d2)＞0；
After the pose adjustment is finished, turning to the second step;
and step eight, finishing the pre-evaluation.
Example (b):
the invention is described in further detail below with reference to the figures and the examples. The invention provides a pose fluctuation amount and assembly characteristic calculation method based on a Monte Carlo method aiming at pose measurement precision pre-evaluation in a large-part digital assembly process, and the pose fluctuation amount and assembly characteristic calculation method is realized according to a software system shown in figure 2.
The simulation model of the digital measurement system is shown in fig. 3 and 4, the measurement model is constructed by taking a laser tracker as an example, and a simulation measurement method of coordinates of a target point is given. The laser tracker has a distance measuring sensor and two angle measuring sensors inside, and can measure the distance l, horizontal angle alpha and vertical angle beta from the target point P to form polar coordinate P ═ l, alpha, beta)T. In the case of coordinate measuring systems, the measured values are generally given on the basis of a cartesian coordinate system, so that P ═ 1, α, β are calculated according to equation (1)TMeasured value in cartesian coordinate system P ═ (x, y, z)T。
By sources of error to the laser trackerAccording to analysis, the final influence of various error factors on the coordinate measurement of the laser tracker in the measurement process is that each sensor unit introduces a measurement error of epsilon ═ epsilonl，εα，εβ)TAs shown in formula (2), wherein (1)*，α*，β*)TIs the true value of the measurement.
According to the measuring principle of the distance and the angle of the laser tracker, an appropriate probability distribution function is distributed to the uncertainty characteristic of each sensor, the items assume that all sensing units are independent from each other and are in normal distribution with the mean value of 0, and therefore a normal distribution model for obtaining the random error measured by each sensor unit is as follows:
wherein σ1 *Is a standard deviation reference component of the distance measurement error, omega represents a linear variation coefficient of the standard deviation of the distance measurement error in a measurement range thereof, 1 represents a measurement distance of the coordinate point, and omega & l is a linear variation component of the standard deviation of the distance measurement error; sigmaαAnd σβStandard deviations of the measurement errors for the horizontal and vertical angles, respectively. In summary, the measurement model of the laser tracker can be obtained as follows:
based on the measurement model of the formula (4), a Monte Carlo method is adopted, and a probability distribution model of random errors is combined to measure standard deviation parameter sigma of errors of a sensor unit of the laser tracker1，σα，σβRandom sampling is carried out, and sampling values are added into all the sensor units, thereby completing one-time measurement simulation of the laser trackerAnd (5) a true process, and converting the simulation measurement result into a Cartesian coordinate system. The measurement simulation process is circularly executed for n times to obtain a random measurement sample (xi) with the size of n1，ξ2，…，ξn). The above samples were statistically analyzed and the uncertainty was expressed as a 2-fold standard deviation, yielding the measured uncertainty parameter (u) for the coordinate pointx，uy，uz)T。
When most of the relative pose measurement is carried out in a simulation environment, the measurement comprises target point measurement, key point calculation and relative pose calculation. Taking the butt joint of large components connected by multiple shaft holes as an example, the actual measurement points are surface points of a shaft, a hole and a butt joint surface, on the basis, the shaft, the hole and the butt joint surface can be fitted, the intersection point of the axis of the shaft and the axis of the hole and the respective butt joint surface can be obtained, so that key points are obtained, the key points of the two components are subjected to point set matching, and the relative pose of the components can be obtained.
Based on the above contents, the assembly pose evaluation is realized, the Monte Carlo method is adopted to carry out measurement simulation on the relative poses of most pieces, statistical analysis is carried out on the calculated relative poses, and the fluctuation amount of the relative poses is given.
The assembly quality is characterized by the assembly characteristics of the butt joint of the large components of the multi-axis hole connection, which can select the minimum clearance between the shaft holes, see fig. 4, wherein:
wherein d is1The minimum distance between the upper part of the front end of the butt joint shaft and the hole wall, d2Is the minimum distance r from the lower part of the front end of the butt joint shaft to the hole wallhAnd rsRespectively, the radii of the docking hole and the docking shaft, PsAnd PhRespectively representing the coordinates of the center points of the end surfaces of the butt joint hole and the butt joint shaft fpsAnd fphRepresenting the end surface normal vectors of the abutment hole and the abutment shaft, respectively.
The gap is more than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1，d2)＞0。
The characteristic parameters are generated by target measuring points through least square fitting, and the uncertainty of the measuring points forms the measurement uncertainty of the characteristics through fitting adjustment. In the simulation system, the Monte Carlo method is adopted for resolving for multiple times, the results of the formula are solved by substituting n groups of measured values, the variation of the resolving result is caused by the uncertainty of measurement, and min (d) is calculated1，d2) Number n > 01Then the probability p that the assembly pose satisfies the assembly requirement can be expressed as:
P＝n1/n(6)
and p is the probability that the assembly clearance is larger than 0, the probability is output as an assembly pose evaluation result, and the minimum assembly probability x can be set according to the assembly requirement and is used as the minimum allowable assembly pose evaluation probability.
When the assembly pose calculation result exists in min (d)1，d2) Case of < 0, i.e. n1/And n is not equal to 1, and when the n is less than a set value x, the simulation analysis based on the measurement system is represented, the assembly pose result does not meet the assembly requirement, and the measurement evaluation is carried out after the pose of the butt joint section to be assembled needs to be adjusted again.
P for solving position and posture of butt joint section to be assembled according to measurementsAnd PhCoordinate value of center point of butt joint end face, and fpsAnd fPhAnd adjusting the vector value of the normal of the butt joint end face according to the following adjustment principle:
and after the pose is adjusted, repeatedly resolving the probability p that the assembly pose meets the assembly requirement, if p is less than x, indicating that the input coordinates of the measuring station and the target point do not meet the pose measurement requirement, needing to change the coordinates of the measuring station and the target point again (namely, the measurement process), carrying out simulation analysis again, carrying out iterative optimization on the station and the target point, and searching for the optimal solution of the probability p that the assembly pose meets the assembly requirement.
Finally, a monte carlo method-based pre-evaluation method for measurement accuracy of the assembly pose is provided, which comprises the following main contents:
the simulation model of the digital measurement system in some embodiments is specifically characterized by: measuring point calculation and measurement uncertainty calculation are included; calculating coordinates of the measuring points in a Cartesian coordinate system according to the sensor composition and the measurement data of the digital measurement system; and measuring uncertainty calculation is carried out according to the measuring principle of the sensors, a measuring error probability distribution function is distributed to the measured data of each sensor, and measuring point coordinate uncertainty is calculated based on a Monte Carlo method.
The attitude simulation measurements are specifically characterized in some embodiments as: the method comprises the steps of instrument station setting, target point measurement and relative pose resolving; inputting the instrument station and the theoretical coordinate of the target point to be measured in the assembly pose measurement simulation evaluation software system, and outputting a target point coordinate measurement value containing a measurement error according to a digital measurement system simulation model; and resolving the relative pose of the component according to the matching relation between the target point coordinate measurement values of the component to be assembled and the reference component, and outputting the pose of the component containing the measurement error.
The pose estimation specific features in some embodiments are: the method comprises the steps of assembly characteristic calculation, Monte Carlo method simulation and measurement station position selection; the assembly characteristic is an index required to be controlled in the assembly process, and the assembly quality can be calculated and evaluated according to the relative pose of the components; simulating a pose measurement process by a Monte Carlo method, wherein a new target point coordinate measurement value is generated each time, relative pose calculation is performed, finally, a statistical method is used for estimating the pose fluctuation amount, and the assembly pose is estimated according to the assembly characteristics; and (3) giving a station position distribution range of the measuring instrument, analyzing each station position by using a Monte Carlo method, and selecting the station position with the minimum pose fluctuation amount.
The specific features for evaluating the assembly pose by the assembly characteristics in some embodiments are: and adjusting the pose of the to-be-assembled part according to the resolving result in the simulation environment, calculating the assembling characteristic, and finally outputting the probability that the assembling characteristic meets the assembling requirement as an assembling pose evaluation result.
In some embodiments the specialized software features are: various measurement models of the digital measurement system can be provided, simulation measurement is carried out, and the pose of the component is fitted; providing an assembly pose evaluation function, supporting assembly characteristic definition, and calculating pose fluctuation amount and assembly characteristic based on a Monte Carlo method; the station planning can be carried out and displayed in a three-dimensional visual mode.
The operation and use steps of the assembly pose measurement simulation evaluation software system are described in detail as follows:
1. preparing a product three-dimensional model, designing a measurement process according to an assembly process, and generating a point set to be measured;
2. selecting a digital measuring device in a software system and inputting a station position;
3. carrying out measurement process simulation, calculating the relative pose and the assembly characteristic value after adjusting the pose of the component, and verifying the feasibility of the measurement process;
4. evaluating the assembly pose by a Monte Carlo method, and giving the probability that the pose fluctuation quantity and the assembly characteristic meet the assembly process requirement;
5. when the user inputs the station position range of the digital measuring equipment, 3 and 4 operations are carried out on each station position, and the optimal station position or station position range is output.
The invention has the following advantages and beneficial effects:
1. a measurement simulation environment is constructed for most digital assembly processes, an assembly pose evaluation method is provided, and the one-time assembly success rate is favorably improved;
2. the method is suitable for model selection of digital measuring equipment and planning of equipment measuring stations, and provides support for planning of an assembly process.
Claims (1)
1. A method for pre-evaluating the measurement accuracy of an assembly pose based on a Monte Carlo method comprises the steps of evaluating a mobile device inserted or butted fixing device, and measuring the relative pose of a large part in a simulation environment, wherein the measurement comprises target point measurement, key point calculation and relative pose calculation;
placing a moving device and a fixing device on the same track, moving the moving device to a set distance from the fixing device, and placing a laser tracker on the side surface between the moving device and the fixing device; a distance measuring sensor and two angle measuring sensors are arranged in the laser tracker;
adjusting the relative positions of the mobile device and the fixing device, selecting a plurality of measured target points P1 and P2 … Pn related to plugging or butting on the mobile device and the fixing device, and measuring the selected plurality of measuring points one by using a laser tracker; when measuring the target point P, the distance l, the horizontal angle alpha and the vertical angle beta from the measured instrument to the target point P are set to form a polar coordinate P (l, alpha, beta)T(ii) a Similarly, measuring the distances l, the horizontal angle alpha and the vertical angle beta of the plurality of measuring points;
step three, transforming the coordinates of the target point P to be measured as follows,
calculation of P ═ (l, α, β) according to equation (1)TMeasured value in cartesian coordinate system P ═ (x, y, z)T；
From the analysis of the error source of the laser tracker, the final influence of various error factors on the coordinate measurement of the laser tracker in the measurement process is that each sensor unit introduces a measurement error of epsilon ═ epsilon (epsilon)l,εα,εβ)TAs shown in formula (2), wherein (l)*,α*,β*)TIs a true measurement value;
according to the measuring principle of the distance and the angle of the laser tracker, an appropriate probability distribution function is distributed to the uncertainty characteristic of each sensor, the items assume that all sensing units are independent from each other and are in normal distribution with the mean value of 0, and therefore a normal distribution model for obtaining the random error measured by each sensor unit is as follows:
wherein σl *Is a standard deviation reference component of the distance measurement error, omega represents a linear variation coefficient of the standard deviation of the distance measurement error in a measurement range thereof, l represents a measurement distance of the coordinate point, and omega · l is a linear variation component of the standard deviation of the distance measurement error; sigmaαAnd σβRespectively the standard deviation of the measurement errors of the horizontal angle and the vertical angle; in summary, the measurement model of the laser tracker can be obtained as follows:
based on the measurement model of the formula (4), a Monte Carlo method is adopted, and a probability distribution model of random errors is combined to measure standard deviation parameter sigma of errors of a sensor unit of the laser trackerl，σα，σβRandomly sampling, adding the sampling value into each sensor unit, thereby completing the simulation process of one-time measurement of the laser tracker, and converting the simulation measurement result into a Cartesian coordinate system; the measurement simulation process is circularly executed for n times to obtain a random measurement sample (xi) with the size of n1,ξ2,…,ξn) (ii) a The above samples were statistically analyzed and the uncertainty was expressed as a 2-fold standard deviation, yielding the measured uncertainty parameter (u) for the coordinate pointx,uy,uz)T；
Step four, similarly measuring a plurality of measured target points P1 and P2 … Pn like the point P, and obtaining corresponding measurement uncertainty parameters (u)x,uy,uz)T；
Step five, when the large-scale mobile device is butted with the fixing device, measured points are surface points of the shaft, the hole and the butted surfaces, on the basis, the shaft, the hole and the butted surfaces can be fitted, and the intersection points of the axes of the shaft and the hole and the respective butted surfaces are obtained, so that key points are obtained, point set matching is carried out on the key points of the two components, and the relative pose of the components can be obtained;
based on the above contents, the assembly pose evaluation is realized, a Monte Carlo method is adopted to carry out measurement simulation on the relative poses of most pieces, statistical analysis is carried out on the calculated relative poses, and the fluctuation amount of the relative poses is given;
the assembly quality is characterized by the assembly characteristic, and the minimum clearance between the shaft holes can be selected according to the assembly characteristic of the butt joint of the large components connected by the multiple shaft holes, wherein:
wherein d is1The minimum distance between the upper part of the front end of the butt joint shaft and the hole wall, d2Is the minimum distance r from the lower part of the front end of the butt joint shaft to the hole wallhAnd rsRespectively, the radii of the docking hole and the docking shaft, PsAnd PhRespectively representing the coordinates of the center points of the end surfaces of the butt joint hole and the butt joint shaft fpsAnd fphRespectively representing end surface normal vectors of the butt joint hole and the butt joint shaft;
the gap is more than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1,d2)>0；
The characteristic parameters are generated by performing least square fitting on target measuring points, and the uncertainty of the measuring points forms the measurement uncertainty of the characteristic after fitting adjustment; in the simulation system, the Monte Carlo method is adopted for resolving for multiple times, the results of the formula are solved by substituting n groups of measured values, the resolving results are changed due to the uncertainty of measurement, and the (d) is calculated1,d2)>Number n of 01Then the probability q that the assembly pose satisfies the assembly requirement can be expressed as:
q is the probability that the assembly clearance is larger than 0 in multiple measurements, the probability is output as an assembly pose evaluation result, and the minimum assembly probability A can be set according to the assembly requirement and is used as the minimum allowable assembly pose evaluation probability;
step six, when the assembly pose calculation result exists in min (d)1,d2)<Case of 0, i.e. n1The/n is not equal to 1, and when q is smaller than a set value A, the result of the assembly pose does not meet the assembly requirement based on the simulation analysis of a measurement system; turning to the seventh step; if the assembly pose calculation result has min (d)1,d2)>Case of 0, i.e. n1Q 1, or (d) is present1,d2)>Under the condition of 0 and when q is larger than a set value A, representing that the assembly pose result meets the assembly requirement, and turning to the step eight;
seventhly, re-adjusting the pose of the butt joint section of the device to be moved and the fixing device; and adjusting the posture of the section to be butted according to the resolved assembly posture result, wherein the adjusting process is as follows:
calculating coordinate value P of center point of butt joint end facesAnd PhCalculating the vector value fp of the normal of the butt joint end surface by using the difference components on three coordinate axessAnd fphAnd (3) synthesizing the two difference components by using the difference components of the movement amount caused on the three coordinate axes, and respectively moving and compensating the corresponding difference components of the moving device in three dimensions of lifting, left and right, front and back according to the synthesized difference components to ensure that the pose after adjustment meets the adjustment principle as follows:
the gap is larger than 0 in the butt joint process, so that the assembly can be smoothly finished without collision, namely min (d)1,d2)>0；
After the pose adjustment is finished, turning to the second step;
and step eight, finishing the pre-evaluation.
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| CN114812459A (en) * | 2022-03-10 | 2022-07-29 | 西安工业大学 | Large-scale part butt joint pose detection method |
| CN115310028B (en) * | 2022-07-21 | 2023-11-10 | 成都飞机工业（集团）有限责任公司 | Calculation method for uncertainty in measurement of included angle between axis of blind hole and plane |
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