Assembly precision analysis method based on mechanical structure of laser tracking measurement system

Abstract

The invention discloses an assembly precision analysis method based on a mechanical structure of a laser tracking measurement system, and in the laser tracking measurement system, the high precision guarantee of the assembled mechanical system is the premise of realizing accurate measurement. In order to obtain the assembly precision of a mechanical structure of a laser tracking and measuring system, the invention provides an assembly precision analysis method based on Jacobian aiming at a universal joint type two-dimensional rotary mechanical structure of the laser tracking and measuring system. A Jacobian matrix model in a deviation transfer process is combined with a spinor model comprising plane features, cylinder features, plane and cylinder parallel features and plane and plane parallel features, and a shafting assembly precision analysis model of the laser tracking measurement system is established. And a calculation result is subjected to Monte Carlo simulation to simulate an actual assembly error. A result shows that the precision of a rotary shaft system is 3 microns, and the precision of a pitch shaft system is 10 microns. The result shows that the provided method can qualitatively analyze the assembly precision of the laser tracking measurement system.

Description

TECHNICAL FIELD

[0001] The application relates to a kind of assembly precision analysis methods of laser tracking measurement system mechanical structure, especially for (application number / patent number: CN202210191793.4 of "a kind of folding optical path's laser tracking measurement mechanical system") the assembly precision analysis method of laser tracking measurement system three generation prototype gimbaling two-dimensional rotary mechanical structure developed and developed, belongs to laser measurement field. BACKGROUND

[0002] The overall performance of a precision mechanical system is determined by product design, manufacturing and assembly. With the significant improvement of the design level and manufacturing capacity of parts and components, the machining precision can often reach the level of precision or even super-precision. However, the performance of the assembled system is still difficult to be fully guaranteed. Due to the influence of multi-source errors such as size, position and geometric shape of parts during manufacturing and assembly, assembly error transmission and deviation accumulation effects occur between parts of the system, which ultimately affect the assembly precision and quality of the entire mechanical system. Therefore, for high-end complex precision mechanical systems, effective and accurate assembly error prediction before product assembly is the key prerequisite to guarantee and improve the overall assembly performance.

[0003] The laser tracking measurement system is a portable three-dimensional coordinate measurement system, mainly composed of a two-dimensional rotary mechanical mechanism capable of automatic tracking and an optical measurement system. When there is an error between the shaft systems of the two-dimensional rotary mechanical structure of the laser tracking measurement system, it will affect the input angle of the tracking control system, resulting in reduced tracking performance. Therefore, in order to ensure the measurement accuracy of the laser tracking measurement system and prevent the shaft system precision problem caused by assembly error from directly affecting the accuracy of the measurement results, it is of great significance to analyze the assembly precision of the laser tracking measurement system.

[0004] ( Application number / patent number: CN202210191793.4 of "a kind of folding optical path's laser tracking measurement mechanical system"), based on the characteristics of the gimbaling two-dimensional rotary mechanical structure of the laser tracking measurement system, in order to obtain the assembly precision of the laser tracking measurement system, a kind of assembly precision analysis method based on Jacobian rotation is proposed. Through this method, a Jacobian rotation model considering parallel cooperation structure between cylindrical surface and plane and multi-plane parallel structure is established, and finally the shaft system precision of the two-dimensional rotary mechanical structure of the laser tracking measurement system is obtained. SUMMARY

[0005] (Appl.No. / Patent No.: CN202210191793.4, "Laser tracking measurement mechanical system of folded optical path"), the laser tracking measurement system can track the target target in real time to realize the coordinate measurement of the space target. It is mainly composed of a gimbal type two-dimensional rotation system and an optical measurement system. The accuracy of the shaft system caused by the assembly error directly affects the accuracy of the measurement result. Therefore, in order to analyze the influence of the shaft system accuracy on the measurement result and the tracking control, the shaft system accuracy of the laser tracking measurement system after assembly should be obtained first. The purpose of the present application is to provide an assembly accuracy analysis method for the gimbal type two-dimensional rotation mechanical structure of the laser tracking measurement system, which is of great significance for qualitatively analyzing the assembly accuracy of the laser tracking measurement system and subsequently compensating the measurement result to improve the accuracy.

[0006] To achieve the above purpose, the present application adopts the following technical solutions: analyzing the assembly error transmission path according to the assembly characteristics of the gimbal type two-dimensional rotation mechanical structure of the laser tracking measurement system, then establishing a Jacobian rotation model according to the assembly relationship of each part, and finally simulating the accumulated deviation value in the actual assembly process through Monte Carlo simulation. The steps include:

[0007] Step one: establish a three-dimensional model of the rotation shaft system mechanical structure of the laser tracking measurement system in the three-dimensional software Inventor. According to the judgment of the related functional elements of the rotation shaft system assembly, establish a local coordinate system on each related functional element.

[0008] Step two: analyze the assembly deviation transmission path of the laser tracking measurement system rotation shaft, simplify the deviation transmission chain based on the function priority, extract the key dimension chain and constraint relationship, simplify the cylindrical surface parallel assembly feature and the plane parallel assembly feature, and establish the assembly connection diagram of the rotation shaft system.

[0009] Step three: establish the Jacobian matrix according to the coordinate system of the rotation shaft system established in step one, that is:

[0010]

[0011] In the formula, is the direction vector of the i-th local coordinate system to the global coordinate system; is the tilt symmetry position matrix of the i-th local coordinate system.

[0012]

[0013] In the formula, [Dv xi ] 3×1 is the unit direction vector of the x-axis of the local coordinate system i relative to the x-axis of the global coordinate system; [Dv yi ]3×1 is the unit direction vector of the y-axis of the local coordinate system i with respect to the y-axis of the global coordinate system. zi ] 3×1 is the unit direction vector of the z-axis of the local coordinate system i with respect to the z-axis of the global coordinate system.

[0014]

[0015] wherein, is the position vector of the i-th local coordinate system to the x-axis direction of the global coordinate system, ; is the position vector of the i-th local coordinate system to the y-axis direction of the global coordinate system, ; is the position vector of the i-th local coordinate system to the z-axis direction of the global coordinate system, .

[0016] Step four: according to the obtained assembly connection diagram of the rotary axis system, a torsor model of the rotary axis system is established, which is calculated based on the assembly connection diagram, especially along the main path. For planar features, based on the small displacement torsor (SDT) theory, the spatial pose change can be simplified as a three-dimensional parameter vector T = [0, 0, w, a, b, 0] T . Wherein, w is the translation deviation in the Z-axis direction, a and b are the rotation deviations around the X-axis direction and the Y-axis direction, respectively. According to the constraint of the position tolerance t, the torsor model is:

[0017]

[0018] wherein, and are the lengths of the planar assembly surface along the x-axis and the y-axis, respectively.

[0019] Parts containing cylindrical features include shaft parts and hole parts. Based on the small displacement torsor theory, the spatial pose change can be simplified as a four-dimensional parameter vector T = [u, v, 0, a, b, 0] T . Wherein, u and v represent the translation deviations along the X-axis and Y-axis directions, and a and b represent the rotation deviations around the X-axis direction and Y-axis direction, respectively. Based on the dimension tolerance t of the cylindrical surface, the small displacement torsor variation range of the cylindrical feature is:

[0020]

[0021] wherein, h represents the length of the cylindrical assembly feature.

[0022] Step five: According to the assembly connection diagram of the rotating shaft system, the Jacobian matrix of the rotating shaft system and the screw are brought into the final Jacobian screw model to obtain the final deviation FR. The Monte Carlo method is used to simulate the normal distribution of the deviation transmission process. The mean and standard deviation of each vector in the screw are calculated, which are used as the generation parameters of random numbers, and the calculation formulas are as follows:

[0023]

[0024]

[0025] In the formula, μ is the mean of the vector in the screw; σ is the standard deviation of the vector in the screw; V SU is the upper limit of the variable range of the vector in the screw; V SL is the lower limit of the variable range of the vector in the screw; Z is the standardized normal number.

[0026] Step six: A three-dimensional model of the mechanical structure of the pitch axis system of the laser tracking measurement system is established in the three-dimensional software Inventor. According to the mechanical structure, the related functional elements of the pitch axis system assembly are judged, and a local coordinate system is established on each related functional element.

[0027] Step seven: The pitch axis assembly deviation transmission path of the laser tracking measurement system is analyzed, the deviation transmission chain is simplified based on the function priority, the key size chain and constraint relationship are extracted, the multi-plane parallel assembly characteristics are simplified, and the assembly connection diagram of the pitch axis system is established.

[0028] Step eight: The Jacobian matrix of the pitch axis system is established according to the method of constructing the Jacobian matrix of the rotating shaft system in step three.

[0029] Step nine: According to the obtained assembly connection diagram of the pitch axis system, the screw model of the pitch axis system is constructed, and the construction method is the same as that of the rotating shaft system screw model.

[0030] Step ten: According to the assembly connection diagram of the pitch axis system, the Jacobian matrix of the pitch axis system and the screw are brought into the final Jacobian screw model to obtain the final deviation FR, and the Monte Carlo method is used to simulate the normal distribution of the deviation transmission process. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 Coordinate system diagram of the rotating shaft system;

[0032] Figure 2 Assembly connection relationship diagram of the simplified rotating shaft system;

[0033] Figure 3 Parallel feature diagram of the plane and the cylinder;

[0034] Figure 4 Parallel plane-to-plane feature map;

[0035] Figure 5 Y1O1Z1 plane analysis point deviation map;

[0036] Figure 6 X1O1Z1 plane analysis point deviation map;

[0037] Figure 7 Coaxiality deviation analysis map;

[0038] Figure 8 Rotary shaft system coaxiality deviation simulation result;

[0039] Figure 9 Coordinate system diagram of the pitch shaft system;

[0040] Figure 10 Simplified pitch shaft system assembly connection relationship diagram;

[0041] Figure 11 Pitch shaft system coaxiality deviation simulation result; DETAILED DESCRIPTION

[0042] The application will be further described in detail below with reference to the accompanying drawings, so that those skilled in the art can implement the application according to the description.

[0043] The specific implementation process is as follows:

[0044] Step 1: Establish a three-dimensional model of the rotary shaft system mechanical structure of the laser tracking measurement system in the three-dimensional software Inventor according to (application number / patent number: CN202210191793.4 “laser tracking measurement mechanical system of folded optical path”). Figure 1 As shown in the figure, since the installation of the entire system mechanical structure is taken as the bottom surface of the base as the reference, the reference coordinate system (global coordinate system) is established at the geometric center of the base. The coordinate system O H1 , O H2 is the local coordinate system of the standard ball fixed column and the base cylindrical surface assembly feature. The coordinate system O H3 , O H4 is the local coordinate system of the base and the standard ball fixed column and the motor base plane assembly feature. The coordinate system O H5 , O H6 , O H7 is the local coordinate system of the motor base and the motor support plate plane assembly feature. The coordinate system O H8 , O H9 , O H10 , O H11 , O H12 , OH13 H14 H15 O is the local coordinate system of the cylindrical surface assembly feature of the motor base and the positioning pin. The coordinate system O H16 H17 H18 H19 H20 H21 H22 H23 O is the local coordinate system of the cylindrical surface assembly feature of the motor support plate and the positioning pin. The coordinate system O H24 H25 H26 H27 H28 H29 H30 H31 O is the local coordinate system of the planar assembly feature of the motor support plate and the rotary motor fixing plate. The coordinate system O H32 H33 O is the local coordinate system of the planar assembly feature of the rotary motor fixing plate and the rotary motor. The coordinate system O H34 H35 O is the local coordinate system of the cylindrical surface assembly feature of the standard ball and the standard ball fixing column. The coordinate system O H36 H37 O is the local coordinate system of the planar assembly feature of the standard ball and the standard ball fixing column. The coordinate system O H38 O is the local coordinate system of the ball center of the standard ball. The coordinate system O H39 O is the rotary shaft coordinate system of the rotary motor. The assembly deviation of the rotary shaft system is the deviation between the coordinate system O H38 and the coordinate system O H39 in the X-axis and Y-axis directions.

[0045] Step two: analyze the rotary shaft assembly deviation transmission path of the laser tracking measurement system, simplify the cylindrical parallel assembly feature and the planar parallel assembly feature, and in order to solve the matrix transformation problem, change the starting point, change the assembly relationship established according to the actual reference to the assembly relationship with the standard ball center as the reference, and get the assembly connection relationship diagram of the rotary shaft system as shown in Figure 2 The main path of the deviation transmission of the standard ball center rotary shaft and the rotary motor shaft is: IFE1-CFE1-IFE2-CFE2-CFE3-PFE1-(PFE 12 , PFE 13 )- (PFE 14 , PFE 15 ​​​​​​​​​​​​​​​​​​​) - CFE6 - IFE9 - FR. Some parallel paths are also included: CFE3 - PFE2 - PFE4 - IFE3 - PFE6 - IFE5 - PFE 10 - CFE4 - IFE7 - CFE6 and CFE3 - PFE3 - PFE5 - IFE4 - PFE7 - IFE6 - PFE 11 - CFE5 - IFE8 - CFE6.

[0046] Step three: The Jacobian model of the rotating shaft system is established based on the local coordinate system diagram of the rotating shaft system main path and the assembly connection relationship diagram. The construction of the Jacobian matrix is based on formula 1. The local coordinate system is established at the geometric center of the contact feature between each functional component and its adjacent functional component. The upper right matrix in the formula is obtained by subtracting the local coordinate system of each functional component from the local coordinate system of the last functional component. The matrix on the main diagonal is the unit matrix, because the XYZ axes of each local coordinate system are aligned with the global coordinate system, so no rotation transformation is needed.

[0047] Step four: The establishment of the screw, which is calculated according to the assembly connection diagram, especially along the main path. The screw value is determined by the different assembly types of each functional pair in the functional component. For parallel and cylindrical features, as shown in Figure 3 , only the rotation deviation around Y is retained. The result of adding these two screws is still a screw, because in fact there is interaction between the two parts, the rotation movement of the cylindrical feature will be affected by the rotation movement of the planar feature. In order to avoid interference in this assembly, the rotation parameters in the screw must be determined by the minimum value between the two feature screws before the change. The w of the planar feature and the u and v of the cylindrical feature have no intersection, so the movement freedom parameter takes the union of the two feature screw parameters. Therefore, the new screw can be represented as:

[0048]

[0049] In the formula, T' is the screw of the planar feature; T" is the screw of the cylindrical feature.

[0050] For parallel and parallel features, as shown in Figure 4 , when the normal vector directions of the three planes are the same, this matching relationship is the same as that of two planes, which restricts three degrees of freedom, so the pose change of the upper surface of the part can be represented by three parameters [w, a, b], T = [0, 0, w, a, b, 0] T . Figure 5The diagram shows the deviation of the mating plane within the Y1O1Z1 plane. With the plane center point M0 as the theoretical analysis point, M0C0 as the offset along the Z-axis, and ∠CB1A1 as the rotational deviation along the X-axis, since the value of α is very small, it can be written as:

[0051]

[0052] M0C0 can be obtained through trigonometric relationships:

[0053]

[0054]

[0055]

[0056] like Figure 6 The diagram shows the deviation of the mating plane within the X1O1Z1 plane. The center point M0 of the plane is taken as the theoretical analysis point, and ∠P1P2N1 represents the rotational deviation along the Y-axis.

[0057] Since the value of β is very small, it can be written as:

[0058]

[0059] Therefore, the spinor of the parallel characteristics of planes is expressed as:

[0060]

[0061] Step 5: According to Figure 2 The assembly connection diagram of the rotary shaft system shown is used to input the corresponding Jacobian matrix and screw into the final Jacobian screw model to obtain the final deviation FR of the rotary shaft system.

[0062]

[0063] The Monte Carlo method was used to simulate the deviation propagation process based on a normal distribution. The functional units of each level of the rotary shaft system assembly were simplified as cylinders. A schematic diagram of the coaxiality deviation during assembly is shown below. Figure 7 As shown. By setting up a global coordinate system and a local coordinate system, the cumulative deviation of the origin of the local coordinate system of each functional element in the global coordinate system can be obtained.

[0064] Based on the shape and definition of the concentricity tolerance domain of the points, and by using the cumulative deviations in the X and Y directions of the translation vectors from the FR calculation results, the coaxiality deviation of the rotating shaft system can be obtained, and its expression is:

[0065]

[0066] The coaxiality deviation was determined by analyzing 5000 simulations, and the results are as follows: Figure 8 As shown, the coaxiality deviation of the rotary shaft system fluctuates between 0.001 mm and 0.005 mm, with an average coaxiality deviation of 0.003 mm.

[0067] Step Six: Based on the patent application (Application No. / Patent No.: CN202210191793.4) ​​entitled "A Laser Tracking Measurement Mechanical System with Folded Optical Path", establish a 3D model of the pitch axis mechanical structure of the laser tracking measurement system in the 3D software Inventor. Establish local coordinate systems on each relevant functional element, such as... Figure 9 As shown. Since the entire pitch axis system is mounted on the rotary motor based on the rotary flange, the accuracy of the rotary axis system will be carried over to the pitch axis system. Therefore, the reference coordinate system of the pitch axis system will be established at the geometric center of the rotary motor. Coordinate system O P0 O P1 This is a local coordinate system for the planar assembly features of the rotary motor and the rotary flange. Coordinate system O P2 O P3 O P4 O P5 O P6 O P7 This is a local coordinate system for the planar assembly features of the slewing flange and the pitch motor mounting bracket. Coordinate system O P8 O P9 This is the local coordinate system for the cylindrical assembly feature of the pitch motor mounting bracket and the pitch motor. Coordinate system O P10 O P11 O P12 This is a local coordinate system for the planar assembly features between the pitch motor mounting bracket and the pitch motor auxiliary fixation. Coordinate system O P13 O P14 O P15 This is a local coordinate system for the cylindrical surface assembly feature between the pitch motor and its auxiliary fixing point. Coordinate system O P17 Let O be a local coordinate system of the center of a standard sphere. P16 For the pitch axis coordinate system of the rotary motor, the assembly deviation of the pitch axis system is the coordinate system O. P16 With coordinate system O P17 The deviation between them in the Y-axis and Z-axis directions.

[0068] Step 7: Analyze the pitch axis assembly deviation transmission path of the laser tracking measurement system, simplify the multi-plane parallel assembly characteristics, and obtain the assembly connection diagram of the pitch axis system as shown below. Figure 10The main path for transmitting the deviation between the pitch axis and the pitch axis motor shaft at the standard ball center is: CFE1–CFE2–IFE1–CFE3–IFE2–PFE1–CFE4–PFE8–FR. This also includes some parallel paths: IFE2–PFE2–PFE4–PFE6–PFE9 and IFE2–PFE3–PFE5–PFE7–PFE9.

[0069] Step 8: Based on the local coordinate system diagram of the pitch axis main path and the assembly connection diagram, establish the Jacobian screw model of the rotation axis. The method for constructing the Jacobian matrix is ​​the same as that for the rotation axis.

[0070] Step Nine: The method for constructing the pitch axis spin is the same as the method for constructing the rotation axis spin in Step Four.

[0071] Step 10: According to Figure 10 The assembly connection diagram of the pitch axis system is shown. Substituting the corresponding Jacobian matrix and screw into the final Jacobian screw model, we obtain the final deviation FR of the pitch axis system.

[0072]

[0073] By accumulating the deviations in the Y and Z directions of the translational vectors in FR, the range of coaxiality deviation of the pitch axis system can be obtained, and its expression is:

[0074]

[0075] The coaxiality deviation was solved by simulating 5000 pitch axis simulations using the Monte Carlo method. The results are as follows: Figure 11 As shown, the coaxiality deviation of the pitch axis fluctuates between 0.009 mm and 0.011 mm, with an average coaxiality deviation of 0.010 mm.

Claims

1. A method for analyzing the assembly accuracy of mechanical structures based on a laser tracking measurement system, characterized in that: Includes the following steps: Step 1: Create a 3D model of the rotary shaft system mechanical structure of the laser tracking measurement system in the 3D software Inventor; determine the relevant functional elements of the rotary shaft system assembly based on the mechanical structure, and establish a local coordinate system on each relevant functional element; Step 2: Analyze the propagation path of the rotary shaft assembly deviation in the laser tracking measurement system, simplify the deviation propagation chain based on functional priority, extract the key dimension chain and constraint relationship, simplify the cylindrical parallel assembly features and planar parallel assembly features, and establish the assembly connection diagram of the rotary shaft system. Step 3: Establish the Jacobian matrix based on the coordinate system of the rotation axis established in Step 1; Step 4: Establish the screw model of the rotary shaft system based on the obtained assembly connection diagram. The calculation is based on the assembly connection diagram. For planar features, based on the small displacement screw theory (SDT), its spatial pose change is simplified to a three-dimensional parameter vector T=[0,0,w,α,β,0]. T Where w is the translational deviation in the Z-axis direction, and α and β are the rotational deviations around the X-axis and Y-axis directions, respectively; Step 5: Based on the assembly connection diagram of the rotary shaft system, substitute the Jacobian matrix and screw of the rotary shaft system into the final Jacobian screw model to obtain the final deviation FR; use the Monte Carlo method to simulate the deviation propagation process based on the normal distribution; Step 6: Create a 3D model of the pitch axis mechanical structure of the laser tracking measurement system in the 3D software Inventor; determine the relevant functional elements of the pitch axis assembly based on the mechanical structure, and establish a local coordinate system on each relevant functional element; Step 7: Analyze the pitch axis assembly deviation transmission path of the laser tracking measurement system, simplify the deviation transmission chain based on functional priority, extract key dimension chains and constraint relationships, simplify the multi-plane parallel assembly features, and establish the assembly connection diagram of the pitch axis system. Step 8: Construct the Jacobian matrix of the pitch axis system using the method described in Step 3 for constructing the Jacobian matrix of the rotation axis system; Step 9: Construct the screw model of the pitch axis system based on the obtained assembly connection diagram of the pitch axis system. The construction method is the same as that of the screw model of the rotation axis system. Step 10: Based on the assembly connection diagram of the pitch axis system, substitute the Jacobian matrix and screw of the pitch axis system into the final Jacobian screw model to obtain the final deviation FR, and use the Monte Carlo method to simulate the deviation propagation process based on the normal distribution.

2. The assembly accuracy analysis method for mechanical structures based on a laser tracking measurement system according to claim 1, characterized in that: The Jacobian matrix in step three is: ； In the formula, Let i be the direction vector from the i-th local coordinate system to the global coordinate system; Let be the tilt-symmetric position matrix of the i-th local coordinate system; ； In the formula, [Dv xi ] 3×1 [Dv] is the unit direction vector of the x-axis of the local coordinate system i relative to the x-axis of the global coordinate system; yi ] 3×1 [Dv] is the unit direction vector of the y-axis of the local coordinate system i relative to the y-axis of the global coordinate system; zi ] 3×1 Let z be the unit direction vector of the z-axis of the local coordinate system i relative to the z-axis of the global coordinate system; ； In the formula, Let be the position vector along the x-axis from the i-th local coordinate system to the global coordinate system. ; Let be the position vector along the y-axis from the i-th local coordinate system to the global coordinate system. ; Let i be the position vector in the z-axis direction from the i-th local coordinate system to the global coordinate system. .

3. The assembly accuracy analysis method for mechanical structures based on a laser tracking measurement system according to claim 1, characterized in that: In step four, based on the constraint of positional tolerance t, its screw model is: ； In the formula, and These are the lengths of the planar assembly surface along the x-axis and y-axis, respectively; There are two types of parts that contain cylindrical features: shaft parts and hole parts. Based on the small displacement spinor theory, their spatial pose change can be simplified to a four-dimensional parameter vector T=[u,v,0,α,β,0]. T Where u and v represent translational deviations along the X and Y axes, and α and β represent rotational deviations around the X and Y axes, respectively; based on the dimensional tolerance t of the cylindrical surface, the range of small displacement spin variation of the cylindrical feature is established as follows: ； In the formula, h represents the length of the cylindrical assembly feature.

4. The assembly accuracy analysis method for mechanical structures based on a laser tracking measurement system according to claim 1, characterized in that: In step four, the mean and standard deviation of each vector in the spinor are calculated and used as parameters for generating random numbers. The calculation formulas are as follows: ； ； In the formula, μ is the mean of the spinor vector; σ is the standard deviation of the spinor vector; V SU V is the upper limit of the range of variation of the vector in the spinor. SL Z is the lower limit of the range of variation of the vector in the spinor; Z is the standardized normal number.

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