Assembly precision analysis method for mechanical structure pitch axis system based on laser tracking measurement system

Abstract

The invention discloses an assembly precision analysis method based on a pitch axis system of a mechanical structure of a laser tracking measurement system. The method comprises the following steps: step 1, establishing a three-dimensional model of the pitch axis system of the mechanical structure of the laser tracking measurement system; 2, establishing a local coordinate system at the geometric center matched with each part of the laser tracking measurement system; and 3, according to the part assembly contact condition, carrying out laser tracking to measure the system assembly relationship, simplifying a parallel path in the overall deviation transmission path, and simplifying the parallel path into a main series transmission path to obtain a simplified tolerance transmission model. 4, establishing a Jacobian matrix aiming at the final functional target; and 5, calculating the influence on the precision of the final laser tracking measurement system by using the mechanical structure of the laser tracking measurement system. According to the method, the design requirement and the measurement precision of the pitch axis system of the laser tracking measurement system can be ensured.

Description

Technical Field

[0001] This invention relates to a method for analyzing the assembly accuracy of the pitch axis system of a laser tracking measurement system, and particularly to the assembly accuracy analysis method for the second-generation prototype of the laser tracking measurement system developed (application number / patent number: 201910459007.2, "A laser tracking measurement system with added counterweight balance and a standard ball as a reflective device"), belonging to the field of laser measurement. Background Technology

[0002] Mechanical assembly precision directly determines the performance, operational stability, and product consistency of equipment. High assembly precision effectively reduces the fit errors between parts, allowing transmission, positioning, and other functional mechanisms to operate in optimal condition, thereby improving the efficiency, lifespan, and reliability of the machinery. During manufacturing and assembly, mechanical systems are affected by multi-source errors, such as those related to the size, position, and geometry of parts, leading to the transmission and accumulation of assembly errors between components, ultimately impacting the overall assembly precision and quality of the mechanical system. Therefore, mechanical assembly precision is a crucial link connecting design, processing, and operational performance, and an indispensable core indicator for ensuring high-quality equipment operation. Effective and accurate prediction of assembly errors before product assembly is a key prerequisite for ensuring and improving the overall assembly performance of the machine.

[0003] Laser tracking measurement systems are commonly used devices based on laser measurement technology. Due to the tolerances inherent in the machining of mechanical parts, the geometric errors of each part are transmitted and accumulated through the assembly surfaces after all parts are assembled into a system. When errors exist between the shafts of the two-dimensional rotary mechanical structure of the laser tracking measurement system, they will affect the input angle of the tracking control system, leading to a decrease in tracking performance. Therefore, in order to ensure the measurement accuracy of the laser tracking measurement system and prevent shaft accuracy problems caused by assembly errors from directly affecting the accuracy of the measurement results, analyzing the assembly accuracy of the laser tracking measurement system is of great significance.

[0004] (Application No. / Patent No.: 201910459007.2 "A laser tracking measurement system with a standard ball as a reflective device and added counterweight balance") Based on the mechanical structure of this laser tracking measurement system, in order to determine the influence of the geometric tolerance of the mechanical structure parts on the final accuracy of the laser tracking measurement system during operation, it is necessary to propose a method for analyzing the assembly accuracy of the mechanical structure of the laser tracking measurement system. Before processing, the mechanical structure of this laser tracking measurement system should be further analyzed so as to predict the assembly accuracy error of the system's mechanical structure through this method, thereby improving the overall accuracy of the system during operation. Summary of the Invention

[0005] (Application No. / Patent No.: 201910459007.2 "A Laser Tracking Measurement System with a Standard Ball as a Reflector and Added Counterweight Balancing") Before processing the mechanical components of this laser tracking measurement system, the following issues need to be considered: the geometric tolerances generated during the processing of these mechanical components will accumulate and amplify as they are sequentially transferred to the final standard ball during assembly, leading to increased errors in the laser tracking measurement system. The purpose of this invention is to propose an assembly accuracy analysis method based on the Jacobi screw model error propagation principle of the mechanical structure of a laser tracking measurement system. This method is of great significance for improving the mechanical structure of the laser tracking measurement system and enhancing its tracking accuracy performance.

[0006] To achieve the above objectives, this invention adopts the following technical solution: It studies methods for analyzing assembly accuracy in laser tracking measurement systems and establishes an assembly accuracy model based on Jacobi-spin quantity for hybrid assembly structures of laser tracking measurement systems, and verifies the assembly accuracy through 3DCS Variation Analyst simulation. This includes the following steps:

[0007] Step 1: Create a 3D model of the pitch axis system of the mechanical structure of the laser tracking measurement system in the 3D software Inventor.

[0008] Step 2: Establish a global coordinate system at a suitable location on the assembly model, and establish a local coordinate system at the geometric center of each part mating in the laser tracking measurement system. If the contact surface is a circular plane, establish a local coordinate system at the center of the circle; if the contact surface is a rectangular plane, establish a local coordinate system at the midpoint of the length and width; if the contact surface is a cylindrical surface, establish a local coordinate system at the geometric center of the cylinder.

[0009] Step 3: Based on the assembly contact of the parts, perform assembly relationship analysis of the laser tracking measurement system, model the components, local coordinate system and functional pairs, and simplify the parallel path in the assembly relationship modeling. The parallel assembly features of local cylindrical surfaces and planes are simplified into series tolerance transfer paths. Then, the parallel paths in the overall deviation transfer path are simplified to the main series transfer paths to obtain the simplified tolerance transfer model.

[0010] Step 4: Based on the established local coordinate system, establish the Jacobian matrix for the final functional target: The Jacobian matrix is ​​established based on the coordinate system of the rotation axis established in Step 1, i.e.:

[0011]

[0012] 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.

[0013]

[0014] 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.

[0015]

[0016] 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. .

[0017] Then, based on the machining drawings of each part in the deviation transmission path, establish the screw model of each functional subdivision: For planar features, based on the Small Displacement Torsor (SDT) theory, its spatial pose change can be 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. Based on the positional tolerance t constraint, its screw model is:

[0018]

[0019] In the formula, and These are the lengths of the planar assembly surface along the x-axis and y-axis, respectively.

[0020] There are two types of parts containing 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]. TWhere 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 for the cylindrical feature is established as follows:

[0021]

[0022] In the formula, h represents the length of the cylindrical assembly feature.

[0023] Step 5: Calculate the Jacobi-spinator model based on the tolerance transfer path for the functional target to obtain the final six-degree-of-freedom tolerance range. Perform Monte Carlo uncertainty analysis using MATLAB to obtain the exact value of the final six-degree-of-freedom tolerance. This allows for the calculation of the influence of the mechanical structure of the laser tracking measurement system on the final accuracy of the laser tracking measurement system, resulting in the final deviation FR.

[0024] The technical solution described in this invention addresses the assembly accuracy analysis problem of the pitch axis system in a laser tracking measurement system. It proposes an improved method based on the Jacobi-spinator model and Monte Carlo analysis, providing theoretical support for high-precision assembly and error compensation. Finally, 3DCS Variation Analys software was used to verify the influence of the mechanical structure and geometric tolerances of the laser tracking measurement system's parts machining on the accuracy of the pitch axis system, ensuring the design requirements and measurement accuracy of the pitch axis system. Attached Figure Description

[0025] Figure 1 A complete model of the pitch axis mechanical structure;

[0026] Figure 2a Exploded view of parts showing the pitch axis tolerance transfer path;

[0027] Figure 2b Exploded view of parts showing the tolerance transfer path of the rotary shaft;

[0028] Figure 3a Schematic diagram of the pitch axis local coordinate system;

[0029] Figure 3b Schematic diagram of the local coordinate system of the rotation axis;

[0030] Figure 4a Schematic diagram of pitch axis assembly relationship;

[0031] Figure 4b Simplified schematic diagram of the pitch axis assembly relationship;

[0032] Figure 4c Schematic diagram of the assembly relationship of the rotary shaft;

[0033] Figure 4dSchematic diagram of the assembly relationship of the rotary shaft;

[0034] Figure 5 Monte Carlo uncertainty analysis image of pitch axis total tolerance; Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0036] The specific implementation process is as follows:

[0037] Step 1: Establish a 3D model of the mechanical structure of the laser tracking measurement system. Based on (Application No. / Patent No.: 201910459007.2 "A laser tracking measurement system with added counterweight balancing and a standard sphere as a reflective device"), establish a 3D model of the mechanical structure of the laser tracking measurement system in Inventor as follows: Figure 1 As shown.

[0038] Step Two: Create a 3D model of the mechanical structure of the laser tracking measurement system using Inventor software. Remove some complex parts such as screws, nuts, and springs. The pitch axis system mainly includes the pitch motor, pitch motor bracket, rotary support platform, U-shaped connecting rod, screws for the U-shaped connecting rod, T-shaped fine-tuning nut, V-groove connecting rod, guide rail plate, flange, rotary axis motor, vertical axis motor bracket, rotary motor support column, base plate, GCM-T13M2L, standard ball support plate, LMK13ML, T-shaped shaft, and standard ball. Establish the global coordinate system directly below the geometric center of the rotary motor on the surface of the base plate. Label the main components along the tolerance transfer path as follows: Figure 2a , Figure 2b As shown, a global coordinate system is established on the surface of the base plate, directly below the geometric center of the rotary motor. Local coordinate systems are established at the geometric centers of each component in the pitch axis system of the laser tracking measurement system. Coordinate system O0 is the local coordinate system for the pitch motor's central axis; coordinate systems O2 and O4 are the local coordinate systems for the planar assembly features of the pitch motor and its support; coordinate systems O1 and O3 are the local coordinate systems for the cylindrical assembly features of the pitch motor and its support; coordinate systems O5 and O6 are the local coordinate systems for the planar assembly features of the pitch motor support and the rotary motor support platform; and coordinate systems O7 and O8 are also included. 11 This is a local coordinate system for the assembly features of the rotary motor support platform and the screw cylinder. Coordinate system O 12 O 23 Local coordinate system for the assembly features of the screw and the U-shaped connecting rod cylinder. Coordinate system O 18 O 22 This is a local coordinate system for the planar assembly features of the screw and the U-shaped connecting rod. Coordinate system O8, O 14This is a local coordinate system for the assembly features of the rotary motor support platform and the screw cylinder. Coordinate system O 15 O 24 This is a local coordinate system for the assembly features of the screw and the U-shaped connecting rod cylinder. Coordinate system O 16 O 25 This is a local coordinate system for the planar assembly features of the screw and the U-shaped connecting rod. Coordinate system O 26 O 29 This is a local coordinate system for the assembly features of the U-shaped connecting rod and the guide plate. Coordinate system O 10 O 18 This is the local coordinate system for the assembly features of the rotary motor support platform and the T-shaped fine-tuning plane. Coordinate system O 19 O 20 This is the local coordinate system for the cylindrical assembly features of the T-type fine-tuning and horizontal fine-tuning nuts. Coordinate system O 21 O 28 This is a local coordinate system for the cylindrical assembly feature of the horizontal fine-tuning nut and the guide plate. Coordinate system O9, O 17 This is a local coordinate system for the assembly features of the rotary motor support platform and the V-shaped connecting groove cylinder. Coordinate system O 17 O 27 This is a local coordinate system for the V-shaped connecting groove and the cylindrical guide plate assembly feature. Coordinate system O 30 O 31 This is a local coordinate system for the assembly features of the guide rail plate and the flange plane. Coordinate system O 32 O 33 This is a local coordinate system for the planar assembly features of the flange and the rotary shaft motor. Coordinate system O 34 For the local coordinate system of the planar assembly features of the rotary axis motor and the vertical axis motor bracket, coordinate system O 35 This is a local coordinate system at the center of a standard sphere. The assembly deviation of the pitch axis system is the deviation between coordinate system O0 and coordinate system O36 in the X and Z axes. For example... Figure 3a , Figure 3b As shown.

[0039] Step 3: Model the assembly relationship of the laser tracking measurement system based on the tolerance transfer path, as follows: Figure 4a , Figure 4c As shown, square patterns represent mechanical components, circular patterns represent local coordinate systems, IFE represents internal functional pairs, CFE represents contact functional pairs, and PFE represents parallel functional pairs on parallel transmission paths. The simplification of the cylindrical parallel assembly feature and the simplification of the parallel path and main path are also addressed. Simultaneously, the constrained direction takes the intersection of two values. The planar feature's dz and the cylindrical feature's dx and dy do not intersect, so the translational degree of freedom parameters take the union of the two feature screw parameters. The simplified formula is as follows:

[0040]

[0041] In the formula, T′ is the screw of the planar feature; T″ is the screw of the cylindrical feature. The simplification of parallel paths and main paths is similar. Figure 4a In the laser tracking measurement system, there are numerous parallel error transmission paths in the pitch axis system.

[0042]

[0043] After simplification, we obtain the assembly relationship diagram and the simplified functional components. Figure 4b , Figure 4d As shown, the final laser tracking measurement system pitch axis series tolerance transfer path is:

[0044]

[0045] Step 4: Based on the local coordinate system established in Step 2, establish the Jacobian matrix for the final functional objective.

[0046]

[0047] in This represents the coordinate transformation matrix of local coordinate system i relative to global coordinate system O.

[0048]

[0049] In formula (2): ; ; ;n represents the target feature assembly function requirements; This represents the position coordinates of the origin of the i-th local coordinate system in the global coordinate system.

[0050] Then, based on the machining drawings of each part in the deviation transmission path, screw models for each functional subdivision are established. Table 1 shows some of the Jacobi-screw model establishment data.

[0051] Table 1. Jacobi spinor model for pitch axis

[0052]

[0053] Step 5: Calculate the Jacobi-spinator model based on the tolerance transfer path for the functional objective to obtain the final six-degree-of-freedom tolerance range:

[0054]

[0055] Use MATLAB to edit the matrix calculation program, and combine the Jacobian matrix calculated in step four with the data from the screw model according to... Figure 4b , Figure 4c The calculations are performed in sequence to obtain the final six-degree-of-freedom deviation of the pitch motor of the laser tracking measurement system relative to the standard sphere.

[0056]

[0057] Based on MATLAB, the above equations were calculated using the Jacobi spinor model calculation method proposed earlier. The Monte Carlo method was used to simulate 5000 deviation propagation processes. First, the mean and standard deviation of each vector in the spinor of each calculation formula were calculated, and random numbers were generated. Then, the calculated mean and standard deviation were used to generate random numbers, thus obtaining the reliable six-degree-of-freedom deviation based on the Monte Carlo uncertainty analysis method. Next, according to the shape and definition of the concentricity tolerance domain of a point, the pitch axis coaxiality deviation can be obtained by using the cumulative deviation of the translation vectors in the X and Z directions in FR. Its expression is:

[0058]

[0059] The influence of the mechanical structure of the laser tracking measurement system on the final accuracy of the laser tracking measurement system was calculated. The coaxiality deviation was solved by analyzing 5000 simulation results, as shown below. Figure 5 As shown, the pitch axis coaxiality deviation fluctuates between 0.037 mm and 0.039 mm, with an average deviation of 0.038 mm.

Claims

1. A method for analyzing the assembly accuracy of the pitch axis system of a mechanical structure based on a laser tracking measurement system, characterized in that, Includes the following steps: Step 1: Create a 3D assembly model of the pitch axis system of the mechanical structure of the laser tracking measurement system in the 3D software Inventor; Step 2: Establish a global coordinate system in the 3D assembly model, and establish a local coordinate system at the geometric center of each part mating in the laser tracking measurement system; if the contact surface is a circular plane, establish a local coordinate system at the center of the circle; if the contact surface is a rectangular plane, establish a local coordinate system at the midpoint of the length and width; if the contact surface is a cylindrical surface, establish a local coordinate system at the geometric center of the cylinder. Step 3: Based on the assembly contact of the parts, perform assembly relationship of the laser tracking measurement system, model the components, local coordinate system and functional pairs, and simplify the parallel path in the assembly relationship modeling. The parallel assembly features of local cylindrical surface and plane are simplified into series tolerance transfer path. Then, the parallel path in the overall deviation transfer path is simplified into series transfer path to obtain the simplified tolerance transfer model. Step 4: Based on the established local coordinate system, establish the Jacobian matrix for the final functional target: Establish the Jacobian matrix based on the coordinate system of the rotation axis established in Step 1; Step 5: Calculate the Jacobi-spinator model based on the tolerance transfer path for the functional target to obtain the final six-degree-of-freedom tolerance range. Perform Monte Carlo uncertainty analysis using MATLAB to obtain the exact value of the final six-degree-of-freedom tolerance. This allows for the calculation of the influence of the mechanical structure of the laser tracking measurement system on the final accuracy of the laser tracking measurement system, resulting in the final deviation FR.

2. The assembly accuracy analysis method for the pitch axis system of a mechanical structure based on a laser tracking measurement system according to claim 1, characterized in that, The Jacobian matrix in step four 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. ; Then, based on the machining drawings of each part in the deviation transmission path, establish the screw model of each functional subdivision: For planar features, based on the small displacement screw theory (SDT), its spatial pose change can be 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; according to the constraint of the 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.

3. The assembly accuracy analysis method for the pitch axis system of a mechanical structure based on a laser tracking measurement system according to claim 1, characterized in that, Local coordinate systems are established at the geometric centers of each component in the pitch axis system of the laser tracking measurement system. Coordinate system O0 is the local coordinate system for the pitch motor central axis; coordinate systems O2 and O4 are the local coordinate systems for the planar assembly features of the pitch motor and its support; coordinate systems O1 and O3 are the local coordinate systems for the cylindrical assembly features of the pitch motor and its support; coordinate systems O5 and O6 are the local coordinate systems for the planar assembly features of the pitch motor support and the rotary motor support platform; coordinate systems O7 and O8 are also local coordinate systems for the planar assembly features of the pitch motor support and the rotary motor support platform. 11 The local coordinate system for the rotary motor support platform and the screw cylinder assembly features; coordinate system O 12 O 23 Local coordinate system for the assembly features of the screw and the U-shaped connecting rod cylindrical joint; coordinate system O 18 O 22 A local coordinate system for the planar assembly features of the screw and the U-shaped connecting rod; coordinate system O8, O 14 The local coordinate system for the rotary motor support platform and the screw cylinder assembly features; coordinate system O 15 O 24 A local coordinate system for the assembly features of the screw and the U-shaped connecting rod cylindrical part; coordinate system O 16 O 25 A local coordinate system for the planar assembly features of the screw and the U-shaped connecting rod; coordinate system O 26 O 29 A local coordinate system for the planar assembly features of the U-shaped connecting rod and the guide plate; coordinate system O 10 O 18 The local coordinate system for the assembly features of the rotary motor support platform and the T-shaped fine-tuning plane; coordinate system O 19 O 20 The local coordinate system for the cylindrical assembly features of the T-type fine-tuning and horizontal fine-tuning nuts; coordinate system O 21 O 28 A local coordinate system for the cylindrical assembly features of the horizontal fine-tuning nut and the guide plate; coordinate system O9, O 17 A local coordinate system for the assembly features of the rotary motor support platform and the V-shaped connecting groove cylinder; coordinate system O 17 O 27 A local coordinate system for the V-shaped connecting groove and the cylindrical assembly feature of the guide plate; coordinate system O 30 O 31 A local coordinate system for the planar assembly features of the guide rail plate and flange; coordinate system O 32 O 33 A local coordinate system for the planar assembly features of the flange and the rotary shaft motor; coordinate system O 34 For the local coordinate system of the planar assembly features of the rotary axis motor and the vertical axis motor bracket, coordinate system O 35 The local coordinate system is the center of the standard sphere; the assembly deviation of the pitch axis system is the deviation between coordinate system O0 and coordinate system O36 in the X and Z axis directions.

4. The assembly accuracy analysis method for the pitch axis system of a mechanical structure based on a laser tracking measurement system according to claim 1, characterized in that, In step three, the assembly relationship of the laser tracking measurement system is modeled according to the tolerance transfer path. The square pattern represents mechanical components, the circular pattern represents the local coordinate system, IFE is the internal functional pair, CFE is the contact functional pair, and PFE is the parallel functional pair on the parallel transfer path. The model simplifies the parallel assembly features of the cylindrical surface and the parallel path with the main path. Simultaneously, the direction with constraints is taken as the intersection of two values. The dz of the planar feature does not intersect with the dx and dy of the cylindrical feature, so the translational degree of freedom parameter is taken as the union of the two feature screw parameters. The simplified formula is as follows: ； In the formula, T′ is the screw of the planar feature; T″ is the screw of the cylindrical feature; the pitch axis system of the laser tracking measurement system has parallel deviation transmission paths. ; ; ; ； The final pitch axis series tolerance transfer path for the laser tracking measurement system is as follows: ； Step 4: Based on the local coordinate system established in Step 2, establish the Jacobian matrix for the final functional objective. ； in Represents the coordinate transformation matrix of local coordinate system i relative to global coordinate system O; ； In formula (2): ; ; ;n represents the target feature assembly function requirements; This represents the position coordinates of the origin of the i-th local coordinate system in the global coordinate system. Then, based on the machining drawings of each part in the deviation transmission path, establish the spinor model of each functional sub-component.

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