Assembly precision analysis method for mechanical structure rotating shaft system based on laser tracking measurement system

Abstract

The invention discloses an assembly precision analysis method for a rotary shaft system of a mechanical structure based on a laser tracking measurement system, and in the laser tracking measurement system, the high precision guarantee of an assembled mechanical system is the premise of realizing accurate measurement. In order to obtain the assembly precision of a laser tracking measurement system, the invention provides an assembly precision analysis method based on Jacobi-spinor for a rotary shaft mechanical structure of the laser tracking measurement system. A Jacobian matrix model in the deviation transfer process and a spinor model comprising plane features, cylinder features and plane and cylinder parallel features are combined, a laser tracking measurement system rotating shaft assembly precision analysis model is established, and Monte Carlo simulation is adopted for calculation results to simulate actual assembly errors. A result shows that a difference value between a theoretical assembling condition and an analogue simulation actual assembling condition is 6.79 microns. The result shows that the provided method can qualitatively analyze the assembly precision of the rotating shaft of the laser tracking measurement system.

Description

A Method for Analyzing Assembly Accuracy of Rotating Shaft Systems in Mechanical Structures Based on Laser Tracking Measurement System Technical Field

[0001] This invention relates to a method for analyzing the assembly accuracy of the rotary shaft system of the mechanical structure of a laser tracking measurement system, and in particular 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 added counterweight balancing and a standard ball as a reflective device") Based on the mechanical structure of the rotary shaft system 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, it is necessary to propose a method for analyzing the assembly accuracy of the mechanical structure of the rotary shaft system of the laser tracking measurement system. Before processing, the mechanical structure of this laser tracking measurement system is 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 a Jacobi-spinner model assembly accuracy analysis method based on the Jacobi-spinner 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 laser tracking measurement systems and enhancing their 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 rotating shaft 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.

[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 objective: Establish the Jacobian matrix based on the coordinate system of the rotation axis established in Step 2, i.e.:

[0011]

[0012] in, The directional change of the i-th local coordinate system relative to the global coordinate system can be represented as: , , , x in local coordinate system i i y i and z i The unit direction vectors of the coordinate axes relative to the three coordinate axes of the global coordinate system; The inconsistency between the tolerance analysis direction and the i-th local coordinate system can be represented as: , , , These are the direction vectors of the three directions in the i-th local coordinate system for the tolerance analysis; Let be a skew-symmetric matrix, representing the positional change of the i-th local coordinate system relative to the n-th local coordinate system, which can be expressed as follows:

[0013]

[0014] 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. .

[0015] 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:

[0016]

[0017] In the formula, and Let x and y be the lengths of the planar assembly surfaces along the x-axis and y-axis, respectively. The planar contact spinor parameter is expressed as:

[0018]

[0019] 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]. 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 for the cylindrical feature is established as follows:

[0020]

[0021] In the formula, h represents the length of the cylindrical assembly feature, and the contact spin parameter of the cylindrical surface is expressed as:

[0022]

[0023] Step 5: Calculate the Jacobi-screw model based on the tolerance transfer path for the functional objective to obtain the final six-degree-of-freedom tolerance range. The Jacobi-screw model can be expressed as:

[0024]

[0025] in , , , , , Representing the spinor model , , , , , The lower limit, , , , , , Representing the spinor model , , , , , The upper limit.

[0026] Monte Carlo uncertainty analysis is performed to calculate the mean and standard deviation of each vector in the spinor, which are then used as parameters for generating random numbers. The calculation formulas are as follows:

[0027]

[0028]

[0029] 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.

[0030] By obtaining the exact value of the final six-degree-of-freedom tolerance, the influence of the mechanical structure of the laser tracking measurement system on the final accuracy of the laser tracking measurement system can be calculated, and the final deviation FR can be obtained.

[0031] Step 6: Perform assembly accuracy simulation verification based on 3DCS Variation Analys, obtain the difference between the theoretical and simulated actual assembly conditions, and verify the reliability of the laser tracking system assembly accuracy analysis method.

[0032] The technical solution described in this invention addresses the assembly accuracy analysis problem of the rotary axis system in a laser tracking measurement system. It proposes an improved method based on the Jacobi-spinometer 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 parts machining on the accuracy of the rotary axis system, ensuring the design requirements and measurement accuracy of the rotary axis system.

[0033] Figure 1. Complete model of the mechanical structure of the rotary shaft;

[0034] Figure 2. Exploded view of the parts showing the tolerance transfer path of the rotary shaft;

[0035] Figure 3. Schematic diagram of the local coordinate system of the rotation axis;

[0036] Figure 4a shows a schematic diagram of the assembly relationship of the rotary shaft;

[0037] Figure 4b is a simplified schematic diagram of the assembly relationship of the rotary shaft;

[0038] Figure 5 Monte Carlo uncertainty analysis image of total tolerance of the rotary shaft;

[0039] Figure 6. Simulation results of the relative displacement deviation of the rotating axis of the laser tracking measurement system using 3DCS Variation Analyzer.

[0040] 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.

[0041] The specific implementation process is as follows:

[0042] 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 balance and a standard ball as a reflective device"), a 3D model of the mechanical structure of the laser tracking measurement system is established in Inventor as shown in Figure 1.

[0043] Step 2: Based on the 3D model of the mechanical structure of the laser tracking measurement system created in Inventor software, some complex parts such as screws, nuts, and springs are removed. The rotary axis system mainly includes nine components: 1. Rotary motor, 2. Vertical axis motor bracket, 3. Rotary motor support column, 4. Base plate, 5. GCM-T13M2L, 6. Standard ball support plate, 7. LMK13ML, 8. T-shaped rod, and 9. Standard ball, as shown in Figure 2. The reference coordinate system (global coordinate system) is established at the geometric center of the assembly feature between GCM-T13M2L and the base plate. Local coordinate systems are established at the geometric center of each component's mating in the rotary axis system of the laser tracking measurement system. If the contact surface is a circular plane, a local coordinate system is established at the center of the circle; if the contact surface is a rectangular plane, a local coordinate system is established at the midpoint of the length and width; if the contact surface is a cylindrical surface, a local coordinate system is established at the geometric center of the cylinder. Coordinate systems O0 and O2 are the local coordinate systems for the mating features between the rotary motor and the vertical axis motor bracket. Coordinate systems O1 and O3 are local coordinate systems for the cylindrical assembly feature of the rotary motor and the vertical axis motor bracket. Coordinate systems O4 and O8 are local coordinate systems for the planar assembly feature of the vertical axis motor bracket and the rotary motor support column 1. Coordinate systems O5 and O... 10 This is a local coordinate system for the planar assembly features of the vertical axis motor bracket and the rotary motor support column 2. Coordinate system O6, O 12 This is a local coordinate system for the assembly features of the vertical axis motor bracket and the rotary motor support column on plane 3. Coordinate system O7, O 14 This is a local coordinate system for the assembly features of the vertical axis motor bracket and the rotary motor support column on plane 4. Coordinate system O9, O 16 This is a local coordinate system for the assembly features of the rotary motor support column 1 and the base plate plane. Coordinate system O 11 O 17 This is a local coordinate system for the assembly features of the rotary motor support column 2 and the base plate plane. Coordinate system O 13 O 18 This is a local coordinate system for the assembly features of the rotary motor support column 3 and the base plate plane. Coordinate system O15 O 19 This is a local coordinate system for the assembly features of the rotary motor support column 4 and the base plate plane. Coordinate system O 20 O 21 This is the local coordinate system for the assembly features of the base plate and the GCM-T13M2L plane. Coordinate system O 22 O 23 This is the local coordinate system for the planar assembly features of GCM-T13M2L and the standard spherical support plate. Coordinate system O 24 O 25 O 28 This is the local coordinate system for the planar assembly features of the standard spherical support plate, the T-shaped shaft, and the LMK13ML. Coordinate system O 26 O 27 This is the local coordinate system for the LMK13ML assembly feature with the T-shaped shaft cylinder. Coordinate system O 29 O 30 This is the local coordinate system for the assembly feature of the T-shaped shaft and the standard spherical cylinder. Coordinate system O 31 O 32 This is the local coordinate system for the assembly feature of the T-shaped axis and the standard spherical plane. Coordinate system O 33 This is a standard sphere-centered coordinate system. The assembly deviation of the rotation axis system is the difference between coordinate system O0 and coordinate system O. 33 The deviations between them in the X and Y axes are shown in Figure 3, and the establishment of the local coordinate system is illustrated in Figure 3.

[0044] Step 3: Model the assembly relationship of the laser tracking measurement system based on the tolerance transfer path, as shown in Figure 4a. 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. Simplification is then performed on the parallel assembly features of the cylindrical surface and the parallel path and main path. Simultaneously, the constrained direction is taken as the intersection of two values. The planar feature's dz does not intersect with the cylindrical feature's dx and dy, so the translational degree of freedom parameter is taken as the union of the two feature screw parameters. The simplified formula is:

[0045]

[0046] 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 the main path follows the same principle. In Figure 4a, the laser tracking measurement system's rotating axis system has numerous parallel deviation transmission paths. , ,

[0047] ,

[0048] ,

[0049] After simplification, the assembly relationship diagram is shown in Figure 4b. The final laser tracking measurement system rotary shaft series tolerance transfer path is as follows:

[0050]

[0051] Step 4: Based on the local coordinate system established in Step 2, establish the Jacobian matrix for the final functional target. Based on the machining drawings of each part in the deviation propagation path, establish the screw model for each functional sub-component. Table 1 shows some of the data from the Jacobian-screw model establishment.

[0052] Table 1. Jacobi spinor model of the axis of rotation

[0053]

[0054]

[0055] 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:

[0056]

[0057] The Jacobian matrix and spinor model data calculated in step four are then used to calculate the final six-degree-of-freedom deviation of the rotary motor of the laser tracking measurement system relative to the standard sphere, according to the order shown in Figure 4b.

[0058]

[0059] The Monte Carlo method was used to simulate 5000 bias 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 a reliable six-degree-of-freedom bias based on the Monte Carlo uncertainty analysis method.

[0060] Table 2. Monte Carlo method calculation data

[0061]

[0062] Based on the shape and definition of the concentricity tolerance domain of the points, and using the cumulative deviations in the X and Y directions of the translation vectors in FR, the coaxiality deviation of the rotating shaft system can be obtained, and its expression is:

[0063]

[0064] 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 simulations, and the results are shown in Figure 5. Confidence level: 99.7%. Calculations show that the coaxiality deviation of the rotating shaft system fluctuates between 0.030 mm and 0.031 mm, with an average deviation of 0.0306 mm.

[0065] Step Six: Perform assembly accuracy simulation verification based on 3DCS Variation Analyses. Import the model into SolidWorks' 3DCS Variation Analyses, then apply Feature constraints to each part. After Normalbuild, the result should be consistent with the Inventor software modeling in Step One. Finally, add geometric tolerances for each component according to the part production drawings. After running the simulation, the 3DCS Variation Analyses simulation results of the relative displacement deviation of the rotary axis of the laser tracking measurement system can be obtained, as shown in Figure 6.

[0066]

[0067] The difference between the theoretical and simulated actual assembly conditions was obtained, and the difference was 0.00679 mm.

[0068] The reliability of the laser tracking system assembly accuracy analysis method was verified.

Claims

1. A method for analyzing the assembly accuracy of a mechanical structure's rotating shaft system based on a laser tracking measurement system, characterized in that: This paper studies the method of assembly accuracy analysis for laser tracking measurement systems and establishes an assembly accuracy model based on Jacobi-spin quantity for the hybrid assembly structure of laser tracking measurement systems. The assembly accuracy is then verified through simulation using 3DCS Variation Analyst. The steps include: Step 1: Establishing a 3D model of the mechanical structure rotation axis system of the laser tracking measurement system in Inventor software; Step 2: Establishing a global coordinate system at appropriate locations on the assembly model and a local coordinate system at the geometric center of each part's mating position in the laser tracking measurement system; Step 3: Based on the part assembly contact conditions, the assembly relationships of the laser tracking measurement system are determined. Components, local coordinate systems, and functional pairs are modeled. For parallel paths in the assembly relationship modeling, the parallel assembly features of local cylindrical and planar surfaces are simplified into series tolerance transfer paths, and then the overall deviation transfer path is further simplified. The parallel paths in the model are simplified to a series transmission path, resulting in a simplified tolerance transmission model. Step 4: Based on the established local coordinate system, a Jacobian matrix for the final functional target is established: the Jacobian matrix is ​​established based on the coordinate system of the rotation axis established in Step 2. Step 5: The Jacobian-screw model is calculated based on the tolerance transmission path for the functional target to obtain the final six-degree-of-freedom tolerance range and the Jacobian-screw model. The exact value of the final six-degree-of-freedom tolerance is obtained, thereby calculating the influence of the mechanical structure of the laser tracking measurement system on the final accuracy of the laser tracking measurement system and obtaining the final deviation FR. Step 6: Assembly accuracy simulation verification is performed based on 3DCS Variation Analys to obtain the difference between the theoretical and simulated actual assembly conditions, verifying the reliability of the laser tracking system assembly accuracy analysis method.

2. The assembly accuracy analysis method for a mechanical structure rotary shaft system based on a laser tracking measurement system according to claim 1, characterized in that: Step four: The Jacobian matrix is: ;in, The directional change of the i-th local coordinate system relative to the global coordinate system is represented as: ， ， ， x in local coordinate system i i y i and z i The unit direction vectors of the coordinate axes relative to the three coordinate axes of the global coordinate system; This indicates that the direction of the tolerance analysis is inconsistent with the direction of the i-th local coordinate system, and is represented as: ， ， ， These are the direction vectors of the three directions in the i-th local coordinate system for the tolerance analysis; Let be a skew-symmetric matrix, representing the positional change of the i-th local coordinate system relative to the n-th local coordinate system, expressed as follows: 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 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; according to the constraint of the positional tolerance t, its screw model is: In the formula, and Let x and y be the lengths of the planar assembly surfaces along the x-axis and y-axis, respectively. The planar contact spinor parameter is expressed as: There are two types of parts containing cylindrical features: shaft parts and hole parts. Based on the small displacement spinor theory, its 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, and the contact spin parameter of the cylindrical surface is expressed as: 。 3. The assembly accuracy analysis method for a mechanical structure rotary shaft system based on a laser tracking measurement system according to claim 1, characterized in that: The Jacobi-spinator model for step five is expressed as: ;in ， ， ， ， ， Representing the spinor model ， ， ， ， ， The lower limit, ， ， ， ， ， Representing the spinor model ， ， ， ， ， The upper limit; Monte Carlo uncertainty analysis is performed to calculate the mean and standard deviation of each vector in the spinor, which are then 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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