A multi-size chain parallel assembly error analysis method based on jacobian wrench

Abstract

The application discloses a multi-size chain parallel assembly error analysis method based on Jacobian screw, which comprises the following steps: analyzing the assembly relationship of each part of an assembly body to determine a plurality of parallel assembly size chains, setting an analysis datum as the starting end of the size chains, taking a target assembly feature as the end of the size chains, and establishing an error transmission relationship diagram; calculating the screw of the target assembly feature relative to the analysis datum in each size chain; based on the Jacobian screw model, the vector variation range of the screw of each size chain on each degree of freedom in the Jacobian screw model is obtained; and the vector variation range on each degree of freedom is subjected to intersection operation to obtain the multi-size chain parallel assembly error. The error analysis method establishes a coupling model for the assembly error analysis of the parallel multi-size chains, and the coupling of the error of the target assembly feature under the influence of the multi-size chains is realized by using the intersection operation between the screws of the multi-size chains in the model, so that the accuracy of the error analysis conclusion of the complex assembly body can be remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of mechanical assembly technology, and more specifically, relates to a method for error analysis of multi-dimensional chain parallel assembly based on Jacobi spinor. Background Technology

[0002] In error analysis of assemblies, there are situations where the fit relationships between parts are complex and the error propagation path is unclear. Moreover, the key issue is that assembly errors may be a common closed loop of multiple unrelated dimensional chains.

[0003] The Jacobi screw model is an important theoretical tool for analyzing assembly errors in complex mechanical structures and is currently widely used in the assembly error analysis of important mechanical equipment such as machine tools, vehicles, and ships. Currently, when calculating assembly errors, most methods simplify local parallel dimensional chains into a single serial dimensional chain. However, for mechanisms with complex mating relationships, the assembly errors of parts are often influenced by multiple unrelated dimensional chains. The critical assembly error may be a common closed loop of multiple dimensional chains, but existing methods only consider a single serial dimensional chain, which has certain limitations, and the calculated results deviate significantly from the actual situation. Therefore, it is necessary to study a multi-dimensional chain parallel assembly error analysis method based on Jacobi screw. Summary of the Invention

[0004] To address at least one deficiency or improvement requirement in existing technologies, this invention provides a method for analyzing assembly errors in parallel multi-dimensional chains based on Jacobi screws. By establishing a coupled assembly error analysis model with multiple parallel dimensional chains, the method utilizes the "intersection" operation between screws to couple the target assembly clearance error under the influence of multiple dimensional chains. Furthermore, by calculating and normalizing the error contribution, the method adjusts the vector variation range of the target assembly features, thereby evaluating the rationality of error design and optimizing errors. This significantly improves the accuracy of error analysis in complex assemblies and the efficiency of reasonable error adjustment.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for error analysis of multi-size chain parallel assembly based on Jacobi spinor is provided, comprising the following steps: Analyze the assembly relationships of each part in the assembly to determine multiple parallel assembly dimension chains, set the analysis datum as the starting end of the dimension chain, take the target assembly feature as the ending end of the dimension chain, and establish an error propagation relationship diagram. Calculate the spin of the target assembly feature relative to the analysis datum in each dimension chain. ; The vector offset range of the screw of each dimension chain in each degree of freedom in the Jacobi screw model is calculated based on the Jacobi screw model. The multi-dimensional chain parallel assembly error is obtained by intersecting the vector offset ranges on each degree of freedom. .

[0006] Preferably, the calculation of the spin of the target assembly feature relative to the analysis reference in each dimension chain is performed. include: A global coordinate system is established in the assembly based on the aforementioned analysis datum. A Jacobian matrix is ​​then established based on the relative positions of the local coordinate systems of individual functional elements and the end coordinate systems of the target assembly features. spinor The calculation formula is: ; In the formula, Representing the Chain of a certain size, The first in the error propagation diagram Functional elements Functional elements in the error propagation diagram The spinor expression.

[0007] Preferably, the multi-size chain parallel assembly error The calculation is as follows: , In the formula, These respectively represent the Jacobi spinor model u, v, w, Take the intersection of the vector offset ranges of each dimension chain on the six degrees of freedom; The number of size chains.

[0008] Preferably, the method further includes calculating the error contribution rate, wherein the error contribution rate is calculated using the following formula: Calculate a single functional element Jacobian matrix Its product with spinor , ; Calculate the sum of the products of the Jacobian matrices and their spinors for all functional elements. ,

[0009] Individual functional elements Error contribution ; In the formula, and They are respectively and A vector in a certain degree of freedom direction. The number of representative functional elements.

[0010] Preferably, the error contribution rate of the individual functional element Normalization is performed, specifically including: Calculate the proportionality coefficient K at different degrees of freedom for a single functional element. Error contribution Multiply by the scaling factor K to obtain the normalized error contribution.

[0011] According to another aspect of the present invention, a computer device is also provided, including a memory and a processor, the memory storing a computer program, characterized in that the processor executes the computer program to implement the steps of the method described in any of the preceding claims.

[0012] According to another aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, characterized in that the computer program, when executed by a processor, implements the steps of the method described in any of the preceding claims.

[0013] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: (1) The present invention provides a method for analyzing the parallel assembly error of multiple dimension chains based on Jacobi screws. In analyzing the assembly relationship of parts in an assembly, multiple dimension chains are connected in parallel to the error transmission chain. The influence of multiple parallel dimension chains on the error is taken into account. By performing screw calculation on each dimension chain, and then summarizing the intersection calculation results of the vector change range of each dimension chain on each degree of freedom of Jacobi screws, the error of the final target assembly feature under the joint influence of multiple dimension chains is obtained. By coupling the target assembly gap error under the influence of multiple dimension chains as described above, a parallel assembly error analysis model of multiple dimension chains is established, thereby obtaining a more accurate and precise error analysis method.

[0014] (2) The present invention provides a method for analyzing the error of a multi-dimensional chain parallel assembly based on Jacobi spinor. By calculating the error contribution of a single functional element to the functional requirements and normalizing the error contribution from different dimension chains, it can intuitively reflect the influence of each error link on the assembly gap. It also allows designers to adjust the vector change range of the target assembly feature by the magnitude of the contribution, thereby improving the accuracy of error analysis of complex assemblies and the efficiency of reasonable adjustment of the error range. Attached Figure Description

[0015] Figure 1 This is an error propagation relationship diagram provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of planar features provided in an embodiment of the present invention; Figure 3 This is the error contribution normalized histogram provided in the embodiments of the present invention; Figure 4 This is an assembly diagram of the assembly provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the functional requirements of the assembly provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the assembly relationship provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the intersection operation of parallel dimension chains provided in an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0017] In the following, the terms “comprising” or “may include” as used in various embodiments of the invention indicate the presence of an inventive function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in various embodiments of the invention, the terms “comprising,” “having,” and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or adding one or more combinations of the foregoing.

[0018] The Jacobian screw model, composed of a Jacobian matrix and a screw model, is a three-dimensional error analysis model that combines a screw model expressing error information with a Jacobian model expressing error propagation relationships. It accurately describes the variation of mating features within the error domain and the error propagation relationship from the mating features to the end of the dimensional chain. The screw model decomposes the variation of the actual mating features relative to the ideal datum into small displacement vectors on six degrees of freedom, including along... Translation vector of the axis and around Rotation vector of the axis , The small displacement variations of each mating feature are then transmitted to the end of the dimension chain via the Jacobian matrix.

[0019] The Jacobi screw model essentially uses six-degree-of-freedom screws to describe the translation and rotation of the actual mating features of parts in space, and uses the Jacobi matrix to transfer the variation of these mating features relative to the ideal situation to the closed loop of the dimensional chain. When analyzing the critical assembly errors of complex assemblies, the closed loop is often affected by multiple dimensional chains. Calculating it using the existing simplification of a single serial dimensional chain will result in a significant deviation from the actual situation.

[0020] Based on this, the core concept of this invention lies in considering the combined error influence of multiple dimensional chains within the assembly during the analysis of errors in complex assemblies. These dimensional chains are plotted on an error propagation diagram, and the vector variation range with the greatest constraint effect of each dimensional chain at each degree of freedom is taken as the final variation range of the assembly error. The intersection calculation results at each degree of freedom are then summarized as the error of the final target assembly feature under the combined influence of multiple dimensional chains. This results in a more precise and accurate error analysis method. The multi-dimensional chain parallel assembly error analysis method implemented according to this invention includes the following steps: S1: Analyze the assembly relationships of each part in the assembly to determine multiple parallel assembly dimension chains. Set the analysis datum as the starting point of the dimension chain and the target assembly feature as the ending point of the dimension chain to establish an error propagation diagram; such as Figure 1 The diagram shown is an error propagation diagram, which contains n parallel dimension chains from 1 to n.

[0021] S2: Calculate the spin of the target assembly feature relative to the analysis datum in each dimension chain.

[0022] Specifically, a global coordinate system is established in the assembly based on the analysis datum, and local coordinate systems are established on each functional element. A Jacobian matrix is ​​then established based on the relative position between the local coordinate system of an individual functional element and the end coordinate system of the target assembly feature. : According to the expression of the Jacobi spinor model: (1) In the formula, Functional elements of a part The number of functional elements involved. Let be the Jacobian matrix of each functional element involved in the error propagation chain. This represents the screw representation of the functional elements involved in the error dimension chain. The expression is: (2) In the formula, [ R 0 i ]={[C 1i ] 3×1 [ C 2i ] 3×1 [ C 2i ] 3×1} is a local coordinate system O i Relative global coordinate system O The direction vectors of the three coordinate axes of 0; W i n ] 3×3 Local coordinate system O i With end coordinate system O n Distance matrix between: (3) In the formula, dx i n , dy i n , dz i n Local coordinate system O i To the end coordinate system O n relative distance of the origin u , v , w , α , β , γ respectively along X , Y , Z Translation vector in the axial direction and the rotation around X , Y , Z Rotation vector of the axis. The screw representations of common planar and cylindrical geometric features are shown in Table 1.

[0023] Table 1. Screw representation of planar and cylindrical features

[0024] in, a For the plane in Y Length in direction, b For the plane in Z Length in direction, l The length of the cylindrical surface. t PO This refers to the size of the dimensional or positioning error range for the plane and cylindrical axes.t ORI The magnitude of the orientation error domain for the plane and cylindrical axis is represented by the screw expression. "0" in the screw expression indicates that the vector variation in that direction has no effect on the error analysis of this feature.

[0025] Based on the Jacobi screw model calculation formula described above, the screw of the target assembly feature relative to the analysis datum in each of the 1 to n dimension chains is calculated. The calculation formula is as follows: spinor The calculation formula is:

[0026]

[0027]

[0028]

[0029] In the formula, Representing the Chain of a certain size, The first in the error propagation diagram Functional elements.

[0030] S3: Based on the Jacobi spinor model, obtain the vector offset range of the spinor of each dimension chain in each degree of freedom of the Jacobi spinor model; The multi-dimensional chain parallel assembly error is obtained by intersecting the vector offset ranges on each degree of freedom. .

[0031] , In the formula, This is due to assembly error; These respectively represent the Jacobi spinor model u, v, w, The vector offset ranges of each dimension chain in the six degrees of freedom are taken as the intersection, and the vector with the smallest interval, that is, the one with the greatest limiting effect, is taken as the final variation range of assembly error. The number of size chains.

[0032] S4: Contribution Calculation The contribution rate characterizes the degree of impact of the error component on functional requirements, and is an important basis for evaluating the rationality of the error design and for optimizing the error. First, calculate the individual functional elements. Jacobian matrix Its product with spinor , represents the impact of a single functional element on functional requirements. In the calculation, the six degrees of freedom vectors in its screw are all taken as extreme values ​​within their range of variation. The calculation formula is as follows: ; Calculate the sum of the products of the Jacobian matrices and their spinors for all functional elements. ,

[0033] Individual functional elements Error contribution ; In the formula, and They are respectively and A vector in a certain degree of freedom direction. The number of representative functional elements.

[0034] Since the error contribution only reflects the influence of each error link on the single-direction screw amount of the target assembly feature, the screw amount variation range may be taken from different size chains when multiple size chains are connected in parallel. Therefore, the feedback of error contribution information has certain limitations. It is necessary to summarize and normalize the error contribution from different sources to intuitively reflect the influence of each error link on the assembly gap, so as to facilitate the designer to adjust the error level.

[0035] In one specific embodiment, the present invention provides a method for normalizing the error contribution, the specific steps of which are as follows: like Figure 2 The planar feature diagram shown has four vertices that represent the points of maximum displacement along the plane's normal. A coordinate system is established based on the directions illustrated. The displacement is influenced by the rotational spins of the movement along the x-axis and the rotations around the y and z axes. u, β, γ Displacement at the point of maximum displacement in the plane : ; Calculate the proportionality coefficient K in different degrees of freedom directions respectively:

[0036] Calculate the normalized error contribution based on the proportionality coefficient. PCk : (12) Based on the normalized tolerance contribution, a histogram is plotted, such as... Figure 3As shown, 3(a) represents the error contribution in different degrees of freedom directions before normalization, and 3(b) represents the error contribution after normalization. By normalizing the error contribution in different degrees of freedom directions to the same histogram, the influence of each error link on the assembly gap can be reflected more intuitively, making it easier for designers to adjust the error level.

[0037] To further illustrate the calculation process of the multi-size chain parallel assembly error analysis method based on Jacobi spinor of this invention, a specific analysis is conducted below using an assembly as an example. Figure 4 The image shown is a schematic diagram of an assembly, as follows: Figure 5 The diagram shown illustrates the functional requirements of the assembly. The assembly relationships of the various parts are analyzed to determine multiple parallel assembly dimension chains. A coordinate system is established with the axis pointing left as the positive z-axis. Based on the part characteristics and assembly features, an error propagation diagram is established as follows. Figure 6 As shown. The assembly consists of housings ①②③, shaft parts ①②③, and bushings. The key assembly step FR is the coaxiality error between the outer cylindrical surface of shaft part ③ and the axis of shaft part ①.

[0038] As can be seen from the assembly relationship, starting from the axis of shaft part ①, passing through multiple segments of the box body and shaft parts, and ending at the axis of shaft part ③, two parallel series dimension chains are formed: Size chain ①: Shaft parts ① — Housing ① — Housing ② — Housing ③ — Bushing — Shaft parts ③; Size chain ②: Shaft-type parts ① — Shaft-type parts ② — Shaft-type parts ③.

[0039] According to the Jacobian spinor theory, the following information can be obtained: Table 2 Assembly features and screw designations

[0040]

[0041]

[0042] In this context, IFE represents the internal functional characteristics of a part, and CFE represents the connection functional characteristics between parts. Each screw quantity expresses the range of vector variation in the form of upper and lower limits, or simply variation. The determination of variation is related to the size (area) of the feature and the assigned error.

[0043] Calculate the rotation of the axis of shaft-type parts ③ in dimensional chains ① and ② respectively. and The calculation formula is as follows:

[0044]

[0045]

[0046] Solving the above Jacobi spinor model yields the vector offset range data set:

[0047]

[0048] In the formula: V Indicates vector in u , v , w、α , β , γ The offset range in six directions, with its upper and lower limits being the maximum offset of the vector.

[0049] So far, the effects of dimensional chains ① and ② on the target assembly feature error have been calculated separately. Since the maximum offset of the target assembly feature error is the cumulative sum of the maximum effects of the component loop errors on the closed loop, in order to determine the final spin variation range... Need to FR 1 and FR 2. Perform intersection operation: (17) In the formula, the symbol " The "" represents the "intersection" operation, which depends on whether there is overlap between the corresponding vectors of the two spinors involved in the calculation. FR 1 and FR 2. If the target assembly error is affected in a certain vector direction, then the minimum of the two maximum offsets should be taken, i.e., the "intersection" should be taken: For example, when u Rotation in direction (along) x (axis movement) Less than At times, such as Figure 7 As shown in (a), the dimensional chain ① has a significant limiting effect on the fit error of the target shaft and hole, and the variation in the fit error at the end will be within the range of... Within the range, therefore Should be taken as ( , As u The final spinor variation range in the direction; for special cases, where one of the dimensional chains does not limit the target fit error in a certain vector direction, such as... Figure 7 As shown in (b), at this time, its spinor variation range can be regarded as infinitely large, and the intersection operation is performed in the same way. The one with the greater limiting effect is taken as the final spinor variation range.

[0050] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for error analysis of multi-dimensional chain parallel assembly based on Jacobi spinor, characterized in that, Includes the following steps: Analyze the assembly relationships of each part in the assembly to determine multiple parallel assembly dimension chains, set the analysis datum as the starting end of the dimension chain, take the target assembly feature as the ending end of the dimension chain, and establish an error propagation relationship diagram. Calculate the spin of the target assembly feature relative to the analysis datum in each dimension chain. ; The vector offset range of the screw of each dimension chain in each degree of freedom in the Jacobi screw model is obtained by solving the Jacobi screw model. The multi-dimensional chain parallel assembly error is obtained by intersecting the vector offset ranges on each degree of freedom. ; The error contribution rate is calculated using the following formula: Calculate the contribution rate of a single functional element. Jacobian matrix Its product with spinor , ; Calculate the sum of the products of the Jacobian matrices and their spinors for all functional elements. , Individual functional elements Error contribution In the formula, and They are respectively and A vector in a certain degree of freedom direction. The number of functional elements in the error propagation diagram; Error contribution to the individual functional element Normalization processing is performed, specifically including: calculating the proportionality coefficient K for different degrees of freedom, and normalizing the individual functional elements. Error contribution Multiplying by the scaling factor K yields the normalized error contribution; where the four vertices of the plane are the points of maximum displacement along the plane's normal direction. A spatial rectangular coordinate system Oxyz is established, and its displacement is influenced by the rotational spins of movement along the x-axis and rotations about the y and z axes. u, β, γ Displacement at the point of maximum displacement in the plane : ； Calculate the proportionality coefficient K in different degrees of freedom directions respectively: In the formula, and These are the lengths of the plane along the y-axis and z-axis, respectively.

2. The method for analyzing the error of multi-size chain parallel assembly based on Jacobi spinor as described in claim 1, characterized in that, The spin of the target assembly feature relative to the analysis datum is calculated for each dimension chain. include: A global coordinate system is established in the assembly based on the aforementioned analysis datum. A Jacobian matrix is ​​then established based on the relative positions of the local coordinate systems of individual functional elements and the end coordinate systems of the target assembly features. spinor The calculation formula is: ； In the formula, Representing the Chain of a certain size, The first in the error propagation diagram Functional elements Functional elements in the error propagation diagram The spinor expression.

3. The method for analyzing the error of multi-size chain parallel assembly based on Jacobi spinor as described in claim 1, characterized in that, The multi-size chain parallel assembly error The calculation is as follows: ， In the formula, These respectively represent the Jacobi spinor model u, v, w, Take the intersection of the vector offset ranges of each dimension chain on the six degrees of freedom; The number of size chains.

4. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-3.

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