Fuzzy interval analysis method for assembly deviation of aerospace products based on Jacobian screw

Abstract

The present invention discloses a fuzzy interval analysis method for assembly deviation of aerospace products based on Jacobian spinors, which includes: establishing an assembly connection relationship diagram of product assembly; combining the structural dimensions of the product and the position of the coordinate system to obtain the Jacobian matrix of each functional feature; characterizing the deviation of each functional feature of the product based on the spinor method, and expressing it in the form of an interval; using a fuzzy method to discretize the deviation interval into confidence intervals of deviation sources under different confidence levels, and jointly establishing a Jacobian matrix to predict the deviation interval of the assembly function requirements of the final product under different confidence levels; establishing a deviation contribution calculation model to calculate the contribution value of each deviation source to the deviation of the assembly function requirements. The method can predict the possible interval of the deviation of the assembly function requirements in the actual assembly process according to the calculation results, and at the same time reasonably select the deviation source combination under different confidence intervals according to the deviation of the assembly function requirements, so as to minimize the manufacturing cost while ensuring the assembly accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of digital tolerance of aerospace products, and in particular to a fuzzy interval analysis method of aerospace product assembly deviation based on Jacobi screw. Background Art

[0002] Tolerance modeling refers to the process of characterizing, transferring, and allocating tolerance features of an assembly entity in a computer, and reasonably interpreting its rich semantics. At present, there are many tolerance modeling methods, such as (1) TTRS model (2) matrix model (3) vector model (4) T-Map model, etc. These methods have their own scope of application. The Jacobi spinor model combines the characteristics of spinor being easy to characterize tolerance information and Jacobi matrix being suitable for transmitting tolerance information, while also being able to achieve tolerance allocation. It is an innovative theory in the field of tolerance modeling. In past studies, the Jacobi spinor model often uses extreme value method and statistical method for calculation. The extreme value method often requires the product to achieve interchangeability, resulting in high manufacturing process costs. Although the statistical method can avoid the situation where the tolerance range is too small and can provide the tolerance distribution required by the final product assembly function, the statistical distribution given is often not suitable for technical field use. At the same time, aerospace products are small batch types, often lack deviation source data, and it is not easy to obtain the initial distribution of the deviation source. Therefore, the present invention proposes a fuzzy interval method for complex aerospace product assembly deviation based on Jacobian spinor, considering the use of fuzzy intervals to express deviation source information, and finally giving the range of assembly function requirement deviation under different confidence levels. At the same time, a deviation contribution model is established, and a reasonable selection of deviation source combinations under known assembly function requirement deviations is proposed. This method can predict the tolerance information of small batches of aerospace products after assembly in advance, and can also allocate tolerances under different confidence levels according to the required tolerances, thereby providing a basis for product design and manufacturing. Summary of the invention

[0003] In view of the above-mentioned defects of the prior art, the present invention provides a fuzzy interval analysis method for aerospace product assembly deviation based on Jacobi spinor. Through this method, the deviation source combination under different confidence intervals can be reasonably selected according to the deviation of assembly function requirements, so as to minimize the manufacturing cost while ensuring the assembly accuracy.

[0004] To achieve the above-mentioned purpose, the present invention provides a fuzzy interval analysis method for assembly deviation of aerospace products based on Jacobian spinor, which includes: establishing an assembly connection relationship diagram of product assembly, and establishing a coordinate system of internal functional features and connection functional features in the assembly process based on the assembly connection relationship diagram; obtaining the Jacobian matrix of each functional feature in combination with the structural dimensions of the product and the position of establishing the coordinate system; characterizing the deviation of each functional feature of the product based on the spinor method, defining the deviation as a deviation source, and expressing it in the form of an interval; using a fuzzy method to discretize the deviation interval into confidence intervals of the deviation source under different confidence levels, and jointly establishing the Jacobian matrix to predict the deviation interval of the assembly function requirements of the final product under different confidence levels; establishing a deviation contribution calculation model to calculate the contribution value of each deviation source to the deviation of the assembly function requirements.

[0005] The fuzzy interval analysis method of aerospace product assembly deviation based on Jacobian screw proposed in the present invention has the following specific steps:

[0006] (1) Establish an assembly connection relationship diagram for the assembly, and establish a coordinate system for the internal functional features and connection functional features in the assembly process based on the assembly connection relationship diagram; combine the structural dimensions of the product and the location of the established coordinate system to obtain the Jacobian matrix of each functional feature. The connection relationship diagram contains the parts, internal functional features and connection functional features of the product, and uses symbols to represent the assembly parts and assembly connection relationships. Internal functional features refer to the deviations between the various shape features in the parts; connection functional features refer to the deviations between parts due to the assembly relationship; the deviation source refers to a unified representation of the deviations caused by internal functional features and connection functional features. Solve the Jacobian matrix of the kth functional pair [J] FEk , which can be expressed as:

[0007]

[0008]

[0009]

[0010] Among them: [C 1i ]、[C 2i ] and [C 3i ] is x in the local coordinate system i i ,y i and z i The axes are the unit direction vectors of the three coordinate axes relative to the global coordinate system 0; n represents the target point.

[0011] (2) Characterize the deviation of each functional feature of the product based on the screw method, define the deviation of each functional feature as a deviation source, and express it in the form of an interval. In this step, the possible maximum value and possible minimum value of the deviation value of each deviation source are obtained. The manufacturing deviation characteristics of the manufacturing deviation source are directly expressed by the tolerance interval. The welding deviation characteristics and bolt connection deviation characteristics can be obtained by simulation or experimental methods. In this step, the interval small displacement screw method is used for expression:

[0012]

[0013] Where:

[0014] u, v, and w are the small translational displacement spinors along the x-axis, y-axis, and z-axis, respectively;

[0015] α, β, and γ are the small displacement rotations around the x-axis, the y-axis, and the z-axis respectively;

[0016] u , v , w , α , β , γ They represent the practical minimum values ​​of the six small displacement spinors respectively;

[0017] They represent the actual possible maximum values ​​of the six small displacement spinors.

[0018] (3) Establish a Jacobian spinor model for assembly deviation characterization, deviation transfer, and tolerance allocation, [FR] = [J] [FE]. Where [J] is the Jacobian transfer matrix, and [FE] is the small fluctuation of each functional feature (such as tolerance or kinematic pair error, etc.), that is, the deviation small displacement spinor. By calculating the small displacement spinor of each functional feature and combining it with the Jacobian matrix in process (1), a complete Jacobian spinor model can be obtained. Its basic mathematical expression is:

[0019]

[0020] in:

[0021] The maximum and minimum values ​​that can be obtained for the six degrees of freedom corresponding to the assembly functional requirements.

[0022] (4) The cut-off method in fuzzy theory is used to divide the spinor interval of each deviation source into a certain number of discrete intervals (the specific number of divisions is reasonably selected according to the product characteristics. The more divisions there are, the more accurate the calculation results will be, but the amount of calculation will also be greater) and expressed using the Zadeh representation. For example, the cut-set method can be used to discretize it into:

[0023]

[0024] in:

[0025] Represents different discrete intervals;

[0026] μ1,μ2,…μ m Represents the confidence level corresponding to different discrete intervals;

[0027] The value of m is selected according to the accuracy required for the solution.

[0028] (5) The contribution of the screw parameter item component of each deviation source to the deviation of the assembly function requirement is studied at different confidence levels. The interval small displacement screw of each deviation source can be converted into the form of symmetrical deviation under the nominal size. The symmetrical interval deviation of the nominal size is used to obtain each [J] FEk [FE] k The size of the dimension deviation term relative to the assembly function requirement deviation can be expressed as:

[0029]

[0030]

[0031]

[0032] in: They respectively represent the contribution of the deviation interval of each deviation source to the corresponding deviation item in the assembly function requirement deviation.

[0033] (6) Based on step (5), the Sobol quasi-random sequence method is used to obtain the contribution of the interval small displacement spinor of each deviation source to the deviation interval of its assembly function requirement. First, the boundary value of each interval small displacement spinor is taken as a discrete value, and all possible permutations are listed as two arrays A and B (both arrays are N×k arrays, where k=6), each array contains half of the samples.

[0034]

[0035]

[0036] Define a matrix C i , consisting of all the columns in B except the i-th column, where the i-th column comes from the i-th column in A.

[0037]

[0038] Using sample matrices A, B, C iSubstitute all input values ​​into [J] FEk [FE] k In the above example, (k+2) N×1-dimensional model output vectors are obtained. Finally, the contribution coefficient of each deviation item of each deviation source to the deviation of its assembly function requirement is obtained.

[0039]

[0040] (7) Use Multiply it by the contribution δ of the corresponding deviation term of the deviation interval of each deviation source to the assembly function requirement deviation in (5) to obtain the contribution of each deviation term of each deviation source to the assembly function requirement deviation.

[0041] The device and method provided by the present invention have the following technical effects: the possible interval of the deviation of the assembly function requirement in the actual assembly process can be predicted according to the calculation results, and at the same time, the deviation source combination under different confidence intervals can be reasonably selected according to the deviation of the assembly function requirement, so as to minimize the manufacturing cost while ensuring the assembly accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of a rocket engine product in an embodiment;

[0043] Figure 2 This is a schematic diagram of the assembly connection relationship of the rocket engine of the embodiment;

[0044] Figure 3 A schematic diagram of a reference coordinate system established for assembly features of an embodiment;

[0045] Figure 4 It is a schematic diagram of the method of expressing the tolerance screw interval of a plane feature;

[0046] Figure 5 It is a schematic diagram of the method for expressing the screw interval of cylindrical feature tolerance;

[0047] Figure 6 A schematic diagram of a method for obtaining a welding process deviation interval in an embodiment;

[0048] Figure 7 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0049] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0050] While some exemplary embodiments of the present invention have been described for the purpose of illustration, it should be understood that the present invention may be implemented in other ways not specifically shown in the drawings.

[0051] Example: Please refer to Figure 1 and Figure 7 This embodiment uses a rocket engine as an example for example analysis. Figure 1 The figure shows the assembly feature diagram of the product. The assembly function requirement deviation is the deviation from the upper end face of the thrust chamber to the position of each flange.

[0052] The first step is to establish the assembly connection diagram of the assembly embodiment as shown in Figure 2 As shown, the reference coordinate system of the functional features of the embodiment is established as Figure 3 As shown, according to the established reference coordinate system posture, combined with the relative positions between the functional features of the embodiment as shown in Table 1, the Jacobian matrix of the kth functional pair can be solved [J] FEk .

[0053] Table 1 Numerical table for establishing relative positions between reference coordinate systems

[0054]

[0055]

[0056] The second step is to obtain the possible maximum and minimum values ​​of the deviation value of each deviation source. For manufacturing deviation, it is often given by given tolerance information and can be characterized by small displacement screw. Figure 4 A schematic diagram showing the spinor representation of typical planar features. Figure 5 The schematic diagram of the screw characterization of typical cylindrical features is shown, and finally the maximum range of possible deviation value changes is solved as the deviation source interval through the specific tolerance information. For assembly deviation sources such as bolt connection and welding, the possible maximum and minimum values ​​of their deformation can be obtained through finite element simulation or experimental methods as the interval boundary of the deviation source. Figure 6 A schematic diagram of the process of obtaining the deviation source interval during the welding process is shown.

[0057] In the third step, based on the spinor interval and Jacobian matrix obtained in the first and second steps, a Jacobian spinor model [FR] = [J] [FE] for assembly deviation characterization, deviation transfer, and tolerance allocation is established.

[0058] The fourth step is to use the cut-set method in fuzzy theory to divide the small displacement spinor interval of each deviation source into a certain number of discrete intervals, and express them using the Zadeh representation method. In the embodiment, the deviation value of the IFE1 deviation source along the x-axis is For example, its deviation value is [-0.03, 0.03], which can be discretized using a cut set and expressed using the Zadeh representation.

[0059]

[0060] The fifth step is to study the contribution of each deviation source to the deviation of the assembly function requirements under different confidence levels. First, the deviation interval of each deviation source is converted into the form of symmetrical deviation under the nominal size, and finally expressed in the form of discrete intervals with different confidence levels in the fourth step, and substituted into the Jacobian spinor model [FR] under a certain deviation feature in the third step (such as IFE1) k =[J] FEk [FE] k At the same time, each deviation is substituted into the total Jacobian model [FR] = [J] [FE] to obtain the deviation of the assembly function requirement. The contribution of the six small displacement screws of the functional requirements under the IFE1 feature to the deviation term of the assembly function requirement deviation can be expressed as:

[0061]

[0062]

[0063] The sixth step is to use the Sobol quasi-random sequence method to obtain the contribution of the interval small displacement spinor of each deviation source to the deviation interval of its assembly function requirement. Taking the first deviation of IFE1 as an example, that is, to establish and The relationship between the contribution degrees. First, discretize the boundary values ​​of the small displacement spinors in each interval. Taking the deviation value in the fifth step as an example, the boundary values ​​of the discrete interval of u can be taken out to form a set {-0.3, -0.24, -0.18, -0.12, -0.06, 0, 0.06, 0.12, 0.18, 0.24, 0.3}, and use this value as the input of u. In addition, v, w, α, β, and γ are also represented in the same way. All possible permutations of the six small displacement spinors are listed as two arrays A and B, each of which contains half of the samples. The following two arrays only show the possible permutations of u, which are not actually listed in full.

[0064]

[0065]

[0066] Define a matrix C i , consisting of all the columns in B except the i-th column, where the i-th column comes from the i-th column in A.

[0067]

[0068] Among them: 1≤i≤6, k=6.

[0069] Using sample matrices A, B, C i Substitute all input values ​​into [J] FEk [FE] k In the above equation, we get (k+2) N×1-dimensional model output vectors. Finally, we get the contribution coefficient of each deviation item of each deviation source to its assembly function requirement through the following formula:

[0070]

[0071] In the embodiment, for IFE1, the contribution of its six small displacement spinors to its functional requirements is respectively

[0072] Step 7: Finally, use Multiply it by the contribution δ of the deviation interval of each deviation source to the deviation of the assembly function requirement in the fifth step, and finally obtain the contribution of each deviation item of each deviation source to the deviation item of the assembly function requirement deviation.

[0073] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A fuzzy interval analysis method for aerospace product assembly deviation based on Jacobi spinor, comprising: Establish an assembly connection relationship diagram for product assembly, and establish a coordinate system for internal functional features and connection functional features in the assembly process based on the assembly connection relationship diagram; combine the structural dimensions of the product and the location of the established coordinate system to obtain the Jacobian matrix of each functional feature; Characterize the deviation of each functional feature of the product based on the screw method, define the deviation as the deviation source, and express it in the form of interval; The fuzzy method is used to discretize the deviation interval into confidence intervals of deviation sources at different confidence levels, and the jointly established Jacobian matrix predicts the deviation intervals of the assembly function requirements of the final product at different confidence levels. Establish a deviation contribution calculation model to calculate the contribution value of each deviation source to the deviation of assembly function requirements; The deviation of each deviation source of the product is characterized by the screw method and expressed in the form of an interval, which specifically includes: according to the type of deviation, obtaining the possible interval of the deviation source by a corresponding method, that is, the maximum possible value and the minimum possible value of the deviation source; The fuzzy method is used to characterize the deviation source, specifically including: using the cut-set method in fuzzy theory to obtain the deviation source confidence interval at different confidence levels; each deviation source confidence interval is a discrete interval; In the deviation contribution calculation model, for each spinor of a deviation source, the Sobol quasi-random sequence method is used to solve the contribution value of each spinor parameter item of the deviation source spinor to the deviation of the assembly function requirement.

2. The fuzzy interval analysis method for aerospace product assembly deviation based on Jacobian screw according to claim 1 is characterized in that: The connection relationship diagram includes the parts, internal functional characteristics and connection functional characteristics of the product, and represents the assembly parts and assembly connection relationships in the form of symbols.

3. The fuzzy interval analysis method for aerospace product assembly deviation based on Jacobian screw according to claim 1 is characterized by: The internal functional features refer to the deviations between the various shape features in the parts; the connection functional features refer to the deviations between the parts due to the assembly relationship; the deviation source refers to a unified representation of the deviations caused by the internal functional features and the connection functional features.

4. The fuzzy interval analysis method for aerospace product assembly deviation based on Jacobian screw according to claim 1 is characterized in that: The types of deviations include manufacturing deviation characteristics, welding deviation characteristics, and bolt connection deviation characteristics; manufacturing deviation characteristics are characterized by tolerance intervals; welding deviation characteristics and bolt connection deviation characteristics obtain the maximum and minimum values ​​of the deviation sources through experiments or finite element simulation methods.

5. The fuzzy interval analysis method for aerospace product assembly deviation based on Jacobian screw according to claim 1 is characterized in that: The jointly established Jacobian matrix predicts the deviation intervals of the assembly function requirements of the final product at different confidence levels, specifically including: substituting the discrete intervals at different confidence levels into the established Jacobian matrix to obtain the deviation intervals at different confidence levels.

6. The fuzzy interval analysis method for aerospace product assembly deviation based on Jacobian screw according to claim 1 is characterized in that: Reasonably select the deviation source combination under different confidence intervals according to the deviation of assembly function requirements; specifically including: In order to control the cost while ensuring the deviation of the matching function requirement, the deviation source combination is determined by reducing the spin parameter item component of the deviation source with large contribution and relaxing the spin parameter item component of the deviation source with small contribution.

Images