Assembly deviation analysis and tolerance optimization design method for divertor unit of magnetic confinement nuclear fusion device

Abstract

The invention discloses an assembly deviation analysis and tolerance optimization design method for a divertor unit of a magnetic confinement nuclear fusion device. The method comprises the following steps of S1, performing spinor expression derivation of a local parallel structure which is composed of two mutually vertical plane connection pairs and considers a leverage effect; s2, performing spinor expression derivation of a local parallel structure which is composed of two cylindrical surface connecting pairs with parallel axes and considers the lever effect; s3, constructing a divertor unit assembly deviation analysis model; s4, analyzing tolerance contribution degree and tolerance sensitivity; and S5, divertor unit tolerance optimization design is carried out. According to the method, the assembly precision of the divertor unit of the magnetic confinement nuclear fusion device can be effectively guaranteed, the tolerance optimization design is realized, and the manufacturing cost of the divertor unit is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical assembly precision analysis, and in particular relates to an assembly deviation analysis and tolerance optimization design method for a divertor unit of a magnetic confinement nuclear fusion device. Background Art

[0002] The divertor unit is a key component in a magnetic confinement fusion device, and its assembly accuracy is crucial to its overall performance. However, due to its complex structure and difficult assembly, the actual development process often faces the problem of assembly accuracy failing to meet design requirements. In this context, developing effective assembly deviation analysis and tolerance optimization methods for divertor units in magnetic confinement fusion devices is of great significance for ensuring divertor unit assembly accuracy and reducing divertor unit manufacturing costs. Summary of the Invention

[0003] To address the above problems, the present invention proposes an assembly deviation analysis method for a local parallel structure considering the geometric leverage effect, and constructs a deviation analysis model for the divertor unit. Based on the deviation analysis model, a tolerance optimization model is constructed in combination with a genetic algorithm, with the goal of minimizing machining costs and the constraints of assembly accuracy and machining capacity.

[0004] In order to achieve the above object, the technical solution of the present invention is as follows:

[0005] A method for analyzing assembly deviations and optimizing tolerances of a divertor unit for a magnetic confinement nuclear fusion device comprises the following steps:

[0006] S1: Detailed derivation of the spinor expression of the local parallel structure consisting of two mutually perpendicular plane connection pairs in the assembly process of the divertor unit considering the geometric leverage effect;

[0007] S2: Detailed derivation of the spinor expression of the local parallel structure consisting of two cylindrical connection pairs with parallel axes in the assembly process of the divertor unit, considering the geometric leverage effect;

[0008] S3: Constructing a divertor unit assembly deviation analysis model;

[0009] S4: Tolerance contribution and tolerance sensitivity analysis;

[0010] S5: Tolerance optimization design of divertor unit.

[0011] Compared with other local parallel structures, the expression of the spinor model of the local parallel structure considering the geometric leverage effect is affected by the distance between the connection pairs forming the local parallel structure.

[0012] The algebraic operation method is a method of converting two groups of small displacement spinors into one group of small displacement spinors through intersection and union operations.

[0013] The beneficial effects of the present invention are:

[0014] This method for analyzing assembly deviations and optimizing tolerances for the divertor unit in a magnetic confinement nuclear fusion device considers the shape, position, and dimensional tolerances of each divertor unit component, as well as the geometric leverage effect inherent in parallel assembly. This method constructs a realistic assembly deviation analysis model, effectively analyzing the actual assembly accuracy based on the tolerances of each divertor unit component. A tolerance design optimization model, constructed based on the deviation analysis model and combined with a genetic algorithm, further optimizes the divertor unit tolerance design scheme, effectively improving design efficiency and reducing manufacturing costs while ensuring assembly quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a local parallel structure that takes into account the geometric leverage effect and is formed by two mutually perpendicular plane connection pairs during the assembly process of the divertor unit.

[0016] Figure 2 for Figure 1 Assembly connection diagram of two parts

[0017] Figure 3 A comparison chart of the analysis results of serial assembly analysis, local parallel assembly analysis, and improved Jacobi spinor model.

[0018] Figure 4 The local parallel structure considering the geometric leverage effect is formed by the connection of two cylindrical surfaces with parallel axes in the assembly process of the divertor unit.

[0019] Figure 5 Flowchart for deviation analysis of assembly of divertor unit for magnetic confinement nuclear fusion device

[0020] Figure 6 Assembly connection diagram of the divertor unit with local parallel structure

[0021] Figure 7 This is the pure series assembly connection diagram of the divertor unit

[0022] Figure 8 Tolerance requirements and dimensions for box parts

[0023] Figure 9 Tolerance requirements and dimensions for transition support parts

[0024] Figure 10 Tolerance requirements and dimensions for PFU parts

[0025] Figure 11 Schematic diagram of the local coordinate system and global coordinate system of each functional element

[0026] Figure 12 Comparison of results between Case 1 and Case 2

[0027] Figure 13 Comparison of results between Case 1 and Case 3

[0028] Figure 14 Comparison of results between Case 2 and Case 3

[0029] Figure 15 Tolerance contribution decomposition flow chart

[0030] Figure 16 The contribution of each tolerance to the final assembly deviation along the x, y and z directions

[0031] Figure 17 The sensitivity of each tolerance to the final assembly deviation along the x, y and z directions

[0032] Figure 18 Patent abstract attached DETAILED DESCRIPTION

[0033] The present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0034] S1: Derivation of the spinor expression for a local parallel structure consisting of two mutually perpendicular planar connection pairs considering the geometric leverage effect.

[0035] S11: Figure 1 As shown, the spinor expression derivation of the local parallel structure composed of two mutually perpendicular plane connection pairs considering the geometric lever effect proposed in the present invention includes the following steps:

[0036] (1) Analyze and determine which parameters in the spinor model that constitutes the local parallel structure connection have an impact on the geometric leverage effect;

[0037] (2) Figure 1 As shown in , the existence of plane connection pair 2 will affect the α1 and β1 parameters in the spinor model of plane connection pair 1, and correspondingly, plane connection pair 1 will affect the β2 and γ2 parameters in the spinor of plane connection pair 2;

[0038] (3) The upper and lower limits of the β1 parameter under the constraint of leverage effect are and β 1, can be calculated by formula (1) and (2), when and β1 satisfy When , the constraint of the leverage effect on the spinor parameters is stronger than the constraint of the tolerance domain. At this time, T p1 The range of the spinor parameter β1 is

[0039]

[0040] (4) The upper and lower limits of the β2 parameter in the planar connection pair 2 spinor under the action of the lever effect are and β2 , can be calculated by formula (3) and (4). and β2 satisfy When the lever effect constrains the spinor parameters more than the tolerance domain, the corresponding T p2 The range of parameter β2 in the spinor is

[0041]

[0042]

[0043] (5) For the spin parameter α1, O1M is the ideal position, and O1N is the limit position of clockwise rotation around point O1 under the tolerance domain constraint. The angle between them is the limit of the α1 spin parameter. Similarly, the upper limit of the γ2 spin parameter is the angle between O2M and O2N. Since the tolerance domain is symmetric with respect to the rotation center, the upper and lower limits of the α1 and γ2 spin parameters are the same under the influence of the leverage effect, which can be calculated using Equations (5) and (6).

[0044]

[0045] S12: After incorporating the leverage effect caused by the distance between the connection pairs into the screw model of each connection pair, the screw parameters, variation range and constraint equations of the two planar connection pairs are shown in the following table.

[0046] Table 1 Screw models of each connection pair considering the lever effect

[0047]

[0048] In summary, for Figure 1 The local parallel structure shown in Table 2 is obtained by performing intersection and union operations on the spinors in each connection pair in Table 1 to obtain the spinor expression of the local parallel structure.

[0049] Table 2 The spinor model of the local parallel structure formed by the planar connection pair and the planar connection pair considering the geometric leverage effect

[0050]

[0051] S13: Case study verifies the validity of the spinor model:

[0052] (1) Figure 1 As shown, the assembly consists of two parts, and its dimensions and tolerances are designed as shown in the figure.

[0053] (Functional requirement) is the position deviation of the origin of the local coordinate system 5 relative to the global coordinate system 0;

[0054] (2) Construct Figure 2 The assembly connection diagram shown;

[0055] (3) Constructing a spinor model of each functional element considering the leverage effect;

[0056] (4) Perform algebraic operations on the spinor model to obtain the spinor expression of the local parallel structure;

[0057] (5) Calculate the Jacobian matrix corresponding to each functional element and construct an assembly deviation analysis model;

[0058] (6) Construct the serial assembly and JT coupling deviation analysis models for comparative analysis. The results are as follows: Figure 3 Compared with the analysis methods based on serial assembly and JT coupling deviation, the analysis accuracy of the improved Jacobi spinor model is improved.

[0059] S2: Derivation of the screw expression for a local parallel structure consisting of two cylindrical connection pairs with parallel axes, taking into account the geometric leverage effect.

[0060] S21: Figure 4 As shown, the derivation of the spinor expression of the local parallel structure composed of two cylindrical connection pairs with parallel axes considering the geometric leverage effect proposed in the present invention includes the following steps:

[0061] (1) Analyze and determine which parameters in the spinor model that constitutes the local parallel structure connection have an impact on the geometric leverage effect;

[0062] (2) First, we discuss the influence of the spin parameter α, the cylindrical surface connecting the spinor T c1 and T c2 The α-spin parameter is zero, that is, a single cylindrical connection pair does not constrain the α-spin parameter. Therefore, in T c1 and T c2 The upper and lower limits of the α parameter in the screw due to the lever effect should be the same. The upper and lower limits of the α parameter are:

[0063]

[0064] (3) For the spinor parameter γ, the calculation method of γ1 is shown in formula (8), and the calculation method of γ2 is shown in formula (9). When the upper and lower limits of γ1 satisfy When , the constraint of the leverage effect on the spinor parameter is greater than the constraint of the tolerance domain, and the upper and lower limits of the spinor parameter γ1 are Similarly, when the upper and lower bounds of γ2 satisfy When , the constraint of the leverage effect on the spinor parameter is greater than the constraint of the tolerance domain, and the upper and lower limits of the spinor parameter γ2 are

[0065]

[0066] S22: After incorporating the leverage effect caused by the distance between the joints into the screw model of each joint, the screw parameters, variation ranges, and constraint equations of the two planar joints are shown in the following table:

[0067] Table 3 Screw model of cylindrical connection considering lever effect

[0068]

[0069] for Figure 4 The local parallel structure is obtained by performing intersection and union operations on the spinors of the cylindrical surface connections after considering the leverage effect in Table 3, and the spinor expression of the local parallel structure is obtained, as shown in Table 4.

[0070] Table 4. The spinor model of the local parallel structure formed by the cylindrical connection pair and the cylindrical connection pair considering the geometric leverage effect.

[0071]

[0072] S3: Constructing a model for analyzing the assembly deviation of the divertor unit

[0073] S31: Construct Figure 6 The assembly connection diagram of the divertor unit with a local parallel structure is shown;

[0074] S32: Calculate the spinor model of each functional element with and without considering the geometric leverage effect;

[0075] S33: Use the intersection and union operation to obtain the spinor expression of the local parallel structure, and convert the series assembly relationship containing the local parallel structure into a pure series assembly relationship. The conversion result is as follows: Figure 7 As shown;

[0076] S34: Calculate the Jacobian matrix corresponding to each functional element in the new series relationship;

[0077] S35: Calculation of divertor unit assembly deviation. To analyze and verify the influence of leverage effect and local parallel assembly on divertor unit assembly deviation analysis. The factors considered in each case are shown in Table 4. The results are as follows Figure 12 、 Figure 13 and Figure 14The horizontal axis represents the deviation value, and the vertical axis represents the number of times this value appears in 20,000 Monte Carlo simulations. The results show that the range and frequency distribution of assembly deviations vary significantly between cases, indicating that local parallel assembly and leverage effects have significant impacts on the assembly deviation analysis of divertor units and cannot be ignored when conducting assembly deviation analysis.

[0078] Table 5 Factors considered in Case 1-3

[0079]

[0080] S4: Tolerance contribution and tolerance sensitivity analysis

[0081] S41: According to the relevant knowledge of probability statistics, in the statistical calculation process, the sample data generated by each functional element and the sample data of the functional requirement follow the square root principle. Therefore, when the sample data satisfies the normal distribution, the functional requirement (FR) and the functional element FE i The relationship between the standard deviations of can be expressed as formula (10).

[0082]

[0083] Where σ FR is the standard deviation of functional requirements, is the standard deviation of the functional element. can be written as:

[0084]

[0085] By dynamically adjusting a tolerance parameter in a combined tolerance while keeping other tolerances unchanged, the standard deviation (σ) of the tolerance and the functional element can be established. FEi ) mapping relationship. By performing the same process on other tolerances in the combined tolerance, a set describing the mapping relationship between each tolerance and the functional element can be generated. By fitting the data in the mapping relationship set, the mapping relationship between each tolerance in the combined tolerance and σ can be established. FEi The approximate mathematical relationship between them can ultimately determine the contribution of each tolerance within the combined tolerance.

[0086] The tolerance contribution decomposition algorithm is mainly divided into the following steps:

[0087] 1) FE obtained from Monte Carlo simulation i The standard deviation σ FEi and the standard deviation σ of the functional requirement FR FR , calculate the FE of each functional element i Contribution of

[0088] 2) Determine the FE to be decomposed iIs it a combined tolerance? If it contains only one tolerance, the FE i The tolerance contribution is the contribution of the tolerance, otherwise it needs to be decomposed;

[0089] 3) Use the control variable method to change a tolerance value at a certain step size each time to obtain the tolerance value and the FE containing the tolerance i The standard deviation σ FEi The mapping relationship between them;

[0090] 4) fitting the mapping relationship obtained in step (3);

[0091] 5) Calculate the tolerance contribution of each tolerance to FR.

[0092] S42: The contribution of tolerance to FR deviation along x, y and z axes is as follows Figure 16 shown.

[0093] S43: Single parameter perturbation method

[0094] The single parameter perturbation method is based on the local sensitivity theory. By adjusting a single tolerance parameter independently, its linear effect on the assembly error is observed. Assume that the assembly error transfer function is T = f(t1, t2, ..., t n ), where t i is the ith tolerance parameter. i When , the sensitivity coefficient is defined as:

[0095]

[0096] Where S i is the tolerance sensitivity; ΔT is the change in assembly deviation; Δt i is the change of the ith tolerance;

[0097] S44: Tolerance sensitivity to FR deviation along x, y and z axes Figure 17 shown.

[0098] S5: Divertor unit tolerance optimization design

[0099] S51: Assembly function requirement constraints:

[0100]

[0101] v max ≤[v] FR (14)

[0102] Where, [d] FR is the maximum normal offset distance of FR under design requirements, u max is the maximum value of the FR spinor parameter u, w maxis the maximum value of the FR spinor parameter w, v max is the maximum value of the FR spinor parameter v, [v] FR The maximum circumferential offset distance of FR under design requirements. In this paper, the design requirements [d] FR =0.5mm, [v] FR =0.3mm.

[0103] S52: Processing capacity constraints

[0104] In tolerance optimization design, processing capability constraints refer to the limitations on processing accuracy caused by factors such as equipment, processes, and materials during the actual processing of parts. These constraints determine the scope of tolerance design, that is, the designed tolerance value must be within the range allowed by the processing capability. If it is too strict, it will lead to impossibility or excessive cost, while if it is too loose, it will affect product performance.

[0105]

[0106] Where, T i 、 Indicates the upper and lower bounds of the ith tolerance. In this paper, according to the processing capability of each tolerance, the search space of the optimization algorithm is set as shown in Table 6.

[0107] Table 6 Upper and lower bounds of optimization algorithm search

[0108]

[0109] S53: Optimization equations

[0110]

[0111] S54: Genetic Algorithm Improvement

[0112] (1) Hybrid initialization

[0113] Random initialization, randomly generate a part of the population individuals to cover the entire search space. Confirm the upper and lower limits of each tolerance according to the processing capability requirements Then, tolerance values ​​are randomly generated within the tolerance range to form an individual and increase genetic diversity.

[0114] In the divertor unit tolerance optimization design problem, heuristic initialization prioritizes larger tolerance values ​​for tolerances with lower contributions, based on the calculated tolerance contributions, to reduce processing costs. Next, the generated individuals are verified for assembly accuracy, and those that do not meet the constraints are eliminated. Ultimately, a high-quality initial solution is generated that meets both assembly accuracy constraints and has low processing costs. This approach improves the overall quality of the initial population and lays a good foundation for subsequent genetic algorithm optimization. Tolerance initialization formula:

[0115]

[0116] Where, and T i is the upper and lower limits of the ith tolerance; PC i is the tolerance contribution of the i-th tolerance; n is the total number of tolerances; rand is the random number corresponding to the individual in the range of (0,1).

[0117] (2) Adaptive mutation

[0118] The variation amplitude controls the size of individual gene changes in the genetic algorithm. The variation operation is adjusted in combination with the optimization problem. The variation amplitude is determined according to the sensitivity of the tolerance. For high-sensitivity tolerances, the variation amplitude is reduced to avoid a significant impact on assembly accuracy. Conversely, the variation amplitude is increased to enhance the global search capability. The variation amplitude formula is as follows:

[0119]

[0120] Where ΔT is the tolerance variation of the i-th value, T base is the basic variation range, S i is the sensitivity of the ith tolerance, n is the total number of tolerances, and rand is the random number of the individual in the range of (0,1).

[0121]

[0122] Where, f avg is the average fitness value of the population, f max is the maximum fitness value in the population, the fitness value of the parent individual during the f' mutation operation, R is the total number of algorithm iterations, and r is the number of iterations in which the optimal individual in the current population has not changed. Among them, λ1,λ2∈(0,1) are the upper and lower limits of the adaptive crossover probability, and λ1>λ2.

[0123] (3) Adaptive crossover probability

[0124]

[0125] Where, f avg is the average fitness value of all individuals in the current population, f max is the fitness value of the optimal individual, f c is the maximum fitness of the parent individuals in the crossover operation, R is the total number of algorithm iterations, and r is the number of iterations in which the optimal individual in the current population has not changed. Among them, λ1,λ2∈(0,1) are the upper and lower limits of the adaptive crossover probability, and the size relationship is λ1>λ2.

[0126] S55: Optimization results

[0127] Table 7 Comparison between GA algorithm and improved GA algorithm

[0128]

[0129] The experimental results show that the total processing cost is reduced by 28.32% when the GA algorithm before improvement is used, while the total processing cost is reduced by 14.80% and the average processing time is reduced by 23.31% when the GA algorithm after improvement is used.

Claims

1. A method for analyzing assembly deviations and optimizing tolerances of a divertor unit for a magnetic confinement nuclear fusion device, characterized in that: The following steps are involved: S1: Derivation of the spinor expression of a local parallel structure consisting of two mutually perpendicular plane connection pairs considering the geometric leverage effect; S2: Derivation of the screw expression for a local parallel structure consisting of two cylindrical surfaces with parallel axes, taking into account the geometric leverage effect; S3: Constructing a divertor unit assembly deviation analysis model; S4: Tolerance contribution and tolerance sensitivity analysis; S5: Tolerance optimization design of divertor unit.

2. The derivation of the two spinor expressions for local parallel structures considering geometric leverage effects according to claim 1 is characterized in that The leverage effect in the local parallel structure is incorporated into the spinor model of each connection pair, and then the spinor expression of the local parallel structure is obtained through algebraic operations.

3. The construction of the divertor unit assembly deviation analysis model according to claim 1 is characterized in that By using the aforementioned method for constructing a spinor model of a local parallel structure taking into account the geometric leverage effect, the spinor model of the local parallel structure formed during the assembly of the divertor unit is constructed, thereby converting the series connection relationship containing the local parallel structure into a pure series connection relationship.

4. The tolerance contribution and tolerance sensitivity analysis according to claim 1, characterized in that Based on statistical methods, specific tolerances within functional elements are dynamically adjusted to record their tolerance values ​​and deviation values ​​of functional element prescriptions. The relationship between tolerance values ​​and deviations is analyzed through linear regression, thereby decomposing the tolerance contribution to a specific tolerance. The sensitivity of each tolerance to the final deviation is calculated through the single-parameter perturbation method.

5. The tolerance optimization design method according to claim 1, characterized in that The traditional genetic algorithm is improved by combining tolerance contribution and tolerance sensitivity, which effectively improves the solving efficiency and solution quality of the genetic algorithm.

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