CN106156409B - Two-parameter special-shaped bolt hole robust design method based on minimum contour change - Google Patents

Abstract

The invention discloses a robust design method for two-parameter special-shaped bolt holes based on the minimum contour change. In the optimized design, the invention adopts (a) reducing the stress on the edge of the hole to a specified value and (b) controlling the change range of the special-shaped hole contour (that is, to avoid the excessive difference between the contour of the special-shaped hole and the original circular contour) and other optimization goals. In the optimization model, a comprehensive optimization design model for special-shaped holes is established by performing a reasonable weighted summation process for each optimization objective. At the same time, the dynamic adjustment method of the weight coefficient in which the contribution of different design objectives to the comprehensive optimization objective is balanced is adopted, and the balanced optimization design effect of the special-shaped hole under the condition of multiple objectives is obtained, which fundamentally eliminates the optimization results of each design variable (ie arc size) of the special-shaped hole. The dependence on the value range of the design variables can be quickly optimized to obtain the best special-shaped hole contour that meets the requirements of the strength design task and has the smallest contour size change. The design results have good consistency.

Description

A Robust Design Method for Two-Parameter Special-shaped Bolt Holes Based on Minimum Profile Variation

technical field

The invention belongs to the structural optimization design of aero-engine turbine rotor components, in particular to a multi-objective optimization design model of the contour shape of a turbine disk biaxially symmetrical special-shaped bolt hole.

Background technique

The long-term working environment of aero-engine high-pressure turbine disks is harsh, and the bolt holes on the front mounting side often cause cracks on the side of the holes due to stress concentration, which is an important reason for the failure of the disk.

The patent "multi-arc special-shaped hole" (patent number: ZL2013 1 0287309.9) proposes an eight-arc special-shaped hole structure. But there are still the following shortcomings:

1. The optimal value of the objective function in the existing optimization model has an over-optimization phenomenon (that is, the drop of the hole edge stress exceeds the design requirement).

2. The results of the optimal design are overly dependent on the setting of the value range of the design variables. In the actual design, continuous trial calculations are required to determine the reasonable range of the design variables, and the design efficiency is low.

3. The robustness of the optimization design results is poor, and the convergence speed of the optimization process is slow.

SUMMARY OF THE INVENTION

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a robust design method for two-parameter special-shaped bolt holes based on minimum contour changes, which can avoid cumbersome and inefficient boundary trial calculations during optimal design, and improve design. the rationality and stability, and greatly improve the design efficiency.

Technical scheme: In order to realize the above-mentioned purpose, the technical scheme adopted in the present invention is:

A robust design method for two-parameter special-shaped bolt holes based on minimal contour variation, including the following steps:

Step 1. Establish a multi-objective optimization model for special-shaped holes according to the given target value of the task, the radius of the main arc, the radius of the transition arc, the target of stress reduction, the target of the size of the main arc of the special-shaped hole and the change of the size of the transition arc.

Step 2. Determine the size constraints of the multi-objective optimization model of the special-shaped hole in step 1 according to the upper bound of the main arc radius and the lower bound of the transition arc radius.

Step 3. Referring to the weighting coefficient, the multi-objective optimization model of the special-shaped hole is converted into a single comprehensive objective optimization model of the special-shaped hole.

Step 4. Optimize the single comprehensive target optimization model of the special-shaped hole according to the change value of the fixed contour and the allowable error, obtain each design variable of the special-shaped hole, and complete the design of the special-shaped hole.

The method for establishing a multi-objective optimization model for the special-shaped hole in the step 1 includes the following steps:

Step 11: Establish a dimensionless stress reduction objective function according to the given target value of the task, the radius of the main arc, and the radius of the transition arc.

Step 12: Establish the main arc radius dimensionless special-shaped hole contour control objective function according to the original bolt through hole radius and the main arc radius.

Step 13 , according to the original bolt through hole radius and the transition arc radius, establish the transition arc radius dimensionless special-shaped hole contour control objective function.

Step 14, establish according to the objective function of the dimensionless stress reduction amplitude established in step 11, the main arc radius dimensionless special-shaped hole contour control objective function established in step 12, and the transition arc radius dimensionless special-shaped hole contour control objective function established in step 13. A multi-objective optimization model for shaped holes.

In the step 11, the expression of the objective function of the dimensionless stress reduction amplitude is as follows:

f ₁ (σ _max ) is the objective function of the dimensionless stress reduction range, σ _max is the maximum principal stress at the edge of the hole, σ _max =σ _max (R ₁ , R ₂ ), R ₁ is the main arc radius, and R ₂ is the transition circle Arc radius, σ _o represents the task given target value.

In described step 12, the expression of the main arc radius dimensionless special-shaped hole contour control objective function is as follows:

Among them, f ₂ (R ₁ ) is the main arc radius of the dimensionless special-shaped hole contour control objective function, R ₁ is the main arc radius, and R* represents the original bolt through hole radius.

In described step 13, the expression of the control objective function of the non-dimensionally shaped hole contour of the transition arc radius is as follows:

Among them, f ₃ (R ₂ ) is the transition arc radius dimensionless hole contour control objective function, R ₂ is the transition arc radius, and R* represents the original bolt through hole radius.

The expression of the multi-objective optimization model for special-shaped holes in the step 14 is as follows:

minf(y ₁ =f ₁ (σ _max ), y ₂ =f ₂ (R ₁ ), y ₃ =f ₃ (R ₂ )).

The size constraints established in step 2 are:

Among them, R _1max is the upper bound of the main arc radius, R _2min is the lower bound of the transition arc radius, R ₁ is the main arc radius, R ₂ is the transition arc radius, and R* represents the original bolt through hole radius.

The single comprehensive objective optimization model of the special-shaped hole in the step 3 is:

f(f ₁ , f ₂ , f ₃ )=k ₁ ·f ₁ (σ _max )+k ₂ ·f ₂ (R ₁ )+k ₃ ·f ₃ (R ₂ ).

Among them, k ₁ is the weighting coefficient of the objective function of dimensionless stress reduction amplitude, f ₁ (σ _max ) is the objective function of dimensionless stress reduction amplitude, k ₂ is the weighting coefficient of the main arc radius dimensionless special-shaped hole contour control objective function, f ₂ (R ₁ ) the main arc radius dimensionless special-shaped hole contour control objective function, k ₃ is the weighting coefficient of the transition arc radius dimensionless special-shaped hole contour control objective function, f ₃ (R ₂ ) is the transition arc radius infinite The contour control objective function of the special-shaped hole.

The method for determining the weighting coefficient in the step 3 is as follows:

The weighting coefficient k 1 of the objective function of the dimensional stress reduction amplitude, the weighting coefficient k ₂ of the main arc radius dimensionless special-shaped hole contour control objective function, the weighting coefficient k ₃ of the transition arc radius dimensionless special-shaped hole contour control objective function varies with _{R 1} The value range of the main arc radius and the target value of σ _o stress vary dynamically, among which: when the value range of the main arc radius R ₁ and the transition arc radius R ₂ changes, the impact on the hole edge stress is different.

When R _1max changes:

k ₂ =0.008～0.012

Between k ₂ and k ₃ :

k ₃ =g ₁ (k ₂ ,R _1max )=(1.25 to 2.1)·k ₂ ·R _1max

Between k ₁ and k ₂ , k ₃ satisfies:

Among them, σ _1r is the maximum principal stress value of the original circular bolt through hole edge.

When optimizing the single comprehensive target optimization model of the special-shaped hole in the step 4, only when the optimized special-shaped hole hole edge stress meets the predetermined requirements, that is, |σ _max -σ _o |≤ε, ε is the allowable error. And compared with the original bolt circular through hole, when the contour change of the special-shaped bolt hole is less than the given contour change value, the design parameters or variables are the optimized values that meet the requirements.

Beneficial effects: Compared with the prior art, a robust design method for two-parameter special-shaped bolt holes based on minimum profile changes provided by the present invention has the following beneficial effects:

1. The optimization objective of the two-variable special-shaped hole optimization problem is improved, so that the obtained optimal solution can reduce the hole edge stress according to the expected objective.

2. The contour size of the special-shaped hole obtained by the optimized design can not only meet the stress reduction to the specified value, but also not deviate too much from the original contour, so the design is more robust.

3. Overcome the problem that the original optimization result relies too much on the value range of design variables, and it is not necessary to repeatedly adjust the design range of each arc size (R ₁ , R ₂ ) of the special-shaped hole in the optimization design, thereby improving the optimization design point. The stability makes the final design scheme more reasonable, and the design efficiency is also significantly improved.

Description of drawings

Fig. 1 is a flow chart of dynamic determination of weighting coefficients k ₁ , k ₂ , k ₃ ;

Figure 2 is the contour of the special-shaped hole obtained based on the multi-objective two-variable optimization model;

Among them: 1- the main arc R ₁ of the two-variable special-shaped hole; 2- the transition arc R ₂ of the two-variable special-shaped hole; 3- the traditional bolt through hole (base circle).

Detailed ways

Below in conjunction with the accompanying drawings and specific embodiments, the present invention will be further clarified. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. Modifications in the form of valence all fall within the scope defined by the appended claims of the present application.

A robust design method for two-parameter special-shaped bolt holes based on minimum contour changes. This model proposes a robust design method for the contour optimization problem of special-shaped bolt through holes (hereinafter referred to as special-shaped holes) on aero-engine high-pressure turbine disks. In the optimization design, optimization objectives such as (a) reducing the stress on the edge of the hole to the specified value of the task and (b) controlling the variation range of the contour of the special-shaped hole (that is, to avoid the excessive difference between the contour of the special-shaped hole and the original circular contour) are adopted to obtain Reasonable and robust design. In the optimization model, a comprehensive optimization design model for special-shaped holes is established by performing a reasonable weighted summation process for each optimization objective. In the comprehensive optimization model, since the weight of each objective will change with the value range of the special-shaped hole design variables, the patent inventor designed a dynamic weight coefficient that can keep the contribution of different design objectives to the comprehensive optimization objective balanced. The adjustment method makes the weight coefficient (k ₁ ) related to the stress control target associated with the value range of the contour design variables of the special-shaped hole. When the latter changes, k ₁ can be automatically adjusted, thus obtaining the special-shaped hole under the multi-objective condition. The effect of hole balance optimization design fundamentally eliminates the dependence of the optimization results of each design variable (ie arc size) of the special-shaped hole on the value range of the design variables, and can be quickly optimized to meet the requirements of the strength design task with the smallest change in the contour size. optimum hole profile. The invention enables the two-variable special-shaped hole contour design to be optimally designed according to the target value of the hole edge stress given by the task, and at the same time, it is not necessary to repeatedly test and adjust the size range of each design variable of the special-shaped hole, and the design results have good consistency.

Specifically include the following steps:

Step 1. Establish a multi-objective optimization model for special-shaped holes according to the given target value of the task, the radius of the main arc, the radius of the transition arc, the target of stress reduction, the target of the size of the main arc of the special-shaped hole and the change of the size of the transition arc.

Specifically include the following steps:

Step 11: According to the given target value of the task, the radius of the main arc, and the radius of the transition arc, a dimensionless stress reduction range objective function is established, f ₁ (σ _max ) is the dimensionless stress reduction range objective function, and it is necessary to ensure that the maximum hole edge The principal stress is sufficiently close to a certain target value σ _o set in advance (task given). Its expression is as follows:

f ₁ (σ _max )=mind

d represents the dimensionless difference between the maximum principal stress σ _max described by f ₁ (R) and the pre-set stress target value σ _o .

f ₁ (σ _max ) is the objective function of the dimensionless stress reduction range, σ _max is the maximum principal stress at the edge of the hole, σ _max =σ _max (R ₁ , R ₂ ), R ₁ is the main arc radius, and R ₂ is the transition circle Arc radius, σ _o represents the task given target value. In the specific implementation, the σ _o stress target value should be determined according to the design task objectives and working conditions

Step 12, establish the main arc radius dimensionless special-shaped hole contour control objective function according to the original bolt through-hole radius and the main arc radius. Robust design point. Based on the original bolt through hole radius R*. Its expression is as follows:

Among them, f ₂ (R ₁ ) is the main arc radius of the dimensionless special-shaped hole contour control objective function, R ₁ is the main arc radius, and R* represents the original bolt through hole radius.

On the premise that the objective functions f ₂ (R ₁ ) and f ₃ (R ₂ ) can satisfy the objective f ₁ (R), the obtained profile size R(R ₁ , R ₂ ) of the special-shaped hole is as close as possible to the traditionally designed bolt through hole contour for a more robust design point.

f ₂ (R ₁ )=minδ ₁ , f ₃ (R ₂ )=minδ ₂ ;

Among them, δ ₁ and δ ₂ respectively represent the dimensionless difference between the main arc R ₁ and transition arc radius R ₂ of the special-shaped hole and the base circle radius of the bolt hole, as follows.

Step 13: According to the original bolt through hole radius and the transition arc radius, establish the transition arc radius dimensionless special-shaped hole contour control objective function, which will make the difference between the optimized special-shaped hole contour and the original contour as small as possible, so as to obtain more Robust design point. Based on the original bolt through hole radius R*. Its expression is as follows:

Among them, f ₃ (R ₂ ) is the transition arc radius dimensionless hole contour control objective function, R ₂ is the transition arc radius, and R* represents the original bolt through hole radius.

In the optimization design, when determining the value range of the design variables, R _1max (the upper bound of the main arc radius) can be taken as 8~20R* (R* is the base circle radius) according to the actual bolt hole diameter; R _2min is the transition arc radius The lower bound depends on the minimum radius under actual machining conditions, and the actual minimum diameter tool radius can be taken.

Step 14, establish according to the objective function of the dimensionless stress reduction amplitude established in step 11, the main arc radius dimensionless special-shaped hole contour control objective function established in step 12, and the transition arc radius dimensionless special-shaped hole contour control objective function established in step 13. The multi-objective optimization model for special-shaped holes is expressed as follows:

minf(y ₁ =f ₁ (σ _max ),y ₂ =f ₂ (R ₁ ),y ₃ =f ₃ (R ₂ ))

When solving a specific optimization problem, all design points R _i (R ₁ , R ₂ ) correspond to f ₁ , f ₂ , f ₃ of the objective function to form a criterion space, which is represented by F, as follows:

F={f _i (f ₁ , f ₂ , f ₃ )∈R ³ |f ₁ =f ₁ (σ _maxi ),f ₂ =f ₂ (R ₁ ),f ₃ =f ₃ (R ₂ )}

f _i =(f ₁ , f ₂ , f ₃ ) is a vector composed of three objective function values. The optimization process is the evaluation process of all vectors f _i in the criterion space.

σ _max =σ _max (R ₁ , R ₂ ), R ₁ , R ₂ represent the main arc and the transition arc respectively, which represent the design point R; f ₁ (σ _max ) is the same as the design point R(R ₁ , R ₂ ) corresponds to the objective function of the stress drop amplitude; f ₂ (R ₁ ) is the objective function of the change control of the main arc R ₁ ; f ₃ (R ₂ ) is the objective function of the change of the transition arc R ₂ . R* is the radius of the base circle (that is, the traditional design bolt through hole), R _1max is the upper bound of the main arc radius, and R _2min is the lower bound of the transition arc radius.

The multi-objective optimization model of special-shaped holes satisfies:

(1) Reduce the stress on the edge of the hole to the given target of the strength design task;

(2) The size of the hole contour changes the smallest;

(3) Effectively reduce the dependence of the contour size of the special-shaped hole obtained by optimization on the value range of the design variables, and improve the robustness of the design.

Step 2. Determine the size constraints of the multi-objective optimization model of the special-shaped hole in step 1 according to the upper bound of the main arc radius and the lower bound of the transition arc radius.

Its size constraints are:

Among them, R _1max is the upper bound of the main arc radius, which can be any value within a reasonable range, R _2min is the lower bound of the transition arc radius, R ₁ is the main arc radius, R ₂ is the transition arc radius, and R* represents the base Circle, i.e. traditional design (original) bolt through hole radius.

Step 3. Convert the multi-objective optimization model of special-shaped holes into a single comprehensive objective optimization model of special-shaped holes by referring to the weighting coefficient, that is, weighted calculation of the objectives f ₁ (σ _max ), f ₂ (R ₁ ) and f ₃ (R ₂ ) and processing, reducing the multi-objective optimization problem into a single comprehensive objective.

The single comprehensive objective optimization model for special-shaped holes is:

f(f ₁ , f ₂ , f ₃ )=k ₁ ·f ₁ (σ _max )+k ₂ ·f ₂ (R ₁ )+k ₃ ·f ₃ (R ₂ ).

Among them, k ₁ is the weighting coefficient of the objective function of dimensionless stress reduction amplitude, f ₁ (σ _max ) is the objective function of dimensionless stress reduction amplitude, k ₂ is the weighting coefficient of the main arc radius dimensionless special-shaped hole contour control objective function, f ₂ (R ₁ ) the main arc radius dimensionless special-shaped hole contour control objective function, k ₃ is the weighting coefficient of the transition arc radius dimensionless special-shaped hole contour control objective function, f ₃ (R ₂ ) is the transition arc radius infinite The contour control objective function of the special-shaped hole.

The multi-objective optimization design model composed of three new objective functions in the present invention can control the maximum principal stress reduction range of the hole edge and the profile size change of the special-shaped hole at the same time, so that the reduction range of the hole edge stress can meet the set target, and the hole shape design is more efficient. Robust, the pass parameters are more stable.

The contribution of the three single optimization objectives to the comprehensive optimization objective can be adjusted by the weighting coefficients k ₁ , k ₂ , and k ₃ .

As shown in accompanying drawing 1, the determination method of weighting coefficient is as follows:

The weighting coefficient k 1 of the objective function of the dimensional stress reduction amplitude, the weighting coefficient k ₂ of the main arc radius dimensionless special-shaped hole contour control objective function, the weighting coefficient k ₃ of the transition arc radius dimensionless special-shaped hole contour control objective function varies with _{R 1} The value range of the main arc radius and the target value of σ _o stress vary dynamically, among which: when the value range of the main arc radius R ₁ and the transition arc radius R ₂ changes, the impact on the hole edge stress is different.

When R _1max changes:

k ₂ =0.008～0.012

Between k ₂ and k ₃ :

k ₃ =g ₁ (k ₂ ,R _1max )=(1.25 to 2.1)·k ₂ ·R _1max

Between k ₁ and k ₂ , k ₃ satisfies:

Among them, σ _1r is the maximum principal stress value of the original circular bolt through hole edge.

The generated weighting coefficients k ₁ , k ₂ , and k ₃ can make the variation of each design parameter more balanced, and obtain a robust design point.

Step 4. Optimize the single comprehensive target optimization model of the special-shaped hole according to the change value of the fixed contour and the allowable error, obtain each design variable of the special-shaped hole, and complete the design of the special-shaped hole.

When optimizing the single comprehensive objective optimization model of the special-shaped hole, only when the optimized special-shaped hole hole edge stress meets the established requirements, that is, |σ _max -σ _o |≤ε, ε is the allowable error. And compared with the circular through hole of the original bolt, when the contour change of the special-shaped bolt hole is smaller than the given contour change value, the design parameters or variables are the optimized values that meet the requirements. In the given multi-objective optimization model, three single parameters are required. Objectives contribute equally to the overall design results. Since the weighting coefficients k ₁ , k ₂ , k ₃ are related to the value range of the design variables, a dynamic generation method for the weighting coefficients k ₁ , k ₂ , k ₃ is given, so that the values of k ₁ , k ₂ , k ₃ can be With the different value ranges of R _1max , adjust the value to meet the balance between the three single optimization objectives, and finally obtain a more robust and stable design point that meets the strength design requirements, ensuring that the three have appropriate influencing factors , thus ensuring the robustness of the final optimal solution.

The multi-objective optimization design method proposed in the present invention can obtain a hole shape design scheme with smaller hole profile changes and more robust on the basis of satisfying the stress design objective (task value); in addition, in the optimization design, the special-shaped hole arc When the allowable variation range of the size changes significantly, the stable optimal solution can still be maintained, so that the final optimal design result can get rid of the dependence on the setting range value of the arc design variable and improve the design efficiency. The two-parameter shaped pore structure obtained under the multi-objective optimization model is shown in FIG. 2 .

The invention provides a new multi-objective optimization design model, which can give a robust and stable design scheme according to the drop range of the hole edge stress specified by the task. The multi-objective optimization model consists of (a) the stress reduction objective, (b) the change objective of the main arc size R1 _of the special-shaped hole and (c) the change objective of the transition arc size R2 _; in the multi-objective optimization model, three single objectives (i.e. (a), (b) and (c)) the contribution to the comprehensive goal should satisfy the equilibrium condition; the new model and algorithm provided can avoid the tedious and inefficient boundary trial calculation when optimizing the design, and improve the rationality of the design and stability, while greatly improving design efficiency.

The above is only the preferred embodiment of the present invention, it should be pointed out that: for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can also be made, and these improvements and modifications are also It should be regarded as the protection scope of the present invention.

Claims (5)

1. a robust design method for two-parameter special-shaped bolt holes based on minimum profile changes, is characterized in that, comprises the following steps: Step 1. According to the given target value of the task, the radius of the main arc, the radius of the transition arc, the target of stress reduction, the target of the size of the main arc of the special-shaped hole and the change of the size of the transition arc, the multi-objective optimization model of the special-shaped hole is established; The method for establishing a multi-objective optimization model for special-shaped holes includes the following steps: Step 11, establish a dimensionless stress drop range objective function according to the given target value of the task, the radius of the main arc, and the radius of the transition arc; The expression of the objective function of dimensionless stress drop amplitude is as follows:

f ₁ (σ _max ) is the objective function of the dimensionless stress reduction range, σ _max is the maximum principal stress at the edge of the hole, σ _max =σ _max (R ₁ , R ₂ ), R ₁ is the main arc radius, and R ₂ is the transition circle Arc radius, σ _o represents the given target value of the task; Step 12, establish the main arc radius dimensionless special-shaped hole contour control objective function according to the original bolt through hole radius and the main arc radius; In described step 12, the expression of the main arc radius dimensionless special-shaped hole contour control objective function is as follows:

Among them, f ₂ (R ₁ ) is the main arc radius of the dimensionless special-shaped hole contour control objective function, R ₁ is the main arc radius, and R* represents the original bolt through hole radius; Step 13, according to the original bolt through hole radius and the transition arc radius, establish the transition arc radius dimensionless special-shaped hole contour control objective function; The expression of the objective function of the transition arc radius dimensionless hole contour control is as follows:

Among them, f ₃ (R ₂ ) is the transition arc radius dimensionless hole profile control objective function, R ₂ is the transition arc radius, and R* represents the original bolt through hole radius; Step 14, establish according to the objective function of the dimensionless stress reduction amplitude established in step 11, the main arc radius dimensionless special-shaped hole contour control objective function established in step 12, and the transition arc radius dimensionless special-shaped hole contour control objective function established in step 13. Special-shaped hole multi-objective optimization model; The expression of the multi-objective optimization model for special-shaped holes is as follows: minf(y ₁ =f ₁ (σ _max ),y ₂ =f ₂ (R ₁ ),y ₃ =f ₃ (R ₂ )); Step 2. Determine the size constraints of the multi-objective optimization model of the special-shaped hole in step 1 according to the upper bound of the main arc radius and the lower bound of the transition arc radius; Step 3. Quoting the weighting coefficient, convert the multi-objective optimization model of the special-shaped hole into a single comprehensive target optimization model of the special-shaped hole; Step 4. Optimize the single comprehensive target optimization model of the special-shaped hole according to the change value of the fixed contour and the allowable error, obtain each design variable of the special-shaped hole, and complete the design of the special-shaped hole. 2. The robust design method for two-parameter special-shaped bolt holes based on minimum profile changes according to claim 1, wherein the size constraints established in the step 2 are:

Among them, R _1max is the upper bound of the main arc radius, R _2min is the lower bound of the transition arc radius, R ₁ is the main arc radius, R ₂ is the transition arc radius, and R* represents the original bolt through hole radius. 3. The robust design method for two-parameter special-shaped bolt holes based on minimum profile changes according to claim 2, wherein: the special-shaped hole single comprehensive target optimization model in the step 3 is: f(f ₁ , f ₂ , f ₃ )=k ₁ ·f ₁ (σ _max )+k ₂ ·f ₂ (R ₁ )+k ₃ ·f ₃ (R ₂ ); Among them, k ₁ is the weighting coefficient of the objective function of dimensionless stress reduction amplitude, f ₁ (σ _max ) is the objective function of dimensionless stress reduction amplitude, k ₂ is the weighting coefficient of the main arc radius dimensionless special-shaped hole contour control objective function, f ₂ (R ₁ ) the main arc radius dimensionless special-shaped hole contour control objective function, k ₃ is the weighting coefficient of the transition arc radius dimensionless special-shaped hole contour control objective function, f ₃ (R ₂ ) is the transition arc radius infinite The contour control objective function of the special-shaped hole. 4. The robust design method for two-parameter special-shaped bolt holes based on minimum profile changes according to claim 3, wherein the method for determining the weighting coefficient in the step 3 is as follows: The weighting coefficient k 1 of the objective function of the dimensional stress reduction amplitude, the weighting coefficient k ₂ of the main arc radius dimensionless special-shaped hole contour control objective function, the weighting coefficient k ₃ of the transition arc radius dimensionless special-shaped hole contour control objective function varies with _{R 1} The value range of the main arc radius and the target value of σ _o stress vary dynamically, among which: when the value ranges of the main arc radius R ₁ and the transition arc radius R ₂ change, the impact on the stress on the edge of the hole is different; When R _1max changes: k ₂ =0.008～0.012 Between k ₂ and k ₃ : k ₃ =g ₁ (k ₂ ,R _1max )=(1.25 to 2.1)·k ₂ ·R _1max Between k ₁ and k ₂ , k ₃ satisfies:

Among them, σ _1r is the maximum principal stress value of the original circular bolt through hole edge. 5. The method for robust design of two-parameter special-shaped bolt holes based on minimum contour changes according to claim 4, characterized in that: in the step 4, when optimizing a single comprehensive target optimization model for special-shaped holes, only the optimized special-shaped The hole edge stress meets the established requirements, that is, |σ _max -σ _o |≤ε, ε is the allowable error; and when the contour change of the special-shaped bolt hole is smaller than the given contour change value compared with the original bolt circular through hole, the design parameters Or variable is the optimized value that satisfies the requirement.

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