Two-stage fingertip seal structure optimization method based on Taguchi method

Abstract

The invention particularly relates to a two-stage fingertip sealing structure optimization method based on a Taguchi method, and belongs to the technical field of mechanical sealing. According to the method, the leakage rate, the inter-stage pressure difference rate and the highest temperature serve as optimization targets, six key structure parameters including the first-stage fingertip seal shoe height Xg1, the second-stage fingertip seal shoe height Xg2, the rear baffle height Hb1, the rear baffle height Hb2 and the fingertip sheet layer number N1 and N2 are selected as control factors, five levels are set for each factor, and an L25 (65) orthogonal test table containing 25 test combinations is constructed. FLUENT fluid simulation software is used for simulating each test combination, corresponding performance indexes are obtained, and through mean value analysis and variance analysis, a control factor which has the largest influence on each response target and an optimal level combination of the control factor are determined. The accuracy of the optimization result can be ensured, the optimization efficiency of the structural parameters is improved, and the result is accurate and reliable; the two-stage fingertip seal optimization design method based on the Taguchi method is adopted, and the sealing performance of the two-stage fingertip seal can be effectively improved; the test frequency is greatly reduced, and a large amount of test time and cost can be saved.

Description

Technical Field

[0001] The invention relates to a two-stage fingertip seal structure optimization method based on the Taguchi method, and belongs to the technical field of mechanical seals. Background Art

[0002] With the continuous advancement of aircraft engine technology, the requirements for thrust-to-weight ratio, fuel efficiency, reliability and operating costs are increasing. Traditional fingertip seals are prone to large leakage, severe wear and reduced service life under high axial pressure. In order to adapt to high axial pressure differential conditions, two-stage fingertip seals are widely used in air path seals and main shaft seals of aircraft engines.

[0003] The two-stage fingertip seal consists of the first-stage fingertip seal, the middle partition and the second-stage fingertip seal. They have the same structure and are assembled from a front baffle, a partition, a multi-layer fingertip sheet and a rear baffle. Due to the interference with the rotor surface, friction heat will be generated between the fingertip boot and the rotor surface, which will affect the seal life. At the same time, the leakage airflow will produce a large pressure drop at the second-stage fingertip seal, resulting in an unbalanced pressure drop between stages, which may cause the second-stage seal to fail prematurely and affect the overall performance.

[0004] The key to improving the performance of two-stage fingertip seals is to reduce leakage and local maximum temperature, while balancing the interstage pressure drop between the two-stage seals. The main influencing structural parameters include the boot height X of the first and second stage fingertip seals. g1 , X g2 , height of rear baffle H b1 ,H b2 And the number of fingertip sheet layers N1 and N2.

[0005] Traditional optimization methods such as the control variable method, the full factor method and the global optimization algorithm have problems such as low efficiency, large amount of experiments and insufficient precision, and it is difficult to meet the needs of fast and efficient optimization of two-stage fingertip seals. Summary of the invention

[0006] The purpose of the present invention is to propose a two-stage fingertip seal structure optimization method based on the Taguchi method to solve the problems of low optimization efficiency, large test volume, insufficient precision, etc. of the existing two-stage fingertip seal structure.

[0007] The technical solution of the present invention comprises the following steps:

[0008] Step 1: Determine the two-stage fingertip seal performance index as the response target, select the leakage volume Q, inter-stage pressure difference rate and maximum temperature T max As the performance index of the two-stage fingertip seal, the performance index is the optimization target, among which the leakage Q reflects the airflow leakage level of the two-stage fingertip seal, and the pressure difference rate between the stages Reflects the deviation of the ratio of the pressure drop of the second-stage fingertip seal to the pressure drop of the first-stage fingertip seal, the maximum temperature T max The maximum temperature of the fingertip boot when the fingertip seal is in working condition;

[0009] Step 2: Determine the control factors and their levels. The structural parameters that affect the performance of the two-stage fingertip seal are: the height of the first-stage fingertip seal boot x g1 , Level 2 fingertip seal boots high X g2 、Height H of rear baffle for first-stage fingertip seal b1 、The height of the rear baffle plate of the second-stage fingertip seal is H b2 , the number of layers of the first-level fingertip sealing sheet N1 and the number of layers of the second-level fingertip sealing sheet N2, each structural parameter is set as a control factor, and each structural parameter is set to 5 values, each value is the level of each control factor, as shown in Table 1

[0010] Table 1 Orthogonal factor level table

[0011] Factor Level 1 Level 1 Level 3 Level 4 Level 5 <![CDATA[X g1 ]]> 1 1.2 1.4 1.6 1.8 <![CDATA[X g2 ]]> 1 1.2 1.4 1.6 1.8 <![CDATA[H b1 ]]> 0.8 1 1.2 1.4 1.6 <![CDATA[H b2 ]]> 0.8 1 1.2 1.4 1.6 N1 2 3 4 5 6 N2 2 3 4 5 6

[0012] Step 3: Construct an orthogonal test table based on the control factors and levels in Step 2. To ensure the balance and effectiveness of the experimental design, construct an L25 (65) orthogonal test table and design 25 test combinations.

[0013] Step 4: Use FLUENT fluid simulation software to simulate each test combination in Step 3 and calculate the performance indicators of each experimental combination, namely leakage Q, interstage pressure difference rate and maximum temperature T max , the performance index is the corresponding response target value, as shown in Table 2:

[0014] Table 2 Orthogonal test table and response target results

[0015]

[0016]

[0017] Step 5: Calculate the response target values ​​obtained in Step 4, i.e., the leakage volume Q and the inter-stage pressure difference rate. and maximum temperature T max Using the total mean m and the level mean M kji By performing mean analysis and variance analysis, we can determine the control factors that have the greatest impact on leakage, interstage pressure difference rate and maximum temperature and their optimal level combination. The average value is:

[0018]

[0019] Where m is the average value of each corresponding target, n is the number of trials, and TI is the response target value of the ith trial;

[0020] The average level is:

[0021]

[0022] Among them, M kij is the mean of the kth response target at the jth level of the ith factor, a is the experimental number of the jth level of the ith factor, T ijn is the target value of the response at the jth level of the i-th factor;

[0023] The variance is:

[0024]

[0025] Among them, S kij is the variance value of the kth response target under the i-th factor;

[0026] The specific gravity is:

[0027]

[0028] Among them, W kj is the proportion of each factor variance to the total variance;

[0029] (1) Mean analysis: The Taguchi orthogonal test table (Table 2) was subjected to mean analysis using formula (6) to calculate the average value of the two-stage fingertip seal response target at a certain level of a certain factor. The calculation results are shown in Table 3.

[0030] Table 3 Average values ​​of each response target at each level of each factor

[0031]

[0032] According to the mean values ​​of each response target of the two-level fingertip seal established in Table 3 at each level of each factor, the following is drawn: Figure 3-5 The mean change trend of each factor at different levels is shown in the figure, and the letters A, B, C, D, E, and F are used to represent X respectively. g1 , X g2 , H b1 , H b2 , N1, N2, it can be seen that when the leakage Q of the two-stage fingertip seal is the smallest, the optimal two-stage fingertip seal structural parameter combination is: A4B4 C1 D1 E2 F5; the inter-stage pressure difference rate of the two-stage fingertip seal is When it is close to 1, the optimal two-stage fingertip seal structural parameter combination is: A4B1C1 D3 E1 F2; when the maximum temperature of the boot of the two-stage fingertip seal is the lowest, the optimal two-stage fingertip seal structural parameter combination is: A2 B2 C4 D2 E2 F2.

[0033] (2) Analysis of variance

[0034] The total mean values ​​of each response target of the two-stage fingertip seal under the total test are calculated, as shown in Table 4;

[0035] Table 4 Total mean values ​​of each response target in the total test

[0036] Q(g / s) φ <![CDATA[T max (K) <!-- 4 -->]]> Overall mean 47.0832 2.3908 329.905

[0037] According to formula 7, formula 8 and the data in Tables 3 and 4, the variance and weight of the two-level fingertip seal response target under each factor and each level are calculated, as shown in Table 5;

[0038] Table 5 is the variance analysis table of the two-level fingertip seal response target under each factor and each level;

[0039]

[0040] According to the variance and proportion of the two-level fingertip seal response target established in Table 5, a variance proportion bar chart is drawn; from the variance analysis table and the variance proportion bar chart, it can be obtained that: Level 1 fingertip seal boot height x g1 The greatest impact on the inter-stage pressure difference rate, X g1 Select the level that minimizes the interstage pressure difference rate, i.e. level 4; the second stage fingertip seal boot height X g2 The greatest impact on the maximum temperature, X g2 Select the level that minimizes the maximum temperature, i.e. level 2; the height of the rear baffle of the first level fingertip seal is H b1 The greatest influence on the inter-stage pressure difference rate, H b1 Select the level that minimizes the interstage pressure difference rate, i.e. level 1; the height of the baffle after the second stage fingertip seal is H b2 The biggest influence on leakage is H b2 Select the level with the lowest leakage, i.e., level 1; the number of layers of the first-level fingertip seal sheet N1 has the greatest impact on the maximum temperature, and N1 selects the level with the minimum maximum temperature, i.e., level 2; the number of layers of the second-level fingertip seal sheet N2 has the greatest impact on the maximum temperature, and N2 selects the level with the minimum maximum temperature, i.e., level 2; finally, the optimal factor level combination of the two-level fingertip seal response target obtained by variance analysis is: A4 B2 C1 D1 E2 F2;

[0041] Step 6: Based on the optimal factor combination obtained in Step 5, that is, the optimal structural parameter combination, the FLUENT fluid simulation software is used to build a model according to the optimal structural parameter combination, and the performance indicators of the two-stage fingertip seal are simulated and analyzed. The performance indicators are compared with the response target values ​​of the 25 test combinations, the optimization effect is evaluated, and the final optimization scheme is determined, as shown in Table 6.

[0042] Table 6 shows the comparison of the two-stage fingertip seal performance before and after optimization

[0043]

[0044] The Level 1 fingertip seal boots high x g1 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, 1.8mm respectively. The second level fingertip seal boot height is X g2 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, and 1.8mm respectively. The height of the baffle after the first-level fingertip seal is H b1 The values ​​are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm respectively. The height of the baffle after the second-level fingertip seal is H b2 The values ​​of are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm, the values ​​of the number of first-level fingertip sealing sheets N1 are 2, 3, 4, 5, and 6, respectively, and the values ​​of the number of second-level fingertip sealing sheets N2 are 2, 3, 4, 5, and 6, respectively.

[0045] The beneficial effects of the present invention are:

[0046] 1. The present invention adopts the FLUENT fluid simulation platform to provide a data source for the Taguchi orthogonal test table. The response target result obtained from each simulation test is used as the optimization basis. The accurate simulation data provides an effective basis for mean analysis and variance analysis, which can ensure the accuracy of the optimization results, improve the optimization efficiency of the structural parameters, and the results are accurate and reliable.

[0047] 2. The present invention adopts a two-stage fingertip seal optimization design method based on the Taguchi method, which can effectively improve the sealing performance of the two-stage fingertip seal;

[0048] 3. The present invention selects 6 control factors in the optimization process, each factor has 5 levels, and only 25 experiments are required. Compared with the 15625 experiments required by the full factorial experiment method, the number of experiments is greatly reduced, which can save a lot of experimental time and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is the overall flow chart of the present invention;

[0050] Figure 2This is a simulation optimization framework structure diagram of the problem-solving model proposed in the present invention;

[0051] Figure 3 This is an analysis diagram of the influence of different levels of various factors on leakage in the present invention;

[0052] Figure 4 This is an analysis diagram of the influence of different levels of various factors on the inter-stage pressure difference rate of the present invention;

[0053] Figure 5 This is an analysis diagram of the influence of different levels of various factors on the maximum temperature of the present invention. DETAILED DESCRIPTION

[0054] Example 1: Figure 1-5 As shown, the technical solution of the present invention comprises the following steps:

[0055] Step 1: Determine the two-stage fingertip seal performance index as the response target, select the leakage volume Q, inter-stage pressure difference rate and maximum temperature T max As the performance index of the two-stage fingertip seal, the performance index is the optimization target, among which the leakage Q reflects the airflow leakage level of the two-stage fingertip seal, and the pressure difference rate between the stages Reflects the deviation of the ratio of the pressure drop of the second-stage fingertip seal to the pressure drop of the first-stage fingertip seal, the maximum temperature T max The maximum temperature of the fingertip boot when the fingertip seal is in working condition;

[0056] Step 2: Determine the control factors and their levels. The structural parameters that affect the performance of the two-stage fingertip seal are: the height of the first-stage fingertip seal boot x g1 , Level 2 fingertip seal boots high X g2 、Height H of rear baffle for first-stage fingertip seal b1 、The height of the rear baffle plate of the second-stage fingertip seal is H b2 , the number of layers of the first-level fingertip sealing sheet N1 and the number of layers of the second-level fingertip sealing sheet N2, each structural parameter is set as a control factor, and each structural parameter is set to 5 values, each value is the level of each control factor, as shown in Table 1

[0057] Table 1 Orthogonal factor level table

[0058] Factor Level 1 Level 1 Level 3 Level 4 Level 5 <![CDATA[X g1 ]]> 1 1.2 1.4 1.6 1.8 <![CDATA[X g2 ]]> 1 1.2 1.4 1.6 1.8 <![CDATA[H b1 ]]> 0.8 1 1.2 1.4 1.6 <![CDATA[H b2 ]]> 0.8 1 1.2 1.4 1.6 N1 2 3 4 5 6 N2 2 3 4 5 6

[0059] Step 3: Construct an orthogonal test table based on the control factors and levels in Step 2. To ensure the balance and effectiveness of the experimental design, construct an L25 (65) orthogonal test table and design 25 test combinations.

[0060] Step 4: Use FLUENT fluid simulation software to simulate each test combination in Step 3 and calculate the performance indicators of each experimental combination, namely leakage Q, interstage pressure difference rate and maximum temperature T max , the performance index is the corresponding response target value, as shown in Table 2:

[0061] Table 2 Orthogonal test table and response target results

[0062]

[0063] Step 5: Calculate the response target values ​​obtained in Step 4, i.e., the leakage volume Q and the inter-stage pressure difference rate. and maximum temperature T max Using the total mean m and the level mean M kji By performing mean analysis and variance analysis, we can determine the control factors that have the greatest impact on leakage, interstage pressure difference rate and maximum temperature and their optimal level combination. The average value is:

[0064]

[0065] Where m is the average value of each corresponding target, n is the number of trials, and T I is the response target value of the ith trial;

[0066] The average level is:

[0067]

[0068] Among them, M kij is the mean of the kth response target at the jth level of the ith factor, a is the experimental number of the jth level of the ith factor, T ijn is the target value of the response at the jth level of the i-th factor;

[0069] The variance is:

[0070]

[0071] Among them, S kij is the variance value of the kth response target under the i-th factor;

[0072] The specific gravity is:

[0073]

[0074] Among them, W kj is the proportion of each factor variance to the total variance;

[0075] (1) Mean analysis: The Taguchi orthogonal test table (Table 2) was subjected to mean analysis using formula (6) to calculate the average value of the two-stage fingertip seal response target at a certain level of a certain factor. The calculation results are shown in Table 3.

[0076] Table 3 Average values ​​of each response target at each level of each factor

[0077]

[0078]

[0079] According to the mean values ​​of each response target of the two-level fingertip seal established in Table 3 at each level of each factor, the following is drawn: Figure 3-5 The mean change trend of each factor at different levels is shown in the figure, and the letters A, B, C, D, E, and F are used to represent X respectively. g1 , X g2 , H b1 , H b2 , N1, N2, it can be seen that when the leakage Q of the two-stage fingertip seal is the smallest, the optimal two-stage fingertip seal structural parameter combination is: A4B4 C1 D1 E2 F5; the inter-stage pressure difference rate of the two-stage fingertip seal is When it is close to 1, the optimal two-stage fingertip seal structural parameter combination is: A4B1C1 D3 E1 F2; when the maximum temperature of the boot of the two-stage fingertip seal is the lowest, the optimal two-stage fingertip seal structural parameter combination is: A2 B2 C4 D2 E2 F2.

[0080] (2) Analysis of variance

[0081] The total mean values ​​of each response target of the two-stage fingertip seal under the total test are calculated, as shown in Table 4;

[0082] Table 4 Total mean values ​​of each response target in the total test

[0083] Q(g / s) φ <![CDATA[T max (K)]]> Overall mean 47.0832 2.3908 329.905

[0084] According to formula 7, formula 8 and the data in Tables 3 and 4, the variance and weight of the two-level fingertip seal response target under each factor and each level are calculated, as shown in Table 5;

[0085] Table 5 is the variance analysis table of the two-level fingertip seal response target under each factor and each level;

[0086]

[0087]

[0088] According to the variance and proportion of the two-level fingertip seal response target established in Table 5, a variance proportion bar chart is drawn; from the variance analysis table and the variance proportion bar chart, it can be obtained that: Level 1 fingertip seal boot height x g1 The greatest impact on the inter-stage pressure difference rate, X g1 Select the level that minimizes the interstage pressure difference rate, i.e. level 4; the second stage fingertip seal boot height X g2 The greatest impact on the maximum temperature, X g2 Select the level that minimizes the maximum temperature, i.e. level 2; the height of the rear baffle of the first level fingertip seal is H b1 The greatest influence on the inter-stage pressure difference rate, H b1 Select the level that minimizes the interstage pressure difference rate, i.e. level 1; the height of the baffle after the second stage fingertip seal is H b2 The biggest influence on leakage is H b2 Select the level with the lowest leakage, i.e., level 1; the number of layers of the first-level fingertip seal sheet N1 has the greatest impact on the maximum temperature, and N1 selects the level with the minimum maximum temperature, i.e., level 2; the number of layers of the second-level fingertip seal sheet N2 has the greatest impact on the maximum temperature, and N2 selects the level with the minimum maximum temperature, i.e., level 2; finally, the optimal factor level combination of the two-level fingertip seal response target obtained by variance analysis is: A4 B2 C1 D1 E2 F2;

[0089] Step 6: Based on the optimal factor combination obtained in Step 5, that is, the optimal structural parameter combination, the FLUENT fluid simulation software is used to build a model according to the optimal structural parameter combination, and the performance indicators of the two-stage fingertip seal are simulated and analyzed. The performance indicators are compared with the response target values ​​of the 25 test combinations, the optimization effect is evaluated, and the final optimization scheme is determined, as shown in Table 6.

[0090] Table 6 shows the comparison of the two-stage fingertip seal performance before and after optimization

[0091] Q(g / s) φ <![CDATA[T max (K)]]> Before optimization 51.85 1.53 328 After optimization 31.3 1.23 322

[0092] The Level 1 fingertip seal boots high x g1 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, 1.8mm respectively. The second level fingertip seal boot height is X g2 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, and 1.8mm respectively. The height of the baffle after the first-level fingertip seal is H b1 The values ​​are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm respectively. The height of the baffle after the second-level fingertip seal is H b2The values ​​of are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm, the values ​​of the number of first-level fingertip sealing sheets N1 are 2, 3, 4, 5, and 6, respectively, and the values ​​of the number of second-level fingertip sealing sheets N2 are 2, 3, 4, 5, and 6, respectively.

[0093] The specific embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of those skilled in the art without departing from the spirit of the present invention.

Claims

1. A two-stage fingertip seal structure optimization method based on Taguchi method, characterized in that: The following steps are involved: Step 1: Determine the two-stage fingertip seal performance index as the response target, select the leakage volume Q, inter-stage pressure difference rate and maximum temperature T max As the performance index of the two-stage fingertip seal, the performance index is the optimization target, among which the leakage Q reflects the airflow leakage level of the two-stage fingertip seal, and the pressure difference rate between the stages Reflects the deviation of the ratio of the pressure drop of the second-stage fingertip seal to the pressure drop of the first-stage fingertip seal, the maximum temperature T max The maximum temperature of the fingertip boot when the fingertip seal is in working condition; Step 2: Determine the control factors and their levels. The structural parameters that affect the performance of the two-stage fingertip seal are: the height of the first-stage fingertip seal boot x g1 , Level 2 fingertip seal boots high X g2 、Height H of rear baffle for first-stage fingertip seal b1 、The height of the rear baffle plate of the second-stage fingertip seal is H b2 , the number of layers of the first-level fingertip sealing sheet N1 and the number of layers of the second-level fingertip sealing sheet N2, each structural parameter is set as a control factor, and each structural parameter is set to 5 values, and each value is the level of each control factor; Step 3: Construct an orthogonal test table based on the control factors and levels in Step 2. To ensure the balance and effectiveness of the experimental design, construct an L25 (65) orthogonal test table and design 25 test combinations. Step 4: Use FLUENT fluid simulation software to simulate each test combination in Step 3 and calculate the performance indicators of each experimental combination, namely leakage Q, interstage pressure difference rate and maximum temperature T max , the performance index is the corresponding response target value; Step 5: Calculate the response target values ​​obtained in Step 4, i.e., the leakage volume Q and the inter-stage pressure difference rate. and maximum temperature T max Using the total mean m and the level mean M kij By performing mean analysis and variance analysis, we can determine the control factors that have the greatest impact on leakage, interstage pressure difference rate and maximum temperature and their optimal level combination. The average value is: Where m is the average value of each corresponding target, n is the number of trials, and T i is the response target value of the ith trial; The average level is: Among them, M kij is the mean of the kth response target at the jth level of the ith factor, a is the experimental number of the jth level of the ith factor, T ijn is the response target value corresponding to (the jth level of the i-th factor); The variance value is: Among them, S kij is the variance value of the kth response target under the i-th factor; The specific gravity is: Among them, W kj is the proportion of each factor variance to the total variance; Step 6: Based on the optimal factor combination obtained in Step 5, that is, the optimal structural parameter combination, FLUENT fluid simulation software is used to build a model based on the optimal structural parameter combination, and the performance indicators of the two-stage fingertip seal are simulated and analyzed. The performance indicators are compared with the response target values ​​of the 25 test combinations, the optimization effect is evaluated, and the final optimization plan is determined.

2. The two-stage fingertip seal structure optimization method based on the Taguchi method according to claim 1 is characterized in that: The Level 1 fingertip seal boots high x g1 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, 1.8mm respectively. The second level fingertip seal boot height is X g2 The values ​​are 1.0mm, 1.2mm, 1.4mm, 1.6mm, and 1.8mm respectively. The height of the baffle after the first-level fingertip seal is H b1 The values ​​are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm respectively. The height of the baffle after the second-level fingertip seal is H b2 The values ​​of are 0.8mm, 1.0mm, 1.2mm, 1.4mm, and 1.6mm, the values ​​of the number of first-level fingertip sealing sheets N1 are 2, 3, 4, 5, and 6, respectively, and the values ​​of the number of second-level fingertip sealing sheets N2 are 2, 3, 4, 5, and 6, respectively.

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