Limit rolling thinning process parameter setting method suitable for precise stainless steel band cold continuous rolling process
By introducing the pressure ratio benchmark and the "reverse parametric search-forward constraint" calculation method in the cold continuous rolling mill group, the pressure amount of each frame is optimized, and the problem of extreme thinning in the cold continuous rolling process of precision stainless steel strip is solved. , realizes the rapid and accurate setting of process parameters and the expansion of product specifications.
Patent Information
- Application Number
- CN202411469702.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-21
- Publication Date
- 2025-02-14
- Estimated Expiration
- 2044-10-21
AI Technical Summary
Without changing the properties of rolling equipment and materials, it is difficult to break through the product thickness limit thinning during the cold rolling process of precision stainless steel strips, resulting in limited expansion of on-site stainless steel product specifications.
The concept of the proportion of the pressure ratio of each rack in the cold continuous rolling mill group was proposed, and the calculation method of the "reverse parameter-forward constraint" of the maximum total pressure amount of the cold continuous rolling process of precision stainless steel strip is established, and the calculation method is established by optimizing the allocation of each rack The pressure reduction amount can achieve rapid and accurate setting of the ultimate thinning process parameters.
Through this method, the ultimate thinning process parameters of the cold continuous rolling process of precision stainless steel strip can be quickly and accurately determined, expanding the scalability of the limit specifications of precision stainless steel strips, and ensuring the safe production of cold continuous rolling mill equipment.
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Figure CN119426366A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of precision stainless steel strip rolling, and in particular to a method for setting limit thinning process parameters suitable for a precision stainless steel strip cold rolling process. Background Art
[0002] In recent years, with the upgrading of the manufacturing industry and the development of new material technology, the market demand for precision stainless steel strips has continued to grow, and they are widely used in aerospace, medical equipment, precision machinery and other fields. At the same time, downstream application fields have put forward higher and higher requirements on the thickness of stainless steel strip products, and rolling technology is also adapting to the production of thinner precision stainless steel strip products to meet the needs of different industries. Due to the influence of rolling mill equipment capacity, material processing hardening and rolling process parameters, it is difficult to break through the limit of product thickness thinning during the cold rolling process of precision stainless steel strips, which seriously restricts the expansion of the on-site stainless steel product outline. Therefore, without changing the rolling equipment and material properties, the optimization setting of rolling process parameters has become a common problem to break through the limit rolling thickness of stainless steel strips.
[0003] The ultimate rolling capacity of the cold rolling mill of stainless steel strip should not only evaluate the maximum total reduction for specific stainless steel strip products, but also take into account the production efficiency of the unit. The setting of the reduction schedule of the cold rolling mill determines the deformation resistance of the strip steel in each pass. Under specific lubrication conditions and rolling speeds, it further determines the friction coefficient of the rolling deformation zone of each pass. In addition, the influence of the front and rear tension of each frame on the plastic deformation of the strip steel in this pass determines the rolling force of each pass, and it is necessary to ensure that the rolling force of each pass is within the maximum rolling force allowable value of each frame. At the same time, the rolling speed and rolling torque of the strip steel at the exit of each frame determine the rolling power under this pass, and it is necessary to ensure that the rolling power of each pass is within the maximum rolling power allowable value of each frame. In this way, under the premise that the rolling force and rolling power of each frame do not exceed the maximum allowable value of the frame, how the reduction schedule is allocated and how the rolling speed is set directly determines the maximum total reduction of the stainless steel strip after cold rolling. However, due to the large number of stands in the cold rolling mill, the optimization calculation of the reduction schedule is a complicated process. The change of the reduction amount of one stand will not only cause the change of the rolling force and rolling power of the current stand, but also cause the change of the rolling force and rolling power of each subsequent stand. Therefore, it is not possible to isolate each stand and optimize the optimal reduction, which makes it difficult to determine the limit process parameters for stable thinning of precision stainless steel strip. Summary of the invention
[0004] In view of this, the purpose of the present invention is to provide a method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strip. In order to explore the limit rolling capacity of the cold rolling unit to produce precision stainless steel strip, the work hardening of the stainless steel strip in each pass and the maximum allowable values of the rolling force and rolling power of each stand rolling mill are considered. The concept of the reduction ratio benchmark of each stand of the cold rolling unit is proposed, and a "reverse parameter search-forward constraint" calculation method for the maximum total reduction in the cold rolling process of precision stainless steel strip is established to complete the optimal allocation of the reduction above the reduction ratio benchmark of each stand. The method of the present invention can quickly and accurately determine the limit thinning process parameters of the cold rolling process of precision stainless steel strip, which has guiding significance for expanding the limit specifications of precision stainless steel strip and ensuring the safe production of cold rolling unit equipment.
[0005] To achieve the above object, the technical solution of the present invention is as follows:
[0006] A method for setting limit thinning process parameters suitable for a cold rolling process of a precision stainless steel strip comprises the following steps:
[0007] S1. Collect the equipment and process parameters of the cold rolling mill, including: the number of stands n, the working roll diameter D of the i-th stand wi , the maximum allowable rolling force value P of the i-th stand imax , the maximum allowable rolling power value F of the i-th stand imax Friction coefficient μ with the i-th frame i , where i = 1, 2, 3, ... n;
[0008] S2. Collect the material parameters of the precision stainless steel strip to be rolled, including: incoming material thickness h0, incoming material width B, initial deformation resistance σ s0 Carbon equivalent to stainless steel strip C ac ;
[0009] S3, define the strip reduction amount, strip reduction rate and rolling speed of each stand, and give the rolling speed of the nth stand;
[0010] S4. providing a deformation resistance calculation model, a rolling force calculation model and a rolling power calculation model for each stand;
[0011] S5. Set the optimal step length Δ and step length coefficient k z With the maximum total pressure reduction of Δh zmax ;
[0012] S6. Setting the reduction ratio benchmark of each stand during the cold rolling process of precision stainless steel strip;
[0013] S7, judging whether the pressing amount corresponding to the pressing proportion benchmark of each rack can meet the constraint condition: P i ≤P imax And F i≤F imax (1≤i≤n), where P i is the rolling force of the i-th stand, F i is the rolling power of the i-th stand; if it is satisfied, it means that the unit has the surplus capacity to bear the pressure reduction ratio above the benchmark The amount of pressure reduction, where a i is the pressure ratio benchmark of the i-th rack; if it is not satisfied, it means Δh zmax If the setting exceeds the unit capacity, let k z =k z +1, repeat the above process until the corresponding pressing amount of the pressing proportion benchmark of each rack meets the constraint condition;
[0014] S8. Define the step coefficients of racks 1 to n as k1, k2, k3, ..., k n , the cumulative increase in the number of optimal step lengths is where k i is the step coefficient of the i-th rack, which is above the benchmark The total number of optimal steps required to press down is The expression of the pressure reduction of each rack is Δh i =a i Δh zmax +k i Δ; where Δh i is the strip reduction of the i-th stand;
[0015] S9, distributing and calculating the pressing amount of racks 1 to n;
[0016] S10, determine k l ≥n s Is it true? If it is true, go to step S11; if it is not true, let k z =k z +1, go to step S5;
[0017] S11, output k z and the maximum total pressure reduction Δh zmax ;
[0018] S12. Output the reduction amount of each stand and the reduction amount distribution ratio during the cold rolling process of precision stainless steel strip.
[0019] Furthermore, the expression for the strip reduction amount of each rack in S3 is:
[0020] Δh i =h i-1 -h i
[0021] In the formula, Δh i h is the strip reduction of the i-th stand, iis the strip outlet thickness of the i-th rack, h i-1 is the strip outlet thickness of the i-1th stand;
[0022] The expression of strip reduction rate of each stand is:
[0023]
[0024] In the formula, ε i is the strip reduction rate of the i-th stand;
[0025] The expression of the rolling speed of each stand is:
[0026]
[0027] Where V i is the rolling speed of the i-th stand, V n is the rolling speed of the nth stand, h n is the strip outlet thickness of the nth stand.
[0028] Furthermore, the deformation resistance calculation model in S4 is:
[0029]
[0030] In the formula, σ si is the deformation resistance of the i-th rack; σ s(i-1) is the deformation resistance of the i-1th rack; k vi is the speed influence coefficient, k vi =(V i ε i / l i v0) n , where li is the projected length of the contact arc during the rolling process of the i-th stand, obtained from the rolling force calculation model, and v0 is the reference deformation speed, v0 = 1s -1 ; w is the material parameter, w = 0.005; m is the work hardening performance index, m = 110 (1 + 2C ac ) / σ s0 ;
[0031] The rolling force calculation model is:
[0032] P i =f P (h i-1 ,h i ,B,T i-1,i ,T i,i+1 ,σ si ,D wi ,μ i )
[0033] Where P iis the rolling force of the i-th stand; T i-1,i is the post tension, T i,i+1 is the front tension; among them, the rear tension T i-1,i With front tension T i,i+1 is the base value of the unit;
[0034] The rolling power calculation model is:
[0035] F i =f F (h i-1 ,h i ,B,P i ,V i );
[0036] In the formula, F i is the rolling power of the i-th stand.
[0037] Furthermore, in S5, the optimization step length Δ is set to 0.001, and the step length coefficient k z =1, maximum total pressure reduction Δh zmax =h0-k z Δ.
[0038] Furthermore, in S6, according to the pressure distribution rule of each stand during the cold rolling process of the precision stainless steel strip, the minimum pressure ratio of each stand is set to a1, a2, a3, ..., a n ,and A fixed allocation of half of the total reduction is made in advance.
[0039] Furthermore, the specific steps of S9 are as follows:
[0040] S9-1, let j=1;
[0041] S9-2, let k j =0;
[0042] S9-3. Calculate the pressing amount of the j-th rack, Δh j =a j Δh zmax +k j Δ;
[0043] S9-4, according to step S4, calculate the rolling force P of the j~n stands i With rolling power F i , where j≤i≤n;
[0044] S9-5. Determine P i >P imax or F i >F imax (j≤i≤n) is true; if true, go to step S9-6; if not, let kj =k j +1 Go to step S9-3;
[0045] S9-6. Determine P j With F j Whether it exceeds the limit; if P j >P jmax or F j >F jmax , then let k j =k j -1, go to step S9-7; if P j ≤P jmax And F j ≤F jmax , then let k z =k z +1, then go to step S5;
[0046] S9-7, determine whether j<n holds; if so, set j=j+1 and go to step S9-2; if not, go to step S9-8;
[0047] S9-8. Calculate the cumulative increase in the number of optimal step lengths k l , k l =k1+k2+k3+...+k n .
[0048] Compared with the prior art, the present invention has the following beneficial effects:
[0049] The present invention combines the processing deformation characteristics of stainless steel strip during cold rolling with the ultimate capacity of the rolling mill equipment, realizes linkage calculation of the rolling force and rolling power of each cold rolling frame based on the deformation resistance model, and constrains it with the maximum rolling force and maximum rolling power of each frame, avoiding the disadvantage that each frame is isolated and determines the reduction amount, which makes it difficult to achieve the ultimate thinning. At the same time, considering that the total reduction rate of stainless steel strip cold rolling is generally around 60-80%, or even higher, in order to reduce the calculation amount of the combination of reduction rules, a calculation method of the maximum total reduction of stainless steel strip "reverse parameter search-forward constraint" is proposed, which realizes the rapid optimization setting of the ultimate thinning process parameters, improves the specification expansion capability of the cold rolling unit and the stability of ultra-thin rolling of precision stainless steel strip. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 It is the overall flow chart for calculating the maximum total reduction in the cold rolling process of precision stainless steel strip;
[0051] Figure 2 This is a flow chart for calculating the distribution of reduction for each stand of a six-stand cold rolling mill. DETAILED DESCRIPTION
[0052] In order to facilitate the understanding of the present invention, the present invention will be described more fully below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.
[0053] Example
[0054] A method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strips, wherein the overall process for calculating the maximum total reduction in the cold rolling process of precision stainless steel strips is as follows: Figure 1 The specific execution steps are as follows:
[0055] S1. Collect the equipment and process parameters of the cold rolling mill. Take the six-stand cold rolling mill as an example, including: the working roll diameter D of the i-th stand wi , the maximum allowable rolling force value P of the i-th stand imax , the maximum allowable rolling power value F of the i-th stand imax Friction coefficient μ with the i-th frame i , where i = 1, 2, 3...6; as shown in Table 1;
[0056] Table 1 Equipment and process parameters of cold rolling mill
[0057]
[0058] S2. Collect the material parameters of the precision stainless steel strip to be rolled, including the material thickness h0 = 2.533 mm, the material width B = 900 mm, and the initial deformation resistance σ s0 =590MPa, carbon equivalent of stainless steel strip C ac =0.067%;
[0059] S3. Define relevant process parameters, including: strip reduction amount, strip reduction rate and rolling speed of each stand; among which,
[0060] The expression of strip reduction of each rack is:
[0061] Δh i =h i-1 -h i
[0062] In the formula, Δh i h is the strip reduction of the i-th stand, i is the strip outlet thickness of the i-th rack, h i-1 is the strip outlet thickness of the i-1th stand;
[0063] The expression of strip reduction rate of each stand is:
[0064]
[0065] In the formula, ε i is the strip reduction rate of the i-th stand;
[0066] The expression of the rolling speed of each stand is:
[0067]
[0068] Where V i is the rolling speed of the ith stand, V6 is the rolling speed of the 6th stand, and h6 is the strip outlet thickness of the 6th stand.
[0069] S4. Provide relevant calculation models, including: deformation resistance calculation model of each stand, rolling force calculation model and rolling power calculation model; wherein,
[0070] The deformation resistance calculation model is:
[0071]
[0072] In the formula, σ si is the deformation resistance of the i-th rack; σ s(i-1) is the deformation resistance of the i-1th rack; k vi is the speed influence coefficient, k vi =(V i ε i / l i v0) n , where li is the projected length of the contact arc during the rolling process of the i-th stand, obtained from the rolling force calculation model, and v0 is the reference deformation speed, v0 = 1s -1 ; w is the material parameter, w = 0.005; m is the work hardening performance index, m = 110 (1 + 2C ac ) / σ s0 ;
[0073] The rolling force calculation model adopts the Hill formula, which can be described as:
[0074] P i =f P (h i-1 ,h i ,B,T i-1,i ,T i,i+1 ,σ si ,D wi ,μ i )
[0075] Where P i is the rolling force of the i-th stand, T i-1,i is the post tension; T i,i+1 is the front tension; among them, the rear tension T i-1,i With front tension Ti,i+1 It is the base value of the unit, which is 300kN;
[0076] The rolling power calculation model adopts the model of steel rolling machinery, which can be described as:
[0077] F i =f F (h i-1 ,h i ,B,P i ,V i );
[0078] In the formula, F i is the rolling power of the i-th stand.
[0079] S5. Set the optimization step length Δ = 0.001, and the step length coefficient is k z (initial value is 1), the maximum total pressure reduction is Δh zmax =h0-k z Δ;
[0080] S6. Setting the benchmark for the percentage of each stand's pressure reduction during the cold rolling process of precision stainless steel strip;
[0081] According to the pressure distribution law of each stand in the cold rolling process of precision stainless steel strip, the pressure ratio benchmark of each stand process is set, as shown in Table 2, and where a i is the depression ratio benchmark of the i-th rack;
[0082] Table 2 Benchmarks of the percentage of each stand in the cold rolling process of precision stainless steel strip
[0083] frame F1 F2 F3 F4 F5 F6 Depression ratio benchmark 20% 12% 10% 8% 1% 0.1%
[0084] S7. According to the cold rolling reduction ratio benchmark, determine whether the reduction amount corresponding to the reduction ratio benchmark of each stand can meet the constraint condition: P i ≤P imax And F i ≤F imax (1≤i≤6), after calculation, the maximum total pressure is Δh zmax =h0-k z When Δ=2.533-1×0.001=2.532(mm), the constraint condition cannot be met, indicating that Δh zmax If the setting exceeds the unit capacity, let k z =k z +1, repeat the above process until the corresponding pressing amount of each rack pressing proportion benchmark meets the constraint condition, at this time k z =277, Δh zmax =h0-k zΔ=2.533-277×0.001=2.256(mm);
[0085] S8. Define the step coefficients of racks 1 to 6 as k1, k2, k3, k4, k5, and k6 respectively, and the cumulative increase in the number of optimal step lengths is k. l =k1+k2+k3+k4+k5+k6, press down the proportion above the benchmark The total number of steps required to find the optimal step length The expression of the pressing amount of each rack is as follows:
[0086]
[0087] S9, distributing and calculating the pressing amount of racks 1 to 6;
[0088] S9-1, let j=1;
[0089] S9-2, set k1=0;
[0090] S9-3. Calculate the pressing amount of the first frame, Δh1 = a1Δh zmax +k1Δ=20%×2.256+0=0.4512mm;
[0091] S9-4, according to step S4, calculate the rolling force P of the 1st to 6th stands i With rolling power F i , where 1≤i≤6;
[0092] S9-5. Determine P i >P imax or F i >F imax Is (1≤i≤6) true? If true, go to step S9-6; if not, set k1=k1+1 and go to step S9-3; after calculation, the inequality does not hold at this time, set k1=k1+1 and go to step S9-3, and finally the inequality holds when k1=158, go to step S9-6;
[0093] S9-6, determine whether P1 and F1 are out of limit? 1max or F1>F 1max , then set k1 = k1-1 and go to step S9-7; if P1≤P 1max And F1≤F 1max , then let k z =k z +1, then go to step S5; after calculation, at this time, the first rack P1>P 1max , F1>F 1max , then set k1=k1-1 and go to step S9-7;
[0094] S9-7, determine whether j<n is true? If true, set j=j+1 and go to step S9-2; if not true, go to step S9-8; at this time j=1<n=6, set j=j+1 and go to step S9-2, until j<n is not true;
[0095] S9-8. Calculate the cumulative increase in the number of optimal step lengths k l , k l =k1+k2+k3+k4+k5+k6=738
[0096] S10, determine k l ≥n s Is it true? If it is true, go to step S11; if it is not true, let k z =k z +1, go to step S5; after calculation, it is not true at this time, so let k z =k z +1, go to step S5, until the inequality is established;
[0097] S11, output k z =492 and the maximum total pressure reduction Δh zmax =h0-k z Δ=2.041(mm);
[0098] S12. The reduction amount of each stand and the distribution ratio of the reduction amount during the cold rolling process of the output precision stainless steel strip are shown in Table 3.
[0099] Table 3 Extreme thinning process parameters and reduction distribution ratio of precision stainless steel strip
[0100] frame F1 F2 F3 F4 F5 F6 Pressing amount 0.621mm 0.588mm 0.321mm 0.276mm 0.219mm 0.016mm Allocation ratio 30.43% 28.81% 15.73% 13.52% 10.73% 0.78%
[0101] The above description is only for better explaining the embodiments of the present invention, and is not intended to limit the present invention. Any modification or equivalent substitution that does not depart from the spirit and scope of the present invention shall fall within the scope of the present invention.
Claims
1. A method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strip, characterized in that: The following steps are involved: S1. Collect the equipment and process parameters of the cold rolling mill, including: the number of stands n, the working roll diameter D of the i-th stand wi , the maximum allowable rolling force value P of the i-th stand imax , the maximum allowable rolling power value F of the i-th stand imax Friction coefficient μ with the i-th frame i , where i = 1, 2, 3, ... n; S2. Collect the material parameters of the precision stainless steel strip to be rolled, including: incoming material thickness h0, incoming material width B, initial deformation resistance σ s0 Carbon equivalent to stainless steel strip C ac ; S3, define the strip reduction amount, strip reduction rate and rolling speed of each stand, and give the rolling speed of the nth stand; S4. providing a deformation resistance calculation model, a rolling force calculation model and a rolling power calculation model for each stand; S5. Set the optimal step length Δ and step length coefficient k z With the maximum total pressure reduction of Δh zmax ; S6. Setting the reduction ratio benchmark of each stand during the cold rolling process of precision stainless steel strip; S7, judging whether the pressing amount corresponding to the pressing proportion benchmark of each rack can meet the constraint condition: P i ≤P imax And F i ≤F imax (1≤i≤n), where P i is the rolling force of the i-th stand, F i is the rolling power of the i-th stand; if it is satisfied, it means that the unit has the surplus capacity to bear the pressure reduction ratio above the benchmark The amount of pressure reduction, where a i is the pressure ratio benchmark of the i-th rack; if it is not satisfied, it means Δh zmax If the setting exceeds the unit capacity, let k z =k z +1, repeat the above process until the corresponding pressing amount of the pressing proportion benchmark of each rack meets the constraint condition; S8. Define the step coefficients of racks 1 to n as k1, k2, k3, ..., k n , the cumulative increase in the number of optimal step lengths is where k i is the step coefficient of the i-th rack, which is above the benchmark The total number of optimal steps required to press down is The expression of the pressure reduction of each rack is Δh i =a i Δh zmax +k i Δ; where Δh i is the strip reduction of the i-th stand; S9, distributing and calculating the pressing amount of racks 1 to n; S10, determine k l ≥n s Is it true? If it is true, go to step S11; if it is not true, let k z =k z +1, go to step S5; S11, output k z and the maximum total pressure reduction Δh zmax ; S12. Output the reduction amount of each stand and the reduction amount distribution ratio during the cold rolling process of precision stainless steel strip.
2. The method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strip according to claim 1, characterized in that: The expression of the strip reduction amount of each rack in S3 is: Δh i =h i-1 -h i In the formula, Δh i h is the strip reduction of the i-th stand, i is the strip outlet thickness of the i-th rack, h i-1 is the strip outlet thickness of the i-1th stand; The expression of strip reduction rate of each stand is: In the formula, ε i is the strip reduction rate of the i-th stand; The expression of the rolling speed of each stand is: Where V i is the rolling speed of the i-th stand, V n is the rolling speed of the nth stand, h n is the strip outlet thickness of the nth stand.
3. The method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strip according to claim 2, characterized in that: The deformation resistance calculation model in S4 is: In the formula, σ si is the deformation resistance of the i-th rack; σ s(i-1) is the deformation resistance of the i-1th rack; k vi is the speed influence coefficient, k vi =(V i ε i / l i v0) n , where li is the projected length of the contact arc during the rolling process of the i-th stand, obtained from the rolling force calculation model, and v0 is the reference deformation speed, v0 = 1s -1 ; w is the material parameter, w = 0.005; m is the work hardening performance index, m = 110 (1 + 2C ac ) / σ s0 ; The rolling force calculation model is: P i =f P (h i-1 ,h i ,B,T i-1,i ,T i,i+1 ,σ si ,D wi ,μ i ) Where P i is the rolling force of the i-th stand, T i-1,i is the post tension, T i,i+1 is the front tension; among them, the rear tension T i-1,i With front tension T i,i+1 is the base value of the unit; The rolling power calculation model is: F i =f F (h i-1 ,h i ,B,P i ,V i ); In the formula, F i is the rolling power of the i-th stand.
4. A method for setting limit thinning process parameters suitable for cold rolling of precision stainless steel strip according to claim 3, characterized in that: In S5, the optimization step length Δ is set to 0.001, and the step length coefficient k z =1, maximum total pressure reduction Δh zmax =h0-k z Δ.
5. The method for setting the limit thinning process parameters suitable for the cold rolling process of precision stainless steel strip according to claim 4, characterized in that: In S6, according to the pressure distribution law of each stand during the cold rolling process of the precision stainless steel strip, the minimum pressure ratio of each stand is set to a1, a2, a3, ..., a n ,and A fixed allocation of half of the total reduction is made in advance.
6. A method for setting limit thinning process parameters suitable for cold rolling of precision stainless steel strip according to claim 5, characterized in that: The specific steps of S9 are as follows: S9-1, let j=1; S9-2, let k j =0; S9-3. Calculate the pressing amount of the j-th rack, Δh j =a j Δh zmax +k j Δ; S9-4, according to step S4, calculate the rolling force P of the j~n stands i With rolling power F i , where j≤i≤n; S9-5. Determine P i >P imax or F i >F imax (j≤i≤n) is true; if true, go to step S9-6; If not, let k j =k j +1 Go to step S9-3; S9-6. Determine P j With F j Whether it exceeds the limit; if P j >P jmax or F j >F jmax , then let k j =k j -1, go to step S9-7; if P j ≤P jmax And F j ≤F jmax , then let k z =k z +1, then go to step S5; S9-7, determine whether j<n holds; if so, set j=j+1 and go to step S9-2; if not, go to step S9-8; S9-8. Calculate the cumulative increase in the number of optimal step lengths k l , k l =k1+k2+k3+...+k n .
Citation Information
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