A structural optimization method for cylindrical gear reducer based on sine-cosine algorithm

Abstract

A cylindrical gear reducer structure optimization method based on sine-cosine algorithm belongs to the technical field of reducer structure design optimization, comprising the first step, the individual coding in the initial population is divided into two parts, one part is a continuous real number, and the other part is a discrete integer; the second step is to calculate the target function value of all cylindrical gear reducers in the initial population, and record the cylindrical gear reducer P with the smallest volume and the smallest volume value f(p); the third step is to update the cylindrical gear reducers in the population; the fourth step is to perform a combined mutation operation on the continuous real number part of the individuals in the population; the fifth step is to perform a combined mutation operation on the discrete integer part of the individuals in the population; the sixth step is to calculate the target function value of all individuals in the population, and adopt an individual retention method based on a greedy strategy; the seventh step is to output the cylindrical gear reducer P with the smallest volume and the smallest volume value f(p).

Description

Technical Field

[0001] The invention relates to the technical field of reducer structure design optimization, in particular to a cylindrical gear reducer structure optimization method based on sine-cosine algorithm. Background Art

[0002] In the design of previous reducers, designers often ignored the consumption of raw materials while meeting the performance requirements of the reducer, resulting in a huge waste of raw materials. With the continuous expansion of the reducer market, the demand for raw materials such as steel and copper is also increasing. It is particularly important to minimize the consumption of raw materials while meeting the performance requirements of the reducer. In the structural design of traditional reducers, the final solution is generally obtained through repeated trial and error based on experience. Although it meets the design requirements, it is not the optimal solution. The discipline of optimization design has developed rapidly in recent years. Designers can use optimization design methods to select the best solution from many feasible solutions, thereby greatly improving the design quality and design efficiency. For such complex engineering optimization problems, traditional optimization methods cannot solve such optimization problems well due to their own architectural defects. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a cylindrical gear reducer structure optimization method based on sine-cosine algorithm which can reduce the consumption of raw materials and reduce the volume of the cylindrical gear reducer in view of the shortcomings of the prior art.

[0004] The technical problem to be solved by the present invention is achieved through the following technical solutions. The present invention is a cylindrical gear reducer structure optimization method based on sine-cosine algorithm, which is characterized by including:

[0005] Step 1: Randomly generate n cylindrical gear reducers. The individual codes in the initial population are divided into two parts, one part is continuous real numbers and the other part is discrete integers. The continuous real number variables in the initial population individuals are generated first and the discrete integer variables are generated later.

[0006] Step 2: Taking the minimum volume of the cylindrical gear reducer as the objective function, calculate the objective function values ​​of all cylindrical gear reducers in the initial population, and record the cylindrical gear reducer with the smallest volume P and the smallest volume value f(p);

[0007] Step 3: Update the cylindrical gear reducers in the population according to the update formula;

[0008] Step 4: Perform a combined mutation operation on the continuous real number part of the individuals in the population. The combined mutation operator of continuous real numbers includes five mutation operators, the first continuous real number mutation operator, the second continuous real number mutation operator, the third continuous real number mutation operator, the fourth continuous real number mutation operator and the fifth continuous real number mutation operator; the above five mutation operators are selected according to the following steps:

[0009] Step 1: Randomly generate a random number R1 between [0,1];

[0010] Step 2: When 0≤R1<0.3, execute the first continuous real number mutation operator; the first continuous real number mutation operator is:

[0011] When 0.3≤R1<0.6, the second continuous real number mutation operator is executed; the second continuous real number mutation operator is:

[0012] In the formula, v t ik is the k-th dimensional component after the combined mutation of the i-th individual in the population in the t-th iteration, i = 1, 2, ..., n, k = 1, 2, ..., Q; r1, r2, r3, r4, r5 are 5 different individuals randomly selected from the population and none of them is the same as individual i, t is the current iteration number, Fi is the scaling factor with a value of 0.35. The above two mutation operators make full use of the information of other individuals in the population, so they have strong global search capabilities but slow convergence speed.

[0013] When 0.6≤R1<0.7, the third continuous real number mutation operator is executed; the third continuous real number mutation operator is

[0014] When 0.7≤R1<0.9, the fourth continuous real number mutation operator is executed; the fourth continuous real number mutation operator is

[0015] In the formula, r1, r2, r3, and r4 are four different individuals randomly selected from the population and are not the same as individual i. k t is the k-th dimensional component of the optimal individual at the t-th iteration. The above two mutation operators introduce the optimal individual P, which speeds up the convergence speed but is often prone to falling into the local optimal solution.

[0016] When 0.9≤R1≤1, the fifth continuous real number mutation operator is executed; the fifth continuous real number mutation operator is Where r1 and r2 are two different individuals randomly selected from the population and are different from individual i. This mutation operator not only introduces the optimal individual P but also utilizes the information of other individuals in the population, thus taking into account both the local search and global search capabilities of the algorithm.

[0017] Step 5: Perform a combined mutation operation on the discrete integer part of the individuals in the population. The combined mutation operator of discrete integers includes three mutation operators, the first discrete integer mutation operator, the second discrete integer mutation operator and the third discrete integer mutation operator. The above three discrete integer mutation operators are selected according to the following steps:

[0018] Step 1: Randomly generate a random number R2 between [0,1];

[0019] Step 2: When 0≤R2<0.3, execute the first discrete integer mutation operator; the first discrete integer mutation operator is v t ik =x t ik +round(-2.5+5×rand), where x t ik is the k-th dimension component of individual i at the t-th iteration, v t ik is the k-th dimension component after the combination mutation of the i-th individual in the population in the t-th iteration, i = 1, 2, ..., n, k = Q + 1, ..., D; round is a MATLAB function, indicating rounding, rand indicates a random number between [0, 1],

[0020] When 0.3≤R2<0.6, the second discrete integer mutation operator is executed; the second discrete integer mutation operator is In the formula, r1, r2, and r3 are three different individuals randomly selected from the population and are not the same as individual i.

[0021] When 0.6≤R2<0.7, the third discrete integer mutation operator is executed; the third discrete integer mutation operator is In the formula, r1 and r2 are two different individuals randomly selected from the population and are different from individual i.

[0022] Step 6: Calculate the objective function values ​​of all individuals in the population, and adopt the individual retention method based on the greedy strategy. When the volume of the updated cylindrical gear reducer is smaller than the volume of the cylindrical gear reducer before the update, the updated cylindrical gear reducer will be retained for the next generation, otherwise the cylindrical gear reducer before the update will be retained for the next generation.

[0023] Step 7: Output the cylindrical gear reducer P with the smallest volume and the smallest volume value f(p).

[0024] The technical problem to be solved by the present invention can be further achieved by the following technical scheme. In the second step described above, the objective function selects the module m, the number of pinion teeth z1, the tooth width B, the diameter d1' of the driving shaft, the diameter d2' of the driven shaft, and the width L of the reducer housing as design variables, wherein the module m should take the standard value, and the standard module m is mapped to an integer, and m=[m z ], for example m z =9, m=12, the unit is mm. The mapping relationship is shown in the table:

[0025]

[0026] The objective function is expressed as:

[0027] minV=π(1.1875B[m z ] 2 z1 2 +0.262Bd1' 2 -0.282Bd2' 2 +21.25B[m z ] 2 +0.25Ld2' 2 +0.25d2' 2 L+70d1' 2 +80d2' 2 -21.25B[m z ] 2 +0.2Bd2'[m z ]z1-0.4Bd2'[m z ])

[0028] The technical problem to be solved by the present invention can be further achieved by the following technical solution. The update formula in the third step described above is:

[0029] In the formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r3 is a random number between [0, 1], and x t ik is the k-th dimension component of individual i at the t-th iteration.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) Taking the minimum volume of the cylindrical gear reducer as the objective function, a general mathematical model for optimizing the parameters of the reducer shaft system components is established to make the model universal, reduce the consumption of raw materials of the cylindrical gear reducer, save resources, and reduce waste.

[0032] (2) In the study of hybrid algorithms, multiple mutation operators are introduced into the mutation operation to reduce the occurrence of premature convergence, increase population diversity, and improve global search capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the present invention;

[0034] Figure 2 It is a schematic diagram of the individual structure of the population;

[0035] Figure 3 This is a schematic diagram of a cylindrical gear reducer. DETAILED DESCRIPTION

[0036] The specific technical solutions of the present invention are further described below to help those skilled in the art further understand the present invention without limiting the rights thereof.

[0037] Reference Figure 1-Figure 3 , a cylindrical gear reducer structure optimization method based on sine-cosine algorithm, comprising:

[0038] Reference Figure 2 ,The first step: randomly generate n cylindrical gear reducers. The individual codes in the initial population are divided into two parts, one part is continuous real numbers and the other part is discrete integers. The continuous real number variables in the initial population individuals are generated first and the discrete integer variables are generated later;

[0039] Step 2: Taking the minimum volume of the cylindrical gear reducer as the objective function, calculate the objective function values ​​of all cylindrical gear reducers in the initial population, and record the cylindrical gear reducer with the smallest volume P and the smallest volume value f(p);

[0040] Step 3: Update the cylindrical gear reducers in the population according to the update formula;

[0041] Step 4: Perform a combined mutation operation on the continuous real number part of the individuals in the population. The combined mutation operator of continuous real numbers includes five mutation operators, the first continuous real number mutation operator, the second continuous real number mutation operator, the third continuous real number mutation operator, the fourth continuous real number mutation operator and the fifth continuous real number mutation operator; the above five mutation operators are selected according to the following steps:

[0042] Step 1: Randomly generate a random number R1 between [0,1];

[0043] Step 2: When 0≤R1<0.3, execute the first continuous real number mutation operator; the first continuous real number mutation operator is:

[0044] When 0.3≤R1<0.6, the second continuous real number mutation operator is executed; the second continuous real number mutation operator is:

[0045] In the formula, v t ik is the k-th dimensional component after the combined mutation of the i-th individual in the population in the t-th iteration, i = 1, 2, ..., n, k = 1, 2, ..., Q; r1, r2, r3, r4, r5 are 5 different individuals randomly selected from the population and none of them is the same as individual i, t is the current iteration number, Fi is the scaling factor with a value of 0.35. The above two mutation operators make full use of the information of other individuals in the population, so they have strong global search capabilities but slow convergence speed.

[0046] When 0.6≤R1<0.7, the third continuous real number mutation operator is executed; the third continuous real number mutation operator is

[0047] When 0.7≤R1<0.9, the fourth continuous real number mutation operator is executed; the fourth continuous real number mutation operator is

[0048] In the formula, r1, r2, r3, and r4 are four different individuals randomly selected from the population and are not the same as individual i. k t is the k-th dimensional component of the optimal individual at the t-th iteration. The above two mutation operators introduce the optimal individual P, which speeds up the convergence speed but is often prone to falling into the local optimal solution.

[0049] When 0.9≤R1≤1, the fifth continuous real number mutation operator is executed; the fifth continuous real number mutation operator is Where r1 and r2 are two different individuals randomly selected from the population and are different from individual i. This mutation operator not only introduces the optimal individual P but also utilizes the information of other individuals in the population, thus taking into account both the local search and global search capabilities of the algorithm.

[0050] Step 5: Perform a combined mutation operation on the discrete integer part of the individuals in the population. The combined mutation operator of discrete integers includes three mutation operators, the first discrete integer mutation operator, the second discrete integer mutation operator and the third discrete integer mutation operator. The above three discrete integer mutation operators are selected according to the following steps:

[0051] Step 1: Randomly generate a random number R2 between [0,1];

[0052] Step 2: When 0≤R2<0.3, execute the first discrete integer mutation operator; the first discrete integer mutation operator is vt ik =x t ik +round(-2.5+5×rand), where x t ik is the k-th dimension component of individual i at the t-th iteration, v t ik is the k-th dimension component after the combination mutation of the i-th individual in the population in the t-th iteration, i = 1, 2, ..., n, k = Q + 1, ..., D; round is a MATLAB function, indicating rounding, rand indicates a random number between [0, 1],

[0053] When 0.3≤R2<0.6, the second discrete integer mutation operator is executed; the second discrete integer mutation operator is In the formula, r1, r2, and r3 are three different individuals randomly selected from the population and are not the same as individual i.

[0054] When 0.6≤R2<0.7, the third discrete integer mutation operator is executed; the third discrete integer mutation operator is In the formula, r1 and r2 are two different individuals randomly selected from the population and are different from individual i.

[0055] Step 6: Calculate the objective function values ​​of all individuals in the population, and adopt the individual retention method based on the greedy strategy. When the volume of the updated cylindrical gear reducer is smaller than the volume of the cylindrical gear reducer before the update, the updated cylindrical gear reducer will be retained for the next generation, otherwise the cylindrical gear reducer before the update will be retained for the next generation.

[0056] Step 7: Output the cylindrical gear reducer P with the smallest volume and the smallest volume value f(p).

[0057] The technical problem to be solved by the present invention can be further achieved by the following technical scheme. In the second step described above, the objective function selects the module m, the number of pinion teeth z1, the tooth width B, the diameter d1' of the driving shaft, the diameter d2' of the driven shaft, and the width L of the reducer housing as design variables, wherein the module m should take the standard value, and the standard module m is mapped to an integer, and m=[m z ], for example m z =9, m=12, the unit is mm. The mapping relationship is shown in the table:

[0058]

[0059] The objective function is expressed as:

[0060] minV=π(1.1875B[m z ]2 z1 2 +0.262Bd1' 2 -0.282Bd2' 2 +21.25B[m z ] 2 +0.25Ld2' 2 +0.25d2' 2 L+70d1' 2 +80d2' 2 -21.25B[m z ] 2 +0.2Bd2'[m z ]z1-0.4Bd2'[m z ])

[0061] The technical problem to be solved by the present invention can be further achieved by the following technical solution. The update formula in the third step described above is:

[0062] In the formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r3 is a random number between [0, 1], and x t ik is the k-th dimension component of individual i at the t-th iteration.

[0063] Reference Figure 3 Specifically, Z1 is the number of teeth on the small gear, Z2 is the number of teeth on the large gear, B is the tooth width, d1' is the diameter of the driving shaft, d2' is the diameter of the driven shaft, L is the width of the reducer housing, l1 is the length of the driving shaft extending out of the housing, l2 is the length of the driven shaft extending out of the housing, l1 is 280mm, l2 is 320mm,

[0064] The optimal results of various methods are shown in the following table:

[0065]

[0066] HSCA in the table is the abbreviation name based on the sine-cosine algorithm. From the above table, we can see that m z =6, m = 6mm, that is, when the tooth width B = 134.358mm, the module m = 6mm, the box width L = 239.358mm, the driving shaft diameter d1' = 100mm, the driven shaft diameter d2' = 130mm, and the pinion tooth Z1 = 23, the optimal value obtained by the sine-cosine algorithm HSCA is 28630148.370mm 3 ≈28630.148cm 3 , which are better than the other four algorithms, thus proving the effectiveness of this method and proving that this method reduces the volume of the cylindrical gear reducer and the consumption of raw materials.

Claims

1. A method for optimizing the structure of a cylindrical gear reducer based on a sine-cosine algorithm, characterized in that: include Step 1: Randomly generate n cylindrical gear reducers. The individual codes in the initial population are divided into two parts, one part is continuous real numbers and the other part is discrete integers. The continuous real number variables in the initial population individuals are generated first and the discrete integer variables are generated later. Step 2: Taking the minimum volume of the cylindrical gear reducer as the objective function, calculate the objective function values ​​of all cylindrical gear reducers in the initial population, and record the cylindrical gear reducer with the smallest volume P and the smallest volume value f(p); Step 3: Update the cylindrical gear reducers in the population according to the update formula; Step 4: Perform a combined mutation operation on the continuous real number part of the individuals in the population. The combined mutation operator of continuous real numbers includes five mutation operators, the first continuous real number mutation operator, the second continuous real number mutation operator, the third continuous real number mutation operator, the fourth continuous real number mutation operator and the fifth continuous real number mutation operator; the above five mutation operators are selected according to the following steps: Step 1: Randomly generate a random number R1 between [0,1]; Step 2: When 0≤R1<0.3, execute the first continuous real number mutation operator; When 0.3≤R1<0.6, the second continuous real number mutation operator is executed; When 0.6≤R1<0.7, the third continuous real number mutation operator is executed; When 0.7≤R1<0.9, the fourth continuous real number mutation operator is executed; When 0.9≤R1≤1, the fifth continuous real number mutation operator is executed; Step 5: Perform a combined mutation operation on the discrete integer part of the individuals in the population. The combined mutation operator of discrete integers includes three mutation operators, the first discrete integer mutation operator, the second discrete integer mutation operator and the third discrete integer mutation operator. The above three discrete integer mutation operators are selected according to the following steps: Step 1: Randomly generate a random number R2 between [0,1]; Step 2: When 0≤R2<0.3, execute the first discrete integer mutation operator; When 0.3≤R2<0.6, the second discrete integer mutation operator is executed; When 0.6≤R2<0.7, the third discrete integer mutation operator is executed; Step 6: Calculate the objective function values ​​of all individuals in the population, and adopt the individual retention method based on the greedy strategy. When the volume of the updated cylindrical gear reducer is smaller than the volume of the cylindrical gear reducer before the update, the updated cylindrical gear reducer will be retained for the next generation, otherwise the cylindrical gear reducer before the update will be retained for the next generation. Step 7: Output the cylindrical gear reducer P with the smallest volume and the smallest volume value f(p).

2. The method for optimizing the cylindrical gear reducer structure based on the sine-cosine algorithm according to claim 1 is characterized in that: In the second step, the objective function uses the number of pinion teeth z1, tooth width B, the diameter of the driving shaft d1', the diameter of the driven shaft d2', and the width of the reducer housing L as design variables. The objective function is expressed as: minV=π(1.1875B[m z ] 2 z1 2 +0.262Bd1' 2 -0.282Bd2' 2 +21.25B[m z ] 2 +0.25Ld2' 2 +0.25d2' 2 L+70d1' 2 +80d2' 2 -21.25B[m z ] 2 +0.2Bd2'[m z ]z1-0.4Bd2'[m z ])。 3. The method for optimizing the structure of a cylindrical gear reducer based on the sine-cosine algorithm according to claim 1, characterized in that: The update formula in the third step is: In the formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r3 is a random number between [0, 1], and x t ik is the k-th dimension component of individual i at the t-th iteration.

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