Optimization methods for reducing the weight of a speed reducer

Abstract

An optimization method for reducing the weight of a speed reducer comprises the steps of determining the objective function, optimizing the objective function, and determining the weight parameters of the speed reducer. This invention, based on the original chimpanzee optimization method, introduces Cat chaotic sequences, backpropagation, and a somersault foraging strategy. Compared with existing technologies, this improves the convergence speed and optimization accuracy, avoids getting trapped in local optima, and effectively reduces the weight of the speed reducer, obtaining a speed reducer with minimum weight and optimal parameters. Speed ​​reducers designed according to this method have advantages such as reasonable design, small size, light weight, and high safety and reliability, and can be widely used in speed reducer design.

Description

Technical Field

[0001] This invention belongs to the field of mechanical technology, specifically relating to speed reducers. Background Technology

[0002] In the field of mechanical technology, the speed reducer is an important component of the gearbox and can be used in various applications. The speed reducer is a transmission device between the prime mover and the working machine, used to reduce speed and increase torque to meet the requirements of various working machines. Therefore, improving the service life and load-bearing capacity of the speed reducer, as well as reducing its weight, size, and cost, is of great significance.

[0003] In the field of mechanical technology, existing speed reducers are typically designed to be relatively heavy in order to improve safety during torque transmission.

[0004] Minimizing the self-weight of a speed reducer is a nonlinear programming problem under multiple constraints, which is an NP-hard technical problem. The urgent technical problem to be solved in the field of speed reducer technology is to provide a speed reducer that can transmit large torque, is small in size, light in weight, and is safe and reliable. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned prior art and provide an optimized method for reducing the weight of a reducer that is small in size, light in weight, safe and reliable.

[0006] The technical solution adopted to solve the above technical problems is:

[0007] (1) Determine the objective function

[0008] Using mathematical modeling to minimize the reducer's self-weight, the objective function f(x) for minimizing the reducer's self-weight is obtained according to equation (1):

[0009] f(x) = 0.7854x1x2 2 (3.3333x3 2 +14.9334x3-43.0934)-1.508x1(x6 2 +x7 2 )+7.4777(x6 3 +x7 3 )+0.7854(x4x6 2 +x5x7 2 (1)

[0010] x = [x1, x2, ..., x7]

[0011] Where x is a vector, x1 represents the tooth surface width, x2 represents the gear module, x3 represents the number of teeth on the pinion, x4 represents the length of the first shaft between the bearings, x5 represents the length of the second shaft between the bearings, x6 represents the diameter of the first shaft, and x7 represents the diameter of the second shaft.

[0012] (2) Optimize the objective function

[0013] The following approach incorporates Cat chaotic sequences, backpropagation, and somersault foraging strategies into the chimpanzee optimization method;

[0014] Initialize the population using the Cat chaotic sequence and the reverse learning strategy according to equation (2):

[0015]

[0016] N initial vectors x are generated using equation (2). i For each initial vector, a corresponding reverse vector x is generated in the following manner. j :

[0017]

[0018] Where, k∈[0,1]; Let x represent the minimum and maximum values ​​of the d-th dimension vector among all initial vectors, respectively; for the initial vector x i and the reverse vector x j Merge the vectors, sort them in ascending order according to their fitness values, and select the top N vectors with the best fitness values ​​as the initial population, where N∈[20,50].

[0019] The aforementioned somersault foraging strategy is as follows: When the chimpanzee population is in disarray after hunting, they adopt the somersault foraging strategy according to formula (3):

[0020] x ch (t+1)=x ch (t)+S(r1x A (t)-r2x ch (t)) (3)

[0021] Where S represents the somersault factor, S∈[1,3], x A (t) represents the position of the optimal individual, r1 and r2 are coefficients, r1∈[0,1], r2∈[0,1], x ch Let t be the chimpanzee's position vector, and t be the iteration number, where t∈[0,t]. max ], t max t represents the maximum number of iterations. max ∈[500,1500].

[0022] (3) Determine the weight parameters of the reducer

[0023] The method for determining the weight parameters of the reducer is as follows:

[0024] 1) Initialize the population position using Cat chaotic mapping and reverse learning strategy according to equation (2).

[0025] 2) Substitute the values ​​of x1, x2, ..., x7 corresponding to the position of each individual in the population into the objective function to calculate the fitness value of each individual, i.e., the value of f(x) in the reducer weight minimization model. Sort the values ​​and find the optimal vector x. A The second-best vector x B The third optimal vector x C The fourth optimal vector x D .

[0026] 3) Press the formula: chimpanzee x ch Drive and chase prey x p :

[0027] d=|cx p (t)-mx ch (t)|

[0028] x ch (t+1)=x p (t)-ad

[0029] a = 2fr³ - f

[0030] c = 2r4

[0031] Where d is the distance between the chimpanzee and the prey, r3 and r4 are random vectors, f is the convergence factor, the value of f decreases nonlinearly from 2.5 to 0 as the number of iterations increases, a is a random vector that determines the distance between the chimpanzee and the prey, the value of a is a random number between [-2f, 2f], c is a coefficient with a value of [0, 2], and m is the chaotic vector of the chaotic mapping with a value of [0, 1].

[0032] 4) Update the chimpanzee's location using the following formula:

[0033] d A =|c1x A -m1x|

[0034] d B =|c2x B -m2x|

[0035] d C =|c3x C -m3x|

[0036] d D =|c4x D -m4x|

[0037] x1=x A -a1d A

[0038] x2=x B -a2d B

[0039] x3=x C -a3d C

[0040] x4=x D -a4d D

[0041]

[0042] Where x(t+1) represents the updated position vector of the chimpanzee, and c1, c2, c3, and c4 represent coefficients with values ​​of [0,1].

[0043] 5) Chimpanzee populations descend into chaos and exhibit socially stimulating behaviors as follows:

[0044]

[0045] Where, μ∈[0,1];

[0046] 6) Judgment condition t / t max If it is greater than rand, then perform the somersault calculation according to formula (3);

[0047] 7) Repeat steps 2)-6) above until t = t max After completing the iteration, the optimal vector x is obtained. A Output x A The corresponding values ​​of x1, x2, ..., x7 are the optimal parameters of the minimum self-weight reducer, and the objective function value is the minimum self-weight of the reducer.

[0048] In the step of determining the objective function in (1) of this invention, the constraints on x1, x2, ..., x7 are as follows:

[0049] 2.6≤x1≤3.6;0.7≤x2≤0.8;x3∈{17,18,...,28};7.3≤x4;x5≤8.3;2.9≤x6≤3.9;5≤x7≤5.5.

[0050] In the step of determining the objective function in (1) of this invention, the optimal constraints for x1, x2, ..., x7 are:

[0051] x1 takes the value 3.1, x2 takes the value 0.75, x3 ∈ {17, 18, ..., 22}, x4 takes the value 7.5, x5 takes the value 7.8, x6 takes the value 3.4, and x7 takes the value 5.2.

[0052] In the step of optimizing the objective function in (2) of the present invention, the optimal value of the somersault factor S is 2.

[0053] This invention, based on the original chimpanzee optimization method, introduces Cat chaotic sequences, reverse learning, and somersault foraging strategies. Compared with existing technologies, it improves the convergence speed and optimization accuracy of the method, avoids getting trapped in local optima, and can effectively reduce the weight of the reducer, obtaining a reducer with the minimum weight and optimal parameters. The reducer designed according to this method has the advantages of reasonable design, small size, light weight, safety and reliability, and can be widely used in the design of reducers. Attached Figure Description

[0054] Figure 1 This is a flowchart of Embodiment 1 of the present invention. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0056] Example 1

[0057] like Figure 1 As shown, the optimization method for reducing the weight of the reducer in this embodiment consists of the following steps:

[0058] (1) Determine the objective function

[0059] Using mathematical modeling to minimize the reducer's self-weight, the objective function f(x) for minimizing the reducer's self-weight is obtained according to equation (1):

[0060] f(x) = 0.7854x1x2 2 (3.3333x3 2 +14.9334x3-43.0934)-1.508x1(x6 2 +x7 2 )+7.4777(x6 3 +x7 3 )+0.7854(x4x6 2 +x5x7 2 (1)

[0061] x = [x1, x2, ..., x7]

[0062] Where x is a vector, x1 represents the tooth surface width, x2 represents the gear module, x3 represents the number of teeth on the pinion, x4 represents the length of the first shaft between the bearings, x5 represents the length of the second shaft between the bearings, x6 represents the diameter of the first shaft, and x7 represents the diameter of the second shaft.

[0063] The x mentioned 1， The constraints for x2,...,x7 are:

[0064] 2.6≤x1≤3.6;0.7≤x2≤0.8;x3∈{17,18,19,...,28};7.3≤x4;x5≤8.3;2.9≤x6≤3.9;5≤x7≤5.5.

[0065] In this embodiment, the constraint conditions for x1, x2, ..., x7 are:

[0066] x1 takes the value 3.1, x2 takes the value 0.75, x3 ∈ {17, 18, ..., 22}, x4 takes the value 7.5, x5 takes the value 7.8, x6 takes the value 3.4, and x7 takes the value 5.2.

[0067] (2) Optimize the objective function

[0068] The following approach incorporates Cat chaotic sequences, backpropagation, and somersault foraging strategies into the chimpanzee optimization method;

[0069] Initialize the population using the Cat chaotic sequence and the reverse learning strategy according to equation (2):

[0070]

[0071] N initial vectors x are generated using equation (2). i For each initial vector, a corresponding reverse vector x is generated in the following manner. j :

[0072]

[0073] Where k∈[0,1], and in this embodiment, k takes the value of 0.5; Let x and d represent the minimum and maximum values ​​of the d-th dimension vector among all initial vectors, respectively. For the initial vector x... i and the reverse vector x j The vectors are merged and sorted in ascending order according to their fitness values. The top N vectors with the best fitness values ​​are selected as the initial population, where N ∈ [20, 50]. In this embodiment, N is 30.

[0074] The aforementioned somersault foraging strategy is as follows: When the chimpanzee population is in disarray after hunting, they adopt the somersault foraging strategy according to formula (3):

[0075] x ch (t+1)=x ch (t)+S(r1x A (t)-r2x ch (t)) (3)

[0076] Where S represents the somersault factor, S∈[1,3], and in this embodiment, S takes the value of 2, x A (t) represents the position of the optimal individual, r1 and r2 are coefficients, r1∈[0,1], r2∈[0,1], in this embodiment r1 takes the value of 0.5, r2 takes the value of 0.5, x ch Let t be the chimpanzee's position vector, and t be the iteration number, where t∈[0,t]. max ], t max t represents the maximum number of iterations. max ∈[500,1500], and in this embodiment, t takes the value of 1000.

[0077] (3) Determine the weight parameters of the reducer

[0078] The method for determining the weight parameters of the reducer is as follows:

[0079] 1) Initialize the population position using Cat chaotic mapping and reverse learning strategy according to equation (2).

[0080] 2) Substitute the values ​​of x1, x2, ..., x7 corresponding to the position of each individual in the population into the objective function to calculate the fitness value of each individual, i.e., the value of f(x) in the reducer weight minimization model. Sort the values ​​and find the optimal vector x. A The second-best vector x B The third optimal vector x C The fourth optimal vector x D .

[0081] 3) Press the formula: chimpanzee x ch Drive and chase prey x p

[0082] d=|cx p (t)-mx ch (t)|

[0083] x ch (t+1)=x p (t)-ad

[0084] a = 2fr³ - f

[0085] c = 2r4

[0086] Where d is the distance between the chimpanzee and the prey, r3 and r4 are random vectors, f is the convergence factor, the value of f decreases nonlinearly from 2.5 to 0 as the number of iterations increases, a is a random vector that determines the distance between the chimpanzee and the prey, the value of a is a random number between [-2f, 2f], in this embodiment a value of 0f, c is a coefficient, the value of c is [0, 2], in this embodiment c is 1, m is the chaotic vector of the chaotic mapping, the value of m is [0, 1], in this embodiment m is 0.5.

[0087] 4) Update the chimpanzee's location using the following formula.

[0088] d A =|c1x A -m1x|

[0089] d B =|c2x B -m2x|

[0090] d C =|c3x C -m3x|

[0091] d D =|c4x D -m4x|

[0092] x1=x A -a1d A

[0093] x2=x B -a2d B

[0094] x3=x C -a3d C

[0095] x4=x D -a4d D

[0096]

[0097] Where x(t+1) represents the updated position vector of the chimpanzee, and c1, c2, c3, and c4 represent coefficients with values ​​of [0,1]. In this embodiment, c1, c2, c3, and c4 are 0.5, but they can also be arbitrarily selected from [0,1]. They can be the same or different.

[0098] 5) Chimpanzee populations descend into chaos and exhibit socially stimulating behaviors as follows:

[0099]

[0100] Where μ∈[0,1], and in this embodiment, μ takes the value of 0.5.

[0101] 6) Judgment condition t / t max If it is greater than rand, then perform the somersault calculation according to formula (3).

[0102] 7) Repeat steps 2)-6) above until t = t max After completing the iteration, the optimal vector x is obtained. A Output x A The corresponding values ​​of x1, x2, ..., x7 are the optimal parameters of the minimum self-weight reducer, and the objective function value is the minimum self-weight of the reducer.

[0103] This invention, based on the original chimpanzee optimization method, introduces Cat chaotic sequences, back learning, and a somersault foraging strategy. Compared with existing technologies, this improves the convergence speed and optimization accuracy, avoids getting trapped in local optima, effectively reduces the weight of the reducer, and obtains a reducer with minimum weight and optimal parameters. The reducer designed according to this method...

[0104] An optimized method for reducing the weight of the speed reducer was developed.

[0105] Example 2

[0106] The optimization method for reducing the weight of the reducer in this embodiment consists of the following steps:

[0107] (1) Determine the objective function

[0108] Using mathematical modeling to minimize the reducer's self-weight, the objective function f(x) for minimizing the reducer's self-weight is obtained according to equation (1):

[0109] f(x) = 0.7854x1x2 2 (3.3333x3 2 +14.9334x3-43.0934)-1.508x1(x6 2 +x7 2 )+7.4777(x6 3 +x7 3 )+0.7854(x4x6 2 +x5x7 2 (1)

[0110] x = [x1, x2, ..., x7]

[0111] Where x is a vector, x1 represents the tooth surface width, x2 represents the gear module, x3 represents the number of teeth on the pinion, x4 represents the length of the first shaft between the bearings, x5 represents the length of the second shaft between the bearings, x6 represents the diameter of the first shaft, and x7 represents the diameter of the second shaft.

[0112] The constraints on x1, x2, ..., x7 are as follows:

[0113] 2.6≤x1≤3.6;0.7≤x2≤0.8;x3∈{17,18,...,28};7.3≤x4;x5≤8.3;2.9≤x6≤3.9;5≤x7≤5.5.

[0114] In this embodiment, the constraint conditions for x1, x2, ..., x7 are:

[0115] x1 takes the value 2.6, x2 takes the value 0.7, x3 takes the value 17, x4 takes the value 7.3, x5 takes the value 7.5, x6 takes the value 2.9, and x7 takes the value 5.

[0116] (2) Optimize the objective function

[0117] The following approach incorporates Cat chaotic sequences, backpropagation, and somersault foraging strategies into the chimpanzee optimization method;

[0118] Initialize the population using the Cat chaotic sequence and the reverse learning strategy according to equation (2):

[0119]

[0120] N initial vectors x are generated using equation (2). i For each initial vector, a corresponding reverse vector x is generated in the following manner. j :

[0121]

[0122] Where k∈[0,1], and in this embodiment, k takes the value of 0; Let x and d represent the minimum and maximum values ​​of the d-th dimension vector among all initial vectors, respectively. For the initial vector x... i and the reverse vector x j The vectors are merged and sorted in ascending order according to their fitness values. The top N vectors with the best fitness values ​​are selected as the initial population, where N ∈ [20, 50]. In this embodiment, N is 20.

[0123] The aforementioned somersault foraging strategy is as follows: When the chimpanzee population is in disarray after hunting, they adopt the somersault foraging strategy according to formula (3):

[0124] x ch (t+1)=x ch (t)+S(r1x A (t)-r2x ch (t)) (3)

[0125] Where S represents the somersault factor, S∈[1,3], and in this embodiment, S takes the value of 1, xA (t) represents the position of the optimal individual, r1 and r2 are coefficients, r1∈[0,1], r2∈[0,1], in this embodiment r1 takes the value of 0, r2 takes the value of 0, x ch Let t be the chimpanzee's position vector, and t be the iteration number, where t∈[0,t]. max ], t max t represents the maximum number of iterations. max ∈[500,1500], and in this embodiment, t takes the value of 500.

[0126] (3) Determine the weight parameters of the reducer

[0127] The method for determining the weight parameters of the reducer is as follows:

[0128] 1) Initialize the population position using Cat chaotic mapping and reverse learning strategy according to equation (2).

[0129] 2) Substitute the values ​​of x1, x2, ..., x7 corresponding to the position of each individual in the population into the objective function to calculate the fitness value of each individual, i.e., the value of f(x) in the reducer weight minimization model. Sort the values ​​and find the optimal vector x. A The second-best vector x B The third optimal vector x C The fourth optimal vector x D .

[0130] 3) Press the formula: chimpanzee x ch Drive and chase prey x p

[0131] d=|cx p (t)-mx ch (t)|

[0132] x ch (t+1)=x p (t)-ad

[0133] a = 2fr³ - f

[0134] c = 2r4

[0135] Where d is the distance between the chimpanzee and the prey, r3 and r4 are random vectors, f is the convergence factor, the value of f decreases nonlinearly from 2.5 to 0 as the number of iterations increases, a is a random vector that determines the distance between the chimpanzee and the prey, the value of a is a random number between [-2f, 2f], in this embodiment a value is -2f, c is a coefficient, the value of c is [0, 2], in this embodiment c is 0, m is the chaotic vector of the chaotic mapping, the value of m is [0, 1], in this embodiment m is 0.

[0136] 4) Update the chimpanzee's location using the following formula.

[0137] d A =|c1x A -m1x|

[0138] d B =|c2x B -m2x|

[0139] d C =|c3x C -m3x|

[0140] d D =|c4x D -m4x|

[0141] x1=x A -a1d A

[0142] x2=x B -a2d B

[0143] x3=x C -a3d C

[0144] x4=x D -a4d D

[0145]

[0146] Where x(t+1) represents the updated position vector of the chimpanzee, and c1, c2, c3, and c4 represent coefficients with values ​​of [0,1]. In this embodiment, c1, c2, c3, and c4 are 0, but they can also be arbitrarily selected from [0,1]. They can be the same or different.

[0147] 5) Chimpanzee populations descend into chaos and exhibit socially stimulating behaviors as follows:

[0148]

[0149] Where μ∈[0,1], and in this embodiment, μ takes the value of 0.

[0150] 6) Judgment condition t / t max If it is greater than rand, then perform the somersault calculation according to formula (3).

[0151] 7) Repeat steps 2)-6) above until t = t max After completing the iteration, the optimal vector x is obtained. A Output x AThe corresponding values ​​of x1, x2, ..., x7 are the optimal parameters of the minimum self-weight reducer, and the objective function value is the minimum self-weight of the reducer.

[0152] An optimized method for reducing the weight of the speed reducer was developed.

[0153] Example 3

[0154] The optimization method for reducing the weight of the reducer in this embodiment consists of the following steps:

[0155] (1) Determine the objective function

[0156] Using mathematical modeling to minimize the reducer's self-weight, the objective function f(x) for minimizing the reducer's self-weight is obtained according to equation (1):

[0157] f(x) = 0.7854x1x2 2 (3.3333x3 2 +14.9334x3-43.0934)-1.508x1(x6 2 +x7 2 )+7.4777(x6 3 +x7 3 )+0.7854(x4x6 2 +x5x7 2 (1)

[0158] x = [x1, x2, ..., x7]

[0159] Where x is a vector, x1 represents the tooth surface width, x2 represents the gear module, x3 represents the number of teeth on the pinion, x4 represents the length of the first shaft between the bearings, x5 represents the length of the second shaft between the bearings, x6 represents the diameter of the first shaft, and x7 represents the diameter of the second shaft.

[0160] The constraints on x1, x2, ..., x7 are as follows:

[0161] 2.6≤x1≤3.6;0.7≤x2≤0.8;x3∈{17,18,...,28};7.3≤x4;x5≤8.3;2.9≤x6≤3.9;5≤x7≤5.5.

[0162] In this embodiment, the constraint conditions for x1, x2, ..., x7 are:

[0163] x1 takes the value 3.6, x2 takes the value 0.8, x3 ∈ {17, 18, ..., 28}, x4 takes the value 8.0, x5 takes the value 8.3, x6 takes the value 3.9, and x7 takes the value 5.5.

[0164] (2) Optimize the objective function

[0165] The following approach incorporates Cat chaotic sequences, backpropagation, and somersault foraging strategies into the chimpanzee optimization method;

[0166] Initialize the population using the Cat chaotic sequence and the reverse learning strategy according to equation (2):

[0167]

[0168] N initial vectors x are generated using equation (2). i For each initial vector, a corresponding reverse vector x is generated in the following manner. j :

[0169]

[0170] Where k∈[0,1], and in this embodiment, k takes the value of 1; Let x and d represent the minimum and maximum values ​​of the d-th dimension vector among all initial vectors, respectively. For the initial vector x... i and the reverse vector x j The vectors are merged and sorted in ascending order according to their fitness values. The top N vectors with the best fitness values ​​are selected as the initial population, where N ∈ [20, 50]. In this embodiment, N is 50.

[0171] The aforementioned somersault foraging strategy is as follows: When the chimpanzee population is in disarray after hunting, they adopt the somersault foraging strategy according to formula (3):

[0172] x ch (t+1)=x ch (t)+S(r1x A (t)-r2x ch (t)) (3)

[0173] Where S represents the somersault factor, S∈[1,3], and in this embodiment, S takes the value of 3, x A (t) represents the position of the optimal individual, r1 and r2 are coefficients, r1∈[0,1], r2∈[0,1], in this embodiment r1 takes the value of 1, r2 takes the value of 1, x ch Let t be the chimpanzee's position vector, and t be the iteration number, where t∈[0,t]. max ], t max t represents the maximum number of iterations. max ∈[500,1500], and in this embodiment, t takes the value of 1500.

[0174] (3) Determine the weight parameters of the reducer

[0175] The method for determining the weight parameters of the reducer is as follows:

[0176] 1) Initialize the population position using Cat chaotic mapping and reverse learning strategy according to equation (2).

[0177] 2) Substitute the values ​​of x1, x2, ..., x7 corresponding to the position of each individual in the population into the objective function to calculate the fitness value of each individual, i.e., the value of f(x) in the reducer weight minimization model. Sort the values ​​and find the optimal vector x. A The second-best vector x B The third optimal vector x C The fourth optimal vector x D .

[0178] 3) Press the formula: chimpanzee x ch Drive and chase prey x p

[0179] d=|cx p (t)-mx ch (t)|

[0180] x ch (t+1)=x p (t)-ad

[0181] a = 2fr³ - f

[0182] c = 2r4

[0183] Where d is the distance between the chimpanzee and the prey, r3 and r4 are random vectors, f is the convergence factor, the value of f decreases nonlinearly from 2.5 to 0 as the number of iterations increases, a is a random vector that determines the distance between the chimpanzee and the prey, the value of a is a random number between [-2f, 2f], in this embodiment a value of 2f, c is a coefficient, the value of c is [0, 2], in this embodiment c value of 2, m is the chaotic vector of the chaotic mapping, the value of m is [0, 1], in this embodiment m value of 1.

[0184] 4) Update the chimpanzee's location using the following formula.

[0185] d A =|c1x A -m1x|

[0186] d B =|c2x B -m2x|

[0187] d C =|c3x C -m3x|

[0188] d D =|c4x D -m4x|

[0189] x1=x A-a1d A

[0190] x2=x B -a2d B

[0191] x3=x C -a3d C

[0192] x4=x D -a4d D

[0193]

[0194] Where x(t+1) represents the updated position vector of the chimpanzee, and c1, c2, c3, and c4 represent coefficients with values ​​in the range [0,1]. In this embodiment, c1, c2, c3, and c4 are all 1, but they can also be arbitrarily chosen within the range [0,1]. They can be the same or different.

[0195] 5) Chimpanzee populations descend into chaos and exhibit socially stimulating behaviors as follows:

[0196]

[0197] Where μ∈[0,1], and in this embodiment, μ takes the value of 1.

[0198] 6) Judgment condition t / t max If it is greater than rand, then perform the somersault calculation according to formula (3).

[0199] 7) Repeat steps 2)-6) above until t = t max After completing the iteration, the optimal vector x is obtained. A Output x A The corresponding values ​​of x1, x2, ..., x7 are the optimal parameters of the minimum self-weight reducer, and the objective function value is the minimum self-weight of the reducer.

[0200] An optimized method for reducing the weight of the speed reducer was developed.

[0201] To verify the beneficial results of this invention, the inventors conducted comparative experiments using the method of Embodiment 1 of this invention against the Chimpanzee Optimization Algorithm (ChOA), Sine-Cosine Algorithm (SCA), Arithmetic Optimization Algorithm (AOA), Particle Swarm Optimization Algorithm (PSO), and Multi-Strategy Chimpanzee Optimization Algorithm (EOSMICOA). Each method was run independently 30 times. The experimental results are shown in Table 1.

[0202] Table 1 Comparative experimental results of the present invention and six other methods

[0203] method <![CDATA[x1]]> <![CDATA[x2]]> <![CDATA[x3]]> <![CDATA[x4]]> <![CDATA[x5]]> <![CDATA[x6]]> <![CDATA[x7]]> f(x) ChOA 3.5365 0.7000 17.0000 7.3000 7.8000 3.3855 5.3163 3038.6757 SCA 3.6000 0.7000 17.0000 7.3000 7.8000 3.3743 5.3206 3063.4174 AOA 3.6000 0.7000 17.0000 8.3000 7.8000 3.4880 5.2982 3088.9137 PSO 3.6000 0.7000 17.0000 8.3000 7.8000 3.3523 5.2869 3045.1020 EOSMICOA 3.6000 0.7000 17.0000 8.3000 7.8000 3.3901 5.2983 3062.2644 This invention 3.5021 0.7000 17.0000 7.3000 7.8773 3.3521 5.3134 3019.2291

[0204] Experimental results show that, compared with the six methods, the reducer designed according to the method of the present invention has the lowest weight under the same experimental conditions.

Claims

1. An optimized method for reducing the weight of a speed reducer, characterized in that... It consists of the following steps: (1) Determine the objective function Using mathematical modeling to minimize the reducer's self-weight, the objective function f(x) for minimizing the reducer's self-weight is obtained according to equation (1): f(x)=0.7854x1x2 2 (3.3333x3 2 +14.9334x3-43.0934)-1.508x1(x6 2 +x7 2 )+7.4777(x6 3 +x7 3 )+0.7854(x4x6 2 +x5x7 2 ) (1) x = [x1, x2, ..., x7] Where x is a vector, x1 represents the tooth surface width, x2 represents the gear module, x3 represents the number of teeth on the pinion, x4 represents the length of the first shaft between the bearings, x5 represents the length of the second shaft between the bearings, x6 represents the diameter of the first shaft, and x7 represents the diameter of the second shaft. (2) Optimize the objective function The following approach incorporates Cat chaotic sequences, back learning, and somersault foraging strategies into the chimpanzee optimization method; Initialize the population using the Cat chaotic sequence and the reverse learning strategy according to equation (2): N initial vectors x are generated using equation (2). i For each initial vector, a corresponding reverse vector x is generated in the following manner. j : Where, k∈[0,1]; Let x represent the minimum and maximum values ​​of the d-th dimension vector among all initial vectors, respectively; for the initial vector x i and the reverse vector x j Merge the vectors, sort them in ascending order according to their fitness values, and select the top N vectors with the best fitness values ​​as the initial population, where N∈[20,50]. The aforementioned somersault foraging strategy is as follows: When the chimpanzee population is in disarray after hunting, they adopt the somersault foraging strategy according to formula (3): x ch (t+1)=x ch (t)+S(r1x A (t)-r2x ch (t)) (3) Where S represents the somersault factor, S∈[1,3], x A (t) represents the position of the optimal individual, r1 and r2 are coefficients, r1∈[0,1], r2∈[0,1], x ch Let t be the chimpanzee's position vector, and t be the iteration number, where t∈[0,t]. max ], t max t represents the maximum number of iterations. max ∈[500,1500]; (3) Determine the weight parameters of the reducer The method for determining the weight parameters of the reducer is as follows: 1) Initialize the population position using Cat chaotic mapping and reverse learning strategy according to equation (2); 2) Substitute the values ​​of x1, x2, ..., x7 corresponding to the position of each individual in the population into the objective function to calculate the fitness value of each individual, i.e., the value of f(x) in the reducer weight minimization model. Sort the values ​​and find the optimal vector x. A The second-best vector x B The third optimal vector x C The fourth optimal vector x D ; 3) Press the formula: chimpanzee x ch Drive and chase prey x p d=|cx p (t)-mx ch (t)| x ch (t+1)=x p (t)-ad a = 2fr³ - f c＝2r4 Where d is the distance between the chimpanzee and the prey, r3 and r4 are random vectors, f is the convergence factor, the value of f decreases nonlinearly from 2.5 to 0 as the number of iterations increases, a is a random vector that determines the distance between the chimpanzee and the prey, the value of a is a random number between [-2f, 2f], c is a coefficient, the value of which is [0, 2], and m is the chaotic vector of the chaotic mapping, the value of which is [0, 1]. 4) Update the chimpanzee's location using the following formula. d A =|c1x A -m1x| d B =|c2x B -m2x| d C =|c3x C -m3x| d D =|c4x D -m4x| x1=x A -a1d A x2=x B -a2d B x3=x C -a3d C x4=x D -a4d D Where x(t+1) represents the updated position vector of the chimpanzee, and c1, c2, c3, and c4 represent coefficients with values ​​of [0,1]. 5) Chimpanzee populations descend into chaos and exhibit socially stimulating behaviors as follows: Where, μ∈[0,1]; 6) Judgment condition t / t max If it is greater than rand, then perform the somersault calculation according to formula (3); 7) Repeat steps 2)-6) above until t = t max After completing the iteration, the optimal vector x is obtained. A Output x A The corresponding values ​​of x1, x2, ..., x7 are the optimal parameters of the minimum self-weight reducer, and the objective function value is the minimum self-weight of the reducer.

2. The optimization method for reducing the weight of the reducer according to claim 1, characterized in that... In step (1) of determining the objective function, the constraints on x1, x2, ..., x7 are as follows: 2.6≤x1≤3.6;0.7≤x2≤0.8;x3∈{17,18,...,28};7.3≤x4;x5≤8.3;2.9≤x6≤3.9;5≤x7≤5.

5.

3. The optimization method for reducing the weight of the reducer according to claim 1, characterized in that... In step (1) of determining the objective function, the constraints on x1, x2, ..., x7 are as follows: x1 takes the value 3.1, x2 takes the value 0.75, x3 ∈ {17, 18, ..., 22}, x4 takes the value 7.5, x5 takes the value 7.8, x6 takes the value 3.4, and x7 takes the value 5.

2.

4. The optimization method for reducing the weight of the reducer according to claim 1, characterized in that: In step (2) of optimizing the objective function, the value of the somersault factor S is 2.

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