Electric cylinder optimization design based on grey wolf algorithm

Abstract

The invention discloses an electric cylinder structure optimization design method based on a grey wolf optimization algorithm, and relates to the technical field of mechanical design. The method comprises the steps that firstly, the requirement is determined, an axial deformation static model of the electric cylinder is established, push rod axial deformation, ball screw contact deformation, lead screw tensile deformation and bearing axial deformation are regarded as the series relation, and the total deformation amount is calculated; then, selecting structural parameters such as the length of a push rod and the effective stroke of a lead screw as design variables, constructing coupling constraint conditions among the design variables, and establishing an optimization model by taking minimization of total axial deformation and reduction of material consumption as targets; a grey wolf optimization algorithm is used for simulating the processes of surrounding preys, hunting and position updating by grey wolves, and optimal design parameters are searched for iteratively; the axial deformation is reduced, the overall rigidity is improved, and the manufacturing cost is reduced. According to the method, an intelligent optimization algorithm is combined with mechanical structure design, the design efficiency of the electric cylinder is improved, the balance between performance and cost is optimized, and the method is suitable for high-precision linear driving equipment.

Description

Technical Field

[0001] This invention relates to the field of mechanical design technology, and in particular to a structural optimization design method for electric cylinders based on the gray wolf optimization algorithm. Background Technology

[0002] With the rapid improvement of industrial automation and the continuous expansion of electromechanical system application scenarios, electric cylinders, with their advantages of high transmission efficiency, high positioning accuracy, fast response, simple structure, small footprint, convenient maintenance, long life, and strong environmental adaptability, are widely used by relevant manufacturers in fields such as robotics, logistics handling, and military industry. Compared with hydraulic drive systems, they effectively avoid problems such as leakage and solidification of the working medium, and are gradually showing significant replacement potential in industrial equipment and other fields.

[0003] However, in actual production applications, electric cylinders often need to consider their material costs and performance. When subjected to tensile and compressive loads, their axial deformation will seriously affect the positioning accuracy and transmission quality of the electric cylinder. Traditional electric cylinder structural designs only use simple parameter matching, or simply increase or decrease the size of individual parts without considering the impact of too many structural design parameters on the overall anti-deformation performance. In addition, there is room for optimization in the overall cost of electric cylinders. Summary of the Invention

[0004] The purpose of this invention is to provide a structural optimization design method for electric cylinders based on the gray wolf optimization algorithm, which aims to solve or improve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] An electric cylinder structural optimization design method based on the gray wolf optimization algorithm includes:

[0007] a) Establish an axial deformation static model of the electric cylinder, which includes axial deformation of the push rod, axial deformation of the ball screw contact, tensile deformation of the screw and axial deformation of the bearing, and the deformations are connected in series to form the total axial deformation of the electric cylinder.

[0008] b) Select the push rod length, the effective stroke of the lead screw in the cylinder, the distance from the tail end to the nut end during contraction, and the axial length of the cylinder as design variables, establish an optimization model with the goal of minimizing the total axial deformation and reducing the amount of material used, and construct the coupling constraint relationship between the design variables;

[0009] c) The design variables are optimized using the gray wolf optimization algorithm, which simulates the process of a gray wolf surrounding prey, hunting, and updating its position, and iteratively searches for the optimal design parameters.

[0010] d) Adjust the structural parameters of the electric cylinder based on the optimization results to reduce axial deformation, improve overall rigidity and reduce manufacturing costs.

[0011] Optionally, the axial deformation of the push rod is calculated using the tension-compression formula for a hollow cylinder, with an outer diameter of D1, an inner diameter of D2, and a length of L. R The Young's modulus of the material is E.

[0012] Optionally, in the axial deformation static model, the axial deformation of the electric cylinder is composed of the push rod deformation, the ball screw contact axial deformation, the screw tensile deformation, and the bearing axial deformation in series.

[0013] Optionally, the gray wolf optimization algorithm finds the optimal design parameters by simulating the hunting behavior of gray wolves, including three stages: surrounding prey, hunting, and position updating.

[0014] Optionally, the goal of the optimization design is to minimize the total deformation of the electric cylinder under a given axial load.

[0015] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0016] This invention discloses a structural optimization design method for electric cylinders based on the Grey Wolf optimization algorithm. The method takes the electric cylinder as the research object; constructs a static model of the axial deformation of the electric cylinder, studies key components such as push rods and ball screws, constructs an optimization model, and uses an intelligent optimization algorithm to find the optimal solution; ultimately achieving the goal of increasing stiffness and reducing cost. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A simplified diagram of the forces acting on the push rod of an electric cylinder;

[0019] Figure 2 Diagram showing the telescopic dimensions of the electric cylinder;

[0020] Figure 3 Optimize the algorithm flowchart for gwo;

[0021] Figure 4 Design a variable optimization iterative graph;

[0022] Figure 5 Design a comparison chart of the variables before and after optimization. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] The purpose of this invention is to provide a structural optimization design method for electric cylinders based on the gray wolf optimization algorithm, which aims to solve or improve at least one of the above-mentioned technical problems.

[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] like Figure 1 As shown, this invention provides a structural optimization design method for electric cylinders based on the Grey Wolf optimization algorithm. The electric cylinders are classified into single-stage and multi-stage electric cylinders according to their structural form; and into linear and reciprocating electric cylinders according to their installation method. Since single-stage linear electric cylinders are more commonly used, this method is used as an example to outline the structural process and perform modeling and solution:

[0027] Step 1: Theoretical Modeling

[0028] Because the ball screw nut of the electric cylinder will also deform under axial load, and the connection between the nut and the push rod will also undergo slight deformation, for ease of calculation, this paper defines the length from the end of the nut to the front end of the push rod as the push rod length, and includes the deformation of the nut and the connection in the push rod deformation. Therefore, when the electric cylinder is subjected to an external axial load F a During operation, it generates a total elastic deformation *l* in the axial direction. If the influence of the bolt group on the axial displacement of the electric cylinder is ignored, it is easy to see that the push rod deformation *l1*, the ball screw contact axial deformation *l2*, the tensile deformation of the screw portion from the bearing *l3*, and the bearing axial deformation *l4* are in series and all have a certain influence on *l*. The overall axial stiffness of the electric cylinder is denoted as *K*. However, under constant load, the larger the deformation, the smaller the stiffness. Therefore, the magnitude of the deformation is used to characterize the stiffness. Thus, the mathematical relationship is:

[0029]

[0030] The push rod and nut are connected by bolts. Ignoring minor deformations at the connection point, this can be simplified to a tension / compression relationship with a hollow cylinder. D1 is the design value for the outer diameter, D2 is the design value for the inner diameter, and the original design value for the push rod length is L. R1 The formula for solving the tensile and compressive deformation of the E1 reference material is as follows; the solution shows that the deformation l of the push rod under the original parameters is... 11 .

[0031]

[0032] For the axial contact deformation of the ball screw, according to existing mature theories: assuming uniform load distribution, and combining the Hertzian contact theory formula, the axial contact deformation of the original design ball screw can be obtained as l. 21 After optimization, the axial contact deformation of the ball screw is l 22 .

[0033]

[0034] Next, the tensile deformation of the lead screw section from the bearing is analyzed. Since the electric cylinder is installed with one end fixed and the other free, the length of the lead screw subjected to axial load is not fixed as the nut moves. Therefore, assuming the electric cylinder is in its maximum elongation condition, the lead screw section from the bearing to the nut (length LS1 = 600 mm) will undergo axial deformation l3 under axial force Fa. The formula is as follows, where D is the nominal diameter of the lead screw and E2 is the Young's modulus of the lead screw body. The calculated l31 is:

[0035]

[0036] Since the bearings are standard parts and are purchased directly, the bearings used in this type of electric cylinder have an axial stiffness of 2650 N / μm. When subjected to an axial load of 5000 N, they will deform by l4.

[0037] In summary, considering the overall structural layout of the electric cylinder, it can be seen that the various components are connected in series. Based on the above analysis, the deformation of each part is calculated and summed to obtain the total deformation l of the electric cylinder before optimization under the applied Fa load in the elongated state. The formula is as follows:

[0038] l = l1 + l2 + l3 + l4 (6)

[0039] Step 2: GWO Optimization Process Construction

[0040] (1) Initialize and determine the level

[0041] First, the wolf pack is divided into four groups: α, β, δ, and ω. In the optimization, the optimal solution is defined as α, β, and δ in sequence; the candidate solution is defined as ω; and ω is updated around α, β, and δ.

[0042] (2) Main loop iteration

[0043] First, the distance between the current individual and α, β, and δ is calculated using equation (7); then, the vector moving towards these three values ​​is calculated using equation (8); finally, the three vectors are combined using equation (8) to determine the next generation's position.

[0044] D = |C·X P(t)-X(t)| (7)

[0045] X(t+1)=X P (t)-A·D (8)

[0046] In equation (8), Xp represents the position vectors of α, β, and δ, X represents the current position vector of the gray wolf, and t is the iteration number; in equations (7) and (8), A and C are the vector coefficients represented by equations (9) and (10), where r 1,2 Let be a random number in the interval [0,1], and let a be the convergence factor that decreases linearly from 2 to 0.

[0047] A = 2a·r1-a (9)

[0048] C = 2·r² (10)

[0049] Expanding further, this step represents the hunting behavior of gray wolves, who can identify the location of prey and surround them. Once the gray wolves have identified the prey's location, β and δ, led by α, guide the pack to surround the prey. In the optimization problem, the optimal solution (the location of the prey) is unknown. Therefore, by simulating the gray wolf's hunting behavior and evaluating α, β, and δ after initialization, it is determined that α, β, and δ are closer to the potential location of the optimal solution. Using the positions of these three values, the location of the prey is determined, while simultaneously forcing other gray wolves (including ω) to update their positions based on the position of the optimal gray wolf, gradually approaching the prey. The wolf prey tracking using α, β, and δ is shown below:

[0050] D α =|C1·X a -X| (11)

[0051] D β =|C2·X β -X| (12)

[0052] D δ =|C3·X δ -X| (13)

[0053] In equations (11), (12), and (13), D represents the distance between an individual wolf and wolves α, β, and δ; C1, C2, and C3 are random vectors.

[0054] X1 = X α -A1·(D α (14)

[0055] X2 = X β -A2·(D β (15)

[0056] X3 = X δ -A3·(D δ (16)

[0057]

[0058] Equations (14), (15), and (16) above mean that various groups move towards the α, β, and δ wolf directions. Equation (17) is the synthesis of three vectors, which will eventually serve as the direction for the next iteration.

[0059] (3) Level update and iteration

[0060] After each iteration, new α, β, and δ individuals are re-evaluated and selected.

[0061] (4) Termination judgment

[0062] When the iteration number t <T max When t = t + 1, when t = T max When the iteration stops, output α as the optimal solution.

[0063] Step 3: Optimize the model

[0064] Since the bearings and ball screws are purchased directly, the contact deformation of the bearings and ball screws cannot be changed. Therefore, the optimization focuses on the length of the screw and the length of the push rod. Furthermore, considering that the screw length must be less than the push rod length, there is a certain coupling relationship between the two. The optimization needs to be carried out in a coordinated manner, and the GWO optimization algorithm is used to optimize the electric cylinder. The objective function is to minimize the push rod length within the constraints.

[0065] In addition, the structural parameters that can be modified are defined as design variables, as detailed in the table below:

[0066] Table 1. Information related to design variables

[0067]

[0068] The following constraint conditions are constructed based on the coupling relationship of various structural parameters during the extension and retraction process of the electric cylinder:

[0069] L R =L T -Δx (18)

[0070] L B =L R -L F +Δx (19)

[0071] L S =L B -Δx-Δy (20)

[0072] L R -L F ≥L S +Δy (21)

[0073] L R ≥L D -L B -Δy (22)

[0074] Based on the above technical solution, the following embodiments are provided.

[0075] The original design of a certain model of electric cylinder is shown in the table below:

[0076] Table 2 Original Design Parameters of a Certain Model Electric Cylinder

[0077]

[0078] Based on the relationships shown in the diagram and the above arguments, an optimization model is constructed; the values ​​of the design variables fluctuate within a reasonable range above and below the original design parameters. The range of values ​​is detailed in the table below, and the optimization model is shown in equation (23):

[0079] min f(x)=f(x1,x2,x3,x4,x5,x6,x7,x8)=x1

[0080] =f(L R ,L S ,Δx,L B ,L F ,Δy,L D ,L T )

[0081] stx1+x3-x8=0

[0082] x1 + x3 - x5 + x4 = 0

[0083] x⁴ + x³ - x⁶ + x² = 0

[0084] x4 + x5 - x7 + x2 = 0

[0085] x² + x⁵ - x¹ + x⁶ ≤ 0

[0086] x7-x4-x1+x6≤0

[0087] x i L -x i ≤0

[0088] x i -x i U ≤0 (23)

[0089] Table 3 Range of Optimized Design Parameters

[0090]

[0091]

[0092] After the optimization model is built, the population is initialized. First, a single individual is initialized. A set of parameters is randomly selected and their values ​​are calculated. If the parameters meet the constraints, the individual is generated; otherwise, it is re-initialized.

[0093] Secondly, repeat the individual initialization process described above until the population size reaches the preset number of individuals N. P (This example selects N) P =50), forming an initial population, and calculating the fitness value of each individual in the initial population. Based on the fitness value, the three best individuals are determined and labeled as α wolf, β wolf and δ wolf respectively.

[0094] After initialization, enter the main iteration loop: set the current iteration number t = 1, and the maximum iteration number T. max (This example selects T) max =500), calculate the convergence factor a = 2 - 2t / T max This factor decreases linearly from 2 to 0 during the iteration process; for each individual X in the population i(t) Based on formulas (9) and (10), the coefficient vectors A and C are calculated.

[0095] Based on the social hierarchy and cooperative hunting mechanisms of gray wolf packs, each individual gray wolf is identified by the location information X of the alpha, beta, and delta wolves. α X β X δ To update the position, first calculate the distance between the current individual and the three other individuals: D α =|C1·X α -X_ i (t)|、D β =|C2·X β -X i (t)|、D δ =|C3·X δ -X i (t)|, where C1, C2, and C3 are the coefficient vectors C corresponding to α, β, and δ wolves, respectively.

[0096] Then calculate the displacement components towards the three: X_1 = X α -A1·D α X2 = X β -A2·D β X3 = X δ -A3·D δ , where A1, A2, and A3 are the coefficient vectors A corresponding to α, β, and δ wolves, respectively.

[0097] Finally, by combining the information from all three sources, the next generation's position was determined: X i(t+1)=(X1+X2+X3) / 3.

[0098] After updating the positions of all individuals, re-evaluate the fitness value of each new individual. If the fitness of the new individual is better than before the update and meets the constraints, retain the individual; otherwise, restore it to its original position. Recalculate the population fitness values ​​and update the rank ranking of α wolves, β wolves, and δ wolves. Let the iteration count t = t + 1, and determine whether t has reached T. max If the target is not reached, continue iterating; otherwise, terminate the loop and output the position X of wolf α. α As the optimal solution.

[0099] The method of this invention employs the Grey Wolf optimization algorithm as a solution for the design of elastic rubber components. This algorithm enables rapid optimization within the design space to find optimal design values, thereby improving design efficiency. This method is applicable to electric cylinder design problems, unrestricted by specific shapes or environments, and can be applied to various electric cylinder designs. The Grey Wolf optimization algorithm automatically optimizes parameters without manual intervention, reducing the complexity of manual design. The algorithm can produce design results in a relatively short time, making it suitable for rapid design and optimization needs in engineering practice.

[0100] After calculation, it is clear that the optimized push rod length is 800mm, which is an effective improvement compared to the original design. (See the optimization iteration diagram.) Figure 4 In addition, other design variables have also been modified to some extent. See the comparison below. Figure 5 .

[0101] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0102] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A structural optimization design method for an electric cylinder based on the gray wolf optimization algorithm, characterized in that, include: a) Establish an axial deformation static model of the electric cylinder, which includes axial deformation of the push rod, axial deformation of the ball screw contact, tensile deformation of the screw and axial deformation of the bearing, and the deformations are connected in series to form the total axial deformation of the electric cylinder. b) Select the push rod length, the effective stroke of the lead screw in the cylinder, the distance from the tail end to the nut end during contraction, and the axial length of the cylinder as design variables, establish an optimization model with the goal of minimizing the total axial deformation and reducing the amount of material used, and construct the coupling constraint relationship between the design variables; c) The design variables are optimized using the gray wolf optimization algorithm, which simulates the process of a gray wolf surrounding prey, hunting, and updating its position, and iteratively searches for the optimal design parameters. d) Adjust the structural parameters of the electric cylinder based on the optimization results to reduce axial deformation, improve overall rigidity and reduce manufacturing costs.

2. The electric cylinder structure optimization design method based on the gray wolf optimization algorithm according to claim 1, characterized in that, The axial deformation of the push rod is calculated using the tension-compression formula for a hollow cylinder, with an outer diameter of D1, an inner diameter of D2, and a length of L. R The Young's modulus of the material is E.

3. The electric cylinder structure optimization design method based on the gray wolf optimization algorithm according to claim 1, characterized in that, In the static model of axial deformation, the axial deformation of the electric cylinder is composed of the series of push rod deformation, ball screw contact axial deformation, screw tensile deformation and bearing axial deformation.

4. The electric cylinder structure optimization design method based on the gray wolf optimization algorithm according to claim 1, characterized in that, The gray wolf optimization algorithm finds the optimal design parameters by simulating the hunting behavior of gray wolves, including three stages: surrounding prey, hunting, and position updating.

5. The electric cylinder structure optimization design method based on the gray wolf optimization algorithm according to claim 1, characterized in that, The goal of the optimization design is to minimize the total deformation of the electric cylinder under a given axial load.

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