Pneumatic Air Chain Hoist With Trolley
In any environment where safety is a priority, the ITA pneumatic hoist is the best choice. Compared with current driving, using compressed gas as the driving medium will not produce any sparks. The characteristics of this structure make Makita ITA pneumatic hoists especially suitable for working in hazardous environments. ITA pneumatic hoist products are very strong and reliable, so they are suitable for use in harsh industries and even in connected conditions. According to different needs, we have different controllers and rollers. For lateral loading, we have a variety of lines. Walk the trolley to meet your needs.
Applicable industries of pneumatic hoist: aircraft manufacturing, assembly line, chemical industry, dairy processing factory, electroplating factory, fireworks factory, food industry, foundry, furniture factory, glass industry, paint factory, match factory, mechanical engineering, automobile industry, Oil depots, onshore and offshore operations, paint shops, paper industry, power plants, finishing plants, sawmills, shipbuilding, space technology, steel mills, textile industries.
Standard configuration EXI12GDIIAT4/II3GDIIBT4
Pneumatic Air Chain Hoist With Trolley,Air Push Hoist,Chain Hoists For Mining Industry,Chain Hoist With Hook Mounted Hengshui Tianqin Import and Export Trade Co.,Ltd , https://www.itahoists.com
Introduction Genetic algorithm itself is independent of fuzzy model control and so on. Therefore, genetic algorithm can be used to optimize fuzzy control rules and adjust membership functions. The genetic algorithm is to represent the solution of the problem as a chromosome (used by computer programming, usually represented by a binary code string) to form a group of chromosomes. Put them in the problem environment, according to the principle of survival of the fittest, select the chromosomes that adapt to the environment for replication, that is, Selection, and generate new ones through two kinds of genetic operations: Crossover and Mutation. A generation of chromosomal groups that are more adaptive to the environment, so that they evolved from generation to generation and finally converge on the most adaptable individuals to find the optimal solution to the problem.
In the process of actual solution, the optimization design method often fails because the objective function or the constraint function cannot be mathematically expressed by the design variable or the function is complicated, which leads to the decrease of computational efficiency, but the design variable and the single objective function are deterministic, so The ambiguity of the target optimization design problem is mainly reflected in the ambiguity of the multi-objective function and the ambiguity of the constraint. In this paper, the multi-objective fuzzy genetic algorithm is used to solve the multi-objective optimization design of planetary gears. It is proved by examples that the genetic algorithm based on multi-objective fuzzy optimization is very effective for improving the volume and maximum carrying capacity of planetary transmission.
1 Mathematical model of multi-objective optimization 1.1 Mathematical model Find the design variable XRn so that the objective function F(X)=[F1(X)F2(X)Fm(X)]min and satisfy the constraint gi(X)(i=1, In the formula 2, q), n is the number of design variables; m is the number of objective functions; q is the number of constraints.
In planetary transmission design, designers always want to design a planetary transmission with small size, light weight and high carrying capacity. Therefore, this paper pursues the goal of multi-objective fuzzy optimization of planetary transmission with the minimum volume and maximum carrying capacity as the goal.
1.2 Establishing the objective function (1) The minimum volume takes the sum of the volume of the sun gear and all the planet wheels as the objective function of the planetary transmission volume, ie minF1(X)=16m2bzt2[4 ax(i-1)2](1) m is the gear modulus; b is the nominal width of the gear; zt is the number of teeth of the sun; ax is the number of planet wheels; i is the gear ratio of the gear sun gear.
(2) The maximum bearing capacity takes the input torque T as the objective function of the bearing capacity, that is, maxF2(X)=T(2)1.3 determines that the design variable is known from equations (1) and (2), F1(X), F2 (X) is determined by five independent design parameters such as m, b, zt, ax, and T. The design variables are X=[x1,x2,x3,x4,x5]T=[zt,b,m,ax,T ]T(3)1.4 establish fuzzy constraint conditions (1) Gear strength constraint In the planetary transmission design process, only the gear contact strength and bending strength between the sun gear and the planetary gear are usually considered, (5), KA is the load factor; YF is the tooth shape coefficient; YS is the stress correction coefficient; it is the gear meshing angle; KV is the dynamic load coefficient; E is the elastic modulus of the gear material; H is the contact stress calculated by the tooth surface; F is the bending stress calculated by the tooth root; [F] The upper limit of the bending stress is allowed for the tooth surface; [H] is the upper limit of the allowable contact stress of the gear; i is the transmission ratio.
(2) Adjacent conditional constraints In planetary transmissions, adjacent conditions must satisfy adjacent conditions l=x12(i-1)(1-sinx4)-x12sinx4l(6) where l is ambiguous The lower limit of the adjacent planetary wheel gap.
(3) The aperture condition is constrained to the root height of the planet gear; d is the shaft diameter of the planet wheel; it is the lower limit of the tooth root to the outer wall thickness of the vortex.
(4) Matching condition constraint x1 x1ix4=(8) where is a positive integer.
(5) Upper and lower constraints of each design variable (13) Through discussion, the planetary multi-objective optimization mathematical model discussed in this paper is a multi-objective fuzzy optimization problem.
2 Multi-objective model based on genetic algorithm 2.1 Fuzzy constraint processing In this paper, the optimal horizontal cut-off method is used to transform the fuzzy optimization condition into ordinary constraint, and the problem is transformed into the non-fuzzy optimization mathematical model on the optimal horizontal cut set. X=[x1,x2,x3,x4,x5]TminF1(X),maxF2(X)QiQiU-(QiU-Qil)(i=1,2,,4)gjgjU (gjU-gjl)(i=1, 2,, 5) gjgjl (gjU-gjl) (14) where Q is F, H, and l in the formula (4) (7); gi is the design in the formula (8) (12) Variable; the optimal level value obtained by fuzzy comprehensive evaluation.
2.2 Solution Steps Apply fuzzy theory and genetic algorithm to solve the multi-objective fuzzy optimization mathematical model (13) to find the optimal solution. The specific steps are as follows: 1) The coding genetic algorithm encodes the variable into a fixed length before searching. Encoding is represented by a binary string, and the different combinations of these strings form different search points for the search space.
2) The initial population is generated randomly to generate N strings, each string representing an individual.
3) Crossing the selected N individuals in pairs to produce N new progeny individuals.
4) Calculating fitness The fuzzy preference method is used to calculate the relative superiority of 2N individuals of the offspring and the parent, and the relative superiority is taken as the fitness value.
5) Select adaptively sorting 2N individuals of the offspring and the parent, and select the N individuals in the front.
6) Variation The N individuals selected in step 4) are mutated according to a given probability to form a new generation group.
7) Determine whether the new generation group meets the end condition, and if it is satisfied, stop; otherwise, go to step 3) to continue.
3 Application examples and analysis In order to verify the effectiveness of genetic algorithm in multi-objective fuzzy optimization of planetary gears, the gear ratio of a planetary gear reducer is 4.78, the gear material is 38SiMnMo, and the surface quenching is 55HRC65HRC. The corresponding allowable stress range is [H]=1250MPa1700MPa,[F]=425MPa9000MPa; the allowable value of the torque acting on the planetary gear is 1240N.m1550N.m. Other fuzzy conditions are high design level, good reliability of the reducer, good material selection, Good use conditions.
Try to design the planetary reducer with the smallest volume and maximum load capacity (the allowable torque of the sun gear). According to the planetary transmission multi-objective fuzzy optimization method introduced in this paper, the multi-objective optimization mathematical model (1) (14) is established for the planetary reducer, and the model is optimized by genetic algorithm. The population size is 50; evolutionary algebra Is 200; the crossover probability is 0.
8; the probability of variation is 0.01; = 0.446, and the solution result is X = [x1, x2, x3, x4, x5] T = [25, 47, 6, 2, 1478] TF1 (X) = 4835295.8 mm3, F2 ( X)=143112Nm and compared with the single-objective optimization design parameters, the volume of the planetary transmission designed in this paper decreases by 1.32. The allowable bearing capacity is improved by 19.12. Since the genetic algorithm is optimized from multiple initial points, it solves multiple targets in it. In the optimization design process, the global optimal solution of the whole optimization problem can be obtained without the local optimal solution.
4 Conclusions The mathematical model of multi-objective fuzzy optimization design and the advantages of genetic algorithm are used to optimize the planetary gears. The optimization results show that the volume and maximum carrying capacity of planetary power transmission are improved. Compared with the traditional monocular optimization design, it has the advantage of being closer to the global optimal solution. The genetic algorithm has a good application prospect in mechanical multi-objective optimization.
Enhanced spark protection configuration: EXII2GDIIBT4
Enhanced spark protection for explosion protection group IIC configuration: EXII2GDIICT4
Application of Conduction Algorithm in Multi-objective Unclear and Improved Presets of Galaxy Gears
Prev Article
Submersible pump use points