Tungsten carbide roller has characteristics of good wear resistance, high temperature red hardness, thermal fatigue resistance and thermal conductivity and high strength , have been widely used in high-speed wire rod, bar, rebar, seamless steel tubes, etc. Domestic production of tungsten carbide roller materials mostly WC- Co, WC- Co- Ni- Cr two series, and the content of Co, Co- Ni - Cr is in the range of 6wt% ~ 30wt%. From the use of perspective, tungsten carbide rollers has good mechanical properties, its flexural strength up to 2200 MPa or more, shock toughness up (4 ~ 6) × 10^6 J/ m^2, Rockwell hardness (HRA) is up to 78 to 90, widely in the high-speed wire rod rolling process, which is much higher than single-slot chilled cast steel or high speed steel rolls.Tungsten carbide is made of Tungsten Carbide Powder and binder phase (such as drilling, nickel, etc.), and then pressing and sintering, regardless of the conditions under cold rolled or hot rolled has excellent wear resistance, tungsten carbide rollers has been widely used in pre-finishing mill and finishing of high-speed wire rod currently. On the performance of tungsten carbide roller in hot-rolling wire rod , the material must meet the following requirements:
Tungsten carbide roller material design
Tungsten carbide roller category
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1 Optimum design of helical gear transmission The mathematical model of the helical gear transmission can be optimized to establish a variety of single objective functions or multi-objective functions. In this paper, the mathematical model is established with the minimum center distance and the smallest volume of the transmission as the objective function, and the optimization design is carried out.
1.1 Establishing the objective function The minimum objective function is F1(X)=mina=mnz12cosβ(1 i)(1) The smallest objective function is F2(X)=minV=14π(mnz12cosβ)3(1 i2)φa( 2) where z1 is the number of pinion teeth; mn is the normal modulus; β is the helix angle; i gear ratio; φa is the tooth width coefficient.
1.2 Determining the design variables From equations (1) and (2), F1(X) and F2(X) are determined by four independent design parameters such as z1, mn, β, φa, so the design variables are: X=[x1 ,x2,x3,x4]T=[z,mn,β,φa](3)
1.3 Constraints 1) Tooth number constraint Normally, closed gear transmission z1 ≥ 20 ~ 40, from which g1 (x) = x1-20 ≥ 0 (4) g2 (x) = 40 - x1 ≥ 0 (5) 2 The modulus of the modulus-constrained power transmission is mn ≥ 2mm, so g3(x)=x2-2≥0(6)
3) The helix angle constraint can generally take β=8°～20°. If the β angle is too large, the axial force of the transmission will increase, and the gear processing is difficult. The optimum value of the β angle is between 8° and 15°. Therefore, g4(x)=15-x3≥0(7)g5(x)=x3-8≥0(8)
4) Tooth width coefficient constraint tooth width coefficient generally takes φa=0.1～1.2
Increase the center-to-center distance of the tooth width coefficient, but increase the tooth width to distribute the load evenly along the tooth width direction. Therefore, g6(x)=x4-0.1≥0(9)g7(x)=1.2-x4≥0(10)
5) Tooth surface contact fatigue strength Constrained tooth surface contact stress σH is less than or equal to the allowable contact stress [σH], and g8(x)=[σH]-σH≥0(11)6) Root root bending fatigue strength confines root bending The stress σF is less than or equal to the allowable bending stress [σF], and the calculation of the g9(x)=[σF]-σF≥0(12) tooth surface contact stress σH and the root bending stress σF is considered in the literature [1].
7) The longitudinal coincidence degree εβ constraint εβ can be calculated according to the following formula: εβ[3]=bsinβΠ(πmn)≥1, from which the constraint g10(x)=x1x41-cosx24-πcosx4≥0(13) can be obtained. The mathematical model for the optimal design of helical gear transmission is X=[x1,x2,x3,x4]T,minF1(X),minF2(X),s.tgu(x)≥0u=4,5,... , 13
2 Genetic algorithm-based optimization model solution 2.1 Gene coding uses floating-point number coding, each design variable as a chromosome gene. The chromosome code of the optimization problem is: X = [x1, x2, x3, x4] T = [z1, mn, β, φa] 2.2 fitness function and initial population generation GA generally does not require other external information during the search evolution process, It is only necessary to reasonably define the fitness function according to the objective function of the problem, to evaluate the individual's ability to adapt to the problem environment, that is, the advantages and disadvantages of the solution, and as the basis for future genetic operations.
Since the fitness function contains the influence of constraints, the N individual chromosomes in the initial population can be generated by a random method within the range of values ​​of each gene.
2.3 Genetic manipulation On the basis of the previous generation of chromosome groups, each individual of the population consisting of N chromosomes performs genetic operations such as selection, crossover and mutation according to the fitness function values, resulting in higher fitness function values. A new generation of groups that have evolved.
1) The selection operation is to select the better individuals from the previous generation to participate in the breeding of the next generation of populations. Generally, the method of fitness function value ratio is adopted, that is, the probability Pi of each individual is Pi=fiΠ∑ni=1fi, Pi—the probability that the i-th individual is selected; n—the size of the population; fi—the fitness function value of the i-th individual. 2) The cross-over operation is a chromosome randomly selected for cross-operation and two The two combinations constitute the parents who perform the crossover operation, exchanging the gene chain code information of the parents, so that each pair of parents produces two offspring to form a new generation of optimized individuals. In this paper, two points are crossed, and X and Y are used as parents, and the two intersections are located in the second and fourth genes, respectively.
X=[x1,x2,x3,x4]T
Y=[y1,y2,y3,y4]T The new chromosome X', Y' obtained after gene exchange is X'=[x1,x2,y3,y4]T
Y'=[y1,y2,x3,x4]T sets the crossover probability to Pc, then the PcN chromosomes in the population participate in the intersection, and the magnitude of the crossover probability Pc affects the convergence speed of the genetic algorithm.
3) Mutation For a selected chromosome, randomly select one or several genes and change their gene coding to generate a new chromosome with one or several genes different from the previous chromosome.
In this paper, two-point cross mutation was used and the mutation point was selected as the second gene. A new gene x2 was randomly selected in the range of the variation gene to replace x2, and a new chromosome X'=[x1,x2,x3,x4] was obtained. T.
4) Compose a new generation of groups to replace the previous generation group by a new generation of groups obtained by the aforementioned selection, intersection, and variation. Obviously, the average quality of the new group and the quality of the best individual are better than those of the previous generation. In this way, after several generations of iterative inheritance, when the fitness value of the group tends to be stable, the genetic operation is stopped, and the individual with the best fitness in the group is taken as the optimal solution to the optimization problem.
3 Optimization Example 3.1 Raw Data Design The helical gear transmission of the single-stage gear reducer for the belt conveyor. Known: transmission power P = 12KW, drive wheel speed n1 = 970, transmission ratio i = 4.8, one-way rotation, slight load shock, service life of 10 years, gear accuracy of 8 grades, material: pinion 45 steel, quenching and tempering, HB240～270; large gear 45 steel, normalizing, HB180～210.
3.2GA algorithm implementation and results In the GA algorithm, the population size is N=100, the crossover probability is Pc=0.75, and the mutation probability is Pm=0.03. After 30 generations of genetic manipulation, the fitness value of the chromosome population tends to be stable, and the optimization problem is obtained. The optimal solution. This paper also uses conventional design methods and traditional optimization design methods to design, the results are more common.
By optimizing the design of the helical gear transmission with GA, the results obtained by the GA method are obviously superior to the conventional design and the traditional optimization design.
1Computation result comparison 4 Conclusions (1) Genetic algorithm as a non-numerical iterative global search algorithm has strong adaptability to objective function and constraint function, suitable for dealing with more complicated engineering optimization problems, and easy to get problems. Global optimal solution.
(2) This paper uses genetic algorithm to solve the optimization design of the helical gear transmission structural parameters is a new attempt, and obtained satisfactory results (center distance reduction of 26.6, volume reduction of 60.5), thus making the structure more compact The transmission stability is improved, the helix angle is increased, and the bearing capacity is further enhanced. Although the basic theory and application fields of genetic algorithms have yet to be further explored and discussed, its advantages over conventional methods will certainly make genetic algorithms more widely used.
1. Sufficient anti-fracture strength;
2. Good abrasion resistance;
3. The smooth surface finish;
4. Excellent corrosion resistance, thermal fatigue, thermal cracking performance.
Tungsten carbide roller rings can working in bad conditions , small profile rolling (especially rebar rolling) process conditions is harsher than the high-speed wire rod, and therefore corresponds to the profile rolling ,tungsten carbide rollers recommend using high binder phase carbide.
Pre-finishing all vehicles roller should ensure its high toughness, strength, rigidity and thermal conductivity, followed before considering its wear resistance. When designing each vehicles roller, pre-finishing materials should choose carbide grades of Co, Co- Ni- Cr binder content is high (greater than or equal to 25wt%) , requiring an average WC grain size of coarse (5μm ~ 6μm), to obtain a higher shock toughness, proper strength and hardness. For the finishing of the roller movements, particularly the last two rollers of the finish rolling, which suffered load is small, and high relative velocity of the material to be pressed (80 m / min ~ 120 m / min). In this case, the wear resistance of the roller to be the most important requirements, and must ensure the strength , timpact toughness and hardness of a reasonable match, so the binder of Co / Ni content ratio and the average grain WC control of particle size and other factors must have greater control in front of different pre-finishing rolling roll.
According to the structure of tungsten carbide rollers, it can be divided into solid tungsten carbide roller and composite tungsten carbide roller. Solid tungsten carbide rollers have been widely used in pre-finishing and finishing stands high speed wire rod mill (including fixed reducing the rack, pinch roller rack). Composite tungsten carbide roller is made of cemented carbide and other materials, and it can be divided into tungsten carbide composite roll rings and solid tungsten carbide composite roller. Tungsten carbide composite roll rings mounted on the roller shaft; solid tungsten carbide composite roller will be directly cast in the roll axis to form a whole, a large load is applied to the rolling mill.
Tungsten carbide rollers produced by powder metallurgy method, the key to its process control is the chemical composition of the material and the mixture was prepared, pressed molding, sintering and deep processing and other preparation process parameters.
1. Preparation of starting material (WC focus quality): As the WC raw material and quality control of the use of different levels of quality may fluctuate, resulting in adverse effects on microstructure.
2. Preparation of the mixture: Mixture preparation is the key to the production process of the roller, the roller of failure modes - trachoma, mainly generated by this procedure.
3. Pressing: roller pressing is an important process of the roller mill.
4. Sintering: roller sintering is to determine the final quality of the roller production processes, use of advanced low-pressure sintering technology, HIP sintering technology can greatly improve the performance of roller.
5. Deep processing: deep processing rollers have a greater impact on the quality and accuracy of the roller surface.