Experimental study in cutting engineering ceramics based on a genetic algorithm in optimization.
Engineering ceramics, which have interest of grinding of advanced ceramics over the last two decades, are widely used in several areas for example in the aerospace, petrochemical, marine, electrical, automobile and manufacturing industry. The machining technology of engineering ceramics use laser, electro discharge machining (EDM), ultrasound, plasma technology, cutting, grinding and turning in order to improve efficiency and reduce expenses. They are typical because of their high hardness, high strength, and brittleness. Therefore, the optimization of cutting parameters such as cutting speed, feed speed, cutting depth, and tool cutting edge angle should be determined before experiments were carried out. Moreover, the optimal results are that materials removal rate ? is relatively large and the cutting tool wear rate ? sis relatively small. Multi-objective optimization was made to optimize cutting parameters for prediction models using response surface methodology.
In this case genetic algorithms were usually used to optimize cutting parameters. Moreover in the following investigation the reaction surface approach was used to develop into regression model cutting force by manipulating experimental measurements from these cutting forces. The regression model was then combine with genetic algorithm to establish optimum end mill process parameter. The cutting speed was the dominant factor, followed by the cutting feed rate, and the axial depth of cut. Genetic algorithms was used to get regression equations between material removal rate, surface roughness, and input parameters such as cutting speed, feed rate, and depth of cut, etc. The genetic algorithm-based approach yielded maximum value of material removed rate (MRR). In addition, materials removal rate and cutting tool wear rate were predicted by the least squares method. Finally, the principal objective optimization of cutting parameters was obtained from genetic algorithms, and those parameters will be explained in detail in the following paragraphs.
center93027500Cutting tests of engineering ceramics with gage sections 30mm in diameter and 180 mm in axial length-Fluorophlogopite (a type of mineral) were conducted on CK6136 type machine tools. The bending strength of the material is 108 MPa (mega pascal) and thermal conductivity is 2.1 W/m·K (Watts, meters, kelvin).
The mechanical performances of cemented carbide cutting tool (YT) are on the next table (The work tool).
The cutting procedure includes different cutting parameters for example, cutting speed, feed speed, and cutting depth. Single factor tests were firstly carried out to machine the engineering ceramics material—Fluorophlogopite, as shown below.
Materials removal rate ?
Historically it has been shown that input parameters, for example, cutting pace, feed speed, and cutting profundity has impact on the reaction of material removal rate. The info parameters for material removal rate had expanding pattern. It is also well known that material removal rate in cutting operations was defined as the volume of material that was removed per unit time in millimeters cube per minute. For each revolution of workpiece, a ring shaped layer of material was removed.
Where D and d are the diameters of workpiece before and after cutting, respectively. f is the feed speed, N is spindle speed in rpm.
Based on cutting experimental data, the empirical model of material removal rate ? was expressed as:
center4184015In this investigation, the material removal rate which was a function of the main angle, which was expressed as:
Cutting tool wear rate ?
Cutting tool will be usually used in the cutting process. When tool wear reached a precise amount, cutting force and temperature will be upgraded, etc. Disrepair occurs in tool front face, flank, and both wear. The best possible evaluation of hardware wear requires some quantitative attributes. The characteristics of the tool geometry were shown in the next image.
center972820The device wear proportion (?) is characterized as the volume of material expelled VT from the wheel isolated by the volume of material expelled Vw from the workpiece. The following condition demonstrates the calculations utilized for evaluating the estimations of the instrument wear proportion.
The parameter VB (the ratio of the average width of the flank wear) was measured by microscope observation, as shown in the next images. And it was concluded that the cutting tool wear on surface quality was significant.
center370205000Where the machining time is represented as T.
In the view of the cutting experimental data, the empirical model of material expulsion rate ? was expressed as:
Also the material expulsion rate is in function of the main angle, which was defined as:
Genetic algorithms are seek calculations demonstrated after natural frameworks in which a populace of life forms advances through the procedure of natural selection. It utilizes just the fitness value and no other information is required for its activity. There are three essential administrators of Genetic algorithms, reproduction, crossover, and mutation. The course of action of the genetic algorithms is shown below in the following diagram:
It is shown in the process that it’s assumed that this model is for random individuals x1, x2,…, xn which was decision variable. V=(x1,x2,…,xn), which must satisfy all the restraint conditions, represented the chromosome. Fitness function was then used to assess the superiority-inferiority of each individual.
The fundamental thought behind the reproduction mechanism is better people get higher possibility. The essential target of the reproduction mechanism is to make copies of good arrangements and dispose of terrible arrangements in a populace, while keeping the populace measure steady. The best individuals out of the best individuals get copy in a matting pool.
A crossover operator is a component, which makes new people by joining parts from two people, in other words, is connected alongside the strings of the mating pool. Two strings are picked from the mating pool aimlessly and a few parts of the strings are traded between the strings at the crossover site to make two new strings.
Crossover occurs only with some probability Pc (Crossover probability or crossover rate). When the solutions are not crossover, they remain unmodified,
Where fmax was the maximum fitness of the populace, favg was frontier average fitness, f ‘ was the larger fitness of two crossed individual, k1, and k2 were self-versatile change, took (0, 1) interim quantities.
RC was a random between zero and one. If rc<Pc, the following equation will be satisfied,
Where c was a random between zero and one. V1 and V2 were father individual. V1′ and V2′ were son individual.
The mutation operator, which makes new individual by making changes in a solitary individual, is utilized for the pursuit viewpoint of genetic algorithms. No one but a mutation can present new data. Mutation probability is a mutation that includes the alteration of the estimation of every “gene” of an answer with some probability Pm.
center6203315Optimization objective of genetic algorithms was:
W1, W2 was the minimum and maximum, respectively.
Therefore, the mathematic model of bi-objective optimization was:
Where, s.f., is the abbreviation of “subject to”.
The solution was calculated by selection sorting method. It was conducted with a population size of 100. The number of Pareto solution was n=0.3×100=30. The optimization range of cutting parameters was vc=0.55~ 0.6 m/s, f=0.09~0.1 mm/r, ap=0.07~0.08 mm, and ?r=54~55°.
The output parameters or the yield parameters, for example, materials evacuation rate and cutting instrument wear rate were affected by the machining procedure parameters, for example, cutting rate, cutting profundity, feed speed, and tool cutting edge angle. With the end goal to show signs of improvement yield parameters like material expulsion rate, cutting instrument wear, surface complete and so forth, genetic algorithm calculation was received for optimizing the information parameters to get yield parameters.