Abstract: Plastic products, as one of main structural parts of modern industrial products, have been widely used in many fields of various industries. Due to complexity of injection molding, molded products are prone to defects. Weld marks are one of the more typical injection molding defects. It not only affects appearance of parts, but also affects strength of products, damages mechanical properties of products, and brings safety hazards to normal use of products. Formation of weld marks is quite complicated, and it is related to many factors, such as part shape, mold structure, injection molding process, etc. At present, in production practice, control of weld marks still relies on experience of designers to a large extent. Therefore, it is of great significance to accurately analyze factors that have a more serious impact on weld marks, then obtain a more ideal weld mark size and position, which is of great significance to improving product quality.
This paper proposes a method to optimize length and position of weld marks using genetic algorithms, with goal of making length of weld marks the shortest and the farthest from sensitive area specified by user. Genetic algorithm is combined with injection molding software Moldflow®, and multiple steps such as setting relevant process parameters, calling Moldflow simulation analysis, extracting analysis results, calculating objective function, etc. are performed. Following search path of genetic algorithm, after multiple generations of search, optimal injection time, melt temperature, mold temperature, gate position and other process parameters for length and position of weld marks are finally obtained.
Paper uses Microsoft Visual C++ 6.0 as compilation environment, develops an implementation program for weld mark optimization based on genetic algorithms on MFC platform. At the end of paper, two cases are used to optimize various injection molding parameters that affect weld mark, a relatively good weld mark position and size are obtained. This research result can improve processing quality of injection molded products to a certain extent, thereby improving market competitiveness of injection molded products.

 

With rapid development of various industries, plastic products have been widely used in all aspects of production and life, especially in automobile, instrumentation, machinery manufacturing, transportation, communication, daily necessities and home appliance industries. Many parts have been developed in direction of plasticization. It is expected that with lightweight of vehicles such as automobiles and the further popularization of computers, scope of use of plastic products will become wider and wider. At the same time, with rapid development of world economy and the improvement of people's living standards, people's requirements for plastic products are getting higher and higher, relatively high requirements are put forward for accuracy and complexity of products.
Injection molding is one of main means of producing plastic products. Injection molding is a plastic product processing method developed and matured based on earlier metal die-casting principle. It uses injection molding machines and injection molds to mold plastic raw materials into plastic products. Basic processing principle is to utilize plasticity of plastics. First, granular plastics are transported from hopper of injection molding machine to barrel heated by an electric heater for heating and plasticization. Screw rotates to generate a large amount of shear heat, which turns plastic into a molten state. Screw then pushes melt through nozzle at the front end of barrel, main channel, branch channel, gate of mold at a high flow rate and injects it into mold cavity. Since temperature of mold is lower than softening temperature of plastic, mold quickly absorbs heat of plastic melt and gradually solidifies it. When plastic product solidifies to an appropriate thickness and has a certain rigidity, mold opens and ejection mechanism ejects molded product from mold cavity.
A very common quality problem of injection molding products is presence of weld marks. Weld marks are caused by molten plastic in cavity. When it encounters insert holes, flow rate discontinuity areas, and mold filling material flow interruption areas, it cannot be completely fused in multiple strands, resulting in seams. Existence of weld marks not only affects appearance quality of plastic products, but also has a great impact on mechanical properties of products, which will seriously affect service life of products. Therefore, weld marks must be eliminated as much as possible. However, in many cases, weld marks are difficult to avoid due to various factors. At this time, it is necessary to minimize length of weld marks, improve strength of weld marks, try to make weld marks in places that do not affect appearance and strength.
For a long time, design of injection molds in China has mainly relied on experience and intuition of designers and lacks scientific basis. Defects in design are mainly solved by repeated mold trials and mold repairs, which is very blind, not only makes production cycle of mold long and cost high. At the same time, molds produced by this method have poor overall considerations. Holes, grooves, inserts on products, number and position of gates of mold often appear unreasonable, which directly leads to inability of material flow to balance mold filling during injection molding process, incomplete fusion, and a large number of weld marks.
In recent years, widespread application of computer-aided engineering (CAE) has provided us with a powerful auxiliary tool to solve this problem. By using injection mold CAE technology, mold design and molding process can be analyzed and simulated on computer before mold manufacturing and product production, predicting potential defects in design and providing a scientific basis for designers. At present, injection molding simulation technology has become a powerful auxiliary tool for molding and mold design, but it is still only at level of verifying rationality of design. Therefore, how to apply modern optimization design theory to plastic molding has become a hot research issue in molding and mold optimization.

A weld mark refers to a three-dimensional area formed when front edges of molten plastic of two streams come into contact, where morphological structure and mechanical properties are different from those of other parts of plastic part. Since existence of weld marks has a great impact on appearance and strength of plastic parts, many experts at home and abroad have done a lot of research on formation of weld marks, processing parameters, and numerical simulation.
Feng Liangwei et al. established a weld mark formation model based on analysis of injection molding process. In filling stage, concept of fountain flow in the front zone was used to establish a "fountain encounter flow" model; in cooling stage, molecular diffusion theory was used to establish a weak connection model of weld zone; three characteristics of weld mark (weak connection, vertical orientation and surface V-groove) and formation process were analyzed, pointing out that vertical orientation is generated in filling process, weak connection and surface V-groove are formed in cooling stage. Lu Xiaomei et al. introduced causes and influencing factors of weld mark formation, predicted position of weld mark by numerical calculation method, and verified reliability of algorithm with examples, but this method has low calculation efficiency and uncertainty. Zhou Huamin et al. proposed a new algorithm for weld mark position based on node characteristic model based on injection molding flow holding simulation results. Through in-depth analysis of factors affecting weld mark performance, a weld mark performance evaluation model based on artificial neural network method was created to achieve quantitative prediction of weld mark. Hongsheng Li et al. used Taguchi experimental method to reduce number of weld marks, but authors only considered effects of injection speed, molten plastic temperature, and injection pressure on weld marks, while ignoring gate position factor which has a great influence on weld marks.
Other experts and scholars have tried to describe weld mark problem from a qualitative perspective. For example, Yu Tongmin et al. analyzed some factors that affect weld marks on products and proposed some corresponding control measures. However, since they only analyzed how to control weld marks from a qualitative perspective, they did not propose a method to optimize weld marks. Shen Changyu et al. also proposed through a qualitative analysis of weld marks that methods to eliminate influence of weld marks on product quality can be summarized into following aspects. In terms of injection molding parameter setting: 1) appropriately increase injection pressure and speed; 2) appropriately increase melt and mold temperature; 3) try to keep temperature difference between two melt fronts less than 10℃. In terms of mold design: 1) increase gate and runner size; 2) set vent holes near weld mark. In terms of product design: 1) appropriately increase wall thickness to facilitate pressure transmission; 2) try to avoid weld marks appearing at the weakest part of part.
In injection molding process, it is almost impossible to completely eliminate weld marks, but measures can be taken to minimize their impact on appearance and performance of plastic parts. There are usually two methods. That is, traditional trial, error method and simulation prediction method that has emerged in recent years. The former method is to obtain relatively satisfactory results by changing processing parameters, mold design and continuously trial-producing. The latter method is to use digital simulation to predict impact of changes in processing parameters and plastic part geometry on formation of weld marks, and to minimize impact of weld marks on plastic parts by adjusting processing parameters on computer or changing mold structure. Compared with the former method, simulation prediction method can greatly reduce production cycle and save production costs, so the latter method is development direction for solving weld mark problem.
Regarding molding simulation, as early as the 1950s, American scholars conducted a series of research on numerical simulation modeling of injection molding. Tadmor and Klein first described a complete model of plasticizing extrusion, including solid transport, plasticizing and melt transport. By the 1960s, scholars in United Kingdom, United States, Canada and other countries completed one-dimensional flow and cooling numerical simulations, and in 1970s, two-dimensional analysis programs were completed. At the same time, many university and corporate researchers were committed to study of computational models for injection, extrusion and other processes. However, these computational models did not have a great impact on enterprise-level processing technology until 1978, when Moldflow launched the first commercial simulation software for filling stage of injection molding, Moldflow, which mainly includes flow simulation, cooling analysis, warping analysis and stress analysis. In the 1980s, with advent of C-Mold software from AC-Tech in United States and widespread application of some other software in injection molding process, mold technology has been widely dependent on computer-predicted engineering science. At the same time, many research groups in Europe and North America have conducted in-depth investigations and studies on various aspects of injection molding, such as melt flow through pipes, gate locations, and molding equipment. They have also launched finite element analysis software for polymer flow, such as Fidap, Polyflow, NekTon, and Polycad. By 1990s, focus of research had been placed on viscoelasticity of materials and complex three-dimensional flow simulation, while integrated research on the entire injection molding process of flow, pressure holding, cooling, and stress analysis was carried out.
Research on injection mold CAE technology in my country began in the late 1970s. With support of national "Eighth Five-Year Plan" scientific and technological research project, my country has made great progress in injection flow simulation, cooling simulation and other aspects. For example, national key scientific and technological research project "Injection Mold CAD/CAE/CAM Integrated System" jointly conducted by Beijing University of Aeronautics and Astronautics, Huazhong University of Science and Technology, Sichuan Union University and other units has passed appraisal, and some of results have been put into practical use. At present, self-copyrighted software related to injection molding in my country include: CAD/CAE/CAM system HSC2.0 developed by Huazhong University of Science and Technology, Z-Mold analysis software developed by Zhengzhou University, etc. These software are being promoted and applied in some mold companies, but they still need to be further improved and perfected. It is undeniable that compared with advanced foreign injection molding simulation software, technology of China's self-developed injection molding simulation software is not very mature. Most domestic injection molding software is still in the stage of imitating and tracking foreign excellent injection molding simulation software such as Moldflow and C-Mold.
However, if we only rely on injection molding simulation software to solve weld mark problem, we need to constantly try and match on the computer to obtain a relatively ideal weld mark position and size. At the same time, it also requires user of injection molding simulation software to have certain engineering experience. Therefore, it is necessary to study molding optimization method based on injection molding simulation. At present, some scholars have done a lot of research work. For example, Zhai Ming et al. used genetic algorithms to propose an optimization design method for location and number of injection mold gates to achieve balanced filling and reduce warpage of plastic parts. Deng Y-M et al. proposed to control various parameters in injection molding such as mold temperature, melt temperature, injection time, etc. to achieve uniformity of plastic flow, minimum residual stress, consistent cooling time, etc. Zhu Yu et al. used genetic algorithms to optimize injection time, cooling time and injection pressure, and established a weighted sum function with these three parameters to optimize injection molding process. At present, research on injection mold CAE at home and abroad has become relatively mature, but specific problem of weld mark optimization needs to be further improved. This may be related to fact that weld marks are affected by many factors such as mold structure, plastic part geometry, plastic material, gate location and injection molding process conditions. According to information currently available, there is no very successful example of how to combine modern optimization algorithms with mature CAE software to optimize weld marks at home and abroad.

Before World War II, main methods for dealing with optimization problems were classical differential calculus and variational calculus. During World War II, operations research was born due to military needs, and a large number of optimization problems that could not be solved by above classical methods were proposed. As a result, new methods such as linear programming, nonlinear programming, dynamic programming, and graph theory were derived. Since then, theory and methods of optimization have gradually developed. Since 1960s, it has developed into an emerging discipline and has been widely used. Because optimization method searches for the best solution among all possible solutions, it requires a lot of calculations, and rapid development of computer technology has undoubtedly provided a broader development space for optimization methods.
Modern optimization algorithms include tabu search, simulated annealing, neural network algorithms, genetic algorithms, and other algorithms. These algorithms involve concepts such as biological evolution, artificial intelligence, mathematics and physical science, nervous system and statistical mechanics. They are all constructed on a certain intuitive basis and are called heuristic algorithms. Rise of heuristic algorithms is closely related to formation of computational complexity theory. Here is a brief introduction to the following optimization algorithms:

The earliest idea of simulated annealing algorithm was proposed by Metropolis in 1953, and Kirkpatriek successfully applied it to optimization problems in 1983. Simulated annealing algorithm is derived from principle of solid annealing. Solid is heated to a sufficient temperature and then slowly cooled. When heated, particles inside solid become disordered as temperature rises, and internal energy increases. When slowly cooled, particles gradually become ordered, reaching equilibrium at each temperature, and finally reaching ground state at room temperature, with internal energy reduced to a minimum. According to Metropolis criterion, probability of a particle tending to equilibrium at temperature T is e-ΔE/(kT), where E is internal energy at temperature T, ΔE is its change, and k is Boltzmann constant. Combinatorial optimization problem is simulated by solid annealing. Internal energy E is simulated as objective function value f, and temperature T is evolved into control parameter t. Simulated annealing algorithm for solving combinatorial optimization problem is obtained: starting from initial solution i and initial value t of control parameter, iteration of "generate a new solution → calculate objective function difference → accept or discard" is repeated for current solution, and t value is gradually decayed. Current solution at the end of algorithm is approximate optimal solution. This is a heuristic random search process based on Monte Carlo iterative solution method. Annealing process is controlled by cooling schedule, including initial value t of control parameter and its decay factor Δt, number of iterations L at each t value, and stopping condition S.

Idea of Tabu Search was first proposed by Glover (1986). It is an extension of local domain search, a global step-by-step optimization algorithm, and a simulation of human intelligence process. Taboo search algorithm avoids roundabout search by introducing a flexible storage structure and corresponding taboo criteria, and pardons some tabooed good states by defying criteria, thereby ensuring diversified effective exploration to ultimately achieve global optimization.
Its algorithm is to create an initialization scheme, based on which algorithm "moves" to adjacent schemes. Generally speaking, many moves are continuous processes, and quality of scheme is improved. A taboo Tabu list is used to guide search. When a special interruption condition is reached, algorithm ends. It is a deterministic search algorithm. So far, taboo search algorithm has achieved great success in the fields of combinatorial optimization, production scheduling, machine learning, circuit design, and neural networks. In recent years, it has been studied more in the field of global optimization of functions, and there is a great trend of development.

Neural networks are abstractions and simulations of some basic characteristics of human brain or natural neural networks. Artificial neural networks are based on results of physiological research on brain. Its purpose is to simulate certain mechanisms and mechanisms of the brain and realize certain functions. Hecht-Nielsen, an internationally renowned expert in neural network research, defines artificial neural networks as follows: "Artificial neural networks are artificially established dynamic systems with directed graphs as their topological structure. They process information by responding to continuous or discontinuous inputs in a state-dependent manner." Study of artificial neural networks can be traced back to perceptron model proposed by Rosenblatt in 1957. In 1980s, people obtained practical algorithms for artificial neural networks. Currently, multiple schools of thought have been formed in research methods of neural networks. The most fruitful research work includes: multi-layer network BP algorithm, Hopfield network model, adaptive resonance theory, self-organizing feature mapping theory, etc.
Characteristics and advantages of neural network algorithms are reflected in following three aspects: self-learning function; associative storage function; and ability to find optimized solutions at high speed. Therefore, neural network algorithms have received great attention in recent years.

Genetic algorithm is a type of search algorithm constructed artificially by simulating biological genetics and natural selection mechanisms. To some extent, genetic algorithm is a mathematical simulation of biological evolution process. Holland first proposed genetic algorithm in his book "Adaptation in Natural and Artificial Systems", it was mainly developed by him and his students.
Survival process of biological populations generally follows Darwin's evolutionary principle. Individuals in group are selected or eliminated by nature according to their adaptability to environment. Result of evolutionary process is reflected in structure of individual. Its chromosome contains several genes. Corresponding connection between phenotype and genotype reflects logical relationship between external characteristics and internal mechanisms of individual. Adapt to natural environment through crossover and mutation between individuals. Biological chromosomes are expressed in mathematical or computer ways as a string of numbers, still called chromosomes, and sometimes individuals; adaptability is measured by a value corresponding to a chromosome; selection or elimination of chromosomes is carried out according to whether problem faced is to seek maximum or minimum.
Since genetic algorithm was proposed in 1965, it has become a relatively active research field in the world and has been used to solve some problems with application prospects, such as genetic programming, function optimization, sorting problems, artificial neural networks, classification systems, computer image processing and robot motion planning.

This paper will carry out optimization research on size and position of weld marks from following two aspects:
1) Analyze influence of some main parameters of plastic products in injection molding simulation process, such as injection time, molten plastic temperature, mold temperature, gate position, etc. on weld marks.
2) Propose and establish a process parameter optimization model based on genetic algorithm, optimize process parameters by calling Moldflow software and optimization algorithm to reduce length of weld marks, avoid making them appear in areas that are sensitive to product appearance and strength.

1) Determine factors that affect size and position of weld mark, that is, optimization variables, determine their allowable range of variation, determine constraint space for each optimization variable, thus determine the search space of optimization problem.
2) Determine target value of objective function based on weld mark position that user wants to avoid and acceptable weld mark size. Since optimization involved in this project is a typical multi-objective optimization problem, each target item has its ideal target value.
3) Determine a value of optimization variable in search space to constitute a possible solution to optimization problem. Using Moldflow, analyze and simulate injection molding process corresponding to possible solution, extract relevant data of size and position of weld mark obtained in simulation process. Then, based on selected optimization method, calculate realization of each optimization target and realization of the total optimization target; that is, determine whether size and position of weld mark have reached ideal state; if not, how far away from ideal state is. According to this result, next possible solution is determined according to search direction specified by multi-objective optimization method selected above, and process of simulation analysis, result extraction and objective function calculation is repeated. This is an optimization search process that requires multiple reciprocating times until final optimization solution is obtained.
This paper uses Microsoft Visual C++6.0[21-22] as compilation environment and develops an implementation program for injection molded parts weld mark optimization based on genetic algorithms on MFC platform.

This chapter introduces weld mark problem that is currently widely present in the field of injection molding, focuses on current research status of domestic and foreign solutions to weld mark problem and commonly used algorithms in the field of optimization technology. Finally, a specific research plan for paper is proposed.

So-called injection molding refers to method of injecting heated molten plastic into a mold, cooling and solidifying it to obtain a finished product. Process of converting resin raw materials into plastic products after injection molding mainly includes pre-molding, metering, injection molding, cooling and shaping. In injection molding industry, people gradually realize that using injection mold CAE technology to transform traditional injection molding processes can greatly improve product quality, shorten development cycles, reduce product costs, and thus improve product market competitiveness.

Injection molding machine is a device that melts plastic and molds it in a mold. Its injection molding system mainly includes a feeding device, a barrel, a screw or a plunger, a clamping mechanism, a mold, etc. As shown in Figure 2.1:

 

Figure 2.1 Schematic diagram of injection molding system
Feeding device of injection molding machine is generally a hopper. At present, in practical production, it is often equipped with an automatic feeding device and a heating device. This reduces labor intensity and improves production efficiency. More importantly, it is conducive to drying and purity of plastics.
Barrel of injection molding machine is generally equipped with a heating device, which usually has a segmented heating function, so as to better control plastic.
Screw or plunger is a very important component in injection molding machine. At present, most injection molding machines are screw injection molding machines. Screw mainly uses its own rotation to gradually push forward, compact, exhaust and plasticize plastic in barrel, while screw itself slowly moves backward due to pressure of melt. At the same time, when screw rotates, it stirs plastic, generates a large amount of heat, and promotes plasticization of plastic. During injection molding, it transmits hydraulic pressure to inject molten plastic into mold.
Clamping mechanism on injection molding machine has functions of opening and closing mold, locking mold, and ejecting product. Molten plastic is injected into mold through nozzle under high pressure. Injection molding machine must apply a sufficiently large clamping force to ensure that mold is tightly closed, otherwise processed plastic products are prone to flash. However, excessive clamping force will lead to waste of injection molding machine capacity and shorten mold life.
Injection mold mainly makes molten plastic into a certain shape required by user. If mold is divided according to its functional structure, it can be divided into: molding part, side parting and core pulling part, pouring part, guide part, ejection and reset part, fixing and supporting fastening part, cooling and heating part, overflow discharge part, etc. Injection molding process mainly includes four parts: plasticization, injection molding, pressure holding, cooling and shaping.

Plasticization process refers to the whole process in which plastic particles reach a good plastic flow state through feeding device under joint action of barrel and rotating screw. It can be said that plasticization process is preparation process for injection molding. Before molten plastic enters mold cavity, it should have a specified molding temperature and reach a sufficient amount within specified time. At the same time, melt temperature should be consistent, and plastic should not be thermally decomposed, so as to ensure quality of produced products.

Injection molding process is that screw, under thrust of injection cylinder, injects plasticized melt in metering chamber into nozzle and mold runner, and finally fills mold cavity through gate, as shown in Figure 2.2.

 

Figure 2.2 Injection molding process
Flow characteristics of injection molding stage are nonlinear functions of pressure changes with time. There is no pressure in mold cavity for a period of time after mold filling begins. When mold cavity is full, material flow pressure rises rapidly and reaches maximum value. The longer mold filling time is, the more plastic that enters mold first is cooled, and viscosity increases. Plastic that follows needs greater pressure to enter mold cavity. In this case, plastic is subjected to greater shear stress, and molecular orientation degree is relatively large. This kind of product is prone to cracks during use in places with large temperature changes, and direction of cracks is consistent with direction of molecular orientation. At the same time, thermal stability of this product is relatively poor. When mold is filled at high speed, molten plastic will generate more friction heat when passing through nozzle, main channel, branch channel and gate, which will increase material temperature. This can keep molten plastic at a higher temperature, thereby reducing degree of molecular orientation. However, if mold is filled too quickly, a higher hydraulic driving force is required. At the same time, if mold is filled too quickly, temperature of molten plastic will be too high, and plastic will degrade.
Therefore, at this stage, the more important injection molding process parameters are: temperature of molten plastic, injection pressure and filling time.

Holding process mainly refers to period from when molten plastic fills mold cavity to when screw is withdrawn. As shown in Figure 2.3.

 

Figure 2.3 Holding process
During holding stage, molten plastic shrinks due to cooling, but plastic is still under steady pressure of screw, molten plastic in barrel will continue to be injected into mold cavity to fill gap left by plastic cooling and shrinking. If screw remains stationary during holding stage, pressure in mold cavity will drop slightly due to shrinkage of plastic. Therefore, to keep pressure in cavity unchanged, screw should be moved forward slightly as molten material enters mold. Holding stage has a certain influence on increasing density of product, reducing shrinkage and overcoming surface defects of product.
In this stage, the more important injection molding process parameters are: holding time and holding pressure. If holding time is too short or holding pressure is insufficient, holding effect will not be achieved, resulting in excessive shrinkage of product; if holding time is too long or holding pressure is too high, it is easy to cause over-holding, resulting in difficulty in demolding, causing defects such as part tearing.

Cooling and shaping stage refers to period during which plastic at gate is completely frozen, but plastic in cavity continues to cool. When it is cooled enough to be ejected, cooling ends. During this stage, screw retreats and melt is stored to prepare for next injection. As shown in Figure 2.4.

 

Figure 2.4 Cooling and shaping process
In this stage, although no plastic flows out of or into gate, a small amount of plastic still flows in mold cavity, so a certain molecular orientation will be generated. In this stage, temperature and pressure of plastic in mold cavity will change. When pressure in mold is not equal to external pressure, residual pressure will be generated. When residual pressure is positive, it is easy to cause demoulding difficulties and scratches on product; when residual pressure is negative, there will be shrinkage marks on the surface of product. Therefore, residual pressure should be close to zero to ensure a relatively satisfactory product. In addition, the most important process parameter in cooling stage is cooling time, because cooling time is the most time-consuming stage in injection molding process. Too long cooling time will lead to low processing efficiency, and too short cooling time will lead to a series of quality problems, such as stress marks, shrinkage and other defects. Approximate time spent in each stage of injection molding can be represented by Figure 2.5:

 

Figure 2.5  Injection molding cycle

A basic injection molding CAE system is generally composed of a certain number of hardware systems and corresponding software systems. Injection mold CAE system generally requires a lot of calculations, so it has high requirements for computer hardware system, requires a host and graphics processing system with excellent performance and powerful functions. Software system consists of system software, professional application software and auxiliary software. System software is provided by manufacturer and it should be coordinated with hardware. Computer cannot function without system software. At present, CAE system software on microcomputers generally uses Windows operating system and Unix operating system. Professional application software is core of injection mold CAE system. It generally refers to commercial software packages that can be used for engineering simulation analysis. It can perform flow analysis simulation and cooling simulation on plastics. Among them, the more famous software packages include Moldflow and C-Mold (now merged into Moldflow). Support software is usually also called functional software or general software. It is based on system software and is used to develop general software required for CAE application software. It can be said that support software is basic software of CAE system, such as various graphics processing software. Common software packages include Pro/E, UG, and Soildworks.

Development of injection mold CAE software has experienced three important milestones from midplane flow technology to two-plane flow technology and then to solid flow technology. At present, due to imperfection of algorithms of two-plane flow technology and solid flow technology, these three analysis technologies still coexist. Midplane flow technology is the earliest injection molding simulation technology, which began in the 1980s. So-called mid-plane flow technology is to extract middle layer between mold cavity and core to simplify 3D model, replace 3D algorithm with a one-dimensional and two-dimensional coupling algorithm. Injection molding simulation technology based on mid-plane flow model can successfully predict pressure field, velocity field, temperature distribution, weld mark position and other information during filling process, and has some obvious advantages: first, technical principle is concise and easy to understand; second, mesh division result is simple and number of units is small; third, calculation amount is small. However, practice has proved that it also has great limitations, such as: mid-plane model automatically generated by CAE software based on three-dimensional model of product is not very ideal, and mesh repair workload is relatively large; at the same time, in mid-plane simulation technology, considering that thickness of product is much smaller than dimensions in the other two directions, velocity component of melt in thickness direction is ignored, it is assumed that pressure of melt does not change along thickness direction, and three-dimensional flow problem is simplified to a two-dimensional problem in flow direction and a one-dimensional analysis in thickness direction, so a hypothetical model is used, information generated is inevitably limited and incomplete. It can be seen that mid-plane model has become a bottleneck in development of injection mold CAE technology. The most direct way to replace mid-surface model technology is to use three-dimensional finite element method to replace coupling algorithm of two-dimensional finite element in flow direction and one-dimensional difference in thickness direction in mid-surface model. However, three-dimensional flow simulation technology has many difficulties, a short time of practical experience, huge technical workload, and long calculation time, which is in sharp contrast to simplicity, long-tested, small calculation workload, and short calculation time of mid-surface model. At the time when three-dimensional flow simulation technology was not yet mature, a new method of injection molding flow simulation analysis that retained technical characteristics of mid-surface model and was based on solid surface model was born in the late 1990s. It is double-surface flow model (Fusion) technology. Double-surface flow refers to generation of finite element meshes on inner and outer surfaces of product, rather than on mid-plane. Principle used by double-surface flow technology is essentially same as that of mid-surface flow technology. Difference is that single-layer material flow of mid-surface flow is transformed into a double-layer material flow that flows in coordination along upper and lower surfaces. Since meshes of upper and lower surfaces cannot correspond one to one, and mesh shape, size, orientation and size cannot be completely symmetrical, if injection molding analysis is directly performed on this, melt flow simulation of upper and lower surfaces will be carried out independently during analysis process, and there is no connection or influence between them, which is different from actual situation of plastic production. Therefore, in order to solve this problem, nodes of surface mesh must be paired in thickness direction to try to make melt flow consistent on two surfaces of product. Obviously, from mid-surface simulation technology to double-sided simulation technology, it can be said to be a great progress, it has been supported and praised by many users. However, it also has certain shortcomings, such as:

1) Analyzed data is similar to mid-surface model, and there is no substantial improvement, so analyzed data is still incomplete. In addition to using finite element difference method to solve temperature difference in wall thickness direction, it rarely considers consideration of other physical quantities in thickness direction.

2) It cannot accurately solve complex problems. With development of current injection molding process, structure of plastic products is becoming more and more complex, simulation of wall thickness direction is becoming more and more important. Simulation of double-sided simulation technology in this regard is not optimistic.

3) Simulation results lack a sense of reality. Since simulation is only performed on the surface of model, rather than on uniform flow in product, analysis results are inevitably different from actual situation. Therefore, it can be said that double-sided simulation technology is only a transitional stage from mid-surface simulation technology to solid model. When three-dimensional simulation technology matures, application space of double-sided simulation technology will become smaller and smaller, and solid flow technology will eventually replace double-sided flow technology. Solid flow technology is still same as mid-surface flow technology in terms of implementation principle, but difference is that numerical analysis method is quite different. In solid flow technology, physical quantity change in thickness direction of melt is no longer ignored. At this time, only three-dimensional finite element grid can be used to perform numerical analysis on filling flow of melt by relying on three-dimensional finite difference method or three-dimensional finite element method. Therefore, compared with mid-surface flow or two-surface flow, the biggest problem of injection mold CAE software based on solid flow technology is large amount of calculation and long calculation time. For example, for plastic products such as mobile phone structural parts, it still takes hundreds of hours to calculate a complete solution using current injection mold CAE software and the best configured computer. This is contrary to current mold development cycle and has become a bottleneck restricting comprehensive promotion of injection mold CAE technology. Therefore, to truly promote injection mold CAE software based on solid flow technology, it is still necessary to improve software algorithm and increase speed of computer hardware equipment. So these three injection molding simulation methods have their own advantages in technology. In practical applications, the most appropriate analysis technology should be used to obtain relatively satisfactory analysis results.

CAE technology is a relatively new technology that takes improvement of CAD technology level as driving force for development, high-performance computers and graphic display equipment as development conditions, and finite element analysis technology, mechanism optimization design, model analysis and other methods as theoretical basis. Injection molding technology is flow and molding of plastic in mold cavity during injection molding process, which is related to factors such as material properties, product shape and size, molding temperature, injection pressure, molding time, mold temperature, and mold design. Therefore, for trial production of new products or some products with complex shapes, high precision and quality requirements, even experienced process and mold designers can hardly guarantee successful design of qualified molds and setting of reasonable injection molding parameters. Therefore, after preliminary design of mold is completed, some defects in mold design can be found through CAE analysis of injection mold, so as to ensure rationality of mold design, improve success rate of mold trial, reduce enterprise costs, and improve competitiveness of enterprise. Content and results of injection molding CAE system analysis provide a reference data for mold design and injection molding process parameter optimization, including: balance of pouring system, number, size, and position of gates, etc.; prediction of position of weld mark; temperature change in cavity; injection pressure in injection molding and pressure distribution of molten plastic in filling process; temperature change of molten plastic in cavity; shear stress and shear rate of molten plastic in cavity, etc. At the same time, in injection molding CAE system, some simulation results obtained should also follow some principles, so as to judge whether mold and injection molding parameters are optimal. These basic principles include: pressure difference of each flow channel should be relatively small, and pressure loss should be basically consistent; the entire pouring system should be balanced, that is, to ensure that molten plastic can reach and fill cavity at the same time; injection molding cycle should be relatively short and injection molding pressure should be relatively small; after filling, temperature gradient of molten plastic should be relatively small, so as to reduce residual stress; weld marks and bubbles should be as few as possible, and they should be placed in places that do not affect product quality.

Moldflow is a software development and consulting company specializing in plastic molding CAE. Since release of the world's first flow analysis software in 1976, it has been dominating plastic CAE software market. MPI (Moldflow Plastics Insight) is an upgraded product of original Moldflow dynamic series. It is a more in-depth software integration for part and mold design analysis, providing powerful analysis functions, visualization functions and project management tools. MPI can select geometry of product, material, mold design and processing parameter settings, so as to obtain better design parameters and obtain high-quality products. Optimization of weld mark of plastic products in this paper is carried out and completed in MPI environment. MPI can simulate manufacturing process of the most extensive thermoplastics and thermosetting plastics injection molding. For example, it can simulate filling, holding and cooling stages of injection molding process of the more common thermoplastics in daily life, and can also predict defects of product after molding, such as product warping, deformation, and appearance of product. It can even analyze dynamic filling status of plastic and orientation of molecules, thus providing a useful reference for plastic warping. MPI can also simulate other plastic processing processes besides the more traditional injection molding process, such as gas-assisted injection molding, thermosetting injection molding, reaction injection molding, etc.
Moldflow software can play a role in following aspects:

1) Improve design of plastic products.

Traditional plastic parts design is usually designed independently by plastic parts structural engineers, and quality of designed products is often determined by experience of engineers. Since structural engineers usually consider more about structure and strength, and often ignore feasibility of mold, it leads to constant design changes, which is time-consuming and laborious, and designed products are often not satisfactory. If plastic parts structural engineers use Moldflow software, they can avoid many design defects and quickly design ideal plastic products. At the same time, they can get actual minimum wall thickness of product, reduce material costs, shorten production cycles, and ensure that product can be fully filled.

2) Improve plastic mold design.

Number, position and flow system design of mold gate are of great importance to success and quality of plastic products. In the past, design usually relied on experience of mold designers and structural parts designers. However, due to diversity and complexity of plastic products and limitations of designers' experience, traditional mold design often requires repeated mold trials and mold repairs to succeed. Using Moldflow software, you can optimize design of cavity size, gate position, form, number, flow channel layout, cooling system, etc., perform mold trials and mold repairs on computer, which can greatly improve mold quality and reduce number of mold trials, thereby improving processing efficiency and product competitiveness.

3) Reasonable setting of injection molding process parameters. 

Due to limitations of experience, it is difficult for engineering and technical personnel to accurately set the most reasonable processing parameters for products, select suitable plastic materials and determine optimal process plan. Use of Moldflow software can help engineering and technical personnel determine relatively reasonable injection pressure, holding pressure, mold temperature, melt temperature, injection time, holding time and cooling time to inject high-quality plastic products.

This chapter introduces basic principles of injection molding and describes process of each stage in injection molding in detail. Then composition, development and characteristics of injection mold CAE system are introduced, finally characteristics and functions of Moldflow software are briefly introduced.

Genetic Algorithm is a type of randomized search method evolved from evolutionary law of biological world (survival of the fittest, genetic mechanism of survival of the fittest). It was first proposed by Professor J. Holland of United States in 1975. Its main features are that it operates directly on structural objects, does not have limitation of derivative and function continuity, has inherent implicit parallelism and better global optimization ability, adopts probabilistic optimization method, can automatically obtain and guide optimization search space, and adjust search direction adaptively without need for definite rules. These properties of genetic algorithms have been widely used in the fields of combinatorial optimization, machine learning, signal processing, adaptive control and artificial life. It is one of the key technologies in modern intelligent computing.

Genetic algorithms originated from computer simulations of biological systems. As early as the 1950s and 1960s, a few computer scientists independently conducted research on so-called "artificial evolution system", with starting point that idea of evolution can be developed into an optimization tool for many engineering problems. These early studies have formed prototype of genetic algorithms. For example, most systems follow natural law of "survival of the fittest", some systems adopt population-based design schemes, add natural selection and mutation operations. Some systems abstract biological chromosome coding and apply binary coding. Since the early optimization algorithms lacked a universal coding scheme, people could only generate new genetic structures through mutation rather than crossover, so the early algorithms had little effect. It was not until the mid-1960s that John Holland proposed bit string code technology based on the work of A. S. Fraser and H. J. Bremermann. This technology is applicable to both mutation operations and crossover operations, and emphasizes crossover operations as main genetic operation. Subsequently, Holland used algorithm to study adaptive behavior of natural and artificial systems, systematically expounded basic principles and methods of genetic algorithms in his famous book "Adaptation in Natural and Artificial Systems" published in 1975, proposed pattern theory which is extremely important for theoretical research and development of genetic algorithms. Pattern theory reveals that sample of excellent individuals in a group will grow exponentially, thus theoretically ensuring that genetic algorithm is an optimization process that can be used to seek feasible solutions. Many of Holland's early concepts about genetic algorithms have been used to this day, which shows that he has made pioneering contributions to genetic algorithms. Application of genetic algorithms to optimization problems should also be attributed to Holland's student De Jong, who used genetic algorithms for function optimization in his doctoral thesis "Behavior Analysis of a Genetic Algorithm Adaptive System" and established famous De Jong five-function test platform, laying foundation for application of this technology. It can be considered that De Jong's research work is a milestone in development of genetic algorithms. Gerfenstette developed the first genetic algorithm software - GENESIS, which made a significant contribution to popularization and promotion of genetic algorithms. In the 1980s, genetic algorithms ushered in a period of prosperity and development. Both theoretical research and applied research have become very popular topics. In particular, application field of genetic algorithms has continued to expand. With development of times, people are increasingly aware of limitations of traditional artificial intelligence methods. At the same time, with improvement of computer speed and popularization of parallel computers, requirements of genetic algorithms and evolutionary computing for computer speed are no longer a factor restricting their development. At present, main fields involved in genetic algorithms include automatic control, planning and design, combinatorial optimization, image processing, signal processing, artificial life, etc. Since advantages of genetic algorithms in applied research are mainly due to their effectiveness in solving problems and ease of simulation, it can be expected that in the near future, with continuous deepening of theoretical research and continuous expansion of application fields, genetic algorithms and evolutionary research will achieve more rapid development. Research on genetic algorithms and evolutionary computing in my country is still in a period of continuous absorption of foreign advanced achievements and continuous growth. In particular, this year, remarkable research has been achieved in genetic algorithms and evolutionary computing. A large number of articles on genetic algorithms emerge every year in national first- and second-level journals. At the same time, some books on genetic algorithms have also been published, such as "Non-numerical Parallel Computation-Genetic Algorithms" published by Liu Yong, Kang Lishan, etc. of Wuhan University in 1995; "Principles and Applications of Genetic Algorithms" published by Zhou Ming and Sun Shudong in 1999; "Genetic Algorithms-Theory, Application and Software Implementation" published by Wang Xiaoping and Cao Liming in 2002.

Algorithm Genetic algorithm is an iterative process. It imitates mechanism of inheritance and evolution of organisms in natural environment. It repeatedly applies selection operators, crossover operators, and mutation operators to population, and finally obtains optimal solution or approximate solution of problem. Genetic algorithm provides a general framework for solving complex system optimization problems, which does not depend on the field and type of problem. For practical problems that require optimization calculation, following steps can be used to construct a genetic algorithm for solving practical problems:

1) Determine decision variables and constraints.

2) Determine chromosome encoding and decoding methods.

3) Initialization.

Select a population, that is, select a set of strings or individuals. This initial population is also a set of hypothetical solutions to problem. Optimal solution to problem will be obtained from these initial hypothetical solutions.
4) Selection operator. Function of selection operator is to select some relatively good individuals from current generation population and copy them to next generation population. The most commonly used selection operator is proportional selection operator, which is to use fitness as selection criterion during selection. Individuals with high fitness are more likely to be selected and inherited to next generation population.
Proportional selection is also called Roulette Wheel selection, because this selection method is very similar to operation principle of roulette wheel in gambling. In genetic algorithm, the entire population is divided by individuals, and proportion of fitness of each individual to sum of fitness of all individuals is also different. This proportion divides the entire roulette wheel and determines probability of each individual being inherited to next generation. It can be expressed by following formula:
(Formula 3.1).
Where P is number of times an individual is selected, and f (bi) is fitness of individual,  is sum of fitness of all individuals. From above formula, we can know that individuals with high fitness will reproduce more to next generation; on the contrary, individuals with low fitness will reproduce less to next generation, or even be eliminated. In this way, offspring with strong adaptability to the environment are produced.

4) Crossover operator.

So-called crossover operation in genetic algorithm refers to exchanging some genes of two paired chromosomes in a certain way to form two new individuals. Crossover operation is an important feature that distinguishes genetic algorithms from other evolutionary algorithms. It plays a key role in genetic algorithms and is main method for generating new individuals. Design and implementation of crossover operator generally requires that it should not destroy too much excellent pattern representing excellent shape in individual code string, and can effectively generate some better new individual patterns. The most commonly used crossover operator is single-point crossover. At present, many crossover operators have been developed, such as: double-point crossover and multi-point crossover, uniform crossover, arithmetic crossover, etc. Here we only introduce single-point crossover operator. First, randomly pair individuals in population. If population size is M, there are M/2 pairs of paired individuals. Among them, M/2 should be an integer. For each pair of paired individuals, position after a certain gene locus is randomly set as crossover point. Then for each pair of paired individuals, crossover probability pc is set in turn to exchange part of chromosomes of two individuals at their crossover points, thereby generating new individuals. Assume that S1=1001101, S2=1110011, select their right 3 bits for crossover operation, then S1=1001011, S2=1110101.

5) Mutation operator.

Mutation operator in genetic algorithm refers to replacing gene values at certain loci in individual chromosome code string with other alleles of loci to form a new individual. Commonly used mutation operators include basic position mutation, uniform mutation, boundary mutation, non-uniform mutation, Gaussian mutation, etc., and only basic position mutation is introduced here. Assume that genotype of an individual is S=100110, and the third position is mutated, then S=101110 after mutation. Compared with crossover probability pc, mutation probability pm is smaller. This is mainly related to different roles played by crossover operator and mutation operator. Crossover operator is main method for generating new individuals, which determines global search capability of genetic algorithm; while mutation operation is only an auxiliary method for generating new individuals, but it is also an indispensable operation step because it determines local search capability of genetic algorithm. Crossover operator and mutation operator work together to complete global search and local search of search space, so that genetic algorithm can have better search performance to complete optimization process of optimization problem. Crossover operator mainly improves local search capability of genetic algorithm, while maintaining diversity of population and preventing occurrence of premature phenomenon.

6) Global optimal convergence.

When fitness of optimal individual reaches given threshold, or genetic algorithm stops running after running to specified evolutionary generation, and outputs the best individual in current population as optimal solution to problem, algorithm ends at this time. Otherwise, new generation of population obtained through selection, crossover, mutation will replace previous generation of population, and return to selection operation in step 4 to continue cycle. Specific algorithm flow chart is represented by Figure 3.1:

 

Figure 3.1 Genetic algorithm flow chart

Genetic algorithms are a type of search method that can be used for optimization calculations of complex systems. Compared with some other optimization algorithms, it has following characteristics:

1) Genetic algorithms start searching from solution set of problem solution, rather than from a single solution. This is a huge difference between genetic algorithms and traditional optimization algorithms. Traditional optimization algorithms iterate to find optimal solution from a single initial value, so efficiency is not high, and sometimes even search process is stuck in a local optimal solution. Genetic algorithms start searching from a set of strings, rather than from a single individual. Selection, crossover, mutation and other operations are performed on this group to generate a new generation of groups. Therefore, genetic algorithms have a wide coverage and are conducive to global optimization.

2) Genetic algorithms use very little information about specific problems when solving problems, and are easy to form general algorithm programs. Traditional optimization algorithms not only need to use value of objective function, but also often need other auxiliary information such as derivative value of objective function to determine search method. Genetic algorithms only need fitness function to determine search direction, and do not need derivative information. Therefore, genetic algorithms are more suitable for optimization problems where objective function cannot or is difficult to be derived.

3) Genetic algorithms have extremely strong fault tolerance. Initial string set of genetic algorithm itself carries a lot of information that is far from optimal solution; through selection, crossover, and mutation operations, strings that are extremely different from optimal solution can be quickly eliminated; this is a strong filtering process; and it is a parallel filtering mechanism. Therefore, genetic algorithms have high fault tolerance.

4) Genetic algorithms use a random search technology. Many traditional optimization algorithms often use deterministic search methods. There is a certain transfer method for the transfer from one search point to another. However, it is precisely because of this certain transfer method that searched solution often falls into local optimal solution rather than global optimal solution, which limits scope of application of traditional optimization algorithms. Genetic algorithm is an adaptive optimization method. Selection in algorithm reflects approach to optimal solution, crossover reflects generation of optimal solution, and mutation reflects coverage of global optimal solution. Of course, in crossover and mutation operators, how to choose crossover probability and mutation operator will also affect search effect and search efficiency of algorithm, so how to choose these parameters has a great impact on application of genetic algorithms.

Since genetic algorithms provide a general framework for solving complex system optimization problems, which does not depend on specific field of problem, they are widely used in many fields:

1) Numerical function optimization calculation. In research work of genetic algorithms, pure numerical function optimization calculation problems have received great attention. In the early days of genetic algorithms, many scholars were studying this problem, such as De Jong. Until now, many scholars continue to use genetic algorithms to solve optimization problem of numerical functions. This is mainly because many practical problems can be modeled mathematically and abstracted into mathematical problems. Many of these mathematical problems are nonlinear and multi-constrained, and it is difficult to calculate the best results using traditional mathematical methods such as derivation. Genetic algorithms provide a general framework for solving such optimization problems, which can easily obtain better results.

2) Production scheduling problems. In many cases, mathematical models established for production scheduling problems are difficult to solve using traditional optimization methods. Now many companies still rely mainly on experience for scheduling in reality. Results obtained are very blind and it is difficult to obtain the best scheduling solution. Nowadays, genetic algorithms have been used to solve some relatively complex scheduling problems and have been effectively applied.

3) Multi-objective optimization problems. In practical applications, we often encounter optimization problems in which multiple objectives are optimized as much as possible in a given area. For example, in optimization of injection molding weld marks, it is a typical multi-objective optimization problem. Number of weld marks should be as small as possible, and they should be avoided in areas that are sensitive to workpiece. These goals may conflict with each other. For such complex problems, people have realized that they should focus on seeking a more satisfactory solution, and genetic algorithms are one of the best tools for seeking such a satisfactory solution.

4) Robotics. Robots are complex artificial systems that are difficult to accurately calculate, and the origin of genetic algorithms is study of artificial adaptive systems. Therefore, the two have many similarities. Genetic algorithms are often used in programs for robot movement paths and joint movements.

5) Machine learning. Learning ability is one of capabilities that advanced adaptive systems should have. Machine learning based on genetic algorithms has been applied in many fields. For example, genetic algorithms are used to learn rules of fuzzy control, thereby better improving performance of fuzzy control systems; machine learning based on genetic algorithms is also used in artificial neural networks, thereby optimizing structural optimization design of artificial neural networks.

6) Image processing. Image processing is an important research field in computer vision. In process of image processing, such as image segmentation and extraction of image features, some inevitable errors often occur, which will affect effect of image processing. How to minimize these errors is an important requirement for practical application of computer vision. Genetic algorithms are very useful in reducing errors, and have been widely used in image processing. Although genetic algorithms have been applied in many fields, have demonstrated their potential and broad prospects, there are still many problems to be studied in genetic algorithms, and there are still various shortcomings. First, when there are many variables, a large range of values or no given range, convergence speed decreases; second, optimal solution can be found, but optimal solution cannot be accurately determined; finally, there is no quantitative method for parameter selection of genetic algorithms, and it often takes a lot of qualitative attempts to determine relatively good parameters. For genetic algorithms, it is necessary to further study their mathematical basic theories, at the same time theoretically prove their advantages, disadvantages and reasons compared with other optimization techniques, as well as the general programming and form of genetic algorithms.

Genetic algorithm is an adaptive probability search algorithm for global optimization developed by borrowing from natural selection and genetic evolution mechanism of organisms. This chapter first introduces origin and development of genetic algorithms, then focuses on biological principles and specific implementation methods of genetic algorithms. At the same time, it summarizes characteristics and applications of genetic algorithms, finally briefly explains some shortcomings and development directions of genetic algorithms.

In order to optimize weld mark of injection molding, many scholars have proposed numerical models for formation of weld marks. These algorithms are generally based on non-Newtonian fluid mechanics. This is a method that starts from bottom up. Its disadvantages are that development cycle is relatively long and algorithm is less universal. Another more direct method is to use injection molding CAE software to achieve weld mark optimization. However, strictly speaking, direct use of injection molding CAE software cannot achieve purpose of optimization. Injection molding CAE software simply transplants actual mold trial, mold repair and other steps to computer for simulation. Advantage of this is that it greatly reduces cost and time of mold trial, but it cannot directly provide users with optimal injection molding process parameters. For example, for popular Moldflow software, general practice is to first perform solid modeling of injection molded product in CAD software such as Pro/E and UG, convert it into a neutral file such as an STL file, import it into Moldflow, and divide finite element mesh. These steps are preliminary preparations for CAE analysis. Then, user finds required injection molding material in Moldflow material library, and inputs injection molding parameters such as molten plastic temperature, mold temperature, gate position, injection time, etc. based on previous injection molding work experience. Moldflow software analyzes information input by user and generates simulation analysis results, such as whether flow is balanced, whether there are many weld marks, how position is, whether warpage is within design range, etc. If user is not satisfied with generated simulation results, injection molding parameters need to be modified until user obtains a relatively satisfactory result. It can be seen that this process is a trial and error process, which requires user's engineering experience, and results obtained cannot be guaranteed to be optimal solution. If user's actual experience is insufficient, it is difficult to use Moldflow to obtain optimized design results. Based on previous research results and comparisons of various optimization algorithms, this paper proposes a method to optimize weld marks by using genetic algorithms and combining them with injection molding simulation software Moldflow. Basic process is to set relevant process parameters, call Moldflow simulation analysis, extract analysis results, calculate objective function, then follow search path of genetic algorithm. After multiple generations of search, optimal process parameters such as injection time, melt temperature, mold temperature, gate position, etc. corresponding to length and position of weld mark are finally obtained. Weld mark and various factors affecting it are introduced below, then method proposed in this paper is explained.

Formation of weld marks is related to welding method, and welding method can be classified according to flow rate when melt fronts converge. If weld mark is formed by convergence of melt fronts flowing in opposite directions and is fixed almost immediately, this welding method is usually called cold welding. If melt fronts continue to flow in cavity after merging, weld line is formed during flow process. This type of welding is called hot welding. Cold welding is generally considered to be the worst type of welding. Examples of cold welding and hot welding are shown in Figure 4.1.

 

Figure 4.1 Schematic diagram of hot welding and cold welding.
From the perspective of form of weld mark, it can be divided into two types: curve and straight line. From perspective of location of weld marks, there are surface weld marks, internal weld marks, through weld marks, etc. Formation of weld marks can be divided into following stages.

1) Before two melts merge, pressure at the front of melt is zero, and front spring flow stretches molecules at the front of melt, and molecular chain orientation at the front is parallel to flow direction. However, at the front end of melt, there is an arc surface, flow direction and molecular orientation are along normal of free surface, which will affect molecular fusion.

 2)  When two melts converge, pressure on the front surface of melt suddenly increases, melt stops flowing, two free surfaces contact each other and undergo nonlinear viscoelastic deformation.

3) Due to diffusion and molecular movement, molecular chains on contact surface begin to relax, entangle and migrate. Result of this movement provides connection strength for weld mark. Therefore, bonding strength of weld mark increases with increase of molecular chain entanglement strength.

4) Finally, orientation of weld mark will be perpendicular to flow direction due to extrusion. At the same time, in most cases, V-shaped notches are often generated because volatiles generated by air or plastic during filling process are not discharged in time.

Weld mark of injection molded products, like other types of defects, is not a single factor, but result of interaction of multiple factors, and relationship between factors is quite complex. These factors can be summarized into following aspects.

1) Influence of weld line type. Using same material and same molding conditions such as same melt temperature and mold temperature, different weld line types can be obtained. Strength of hot weld lines is significantly higher than that of cold weld lines. For example, for PP samples molded under same conditions, joint coefficient of cold weld is 0.95, and joint coefficient of hot weld is 0.98; joint coefficient of hot weld of EPDM and PP blend is 0.88, and joint coefficient of cold weld is 0.68; for calcium carbonate reinforced PP, joint coefficient of hot weld is 0.99, and joint coefficient of cold weld is 0.85.

2) Influence of product materials. Plastic materials also have a great influence on position and strength of weld lines. For example, macromolecular chain structure of material and fillers added to improve performance of product are both internal factors that affect weld lines. If molecular chain structure of material is rigid and molecular weight is relatively large, melt viscosity is high, internal friction resistance between molecules is large, flow is difficult, and melt temperature is easily reduced when it flows. If temperature of front melt is lower than viscosity temperature of melt when two streams converge, melt on the front surface cannot be fully dissolved, which will inevitably lead to formation of weld marks. According to this principle, it is not difficult to explain that under same injection molding conditions, PC materials generally produce more weld marks than ABS materials. Reinforcing materials in plastics also have a great influence on strength of weld marks. Melt with high fiber filler content has poor fluidity, which will also cause difficulty in fusion when two streams converge. At the same time, fibers dispersed in melt and their orientation structure will also hinder mutual diffusion and entanglement between macromolecules on the front surface, making weld mark more severe. For example, for PP material, when there is no filler content, weld mark strength coefficient is 86%, but when 20% glass fiber is added to PP material, strength has dropped significantly, and weld mark strength coefficient becomes 47%. In addition, for same material, same filler content is added, but type and form are different, and strength of weld mark is also very different. For example, strength of products containing long fiber reinforcement is obviously much lower than that of short fiber reinforcement. This is mainly because during molecular diffusion and welding process, larger fiber fillers cannot be completely entangled with each other, resulting in a significant reduction in strength at weld mark.

3) Influence of product functional structure. Various types of holes, grooves, inserts and other structures on product must be processed with core of mold. When molten plastic flows into mold, due to obstruction of core, material flow will bypass core, and branch flow will inevitably occur. After convergence, a weld mark will be generated. Uneven wall thickness of product will also produce weld marks. This is because uneven wall thickness causes different resistances when melt flows into mold. Melt has a large flow space, small flow resistance and fast flow speed at thick section; flow speed is slowed down at thin section due to flow obstruction. It is precisely because of this difference in flow speed that melts from different wall thicknesses converge at different flow rates, and eventually form obvious weld marks at convergence point. It can be seen that even if there are no holes, grooves or other structures that are prone to weld marks on part, as long as wall thickness difference is large, obvious weld marks will still be formed. This requires that when designing parts, wall thickness of parts should be as uniform as possible while ensuring function of parts, and at the same time, use of holes, grooves and other structures should be minimized, so as to reduce number of material flow branches and thus number of weld marks.

4) Influence of mold structure. Location and number of mold gates will have a great influence on formation of weld marks. When filling mold with multiple gates, if number of gates is n, number of weld marks is at least n-1. The more gates there are, the more weld marks will be produced. If material flow fronts from each gate cannot be well fused, strength of weld mark will decrease, seriously affecting quality of product. However, for products with larger sizes, if multiple gates are used, filling process and time will be greatly shortened compared with a single gate. At this time, temperature and pressure loss of melt in flow will be reduced, which is conducive to mutual fusion of melt in the front of material flow, reducing obvious appearance of weld mark and improving its strength. Location of gate will also affect appearance and strength of weld mark. Improper gate location will increase obviousness of weld mark, even cause melt at confluence to not be completely fused or make weld mark appear in the area that is sensitive to appearance and strength of product. Reasonable gate location can improve fusion quality when melt converges or make weld mark in a position where appearance is not obvious, improve appearance quality of product, and improve mechanical properties. Gate setting should also try to avoid cold welding, because cold welding is main reason for formation of weak weld marks. Poor mold exhaust will also hinder flow of melt filling. If there is gas at confluence of material flow, area of mutual melting of melt will be reduced, or high-temperature gas will be generated to burn product, seriously damaging strength of weld mark. Therefore, setting a reasonable exhaust hole also has a relatively important influence on weld mark. During mold design, if cooling water channel is too close to melt confluence, melt at joint will not be fully fused due to lower temperature and increased viscosity, and obvious weld marks will be produced. Improper cooling design will also cause temperature distribution of mold to differ too much, resulting in different filling speeds in different parts of cavity due to temperature differences when melt is filled into mold, thus causing weld marks. The lower mold temperature, the less conducive it is to full fusion of melt. Surface roughness of mold cavity and core will also affect weld mark. This is mainly because rough cavity surface will cause inconsistent melt speeds, thus leading to formation of weld marks.

5)  Influence of process conditions on weld marks. Since strength of weld marks is related to degree of material fusion at joint, molecular chain diffusion, entanglement and other factors, all factors that are conducive to fusion and entanglement of polymer molecular chains are conducive to strength of weld marks. On the contrary, strength of weld marks will be reduced. Therefore, influence of injection molding process conditions on weld marks cannot be ignored. Although it cannot effectively change position of weld marks, it can significantly affect appearance quality and weld strength of weld marks. Reasonable process conditions are an effective means to improve or enhance quality of weld marks. Among many process parameters, factors that have the greatest impact on weld marks are melt temperature, mold temperature and injection pressure.Temperature of molten plastic is direct factor in formation of weld marks. When different material flows converge, the reason why front melt is poorly fused is that temperature of front melt drops, resulting in an increase in viscosity, which weakens activity of resin macromolecules themselves, cannot fully diffuse and entangle, resulting in the formation of weld marks on the surface of product. Obviously, the higher melt temperature during molding process, the better its flow state, the faster mold filling speed, and the less temperature drop of melt when it flows. If melt temperature of front surface is approximately equal to temperature of inner side of front surface, then weld mark can be basically eliminated, and weld mark is almost invisible on appearance of product. However, the higher melt temperature is, the better. Too high a temperature will cause chemical properties of plastic melt to change, and will also affect quality of product. Increasing mold temperature can keep melt molecules more active for a long time, which is conducive to fusion, diffusion and entanglement of melt at the joint, thus extending relaxation time of molecular chain at joint under orientation stress state, thereby facilitating improvement of joint strength. However, if mold temperature is too high, cooling time will be correspondingly extended, production cycle will be increased, production capacity will be affected, and thus economic benefits will be affected. Injection pressure will also affect weld mark. If injection pressure is too low, melt flow resistance will be large. At the same time, pressure behind material flow cannot be effectively transmitted to the front of material flow. When front melts meet, they cannot merge under higher pressure, thus reducing strength of weld. Properly increasing injection pressure can enhance weldability of melts from different material flows and reduce weld mark. Injection time can also reflect injection pressure. If injection time is very short, corresponding injection pressure will be large. Therefore, in general practice, many people use injection time to control injection pressure.

There are generally two methods for controlling weld marks. One is qualitative analysis, that is, judging which process factors are related to weld mark based on experience of engineering and technical personnel, and changing molding process through experience to improve weld mark situation. The other is to achieve optimal weld mark through computer simulation. Following four aspects introduce how to use qualitative analysis to control weld marks:

1)In terms of material selection, materials with low apparent viscosity, small relative molecular weight, no filler or no reinforcement should be selected as much as possible, under premise of meeting requirements of mechanical properties, so as to facilitate good fusion when melts merge. Therefore, designers must exercise caution when dealing with highly filled or fiber reinforced materials and parts with complex geometries.

2) In terms of product design, under premise of meeting functional structural requirements, structures that are easy to produce material flow branches, such as holes and grooves, should be avoided as much as possible. At the same time, inserts should be used as little as possible, and wall thickness should be as consistent as possible. At the same time, thickness of product should be appropriately increased to facilitate flow of melt. Increasing wall thickness at the weld mark is also conducive to fusion of melt, thereby improving strength of weld mark.

3) In terms of mold design, number and position of gates should be based on not only not causing many and obvious weld marks on product, but also being able to fill cavity smoothly. For products with large molding areas or long processes, using multiple gates is more conducive to reducing weld marks than single gates; using hot runner technology is conducive to melt fusion and is not easy to form obvious weld marks. Weld mark can also be set in a low stress area or non-surface area by adjusting position and size of gate or reducing thickness ratio of plastic part. Reasonably increasing flow channel size will reduce resistance of melt flow and increase weld strength. When necessary, vent holes can be set in welding area to eliminate air pockets and reduce depth of V-notch.

4) In terms of process design, process parameters that affect strength of weld mark mainly include melt temperature, mold temperature, injection pressure and injection rate. Reasonable increase of melt injection temperature, mold temperature and filling rate is conducive to ensuring temperature required for mutual diffusion and entanglement between macromolecules when front of material flow converges, so that macromolecules have sufficient mobility to fuse with each other, which helps to reduce or even eliminate weld mark; increasing injection pressure can make melt from different material flows converge at a higher pressure, which is conducive to reducing weld mark. Appropriately increasing holding pressure can reduce depth of poorly fused layer at the joint, and can also improve strength of weld mark to a certain extent.

Traditional method used can help engineers to select reasonable injection molding parameters to avoid weld lines to a certain extent, but this is not scope of optimization. How to design an optimization algorithm to minimize weld marks or make weld marks appear in areas that have little impact on appearance and strength is not only an academic problem, but also an urgent problem to be solved in industry. In view of unique advantages of genetic algorithms introduced in previous chapter, this paper uses genetic algorithms to optimize injection molding weld marks. Before executing genetic algorithm, following preparations need to be completed:

1) Call Moldflow software to divide solid model of product into finite element meshes and generate ela and nda files. Nda file contains specific coordinate positions of each node of finite element mesh, ela file indicates how many nodes are included in each finite element mesh and which nodes they are.

2) By reading and writing gate position file, i.e., bf3 file, gate can be placed at any node of finite element mesh.

3) Set 005 file, which contains parameters required for injection molding, such as injection time, mold temperature, melt temperature, material type, etc.

4) Call Moldflow software, read information in 005 file, perform Moldflow simulation analysis, and generate result data files. Fnr file contains a large amount of result data, such as number and position of bubbles generated, mold filling time, pressure distribution, melt temperature distribution, stress distribution, and other information. Of course, it also includes some parameters of weld line.

(5) Read fnr file to obtain possible node positions through which weld line passes. Then read nda file and compare it with node positions just obtained to obtain specific coordinate positions of nodes through which weld line may pass. Compare coordinate positions of these nodes with ela file. If two nodes are in same finite element mesh, it can be determined that two nodes constitute a weld line or part of a weld line. There are many ways to evaluate quality of a weld line, among which length and position of weld line is an important evaluation criterion. Length of weld line should be as short as possible, position should be as far away as possible from position that is sensitive to appearance and strength. Therefore, it is necessary to calculate the total length and position of weld line. Assuming that weld mark passes through nodes a and b, and nodes a and b are just in a finite element mesh, distance of this weld mark is straight-line distance between points a and b, and the total length of solid weld mark is sum of distances of each weld mark segment. It can be expressed by formula 4.
    （Formula 4.1）
Where (ax, ay) is coordinate of point a, (bx, by) is coordinate of point b, l represents the total length of weld mark, and n is number of weld marks. As for distance between weld mark and specified sensitive area, this paper uses average value of distance from corresponding sensitive point to each weld mark segment to express it. Assume that central node of a sensitive area specified by user is m, and a weld line passes through nodes a and b, then distance from point m to weld line is defined as distance from point m to center of line connecting points a and b. Average distance of all weld lines from sensitive area is sum of distances between point m and each weld line, see formula 4.2, then divided by number of weld lines, see formula 4.3.
(Formula 4.2)
(Formula 4.3) 
In which, (mx  , my   ) is coordinate of sensitive node m  , d is sum of distances between weld line and sensitive area, d is average distance between weld line and sensitive area. Thus, an evaluation function for the overall quality of weld mark can be established, that is, objective function of optimization algorithm, as shown in Formula 4.4:
(Formula 4.4)
 where α is weight of weld mark length on the overall evaluation of weld mark; β is weight of weld mark position on the overall evaluation of weld mark. Based on previous description of factors causing weld mark, this paper selects injection time t, molten plastic temperature Tmelt, mold temperature Tmold, gate position g, etc. as independent variables of optimization algorithm, set as X=[t, Tmelt, Tmold, g]. Range of molten plastic temperature and mold temperature can be extracted from Moldflow material library according to type of plastic; injection time takes a relatively reasonable range according to production practice, such as 0.1s-4s; gate position should be selected on each finite element node of mesh model divided by Moldflow. Therefore, search space of optimization algorithm can be determined by following variable ranges: Injection time t: t1~t2sl Molten plastic temperature Tmelt: a1~b1
l Mold temperature Tmold: a2~b2
l Gate position g: 1~n Where a1, b1 correspond to the lowest molten plastic temperature and the highest molten plastic temperature, a2, b2 are the lowest mold temperature and the highest mold temperature, and n refers to the total number of nodes in finite element mesh.

Injection time t, molten plastic temperature Tmelt, mold temperature Tmold, and gate position g mentioned above can be regarded as phenotype form of genetic algorithm. Mapping from phenotype to genotype is called encoding. This paper adopts binary coding, and optimization parameters x (t, Tmelt, Tmold, g) are represented by k-bit binary code strings. Each individual in population is represented by 4 design variables, among which injection time, mold temperature, and molten plastic temperature correspond to 8-bit binary code strings, and gate position corresponds to a 10-bit binary code string, so chromosome length is 34. At the beginning of genetic algorithm, 34-bit binary codes are randomly generated as individual chromosomes of initial generation. When decoding, 34-bit long binary code string is first cut into 4 binary code strings, then they are converted into corresponding decimal integer codes respectively, and decimal code is converted into corresponding design variable. Decoding formula can be expressed by formula 4.5. Assuming that value range of design variable x is [a, b], decoding algorithm of x is: x = + a   
The greater individual fitness, the greater probability that individual will be inherited to next generation; conversely, the smaller individual fitness, the smaller probability that individual will be inherited to next generation. If direction of change of objective function value is consistent with the fitness, then fitness function is:
f (x) = F(x) (Formula 4.6) Conversely, fitness function to be established is:  f (x) = K − F(x) (Formula 4.7)
In formula, K is a positive constant to ensure that f(x) is a positive value. In this example, when discussing optimization of weld marks, two optimization goals are the shortest weld mark length and the longest average distance from each weld mark to sensitive area. Since a plastic part may have several positions that are sensitive to strength, this article provides single points or multiple points as areas where weld marks should be avoided. When establishing objective function, two optimization objective components should be normalized first. Established objective function is: (Formula 4.8)
In above formula, l refers to length of weld mark, lmax refers to maximum length of weld mark, and lmin refers to the shortest length of weld mark. d refers to average distance of each weld mark from the most sensitive area of plastic part, dmin refers to minimum average distance of each weld mark from the most sensitive area of entity (corresponding to the worst case), which is assumed to be zero in this paper, and dmax refers to maximum average distance of each weld mark from the most sensitive area of entity. If maximum length of an entity is k, length of dmax is k. u, β refer to weights of each optimization index. Since direction of change of objective function value is consistent with fitness, fitness function of this algorithm is:
（Formula 4.9）

Proportional selection operator refers to probability that an individual is selected and inherited to next generation population, which is proportional to fitness of individual. Proportional selection can also be called gambling principle. Specific process should first calculate sum of fitness of all individuals, then calculate relative fitness of each individual, then use simulated gambling operation to determine number of times each individual is selected. In this example, injection molding optimization parameters, namely injection time t, molten plastic temperature Tmelt, mold temperature Tmold, gate position g, are encoded, decoded, and substituted into fitness function. The larger calculated fitness function, the more ideal weld mark state, and the greater probability of injection molding parameters that obtain ideal weld mark being inherited to next generation; conversely, the smaller probability of being inherited to next generation. This ensures that next generation can obtain more ideal injection molding parameters than previous generation.

Crossover operator is an operation that replaces and recombines partial structures of two parent individuals to generate new individuals. Purpose of crossover is to generate new individuals in next generation. There are many types of crossover operations, such as single-point crossover, multi-point crossover, uniform crossover, etc. Among them, the most commonly used is single-point crossover. This paper uses single-point crossover method in weld mark optimization example. In single-point crossover, firstly, two genotype individuals are randomly selected from a population. Among these two genotype individuals, a gene point is randomly selected for crossover operation.
Another important operation is mutation. Mutation can improve local search ability of genetic algorithm and prevent premature phenomenon. In general, increasing mutation rate at the beginning can improve search path, reducing mutation rate at the end can improve search speed and prevent loss of excellent individuals. Therefore, in this example, linear equation will be used to represent mutation operator in weld mark optimization operation. In first 20% of generations, mutation probability is m0, which should be slightly larger; in last 50% of generations, mutation probability is m1, which should be slightly smaller; mutation probability in generations in between is expressed by a linear equation, see Figure 4.2:

 

Figure 4.2  Mutation probability function

In genetic algorithm, there are usually two ways to determine termination. One is that as number of generations increases, individuals in group continue to converge to a certain optimal individual. When similarity of individuals in group exceeds a certain value, it can be determined that inheritance is terminated. Another very common method is to terminate inheritance when it is inherited to a certain generation. In this paper, second method is used in optimization of weld marks. This paper tried several schemes. For example, when number of genetic generations is 100, optimization calculation time is relatively long, and optimization efficiency is not high in last few generations. After continuous attempts and calculations, final termination generation selected is 50. Combined with above genetic algorithm, the entire algorithm flow of weld mark optimization is shown in Figure 4.3.

 

 
Figure 4.3 Weld mark optimization algorithm flow chart

This chapter first analyzes various influencing factors of weld marks; explains how to use Moldflow to optimize weld marks, that is, to obtain a relatively ideal weld mark position by continuously changing injection molding parameters on Moldflow platform; then proposes an optimization design method for weld marks based on Moldflow platform using genetic algorithms, explains in detail principles and steps of this optimization method. Through this method, users can get a reasonable injection molding parameter without trial and error, so that weld mark size is minimized and in a relatively ideal position.

Previous chapters introduced optimization design method of weld marks, that is, through genetic algorithms, using Moldflow simulation analysis results, taking the shortest length of weld marks and the farthest distance from sensitive positions that users do not want to appear as criteria, obtaining ideal molding process parameters through optimization search. This paper uses Microsoft Visual C++'s MFC (Microsoft Foundation Class) platform to write programs and implement this algorithm. This chapter first introduces program's functions and implementation techniques, then analyzes injection molded parts of different shapes through several examples, and performs optimization calculations on weld marks, illustrates correctness of this algorithm.

Program written in this paper can be divided into two parts. The first part is to call Moldflow software and obtain relevant data of weld marks from Moldflow analysis result files. Second part is to set the best injection molding parameters through genetic algorithms to optimize position and length of weld marks. Program is mainly implemented through following main functions.
SetMfEnv();
WinExecMF(m_strMFFolder+"\\mfldd.EXE -input " + inkName+".005", SW_SHOW); //Call Moldflow program to generate relevant data of weld marksn
Getweldnumber()//  Calculate number of weld marks and get length and position of weld marksn
GenerateInitial Population() // Generate initial population, which includes melt temperature, mold temperature, injection time and gate node position
CalculateFitnessValue();// Calculate fitness function value
Selection Operator(); // Select operation to get individuals with relatively large fitness
Crossover Operator(); // Crossover operation
Mutation Operator(); // Mutation operation
Output TextReport(); // Write results of each generation obtained by operation to Notepad Figure 5.1 is main interface of program

 

Figure 5.1 Main interface of program
In "Call Moldflow" module, users can directly enter Moldflow interface, as shown in Figure 5.2.

 

Figure 5.2 Main interface of Moldflow
In "Moldflow Material Library Management" module, users select required material and obtain information such as origin, supplier, and material type of material. As shown in Figure 5.3.

 

Figure 5.3 Material management interface
In "Material Grid Analysis" module, users can obtain finite element division of product, specific location of grid nodes, node location where weld mark passes, and other related information. As shown in Figure 5.4.

 

Figure 5.4 Model analysis interface
In "Plastic Material Performance Analysis" module, users can quickly select required materials according to supplier and material grade, obtain recommended mold temperature and molten plastic temperature according to material. As shown in Figure 5.5.

 

Figure 5.5 Material Performance Analysis Interface
In "Optimization Algorithm" module, users can obtain optimal weld mark length and position according to user-specified material and node position to be avoided, and write optimal injection molding parameters to specified notepad. Interface is shown in Figure 5.6.

 

Figure 5.6 Optimization Algorithm User Selection Interface
Following will analyze how to achieve optimal weld mark through optimization algorithm through several specific cases.

This example takes a plastic panel as an example to explain specific process of obtaining the best weld mark. First, a solid model is built in Pro/E and saved in STL format. Then it is imported into Moldflow’s related module MPI (Moldflow Plastics Insight). Using MPI, plastic panel is divided into finite element meshes, as shown in Figure 5.7. In genetic algorithm, population size is 20, termination generation is 50, crossover probability is 0.9, mutation probability in the first 20% generation is 0.02, and mutation probability in the last 50% generation is 0.005. Mutation probability in the middle generations is obtained using linear equation shown in Figure 4.2. Weight coefficients α and β in Formula 4.9 are each 50%.

 

Figure 5.7 Finite element mesh divided by Moldflow
Assuming that customer chooses ABS as material for plastic panel, user can select one or two points on plastic shell as location where weld mark should be avoided. Assume that user selects area around 731st node as location where plastic panel is most sensitive to appearance and strength. Node location is shown in Figure 5.8. Result of genetic optimization is shown in Figure 5.9. It can be seen from figure that with increase of genetic generations, average fitness of each group develops in direction of "good". Through example, optimal result can be obtained as follows: l Molten plastic temperature 223℃ l Mold temperature 48℃ l Injection time 0.9s l Gate location should be selected at 236th node. At this time, the total length of weld mark is the shortest, which is 1.3cm; length from the most sensitive area is the farthest, with an average distance of 0.8cm. Location of gate after optimization and area where weld mark is located are shown in Figure 5.10.

 

Figure 5.8 Location of sensitive nodes assumed by user

 

Figure 5.9 Genetic algorithm results
As a verification of results obtained by genetic algorithm, this paper uses gate position optimization function of Moldflow to analyze this example, and results are shown in Figure 5.11. It can be seen that weld mark after optimization by genetic algorithm proposed in this paper is significantly improved compared with weld mark produced by gate position optimization of Moldflow.

 

Figure 5.10 Weld mark results before optimization

 

Figure 5.11 Weld mark results after optimization

This example takes a socket panel as an example to illustrate specific process of obtaining the best weld mark. Like previous example, first create a solid model in Pro/E and save it in STL format, then import it into MPI module of Moldflow, and use MPI to divide socket panel into finite element meshes, as shown in Figure 5.12. Parameters of genetic algorithm are same as previous example. Population size is 20, termination number of generations is 50, crossover probability is 0.9, mutation probability of the first 20% generations is 0.02, and mutation probability of last 50% generations is 0.005. Mutation probability in the middle generations is calculated using linear equation shown in Figure 4.2. Weight coefficients u and β are each 50%.

 

Figure 5.12 Finite element mesh divided by Moldflow
Assuming that customer still chooses ABS as material of socket panel, user chooses area around 10th node as location where socket panel is most sensitive to appearance and strength. Location of this node is shown in Figure 5.13. Results of genetic optimization operation are shown in Figure 5.14. Through calculation example, optimal result can be obtained: l Molten plastic temperature 239℃ l Mold temperature 52℃ l Injection time 1.35s l Gate position is 215th node. At this time, the total length of weld mark is the shortest, which is 3.55cm, and length from the most sensitive area is the farthest, with an average distance of 8.06cm. Location of gate and area where weld mark is located after optimization are shown in Figure 5.15, and results obtained by gate position optimization program of Moldflow are shown in Figure 5.16. Comparison shows that optimized weld mark state has improved to a certain extent compared with unoptimized state.

 

Figure 5.13 Position of sensitive nodes assumed by user

 

Figure 5.14 Genetic algorithm results

 

Figure 5.15 Weld mark results before optimization

 

Figure 5.16 Weld mark results after optimization  
When user selects two nodes, assume that user selects 100th node and 200th node as locations where weld mark should be avoided. Nodes are shown in Figure 5.17. Operation results of genetic algorithm are shown in Figure 5.18. Optimization results are: l Molten plastic temperature 235℃ l Mold temperature 58℃l Injection time 0.99s l Gate position is 38th node.
At this time, the total length of weld mark is the shortest, 0.65cm, and length from the most sensitive area is the farthest, with an average distance of 16.9cm. Results are shown in Figure 5.19.

 

Figure 5.17 User assumes that positions of two sensitive nodes are located.

 

Figure 5.18 Genetic algorithm results

 

Figure 5.19 Position of weld mark after genetic algorithm optimization at two sensitive points

This chapter introduces software interface and usage method for optimizing position and size of weld marks, and illustrates feasibility of program through two examples, providing certain guiding reference information for users to reasonably select injection molding process parameters.

In injection molding, weld marks have a great impact on quality of plastic products, and factors that form weld marks are quite complex. Therefore, how to obtain weld marks that users can accept is a very important research topic. Based on injection molding simulation software Moldflow, this paper uses genetic algorithms to optimize weld marks, focusing on following aspects:

1) Size and position of weld marks of injection molded parts are related to which factors of injection molding process, these factors are used as design variables of optimization algorithm, objective function for optimizing length and position of weld marks is proposed.

2) Various optimization algorithms are compared, and finally optimization using genetic algorithms is determined, then optimization steps are determined according to characteristics of genetic algorithm.

3) Optimization algorithm of weld mark is implemented on MFC platform of Visual C++ 6.0, effectiveness and practicability of algorithm are verified through two examples. Innovations are mainly reflected in:

1) Genetic algorithm and injection molding CAE system are combined to optimize weld mark.

2) Indicators of weld mark are modeled, its length and position are taken as optimization target. On the other hand, due to time constraints, there are still many shortcomings in work completed in this paper, which are reflected in:

1) Quality of injection molding includes many aspects, such as strength, warping, bubbles, and filling uniformity of product. Although weld mark is one of the more critical factors, other factors should not be ignored. Therefore, how to comprehensively consider other quality factors to carry out more comprehensive design optimization is a topic worthy of further study.

2) Optimization algorithm proposed in this paper has not been verified in actual injection molding process (injection molding machine and mold). Although running results of Moldflow software are beyond doubt, relevant finite element algorithm has been simplified and implemented under a series of limited conditions, so it is definitely still a certain distance from actual injection molding process. Therefore, failure to complete actual verification should be a shortcoming.

3) Paper optimizes length and position of weld mark, but another important characteristic of weld mark is influence on strength of plastic part. Weld marks of same length at same position will have different strengths due to different weld mark types. Therefore, how to increase processing of weld mark strength in optimization algorithm is also a subject worthy of further study