With the development of plastic synthesis technology, mechanical properties of plastics have been significantly improved, their applications in engineering are becoming more and more extensive. In transmission mechanisms and other occasions with dimensional matching requirements, shape and dimensional accuracy of plastic parts are often very high, requiring precision or even ultra-precision. Therefore, researchers engaged in the field of injection molding processing have been working hard to reduce error in prediction of shrinkage rate of injection molded products, so as to shorten injection mold manufacturing cycle and improve qualified rate of injection molded products.

At first, people focused on influence of fluctuation of injection molding process conditions on shrinkage rate, and conducted a large number of injection molding experiments to try to find out quantitative relationship between injection molding process conditions and shrinkage rate.
After accumulating certain experience, some scholars proposed method of fitting experimental data to predict shrinkage rate of injection molded products under actual production conditions. Basic idea is to measure shrinkage rate of a certain plastic under different process parameters such as barrel temperature, injection pressure, injection time, holding pressure, holding time, mold temperature, and in-mold cooling time through multi-factor orthogonal experiments. Functional relationship between shrinkage rate and various process parameters was fitted according to experimentally measured sample data.
When applying, substitute value of each process parameter used in actual injection molding production into corresponding functional relationship to obtain corresponding shrinkage rate value, perform a weighted average to obtain "actual shrinkage rate" required by mold designer.
However, when shape and size of actual injection molded product and number, location, and size of gate are different from experimental conditions, pressure distribution and temperature distribution inside product will be different from experimental conditions, so that actual injection molding process conditions are different from experimental conditions. There is no comparability between different injection molding process conditions; second, this method does not consider in-mold confinement effect during shrinkage process of product, so it is difficult to use method of fitting experimental data to predict shrinkage rate.

 

In order to predict shrinkage rate more accurately, influence of mold forming structure on shrinkage rate of injection molded product must be considered, mold forming structure is ever-changing and cannot be represented by several typical structures, that is, it is impossible to rely on experiments to determine mold forming structure and product. Because of quantitative relationship between shrinkage rates, research work on mathematical simulation of injection molding process by computer is increasing day by day, and it has become a rapidly developing frontier research field in polymer processing science.
Numerical simulation of injection molding process began in the 1960s. After 1990s, calculation of flow, pressure and cooling analysis has gradually matured, many scholars have begun to predict shape and size of injection molded products on this basis, that is, warpage analysis.
Calculation process is as follows: After pressure holding process is over, calculate thermal shrinkage and crystalline shrinkage caused by pressure change and temperature change of injection molded product according to compressibility coefficient, thermal expansion coefficient and crystallization kinetic equation of plastic, but do not make shrinkage strain. Instead, shrinkage strain is converted into equivalent nodal load, then elastic model or viscoelastic model is used to solve response of injection molded product under equivalent load.
If cooling conditions of upper and lower surfaces of injection molded product are different, temperature and stress distribution in thickness direction will be asymmetrical to that of intermediate layer, causing injection molded product to have a tendency to bend and deform. Since bending deformation of injection molded product cannot occur under constraint of mold cavity, it is converted into residual stress and used as initial stress after demolding; after product is demolded, elastic model or viscoelasticity model is used to solve deformation of injection molded product under action of initial stress load and temperature equivalent load.
IMAP software of Japan's Toyota Central Research Institute and Moldflow software of Australia's MF Company use thermoelastic model to calculate residual stress and warpage deformation of injection molded products; C-MOLD software of ACTech Company of United States, Taiwan scholars Chang et al. and Dr. Li Haimei of Dalian University of Technology used thermal viscoelastic model to calculate residual stress before demoulding, then used thermoelastic model to calculate warping deformation after demoulding.
It can be seen that numerical simulation of warping deformation is mainly divided into two categories: one is to use plastic solid as an elastic material to simplify calculation; the other is to consider viscoelastic properties of plastics, thermal viscoelastic constitutive model is used to calculate residual stress.
When polymer is in glassy state, elasticity plays a dominant role in behavior of polymer; while in high elastic state, its viscoelasticity is more obvious. Therefore, structural analysis of plastic parts after demoulding mostly adopts thermoelastic model, and in-mold curing process of plastic parts is suitable for analysis of thermo-viscoelastic model.
At present, thermal viscoelastic constitutive model used in warpage analysis at home and abroad is a simple thermal rheological material model, which belongs to linear thermal viscoelastic constitutive model. American scholars Bushko and Stokes discussed scope of application of various viscoelastic theories from perspective of viscoelasticity, considered that thermorheological simple material constitutive model is only suitable for isotropic materials.
That is, amorphous plastics composed of non-polar macromolecules, because in this case, temperature affects change of macromolecular orientation in same way, while crystal structure and polar groups in polymer have different effects on temperature change. Resulting reaction is different from non-polar amorphous part, which does not satisfy linearity condition required by Boltzman's superposition principle.
That is to say, only non-polar amorphous plastics conform to thermo-viscoelastic constitutive relation specified by simple material model of thermo-rheology, and other materials, especially crystalline plastics, do not obey simple assumption of thermo-rheology.
Because simple material model of thermal rheology is only suitable for isotropic linear thermal viscoelastic body under small strain conditions, it cannot reflect nonlinear viscoelastic behavior (physical nonlinearity) in small strain range and nonlinear behavior(geometric nonlinearity) caused by large strain. , so there is a theoretical error in numerical simulation of plastic product molding process using simple material model of thermal flow. .
Theoretically, multi-integral expression accurately describes nonlinear viscoelastic behavior, but it leads to great complexity in mathematics. Even if only triple integral is obtained, constitutive relation is still quite complicated, which not only causes tedious calculations, but also requires an astonishing number of experiments to determine material functions involved.
In order to solve the modeling problem of nonlinear viscoelastic constitutive relationship, Korean scholars Lee and Youn proposed to apply neural network to numerical simulation of injection molding: First, injection molding experiment of flat plastic parts was carried out, numerical simulation of flow, pressure holding and cooling of injection molding products is carried out according to injection molding process conditions during experiment. Pressure, temperature and density of each calculation unit obtained by numerical simulation are used as input of neural network, measured plane displacement of plastic part is converted into strain of calculation unit as output of neural network, so as to complete self- training process;
After end of training process, when predicting shrinkage of other injection molded products of same plastic, analysis results of flow, pressure holding and cooling simulation of this product are input into neural network, neural network will output strain of each computing unit, integrate strain of each calculation unit to obtain deformation of injection molded product.
Before obtaining practical mathematical equations to analyze and describe nonlinear viscoelastic behavior, it is worth learning by means of neural network to determine its stress-strain correspondence. But work to be done in order to complete neural network self-training process is too cumbersome and difficult to apply in practice.

Using linear viscoelastic constitutive relation to analyze nonlinear viscoelastic behavior of polymers will bring theoretical errors, but under premise of sufficient performance data of injection molding materials, its calculation accuracy can meet needs of engineering. Problem is that various material constants required by numerical simulation methods are often not available in practical applications, which limits use of numerical simulation methods.
Sichuan University has done a lot of work in measuring performance data of domestic injection molding materials, and built the first injection molding material performance database in my country. Database includes power-law parameters, no-flow temperature, thermal conductivity, specific heat, thermal diffusivity, specific volume and other performance data of 102 commonly used plastics.
But even same plastic produced by same manufacturer will have very different properties when batch number is different. Because acquisition of various material constants of injection molding materials requires expensive experimental equipment, long-term data measurement and a lot of technical processing work, it is unrealistic to require plastic manufacturers to establish these basic databases for different batches of different plastics.
At present, what is urgently needed in my country's injection mold industry is a shrinkage calculation method with engineering practicability.
Many factors that affect shrinkage rate of injection molded products can be divided into three categories: injection molding material properties, injection molding process conditions and mold molding structure. Characteristics of injection molding materials are shown as viscosity, thermal conductivity, specific heat, specific volume, relaxation modulus, elastic modulus, Poisson's ratio and other physical properties data; injection molding process conditions refer to barrel temperature, injection speed, molding pressure and molding time;
Mold forming structure includes shape and size of mold cavity, position and size of gating system, position and size of cooling circuit. Mold forming structure fundamentally determines distribution trend of shrinkage rate of injection molded product, characteristics of injection molding material and injection molding process conditions are specific values that affect shrinkage rate of each point of injection molded product on this basis.
Average shrinkage rate of a certain plastic provided by a plastic manufacturer in a certain batch represents characteristics of injection molding material to a certain extent, so after product shrinkage distribution trend is obtained according to mold forming structure, shrinkage rate of each point of product can be determined in combination with average value of shrinkage of injection molding material provided by plastic manufacturer.
Therefore, work of measuring and solving various material constants of injection materials is eliminated. If prediction of distribution trend of shrinkage rate of injection molded products is in line with reality, then by adjusting injection molding process parameters to make actual shrinkage rate value of injection molded product close to predicted shrinkage rate value, qualified plastic products can be obtained.
To predict distribution trend of product shrinkage rate from mold forming structure, method of mathematical simulation must be adopted. Shrinkage of injection molded products is realized by reducing specific volume, fundamental factors that affect specific volume of polymer are temperature and pressure of polymer. In order to obtain temperature change history and pressure change history of each point of product, it is necessary to carry out flow, pressure holding and cooling analysis.
Solving temperature field and pressure field of injection molded products at every moment involves calculation of physical parameters such as viscosity. Since purpose of mathematical simulation is to obtain shrinkage distribution trend, qualitative conclusions rather than quantitative conclusions are required, two kinds of plastics whose material property data have been measured can be selected to represent amorphous plastics and crystalline plastics, respectively, to solve problem of inputting material property data.
For same reason, quantitative solution of mold wall temperature field can be replaced by a qualitative solution. By superimposing influence of heat sources in runners, heat sources in cavity and cold sources in cooling system on mold wall, distribution trend of mold wall temperature is obtained. Compared with previous method of quantitatively solving mold surface temperature by iteratively calculating mold temperature field and product temperature field, it saves a lot of calculation time.
Usually, after obtaining desired reduction degree of plastic specific volume, it is converted into an equivalent nodal load to solve deformation of plastic products under action of load and deformation constraints. If shrinkage of specific volume can be directly converted into shrinkage displacement of injection molded product, calculation process will be greatly simplified. To this end, it is necessary to clarify shrinkage direction of injection molded products, establish shrinkage rules that can reasonably explain actual shrinkage.
Through theoretical analysis and experimental verification, according to movement characteristics of polymer in injection molding process, it is proposed that injection molding product takes gate as shrinkage center, each point on injection molding product is subjected to shrinkage force from gate in flow area to which it belongs, shrinks toward gate along its flow path during shrinkage process. .
Degree of shrinkage of specific volume is reflected as shortening of grid step size on shrinking path. During process of in-mold shrinkage, shrinkage of each point of product toward gate along flow path is restricted by molding surface of mold, and hindered part of shrinkage displacement cannot occur; after demolding, shrinkage of each point of product is no longer hindered.
By comparing with measured shrinkage rate of injection molded products, it is verified that calculated product shrinkage rate distribution trend is in line with actual situation. In order to connect shrinkage distribution trend with average value Sa of plastic shrinkage, calculated shrinkage rate of each point of product relative to gate(except nodes where in-mold shrinkage process is hindered) can be summed and averaged, with mean value expressed as Sc, then calculated shrinkage rates of all nodes are multiplied by (Sa/Sc) as predicted shrinkage rate value.

Experimental method can be used to study influence of a certain factor on shrinkage of injection molded products, to test accuracy of theoretical inference and numerical simulation, but it cannot completely rely on experimental data to predict shrinkage rate of various shapes of products; numerical simulation method is based on theoretical basis of polymer physics, fluid mechanics, heat transfer and viscoelasticity.
Analysis of injection molding process is more in line with objective laws, but calculation process is complicated and program development cost is high, which leads to high price of software, coupled with lack of various material constants required for numerical simulation in practical applications, these two points have affected acceptance of computer-aided analysis software for injection molding by domestic small and medium-sized mold enterprises.
Now it is proposed to combine distribution trend of shrinkage rate of injection molded products determined by mold forming structure with average shrinkage rate of injection molding materials to solve problem of insufficient material performance data in numerical calculation. By superimposing point source influence field to determine temperature boundary conditions of product, dividing mold cavity into several flow paths starting from gate, making each point shrink toward gate along flow path, calculation process is greatly simplified
Calculated results of the program are in good agreement with measured results, indicating that this calculation method can accurately predict shrinkage rate of each point of injection molded product, and provide a theoretical basis for mold design.

 

Sliding ejector rod mechanism
1 Fixed model core 2 Moving mold core 3 Moving mold plate 4 Moving die fixing plate 5 Lifter core 6 Pulley 7 Guide groove block 8 Push plate a 9 Push plate b
Rod pushes push plates 8 and 9 to drive lifter core 5 to make lifter movement, pulley 6 can slide on guide groove block 7 to complete inner core pulling and ejecting movement. Ejection angle of this ejector mechanism should not be too large, and it should be 5° to 15°. Because of simple manufacture and low cost, core-pulling mechanism is widely used in inner core-pulling with short core-pulling stroke. However, because inclined ejector rod is generally located in the middle of mold, it is not convenient to lubricate, and stroke is too long, which is easy to be pulled, so it needs to be replaced frequently. This mechanism can also be used in outer lifter core pulling with appropriate changes.
It has been proved by production practice that molds using above-mentioned core-pulling mechanisms have simple structure, reliable operation, convenient maintenance and debugging, and effectively reduce production cost.