Evaluation of the effectiveness of the use of additive wax printing technologies for obtaining wax models for lost-wax casting in custom production based on simulation modeling

. The article discusses the technology of casting according to the smelted models, in particular, the processes of manufacturing wax models. We considered methods of manufacturing elements of model blocks with the use of molds and with the help of additive technologies. In this paper we showed the features of the application of additive technologies in the lost-wax casting. A simulation model has been developed to evaluate the effectiveness of using additive wax printing technologies to produce wax models. Based on the results of simulation modeling, conclusions were made about the feasibility of using additive technologies in casting according to smelted models.


Introduction
The method of lost-wax casting (LWC) is widely used in machine-building enterprises and is characterized by high productivity. The LWC technological process in a generalized form consists of the following process stages: the manufacture of wax elements of model blocks (wax models), the assembly of model blocks, the manufacture of shell molds and the manufacture of castings (Fig. 1).

Fig. 1.
Technological preparation of production and process stages of casting by smelted models.
The nomenclature of manufactured wax models is divided into standard and special wax models.
Typical wax models include elements of model blocks that have already been manufactured at the enterprise and for which the necessary documentation and equipment are already available. Such models include wax models of the elements of the sprues and wax models of castings, for which there is already equipment for production. Molds are used for the production of standard wax models [1,2].
Special wax models are manufactured at the enterprise for the first time and require the manufacture of tooling (molds), for which it is necessary to perform technological preparation of production (TPP). Another way to make special wax models is to print them using additive technologies. TPP with this approach will consist in the development of a control program for additive equipment, which is significantly shorter in duration than the manufacture of tooling for the manufacture of models in molds. At the same time, the performance of additive equipment for the manufacture of wax models will be lower than when they are manufactured using molds. This feature must be taken into account in deciding whether to obtain wax models with additive technologies [3].
Thus, we can distinguish two approaches to the manufacture of elements of model blocks for LWC: classical, in which the manufacture of all elements is carried out in molds, and combined, in which part of the elements of model blocks are made in molds, and part using additive technologies. For an enlarged assessment of the effectiveness of the use of additive technologies for printing wax models for casting on cast models in order production, it is proposed to develop a mathematical model that allows modeling LWC processes by classical and combined methods. Simulation modeling was chosen as a method for solving this problem, allowing experiments with various variations of the launch batch and further analysis of the results [2,4].

2
Development of a simulation model for the model blocks manufacture for lost-wax casting AnyLogic software was chosen as a tool for developing a simulation model, which allows modeling the operation of processes and systems with complex logic. To set the model logic, standard objects can be used (using built-in libraries) or proprietary objects developed using the Java programming language.
The simulation model must take into account the sequential-parallel organization scheme of the manufacture of special elements of model blocks: standard elements are made in automated molds, special elements (casting models) are made in parallel by additive technologies or in manual molds. Also, when modeling the manufacture of wax elements of model blocks, the cycles of technological preparation for the production of special wax elements of model blocks, both for manual molds and with the use of additive technologies, should be taken into account. At the first stage, a Gantt diagram of the manufacturing processes of model blocks was developed, visualizing the nature of the processes and their dependence on each other (Fig. 2) [1,5]. The model can be divided into 3 main blocks: • technological preparation of production, • production of wax models, • assembly of model blocks. For modeling and analysis of various methods of manufacturing elements of model forms, two parallel schemes are implemented in the simulation model, describing the logic for the classical approach to the manufacture of model blocks, implying the manufacture of elements in automatic and manual molds, as well as combined methods in which additive technologies are used for the manufacture of wax models (Fig. 3). The logic is implemented using the process modeling library (Queue blocks are used to create buffers, Batch blocks to form links and blocks, Source for creating new agents, etc.) and the production systems library (Transporter Fleet blocks are used to control transporters and Move By Transporter blocks to move objects using transporters). Also, various types of A number of parameters of the simulation model are changeable for user and are stored in an Excel file. The file of changeable parameters contains information about the duration of technological operations and the production plan. The duration of the operations is set in the form of a triangular distribution (minimum, average, maximum) to account for the varying time of their execution. The production plan contains data on castings for which it is necessary to simulate the manufacture of model blocks and contains the following data set: the number of models of castings, sprues, feeders in the link; the number of links in the block; the release program; the manufacturing method: manual molds (MM) or additive technologies (AT) [6][7][8][9].
When the simulation model is launched, the file of changeable parameters is loaded, on the basis of which the nomenclature items that will need to be produced, the method of production models, the compositions of links and blocks, as well as the batch of models are determined. Then casting agents are created in the corresponding model block, which refers to the specified method of manufacturing the model in an amount equal to the size of the release batch [1,10].
For special castings, the first stage is the implementation of TPP processes. TPP processes are performed once for the entire batch. At the end of the documentation process, feeders and gate agents are created in the quantity necessary for the assembly of the block. The logic of processing typical elements of the model block in an automated mold is shown in Figure 4. Processing and manufacturing models of castings, sprues and feeders are carried out for each model separately. At the same time, the manufacturing processes of gate valves and feeders take place on the same installation. After the wax model is made using additive technologies, it is checked for marriage. If it does not pass the test, it is sent to the marriage and the manufacturing process is restarted for a new wax model. At the end of the production of wax models, they are sent to the output buffer, after which they are transferred to the input buffer at the locksmith's table [11].
After the wax models are processed, they are transported using automatic guided trolleys (AGV -Automatic guided vechicle) from the output buffer of the locksmith table to the input buffer at the assembly site. If there is a complete set for assembling the block, the model elements are moved using AGV to the locksmith table to complete the assembly process.
The simulation model implements an interface that visualizes the processes of processing and transporting elements of model blocks, as well as their assembly (Fig. 5).  assembly of model blocks. 5. The AGV section where the AGV are located when they do not have an active task to move objects.
In the process of modeling, it is possible to visualize statistical data on the experiment, containing the duration of the production cycle of manufacturing individual units of the nomenclature (minimum, average, maximum) in table format; the duration of the technological cycle of manufacturing individual units of the nomenclature (minimum, average, maximum) in table format; the current equipment load factor (single-station pressure machine, printing installation wax) in the format of a bar chart; equipment load factor (singlestation pressure machine, wax printing installation) in graph format ( Figure 6). At the end of the simulation, the results of the experiment are saved to an Excel output file containing the following data: the serial number of the experiment, the names of the castings nomenclature, the number of pieces in the batch, the manufacturing method (MM/AT), the duration of the technological cycle of manufacturing individual units of the nomenclature (minimum, average, maximum), the duration of the production cycle of manufacturing individual units of the nomenclature (minimum, average, maximum) and the production time of the batch of casting models [12]. It can be seen from the graph that, taking into account the accepted initial data of the model with a batch size equal to 930 units, both methods have almost the same time required for its manufacture. This point shows the limits of the efficiency of using the additive method. In the manufacture of a batch that includes less than 930 units of wax models, additive technologies justify their use. With an increase in the batch size over 930 units, the performance when using the combined method begins to yield to the classical method. Modeling has shown that during the TPP for manual molds, about 714 castings can be made using additive technologies, which is equivalent to 17 model blocks [1,9].

Conclusions
Thus, with an increase in the batch size, the classical method of making wax models in the MM will be more productive relative to the combined method with the use of additive technologies. In the opposite situation, with small batch volumes, but an increase in the number of different special nomenclature items, the use of the combined method is more effective. The use of additive technologies may be justified when used in small-scale batch production due to the low duration of the TPP relative to the preparation of production for the manufacture of manual molds [13].