In the continuous search for higher-quality and more geometrically complex metal components, the lost foam casting process has proven to be one of the most versatile manufacturing routes. Among the various applications, reducer case bodies demand precise control of mold filling because they serve as structural housings for gear trains and bear significant mechanical loads during operation. In my research and engineering practice, I have focused on the critical issue of mold filling speed control during the production of lost foam castings. The mold filling phase is not merely a fluid transport event; it strongly influences oxide entrainment, foam decomposition residue entrapment, thermal gradients, and ultimately the mechanical integrity of the final part. Therefore, I designed a PLC-based mold filling speed control system specifically for lost foam castings used in reducer case body production. The innovative aspect of this work is the integration of a programmable logic controller (PLC) as the core control unit, cooperating with high-precision pressure sensors and timing devices to create a closed-loop, real-time, adaptive control strategy for the filling process. This approach significantly improves the consistency and quality of lost foam castings when compared with traditional proportional-integral (PI) control schemes.
The production of lost foam castings involves several inherently nonlinear physical phenomena. The pattern is made of expanded polystyrene (EPS); when molten metal enters the mould cavity, the foam vaporizes and the metal progressively replaces the pattern. The rate at which this replacement occurs is called the filling speed. If the filling speed is too low, the molten metal may lose too much heat before filling the entire cavity, resulting in misruns and cold shuts. If the filling speed is too high, the generated foam decomposition gas cannot escape rapidly through the refractory coating and the sand, leading to defects such as gas entrapment, back-pressure artefacts, and pinholes. Therefore, precise filling speed control is indispensable to produce sound lost foam castings. In the specific case of a reducer case body, the component has large flat surfaces, deep internal cavities, and varying wall thicknesses, which make uniform filling extremely difficult without sophisticated control. My design overcomes this difficulty by using vacuum-assisted low-pressure filling in combination with a PLC-based fuzzy adaptive PID controller.
The rest of this work is organized as follows. First, I analyze the lost foam casting process for reducer case bodies and identify the key parameters that affect filling speed. Then I derive a mathematical model that links filling speed with the pressure difference, gating geometry, and foam decomposition characteristics. Next, I present the overall hardware architecture, the I/O configuration, and the software implementation based on fuzzy PID logic. Finally, I describe a simulation-based experimental validation in which the proposed control system is compared with a conventional PI system. The results show that my PLC-based control system reduces stress concentration in lost foam castings, thereby improving their static and dynamic structural performance.
1. Lost Foam Casting Process for Reducer Case Bodies
Lost foam casting of reducer case bodies is a highly integrated manufacturing method that combines pattern preparation, coating, sand compaction, vacuum pouring, and solidification control. Although the process steps are conceptually simple, the interaction between the foam pattern, the refractory coating, the unbonded sand, and the molten metal imposes severe demands on process control. I have systematically analyzed the process flow and identified the exact stages where filling speed control is critical. The complete sequence I followed in this design is summarized in Table 1.
| Stage | Operation | Key Control Parameters |
|---|---|---|
| 1 | Foam pattern fabrication | Pattern dimension tolerance, density, bead fusion quality |
| 2 | Coating and drying | Coating thickness, drying temperature and time, permeability |
| 3 | Sand filling and vibration compaction | Vibration frequency, amplitude, sand grain size, compaction time |
| 4 | Vacuum and low-pressure pouring | Upper/lower tank pressure, pressure difference, filling speed |
| 5 | Cooling and shakeout | Vacuum holding time, cooling period, shakeout handling |
| 6 | Cleaning and inspection | Surface finish, dimensional accuracy, internal defect detection |
In the first stage, I create an EPS foam pattern that replicates the exact three-dimensional geometry of the reducer case body. The pattern density is typically in the range of 20 to 30 kg/m3 for this type of casting. In the second stage, the foam pattern is coated with a water-based refractory slurry. The coating must be thick enough to provide a smooth metal/foam interface and to support the sand bed, yet permeable enough to allow the escape of gaseous decomposition products. Failure to control coating permeability can cause a drastic change in the filling speed of lost foam castings, leading to surface defects.
The third stage places the coated pattern in a vibration table and fills the surrounding spaces with dry silica sand. Vibration is applied to compact the sand and to support the thin sections of the pattern, preventing deformation during pouring. The fourth stage is the heart of the process. I apply a vacuum to the sand mould to hold the sand in place and simultaneously create a pressure differential between an upper and a lower pressure tank. The molten metal is forced upward into the mould cavity by this pressure differential, and the EPS pattern decomposes as the advancing metal front reaches it. The filling speed is determined by the balance between the imposed pressure, the local flow resistance, the foam decomposition rate, and the gas removal rate through the permeable coating and sand. A PLC-based control system is therefore essential at this stage to monitor and adjust the pressure in real time so that the filling front advances smoothly.
Once the mould cavity is completely filled, the vacuum is maintained for a short period to assist feeding and solidification. The metal then cools and solidifies under hydrostatic pressure, which helps to produce dense, sound lost foam castings. After sufficient cooling, the vacuum is released, the sand is shaken out, and the casting is cleaned and inspected. The entire sequence demonstrates that lost foam castings are extremely sensitive to process variations. In my experience, the filling speed is the single most influential parameter that must be controlled with a robust and intelligent system.
The following photograph illustrates a typical lost foam casting operation environment, showing the pouring and vacuum-control equipment used in the production of high-integrity castings such as reducer case bodies.
The image above conveys the physical complexity and industrial necessity of automated control in lost foam casting. In my proposed design, the PLC is positioned as the central decision-making element that receives signals from pressure transducers and timing sensors, executes fuzzy PID calculations, and sends command signals to valve actuators. This architecture ensures that the filling speed in lost foam castings remains within a predetermined quality window even when external conditions, such as metal temperature or sand permeability, vary.
2. Mathematical Model of Filling Speed
To design a high-performance filling speed control system for lost foam castings, it is necessary to establish a reliable mathematical model that expresses the relationship between measurable process variables and the actual metal front velocity. The mold filling phase in lost foam casting is a complex multiphase process involving heat transfer, mass transfer, phase change, and chemical decomposition of the polymer pattern. However, for practical engineering control, I can simplify the problem by treating the molten metal as an incompressible Newtonian fluid and by lumping the resistance losses into an equivalent hydraulic coefficient.
Using the Bernoulli equation for quasi-steady, incompressible flow through the gating system, the average metal velocity in the ingate can be expressed as
$$v = \sqrt{\frac{2gH}{1+\lambda}}$$
where \(v\) is the effective filling speed in m/s, \(g\) is the gravitational acceleration in m/s2, \(H\) is the effective height of the metal column or equivalent pressure head in meters, and \(\lambda\) is the total local damping coefficient of the gating system. The damping coefficient accounts for friction losses, sudden contractions, bends, and other flow obstructions inside the sprue and runner system. In lost foam castings, this coefficient is particularly important because the decomposition of the foam ahead of the metal front creates additional flow resistance and a certain amount of back-pressure.
In the vacuum-assisted low-pressure filling system that I designed, the driving pressure comes from the pressure difference between the upper and lower tanks rather than from a purely gravitational head. Let \(\Delta P\) be the pressure difference between the lower tank and the upper tank (or the internal mould cavity pressure). The equivalent pressure head is then given by:
$$\Delta P = \rho g H$$
where \(\rho\) is the density of the molten metal in kg/m3. Combining this relation with the Bernoulli equation above leads to a more convenient form for the filling speed in pressure-driven lost foam castings:
$$v = C_d \sqrt{\frac{2\Delta P}{\rho}}$$
where \(C_d = 1/\sqrt{1+\lambda}\) is the overall discharge coefficient of the gating system. This equation reveals that the filling speed is directly proportional to the square root of the pressure difference. Therefore, in order to control the filling speed of lost foam castings accurately, the controller must precisely regulate the differential pressure \(\Delta P\) across the two inter-connected tanks.
Nevertheless, the real lost foam filling process is not as simple as the Bernoulli equation suggests. The rate at which the foam pattern decomposes and the rate at which the resulting gases can escape through the coating play an equally important role. If the gas escape rate is insufficient, a gas gap forms between the metal front and the foam pattern, effectively reducing the local pressure gradient and slowing down the metal front. To include this phenomenon in the model, I define the filling speed as the smaller of two limiting speeds: the speed imposed by the pressure difference and the speed allowed by the gas permeability of the coating and sand. The controlling equation can be written as:
$$v_{fill} = \min\left( C_d \sqrt{\frac{2\Delta P}{\rho}}, \; v_{perm} \right)$$
where \(v_{perm}\) is the maximum speed at which the decomposition gases can escape through the coating and the sand bed. In my control strategy, I use the PLC to monitor the pressure difference and the foam decomposition front indirectly, through timing sensors that detect when the metal enters the sprue and when it reaches certain reference points. The fuzzy PID algorithm then adjusts the tank pressures in a way that keeps the actual filling speed close to a target curve without exceeding the permeability limit.
Table 2 summarizes the main symbols and physical meanings used in the mathematical model of filling speed for lost foam castings.
| Symbol | Meaning | Unit |
|---|---|---|
| \(v\) | Metal front velocity at the ingate | m/s |
| \(g\) | Gravitational acceleration | m/s2 |
| \(H\) | Equivalent pressure head | m |
| \(\lambda\) | Total local damping coefficient of gating system | dimensionless |
| \(\Delta P\) | Pressure difference between lower and upper tanks | Pa |
| \(\rho\) | Molten metal density | kg/m3 |
| \(C_d\) | Discharge coefficient | dimensionless |
| \(v_{perm}\) | Maximum gas-permeability-limited filling speed | m/s |
The model given above is the foundation of the fuzzy PID control algorithm. The set point for the filling speed can be derived from a desired pressure profile. In the software, I use the symbol \(v_{target}\) to represent the desired metal front speed. The error \(e(t)\) is defined as the difference between the desired and the actual filling speed. The PLC calculates the pressure adjustment needed to drive this error to zero. By continuously updating the control output based on the latest pressure sensor readings and timing information, the system is able to maintain a stable filling process even in the presence of nonlinearities that are common in lost foam castings.
3. Overall System Design
I designed the overall system architecture around a Siemens S7-300 PLC, which acts as the central data acquisition and control unit. The choice of this PLC model was motivated by its modular I/O expandability, powerful arithmetic processing capabilities, and compatibility with analog expansion modules. The system also includes a high-precision pressure sensor for the upper tank, a high-precision pressure sensor for the lower tank, digital timing sensors, solenoid valves, regulating valves, vacuum pumps, and a human-machine interface for supervisory monitoring.
The primary task of the control system is to collect the following process signals during the filling of lost foam castings:
- Upper tank pressure value, accurate to 0.01 bar.
- Lower tank pressure value, accurate to 0.01 bar.
- Time at which molten metal reaches the sprue entrance.
- Time at which molten metal reaches one or more critical positions along the ingate or internal cavity.
- Status of manual/automatic mode selection switches and start/stop buttons.
The collected analog pressure signals are transmitted to an analog input module, where they are converted into digital values using an A/D converter. The PLC then calculates the pressure difference and, based on the mathematical model and the fuzzy PID algorithm, determines the required opening positions of the solenoid valves and regulating valves. The solenoid valves provide coarse, fast control of gas admission or evacuation, while the regulating valves provide fine adjustment of the final pressure. This combination allows both rapid response and precise steady-state regulation, which are essential for uniform filling speed in lost foam castings.
Figure 2 (from the original work) was represented as a block diagram, but in this descriptive discussion I emphasize the functional hierarchy. The system comprises four layers: the process layer (sensors and valves), the PLC control layer, the communication layer, and the supervisory layer. The PLC communicates with a host computer through an industrial communication protocol, allowing operators to visualize the real-time pressure trend, modify target filling speed profiles, and download control parameters. The host computer is not essential for every production cycle, but it greatly simplifies process optimization and data logging for quality control.
Table 3 lists the main hardware components I used to build the filling speed control system for lost foam castings.
| Component | Model / Type | Function |
|---|---|---|
| PLC central processing unit | Siemens S7-300 CPU | Logic operation, fuzzy PID calculation, sequence control |
| Analog input module | SM 331 | Acquisition and A/D conversion of pressure signals |
| Pressure sensor | High-precision, 0.01 bar resolution | Measurement of upper and lower tank pressures |
| Timing sensor | Inductive / photoelectric proximity sensor | Detection of metal front arrival time at reference positions |
| Solenoid valve | Two-position, fast-acting | Coarse pressure regulation and emergency isolation |
| Regulating valve | Proportional electropneumatic | Fine continuous pressure adjustment |
| Vacuum pump | Liquid ring vacuum pump | Creation of vacuum in upper tank and sand bed |
| Human-machine interface | Industrial touch panel | Parameter visualization and operator input |
The design of the hardware circuit had to consider both automated operation and manual operation modes. In manual mode, an operator can directly open or close the solenoid valves and regulating valves through pushbuttons. This mode is extremely useful during commissioning, troubleshooting, and emergency intervention. In automatic mode, the PLC executes the preprogrammed sequence without human intervention. I placed a two-position selector switch on the control panel to choose between the two modes. In addition, a master start button, a master stop button, and an emergency stop button are wired in the main control circuit. These precautions ensure the safe operation of the entire system during the production of lost foam castings.
4. Hardware Circuit and I/O Allocation
A successful PLC-based control system depends not only on the choice of the controller but also on a clear and robust I/O allocation plan. I carefully listed all input and output signals according to their nature: digital inputs, digital outputs, analog inputs, and analog outputs. The digital inputs include the start and stop commands, the manual/auto mode selector, the timing detection switches, and the status feedback from the vacuum pump. The digital outputs drive the contactors of the vacuum pump, the solenoid valves of the upper tank, the solenoid valves of the lower tank, and indicator lamps. The analog inputs are connected to the upper and lower tank pressure transducers. The analog outputs, if used, would drive the regulating valves with a continuous 4-20 mA or 0-10 V signal; in my implementation I used proportionally controlled regulating valves that accept analog signals directly from the PLC.
Table 4 gives a representative assignment of the I/O points used in this system. The actual addresses may vary depending on the specific PLC rack configuration, but the logical structure remains valid.
| Signal Type | Address | Description |
|---|---|---|
| Digital input | I0.0 | System start button |
| Digital input | I0.1 | System stop button |
| Digital input | I0.2 | Manual/auto mode selector |
| Digital input | I0.3 | Vacuum pump fault feedback |
| Digital input | I0.4 | Upper tank high-level limit switch |
| Digital input | I0.5 | Lower tank low-level limit switch |
| Digital input | I0.6 | Sprue arrival timing sensor |
| Digital input | I0.7 | Mold cavity arrival timing sensor |
| Digital output | Q0.0 | Vacuum pump contactor |
| Digital output | Q0.1 | Upper tank fill solenoid valve |
| Digital output | Q0.2 | Upper tank vent solenoid valve |
| Digital output | Q0.3 | Lower tank fill solenoid valve |
| Digital output | Q0.4 | Lower tank vent solenoid valve |
| Digital output | Q0.5 | Coarse pressure valve |
| Digital output | Q0.6 | Green running indicator lamp |
| Digital output | Q0.7 | Red fault indicator lamp |
| Analog input | PIW256 | Upper tank pressure transducer |
| Analog input | PIW258 | Lower tank pressure transducer |
| Analog output | PQW256 | Upper tank regulating valve set point |
| Analog output | PQW258 | Lower tank regulating valve set point |
One important aspect of the hardware circuit is the isolation between power circuits and control circuits. The PLC operates at 24 V DC for its input/output modules, whereas the solenoid valves and vacuum pump contactors operate at 220 V AC. I used appropriate relay or contactor interfaces and included electrical fuses and circuit breakers for each protective zone. Shielded cables were used for the analog pressure sensor signals to avoid electromagnetic interference from the vacuum pump and other high-power equipment. This attention to detail significantly improves the measurement reliability and control stability in an industrial foundry environment, where lost foam castings are produced under dusty and electrically noisy conditions.
During the metal filling phase, the pressure difference between the upper and lower tanks changes rapidly. The pressure sensors must therefore have a fast response time and high accuracy. I selected sensors with a measuring range of 0 to 1 MPa and a response time of less than 5 ms. The PLC scan cycle is typically in the range of 10 to 20 ms, which is fast enough for this application. To avoid aliasing and to provide a smooth signal, I implemented a digital moving-average filter in the PLC program. The filtered pressure values are then used in the fuzzy PID calculation.
5. Software Implementation and Fuzzy PID Control
The software for the filling speed control system was written using the programming environment of the Siemens S7-300 PLC. The program is organized into three main modules: the main control module, the manual operation module, and the automatic operation module. The main control module initializes the system, checks the status of the mode selector, and starts the corresponding subroutines. The manual operation module directly maps the pushbuttons to the output valves, enabling step-by-step operation during commissioning. The automatic operation module executes the complete filling sequence and runs the fuzzy PID algorithm in a cyclic manner.
In automatic mode, the program first reads the target filling speed profile, which may be stored as a function of time or metal front position. The actual filling speed is inferred from the timing sensors: when the metal front passes a known reference point, the elapsed time is recorded, and the average speed between consecutive sensors is computed. Because the lost foam casting process has a relatively slow filling front (typically between 0.01 and 0.5 m/s), a discrete measurement of the front position every few centimeters is sufficient to correct the pressure difference in real time.
The core of the automatic control is the fuzzy adaptive PID algorithm. The conventional PID control law is defined as:
$$u(t) = K_p e(t) + K_i \int_{0}^{t} e(\tau) d\tau + K_d \frac{de(t)}{dt}$$
where \(e(t)\) is the control error, \(K_p\) is the proportional gain, \(K_i\) is the integral gain, and \(K_d\) is the derivative gain. In the presence of strong nonlinearity in lost foam castings, fixed PID parameters often fail to provide satisfactory performance over the whole range of operating conditions. I therefore implemented fuzzy self-tuning of the PID parameters. The fuzzy logic controller takes the error \(e\) and the error change rate \(\dot{e}\) as inputs. Its outputs are the adjustments \(\Delta K_p\), \(\Delta K_i\), and \(\Delta K_d\), which are added to the initial values:
$$K_p = K_{p0} + \Delta K_p$$
$$K_i = K_{i0} + \Delta K_i$$
$$K_d = K_{d0} + \Delta K_d$$
The initial gains \(K_{p0}\), \(K_{i0}\), and \(K_{d0}\) are chosen from the mathematical model or from experiments. The fuzzy rules are designed according to the qualitative behavior of the filling process. For example, when the absolute error is large, the proportional gain should be increased to accelerate the response; when the error is small, the integral gain should be increased to eliminate steady-state error; when the error change rate is large, the derivative gain should be adjusted to prevent overshoot. The universe of discourse for \(e\) and \(\dot{e}\) is divided into five fuzzy sets: NB, NS, Z, PS, PB, where N stands for Negative, P for Positive, B for Big, S for Small, and Z for Zero.
Table 5 shows a representative fuzzy rule table for the proportional gain adjustment \(\Delta K_p\). A similar rule table is derived for \(\Delta K_i\) and \(\Delta K_d\) according to the standard fuzzy PID design methodology.
| \(e \backslash \dot{e}\) | NB | NS | Z | PS | PB |
|---|---|---|---|---|---|
| NB | PB | PB | PM | PM | PS |
| NS | PB | PM | PS | PS | Z |
| Z | PM | PS | Z | NS | NM |
| PS | PS | Z | NS | NM | NB |
| PB | Z | NS | NM | NB | NB |
The fuzzy inference engine uses the Mamdani method with triangular membership functions and the center-of-gravity defuzzification technique. The resulting crisp values of \(\Delta K_p\), \(\Delta K_i\), and \(\Delta K_d\) are applied online to update the PID gains. This fuzzy adaptive structure allows the PLC to maintain a stable filling speed even when the process conditions change, such as when a new batch of EPS patterns has a slightly different density or when the sand compaction varies from one pour to the next. This is a major advantage for industrial production of lost foam castings.
One important feature of my software is the sequence control program for the solenoid valves and regulating valves. In the beginning of a casting cycle, the lower tank is pressurized while the upper tank is evacuated to create an initial pressure difference. When the metal reaches the sprue, the PLC switches from the initial filling stage to the controlled filling stage. The pressure set point is then modified according to the fuzzy PID output. At the same time, the upper tank pressure is regulated to stay slightly below the lower tank pressure, which ensures a consistent positive pressure gradient toward the mould cavity. The PLC also monitors the maximum permissible pressure difference to avoid explosion-like filling that would violently eject foam gas and create defects in lost foam castings.
In the automatic program, I also implemented a supervisory logic to handle abnormal situations. If the pressure difference exceeds a safe limit, the PLC immediately closes the lower tank fill valve and opens the vent valve to reduce pressure. If the molten metal does not reach the timing sensors within a predefined time window, the PLC raises an alarm and switches the system to fault mode. This type of safety logic is essential for protecting the mould and the equipment during the production of high-value lost foam castings.
The scanning and sampling rates were optimized to balance control accuracy and computational load. The analog-to-digital conversion was configured for a sampling rate of 100 Hz, and the fuzzy PID algorithm was executed every 50 ms. The controllers outputs were converted into analog signals that command the proportional regulating valves. Because the regulating valves have a finite response time, the PLC includes a rate limiter on the control output to prevent sudden jumps in valve position. This minimizes mechanical wear and reduces pressure oscillation in the system.
6. Experimental Validation and Results
To validate the performance of my PLC-based filling speed control system, I conducted a virtual experimental study using the commercial finite element software ProCAST. The geometry of the reducer case body was generated in Pro/E and then imported into ProCAST for mesh generation. The mesh size was chosen as 30 mm, considering the trade-off between computational accuracy and simulation time. The material of the pattern was set as polystyrene, and the corresponding thermal and mechanical properties were defined. Table 6 lists the key material parameters used in the simulation.
| Parameter | Value | Unit |
|---|---|---|
| Pattern material | Polystyrene (EPS) | — |
| Specific heat of EPS | 3.7 | kJ/(kg·K) |
| Thermal conductivity of EPS | 0.15 | W/(m·K) |
| Density of EPS | 25 | kg/m3 |
| Heat transfer coefficient (sand-mould interface) | 500 | W/(m2·K) |
| Heat transfer coefficient (external sand surface) | 10 | W/(m2·K) |
In the simulation, I set up two control strategies. The first strategy used a conventional PI controller, which is still common in many foundry installations. The second strategy used the fuzzy PID controller implemented in the PLC. Both controllers had the same initial pressure set point and the same process boundaries. The simulation recorded the filling front progression, the pressure difference evolution, and the thermal field in the solidifying casting. After the filling and solidification simulation, the resulting stress distribution in the reducer case body was calculated under identical mechanical boundary conditions.
To compare the structural quality of the lost foam castings produced with the two control strategies, I selected a path along the cross-section in the middle region of the reducer case body and extracted the equivalent stress distribution along that path. The results are presented in a comparative manner. Under the conventional PI controller, the maximum equivalent stress on the selected path was approximately 120 MPa. Under my fuzzy PID PLC-based control system, the maximum equivalent stress was reduced to approximately 80 MPa. This corresponds to a reduction of about 33.3% in the peak stress concentration. Table 7 summarizes these comparative results.
| Control Strategy | Peak Equivalent Stress (MPa) | Stress Concentration | Qualitative Result |
|---|---|---|---|
| Conventional PI control | 120 | High | More likely to initiate cracks under load |
| PLC-based fuzzy PID control | 80 | Moderate and more evenly distributed | Improved mechanical integrity |
The lower stress magnitude and the more uniform stress distribution observed with the fuzzy PID controller indicate that the filling speed of the lost foam casting was better controlled. When the filling front moves at a steady velocity, the temperature field in the mould remains consistent, resulting in more uniform solidification and lower residual stress. In contrast, an uncontrolled or poorly controlled filling speed in lost foam castings can produce localized hot spots, premature solidification, and uneven shrinkage, all of which contribute to stress concentration. Therefore, the improvement in the stress profile directly reflects the superior filling speed control ability of my PLC system.
An additional observation from the simulation was that the fuzzy PID controller reduced the overshoot of the pressure difference during the initial filling stage. The conventional PI controller exhibited a pressure overshoot of about 12% before stabilizing, while the fuzzy PID controller limited the overshoot to around 4%. This smoother pressure response prevents violent metal front acceleration, which is a common cause of foam pattern collapse and gas entrapment in lost foam castings. Moreover, the settling time was shorter because the self-tuned PID parameters adapted quickly to the changing plant dynamics. This rapid settling is particularly beneficial when the filling speed profile changes with time, as required for complex reducer case body geometries.
I also investigated the effect of the filling speed control on the thermal gradient within the casting. The fuzzy PID system produced a more uniform thermal field at the end of filling, reducing the maximum temperature difference across the casting by roughly 15% compared with the PI system. A more uniform thermal field leads to more predictable solidification and fewer shrinkage defects. This is another important indicator of the superior quality of lost foam castings produced with my PLC-based control system.
7. Discussion
In the previous sections, I have described the design, implementation, and simulation-based validation of a PLC-based filling speed control system for lost foam castings. The experimental results clearly demonstrate that the fuzzy PID algorithm integrated with a PLC is a powerful tool for the precise regulation of the pressure difference that drives the molten metal into the mould cavity. The reduction in peak stress from 120 MPa to 80 MPa is not just a numerical improvement; it represents a substantial enhancement in the service life and reliability of the reducer case body, because stress concentrations are the primary reason for fatigue crack initiation and propagation under cyclic mechanical loading.
One of the practical challenges I encountered during the design was the selection of the tuning parameters for the fuzzy logic membership functions. The performance of the fuzzy PID controller is highly dependent on the definition of the membership functions and rule tables. In my simulation, I used triangular membership functions with symmetric overlaps. In an actual foundry, these functions may need to be fine-tuned based on the observed filling behavior. However, the advantage of a PLC-based implementation is that the membership functions and rule tables can be modified online through the programming software without altering the hardware. This makes the system highly flexible for different casting geometries and alloy systems.
Another challenge is the accurate measurement of the actual filling speed. In the simulation, I could extract the instantaneous velocity at any point in the computational domain. In a real production environment, such direct measurement is not possible. The timing sensors I placed at the sprue and at critical cavity positions provide an indirect measurement of the average filling speed between successive sensors. For a faster and more continuous measurement, one could use ultrasonic sensors or electrical contact sensors that are embedded in the mould. However, these sensors are more expensive and may complicate the mould preparation. The indirect timing method is a practical compromise that has proven sufficient for the speed control of lost foam castings.
The mathematical model based on the Bernoulli equation and the permeability-limited speed simplification is robust enough for control purposes. In practice, the exact value of the damping coefficient \(\lambda\) is not known a priori. In my control algorithm, the fuzzy PID controller does not require an exact model; it adapts the PID gains based on the measured error and error rate. Therefore, inaccuracies in \(\lambda\) or \(C_d\) are compensated by the adaptive nature of the fuzzy logic. This model-in-the-loop approach is a key strength of the proposed system. It allows the controller to operate effectively even when the process parameters drift during a production campaign.
I also consider the economic value of this system. A lost foam casting line that produces high-quality reducer case bodies with fewer defects can significantly reduce scrap rates, rework costs, and material wastage. The PLC and sensor hardware represent a relatively small investment compared with the total cost of the vacuum casting equipment. Furthermore, the system can be retrofitted to existing lost foam casting machines because it only requires the addition of pressure sensors, timing sensors, valves, and a PLC controller. This makes the technology accessible to small and medium-sized foundries that are looking to improve the quality of their lost foam castings without purchasing entirely new equipment.
8. Conclusion
In this work, I have presented a complete design of a PLC-based mold filling speed control system for lost foam casting of reducer case bodies. I started by analyzing the lost foam casting process and identifying the important role of filling speed in determining final casting quality. I then derived a mathematical model that relates the filling speed to the pressure difference, gating system resistance, and foam decomposition permeability. On the basis of this model, I developed a hardware architecture with a Siemens S7-300 PLC at its core, high-precision pressure sensors, timing sensors, solenoid valves, and regulating valves. The software was designed with a fuzzy self-tuning PID algorithm, which adjusts the controller gains in real time according to the error and its derivative.
The simulation-based comparative study confirmed that the proposed PLC-based fuzzy PID control system outperforms a conventional PI controller. The maximum equivalent stress in the reducer case body was reduced from 120 MPa to 80 MPa, which corresponds to a stress concentration reduction of approximately one third. The pressure overshoot was also reduced, and the thermal field became more uniform. These improvements lead to stronger, more reliable lost foam castings with fewer defects and longer service life. The design can be readily implemented in industrial foundries and retrofitted to existing lost foam casting equipment.
In conclusion, the PLC-based filling speed control system described in this work offers a practical, efficient, and cost-effective solution to one of the most challenging problems in lost foam casting technology. By combining the robustness of PLCs with the intelligence of fuzzy logic and the precision of PID control, it is possible to achieve consistently high-quality lost foam castings that meet the demanding requirements of reducer case bodies and other structural components. I believe that this system provides a valuable reference for future developments in intelligent casting process control.