Since advent of pressure casting in the late 1860s, for a long time, design of gate system and its availability in gate technology have been judged based on statistical accumulation of casting quality, then gate is modified until resulting casting is recognized and accepted. Since the 1960s, a large number of literatures have increasingly clearly mentioned view that: in design of gating system, required die-casting parameters (flow parameters) should take into account output of die-casting machine energy. Therefore, many experts and scholars continue to explore and study inherent relationship between energy required by mold gating system and energy that machine can provide. It was not until the early 1970s that theoretical design, scientific calculation and parameter determination were combined after new technology of PQ2 diagram was published, and it was used as basis for expected evaluation of gating system. It can be determined that birth of PQ2 diagram has transformed availability of gating system design from post-approval to pre-evaluation, which is a sign of combination of die-casting theory and practice.

In die-casting process, from perspective of fluid mechanics, there are two fluid flow systems: one is fluid of liquid metal (molten metal) entering mold cavity from pressure chamber (referring to when passing through inner gate); the other is flow of pressure from accumulator to injection cylinder. The first system represents energy required for process to run; the second system represents power provided during operation. Both of these fluid flow systems follow Bernoulli law of fluid mechanics, which is expressed and explained by relationship between pressure and speed. That is, the greater pressure that drives liquid flow, the faster flow rate of liquid, and pressure is proportional to average of speed.
So-called PQ2 diagram refers to a line diagram that simultaneously reflects characteristics of die-casting machine, mold characteristics and system process characteristics. For die-casting machines, each die-casting machine's injection system has its own characteristics. PQ2 diagram reflects relationship between maximum metal static pressure and flow rate in pressure chamber, indicating characteristics of die-casting machine and ability of die-casting machine to provide injection energy. For mold, after pouring system is determined, mold also forms its unique characteristics, such as each mold has a filling speed limit. See Figure 1.

 

PQ2 diagram reflects relationship between gate flow rate in mold and injection pressure ratio. According to process requirements, mold must obtain a certain injection energy to ensure formation of die-casting part, which shows that mold requires injection energy to ensure formation of die-casting part, and degree to which mold requires injection energy. Combination of these two energy supply and demand forms a die-casting machine-die-casting mold system. After this system is matched, die-casting process range can be more abundant. Therefore, in order to provide flexibility in die-casting process, PQ2 diagram is applied in design stage to make design plan more thorough; for mold that has been made, application of PQ2 diagram for analysis can guide us to optimize injection system by changing some parameters.

PQ2 diagram is theoretical basis of die casting process. P represents pressure and Q represents flow rate, which describes situation of die casting at high-speed injection stage.
It is injected at high speed at gate, but whether soup can be injected at speed we want involves pressure required to achieve this speed and whether die casting machine can provide enough pressure.
PQ2 diagram is used to predict whether die casting machine can provide enough pressure, then predict whether gate speed can meet our requirements.

Die-casting mold is equivalent to load of die-casting machine. Each die-casting mold (gating system) has its own working characteristics. This working characteristic is functional relationship between metal flow and injection pressure established by formula (1):
We can get following formula from fluid mechanics:

 

Where V is gate speed, Cd is opening coefficient or flow coefficient, which represents speed ratio with energy loss and without energy loss. It is usually about 0.5 for magnesium and aluminum, and about 0.6 for zinc (value is between 0.4-0.8). g is acceleration of gravity, ρ is density of molten metal, and P is pressure.
This formula can be interpreted in die casting as: if we want to have a speed of V at gate, we must supply a pressure of P.

 

Where Q is flow rate, V is gate speed, and Ag is gate area. We substitute (1.2) into (1.1) and then sort it out to get

 

For a fixed gate area, draw (2.1.3) on a coordinate plane with pressure P as vertical axis and Q as horizontal axis, and we can get Figure 2.

 

For ease of use, coordinate is usually changed from Q to Q2, so that pressure demand curve becomes a straight line, as shown in Figure 3. Different gate areas can draw different straight lines, as shown in Figure 4. The larger gate area, the more it deviates to lower right.

 

From formula (1.1), we can see that if we want to get speed of V, we must supply P pressure, and source of this pressure is energy storage device of die casting machine. However, pressure of accumulator is not equal to P. They have following relationship:

 

Where P1 is effective pressure in oil cylinder; PA: is maximum pressure provided by accumulator; Vp: is injection speed, that is, speed of molten metal in barrel; VDRY: is air injection speed, which represents injection capacity of this die-casting machine to overcome internal resistance.

 

Figure 5 is a simplified die-casting machine injection system diagram. P1, P2, P are pressures, and A1, A2, A are cross-sectional areas at relative positions. When speed VP in plunger is 0, it can be seen from formula (1.4) that P1=PA; and from static balance, it can be seen that PA=P1A1-P2A2, P=(P1A1-P2A2)/A, when P2 is very small, P=P1; and when VP=VDRA, P=0, which means that all energy supplied is converted into kinetic energy of molten metal. Therefore, meaning of formula (1.4) is: when speed of plunger is zero, effective pressure in feed barrel is the largest, and when plunger has speed, part of energy supplied becomes effective pressure of feed barrel, and part is converted into kinetic energy of metal liquid.

Both gate cross-sectional area and opening coefficient have a significant effect on flow-pressure curve of die-casting mold. Increasing gate cross-sectional area or increasing opening coefficient will reduce flow-pressure slope of die-casting mold. Same pressure will increase flow rate and improve flow efficiency of gating system. For a small opening coefficient or a small gate cross-sectional area, required pressure will increase significantly to achieve same flow rate. Therefore, correctly designing gating system, improving design quality and selecting an appropriate inner gate cross-sectional area can improve flow efficiency of gating system.

Cylinder block die-casting of a certain company is a large die-casting with complex geometry, high air tightness, dimensional accuracy, internal quality requirements, and inlaid with wear-resistant alloy cast iron, as shown in Figure 6.

 

Product information:
Casting weight: 13000g.
Slag bag: 900g.
Gate system weight: 4420g.
Wall thickness of die casting is uneven, most of wall thickness is 3.5mm, some of wall thickness is 20mm, and average wall thickness is 6mm.
Step 1: Determine casting data

Step 2: Determine process window

According to structure, wall thickness and other factors of product, estimate filling speed and filling time:
Filling speed: 40-50m/s.
Filling time: 70ms-100ms.
Step 3: Draw DL (die) line according to gate area.

 

Step 4: Draw equipment line according to die casting machine information.

 

According to calculation of projected area and clamping force of die casting, a die casting machine with model EV220 and clamping force of 2200 tons produced by Buhler, Switzerland, was selected. Diameter of hydraulic cylinder of 2200-ton die-casting machine of Buhler, Switzerland, is 210 mm, pressure of fast-injection accumulator is 16 MPa, the fastest air injection speed is 8 m/s, and diameter of injection punch used to produce cylinder head die-casting is 130 mm. P-Q2 diagram machine tool line is drawn.
Adjustment method:
Adjust injection speed (or opening of two-speed valve).
DL line and ML line intersect within process window.
View data:
Filling speed = 43.7 m/s;
Filling time - 79.5 ms;
Injection speed = 5.3 m/s;
In the early stage of die-casting mold design, PQ diagram can be used to:
1) Analyze factors such as punch stroke, punch speed, filling time, filling speed, and energy matching between mold and machine tool.
2) It is especially practical in setting fast injection speed of punch.
3) Final P-Q diagram analysis results.

 

PQ2 diagram shows relationship between pressure and flow, solves energy matching relationship between die-casting machine and die-casting mold, and can provide rich process information. It is a very useful design and analysis tool for process personnel. However, PQ2 technology still has some limitations in use. Among them, open coefficient is an important parameter in PQ2 technology, but it cannot be accurately calculated at present. It is only determined by personal subjective judgment. However, open coefficient has an important influence on result. Therefore, when applying PQ2 diagram, attention should be paid to this and Cd value should be estimated as accurately as possible.