Summary:Introduce the rheological calculation of nozzle diameter for the hot runner system of plastic injection molds. Provide an example to illustrate the calculation process of nozzle diameter. The method for obtaining rheological calculation data was also stated.

In recent years, mold designers have increasingly applied hot runner technology. The selection of nozzles includes two aspects: the selection of types and the determination of nozzle channel diameter. The smaller transmission cross-sectional area of the nozzle flow channel will increase the pressure loss in the flow channel. Under a certain injection pressure, the molten material injected into the mold cavity cannot reach the required filling rate due to low filling pressure. It can affect the quality of injection molded parts and even make the cavity unable to fill. A larger cross-sectional area will increase the material and energy consumption of the pouring system, and increase the transit time of the melt plastic in the high-temperature flow channel and nozzle. This article introduces the use of rheological principles and methods to calculate and determine the diameter of nozzle flow channels.

1. Nozzle diameter

Calculate and determine the nozzle channel diameter of the hot runner system at a reasonable shear rate, taking into account the viscosity of the plastic melt. The calculation formula originates from plastic rheology and can obtain correct results based on the non Newtonian properties of various plastic melts.

1.1 Calculation formula for nozzle diameter

The inner diameter size of the nozzle in the hot runner system is determined by the material's flow index n and shear rateAnd the volume flow rate of injection is jointly determined. This flow rate qi is the volumetric flow rate of the nozzle injected into the downstream cavity, which can be calculated from the injection amount and injection time emitted by the nozzle

Where q_I——Volume flow rate of the diversion channel, cmthree/S;

T - Filling time for downstream cavity, s;

V_I——Injection volume of a single nozzle, cmthree;

V - Total volume of injection mold cavity, cmthree;

N - Number of channel forks.

In the circular pipe flow channel of the pouring system, the melt filling time t of each section is the same. Given the above data, determining the diameter of the flow channel inside the nozzle based on shear rate can be calculated using the following rheological formula

(3)

In the formula, n - flow index of plastic melt;

         ——The reasonable shear rate of plastic melt, 1/s.

1.2 Application examples

The storage box shown in Figure 1 has a box area of 540 × 210mm, height 220mm, wall thickness 3-4 mm. 3640cm for boxthreeABS plastic injection molding. Our company has designed and manufactured a hot runner system for this injection mold. There are four BS32050 top tube type nozzles with gates on the template. The total length of the nozzle is 102mm, and the pipe diameter is 16mm. Figure 1 shows the flow analysis of the hot runner with the pouring system set as insulation. 6.056s is the state when the total volume of plastic melt is full. The flow filling time of the melt in the hot runner is within 5 seconds. Using Lustran ABS 1146 material from Lanxess company, the melt temperature is 260 ℃.

Figure 1: Four nozzle hot runner system of the box body

The output of each nozzle is 910cmthree. Total injection volume 3640cmthreeAccording to Table 1, the feasible filling time t=4.8s is obtained. Flow rate q through the nozzle_I=190cmthree/S. The rheological curve of this plastic variety provided by the analysis software shows that the flow index of the plastic melt is n=0.32. According to Table 2, open multiple nozzles should have a reasonable shear rate under high flow rates=700s-1. Substituting into equation (3) yields

Considering the injection production, it is also possible to adjust the injection mold filling and shear rate. And rounded to the series size of nozzle diameter. Therefore, a multi nozzle with a flow channel diameter of 16mm is used.

2. Derivation of calculation formula

The above equation (3) is derived from the formula for calculating the flow rate q of non Newtonian fluids in a circular pipeline. Equation (4-5) in "Polymer Rheology and Its Applications" edited by Xu Peixian (Beijing: Chemical Industry Press, 2003)

(4)

In the equation, Dp is the pressure drop for a circular tube with a radius of r and a length of L. K is the plastic melt at a certain temperature and shear rateThe consistency below. N is the flow index, also known as the non Newtonian flow index. The units of consistency and viscosity are the same, commonly used in Pa ? s; For ease of operation, N ? s/cm is also usefultwo.

Among them, the shear rate of the pipe wall is

 (5)

Substitute this equation into equation (4) and organize it into

 (6)

Diameter d=2r, this equation is

 (7)

Rheological calculation formula for obtaining nozzle diameter

(8)

In the equation, can be converted into equation (3).

3. Calculation parameters

3.1 Determination of filling time

The hot runner nozzle is the terminal of the hot runner system, which transports the molten material to the mold cavity or an additional cold runner. In the calculation process of nozzle diameter, the total volume V of the mold cavity is determined by the relationship between injection volume and time to determine the injection time t. The injection time t is based on the conventional pushing rate of the injection machine screw. The corresponding injection filling time when the injection machine has a moderate injection rate. Table 1 shows the relationship between the corresponding filling time and nominal injection volume under the conventional injection rate of the injection molding machine. A large number of engineering calculations have proven that this method can accurately determine the mold filling flow rate of the molten material in the flow channel of the pouring system. It can also adapt to the adjustment of injection machine operation on the filling rate.

V - Injection volume, cmthree;

T - Injection time, s.

When the computer program is running, it is allowed to modify this default time value.

3.2 Reasonable shear rate

A large number of injection molding experiments and computer simulation data have proven that there is a reasonable range of shear rates for each process of the pouring system, from the main flow channel, each diversion channel to the nozzle inner diameter, as shown in Table 2. Plastic melts have a higher viscosity, which is lower at higher temperatures. Another characteristic of plastic melt is its non Newtonian nature, which exhibits the phenomenon of "shear thinning". When shearing flow in a circular tube, the higher the shear rate, the more significant the decrease in viscosity of the melt. The shear rate is mainly related to the volume flow rate within the channel section. Therefore, there are different reasonable shear rate ranges for the main flow nozzle upstream of the hot runner system, the various diversion channels in the midstream, and the sub nozzles downstream. It is beneficial for reducing viscosity, reducing pressure loss along the process, and ensuring successful filling of the formed cavity.

3.3 Method for Obtaining Consistency K and Index n of Plastic Melt Rheological Data

Here, using the Lustran ABS 1146 material from Lanxess company, the method and steps for obtaining the rheological parameters of plastic melt, consistency K and index n.

1) For viscosity at 260 ℃Shear rateRheological curve

2) Read the viscosity value corresponding to the shear rate

Yes, the length of the actual viscosity point segment (mm)/the spacing between viscosity coordinate points (mm)=

  Lg100=2 exponential operation 2 0.974026=2.974026

Gain=10two point nine seven four zero two six=942Pa ? s

Yes, line segment length (mm)/coordinate length (mm)=

Lg100=2 exponential operation 2 0.292208=2.292208

Opponent number acquisition=10two point two nine two two zero eight=196Pa ? s

3) Solving K and n by the simultaneous equation of two points

Obtained after substitution

Solving this equation yields n=0.318=0.32

Substituting into the equation yields Pa ? s

4) Take the average value after verification

Pa ? s

Taking n=0.32 K=2.15 × tenfourPa ? s

In Tables 3-2 of the book "Hot Runner Injection Molding" (see Reference 1), "The apparent consistency K 'and flow index n of some foreign produced plastics" are calculated using the above method for 76 commonly used plastics. The deviation between the apparent K 'and the true consistency K is very small and can be ignored in engineering calculations.

4. Conclusion

The above calculation methods and related data are combined with injection molding flow analysis software to scientifically determine the nozzle channel diameter. Ensure the quality of the runner plate and nozzle of the hot runner system designed and produced.