Are you struggling with complex blown film calculations? Incorrect settings can lead to wasted material and poor quality. We provide simple, clear formulas to help you master your production process.
To calculate blown film parameters, you need key formulas for die area, bubble flow rate, line speed, strain rate, and Draw Down Ratio (DDR). These calculations help you precisely control film thickness, production output, and final film properties.
Mastering these calculations is essential for any blown film operator. It is all about turning theoretical numbers into real-world results. We must look at variables like die dimensions, material density, extruder speed, and the Blow-Up Ratio (BUR). Each one plays a part in the final quality of the film. By understanding how they connect, you can adjust your process with confidence. This leads to less scrap, better consistency, and higher profitability for your business. In this guide, we will break down each calculation step-by-step to give you full control over your machine.
For example, knowing the die area is the first step. It helps determine the initial speed of the polymer melt as it exits the machine. Then, by calculating the flow rate, you understand exactly how much material is moving through the system per second. This directly impacts the line speed. If your line speed is too fast for the flow rate, the film will be too thin and may break. If it's too slow, the film will be too thick and you will waste material. Getting these basic calculations right is the foundation for optimizing your entire production line.
How is the area of the die calculated?
The die is where your film begins its journey. So, calculating its area correctly is the first, crucial step. Let's see exactly how it is done.
*The die area is calculated by finding the area of the outer circle and subtracting the area of the inner circle. The formula is A_d = π (R₁² - R₂²), where R₁ is the outer radius and R₂ is the inner radius of the die opening.**
Understanding the Formula's Components
The formula A_d = π * (R₁² - R₂²) looks simple, but each part is important for an accurate result. Let's break it down.
- π (Pi): This is a mathematical constant, approximately equal to 3.14159.
- R₁ (Outer Radius): This is half of your die's total diameter. You can measure this directly from your equipment.
- R₂ (Inner Radius): This is the outer radius minus the die gap. The die gap is the precise space where the molten polymer exits, and it's a critical setting on any blown film machine.
Step-by-Step Calculation Example
Let's use a real-world example to make this clear. At our factory, we often work with these kinds of specifications.
Given:
- Die Diameter = 250 mm, which is 25 cm.
- Die Gap = 60 mil, which converts to 0.152 cm.
Calculation Steps:
-
Find the Outer Radius (R₁):
The radius is half the diameter.
R₁ = Die Diameter / 2 = 25 cm / 2 = 12.5 cm. -
Find the Inner Radius (R₂):
Subtract the die gap from the outer radius.
R₂ = R₁ - Die Gap = 12.5 cm - 0.152 cm = 12.348 cm. -
Calculate the Area (A_d):
Now, we plug the radii into the formula.
A_d = π ((12.5 cm)² - (12.348 cm)²)
A_d = π (156.25 - 152.47)
A_d = π * 3.78
A_d ≈ 11.9 cm²
Why This Calculation Is So Important
The die area is not just a number on a page. It is the starting point for several other critical calculations that determine your film's quality and your line's efficiency.
- Impact on Melt Velocity: A smaller die area with the same material flow rate will result in a higher exit velocity for the polymer. This affects how the bubble forms and its overall stability.
- Foundation for Other Calculations: If your die area calculation is wrong, all subsequent calculations, like line speed and draw down ratio, will also be wrong. This can lead to production issues that are very hard to diagnose.
- Link to Quality Control: As we always say in our training sessions, "Get the start right, and the finish takes care of itself." An accurate die area measurement is the first step to predictable and repeatable quality.
What is the bubble flow rate at the die, and how is it measured?
After the polymer leaves the die, it forms a bubble. Understanding the flow rate of this material is a key step in managing your production output and maintaining consistency.
The bubble flow rate is the volume of molten polymer exiting the die per unit of time. It's calculated by dividing the extruder's output rate (e.g., in kg/hr) by the density of the molten polymer. This tells you how much material you are processing.
The Difference Between Melt and Solid Density
First, we need to understand a critical detail: polymer density changes with temperature. It's less dense when hot and molten than when it's cooled into a solid film.
- Solid Density (ρ_s): This is the density of the final film product. You can find this value on the material's technical data sheet provided by your resin supplier.
- Melt Density (ρ_m): This is the density of the polymer when it's hot inside the extruder and die. A good rule of thumb is that the melt density is about 80% of the solid density. The formula is *ρ_m ≈ 0.8 ρ_s**.
Using the wrong density will lead to incorrect flow rate calculations, so this distinction is very important.
Calculating the Flow Rate: An Example
Let's walk through an example to see how it works in practice.
Given:
- Extruder Output Rate = 500 lbs/hr
- Solid Density (ρ_s) of the film = 0.919 g/mL
Step 1: Convert Extruder Rate to Consistent Units
We need everything in the same units for the math to work. Let's convert the output rate from lbs/hr to g/s.
- 1 lb = 453.592 g
- 1 hr = 3600 s
- Rate (g/s) = (500 lbs/hr * 453.592 g/lb) / 3600 s/hr ≈ 63.0 g/s
Step 2: Calculate Melt Density (ρ_m)
Now we estimate the melt density using our rule of thumb.
- ρ_m = 0.8 ρ_s = 0.8 0.919 g/mL = 0.735 g/mL
(For practical purposes, this is often rounded to 0.740 g/mL).
Step 3: Calculate the Output Flow at the Die
Finally, we can calculate the flow rate in volume per second.
- Output Flow (at die) = Extruder Rate (g/s) / Melt Density (g/mL)
- Output Flow = 63.0 g/s / 0.740 g/mL ≈ 85.1 mL/s
Flow Rate at the Frost Line Height (FLH)
We can also calculate the flow rate at the frost line, which is where the polymer has cooled and solidified. For this, we use the solid density.
- FLH Flow = Extruder Rate (g/s) / Solid Density (g/mL)
- FLH Flow = 63.0 g/s / 0.919 g/mL = 68.6 mL/s
You will notice the flow rate volume (mL/s) is lower at the frost line. This is because the same mass of material is now denser, so it takes up less space. The mass flow rate (g/s) remains the same throughout the process.
Practical Implications
| Parameter | What it Influences | Why it Matters for You |
|---|---|---|
| Output Flow (Die) | The initial speed of the melt exiting the die. | A higher flow rate allows for faster production but requires precise control to keep the bubble stable. |
| FLH Flow | The final speed of the solid film being pulled by the nip rollers. | This value is a critical input for calculating the final line speed and Draw Down Ratio (DDR). |
| Extruder Rate | The main control for your overall production output in kg/hr or lbs/hr. | Increasing this rate directly increases the amount of film you produce. It's your primary throttle. |
How is the frost line determined in the film blowing process?
The frost line is a visible transition on the film bubble that every operator learns to watch. Where it sits can change everything about your final product. Let's explore what it is and why it is so important.
The frost line, or Frost Line Height (FLH), is the point on the blown film bubble where the molten polymer cools and crystallizes into a solid, hazy state. It is determined mainly by the cooling rate, which you control with airflow from the cooling ring.
What Is Happening at the Frost Line?
The frost line is not just a line; it is a zone of transformation.
- Below the Frost Line: The polymer is hot, clear, and elastic, like thick honey. It is actively being stretched in two directions: outwards by internal air pressure (creating the bubble diameter) and upwards by the pull of the nip rollers.
- At the Frost Line: The polymer's temperature drops to its crystallization point. At this moment, the molecules stop flowing and lock into a more ordered, crystalline structure. The film turns from clear to "frosty," and it becomes a solid.
- Above the Frost Line: The film is now solid. Its diameter and thickness are fixed. It simply travels up the tower to the collapsing frame and nip rollers as a finished product.
Factors Controlling Frost Line Height (FLH)
The FLH is not a fixed value. It is a dynamic parameter that you, the operator, can and must control to produce quality film.
| Control Factor | How it Affects FLH | Practical Tip from Our Team |
|---|---|---|
| Cooling Air Flow | This is your primary control. More air cools the bubble faster, which lowers the FLH. Less air slows the cooling process, which raises the FLH. | Adjust the blower speed for your cooling ring. We advise starting with a moderate setting and making small adjustments. |
| Melt Temperature | A hotter melt takes longer to cool. This naturally tends to raise the FLH. | Keep your extruder temperature profile stable and set it correctly for the specific polymer you are running. |
| Extruder Output Rate | A higher output rate pushes more hot material out of the die. This requires more cooling, and if cooling isn't increased, the FLH will rise. | When you increase production speed, you must also increase cooling to keep the FLH at the same position. |
| Factory Environment | A warmer ambient temperature in your facility will slightly slow the cooling process. This can cause the FLH to rise. | This is usually a minor factor, but it can become noticeable during very hot summer days or cold winter nights. |
The "Right" Frost Line Height
So where should the frost line be? The ideal FLH depends on the polymer you are using and the film properties you want to achieve.
- Low Frost Line: This means the film cools and solidifies very quickly. The polymer molecules have less time to stretch and align themselves before they "freeze" in place. This can result in a film with lower clarity.
- High Frost Line: This creates a longer "liquid" state for the polymer. This gives the molecules more time and space to align themselves in the direction of the pull. This process is called orientation, and it generally leads to much better film properties, including:
- Higher film clarity and lower haze
- Increased tensile strength and stiffness
- Better impact and puncture resistance
For most applications we see, a higher frost line is preferred to achieve superior mechanical properties. In our machines, we often target an FLH of around 36 inches (91.4 cm) as a great starting point for standard materials like polyethylene.
What is the line speed, and how does it affect production?
Line speed is simply how fast you are making your film. It is a simple concept with a huge impact on your total output and final film quality. Let's look at the details behind this number.
Line speed is the velocity at which the finished, solid film is pulled away by the nip rollers at the top of the tower. It is calculated by dividing the flow rate at the frost line (FLH Flow) by the cross-sectional area of the final film bubble.
Calculating Line Speed: A Two-Part Process
To fully understand what is happening, we need to calculate the speed at two different points: the very beginning (at the die exit) and the very end (at the frost line). The difference between these two speeds is what stretches and thins the film.
1. Line Speed at the Die Exit (V₀)
This is the initial speed of the molten polymer as it comes out of the die.
- Formula: V₀ = Output Flow (at die) / Die Area (A_d)
- Using our previous numbers: V₀ = 85.7 mL/s / 11.90 cm² = 7.20 cm/s
(Note: 1 milliliter is equal to 1 cubic centimeter, so the units mL/s and cm³/s are interchangeable, which allows them to cancel out correctly with cm²).
2. Line Speed at the Frost Line (Vf)
This is the final speed of the solid film. It's the speed you see on your machine's control panel, often called simply "line speed."
- First, we need the cross-sectional area of the bubble at the frost line (A_b).
- We use the same area formula as before, but with the bubble's dimensions.
- Let's use our example values:
- BUR (Blow-Up Ratio) = 2.5
- Die Diameter = 25 cm
- Final Film Thickness = 40 microns = 0.004 cm
- Calculate the bubble's dimensions:
- Bubble Diameter = BUR Die Diameter = 2.5 25 cm = 62.5 cm
- Bubble Radius (R₁) = 62.5 cm / 2 = 31.25 cm
- Inner Bubble Radius (R₂) = R₁ - Film Thickness = 31.25 cm - 0.004 cm = 31.246 cm
- Calculate the bubble area (A_b):
- A_b = π * ((31.25)² - (31.246)²) ≈ 0.79 cm²
- Now, we calculate the final line speed (Vf):
- Formula: Vf = FLH Flow / Bubble Area (A_b)
- Using our numbers: Vf = 68.6 mL/s / 0.79 cm² = 87.3 cm/s
The Impact of Line Speed
Line speed is a direct measurement of your productivity. A higher line speed means more meters of film are produced per minute. However, you must always balance it with other factors.
| Increasing Line Speed... | Positive Effect | Potential Negative Effect |
|---|---|---|
| With the same extruder output | Thinner film is produced. Good for downgauging. | The film may become too thin and weak. The bubble may become unstable and break. |
| By also increasing extruder output | Higher production output (more kg/hr). | The system requires more cooling. Film properties may change if the process is not re-balanced. |
| In isolation | Can increase the film's molecular orientation and strength. | Can cause bubble breaks if the line is pulled faster than the polymer's melt strength can handle. |
It is important not to confuse production rate (kg/hr) with line speed (m/min). You can have a high production rate but a low line speed if you are making very thick film. The goal for every manufacturer is to optimize both for their specific product.
How does the strain rate change during processing, and why is it important?
Between the die and the frost line, the film is being stretched. The speed of this stretch is called the strain rate. This is a more advanced concept, but it is one of the most important factors for controlling final film quality.
Strain rate is the rate of deformation or stretching that the material experiences per unit of time. It is calculated by the change in velocity (Vf - V₀) divided by the Frost Line Height (FLH). It is important because it directly controls molecular orientation and final film properties.
Calculating the Average Strain Rate
Strain rate measures how quickly the film is stretched. A higher strain rate means the stretching happens faster over a shorter period.
- Formula: Average Strain Rate = (Vf - V₀) / FLH
Let's use our previously calculated values to find the strain rate:
- Vf (Final Line Speed) = 87.3 cm/s
- V₀ (Initial Line Speed) = 7.20 cm/s
- FLH (Frost Line Height) = 36 inches = 91.4 cm
Now, plug them into the formula:
- Average Strain Rate = (87.3 cm/s - 7.20 cm/s) / 91.4 cm
- Average Strain Rate = 80.1 / 91.4 = 0.88 s⁻¹
The unit s⁻¹ means "per second." This result means the film's length is increasing at a rate of 88% every second while it is in the molten state between the die and the frost line.
Why Strain Rate Matters So Much
Strain rate is a direct measure of the forces acting on the polymer molecules during their most critical phase of transformation. The rate of this stretch determines how the molecules align.
- Low Strain Rate: The polymer is stretched slowly. The molecules have plenty of time to gently untangle and align themselves in the direction of the stretch. This generally leads to high orientation and, as a result, strong and clear film. The downside is that a low rate means slow production.
- High Strain Rate: The polymer is stretched very quickly. The molecules have less time to respond to the force. This can lead to several different outcomes:
- Melt Fracture: If the strain rate is too high for the polymer's natural melt strength, the material can tear or "fracture" while still molten. This causes surface defects or a complete bubble break, stopping production.
- Improved Properties: For many modern materials, a higher strain rate can actually improve orientation and strength, up to a certain point.
- Poor Properties: If the rate is extremely high, the molecules may not have enough time to align at all before they are frozen solid. This can lead to a weaker film with poor properties.
Finding the optimal strain rate is the key to high-performance film production. It's the "sweet spot" where you achieve the best possible film properties at the fastest possible production speed. This "processing window" is different for every polymer. At BagMec®, our blown film machines are engineered with precision motors and cooling systems, giving you the power to find and maintain this optimal strain rate for any material you run.
What are the effects of changing the strain rate on film properties?
Adjusting the strain rate is not just a technical tweak on a machine; it directly changes the physical characteristics of your final product. Let's see how adjusting this one value can transform your film.
Changing the strain rate primarily affects film properties by altering the degree of molecular orientation. A higher strain rate, often achieved by making thinner film or adjusting the Blow-Up Ratio (BUR), can increase tensile strength but may also reduce stability if pushed too far.
How to Change the Strain Rate in Practice
You cannot just set a "strain rate" on a control panel. You change it by adjusting other process parameters. Based on production data, there are two main ways to influence it.
1. By Changing the Film Thickness
If we keep all other settings the same, reducing the film's thickness forces the line speed to increase, which increases the strain rate.
| Film Thickness (μm) | Avg Strain Rate (s⁻¹) | Analysis |
|---|---|---|
| 40 | 0.88 | This is our baseline. |
| 30 | 1.19 | To make the film 25% thinner, the nip rollers pull it away faster. This increases the line speed and therefore the strain rate. |
| 20 | 1.83 | To make the film 50% thinner, the line speed must increase dramatically, which more than doubles the strain rate. |
2. By Changing the Blow-Up Ratio (BUR)
If we keep the film thickness the same, we can still change the strain rate by altering the bubble's width.
| BUR | Avg Strain Rate (s⁻¹) | Layflat Width (cm) | Analysis |
|---|---|---|---|
| 2.2 | 1.01 | 86.4 | A lower BUR creates a narrower bubble. To maintain the same film thickness, the film must be drawn upwards faster, which increases the strain rate. |
| 2.5 | 0.88 | 98.2 | This is our baseline. |
| 2.8 | 0.77 | 110.0 | A higher BUR creates a wider bubble. More of the thinning is done by stretching sideways, so less upward pull is needed. This decreases the strain rate. |
Impact on Key Film Properties
Here is a more detailed look at how these changes affect the finished product you deliver to your customers.
Tensile Strength & Stiffness
- Effect: A higher strain rate generally leads to more molecular chains aligning in the Machine Direction (MD), which is the direction the film is pulled. This increases the film's tensile strength and makes it feel stiffer in that direction.
- Why it Matters: This is critical for applications like heavy-duty sacks or agricultural films, where strength is the most important characteristic.
Tear & Impact Strength
- Effect: A well-balanced strain rate creates biaxial orientation (stretching in both the machine and transverse directions). This improves overall toughness, including tear resistance and impact strength (like the dart drop test). However, an excessively high strain rate focused only in the machine direction can make the film brittle and easy to tear in the other direction.
- Why it Matters: This is crucial for packaging that needs to withstand drops and rough handling, like courier mailers or bags for industrial parts.
Optical Properties (Clarity & Haze)
- Effect: In general, more orientation from a well-managed strain rate reduces haze and improves the film's clarity. The neatly aligned molecules scatter less light.
- Why it Matters: For any retail packaging, from bread bags to produce bags on a roll, high clarity is a primary selling point for consumers.
How is the draw down ratio calculated, and what does it influence?
The Draw Down Ratio, or DDR, is a number that tells you exactly how much the film was thinned out from the moment it left the die to its final, solid form. It is a vital metric for both quality control and process setup.
The Draw Down Ratio (DDR) is a measure of how much the film has been stretched thin. It can be calculated by the ratio of the final line speed to the initial speed (DDR = Vf / V₀), or by comparing the die gap to the final film thickness.
Two Methods for Calculating DDR
The global film industry uses two common methods for this calculation. They measure slightly different things and give different results, so it's important to know which one you are using. We sometimes call them the "European style" and the "North American style".
Method 1: Velocity Ratio ("European Style")
This method directly compares the speed of the film at the end of the process to the speed at the very beginning. It is a measure of a one-directional stretch.
- Formula: DDR = Vf / V₀
- Using example numbers:
- Vf = 80.5 cm/s
- V₀ = 6.64 cm/s
- DDR = 80.5 / 6.64 = 12.1
This result tells us the film is moving 12.1 times faster at the frost line than it was when it exited the die.
Method 2: Area or Thickness Ratio ("North American Style")
This method compares the cross-sectional area of the die opening to the cross-sectional area of the final film. It is a measure of the total stretch, including both length and width.
- Formula: DDR = Die Gap / (Final Film Thickness * BUR)
- Using example numbers:
- Die Gap = 60 mil = 0.152 cm
- Film Thickness = 40 microns = 0.004 cm
- BUR = 2.5
- DDR = 0.152 cm / (0.004 cm * 2.5)
- DDR = 0.152 / 0.01 = 15.2
What Does DDR Influence?
DDR is one of the most critical parameters that an operator can control. It has a direct and powerful influence on the final properties of your film.
| Property | How DDR Influences It | Practical Implication for You |
|---|---|---|
| Molecular Orientation | This is the primary influence. A higher DDR forces the polymer chains to align more strongly in the machine direction. | This is the main lever you can pull to increase the film's MD strength and stiffness. |
| Film Gauge (Thickness) | A higher DDR results in a thinner film, assuming the extruder output is constant. | DDR is the fundamental calculation used to control the final thickness of the film you are producing. |
| Bubble Stability | A very high DDR can lead to instability or bubble breaks. This happens if you try to stretch the material beyond its natural melt strength. | You must find the maximum DDR your specific polymer can handle before production becomes unreliable and inefficient. |
| Balance of Properties | An ideal DDR is balanced with the Blow-Up Ratio (BUR). Too much DDR can make the film strong in one direction but very weak and easy to split in the other. | The goal is not the highest possible DDR, but a balanced DDR and BUR that gives you good properties in both the MD and TD. |
At BagMec®, we understand that a successful operation combines great machinery with a deep knowledge of the process. Whether you use the velocity or area method, consistency is what matters. Our control systems allow you to lock in recipes and parameters so that you can achieve the same DDR and the same high-quality film, day after day.
Conclusion
Mastering blown film calculations transforms your production from guesswork to science. By understanding die area, flow rate, line speed, strain rate, and DDR, you gain precise control. This knowledge empowers you to produce better film with less waste and greater efficiency.
